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+Project Gutenberg's Mysticism and Logic and Other Essays, by Bertrand Russell
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Mysticism and Logic and Other Essays
+
+Author: Bertrand Russell
+
+Release Date: May 12, 2008 [EBook #25447]
+[Last updated: May 5, 2012]
+
+Language: English
+
+Character set encoding: UTF-8
+
+*** START OF THIS PROJECT GUTENBERG EBOOK MYSTICISM AND LOGIC ***
+
+
+
+
+Produced by Jeannie Howse, Adrian Mastronardi and the
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+    | Transcriber's Note:                                       |
+    |                                                           |
+    | Inconsistent hyphenation in the original document has     |
+    | been preserved.                                           |
+    |                                                           |
+    | Mathematical equations and variables are marked with      |
+    | [Math:] to reduce confusion between underscores used for  |
+    | italics and underscores used to indicate subscripts.      |
+    | Subscripts are indicated with underscores, with the       |
+    | subscripted character marked with {}'s, i.e.: x_{t}       |
+    |                                                           |
+    | Obvious typographical errors have been corrected. For     |
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+    |                                                           |
+    +-----------------------------------------------------------+
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+       *       *       *       *       *
+
+
+
+
+BERTRAND RUSSELL
+
+MYSTICISM AND
+LOGIC
+
+AND OTHER ESSAYS
+
+
+
+
+_LONDON_
+GEORGE ALLEN & UNWIN LTD
+RUSKIN HOUSE MUSEUM STREET
+
+
+
+
+MYSTICISM AND LOGIC
+AND OTHER ESSAYS
+
+
+
+
+BY BERTRAND RUSSELL
+
+_The ABC of Relativity_
+_The Analysis of Matter_
+_Human Society in Ethics and Politics_
+_The Impact of Science on Society_
+_New Hopes for a Changing World_
+_Authority and the Individual_
+_Human Knowledge_
+_History of Western Philosophy_
+_The Principles of Mathematics_
+_Introduction to Mathematical Philosophy_
+_The Analysis of Mind_
+_Our Knowledge of the External World_
+_An Outline of Philosophy_
+_The Philosophy of Leibniz_
+_An Inquiry into Meaning and Truth_
+_Logic and Knowledge_
+_The Problems of Philosophy_
+_Principia Mathematica_
+
+_Common Sense and Nuclear Warfare_
+_Why I am Not a Christian_
+_Portraits from Memory_
+_My Philosophical Development_
+_Unpopular Essays_
+_Power_
+_In Praise of Idleness_
+_The Conquest of Happiness_
+_Sceptical Essays_
+_The Scientific Outlook_
+_Marriage and Morals_
+_Education and the Social Order_
+_On Education_
+
+_Freedom and Organization_
+_Principles of Social Reconstruction_
+_Roads to Freedom_
+_Practice and Theory of Bolshevism_
+
+_Satan in The Suburbs_
+_Nightmares of Eminent Persons_
+
+
+
+
+_First published as "Philosophical Essays"_        _October 1910_
+_Second Edition as "Mysticism and Logic"_         _December 1917_
+_Third Impression_                                   _April 1918_
+_Fourth Impression_                               _February 1919_
+_Fifth Impression_                                 _October 1921_
+_Sixth Impression_                                  _August 1925_
+_Seventh Impression_                               _January 1932_
+_Eighth Impression_                                        _1949_
+_Ninth Impression_                                         _1950_
+_Tenth Impression_                                         _1951_
+_Eleventh Impression_                                      _1959_
+
+  _This book is copyright under the Berne Convention. Apart from any
+  fair dealing for the purpose of private study, research, criticism
+  or review, as permitted under the Copyright Act, 1956, no portion
+  may be reproduced by any process without written permission.
+  Enquiry should be made to the publisher._
+
+
+PRINTED IN GREAT BRITAIN
+_by Taylor Garnett Evans & Co. Ltd.,
+Watford, Herts._
+
+
+
+
+PREFACE
+
+
+The following essays have been written and published at various times,
+and my thanks are due to the previous publishers for the permission to
+reprint them.
+
+The essay on "Mysticism and Logic" appeared in the _Hibbert Journal_
+for July, 1914. "The Place of Science in a Liberal Education" appeared
+in two numbers of _The New Statesman_, May 24 and 31, 1913. "The Free
+Man's Worship" and "The Study of Mathematics" were included in a
+former collection (now out of print), _Philosophical Essays_, also
+published by Messrs. Longmans, Green & Co. Both were written in 1902;
+the first appeared originally in the _Independent Review_ for 1903,
+the second in the _New Quarterly_, November, 1907. In theoretical
+Ethics, the position advocated in "The Free Man's Worship" is not
+quite identical with that which I hold now: I feel less convinced than
+I did then of the objectivity of good and evil. But the general
+attitude towards life which is suggested in that essay still seems to
+me, in the main, the one which must be adopted in times of stress and
+difficulty by those who have no dogmatic religious beliefs, if inward
+defeat is to be avoided.
+
+The essay on "Mathematics and the Metaphysicians" was written in 1901,
+and appeared in an American magazine, _The International Monthly_,
+under the title "Recent Work in the Philosophy of Mathematics." Some
+points in this essay require modification in view of later work.
+These are indicated in footnotes. Its tone is partly explained by the
+fact that the editor begged me to make the article "as romantic as
+possible."
+
+All the above essays are entirely popular, but those that follow are
+somewhat more technical. "On Scientific Method in Philosophy" was the
+Herbert Spencer lecture at Oxford in 1914, and was published by the
+Clarendon Press, which has kindly allowed me to include it in this
+collection. "The Ultimate Constituents of Matter" was an address to
+the Manchester Philosophical Society, early in 1915, and was published
+in the _Monist_ in July of that year. The essay on "The Relation of
+Sense-data to Physics" was written in January, 1914, and first
+appeared in No. 4 of that year's volume of _Scientia_, an
+International Review of Scientific Synthesis, edited by M. Eugenio
+Rignano, published monthly by Messrs. Williams and Norgate, London,
+Nicola Zanichelli, Bologna, and Félix Alcan, Paris. The essay "On the
+Notion of Cause" was the presidential address to the Aristotelian
+Society in November, 1912, and was published in their _Proceedings_
+for 1912-13. "Knowledge by Acquaintance and Knowledge by Description"
+was also a paper read before the Aristotelian Society, and published
+in their _Proceedings_ for 1910-11.
+
+  LONDON,
+    _September, 1917_
+
+
+
+
+CONTENTS
+
+
+_Chapter_                                                  _Page_
+
+   I. _Mysticism and Logic_                                     1
+
+  II. _The Place of Science in a Liberal Education_            33
+
+ III. _A Free Man's Worship_                                   46
+
+  IV. _The Study of Mathematics_                               58
+
+   V. _Mathematics and the Metaphysicians_                     74
+
+  VI. _On Scientific Method in Philosophy_                     97
+
+ VII. _The Ultimate Constituents of Matter_                   125
+
+VIII. _The Relation of Sense-data to Physics_                 145
+
+  IX. _On the Notion of Cause_                                180
+
+   X. _Knowledge by Acquaintance and Knowledge by
+       Description_                                           209
+
+
+
+
+MYSTICISM AND LOGIC AND OTHER ESSAYS
+
+
+
+
+I
+
+MYSTICISM AND LOGIC
+
+
+Metaphysics, or the attempt to conceive the world as a whole by means
+of thought, has been developed, from the first, by the union and
+conflict of two very different human impulses, the one urging men
+towards mysticism, the other urging them towards science. Some men
+have achieved greatness through one of these impulses alone, others
+through the other alone: in Hume, for example, the scientific impulse
+reigns quite unchecked, while in Blake a strong hostility to science
+co-exists with profound mystic insight. But the greatest men who have
+been philosophers have felt the need both of science and of mysticism:
+the attempt to harmonise the two was what made their life, and what
+always must, for all its arduous uncertainty, make philosophy, to some
+minds, a greater thing than either science or religion.
+
+Before attempting an explicit characterisation of the scientific and
+the mystical impulses, I will illustrate them by examples from two
+philosophers whose greatness lies in the very intimate blending which
+they achieved. The two philosophers I mean are Heraclitus and Plato.
+
+Heraclitus, as every one knows, was a believer in universal flux: time
+builds and destroys all things. From the few fragments that remain, it
+is not easy to discover how he arrived at his opinions, but there are
+some sayings that strongly suggest scientific observation as the
+source.
+
+"The things that can be seen, heard, and learned," he says, "are what
+I prize the most." This is the language of the empiricist, to whom
+observation is the sole guarantee of truth. "The sun is new every
+day," is another fragment; and this opinion, in spite of its
+paradoxical character, is obviously inspired by scientific reflection,
+and no doubt seemed to him to obviate the difficulty of understanding
+how the sun can work its way underground from west to east during the
+night. Actual observation must also have suggested to him his central
+doctrine, that Fire is the one permanent substance, of which all
+visible things are passing phases. In combustion we see things change
+utterly, while their flame and heat rise up into the air and vanish.
+
+"This world, which is the same for all," he says, "no one of gods or
+men has made; but it was ever, is now, and ever shall be, an
+ever-living Fire, with measures kindling, and measures going out."
+
+"The transformations of Fire are, first of all, sea; and half of the
+sea is earth, half whirlwind."
+
+This theory, though no longer one which science can accept, is
+nevertheless scientific in spirit. Science, too, might have inspired
+the famous saying to which Plato alludes: "You cannot step twice into
+the same rivers; for fresh waters are ever flowing in upon you." But
+we find also another statement among the extant fragments: "We step
+and do not step into the same rivers; we are and are not."
+
+The comparison of this statement, which is mystical, with the one
+quoted by Plato, which is scientific, shows how intimately the two
+tendencies are blended in the system of Heraclitus. Mysticism is, in
+essence, little more than a certain intensity and depth of feeling in
+regard to what is believed about the universe; and this kind of
+feeling leads Heraclitus, on the basis of his science, to strangely
+poignant sayings concerning life and the world, such as:
+
+"Time is a child playing draughts, the kingly power is a child's."
+
+It is poetic imagination, not science, which presents Time as despotic
+lord of the world, with all the irresponsible frivolity of a child. It
+is mysticism, too, which leads Heraclitus to assert the identity of
+opposites: "Good and ill are one," he says; and again: "To God all
+things are fair and good and right, but men hold some things wrong and
+some right."
+
+Much of mysticism underlies the ethics of Heraclitus. It is true that
+a scientific determinism alone might have inspired the statement:
+"Man's character is his fate"; but only a mystic would have said:
+
+"Every beast is driven to the pasture with blows"; and again:
+
+"It is hard to fight with one's heart's desire. Whatever it wishes to
+get, it purchases at the cost of soul"; and again:
+
+"Wisdom is one thing. It is to know the thought by which all things
+are steered through all things."[1]
+
+Examples might be multiplied, but those that have been given are
+enough to show the character of the man: the facts of science, as they
+appeared to him, fed the flame in his soul, and in its light he saw
+into the depths of the world by the reflection of his own dancing
+swiftly penetrating fire. In such a nature we see the true union of
+the mystic and the man of science--the highest eminence, as I think,
+that it is possible to achieve in the world of thought.
+
+In Plato, the same twofold impulse exists, though the mystic impulse
+is distinctly the stronger of the two, and secures ultimate victory
+whenever the conflict is sharp. His description of the cave is the
+classical statement of belief in a knowledge and reality truer and
+more real than that of the senses:
+
+  "Imagine[2] a number of men living in an underground cavernous
+  chamber, with an entrance open to the light, extending along the
+  entire length of the cavern, in which they have been confined, from
+  their childhood, with their legs and necks so shackled that they
+  are obliged to sit still and look straight forwards, because their
+  chains render it impossible for them to turn their heads round: and
+  imagine a bright fire burning some way off, above and behind them,
+  and an elevated roadway passing between the fire and the prisoners,
+  with a low wall built along it, like the screens which conjurors
+  put up in front of their audience, and above which they exhibit
+  their wonders.
+
+  I have it, he replied.
+
+  Also figure to yourself a number of persons walking behind this
+  wall, and carrying with them statues of men, and images of other
+  animals, wrought in wood and stone and all kinds of materials,
+  together with various other articles, which overtop the wall; and,
+  as you might expect, let some of the passers-by be talking, and
+  others silent.
+
+  You are describing a strange scene, and strange prisoners.
+
+  They resemble us, I replied.
+
+  Now consider what would happen if the course of nature brought them
+  a release from their fetters, and a remedy for their foolishness,
+  in the following manner. Let us suppose that one of them has been
+  released, and compelled suddenly to stand up, and turn his neck
+  round and walk with open eyes towards the light; and let us suppose
+  that he goes through all these actions with pain, and that the
+  dazzling splendour renders him incapable of discerning those
+  objects of which he used formerly to see the shadows. What answer
+  should you expect him to make, if some one were to tell him that in
+  those days he was watching foolish phantoms, but that now he is
+  somewhat nearer to reality, and is turned towards things more real,
+  and sees more correctly; above all, if he were to point out to him
+  the several objects that are passing by, and question him, and
+  compel him to answer what they are? Should you not expect him to be
+  puzzled, and to regard his old visions as truer than the objects
+  now forced upon his notice?
+
+  Yes, much truer....
+
+  Hence, I suppose, habit will be necessary to enable him to perceive
+  objects in that upper world. At first he will be most successful in
+  distinguishing shadows; then he will discern the reflections of men
+  and other things in water, and afterwards the realities; and after
+  this he will raise his eyes to encounter the light of the moon and
+  stars, finding it less difficult to study the heavenly bodies and
+  the heaven itself by night, than the sun and the sun's light by
+  day.
+
+  Doubtless.
+
+  Last of all, I imagine, he will be able to observe and contemplate
+  the nature of the sun, not as it _appears_ in water or on alien
+  ground, but as it is in itself in its own territory.
+
+  Of course.
+
+  His next step will be to draw the conclusion, that the sun is the
+  author of the seasons and the years, and the guardian of all things
+  in the visible world, and in a manner the cause of all those things
+  which he and his companions used to see.
+
+  Obviously, this will be his next step....
+
+  Now this imaginary case, my dear Glancon, you must apply in all its
+  parts to our former statements, by comparing the region which the
+  eye reveals to the prison house, and the light of the fire therein
+  to the power of the sun: and if, by the upward ascent and the
+  contemplation of the upper world, you understand the mounting of
+  the soul into the intellectual region, you will hit the tendency of
+  my own surmises, since you desire to be told what they are; though,
+  indeed, God only knows whether they are correct. But, be that as it
+  may, the view which I take of the subject is to the following
+  effect. In the world of knowledge, the essential Form of Good is
+  the limit of our enquiries, and can barely be perceived; but, when
+  perceived, we cannot help concluding that it is in every case the
+  source of all that is bright and beautiful,--in the visible world
+  giving birth to light and its master, and in the intellectual world
+  dispensing, immediately and with full authority, truth and
+  reason;--and that whosoever would act wisely, either in private or
+  in public, must set this Form of Good before his eyes."
+
+But in this passage, as throughout most of Plato's teaching, there is
+an identification of the good with the truly real, which became
+embodied in the philosophical tradition, and is still largely
+operative in our own day. In thus allowing a legislative function to
+the good, Plato produced a divorce between philosophy and science,
+from which, in my opinion, both have suffered ever since and are still
+suffering. The man of science, whatever his hopes may be, must lay
+them aside while he studies nature; and the philosopher, if he is to
+achieve truth, must do the same. Ethical considerations can only
+legitimately appear when the truth has been ascertained: they can and
+should appear as determining our feeling towards the truth, and our
+manner of ordering our lives in view of the truth, but not as
+themselves dictating what the truth is to be.
+
+There are passages in Plato--among those which illustrate the
+scientific side of his mind--where he seems clearly aware of this. The
+most noteworthy is the one in which Socrates, as a young man, is
+explaining the theory of ideas to Parmenides.
+
+After Socrates has explained that there is an idea of the good, but
+not of such things as hair and mud and dirt, Parmenides advises him
+"not to despise even the meanest things," and this advice shows the
+genuine scientific temper. It is with this impartial temper that the
+mystic's apparent insight into a higher reality and a hidden good has
+to be combined if philosophy is to realise its greatest possibilities.
+And it is failure in this respect that has made so much of idealistic
+philosophy thin, lifeless, and insubstantial. It is only in marriage
+with the world that our ideals can bear fruit: divorced from it, they
+remain barren. But marriage with the world is not to be achieved by an
+ideal which shrinks from fact, or demands in advance that the world
+shall conform to its desires.
+
+Parmenides himself is the source of a peculiarly interesting strain
+of mysticism which pervades Plato's thought--the mysticism which may
+be called "logical" because it is embodied in theories on logic. This
+form of mysticism, which appears, so far as the West is concerned, to
+have originated with Parmenides, dominates the reasonings of all the
+great mystical metaphysicians from his day to that of Hegel and his
+modern disciples. Reality, he says, is uncreated, indestructible,
+unchanging, indivisible; it is "immovable in the bonds of mighty
+chains, without beginning and without end; since coming into being and
+passing away have been driven afar, and true belief has cast them
+away." The fundamental principle of his inquiry is stated in a
+sentence which would not be out of place in Hegel: "Thou canst not
+know what is not--that is impossible--nor utter it; for it is the same
+thing that can be thought and that can be." And again: "It needs must
+be that what can be thought and spoken of is; for it is possible for
+it to be, and it is not possible for what is nothing to be." The
+impossibility of change follows from this principle; for what is past
+can be spoken of, and therefore, by the principle, still is.
+
+Mystical philosophy, in all ages and in all parts of the world, is
+characterised by certain beliefs which are illustrated by the
+doctrines we have been considering.
+
+There is, first, the belief in insight as against discursive analytic
+knowledge: the belief in a way of wisdom, sudden, penetrating,
+coercive, which is contrasted with the slow and fallible study of
+outward appearance by a science relying wholly upon the senses. All
+who are capable of absorption in an inward passion must have
+experienced at times the strange feeling of unreality in common
+objects, the loss of contact with daily things, in which the solidity
+of the outer world is lost, and the soul seems, in utter loneliness,
+to bring forth, out of its own depths, the mad dance of fantastic
+phantoms which have hitherto appeared as independently real and
+living. This is the negative side of the mystic's initiation: the
+doubt concerning common knowledge, preparing the way for the reception
+of what seems a higher wisdom. Many men to whom this negative
+experience is familiar do not pass beyond it, but for the mystic it is
+merely the gateway to an ampler world.
+
+The mystic insight begins with the sense of a mystery unveiled, of a
+hidden wisdom now suddenly become certain beyond the possibility of a
+doubt. The sense of certainty and revelation comes earlier than any
+definite belief. The definite beliefs at which mystics arrive are the
+result of reflection upon the inarticulate experience gained in the
+moment of insight. Often, beliefs which have no real connection with
+this moment become subsequently attracted into the central nucleus;
+thus in addition to the convictions which all mystics share, we find,
+in many of them, other convictions of a more local and temporary
+character, which no doubt become amalgamated with what was essentially
+mystical in virtue of their subjective certainty. We may ignore such
+inessential accretions, and confine ourselves to the beliefs which all
+mystics share.
+
+The first and most direct outcome of the moment of illumination is
+belief in the possibility of a way of knowledge which may be called
+revelation or insight or intuition, as contrasted with sense, reason,
+and analysis, which are regarded as blind guides leading to the morass
+of illusion. Closely connected with this belief is the conception of a
+Reality behind the world of appearance and utterly different from it.
+This Reality is regarded with an admiration often amounting to
+worship; it is felt to be always and everywhere close at hand, thinly
+veiled by the shows of sense, ready, for the receptive mind, to shine
+in its glory even through the apparent folly and wickedness of Man.
+The poet, the artist, and the lover are seekers after that glory: the
+haunting beauty that they pursue is the faint reflection of its sun.
+But the mystic lives in the full light of the vision: what others
+dimly seek he knows, with a knowledge beside which all other knowledge
+is ignorance.
+
+The second characteristic of mysticism is its belief in unity, and its
+refusal to admit opposition or division anywhere. We found Heraclitus
+saying "good and ill are one"; and again he says, "the way up and the
+way down is one and the same." The same attitude appears in the
+simultaneous assertion of contradictory propositions, such as: "We
+step and do not step into the same rivers; we are and are not." The
+assertion of Parmenides, that reality is one and indivisible, comes
+from the same impulse towards unity. In Plato, this impulse is less
+prominent, being held in check by his theory of ideas; but it
+reappears, so far as his logic permits, in the doctrine of the primacy
+of the Good.
+
+A third mark of almost all mystical metaphysics is the denial of the
+reality of Time. This is an outcome of the denial of division; if all
+is one, the distinction of past and future must be illusory. We have
+seen this doctrine prominent in Parmenides; and among moderns it is
+fundamental in the systems of Spinoza and Hegel.
+
+The last of the doctrines of mysticism which we have to consider is
+its belief that all evil is mere appearance, an illusion produced by
+the divisions and oppositions of the analytic intellect. Mysticism
+does not maintain that such things as cruelty, for example, are good,
+but it denies that they are real: they belong to that lower world of
+phantoms from which we are to be liberated by the insight of the
+vision. Sometimes--for example in Hegel, and at least verbally in
+Spinoza--not only evil, but good also, is regarded as illusory, though
+nevertheless the emotional attitude towards what is held to be Reality
+is such as would naturally be associated with the belief that Reality
+is good. What is, in all cases, ethically characteristic of mysticism
+is absence of indignation or protest, acceptance with joy, disbelief
+in the ultimate truth of the division into two hostile camps, the good
+and the bad. This attitude is a direct outcome of the nature of the
+mystical experience: with its sense of unity is associated a feeling
+of infinite peace. Indeed it may be suspected that the feeling of
+peace produces, as feelings do in dreams, the whole system of
+associated beliefs which make up the body of mystic doctrine. But this
+is a difficult question, and one on which it cannot be hoped that
+mankind will reach agreement.
+
+Four questions thus arise in considering the truth or falsehood of
+mysticism, namely:
+
+  I. Are there two ways of knowing, which may be called respectively
+  reason and intuition? And if so, is either to be preferred to the
+  other?
+
+  II. Is all plurality and division illusory?
+
+  III. Is time unreal?
+
+  IV. What kind of reality belongs to good and evil?
+
+On all four of these questions, while fully developed mysticism seems
+to me mistaken, I yet believe that, by sufficient restraint, there is
+an element of wisdom to be learned from the mystical way of feeling,
+which does not seem to be attainable in any other manner. If this is
+the truth, mysticism is to be commended as an attitude towards life,
+not as a creed about the world. The meta-physical creed, I shall
+maintain, is a mistaken outcome of the emotion, although this emotion,
+as colouring and informing all other thoughts and feelings, is the
+inspirer of whatever is best in Man. Even the cautious and patient
+investigation of truth by science, which seems the very antithesis of
+the mystic's swift certainty, may be fostered and nourished by that
+very spirit of reverence in which mysticism lives and moves.
+
+
+I. REASON AND INTUITION[3]
+
+Of the reality or unreality of the mystic's world I know nothing. I
+have no wish to deny it, nor even to declare that the insight which
+reveals it is not a genuine insight. What I do wish to maintain--and
+it is here that the scientific attitude becomes imperative--is that
+insight, untested and unsupported, is an insufficient guarantee of
+truth, in spite of the fact that much of the most important truth is
+first suggested by its means. It is common to speak of an opposition
+between instinct and reason; in the eighteenth century, the opposition
+was drawn in favour of reason, but under the influence of Rousseau and
+the romantic movement instinct was given the preference, first by
+those who rebelled against artificial forms of government and thought,
+and then, as the purely rationalistic defence of traditional theology
+became increasingly difficult, by all who felt in science a menace to
+creeds which they associated with a spiritual outlook on life and the
+world. Bergson, under the name of "intuition," has raised instinct to
+the position of sole arbiter of metaphysical truth. But in fact the
+opposition of instinct and reason is mainly illusory. Instinct,
+intuition, or insight is what first leads to the beliefs which
+subsequent reason confirms or confutes; but the confirmation, where it
+is possible, consists, in the last analysis, of agreement with other
+beliefs no less instinctive. Reason is a harmonising, controlling
+force rather than a creative one. Even in the most purely logical
+realm, it is insight that first arrives at what is new.
+
+Where instinct and reason do sometimes conflict is in regard to single
+beliefs, held instinctively, and held with such determination that no
+degree of inconsistency with other beliefs leads to their abandonment.
+Instinct, like all human faculties, is liable to error. Those in whom
+reason is weak are often unwilling to admit this as regards
+themselves, though all admit it in regard to others. Where instinct is
+least liable to error is in practical matters as to which right
+judgment is a help to survival: friendship and hostility in others,
+for instance, are often felt with extraordinary discrimination through
+very careful disguises. But even in such matters a wrong impression
+may be given by reserve or flattery; and in matters less directly
+practical, such as philosophy deals with, very strong instinctive
+beliefs are sometimes wholly mistaken, as we may come to know through
+their perceived inconsistency with other equally strong beliefs. It is
+such considerations that necessitate the harmonising mediation of
+reason, which tests our beliefs by their mutual compatibility, and
+examines, in doubtful cases, the possible sources of error on the one
+side and on the other. In this there is no opposition to instinct as a
+whole, but only to blind reliance upon some one interesting aspect of
+instinct to the exclusion of other more commonplace but not less
+trustworthy aspects. It is such one-sidedness, not instinct itself,
+that reason aims at correcting.
+
+These more or less trite maxims may be illustrated by application to
+Bergson's advocacy of "intuition" as against "intellect." There are,
+he says, "two profoundly different ways of knowing a thing. The first
+implies that we move round the object: the second that we enter into
+it. The first depends on the point of view at which we are placed and
+on the symbols by which we express ourselves. The second neither
+depends on a point of view nor relies on any symbol. The first kind of
+knowledge may be said to stop at the _relative_; the second, in those
+cases where it is possible, to attain the _absolute_."[4] The second
+of these, which is intuition, is, he says, "the kind of _intellectual
+sympathy_ by which one places oneself within an object in order to
+coincide with what is unique in it and therefore inexpressible" (p.
+6). In illustration, he mentions self-knowledge: "there is one
+reality, at least, which we all seize from within, by intuition and
+not by simple analysis. It is our own personality in its flowing
+through time--our self which endures" (p. 8). The rest of Bergson's
+philosophy consists in reporting, through the imperfect medium of
+words, the knowledge gained by intuition, and the consequent complete
+condemnation of all the pretended knowledge derived from science and
+common sense.
+
+This procedure, since it takes sides in a conflict of instinctive
+beliefs, stands in need of justification by proving the greater
+trustworthiness of the beliefs on one side than of those on the other.
+Bergson attempts this justification in two ways, first by explaining
+that intellect is a purely practical faculty to secure biological
+success, secondly by mentioning remarkable feats of instinct in
+animals and by pointing out characteristics of the world which, though
+intuition can apprehend them, are baffling to intellect as he
+interprets it.
+
+Of Bergson's theory that intellect is a purely practical faculty,
+developed in the struggle for survival, and not a source of true
+beliefs, we may say, first, that it is only through intellect that we
+know of the struggle for survival and of the biological ancestry of
+man: if the intellect is misleading, the whole of this merely inferred
+history is presumably untrue. If, on the other hand, we agree with him
+in thinking that evolution took place as Darwin believed, then it is
+not only intellect, but all our faculties, that have been developed
+under the stress of practical utility. Intuition is seen at its best
+where it is directly useful, for example in regard to other people's
+characters and dispositions. Bergson apparently holds that capacity
+for this kind of knowledge is less explicable by the struggle for
+existence than, for example, capacity for pure mathematics. Yet the
+savage deceived by false friendship is likely to pay for his mistake
+with his life; whereas even in the most civilised societies men are
+not put to death for mathematical incompetence. All the most striking
+of his instances of intuition in animals have a very direct survival
+value. The fact is, of course, that both intuition and intellect have
+been developed because they are useful, and that, speaking broadly,
+they are useful when they give truth and become harmful when they give
+falsehood. Intellect, in civilised man, like artistic capacity, has
+occasionally been developed beyond the point where it is useful to the
+individual; intuition, on the other hand, seems on the whole to
+diminish as civilisation increases. It is greater, as a rule, in
+children than in adults, in the uneducated than in the educated.
+Probably in dogs it exceeds anything to be found in human beings. But
+those who see in these facts a recommendation of intuition ought to
+return to running wild in the woods, dyeing themselves with woad and
+living on hips and haws.
+
+Let us next examine whether intuition possesses any such infallibility
+as Bergson claims for it. The best instance of it, according to him,
+is our acquaintance with ourselves; yet self-knowledge is proverbially
+rare and difficult. Most men, for example, have in their nature
+meannesses, vanities, and envies of which they are quite unconscious,
+though even their best friends can perceive them without any
+difficulty. It is true that intuition has a convincingness which is
+lacking to intellect: while it is present, it is almost impossible to
+doubt its truth. But if it should appear, on examination, to be at
+least as fallible as intellect, its greater subjective certainty
+becomes a demerit, making it only the more irresistibly deceptive.
+Apart from self-knowledge, one of the most notable examples of
+intuition is the knowledge people believe themselves to possess of
+those with whom they are in love: the wall between different
+personalities seems to become transparent, and people think they see
+into another soul as into their own. Yet deception in such cases is
+constantly practised with success; and even where there is no
+intentional deception, experience gradually proves, as a rule, that
+the supposed insight was illusory, and that the slower more groping
+methods of the intellect are in the long run more reliable.
+
+Bergson maintains that intellect can only deal with things in so far
+as they resemble what has been experienced in the past, while
+intuition has the power of apprehending the uniqueness and novelty
+that always belong to each fresh moment. That there is something
+unique and new at every moment, is certainly true; it is also true
+that this cannot be fully expressed by means of intellectual concepts.
+Only direct acquaintance can give knowledge of what is unique and new.
+But direct acquaintance of this kind is given fully in sensation, and
+does not require, so far as I can see, any special faculty of
+intuition for its apprehension. It is neither intellect nor intuition,
+but sensation, that supplies new data; but when the data are new in
+any remarkable manner, intellect is much more capable of dealing with
+them than intuition would be. The hen with a brood of ducklings no
+doubt has intuition which seems to place her inside them, and not
+merely to know them analytically; but when the ducklings take to the
+water, the whole apparent intuition is seen to be illusory, and the
+hen is left helpless on the shore. Intuition, in fact, is an aspect
+and development of instinct, and, like all instinct, is admirable in
+those customary surroundings which have moulded the habits of the
+animal in question, but totally incompetent as soon as the
+surroundings are changed in a way which demands some non-habitual mode
+of action.
+
+The theoretical understanding of the world, which is the aim of
+philosophy, is not a matter of great practical importance to animals,
+or to savages, or even to most civilised men. It is hardly to be
+supposed, therefore, that the rapid, rough and ready methods of
+instinct or intuition will find in this field a favourable ground for
+their application. It is the older kinds of activity, which bring out
+our kinship with remote generations of animal and semi-human
+ancestors, that show intuition at its best. In such matters as
+self-preservation and love, intuition will act sometimes (though not
+always) with a swiftness and precision which are astonishing to the
+critical intellect. But philosophy is not one of the pursuits which
+illustrate our affinity with the past: it is a highly refined, highly
+civilised pursuit, demanding, for its success, a certain liberation
+from the life of instinct, and even, at times, a certain aloofness
+from all mundane hopes and fears. It is not in philosophy, therefore,
+that we can hope to see intuition at its best. On the contrary, since
+the true objects of philosophy, and the habit of thought demanded for
+their apprehension, are strange, unusual, and remote, it is here, more
+almost than anywhere else, that intellect proves superior to
+intuition, and that quick unanalysed convictions are least deserving
+of uncritical acceptance.
+
+In advocating the scientific restraint and balance, as against the
+self-assertion of a confident reliance upon intuition, we are only
+urging, in the sphere of knowledge, that largeness of contemplation,
+that impersonal disinterestedness, and that freedom from practical
+preoccupations which have been inculcated by all the great religions
+of the world. Thus our conclusion, however it may conflict with the
+explicit beliefs of many mystics, is, in essence, not contrary to the
+spirit which inspires those beliefs, but rather the outcome of this
+very spirit as applied in the realm of thought.
+
+
+II. UNITY AND PLURALITY
+
+One of the most convincing aspects of the mystic illumination is the
+apparent revelation of the oneness of all things, giving rise to
+pantheism in religion and to monism in philosophy. An elaborate logic,
+beginning with Parmenides, and culminating in Hegel and his followers,
+has been gradually developed, to prove that the universe is one
+indivisible Whole, and that what seem to be its parts, if considered
+as substantial and self-existing, are mere illusion. The conception
+of a Reality quite other than the world of appearance, a reality one,
+indivisible, and unchanging, was introduced into Western philosophy by
+Parmenides, not, nominally at least, for mystical or religious
+reasons, but on the basis of a logical argument as to the
+impossibility of not-being, and most subsequent metaphysical systems
+are the outcome of this fundamental idea.
+
+The logic used in defence of mysticism seems to be faulty as logic,
+and open to technical criticisms, which I have explained elsewhere. I
+shall not here repeat these criticisms, since they are lengthy and
+difficult, but shall instead attempt an analysis of the state of mind
+from which mystical logic has arisen.
+
+Belief in a reality quite different from what appears to the senses
+arises with irresistible force in certain moods, which are the source
+of most mysticism, and of most metaphysics. While such a mood is
+dominant, the need of logic is not felt, and accordingly the more
+thoroughgoing mystics do not employ logic, but appeal directly to the
+immediate deliverance of their insight. But such fully developed
+mysticism is rare in the West. When the intensity of emotional
+conviction subsides, a man who is in the habit of reasoning will
+search for logical grounds in favour of the belief which he finds in
+himself. But since the belief already exists, he will be very
+hospitable to any ground that suggests itself. The paradoxes
+apparently proved by his logic are really the paradoxes of mysticism,
+and are the goal which he feels his logic must reach if it is to be in
+accordance with insight. The resulting logic has rendered most
+philosophers incapable of giving any account of the world of science
+and daily life. If they had been anxious to give such an account, they
+would probably have discovered the errors of their logic; but most of
+them were less anxious to understand the world of science and daily
+life than to convict it of unreality in the interests of a
+super-sensible "real" world.
+
+It is in this way that logic has been pursued by those of the great
+philosophers who were mystics. But since they usually took for granted
+the supposed insight of the mystic emotion, their logical doctrines
+were presented with a certain dryness, and were believed by their
+disciples to be quite independent of the sudden illumination from
+which they sprang. Nevertheless their origin clung to them, and they
+remained--to borrow a useful word from Mr. Santayana--"malicious" in
+regard to the world of science and common sense. It is only so that we
+can account for the complacency with which philosophers have accepted
+the inconsistency of their doctrines with all the common and
+scientific facts which seem best established and most worthy of
+belief.
+
+The logic of mysticism shows, as is natural, the defects which are
+inherent in anything malicious. The impulse to logic, not felt while
+the mystic mood is dominant, reasserts itself as the mood fades, but
+with a desire to retain the vanishing insight, or at least to prove
+that it _was_ insight, and that what seems to contradict it is
+illusion. The logic which thus arises is not quite disinterested or
+candid, and is inspired by a certain hatred of the daily world to
+which it is to be applied. Such an attitude naturally does not tend to
+the best results. Everyone knows that to read an author simply in
+order to refute him is not the way to understand him; and to read the
+book of Nature with a conviction that it is all illusion is just as
+unlikely to lead to understanding. If our logic is to find the common
+world intelligible, it must not be hostile, but must be inspired by a
+genuine acceptance such as is not usually to be found among
+metaphysicians.
+
+
+III. TIME
+
+The unreality of time is a cardinal doctrine of many metaphysical
+systems, often nominally based, as already by Parmenides, upon logical
+arguments, but originally derived, at any rate in the founders of new
+systems, from the certainty which is born in the moment of mystic
+insight. As a Persian Sufi poet says:
+
+    "Past and future are what veil God from our sight.
+    Burn up both of them with fire! How long
+    Wilt thou be partitioned by these segments as a reed?"[5]
+
+The belief that what is ultimately real must be immutable is a very
+common one: it gave rise to the metaphysical notion of substance, and
+finds, even now, a wholly illegitimate satisfaction in such scientific
+doctrines as the conservation of energy and mass.
+
+It is difficult to disentangle the truth and the error in this view.
+The arguments for the contention that time is unreal and that the
+world of sense is illusory must, I think, be regarded as fallacious.
+Nevertheless there is some sense--easier to feel than to state--in
+which time is an unimportant and superficial characteristic of
+reality. Past and future must be acknowledged to be as real as the
+present, and a certain emancipation from slavery to time is essential
+to philosophic thought. The importance of time is rather practical
+than theoretical, rather in relation to our desires than in relation
+to truth. A truer image of the world, I think, is obtained by
+picturing things as entering into the stream of time from an eternal
+world outside, than from a view which regards time as the devouring
+tyrant of all that is. Both in thought and in feeling, even though
+time be real, to realise the unimportance of time is the gate of
+wisdom.
+
+That this is the case may be seen at once by asking ourselves why our
+feelings towards the past are so different from our feelings towards
+the future. The reason for this difference is wholly practical: our
+wishes can affect the future but not the past, the future is to some
+extent subject to our power, while the past is unalterably fixed. But
+every future will some day be past: if we see the past truly now, it
+must, when it was still future, have been just what we now see it to
+be, and what is now future must be just what we shall see it to be
+when it has become past. The felt difference of quality between past
+and future, therefore, is not an intrinsic difference, but only a
+difference in relation to us: to impartial contemplation, it ceases to
+exist. And impartiality of contemplation is, in the intellectual
+sphere, that very same virtue of disinterestedness which, in the
+sphere of action, appears as justice and unselfishness. Whoever wishes
+to see the world truly, to rise in thought above the tyranny of
+practical desires, must learn to overcome the difference of attitude
+towards past and future, and to survey the whole stream of time in one
+comprehensive vision.
+
+The kind of way in which, as it seems to me, time ought not to enter
+into our theoretic philosophical thought, may be illustrated by the
+philosophy which has become associated with the idea of evolution, and
+which is exemplified by Nietzsche, pragmatism, and Bergson. This
+philosophy, on the basis of the development which has led from the
+lowest forms of life up to man, sees in _progress_ the fundamental law
+of the universe, and thus admits the difference between _earlier_ and
+_later_ into the very citadel of its contemplative outlook. With its
+past and future history of the world, conjectural as it is, I do not
+wish to quarrel. But I think that, in the intoxication of a quick
+success, much that is required for a true understanding of the
+universe has been forgotten. Something of Hellenism, something, too,
+of Oriental resignation, must be combined with its hurrying Western
+self-assertion before it can emerge from the ardour of youth into the
+mature wisdom of manhood. In spite of its appeals to science, the true
+scientific philosophy, I think, is something more arduous and more
+aloof, appealing to less mundane hopes, and requiring a severer
+discipline for its successful practice.
+
+Darwin's _Origin of Species_ persuaded the world that the difference
+between different species of animals and plants is not the fixed
+immutable difference that it appears to be. The doctrine of natural
+kinds, which had rendered classification easy and definite, which was
+enshrined in the Aristotelian tradition, and protected by its supposed
+necessity for orthodox dogma, was suddenly swept away for ever out of
+the biological world. The difference between man and the lower
+animals, which to our human conceit appears enormous, was shown to be
+a gradual achievement, involving intermediate being who could not with
+certainty be placed either within or without the human family. The sun
+and the planets had already been shown by Laplace to be very probably
+derived from a primitive more or less undifferentiated nebula. Thus
+the old fixed landmarks became wavering and indistinct, and all sharp
+outlines were blurred. Things and species lost their boundaries, and
+none could say where they began or where they ended.
+
+But if human conceit was staggered for a moment by its kinship with
+the ape, it soon found a way to reassert itself, and that way is the
+"philosophy" of evolution. A process which led from the amœba to Man
+appeared to the philosophers to be obviously a progress--though
+whether the amœba would agree with this opinion is not known. Hence
+the cycle of changes which science had shown to be the probable
+history of the past was welcomed as revealing a law of development
+towards good in the universe--an evolution or unfolding of an idea
+slowly embodying itself in the actual. But such a view, though it
+might satisfy Spencer and those whom we may call Hegelian
+evolutionists, could not be accepted as adequate by the more
+whole-hearted votaries of change. An ideal to which the world
+continuously approaches is, to these minds, too dead and static to be
+inspiring. Not only the aspiration, but the ideal too, must change and
+develop with the course of evolution: there must be no fixed goal, but
+a continual fashioning of fresh needs by the impulse which is life and
+which alone gives unity to the process.
+
+Life, in this philosophy, is a continuous stream, in which all
+divisions are artificial and unreal. Separate things, beginnings and
+endings, are mere convenient fictions: there is only smooth unbroken
+transition. The beliefs of to-day may count as true to-day, if they
+carry us along the stream; but to-morrow they will be false, and must
+be replaced by new beliefs to meet the new situation. All our thinking
+consists of convenient fictions, imaginary congealings of the stream:
+reality flows on in spite of all our fictions, and though it can be
+lived, it cannot be conceived in thought. Somehow, without explicit
+statement, the assurance is slipped in that the future, though we
+cannot foresee it, will be better than the past or the present: the
+reader is like the child which expects a sweet because it has been
+told to open its mouth and shut its eyes. Logic, mathematics, physics
+disappear in this philosophy, because they are too "static"; what is
+real is no impulse and movement towards a goal which, like the
+rainbow, recedes as we advance, and makes every place different when
+it reaches it from what it appeared to be at a distance.
+
+I do not propose to enter upon a technical examination of this
+philosophy. I wish only to maintain that the motives and interests
+which inspire it are so exclusively practical, and the problems with
+which it deals are so special, that it can hardly be regarded as
+touching any of the questions that, to my mind, constitute genuine
+philosophy.
+
+The predominant interest of evolutionism is in the question of human
+destiny, or at least of the destiny of Life. It is more interested in
+morality and happiness than in knowledge for its own sake. It must be
+admitted that the same may be said of many other philosophies, and
+that a desire for the kind of knowledge which philosophy can give is
+very rare. But if philosophy is to attain truth, it is necessary first
+and foremost that philosophers should acquire the disinterested
+intellectual curiosity which characterises the genuine man of science.
+Knowledge concerning the future--which is the kind of knowledge that
+must be sought if we are to know about human destiny--is possible
+within certain narrow limits. It is impossible to say how much the
+limits may be enlarged with the progress of science. But what is
+evident is that any proposition about the future belongs by its
+subject-matter to some particular science, and is to be ascertained,
+if at all, by the methods of that science. Philosophy is not a short
+cut to the same kind of results as those of the other sciences: if it
+is to be a genuine study, it must have a province of its own, and aim
+at results which the other sciences can neither prove nor disprove.
+
+Evolutionism, in basing itself upon the notion of _progress_, which is
+change from the worse to the better, allows the notion of time, as it
+seems to me, to become its tyrant rather than its servant, and thereby
+loses that impartiality of contemplation which is the source of all
+that is best in philosophic thought and feeling. Metaphysicians, as we
+saw, have frequently denied altogether the reality of time. I do not
+wish to do this; I wish only to preserve the mental outlook which
+inspired the denial, the attitude which, in thought, regards the past
+as having the same reality as the present and the same importance as
+the future. "In so far," says Spinoza,[6] "as the mind conceives a
+thing according to the dictate of reason, it will be equally affected
+whether the idea is that of a future, past, or present thing." It is
+this "conceiving according to the dictate of reason" that I find
+lacking in the philosophy which is based on evolution.
+
+
+IV. GOOD AND EVIL
+
+Mysticism maintains that all evil is illusory, and sometimes maintains
+the same view as regards good, but more often holds that all Reality
+is good. Both views are to be found in Heraclitus: "Good and ill are
+one," he says, but again, "To God all things are fair and good and
+right, but men hold some things wrong and some right." A similar
+twofold position is to be found in Spinoza, but he uses the word
+"perfection" when he means to speak of the good that is not merely
+human. "By reality and perfection I mean the same thing," he says;[7]
+but elsewhere we find the definition: "By _good_ I shall mean that
+which we certainly know to be useful to us."[8] Thus perfection
+belongs to Reality in its own nature, but goodness is relative to
+ourselves and our needs, and disappears in an impartial survey. Some
+such distinction, I think, is necessary in order to understand the
+ethical outlook of mysticism: there is a lower mundane kind of good
+and evil, which divides the world of appearance into what seem to be
+conflicting parts; but there is also a higher, mystical kind of good,
+which belongs to Reality and is not opposed by any correlative kind of
+evil.
+
+It is difficult to give a logically tenable account of this position
+without recognising that good and evil are subjective, that what is
+good is merely that towards which we have one kind of feeling, and
+what is evil is merely that towards which we have another kind of
+feeling. In our active life, where we have to exercise choice, and to
+prefer this to that of two possible acts, it is necessary to have a
+distinction of good and evil, or at least of better and worse. But
+this distinction, like everything pertaining to action, belongs to
+what mysticism regards as the world of illusion, if only because it is
+essentially concerned with time. In our contemplative life, where
+action is not called for, it is possible to be impartial, and to
+overcome the ethical dualism which action requires. So long as we
+remain _merely_ impartial, we may be content to say that both the good
+and the evil of action are illusions. But if, as we must do if we have
+the mystic vision, we find the whole world worthy of love and worship,
+if we see
+
+    "The earth, and every common sight....
+    Apparell'd in celestial light,"
+
+we shall say that there is a higher good than that of action, and that
+this higher good belongs to the whole world as it is in reality. In
+this way the twofold attitude and the apparent vacillation of
+mysticism are explained and justified.
+
+The possibility of this universal love and joy in all that exists is
+of supreme importance for the conduct and happiness of life, and gives
+inestimable value to the mystic emotion, apart from any creeds which
+may be built upon it. But if we are not to be led into false beliefs,
+it is necessary to realise exactly _what_ the mystic emotion reveals.
+It reveals a possibility of human nature--a possibility of a nobler,
+happier, freer life than any that can be otherwise achieved. But it
+does not reveal anything about the non-human, or about the nature of
+the universe in general. Good and bad, and even the higher good that
+mysticism finds everywhere, are the reflections of our own emotions on
+other things, not part of the substance of things as they are in
+themselves. And therefore an impartial contemplation, freed from all
+pre-occupation with Self, will not judge things good or bad, although
+it is very easily combined with that feeling of universal love which
+leads the mystic to say that the whole world is good.
+
+The philosophy of evolution, through the notion of progress, is bound
+up with the ethical dualism of the worse and the better, and is thus
+shut out, not only from the kind of survey which discards good and
+evil altogether from its view, but also from the mystical belief in
+the goodness of everything. In this way the distinction of good and
+evil, like time, becomes a tyrant in this philosophy, and introduces
+into thought the restless selectiveness of action. Good and evil, like
+time, are, it would seem, not general or fundamental in the world of
+thought, but late and highly specialised members of the intellectual
+hierarchy.
+
+Although, as we saw, mysticism can be interpreted so as to agree with
+the view that good and evil are not intellectually fundamental, it
+must be admitted that here we are no longer in verbal agreement with
+most of the great philosophers and religious teachers of the past. I
+believe, however, that the elimination of ethical considerations from
+philosophy is both scientifically necessary and--though this may seem
+a paradox--an ethical advance. Both these contentions must be briefly
+defended.
+
+The hope of satisfaction to our more human desires--the hope of
+demonstrating that the world has this or that desirable ethical
+characteristic--is not one which, so far as I can see, a scientific
+philosophy can do anything whatever to satisfy. The difference between
+a good world and a bad one is a difference in the particular
+characteristics of the particular things that exist in these worlds:
+it is not a sufficiently abstract difference to come within the
+province of philosophy. Love and hate, for example, are ethical
+opposites, but to philosophy they are closely analogous attitudes
+towards objects. The general form and structure of those attitudes
+towards objects which constitute mental phenomena is a problem for
+philosophy, but the difference between love and hate is not a
+difference of form or structure, and therefore belongs rather to the
+special science of psychology than to philosophy. Thus the ethical
+interests which have often inspired philosophers must remain in the
+background: some kind of ethical interest may inspire the whole study,
+but none must obtrude in the detail or be expected in the special
+results which are sought.
+
+If this view seems at first sight disappointing, we may remind
+ourselves that a similar change has been found necessary in all the
+other sciences. The physicist or chemist is not now required to prove
+the ethical importance of his ions or atoms; the biologist is not
+expected to prove the utility of the plants or animals which he
+dissects. In pre-scientific ages this was not the case. Astronomy, for
+example, was studied because men believed in astrology: it was thought
+that the movements of the planets had the most direct and important
+bearing upon the lives of human beings. Presumably, when this belief
+decayed and the disinterested study of astronomy began, many who had
+found astrology absorbingly interesting decided that astronomy had too
+little human interest to be worthy of study. Physics, as it appears in
+Plato's Timæus for example, is full of ethical notions: it is an
+essential part of its purpose to show that the earth is worthy of
+admiration. The modern physicist, on the contrary, though he has no
+wish to deny that the earth is admirable, is not concerned, as
+physicist, with its ethical attributes: he is merely concerned to find
+out facts, not to consider whether they are good or bad. In
+psychology, the scientific attitude is even more recent and more
+difficult than in the physical sciences: it is natural to consider
+that human nature is either good or bad, and to suppose that the
+difference between good and bad, so all-important in practice, must be
+important in theory also. It is only during the last century that an
+ethically neutral psychology has grown up; and here too, ethical
+neutrality has been essential to scientific success.
+
+In philosophy, hitherto, ethical neutrality has been seldom sought and
+hardly ever achieved. Men have remembered their wishes, and have
+judged philosophies in relation to their wishes. Driven from the
+particular sciences, the belief that the notions of good and evil must
+afford a key to the understanding of the world has sought a refuge in
+philosophy. But even from this last refuge, if philosophy is not to
+remain a set of pleasing dreams, this belief must be driven forth. It
+is a commonplace that happiness is not best achieved by those who
+seek it directly; and it would seem that the same is true of the good.
+In thought, at any rate, those who forget good and evil and seek only
+to know the facts are more likely to achieve good than those who view
+the world through the distorting medium of their own desires.
+
+We are thus brought back to our seeming paradox, that a philosophy
+which does not seek to impose upon the world its own conceptions of
+good and evil is not only more likely to achieve truth, but is also
+the outcome of a higher ethical standpoint than one which, like
+evolutionism and most traditional systems, is perpetually appraising
+the universe and seeking to find in it an embodiment of present
+ideals. In religion, and in every deeply serious view of the world and
+of human destiny, there is an element of submission, a realisation of
+the limits of human power, which is somewhat lacking in the modern
+world, with its quick material successes and its insolent belief in
+the boundless possibilities of progress. "He that loveth his life
+shall lose it"; and there is danger lest, through a too confident love
+of life, life itself should lose much of what gives it its highest
+worth. The submission which religion inculcates in action is
+essentially the same in spirit as that which science teaches in
+thought; and the ethical neutrality by which its victories have been
+achieved is the outcome of that submission.
+
+The good which it concerns us to remember is the good which it lies in
+our power to create--the good in our own lives and in our attitude
+towards the world. Insistence on belief in an external realisation of
+the good is a form of self-assertion, which, while it cannot secure
+the external good which it desires, can seriously impair the inward
+good which lies within our power, and destroy that reverence towards
+fact which constitutes both what is valuable in humility and what is
+fruitful in the scientific temper.
+
+Human beings cannot, of course, wholly transcend human nature;
+something subjective, if only the interest that determines the
+direction of our attention, must remain in all our thought. But
+scientific philosophy comes nearer to objectivity than any other human
+pursuit, and gives us, therefore, the closest constant and the most
+intimate relation with the outer world that it is possible to achieve.
+To the primitive mind, everything is either friendly or hostile; but
+experience has shown that friendliness and hostility are not the
+conceptions by which the world is to be understood. Scientific
+philosophy thus represents, though as yet only in a nascent condition,
+a higher form of thought than any pre-scientific belief or
+imagination, and, like every approach to self-transcendence, it brings
+with it a rich reward in increase of scope and breadth and
+comprehension. Evolutionism, in spite of its appeals to particular
+scientific facts, fails to be a truly scientific philosophy because of
+its slavery to time, its ethical preoccupations, and its predominant
+interest in our mundane concerns and destiny. A truly scientific
+philosophy will be more humble, more piecemeal, more arduous, offering
+less glitter of outward mirage to flatter fallacious hopes, but more
+indifferent to fate, and more capable of accepting the world without
+the tyrannous imposition of our human and temporary demands.
+
+FOOTNOTES:
+
+[1] All the above quotations are from Burnet's _Early Greek
+Philosophy_, (2nd ed., 1908), pp. 146-156.
+
+[2] _Republic_, 514, translated by Davies and Vaughan.
+
+[3] This section, and also one or two pages in later sections, have
+been printed in a course of Lowell lectures _On our knowledge of the
+external world_, published by the Open Court Publishing Company. But I
+have left them here, as this is the context for which they were
+originally written.
+
+[4] _Introduction to Metaphysics_, p. 1.
+
+[5] Whinfield's translation of the _Masnavi_ (Trübner, 1887), p. 34.
+
+[6] _Ethics_, Bk. IV, Prop. LXII.
+
+[7] Ib., Pt. IV, Df. I.
+
+[8] _Ethics_. Pt. II. Df. VI.
+
+
+
+
+II
+
+THE PLACE OF SCIENCE IN A LIBERAL EDUCATION
+
+
+I
+
+Science, to the ordinary reader of newspapers, is represented by a
+varying selection of sensational triumphs, such as wireless telegraphy
+and aeroplanes, radio-activity and the marvels of modern alchemy. It is
+not of this aspect of science that I wish to speak. Science, in this
+aspect, consists of detached up-to-date fragments, interesting only
+until they are replaced by something newer and more up-to-date,
+displaying nothing of the systems of patiently constructed knowledge
+out of which, almost as a casual incident, have come the practically
+useful results which interest the man in the street. The increased
+command over the forces of nature which is derived from science is
+undoubtedly an amply sufficient reason for encouraging scientific
+research, but this reason has been so often urged and is so easily
+appreciated that other reasons, to my mind quite as important, are apt
+to be overlooked. It is with these other reasons, especially with the
+intrinsic value of a scientific habit of mind in forming our outlook
+on the world, that I shall be concerned in what follows.
+
+The instance of wireless telegraphy will serve to illustrate the
+difference between the two points of view. Almost all the serious
+intellectual labour required for the possibility of this invention is
+due to three men--Faraday, Maxwell, and Hertz. In alternating layers
+of experiment and theory these three men built up the modern theory of
+electromagnetism, and demonstrated the identity of light with
+electromagnetic waves. The system which they discovered is one of
+profound intellectual interest, bringing together and unifying an
+endless variety of apparently detached phenomena, and displaying a
+cumulative mental power which cannot but afford delight to every
+generous spirit. The mechanical details which remained to be adjusted
+in order to utilise their discoveries for a practical system of
+telegraphy demanded, no doubt, very considerable ingenuity, but had
+not that broad sweep and that universality which could give them
+intrinsic interest as an object of disinterested contemplation.
+
+From the point of view of training the mind, of giving that
+well-informed, impersonal outlook which constitutes culture in the
+good sense of this much-misused word, it seems to be generally held
+indisputable that a literary education is superior to one based on
+science. Even the warmest advocates of science are apt to rest their
+claims on the contention that culture ought to be sacrificed to
+utility. Those men of science who respect culture, when they associate
+with men learned in the classics, are apt to admit, not merely
+politely, but sincerely, a certain inferiority on their side,
+compensated doubtless by the services which science renders to
+humanity, but none the less real. And so long as this attitude exists
+among men of science, it tends to verify itself: the intrinsically
+valuable aspects of science tend to be sacrificed to the merely
+useful, and little attempt is made to preserve that leisurely,
+systematic survey by which the finer quality of mind is formed and
+nourished.
+
+But even if there be, in present fact, any such inferiority as is
+supposed in the educational value of science, this is, I believe, not
+the fault of science itself, but the fault of the spirit in which
+science is taught. If its full possibilities were realised by those
+who teach it, I believe that its capacity of producing those habits of
+mind which constitute the highest mental excellence would be at least
+as great as that of literature, and more particularly of Greek and
+Latin literature. In saying this I have no wish whatever to disparage
+a classical education. I have not myself enjoyed its benefits, and my
+knowledge of Greek and Latin authors is derived almost wholly from
+translations. But I am firmly persuaded that the Greeks fully deserve
+all the admiration that is bestowed upon them, and that it is a very
+great and serious loss to be unacquainted with their writings. It is
+not by attacking them, but by drawing attention to neglected
+excellences in science, that I wish to conduct my argument.
+
+One defect, however, does seem inherent in a purely classical
+education--namely, a too exclusive emphasis on the past. By the study
+of what is absolutely ended and can never be renewed, a habit of
+criticism towards the present and the future is engendered. The
+qualities in which the present excels are qualities to which the study
+of the past does not direct attention, and to which, therefore, the
+student of Greek civilisation may easily become blind. In what is new
+and growing there is apt to be something crude, insolent, even a
+little vulgar, which is shocking to the man of sensitive taste;
+quivering from the rough contact, he retires to the trim gardens of a
+polished past, forgetting that they were reclaimed from the wilderness
+by men as rough and earth-soiled as those from whom he shrinks in his
+own day. The habit of being unable to recognise merit until it is
+dead is too apt to be the result of a purely bookish life, and a
+culture based wholly on the past will seldom be able to pierce through
+everyday surroundings to the essential splendour of contemporary
+things, or to the hope of still greater splendour in the future.
+
+    "My eyes saw not the men of old;
+    And now their age away has rolled.
+    I weep--to think I shall not see
+    The heroes of posterity."
+
+So says the Chinese poet; but such impartiality is rare in the more
+pugnacious atmosphere of the West, where the champions of past and
+future fight a never-ending battle, instead of combining to seek out
+the merits of both.
+
+This consideration, which militates not only against the exclusive
+study of the classics, but against every form of culture which has
+become static, traditional, and academic, leads inevitably to the
+fundamental question: What is the true end of education? But before
+attempting to answer this question it will be well to define the sense
+in which we are to use the word "education." For this purpose I shall
+distinguish the sense in which I mean to use it from two others, both
+perfectly legitimate, the one broader and the other narrower than the
+sense in which I mean to use the word.
+
+In the broader sense, education will include not only what we learn
+through instruction, but all that we learn through personal
+experience--the formation of character through the education of life.
+Of this aspect of education, vitally important as it is, I will say
+nothing, since its consideration would introduce topics quite foreign
+to the question with which we are concerned.
+
+In the narrower sense, education may be confined to instruction, the
+imparting of definite information on various subjects, because such
+information, in and for itself, is useful in daily life. Elementary
+education--reading, writing, and arithmetic--is almost wholly of this
+kind. But instruction, necessary as it is, does not _per se_
+constitute education in the sense in which I wish to consider it.
+
+Education, in the sense in which I mean it, may be defined as _the
+formation, by means of instruction, of certain mental habits and a
+certain outlook on life and the world_. It remains to ask ourselves,
+what mental habits, and what sort of outlook, can be hoped for as the
+result of instruction? When we have answered this question we can
+attempt to decide what science has to contribute to the formation of
+the habits and outlook which we desire.
+
+Our whole life is built about a certain number--not a very small
+number--of primary instincts and impulses. Only what is in some way
+connected with these instincts and impulses appears to us desirable or
+important; there is no faculty, whether "reason" or "virtue" or
+whatever it may be called, that can take our active life and our hopes
+and fears outside the region controlled by these first movers of all
+desire. Each of them is like a queen-bee, aided by a hive of workers
+gathering honey; but when the queen is gone the workers languish and
+die, and the cells remain empty of their expected sweetness. So with
+each primary impulse in civilised man: it is surrounded and protected
+by a busy swarm of attendant derivative desires, which store up in its
+service whatever honey the surrounding world affords. But if the
+queen-impulse dies, the death-dealing influence, though retarded a
+little by habit, spreads slowly through all the subsidiary impulses,
+and a whole tract of life becomes inexplicably colourless. What was
+formerly full of zest, and so obviously worth doing that it raised no
+questions, has now grown dreary and purposeless: with a sense of
+disillusion we inquire the meaning of life, and decide, perhaps, that
+all is vanity. The search for an outside meaning that can _compel_ an
+inner response must always be disappointed: all "meaning" must be at
+bottom related to our primary desires, and when they are extinct no
+miracle can restore to the world the value which they reflected upon
+it.
+
+The purpose of education, therefore, cannot be to create any primary
+impulse which is lacking in the uneducated; the purpose can only be to
+enlarge the scope of those that human nature provides, by increasing
+the number and variety of attendant thoughts, and by showing where the
+most permanent satisfaction is to be found. Under the impulse of a
+Calvinistic horror of the "natural man," this obvious truth has been
+too often misconceived in the training of the young; "nature" has been
+falsely regarded as excluding all that is best in what is natural, and
+the endeavour to teach virtue has led to the production of stunted and
+contorted hypocrites instead of full-grown human beings. From such
+mistakes in education a better psychology or a kinder heart is
+beginning to preserve the present generation; we need, therefore,
+waste no more words on the theory that the purpose of education is to
+thwart or eradicate nature.
+
+But although nature must supply the initial force of desire, nature is
+not, in the civilised man, the spasmodic, fragmentary, and yet violent
+set of impulses that it is in the savage. Each impulse has its
+constitutional ministry of thought and knowledge and reflection,
+through which possible conflicts of impulses are foreseen, and
+temporary impulses are controlled by the unifying impulse which may be
+called wisdom. In this way education destroys the crudity of
+instinct, and increases through knowledge the wealth and variety of
+the individual's contacts with the outside world, making him no longer
+an isolated fighting unit, but a citizen of the universe, embracing
+distant countries, remote regions of space, and vast stretches of past
+and future within the circle of his interests. It is this simultaneous
+softening in the insistence of desire and enlargement of its scope
+that is the chief moral end of education.
+
+Closely connected with this moral end is the more purely intellectual
+aim of education, the endeavour to make us see and imagine the world
+in an objective manner, as far as possible as it is in itself, and not
+merely through the distorting medium of personal desire. The complete
+attainment of such an objective view is no doubt an ideal,
+indefinitely approachable, but not actually and fully realisable.
+Education, considered as a process of forming our mental habits and
+our outlook on the world, is to be judged successful in proportion as
+its outcome approximates to this ideal; in proportion, that is to say,
+as it gives us a true view of our place in society, of the relation of
+the whole human society to its non-human environment, and of the
+nature of the non-human world as it is in itself apart from our
+desires and interests. If this standard is admitted, we can return to
+the consideration of science, inquiring how far science contributes to
+such an aim, and whether it is in any respect superior to its rivals
+in educational practice.
+
+
+II
+
+Two opposite and at first sight conflicting merits belong to science
+as against literature and art. The one, which is not inherently
+necessary, but is certainly true at the present day, is hopefulness
+as to the future of human achievement, and in particular as to the
+useful work that may be accomplished by any intelligent student. This
+merit and the cheerful outlook which it engenders prevent what might
+otherwise be the depressing effect of another aspect of science, to my
+mind also a merit, and perhaps its greatest merit--I mean the
+irrelevance of human passions and of the whole subjective apparatus
+where scientific truth is concerned. Each of these reasons for
+preferring the study of science requires some amplification. Let us
+begin with the first.
+
+In the study of literature or art our attention is perpetually riveted
+upon the past: the men of Greece or of the Renaissance did better than
+any men do now; the triumphs of former ages, so far from facilitating
+fresh triumphs in our own age, actually increase the difficulty of
+fresh triumphs by rendering originality harder of attainment; not only
+is artistic achievement not cumulative, but it seems even to depend
+upon a certain freshness and _naïveté_ of impulse and vision which
+civilisation tends to destroy. Hence comes, to those who have been
+nourished on the literary and artistic productions of former ages, a
+certain peevishness and undue fastidiousness towards the present, from
+which there seems no escape except into the deliberate vandalism which
+ignores tradition and in the search after originality achieves only
+the eccentric. But in such vandalism there is none of the simplicity
+and spontaneity out of which great art springs: theory is still the
+canker in its core, and insincerity destroys the advantages of a
+merely pretended ignorance.
+
+The despair thus arising from an education which suggests no
+pre-eminent mental activity except that of artistic creation is wholly
+absent from an education which gives the knowledge of scientific
+method. The discovery of scientific method, except in pure
+mathematics, is a thing of yesterday; speaking broadly, we may say
+that it dates from Galileo. Yet already it has transformed the world,
+and its success proceeds with ever-accelerating velocity. In science
+men have discovered an activity of the very highest value in which
+they are no longer, as in art, dependent for progress upon the
+appearance of continually greater genius, for in science the
+successors stand upon the shoulders of their predecessors; where one
+man of supreme genius has invented a method, a thousand lesser men can
+apply it. No transcendent ability is required in order to make useful
+discoveries in science; the edifice of science needs its masons,
+bricklayers, and common labourers as well as its foremen,
+master-builders, and architects. In art nothing worth doing can be
+done without genius; in science even a very moderate capacity can
+contribute to a supreme achievement.
+
+In science the man of real genius is the man who invents a new method.
+The notable discoveries are often made by his successors, who can
+apply the method with fresh vigour, unimpaired by the previous labour
+of perfecting it; but the mental calibre of the thought required for
+their work, however brilliant, is not so great as that required by the
+first inventor of the method. There are in science immense numbers of
+different methods, appropriate to different classes of problems; but
+over and above them all, there is something not easily definable,
+which may be called _the_ method of science. It was formerly customary
+to identify this with the inductive method, and to associate it with
+the name of Bacon. But the true inductive method was not discovered by
+Bacon, and the true method of science is something which includes
+deduction as much as induction, logic and mathematics as much as
+botany and geology. I shall not attempt the difficult task of stating
+what the scientific method is, but I will try to indicate the temper
+of mind out of which the scientific method grows, which is the second
+of the two merits that were mentioned above as belonging to a
+scientific education.
+
+The kernel of the scientific outlook is a thing so simple, so obvious,
+so seemingly trivial, that the mention of it may almost excite
+derision. The kernel of the scientific outlook is the refusal to
+regard our own desires, tastes, and interests as affording a key to
+the understanding of the world. Stated thus baldly, this may seem no
+more than a trite truism. But to remember it consistently in matters
+arousing our passionate partisanship is by no means easy, especially
+where the available evidence is uncertain and inconclusive. A few
+illustrations will make this clear.
+
+Aristotle, I understand, considered that the stars must move in
+circles because the circle is the most perfect curve. In the absence
+of evidence to the contrary, he allowed himself to decide a question
+of fact by an appeal to æsthetico-moral considerations. In such a case
+it is at once obvious to us that this appeal was unjustifiable. We
+know now how to ascertain as a fact the way in which the heavenly
+bodies move, and we know that they do not move in circles, or even in
+accurate ellipses, or in any other kind of simply describable curve.
+This may be painful to a certain hankering after simplicity of pattern
+in the universe, but we know that in astronomy such feelings are
+irrelevant. Easy as this knowledge seems now, we owe it to the courage
+and insight of the first inventors of scientific method, and more
+especially of Galileo.
+
+We may take as another illustration Malthus's doctrine of population.
+This illustration is all the better for the fact that his actual
+doctrine is now known to be largely erroneous. It is not his
+conclusions that are valuable, but the temper and method of his
+inquiry. As everyone knows, it was to him that Darwin owed an
+essential part of his theory of natural selection, and this was only
+possible because Malthus's outlook was truly scientific. His great
+merit lies in considering man not as the object of praise or blame,
+but as a part of nature, a thing with a certain characteristic
+behaviour from which certain consequences must follow. If the
+behaviour is not quite what Malthus supposed, if the consequences are
+not quite what he inferred, that may falsify his conclusions, but does
+not impair the value of his method. The objections which were made
+when his doctrine was new--that it was horrible and depressing, that
+people ought not to act as he said they did, and so on--were all such
+as implied an unscientific attitude of mind; as against all of them,
+his calm determination to treat man as a natural phenomenon marks an
+important advance over the reformers of the eighteenth century and the
+Revolution.
+
+Under the influence of Darwinism the scientific attitude towards man
+has now become fairly common, and is to some people quite natural,
+though to most it is still a difficult and artificial intellectual
+contortion. There is however, one study which is as yet almost wholly
+untouched by the scientific spirit--I mean the study of philosophy.
+Philosophers and the public imagine that the scientific spirit must
+pervade pages that bristle with allusions to ions, germ-plasms, and
+the eyes of shell-fish. But as the devil can quote Scripture, so the
+philosopher can quote science. The scientific spirit is not an affair
+of quotation, of externally acquired information, any more than
+manners are an affair of the etiquette-book. The scientific attitude
+of mind involves a sweeping away of all other desires in the interests
+of the desire to know--it involves suppression of hopes and fears,
+loves and hates, and the whole subjective emotional life, until we
+become subdued to the material, able to see it frankly, without
+preconceptions, without bias, without any wish except to see it as it
+is, and without any belief that what it is must be determined by some
+relation, positive or negative, to what we should like it to be, or to
+what we can easily imagine it to be.
+
+Now in philosophy this attitude of mind has not as yet been achieved.
+A certain self-absorption, not personal, but human, has marked almost
+all attempts to conceive the universe as a whole. Mind, or some aspect
+of it--thought or will or sentience--has been regarded as the pattern
+after which the universe is to be conceived, for no better reason, at
+bottom, than that such a universe would not seem strange, and would
+give us the cosy feeling that every place is like home. To conceive
+the universe as essentially progressive or essentially deteriorating,
+for example, is to give to our hopes and fears a cosmic importance
+which _may_, of course, be justified, but which we have as yet no
+reason to suppose justified. Until we have learnt to think of it in
+ethically neutral terms, we have not arrived at a scientific attitude
+in philosophy; and until we have arrived at such an attitude, it is
+hardly to be hoped that philosophy will achieve any solid results.
+
+I have spoken so far largely of the negative aspect of the scientific
+spirit, but it is from the positive aspect that its value is derived.
+The instinct of constructiveness, which is one of the chief incentives
+to artistic creation, can find in scientific systems a satisfaction
+more massive than any epic poem. Disinterested curiosity, which is the
+source of almost all intellectual effort, finds with astonished
+delight that science can unveil secrets which might well have seemed
+for ever undiscoverable. The desire for a larger life and wider
+interests, for an escape from private circumstances, and even from the
+whole recurring human cycle of birth and death, is fulfilled by the
+impersonal cosmic outlook of science as by nothing else. To all these
+must be added, as contributing to the happiness of the man of science,
+the admiration of splendid achievement, and the consciousness of
+inestimable utility to the human race. A life devoted to science is
+therefore a happy life, and its happiness is derived from the very
+best sources that are open to dwellers on this troubled and passionate
+planet.
+
+
+
+
+III
+
+A FREE MAN'S WORSHIP[9]
+
+
+To Dr. Faustus in his study Mephistopheles told the history of the
+Creation, saying:
+
+"The endless praises of the choirs of angels had begun to grow
+wearisome; for, after all, did he not deserve their praise? Had he not
+given them endless joy? Would it not be more amusing to obtain
+undeserved praise, to be worshipped by beings whom he tortured? He
+smiled inwardly, and resolved that the great drama should be
+performed.
+
+"For countless ages the hot nebula whirled aimlessly through space. At
+length it began to take shape, the central mass threw off planets, the
+planets cooled, boiling seas and burning mountains heaved and tossed,
+from black masses of cloud hot sheets of rain deluged the barely solid
+crust. And now the first germ of life grew in the depths of the ocean,
+and developed rapidly in the fructifying warmth into vast forest
+trees, huge ferns springing from the damp mould, sea monsters
+breeding, fighting, devouring, and passing away. And from the
+monsters, as the play unfolded itself, Man was born, with the power of
+thought, the knowledge of good and evil, and the cruel thirst for
+worship. And Man saw that all is passing in this mad, monstrous world,
+that all is struggling to snatch, at any cost, a few brief moments of
+life before Death's inexorable decree. And Man said: 'There is a
+hidden purpose, could we but fathom it, and the purpose is good; for
+we must reverence something, and in the visible world there is nothing
+worthy of reverence.' And Man stood aside from the struggle, resolving
+that God intended harmony to come out of chaos by human efforts. And
+when he followed the instincts which God had transmitted to him from
+his ancestry of beasts of prey, he called it Sin, and asked God to
+forgive him. But he doubted whether he could be justly forgiven, until
+he invented a divine Plan by which God's wrath was to have been
+appeased. And seeing the present was bad, he made it yet worse, that
+thereby the future might be better. And he gave God thanks for the
+strength that enabled him to forgo even the joys that were possible.
+And God smiled; and when he saw that Man had become perfect in
+renunciation and worship, he sent another sun through the sky, which
+crashed into Man's sun; and all returned again to nebula.
+
+"'Yes,' he murmured, 'it was a good play; I will have it performed
+again.'"
+
+Such, in outline, but even more purposeless, more void of meaning, is
+the world which Science presents for our belief. Amid such a world, if
+anywhere, our ideals henceforward must find a home. That Man is the
+product of causes which had no prevision of the end they were
+achieving; that his origin, his growth, his hopes and fears, his loves
+and his beliefs, are but the outcome of accidental collocations of
+atoms; that no fire, no heroism, no intensity of thought and feeling,
+can preserve an individual life beyond the grave; that all the labours
+of the ages, all the devotion, all the inspiration, all the noonday
+brightness of human genius, are destined to extinction in the vast
+death of the solar system, and that the whole temple of Man's
+achievement must inevitably be buried beneath the débris of a universe
+in ruins--all these things, if not quite beyond dispute, are yet so
+nearly certain, that no philosophy which rejects them can hope to
+stand. Only within the scaffolding of these truths, only on the firm
+foundation of unyielding despair, can the soul's habitation henceforth
+be safely built.
+
+How, in such an alien and inhuman world, can so powerless a creature
+as Man preserve his aspirations untarnished? A strange mystery it is
+that Nature, omnipotent but blind, in the revolutions of her secular
+hurryings through the abysses of space, has brought forth at last a
+child, subject still to her power, but gifted with sight, with
+knowledge of good and evil, with the capacity of judging all the works
+of his unthinking Mother. In spite of Death, the mark and seal of the
+parental control, Man is yet free, during his brief years, to examine,
+to criticise, to know, and in imagination to create. To him alone, in
+the world with which he is acquainted, this freedom belongs; and in
+this lies his superiority to the resistless forces that control his
+outward life.
+
+The savage, like ourselves, feels the oppression of his impotence
+before the powers of Nature; but having in himself nothing that he
+respects more than Power, he is willing to prostrate himself before
+his gods, without inquiring whether they are worthy of his worship.
+Pathetic and very terrible is the long history of cruelty and torture,
+of degradation and human sacrifice, endured in the hope of placating
+the jealous gods: surely, the trembling believer thinks, when what is
+most precious has been freely given, their lust for blood must be
+appeased, and more will not be required. The religion of Moloch--as
+such creeds may be generically called--is in essence the cringing
+submission of the slave, who dare not, even in his heart, allow the
+thought that his master deserves no adulation. Since the independence
+of ideals is not yet acknowledged, Power may be freely worshipped, and
+receive an unlimited respect, despite its wanton infliction of pain.
+
+But gradually, as morality grows bolder, the claim of the ideal world
+begins to be felt; and worship, if it is not to cease, must be given
+to gods of another kind than those created by the savage. Some, though
+they feel the demands of the ideal, will still consciously reject
+them, still urging that naked Power is worthy of worship. Such is the
+attitude inculcated in God's answer to Job out of the whirlwind: the
+divine power and knowledge are paraded, but of the divine goodness
+there is no hint. Such also is the attitude of those who, in our own
+day, base their morality upon the struggle for survival, maintaining
+that the survivors are necessarily the fittest. But others, not
+content with an answer so repugnant to the moral sense, will adopt the
+position which we have become accustomed to regard as specially
+religious, maintaining that, in some hidden manner, the world of fact
+is really harmonious with the world of ideals. Thus Man creates God,
+all-powerful and all-good, the mystic unity of what is and what should
+be.
+
+But the world of fact, after all, is not good; and, in submitting our
+judgment to it, there is an element of slavishness from which our
+thoughts must be purged. For in all things it is well to exalt the
+dignity of Man, by freeing him as far as possible from the tyranny of
+non-human Power. When we have realised that Power is largely bad, that
+man, with his knowledge of good and evil, is but a helpless atom in a
+world which has no such knowledge, the choice is again presented to
+us: Shall we worship Force, or shall we worship Goodness? Shall our
+God exist and be evil, or shall he be recognised as the creation of
+our own conscience?
+
+The answer to this question is very momentous, and affects profoundly
+our whole morality. The worship of Force, to which Carlyle and
+Nietzsche and the creed of Militarism have accustomed us, is the
+result of failure to maintain our own ideals against a hostile
+universe: it is itself a prostrate submission to evil, a sacrifice of
+our best to Moloch. If strength indeed is to be respected, let us
+respect rather the strength of those who refuse that false
+"recognition of facts" which fails to recognise that facts are often
+bad. Let us admit that, in the world we know, there are many things
+that would be better otherwise, and that the ideals to which we do and
+must adhere are not realised in the realm of matter. Let us preserve
+our respect for truth, for beauty, for the ideal of perfection which
+life does not permit us to attain, though none of these things meet
+with the approval of the unconscious universe. If Power is bad, as it
+seems to be, let us reject it from our hearts. In this lies Man's true
+freedom: in determination to worship only the God created by our own
+love of the good, to respect only the heaven which inspires the
+insight of our best moments. In action, in desire, we must submit
+perpetually to the tyranny of outside forces; but in thought, in
+aspiration, we are free, free from our fellow-men, free from the petty
+planet on which our bodies impotently crawl, free even, while we live,
+from the tyranny of death. Let us learn, then, that energy of faith
+which enables us to live constantly in the vision of the good; and let
+us descend, in action, into the world of fact, with that vision always
+before us.
+
+When first the opposition of fact and ideal grows fully visible, a
+spirit of fiery revolt, of fierce hatred of the gods, seems necessary
+to the assertion of freedom. To defy with Promethean constancy a
+hostile universe, to keep its evil always in view, always actively
+hated, to refuse no pain that the malice of Power can invent, appears
+to be the duty of all who will not bow before the inevitable. But
+indignation is still a bondage, for it compels our thoughts to be
+occupied with an evil world; and in the fierceness of desire from
+which rebellion springs there is a kind of self-assertion which it is
+necessary for the wise to overcome. Indignation is a submission of our
+thoughts, but not of our desires; the Stoic freedom in which wisdom
+consists is found in the submission of our desires, but not of our
+thoughts. From the submission of our desires springs the virtue of
+resignation; from the freedom of our thoughts springs the whole world
+of art and philosophy, and the vision of beauty by which, at last, we
+half reconquer the reluctant world. But the vision of beauty is
+possible only to unfettered contemplation, to thoughts not weighted by
+the load of eager wishes; and thus Freedom comes only to those who no
+longer ask of life that it shall yield them any of those personal
+goods that are subject to the mutations of Time.
+
+Although the necessity of renunciation is evidence of the existence of
+evil, yet Christianity, in preaching it, has shown a wisdom exceeding
+that of the Promethean philosophy of rebellion. It must be admitted
+that, of the things we desire, some, though they prove impossible, are
+yet real goods; others, however, as ardently longed for, do not form
+part of a fully purified ideal. The belief that what must be renounced
+is bad, though sometimes false, is far less often false than untamed
+passion supposes; and the creed of religion, by providing a reason
+for proving that it is never false, has been the means of purifying
+our hopes by the discovery of many austere truths.
+
+But there is in resignation a further good element: even real goods,
+when they are unattainable, ought not to be fretfully desired. To
+every man comes, sooner or later, the great renunciation. For the
+young, there is nothing unattainable; a good thing desired with the
+whole force of a passionate will, and yet impossible, is to them not
+credible. Yet, by death, by illness, by poverty, or by the voice of
+duty, we must learn, each one of us, that the world was not made for
+us, and that, however beautiful may be the things we crave, Fate may
+nevertheless forbid them. It is the part of courage, when misfortune
+comes, to bear without repining the ruin of our hopes, to turn away
+our thoughts from vain regrets. This degree of submission to Power is
+not only just and right: it is the very gate of wisdom.
+
+But passive renunciation is not the whole of wisdom; for not by
+renunciation alone can we build a temple for the worship of our own
+ideals. Haunting foreshadowings of the temple appear in the realm of
+imagination, in music, in architecture, in the untroubled kingdom of
+reason, and in the golden sunset magic of lyrics, where beauty shines
+and glows, remote from the touch of sorrow, remote from the fear of
+change, remote from the failures and disenchantments of the world of
+fact. In the contemplation of these things the vision of heaven will
+shape itself in our hearts, giving at once a touchstone to judge the
+world about us, and an inspiration by which to fashion to our needs
+whatever is not incapable of serving as a stone in the sacred temple.
+
+Except for those rare spirits that are born without sin, there is a
+cavern of darkness to be traversed before that temple can be entered.
+The gate of the cavern is despair, and its floor is paved with the
+gravestones of abandoned hopes. There Self must die; there the
+eagerness, the greed of untamed desire must be slain, for only so can
+the soul be freed from the empire of Fate. But out of the cavern the
+Gate of Renunciation leads again to the daylight of wisdom, by whose
+radiance a new insight, a new joy, a new tenderness, shine forth to
+gladden the pilgrim's heart.
+
+When, without the bitterness of impotent rebellion, we have learnt
+both to resign ourselves to the outward rule of Fate and to recognise
+that the non-human world is unworthy of our worship, it becomes
+possible at last so to transform and refashion the unconscious
+universe, so to transmute it in the crucible of imagination, that a
+new image of shining gold replaces the old idol of clay. In all the
+multiform facts of the world--in the visual shapes of trees and
+mountains and clouds, in the events of the life of man, even in the
+very omnipotence of Death--the insight of creative idealism can find
+the reflection of a beauty which its own thoughts first made. In this
+way mind asserts its subtle mastery over the thoughtless forces of
+Nature. The more evil the material with which it deals, the more
+thwarting to untrained desire, the greater is its achievement in
+inducing the reluctant rock to yield up its hidden treasures, the
+prouder its victory in compelling the opposing forces to swell the
+pageant of its triumph. Of all the arts, Tragedy is the proudest, the
+most triumphant; for it builds its shining citadel in the very centre
+of the enemy's country, on the very summit of his highest mountain;
+from its impregnable watchtowers, his camps and arsenals, his columns
+and forts, are all revealed; within its walls the free life continues,
+while the legions of Death and Pain and Despair, and all the servile
+captains of tyrant Fate, afford the burghers of that dauntless city
+new spectacles of beauty. Happy those sacred ramparts, thrice happy
+the dwellers on that all-seeing eminence. Honour to those brave
+warriors who, through countless ages of warfare, have preserved for us
+the priceless heritage of liberty, and have kept undefiled by
+sacrilegious invaders the home of the unsubdued.
+
+But the beauty of Tragedy does but make visible a quality which, in
+more or less obvious shapes, is present always and everywhere in life.
+In the spectacle of Death, in the endurance of intolerable pain, and
+in the irrevocableness of a vanished past, there is a sacredness, an
+overpowering awe, a feeling of the vastness, the depth, the
+inexhaustible mystery of existence, in which, as by some strange
+marriage of pain, the sufferer is bound to the world by bonds of
+sorrow. In these moments of insight, we lose all eagerness of
+temporary desire, all struggling and striving for petty ends, all care
+for the little trivial things that, to a superficial view, make up the
+common life of day by day; we see, surrounding the narrow raft
+illumined by the flickering light of human comradeship, the dark ocean
+on whose rolling waves we toss for a brief hour; from the great night
+without, a chill blast breaks in upon our refuge; all the loneliness
+of humanity amid hostile forces is concentrated upon the individual
+soul, which must struggle alone, with what of courage it can command,
+against the whole weight of a universe that cares nothing for its
+hopes and fears. Victory, in this struggle with the powers of
+darkness, is the true baptism into the glorious company of heroes, the
+true initiation into the overmastering beauty of human existence. From
+that awful encounter of the soul with the outer world, renunciation,
+wisdom, and charity are born; and with their birth a new life begins.
+To take into the inmost shrine of the soul the irresistible forces
+whose puppets we seem to be--Death and change, the irrevocableness of
+the past, and the powerlessness of man before the blind hurry of the
+universe from vanity to vanity--to feel these things and know them is
+to conquer them.
+
+This is the reason why the Past has such magical power. The beauty of
+its motionless and silent pictures is like the enchanted purity of
+late autumn, when the leaves, though one breath would make them fall,
+still glow against the sky in golden glory. The Past does not change
+or strive; like Duncan, after life's fitful fever it sleeps well; what
+was eager and grasping, what was petty and transitory, has faded away,
+the things that were beautiful and eternal shine out of it like stars
+in the night. Its beauty, to a soul not worthy of it, is unendurable;
+but to a soul which has conquered Fate it is the key of religion.
+
+The life of Man, viewed outwardly, is but a small thing in comparison
+with the forces of Nature. The slave is doomed to worship Time and
+Fate and Death, because they are greater than anything he finds in
+himself, and because all his thoughts are of things which they devour.
+But, great as they are, to think of them greatly, to feel their
+passionless splendour, is greater still. And such thought makes us
+free men; we no longer bow before the inevitable in Oriental
+subjection, but we absorb it, and make it a part of ourselves. To
+abandon the struggle for private happiness, to expel all eagerness of
+temporary desire, to burn with passion for eternal things--this is
+emancipation, and this is the free man's worship. And this liberation
+is effected by a contemplation of Fate; for Fate itself is subdued by
+the mind which leaves nothing to be purged by the purifying fire of
+Time.
+
+United with his fellow-men by the strongest of all ties, the tie of a
+common doom, the free man finds that a new vision is with him always,
+shedding over every daily task the light of love. The life of Man is a
+long march through the night, surrounded by invisible foes, tortured
+by weariness and pain, towards a goal that few can hope to reach, and
+where none may tarry long. One by one, as they march, our comrades
+vanish from our sight, seized by the silent orders of omnipotent
+Death. Very brief is the time in which we can help them, in which
+their happiness or misery is decided. Be it ours to shed sunshine on
+their path, to lighten their sorrows by the balm of sympathy, to give
+them the pure joy of a never-tiring affection, to strengthen failing
+courage, to instil faith in hours of despair. Let us not weigh in
+grudging scales their merits and demerits, but let us think only of
+their need--of the sorrows, the difficulties, perhaps the blindnesses,
+that make the misery of their lives; let us remember that they are
+fellow-sufferers in the same darkness, actors in the same tragedy with
+ourselves. And so, when their day is over, when their good and their
+evil have become eternal by the immortality of the past, be it ours to
+feel that, where they suffered, where they failed, no deed of ours was
+the cause; but wherever a spark of the divine fire kindled in their
+hearts, we were ready with encouragement, with sympathy, with brave
+words in which high courage glowed.
+
+Brief and powerless is Man's life; on him and all his race the slow,
+sure doom falls pitiless and dark. Blind to good and evil, reckless of
+destruction, omnipotent matter rolls on its relentless way; for Man,
+condemned to-day to lose his dearest, to-morrow himself to pass
+through the gate of darkness, it remains only to cherish, ere yet the
+blow falls, the lofty thoughts that ennoble his little day; disdaining
+the coward terrors of the slave of Fate, to worship at the shrine that
+his own hands have built; undismayed by the empire of chance, to
+preserve a mind free from the wanton tyranny that rules his outward
+life; proudly defiant of the irresistible forces that tolerate, for a
+moment, his knowledge and his condemnation, to sustain alone, a weary
+but unyielding Atlas, the world that his own ideals have fashioned
+despite the trampling march of unconscious power.
+
+FOOTNOTES:
+
+[9] Reprinted from the _Independent Review_, December, 1903.
+
+
+
+
+IV
+
+THE STUDY OF MATHEMATICS
+
+
+In regard to every form of human activity it is necessary that the
+question should be asked from time to time, What is its purpose and
+ideal? In what way does it contribute to the beauty of human
+existence? As respects those pursuits which contribute only remotely,
+by providing the mechanism of life, it is well to be reminded that not
+the mere fact of living is to be desired, but the art of living in the
+contemplation of great things. Still more in regard to those
+avocations which have no end outside themselves, which are to be
+justified, if at all, as actually adding to the sum of the world's
+permanent possessions, it is necessary to keep alive a knowledge of
+their aims, a clear prefiguring vision of the temple in which creative
+imagination is to be embodied.
+
+The fulfilment of this need, in what concerns the studies forming the
+material upon which custom has decided to train the youthful mind, is
+indeed sadly remote--so remote as to make the mere statement of such a
+claim appear preposterous. Great men, fully alive to the beauty of the
+contemplations to whose service their lives are devoted, desiring that
+others may share in their joys, persuade mankind to impart to the
+successive generations the mechanical knowledge without which it is
+impossible to cross the threshold. Dry pedants possess themselves of
+the privilege of instilling this knowledge: they forget that it is to
+serve but as a key to open the doors of the temple; though they spend
+their lives on the steps leading up to those sacred doors, they turn
+their backs upon the temple so resolutely that its very existence is
+forgotten, and the eager youth, who would press forward to be
+initiated to its domes and arches, is bidden to turn back and count
+the steps.
+
+Mathematics, perhaps more even than the study of Greece and Rome, has
+suffered from this oblivion of its due place in civilisation. Although
+tradition has decreed that the great bulk of educated men shall know
+at least the elements of the subject, the reasons for which the
+tradition arose are forgotten, buried beneath a great rubbish-heap of
+pedantries and trivialities. To those who inquire as to the purpose of
+mathematics, the usual answer will be that it facilitates the making
+of machines, the travelling from place to place, and the victory over
+foreign nations, whether in war or commerce. If it be objected that
+these ends--all of which are of doubtful value--are not furthered by
+the merely elementary study imposed upon those who do not become
+expert mathematicians, the reply, it is true, will probably be that
+mathematics trains the reasoning faculties. Yet the very men who make
+this reply are, for the most part, unwilling to abandon the teaching
+of definite fallacies, known to be such, and instinctively rejected by
+the unsophisticated mind of every intelligent learner. And the
+reasoning faculty itself is generally conceived, by those who urge its
+cultivation, as merely a means for the avoidance of pitfalls and a
+help in the discovery of rules for the guidance of practical life. All
+these are undeniably important achievements to the credit of
+mathematics; yet it is none of these that entitles mathematics to a
+place in every liberal education. Plato, we know, regarded the
+contemplation of mathematical truths as worthy of the Deity; and
+Plato realised, more perhaps than any other single man, what those
+elements are in human life which merit a place in heaven. There is in
+mathematics, he says, "something which is _necessary_ and cannot be
+set aside ... and, if I mistake not, of divine necessity; for as to
+the human necessities of which the Many talk in this connection,
+nothing can be more ridiculous than such an application of the words.
+_Cleinias._ And what are these necessities of knowledge, Stranger,
+which are divine and not human? _Athenian._ Those things without some
+use or knowledge of which a man cannot become a God to the world, nor
+a spirit, nor yet a hero, nor able earnestly to think and care for
+man" (_Laws_, p. 818).[10] Such was Plato's judgment of mathematics;
+but the mathematicians do not read Plato, while those who read him
+know no mathematics, and regard his opinion upon this question as
+merely a curious aberration.
+
+Mathematics, rightly viewed, possesses not only truth, but supreme
+beauty--a beauty cold and austere, like that of sculpture, without
+appeal to any part of our weaker nature, without the gorgeous
+trappings of painting or music, yet sublimely pure, and capable of a
+stern perfection such as only the greatest art can show. The true
+spirit of delight, the exaltation, the sense of being more than man,
+which is the touchstone of the highest excellence, is to be found in
+mathematics as surely as in poetry. What is best in mathematics
+deserves not merely to be learnt as a task, but to be assimilated as a
+part of daily thought, and brought again and again before the mind
+with ever-renewed encouragement. Real life is, to most men, a long
+second-best, a perpetual compromise between the ideal and the
+possible; but the world of pure reason knows no compromise, no
+practical limitations, no barrier to the creative activity embodying
+in splendid edifices the passionate aspiration after the perfect from
+which all great work springs. Remote from human passions, remote even
+from the pitiful facts of nature, the generations have gradually
+created an ordered cosmos, where pure thought can dwell as in its
+natural home, and where one, at least, of our nobler impulses can
+escape from the dreary exile of the actual world.
+
+So little, however, have mathematicians aimed at beauty, that hardly
+anything in their work has had this conscious purpose. Much, owing to
+irrepressible instincts, which were better than avowed beliefs, has
+been moulded by an unconscious taste; but much also has been spoilt by
+false notions of what was fitting. The characteristic excellence of
+mathematics is only to be found where the reasoning is rigidly
+logical: the rules of logic are to mathematics what those of structure
+are to architecture. In the most beautiful work, a chain of argument
+is presented in which every link is important on its own account, in
+which there is an air of ease and lucidity throughout, and the
+premises achieve more than would have been thought possible, by means
+which appear natural and inevitable. Literature embodies what is
+general in particular circumstances whose universal significance
+shines through their individual dress; but mathematics endeavours to
+present whatever is most general in its purity, without any irrelevant
+trappings.
+
+How should the teaching of mathematics be conducted so as to
+communicate to the learner as much as possible of this high ideal?
+Here experience must, in a great measure, be our guide; but some
+maxims may result from our consideration of the ultimate purpose to be
+achieved.
+
+One of the chief ends served by mathematics, when rightly taught, is
+to awaken the learner's belief in reason, his confidence in the truth
+of what has been demonstrated, and in the value of demonstration. This
+purpose is not served by existing instruction; but it is easy to see
+ways in which it might be served. At present, in what concerns
+arithmetic, the boy or girl is given a set of rules, which present
+themselves as neither true nor false, but as merely the will of the
+teacher, the way in which, for some unfathomable reason, the teacher
+prefers to have the game played. To some degree, in a study of such
+definite practical utility, this is no doubt unavoidable; but as soon
+as possible, the reasons of rules should be set forth by whatever
+means most readily appeal to the childish mind. In geometry, instead
+of the tedious apparatus of fallacious proofs for obvious truisms
+which constitutes the beginning of Euclid, the learner should be
+allowed at first to assume the truth of everything obvious, and should
+be instructed in the demonstrations of theorems which are at once
+startling and easily verifiable by actual drawing, such as those in
+which it is shown that three or more lines meet in a point. In this
+way belief is generated; it is seen that reasoning may lead to
+startling conclusions, which nevertheless the facts will verify; and
+thus the instinctive distrust of whatever is abstract or rational is
+gradually overcome. Where theorems are difficult, they should be first
+taught as exercises in geometrical drawing, until the figure has
+become thoroughly familiar; it will then be an agreeable advance to be
+taught the logical connections of the various lines or circles that
+occur. It is desirable also that the figure illustrating a theorem
+should be drawn in all possible cases and shapes, that so the abstract
+relations with which geometry is concerned may of themselves emerge
+as the residue of similarity amid such great apparent diversity. In
+this way the abstract demonstrations should form but a small part of
+the instruction, and should be given when, by familiarity with
+concrete illustrations, they have come to be felt as the natural
+embodiment of visible fact. In this early stage proofs should not be
+given with pedantic fullness; definitely fallacious methods, such as
+that of superposition, should be rigidly excluded from the first, but
+where, without such methods, the proof would be very difficult, the
+result should be rendered acceptable by arguments and illustrations
+which are explicitly contrasted with demonstrations.
+
+In the beginning of algebra, even the most intelligent child finds, as
+a rule, very great difficulty. The use of letters is a mystery, which
+seems to have no purpose except mystification. It is almost
+impossible, at first, not to think that every letter stands for some
+particular number, if only the teacher would reveal _what_ number it
+stands for. The fact is, that in algebra the mind is first taught to
+consider general truths, truths which are not asserted to hold only of
+this or that particular thing, but of any one of a whole group of
+things. It is in the power of understanding and discovering such
+truths that the mastery of the intellect over the whole world of
+things actual and possible resides; and ability to deal with the
+general as such is one of the gifts that a mathematical education
+should bestow. But how little, as a rule, is the teacher of algebra
+able to explain the chasm which divides it from arithmetic, and how
+little is the learner assisted in his groping efforts at
+comprehension! Usually the method that has been adopted in arithmetic
+is continued: rules are set forth, with no adequate explanation of
+their grounds; the pupil learns to use the rules blindly, and
+presently, when he is able to obtain the answer that the teacher
+desires, he feels that he has mastered the difficulties of the
+subject. But of inner comprehension of the processes employed he has
+probably acquired almost nothing.
+
+When algebra has been learnt, all goes smoothly until we reach those
+studies in which the notion of infinity is employed--the infinitesimal
+calculus and the whole of higher mathematics. The solution of the
+difficulties which formerly surrounded the mathematical infinite is
+probably the greatest achievement of which our own age has to boast.
+Since the beginnings of Greek thought these difficulties have been
+known; in every age the finest intellects have vainly endeavoured to
+answer the apparently unanswerable questions that had been asked by
+Zeno the Eleatic. At last Georg Cantor has found the answer, and has
+conquered for the intellect a new and vast province which had been
+given over to Chaos and old Night. It was assumed as self-evident,
+until Cantor and Dedekind established the opposite, that if, from any
+collection of things, some were taken away, the number of things left
+must always be less than the original number of things. This
+assumption, as a matter of fact, holds only of finite collections; and
+the rejection of it, where the infinite is concerned, has been shown
+to remove all the difficulties that had hitherto baffled human reason
+in this matter, and to render possible the creation of an exact
+science of the infinite. This stupendous fact ought to produce a
+revolution in the higher teaching of mathematics; it has itself added
+immeasurably to the educational value of the subject, and it has at
+last given the means of treating with logical precision many studies
+which, until lately, were wrapped in fallacy and obscurity. By those
+who were educated on the old lines, the new work is considered to be
+appallingly difficult, abstruse, and obscure; and it must be confessed
+that the discoverer, as is so often the case, has hardly himself
+emerged from the mists which the light of his intellect is dispelling.
+But inherently, the new doctrine of the infinite, to all candid and
+inquiring minds, has facilitated the mastery of higher mathematics;
+for hitherto, it has been necessary to learn, by a long process of
+sophistication, to give assent to arguments which, on first
+acquaintance, were rightly judged to be confused and erroneous. So far
+from producing a fearless belief in reason, a bold rejection of
+whatever failed to fulfil the strictest requirements of logic, a
+mathematical training, during the past two centuries, encouraged the
+belief that many things, which a rigid inquiry would reject as
+fallacious, must yet be accepted because they work in what the
+mathematician calls "practice." By this means, a timid, compromising
+spirit, or else a sacerdotal belief in mysteries not intelligible to
+the profane, has been bred where reason alone should have ruled. All
+this it is now time to sweep away; let those who wish to penetrate
+into the arcana of mathematics be taught at once the true theory in
+all its logical purity, and in the concatenation established by the
+very essence of the entities concerned.
+
+If we are considering mathematics as an end in itself, and not as a
+technical training for engineers, it is very desirable to preserve the
+purity and strictness of its reasoning. Accordingly those who have
+attained a sufficient familiarity with its easier portions should be
+led backward from propositions to which they have assented as
+self-evident to more and more fundamental principles from which what
+had previously appeared as premises can be deduced. They should be
+taught--what the theory of infinity very aptly illustrates--that many
+propositions seem self-evident to the untrained mind which,
+nevertheless, a nearer scrutiny shows to be false. By this means they
+will be led to a sceptical inquiry into first principles, an
+examination of the foundations upon which the whole edifice of
+reasoning is built, or, to take perhaps a more fitting metaphor, the
+great trunk from which the spreading branches spring. At this stage,
+it is well to study afresh the elementary portions of mathematics,
+asking no longer merely whether a given proposition is true, but also
+how it grows out of the central principles of logic. Questions of this
+nature can now be answered with a precision and certainty which were
+formerly quite impossible; and in the chains of reasoning that the
+answer requires the unity of all mathematical studies at last unfolds
+itself.
+
+In the great majority of mathematical text-books there is a total lack
+of unity in method and of systematic development of a central theme.
+Propositions of very diverse kinds are proved by whatever means are
+thought most easily intelligible, and much space is devoted to mere
+curiosities which in no way contribute to the main argument. But in
+the greatest works, unity and inevitability are felt as in the
+unfolding of a drama; in the premisses a subject is proposed for
+consideration, and in every subsequent step some definite advance is
+made towards mastery of its nature. The love of system, of
+interconnection, which is perhaps the inmost essence of the
+intellectual impulse, can find free play in mathematics as nowhere
+else. The learner who feels this impulse must not be repelled by an
+array of meaningless examples or distracted by amusing oddities, but
+must be encouraged to dwell upon central principles, to become
+familiar with the structure of the various subjects which are put
+before him, to travel easily over the steps of the more important
+deductions. In this way a good tone of mind is cultivated, and
+selective attention is taught to dwell by preference upon what is
+weighty and essential.
+
+When the separate studies into which mathematics is divided have each
+been viewed as a logical whole, as a natural growth from the
+propositions which constitute their principles, the learner will be
+able to understand the fundamental science which unifies and
+systematises the whole of deductive reasoning. This is symbolic
+logic--a study which, though it owes its inception to Aristotle, is
+yet, in its wider developments, a product, almost wholly, of the
+nineteenth century, and is indeed, in the present day, still growing
+with great rapidity. The true method of discovery in symbolic logic,
+and probably also the best method for introducing the study to a
+learner acquainted with other parts of mathematics, is the analysis of
+actual examples of deductive reasoning, with a view to the discovery
+of the principles employed. These principles, for the most part, are
+so embedded in our ratiocinative instincts, that they are employed
+quite unconsciously, and can be dragged to light only by much patient
+effort. But when at last they have been found, they are seen to be few
+in number, and to be the sole source of everything in pure
+mathematics. The discovery that all mathematics follows inevitably
+from a small collection of fundamental laws is one which immeasurably
+enhances the intellectual beauty of the whole; to those who have been
+oppressed by the fragmentary and incomplete nature of most existing
+chains of deduction this discovery comes with all the overwhelming
+force of a revelation; like a palace emerging from the autumn mist as
+the traveller ascends an Italian hill-side, the stately storeys of the
+mathematical edifice appear in their due order and proportion, with a
+new perfection in every part.
+
+Until symbolic logic had acquired its present development, the
+principles upon which mathematics depends were always supposed to be
+philosophical, and discoverable only by the uncertain, unprogressive
+methods hitherto employed by philosophers. So long as this was
+thought, mathematics seemed to be not autonomous, but dependent upon a
+study which had quite other methods than its own. Moreover, since the
+nature of the postulates from which arithmetic, analysis, and geometry
+are to be deduced was wrapped in all the traditional obscurities of
+metaphysical discussion, the edifice built upon such dubious
+foundations began to be viewed as no better than a castle in the air.
+In this respect, the discovery that the true principles are as much a
+part of mathematics as any of their consequences has very greatly
+increased the intellectual satisfaction to be obtained. This
+satisfaction ought not to be refused to learners capable of enjoying
+it, for it is of a kind to increase our respect for human powers and
+our knowledge of the beauties belonging to the abstract world.
+
+Philosophers have commonly held that the laws of logic, which underlie
+mathematics, are laws of thought, laws regulating the operations of
+our minds. By this opinion the true dignity of reason is very greatly
+lowered: it ceases to be an investigation into the very heart and
+immutable essence of all things actual and possible, becoming,
+instead, an inquiry into something more or less human and subject to
+our limitations. The contemplation of what is non-human, the discovery
+that our minds are capable of dealing with material not created by
+them, above all, the realisation that beauty belongs to the outer
+world as to the inner, are the chief means of overcoming the terrible
+sense of impotence, of weakness, of exile amid hostile powers, which
+is too apt to result from acknowledging the all-but omnipotence of
+alien forces. To reconcile us, by the exhibition of its awful beauty,
+to the reign of Fate--which is merely the literary personification of
+these forces--is the task of tragedy. But mathematics takes us still
+further from what is human, into the region of absolute necessity, to
+which not only the actual world, but every possible world, must
+conform; and even here it builds a habitation, or rather finds a
+habitation eternally standing, where our ideals are fully satisfied
+and our best hopes are not thwarted. It is only when we thoroughly
+understand the entire independence of ourselves, which belongs to this
+world that reason finds, that we can adequately realise the profound
+importance of its beauty.
+
+Not only is mathematics independent of us and our thoughts, but in
+another sense we and the whole universe of existing things are
+independent of mathematics. The apprehension of this purely ideal
+character is indispensable, if we are to understand rightly the place
+of mathematics as one among the arts. It was formerly supposed that
+pure reason could decide, in some respects, as to the nature of the
+actual world: geometry, at least, was thought to deal with the space
+in which we live. But we now know that pure mathematics can never
+pronounce upon questions of actual existence: the world of reason, in
+a sense, controls the world of fact, but it is not at any point
+creative of fact, and in the application of its results to the world
+in time and space, its certainty and precision are lost among
+approximations and working hypotheses. The objects considered by
+mathematicians have, in the past, been mainly of a kind suggested by
+phenomena; but from such restrictions the abstract imagination should
+be wholly free. A reciprocal liberty must thus be accorded: reason
+cannot dictate to the world of facts, but the facts cannot restrict
+reason's privilege of dealing with whatever objects its love of beauty
+may cause to seem worthy of consideration. Here, as elsewhere, we
+build up our own ideals out of the fragments to be found in the world;
+and in the end it is hard to say whether the result is a creation or a
+discovery.
+
+It is very desirable, in instruction, not merely to persuade the
+student of the accuracy of important theorems, but to persuade him in
+the way which itself has, of all possible ways, the most beauty. The
+true interest of a demonstration is not, as traditional modes of
+exposition suggest, concentrated wholly in the result; where this does
+occur, it must be viewed as a defect, to be remedied, if possible, by
+so generalising the steps of the proof that each becomes important in
+and for itself. An argument which serves only to prove a conclusion is
+like a story subordinated to some moral which it is meant to teach:
+for æsthetic perfection no part of the whole should be merely a means.
+A certain practical spirit, a desire for rapid progress, for conquest
+of new realms, is responsible for the undue emphasis upon results
+which prevails in mathematical instruction. The better way is to
+propose some theme for consideration--in geometry, a figure having
+important properties; in analysis, a function of which the study is
+illuminating, and so on. Whenever proofs depend upon some only of the
+marks by which we define the object to be studied, these marks should
+be isolated and investigated on their own account. For it is a defect,
+in an argument, to employ more premisses than the conclusion demands:
+what mathematicians call elegance results from employing only the
+essential principles in virtue of which the thesis is true. It is a
+merit in Euclid that he advances as far as he is able to go without
+employing the axiom of parallels--not, as is often said, because this
+axiom is inherently objectionable, but because, in mathematics, every
+new axiom diminishes the generality of the resulting theorems, and the
+greatest possible generality is before all things to be sought.
+
+Of the effects of mathematics outside its own sphere more has been
+written than on the subject of its own proper ideal. The effect upon
+philosophy has, in the past, been most notable, but most varied; in
+the seventeenth century, idealism and rationalism, in the eighteenth,
+materialism and sensationalism, seemed equally its offspring. Of the
+effect which it is likely to have in the future it would be very rash
+to say much; but in one respect a good result appears probable.
+Against that kind of scepticism which abandons the pursuit of ideals
+because the road is arduous and the goal not certainly attainable,
+mathematics, within its own sphere, is a complete answer. Too often it
+is said that there is no absolute truth, but only opinion and private
+judgment; that each of us is conditioned, in his view of the world, by
+his own peculiarities, his own taste and bias; that there is no
+external kingdom of truth to which, by patience and discipline, we may
+at last obtain admittance, but only truth for me, for you, for every
+separate person. By this habit of mind one of the chief ends of human
+effort is denied, and the supreme virtue of candour, of fearless
+acknowledgment of what is, disappears from our moral vision. Of such
+scepticism mathematics is a perpetual reproof; for its edifice of
+truths stands unshakable and inexpungable to all the weapons of
+doubting cynicism.
+
+The effects of mathematics upon practical life, though they should not
+be regarded as the motive of our studies, may be used to answer a
+doubt to which the solitary student must always be liable. In a world
+so full of evil and suffering, retirement into the cloister of
+contemplation, to the enjoyment of delights which, however noble, must
+always be for the few only, cannot but appear as a somewhat selfish
+refusal to share the burden imposed upon others by accidents in which
+justice plays no part. Have any of us the right, we ask, to withdraw
+from present evils, to leave our fellow-men unaided, while we live a
+life which, though arduous and austere, is yet plainly good in its own
+nature? When these questions arise, the true answer is, no doubt, that
+some must keep alive the sacred fire, some must preserve, in every
+generation, the haunting vision which shadows forth the goal of so
+much striving. But when, as must sometimes occur, this answer seems
+too cold, when we are almost maddened by the spectacle of sorrows to
+which we bring no help, then we may reflect that indirectly the
+mathematician often does more for human happiness than any of his more
+practically active contemporaries. The history of science abundantly
+proves that a body of abstract propositions--even if, as in the case
+of conic sections, it remains two thousand years without effect upon
+daily life--may yet, at any moment, be used to cause a revolution in
+the habitual thoughts and occupations of every citizen. The use of
+steam and electricity--to take striking instances--is rendered
+possible only by mathematics. In the results of abstract thought the
+world possesses a capital of which the employment in enriching the
+common round has no hitherto discoverable limits. Nor does experience
+give any means of deciding what parts of mathematics will be found
+useful. Utility, therefore, can be only a consolation in moments of
+discouragement, not a guide in directing our studies.
+
+For the health of the moral life, for ennobling the tone of an age or
+a nation, the austerer virtues have a strange power, exceeding the
+power of those not informed and purified by thought. Of these austerer
+virtues the love of truth is the chief, and in mathematics, more than
+elsewhere, the love of truth may find encouragement for waning faith.
+Every great study is not only an end in itself, but also a means of
+creating and sustaining a lofty habit of mind; and this purpose should
+be kept always in view throughout the teaching and learning of
+mathematics.
+
+FOOTNOTES:
+
+[10] This passage was pointed out to me by Professor Gilbert Murray.
+
+
+
+
+V
+
+MATHEMATICS AND THE METAPHYSICIANS
+
+
+The nineteenth century, which prided itself upon the invention of
+steam and evolution, might have derived a more legitimate title to
+fame from the discovery of pure mathematics. This science, like most
+others, was baptised long before it was born; and thus we find writers
+before the nineteenth century alluding to what they called pure
+mathematics. But if they had been asked what this subject was, they
+would only have been able to say that it consisted of Arithmetic,
+Algebra, Geometry, and so on. As to what these studies had in common,
+and as to what distinguished them from applied mathematics, our
+ancestors were completely in the dark.
+
+Pure mathematics was discovered by Boole, in a work which he called
+the _Laws of Thought_ (1854). This work abounds in asseverations that
+it is not mathematical, the fact being that Boole was too modest to
+suppose his book the first ever written on mathematics. He was also
+mistaken in supposing that he was dealing with the laws of thought:
+the question how people actually think was quite irrelevant to him,
+and if his book had really contained the laws of thought, it was
+curious that no one should ever have thought in such a way before. His
+book was in fact concerned with formal logic, and this is the same
+thing as mathematics.
+
+Pure mathematics consists entirely of assertions to the effect that,
+if such and such a proposition is true of _anything_, then such and
+such another proposition is true of that thing. It is essential not to
+discuss whether the first proposition is really true, and not to
+mention what the anything is, of which it is supposed to be true. Both
+these points would belong to applied mathematics. We start, in pure
+mathematics, from certain rules of inference, by which we can infer
+that _if_ one proposition is true, then so is some other proposition.
+These rules of inference constitute the major part of the principles
+of formal logic. We then take any hypothesis that seems amusing, and
+deduce its consequences. _If_ our hypothesis is about _anything_, and
+not about some one or more particular things, then our deductions
+constitute mathematics. Thus mathematics may be defined as the subject
+in which we never know what we are talking about, nor whether what we
+are saying is true. People who have been puzzled by the beginnings of
+mathematics will, I hope, find comfort in this definition, and will
+probably agree that it is accurate.
+
+As one of the chief triumphs of modern mathematics consists in having
+discovered what mathematics really is, a few more words on this
+subject may not be amiss. It is common to start any branch of
+mathematics--for instance, Geometry--with a certain number of
+primitive ideas, supposed incapable of definition, and a certain
+number of primitive propositions or axioms, supposed incapable of
+proof. Now the fact is that, though there are indefinables and
+indemonstrables in every branch of applied mathematics, there are none
+in pure mathematics except such as belong to general logic. Logic,
+broadly speaking, is distinguished by the fact that its propositions
+can be put into a form in which they apply to anything whatever. All
+pure mathematics--Arithmetic, Analysis, and Geometry--is built up by
+combinations of the primitive ideas of logic, and its propositions are
+deduced from the general axioms of logic, such as the syllogism and
+the other rules of inference. And this is no longer a dream or an
+aspiration. On the contrary, over the greater and more difficult part
+of the domain of mathematics, it has been already accomplished; in the
+few remaining cases, there is no special difficulty, and it is now
+being rapidly achieved. Philosophers have disputed for ages whether
+such deduction was possible; mathematicians have sat down and made the
+deduction. For the philosophers there is now nothing left but graceful
+acknowledgments.
+
+The subject of formal logic, which has thus at last shown itself to be
+identical with mathematics, was, as every one knows, invented by
+Aristotle, and formed the chief study (other than theology) of the
+Middle Ages. But Aristotle never got beyond the syllogism, which is a
+very small part of the subject, and the schoolmen never got beyond
+Aristotle. If any proof were required of our superiority to the
+mediæval doctors, it might be found in this. Throughout the Middle
+Ages, almost all the best intellects devoted themselves to formal
+logic, whereas in the nineteenth century only an infinitesimal
+proportion of the world's thought went into this subject.
+Nevertheless, in each decade since 1850 more has been done to advance
+the subject than in the whole period from Aristotle to Leibniz. People
+have discovered how to make reasoning symbolic, as it is in Algebra,
+so that deductions are effected by mathematical rules. They have
+discovered many rules besides the syllogism, and a new branch of
+logic, called the Logic of Relatives,[11] has been invented to deal
+with topics that wholly surpassed the powers of the old logic, though
+they form the chief contents of mathematics.
+
+It is not easy for the lay mind to realise the importance of symbolism
+in discussing the foundations of mathematics, and the explanation may
+perhaps seem strangely paradoxical. The fact is that symbolism is
+useful because it makes things difficult. (This is not true of the
+advanced parts of mathematics, but only of the beginnings.) What we
+wish to know is, what can be deduced from what. Now, in the
+beginnings, everything is self-evident; and it is very hard to see
+whether one self-evident proposition follows from another or not.
+Obviousness is always the enemy to correctness. Hence we invent some
+new and difficult symbolism, in which nothing seems obvious. Then we
+set up certain rules for operating on the symbols, and the whole thing
+becomes mechanical. In this way we find out what must be taken as
+premiss and what can be demonstrated or defined. For instance, the
+whole of Arithmetic and Algebra has been shown to require three
+indefinable notions and five indemonstrable propositions. But without
+a symbolism it would have been very hard to find this out. It is so
+obvious that two and two are four, that we can hardly make ourselves
+sufficiently sceptical to doubt whether it can be proved. And the same
+holds in other cases where self-evident things are to be proved.
+
+But the proof of self-evident propositions may seem, to the
+uninitiated, a somewhat frivolous occupation. To this we might reply
+that it is often by no means self-evident that one obvious proposition
+follows from another obvious proposition; so that we are really
+discovering new truths when we prove what is evident by a method which
+is not evident. But a more interesting retort is, that since people
+have tried to prove obvious propositions, they have found that many of
+them are false. Self-evidence is often a mere will-o'-the-wisp, which
+is sure to lead us astray if we take it as our guide. For instance,
+nothing is plainer than that a whole always has more terms than a
+part, or that a number is increased by adding one to it. But these
+propositions are now known to be usually false. Most numbers are
+infinite, and if a number is infinite you may add ones to it as long
+as you like without disturbing it in the least. One of the merits of a
+proof is that it instils a certain doubt as to the result proved; and
+when what is obvious can be proved in some cases, but not in others,
+it becomes possible to suppose that in these other cases it is false.
+
+The great master of the art of formal reasoning, among the men of our
+own day, is an Italian, Professor Peano, of the University of
+Turin.[12] He has reduced the greater part of mathematics (and he or
+his followers will, in time, have reduced the whole) to strict
+symbolic form, in which there are no words at all. In the ordinary
+mathematical books, there are no doubt fewer words than most readers
+would wish. Still, little phrases occur, such as _therefore, let us
+assume, consider_, or _hence it follows_. All these, however, are a
+concession, and are swept away by Professor Peano. For instance, if we
+wish to learn the whole of Arithmetic, Algebra, the Calculus, and
+indeed all that is usually called pure mathematics (except Geometry),
+we must start with a dictionary of three words. One symbol stands for
+_zero_, another for _number_, and a third for _next after_. What these
+ideas mean, it is necessary to know if you wish to become an
+arithmetician. But after symbols have been invented for these three
+ideas, not another word is required in the whole development. All
+future symbols are symbolically explained by means of these three.
+Even these three can be explained by means of the notions of
+_relation_ and _class_; but this requires the Logic of Relations,
+which Professor Peano has never taken up. It must be admitted that
+what a mathematician has to know to begin with is not much. There are
+at most a dozen notions out of which all the notions in all pure
+mathematics (including Geometry) are compounded. Professor Peano, who
+is assisted by a very able school of young Italian disciples, has
+shown how this may be done; and although the method which he has
+invented is capable of being carried a good deal further than he has
+carried it, the honour of the pioneer must belong to him.
+
+Two hundred years ago, Leibniz foresaw the science which Peano has
+perfected, and endeavoured to create it. He was prevented from
+succeeding by respect for the authority of Aristotle, whom he could
+not believe guilty of definite, formal fallacies; but the subject
+which he desired to create now exists, in spite of the patronising
+contempt with which his schemes have been treated by all superior
+persons. From this "Universal Characteristic," as he called it, he
+hoped for a solution of all problems, and an end to all disputes. "If
+controversies were to arise," he says, "there would be no more need of
+disputation between two philosophers than between two accountants. For
+it would suffice to take their pens in their hands, to sit down to
+their desks, and to say to each other (with a friend as witness, if
+they liked), 'Let us calculate.'" This optimism has now appeared to be
+somewhat excessive; there still are problems whose solution is
+doubtful, and disputes which calculation cannot decide. But over an
+enormous field of what was formerly controversial, Leibniz's dream has
+become sober fact. In the whole philosophy of mathematics, which used
+to be at least as full of doubt as any other part of philosophy, order
+and certainty have replaced the confusion and hesitation which
+formerly reigned. Philosophers, of course, have not yet discovered
+this fact, and continue to write on such subjects in the old way. But
+mathematicians, at least in Italy, have now the power of treating the
+principles of mathematics in an exact and masterly manner, by means of
+which the certainty of mathematics extends also to mathematical
+philosophy. Hence many of the topics which used to be placed among the
+great mysteries--for example, the natures of infinity, of continuity,
+of space, time and motion--are now no longer in any degree open to
+doubt or discussion. Those who wish to know the nature of these things
+need only read the works of such men as Peano or Georg Cantor; they
+will there find exact and indubitable expositions of all these quondam
+mysteries.
+
+In this capricious world, nothing is more capricious than posthumous
+fame. One of the most notable examples of posterity's lack of judgment
+is the Eleatic Zeno. This man, who may be regarded as the founder of
+the philosophy of infinity, appears in Plato's Parmenides in the
+privileged position of instructor to Socrates. He invented four
+arguments, all immeasurably subtle and profound, to prove that motion
+is impossible, that Achilles can never overtake the tortoise, and that
+an arrow in flight is really at rest. After being refuted by
+Aristotle, and by every subsequent philosopher from that day to our
+own, these arguments were reinstated, and made the basis of a
+mathematical renaissance, by a German professor, who probably never
+dreamed of any connection between himself and Zeno. Weierstrass,[13]
+by strictly banishing from mathematics the use of infinitesimals, has
+at last shown that we live in an unchanging world, and that the arrow
+in its flight is truly at rest. Zeno's only error lay in inferring (if
+he did infer) that, because there is no such thing as a state of
+change, therefore the world is in the same state at any one time as at
+any other. This is a consequence which by no means follows; and in
+this respect, the German mathematician is more constructive than the
+ingenious Greek. Weierstrass has been able, by embodying his views in
+mathematics, where familiarity with truth eliminates the vulgar
+prejudices of common sense, to invest Zeno's paradoxes with the
+respectable air of platitudes; and if the result is less delightful to
+the lover of reason than Zeno's bold defiance, it is at any rate more
+calculated to appease the mass of academic mankind.
+
+Zeno was concerned, as a matter of fact, with three problems, each
+presented by motion, but each more abstract than motion, and capable
+of a purely arithmetical treatment. These are the problems of the
+infinitesimal, the infinite, and continuity. To state clearly the
+difficulties involved, was to accomplish perhaps the hardest part of
+the philosopher's task. This was done by Zeno. From him to our own
+day, the finest intellects of each generation in turn attacked the
+problems, but achieved, broadly speaking, nothing. In our own time,
+however, three men--Weierstrass, Dedekind, and Cantor--have not merely
+advanced the three problems, but have completely solved them. The
+solutions, for those acquainted with mathematics, are so clear as to
+leave no longer the slightest doubt or difficulty. This achievement is
+probably the greatest of which our age has to boast; and I know of no
+age (except perhaps the golden age of Greece) which has a more
+convincing proof to offer of the transcendent genius of its great men.
+Of the three problems, that of the infinitesimal was solved by
+Weierstrass; the solution of the other two was begun by Dedekind, and
+definitively accomplished by Cantor.
+
+The infinitesimal played formerly a great part in mathematics. It was
+introduced by the Greeks, who regarded a circle as differing
+infinitesimally from a polygon with a very large number of very small
+equal sides. It gradually grew in importance, until, when Leibniz
+invented the Infinitesimal Calculus, it seemed to become the
+fundamental notion of all higher mathematics. Carlyle tells, in his
+_Frederick the Great_, how Leibniz used to discourse to Queen Sophia
+Charlotte of Prussia concerning the infinitely little, and how she
+would reply that on that subject she needed no instruction--the
+behaviour of courtiers had made her thoroughly familiar with it. But
+philosophers and mathematicians--who for the most part had less
+acquaintance with courts--continued to discuss this topic, though
+without making any advance. The Calculus required continuity, and
+continuity was supposed to require the infinitely little; but nobody
+could discover what the infinitely little might be. It was plainly not
+quite zero, because a sufficiently large number of infinitesimals,
+added together, were seen to make up a finite whole. But nobody could
+point out any fraction which was not zero, and yet not finite. Thus
+there was a deadlock. But at last Weierstrass discovered that the
+infinitesimal was not needed at all, and that everything could be
+accomplished without it. Thus there was no longer any need to suppose
+that there was such a thing. Nowadays, therefore, mathematicians are
+more dignified than Leibniz: instead of talking about the infinitely
+small, they talk about the infinitely great--a subject which, however
+appropriate to monarchs, seems, unfortunately, to interest them even
+less than the infinitely little interested the monarchs to whom
+Leibniz discoursed.
+
+The banishment of the infinitesimal has all sorts of odd consequences,
+to which one has to become gradually accustomed. For example, there is
+no such thing as the next moment. The interval between one moment and
+the next would have to be infinitesimal, since, if we take two moments
+with a finite interval between them, there are always other moments in
+the interval. Thus if there are to be no infinitesimals, no two
+moments are quite consecutive, but there are always other moments
+between any two. Hence there must be an infinite number of moments
+between any two; because if there were a finite number one would be
+nearest the first of the two moments, and therefore next to it. This
+might be thought to be a difficulty; but, as a matter of fact, it is
+here that the philosophy of the infinite comes in, and makes all
+straight.
+
+The same sort of thing happens in space. If any piece of matter be cut
+in two, and then each part be halved, and so on, the bits will become
+smaller and smaller, and can theoretically be made as small as we
+please. However small they may be, they can still be cut up and made
+smaller still. But they will always have _some_ finite size, however
+small they may be. We never reach the infinitesimal in this way, and
+no finite number of divisions will bring us to points. Nevertheless
+there _are_ points, only these are not to be reached by successive
+divisions. Here again, the philosophy of the infinite shows us how
+this is possible, and why points are not infinitesimal lengths.
+
+As regards motion and change, we get similarly curious results. People
+used to think that when a thing changes, it must be in a state of
+change, and that when a thing moves, it is in a state of motion. This
+is now known to be a mistake. When a body moves, all that can be said
+is that it is in one place at one time and in another at another. We
+must not say that it will be in a neighbouring place at the next
+instant, since there is no next instant. Philosophers often tell us
+that when a body is in motion, it changes its position within the
+instant. To this view Zeno long ago made the fatal retort that every
+body always is where it is; but a retort so simple and brief was not
+of the kind to which philosophers are accustomed to give weight, and
+they have continued down to our own day to repeat the same phrases
+which roused the Eleatic's destructive ardour. It was only recently
+that it became possible to explain motion in detail in accordance with
+Zeno's platitude, and in opposition to the philosopher's paradox. We
+may now at last indulge the comfortable belief that a body in motion
+is just as truly where it is as a body at rest. Motion consists merely
+in the fact that bodies are sometimes in one place and sometimes in
+another, and that they are at intermediate places at intermediate
+times. Only those who have waded through the quagmire of philosophic
+speculation on this subject can realise what a liberation from antique
+prejudices is involved in this simple and straightforward commonplace.
+
+The philosophy of the infinitesimal, as we have just seen, is mainly
+negative. People used to believe in it, and now they have found out
+their mistake. The philosophy of the infinite, on the other hand, is
+wholly positive. It was formerly supposed that infinite numbers, and
+the mathematical infinite generally, were self-contradictory. But as
+it was obvious that there were infinities--for example, the number of
+numbers--the contradictions of infinity seemed unavoidable, and
+philosophy seemed to have wandered into a "cul-de-sac." This
+difficulty led to Kant's antinomies, and hence, more or less
+indirectly, to much of Hegel's dialectic method. Almost all current
+philosophy is upset by the fact (of which very few philosophers are as
+yet aware) that all the ancient and respectable contradictions in the
+notion of the infinite have been once for all disposed of. The method
+by which this has been done is most interesting and instructive. In
+the first place, though people had talked glibly about infinity ever
+since the beginnings of Greek thought, nobody had ever thought of
+asking, What is infinity? If any philosopher had been asked for a
+definition of infinity, he might have produced some unintelligible
+rigmarole, but he would certainly not have been able to give a
+definition that had any meaning at all. Twenty years ago, roughly
+speaking, Dedekind and Cantor asked this question, and, what is more
+remarkable, they answered it. They found, that is to say, a perfectly
+precise definition of an infinite number or an infinite collection of
+things. This was the first and perhaps the greatest step. It then
+remained to examine the supposed contradictions in this notion. Here
+Cantor proceeded in the only proper way. He took pairs of
+contradictory propositions, in which both sides of the contradiction
+would be usually regarded as demonstrable, and he strictly examined
+the supposed proofs. He found that all proofs adverse to infinity
+involved a certain principle, at first sight obviously true, but
+destructive, in its consequences, of almost all mathematics. The
+proofs favourable to infinity, on the other hand, involved no
+principle that had evil consequences. It thus appeared that common
+sense had allowed itself to be taken in by a specious maxim, and that,
+when once this maxim was rejected, all went well.
+
+The maxim in question is, that if one collection is part of another,
+the one which is a part has fewer terms than the one of which it is a
+part. This maxim is true of finite numbers. For example, Englishmen
+are only some among Europeans, and there are fewer Englishmen than
+Europeans. But when we come to infinite numbers, this is no longer
+true. This breakdown of the maxim gives us the precise definition of
+infinity. A collection of terms is infinite when it contains as parts
+other collections which have just as many terms as it has. If you can
+take away some of the terms of a collection, without diminishing the
+number of terms, then there are an infinite number of terms in the
+collection. For example, there are just as many even numbers as there
+are numbers altogether, since every number can be doubled. This may be
+seen by putting odd and even numbers together in one row, and even
+numbers alone in a row below:--
+
+          1, 2, 3, 4, 5, _ad infinitum_.
+          2, 4, 6, 8, 10, _ad infinitum_.
+
+There are obviously just as many numbers in the row below as in the
+row above, because there is one below for each one above. This
+property, which was formerly thought to be a contradiction, is now
+transformed into a harmless definition of infinity, and shows, in the
+above case, that the number of finite numbers is infinite.
+
+But the uninitiated may wonder how it is possible to deal with a
+number which cannot be counted. It is impossible to count up _all_ the
+numbers, one by one, because, however many we may count, there are
+always more to follow. The fact is that counting is a very vulgar and
+elementary way of finding out how many terms there are in a
+collection. And in any case, counting gives us what mathematicians
+call the _ordinal_ number of our terms; that is to say, it arranges
+our terms in an order or series, and its result tells us what type of
+series results from this arrangement. In other words, it is impossible
+to count things without counting some first and others afterwards, so
+that counting always has to do with order. Now when there are only a
+finite number of terms, we can count them in any order we like; but
+when there are an infinite number, what corresponds to counting will
+give us quite different results according to the way in which we carry
+out the operation. Thus the ordinal number, which results from what,
+in a general sense may be called counting, depends not only upon how
+many terms we have, but also (where the number of terms is infinite)
+upon the way in which the terms are arranged.
+
+The fundamental infinite numbers are not ordinal, but are what is
+called _cardinal_. They are not obtained by putting our terms in order
+and counting them, but by a different method, which tells us, to begin
+with, whether two collections have the same number of terms, or, if
+not, which is the greater.[14] It does not tell us, in the way in
+which counting does, _what_ number of terms a collection has; but if
+we define a number as the number of terms in such and such a
+collection, then this method enables us to discover whether some other
+collection that may be mentioned has more or fewer terms. An
+illustration will show how this is done. If there existed some country
+in which, for one reason or another, it was impossible to take a
+census, but in which it was known that every man had a wife and every
+woman a husband, then (provided polygamy was not a national
+institution) we should know, without counting, that there were exactly
+as many men as there were women in that country, neither more nor
+less. This method can be applied generally. If there is some relation
+which, like marriage, connects the things in one collection each with
+one of the things in another collection, and vice versa, then the two
+collections have the same number of terms. This was the way in which
+we found that there are as many even numbers as there are numbers.
+Every number can be doubled, and every even number can be halved, and
+each process gives just one number corresponding to the one that is
+doubled or halved. And in this way we can find any number of
+collections each of which has just as many terms as there are finite
+numbers. If every term of a collection can be hooked on to a number,
+and all the finite numbers are used once, and only once, in the
+process, then our collection must have just as many terms as there are
+finite numbers. This is the general method by which the numbers of
+infinite collections are defined.
+
+But it must not be supposed that all infinite numbers are equal. On
+the contrary, there are infinitely more infinite numbers than finite
+ones. There are more ways of arranging the finite numbers in different
+types of series than there are finite numbers. There are probably more
+points in space and more moments in time than there are finite
+numbers. There are exactly as many fractions as whole numbers,
+although there are an infinite number of fractions between any two
+whole numbers. But there are more irrational numbers than there are
+whole numbers or fractions. There are probably exactly as many points
+in space as there are irrational numbers, and exactly as many points
+on a line a millionth of an inch long as in the whole of infinite
+space. There is a greatest of all infinite numbers, which is the
+number of things altogether, of every sort and kind. It is obvious
+that there cannot be a greater number than this, because, if
+everything has been taken, there is nothing left to add. Cantor has a
+proof that there is no greatest number, and if this proof were valid,
+the contradictions of infinity would reappear in a sublimated form.
+But in this one point, the master has been guilty of a very subtle
+fallacy, which I hope to explain in some future work.[15]
+
+We can now understand why Zeno believed that Achilles cannot overtake
+the tortoise and why as a matter of fact he can overtake it. We shall
+see that all the people who disagreed with Zeno had no right to do so,
+because they all accepted premises from which his conclusion followed.
+The argument is this: Let Achilles and the tortoise start along a road
+at the same time, the tortoise (as is only fair) being allowed a
+handicap. Let Achilles go twice as fast as the tortoise, or ten times
+or a hundred times as fast. Then he will never reach the tortoise. For
+at every moment the tortoise is somewhere and Achilles is somewhere;
+and neither is ever twice in the same place while the race is going
+on. Thus the tortoise goes to just as many places as Achilles does,
+because each is in one place at one moment, and in another at any
+other moment. But if Achilles were to catch up with the tortoise, the
+places where the tortoise would have been would be only part of the
+places where Achilles would have been. Here, we must suppose, Zeno
+appealed to the maxim that the whole has more terms than the part.[16]
+Thus if Achilles were to overtake the tortoise, he would have been in
+more places than the tortoise; but we saw that he must, in any period,
+be in exactly as many places as the tortoise. Hence we infer that he
+can never catch the tortoise. This argument is strictly correct, if we
+allow the axiom that the whole has more terms than the part. As the
+conclusion is absurd, the axiom must be rejected, and then all goes
+well. But there is no good word to be said for the philosophers of the
+past two thousand years and more, who have all allowed the axiom and
+denied the conclusion.
+
+The retention of this axiom leads to absolute contradictions, while
+its rejection leads only to oddities. Some of these oddities, it must
+be confessed, are very odd. One of them, which I call the paradox of
+Tristram Shandy, is the converse of the Achilles, and shows that the
+tortoise, if you give him time, will go just as far as Achilles.
+Tristram Shandy, as we know, employed two years in chronicling the
+first two days of his life, and lamented that, at this rate, material
+would accumulate faster than he could deal with it, so that, as years
+went by, he would be farther and farther from the end of his history.
+Now I maintain that, if he had lived for ever, and had not wearied of
+his task, then, even if his life had continued as event fully as it
+began, no part of his biography would have remained unwritten. For
+consider: the hundredth day will be described in the hundredth year,
+the thousandth in the thousandth year, and so on. Whatever day we may
+choose as so far on that he cannot hope to reach it, that day will be
+described in the corresponding year. Thus any day that may be
+mentioned will be written up sooner or later, and therefore no part of
+the biography will remain permanently unwritten. This paradoxical but
+perfectly true proposition depends upon the fact that the number of
+days in all time is no greater than the number of years.
+
+Thus on the subject of infinity it is impossible to avoid conclusions
+which at first sight appear paradoxical, and this is the reason why so
+many philosophers have supposed that there were inherent
+contradictions in the infinite. But a little practice enables one to
+grasp the true principles of Cantor's doctrine, and to acquire new and
+better instincts as to the true and the false. The oddities then
+become no odder than the people at the antipodes, who used to be
+thought impossible because they would find it so inconvenient to stand
+on their heads.
+
+The solution of the problems concerning infinity has enabled Cantor to
+solve also the problems of continuity. Of this, as of infinity, he has
+given a perfectly precise definition, and has shown that there are no
+contradictions in the notion so defined. But this subject is so
+technical that it is impossible to give any account of it here.
+
+The notion of continuity depends upon that of _order_, since
+continuity is merely a particular type of order. Mathematics has, in
+modern times, brought order into greater and greater prominence. In
+former days, it was supposed (and philosophers are still apt to
+suppose) that quantity was the fundamental notion of mathematics. But
+nowadays, quantity is banished altogether, except from one little
+corner of Geometry, while order more and more reigns supreme. The
+investigation of different kinds of series and their relations is now
+a very large part of mathematics, and it has been found that this
+investigation can be conducted without any reference to quantity, and,
+for the most part, without any reference to number. All types of
+series are capable of formal definition, and their properties can be
+deduced from the principles of symbolic logic by means of the Algebra
+of Relatives. The notion of a limit, which is fundamental in the
+greater part of higher mathematics, used to be defined by means of
+quantity, as a term to which the terms of some series approximate as
+nearly as we please. But nowadays the limit is defined quite
+differently, and the series which it limits may not approximate to it
+at all. This improvement also is due to Cantor, and it is one which
+has revolutionised mathematics. Only order is now relevant to limits.
+Thus, for instance, the smallest of the infinite integers is the limit
+of the finite integers, though all finite integers are at an infinite
+distance from it. The study of different types of series is a general
+subject of which the study of ordinal numbers (mentioned above) is a
+special and very interesting branch. But the unavoidable
+technicalities of this subject render it impossible to explain to any
+but professed mathematicians.
+
+Geometry, like Arithmetic, has been subsumed, in recent times, under
+the general study of order. It was formerly supposed that Geometry was
+the study of the nature of the space in which we live, and accordingly
+it was urged, by those who held that what exists can only be known
+empirically, that Geometry should really be regarded as belonging to
+applied mathematics. But it has gradually appeared, by the increase of
+non-Euclidean systems, that Geometry throws no more light upon the
+nature of space than Arithmetic throws upon the population of the
+United States. Geometry is a whole collection of deductive sciences
+based on a corresponding collection of sets of axioms. One set of
+axioms is Euclid's; other equally good sets of axioms lead to other
+results. Whether Euclid's axioms are true, is a question as to which
+the pure mathematician is indifferent; and, what is more, it is a
+question which it is theoretically impossible to answer with certainty
+in the affirmative. It might possibly be shown, by very careful
+measurements, that Euclid's axioms are false; but no measurements
+could ever assure us (owing to the errors of observation) that they
+are exactly true. Thus the geometer leaves to the man of science to
+decide, as best he may, what axioms are most nearly true in the actual
+world. The geometer takes any set of axioms that seem interesting, and
+deduces their consequences. What defines Geometry, in this sense, is
+that the axioms must give rise to a series of more than one dimension.
+And it is thus that Geometry becomes a department in the study of
+order.
+
+In Geometry, as in other parts of mathematics, Peano and his disciples
+have done work of the very greatest merit as regards principles.
+Formerly, it was held by philosophers and mathematicians alike that
+the proofs in Geometry depended on the figure; nowadays, this is known
+to be false. In the best books there are no figures at all. The
+reasoning proceeds by the strict rules of formal logic from a set of
+axioms laid down to begin with. If a figure is used, all sorts of
+things seem obviously to follow, which no formal reasoning can prove
+from the explicit axioms, and which, as a matter of fact, are only
+accepted because they are obvious. By banishing the figure, it becomes
+possible to discover _all_ the axioms that are needed; and in this way
+all sorts of possibilities, which would have otherwise remained
+undetected, are brought to light.
+
+One great advance, from the point of view of correctness, has been
+made by introducing points as they are required, and not starting, as
+was formerly done, by assuming the whole of space. This method is due
+partly to Peano, partly to another Italian named Fano. To those
+unaccustomed to it, it has an air of somewhat wilful pedantry. In this
+way, we begin with the following axioms: (1) There is a class of
+entities called _points_. (2) There is at least one point. (3) If _a_
+be a point, there is at least one other point besides _a_. Then we
+bring in the straight line joining two points, and begin again with
+(4), namely, on the straight line joining _a_ and _b_, there is at
+least one other point besides _a_ and _b_. (5) There is at least one
+point not on the line _ab_. And so we go on, till we have the means of
+obtaining as many points as we require. But the word _space_, as Peano
+humorously remarks, is one for which Geometry has no use at all.
+
+The rigid methods employed by modern geometers have deposed Euclid
+from his pinnacle of correctness. It was thought, until recent times,
+that, as Sir Henry Savile remarked in 1621, there were only two
+blemishes in Euclid, the theory of parallels and the theory of
+proportion. It is now known that these are almost the only points in
+which Euclid is free from blemish. Countless errors are involved in
+his first eight propositions. That is to say, not only is it doubtful
+whether his axioms are true, which is a comparatively trivial matter,
+but it is certain that his propositions do not follow from the axioms
+which he enunciates. A vastly greater number of axioms, which Euclid
+unconsciously employs, are required for the proof of his propositions.
+Even in the first proposition of all, where he constructs an
+equilateral triangle on a given base, he uses two circles which are
+assumed to intersect. But no explicit axiom assures us that they do
+so, and in some kinds of spaces they do not always intersect. It is
+quite doubtful whether our space belongs to one of these kinds or not.
+Thus Euclid fails entirely to prove his point in the very first
+proposition. As he is certainly not an easy author, and is terribly
+long-winded, he has no longer any but an historical interest. Under
+these circumstances, it is nothing less than a scandal that he should
+still be taught to boys in England.[17] A book should have either
+intelligibility or correctness; to combine the two is impossible, but
+to lack both is to be unworthy of such a place as Euclid has occupied
+in education.
+
+The most remarkable result of modern methods in mathematics is the
+importance of symbolic logic and of rigid formalism. Mathematicians,
+under the influence of Weierstrass, have shown in modern times a care
+for accuracy, and an aversion to slipshod reasoning, such as had not
+been known among them previously since the time of the Greeks. The
+great inventions of the seventeenth century--Analytical Geometry and
+the Infinitesimal Calculus--were so fruitful in new results that
+mathematicians had neither time nor inclination to examine their
+foundations. Philosophers, who should have taken up the task, had too
+little mathematical ability to invent the new branches of mathematics
+which have now been found necessary for any adequate discussion. Thus
+mathematicians were only awakened from their "dogmatic slumbers" when
+Weierstrass and his followers showed that many of their most cherished
+propositions are in general false. Macaulay, contrasting the certainty
+of mathematics with the uncertainty of philosophy, asks who ever heard
+of a reaction against Taylor's theorem? If he had lived now, he
+himself might have heard of such a reaction, for this is precisely one
+of the theorems which modern investigations have overthrown. Such rude
+shocks to mathematical faith have produced that love of formalism
+which appears, to those who are ignorant of its motive, to be mere
+outrageous pedantry.
+
+The proof that all pure mathematics, including Geometry, is nothing
+but formal logic, is a fatal blow to the Kantian philosophy. Kant,
+rightly perceiving that Euclid's propositions could not be deduced
+from Euclid's axioms without the help of the figures, invented a
+theory of knowledge to account for this fact; and it accounted so
+successfully that, when the fact is shown to be a mere defect in
+Euclid, and not a result of the nature of geometrical reasoning,
+Kant's theory also has to be abandoned. The whole doctrine of _a
+priori_ intuitions, by which Kant explained the possibility of pure
+mathematics, is wholly inapplicable to mathematics in its present
+form. The Aristotelian doctrines of the schoolmen come nearer in
+spirit to the doctrines which modern mathematics inspire; but the
+schoolmen were hampered by the fact that their formal logic was very
+defective, and that the philosophical logic based upon the syllogism
+showed a corresponding narrowness. What is now required is to give the
+greatest possible development to mathematical logic, to allow to the
+full the importance of relations, and then to found upon this secure
+basis a new philosophical logic, which may hope to borrow some of the
+exactitude and certainty of its mathematical foundation. If this can
+be successfully accomplished, there is every reason to hope that the
+near future will be as great an epoch in pure philosophy as the
+immediate past has been in the principles of mathematics. Great
+triumphs inspire great hopes; and pure thought may achieve, within our
+generation, such results as will place our time, in this respect, on a
+level with the greatest age of Greece.[18]
+
+FOOTNOTES:
+
+[11] This subject is due in the main to Mr. C.S. Peirce.
+
+[12] I ought to have added Frege, but his writings were unknown to me
+when this article was written. [Note added in 1917.]
+
+[13] Professor of Mathematics in the University of Berlin. He died in
+1897.
+
+[14] [Note added in 1917.] Although some infinite numbers are greater
+than some others, it cannot be proved that of any two infinite numbers
+one must be the greater.
+
+[15] Cantor was not guilty of a fallacy on this point. His proof that
+there is no greatest number is valid. The solution of the puzzle is
+complicated and depends upon the theory of types, which is explained
+in _Principia Mathematica_, Vol. I (Camb. Univ. Press, 1910). [Note
+added in 1917.]
+
+[16] This must not be regarded as a historically correct account of
+what Zeno actually had in mind. It is a new argument for his
+conclusion, not the argument which influenced him. On this point, see
+e.g. C.D. Broad, "Note on Achilles and the Tortoise," _Mind_, N.S.,
+Vol. XXII, pp. 318-19. Much valuable work on the interpretation of
+Zeno has been done since this article was written. [Note added in
+1917.]
+
+[17] Since the above was written, he has ceased to be used as a
+textbook. But I fear many of the books now used are so bad that the
+change is no great improvement. [Note added in 1917.]
+
+[18] The greatest age of Greece was brought to an end by the
+Peloponnesian War. [Note added in 1917.]
+
+
+
+
+VI
+
+ON SCIENTIFIC METHOD IN PHILOSOPHY
+
+
+When we try to ascertain the motives which have led men to the
+investigation of philosophical questions, we find that, broadly
+speaking, they can be divided into two groups, often antagonistic, and
+leading to very divergent systems. These two groups of motives are, on
+the one hand, those derived from religion and ethics, and, on the
+other hand, those derived from science. Plato, Spinoza, and Hegel may
+be taken as typical of the philosophers whose interests are mainly
+religious and ethical, while Leibniz, Locke, and Hume may be taken as
+representatives of the scientific wing. In Aristotle, Descartes,
+Berkeley, and Kant we find both groups of motives strongly present.
+
+Herbert Spencer, in whose honour we are assembled to-day, would
+naturally be classed among scientific philosophers: it was mainly from
+science that he drew his data, his formulation of problems, and his
+conception of method. But his strong religious sense is obvious in
+much of his writing, and his ethical pre-occupations are what make him
+value the conception of evolution--that conception in which, as a
+whole generation has believed, science and morals are to be united in
+fruitful and indissoluble marriage.
+
+It is my belief that the ethical and religious motives in spite of
+the splendidly imaginative systems to which they have given rise, have
+been on the whole a hindrance to the progress of philosophy, and ought
+now to be consciously thrust aside by those who wish to discover
+philosophical truth. Science, originally, was entangled in similar
+motives, and was thereby hindered in its advances. It is, I maintain,
+from science, rather than from ethics and religion, that philosophy
+should draw its inspiration.
+
+But there are two different ways in which a philosophy may seek to
+base itself upon science. It may emphasise the most general _results_
+of science, and seek to give even greater generality and unity to
+these results. Or it may study the _methods_ of science, and seek to
+apply these methods, with the necessary adaptations, to its own
+peculiar province. Much philosophy inspired by science has gone astray
+through preoccupation with the _results_ momentarily supposed to have
+been achieved. It is not results, but _methods_ that can be
+transferred with profit from the sphere of the special sciences to the
+sphere of philosophy. What I wish to bring to your notice is the
+possibility and importance of applying to philosophical problems
+certain broad principles of method which have been found successful in
+the study of scientific questions.
+
+The opposition between a philosophy guided by scientific method and a
+philosophy dominated by religious and ethical ideas may be illustrated
+by two notions which are very prevalent in the works of philosophers,
+namely the notion of _the universe_, and the notion of _good and
+evil_. A philosopher is expected to tell us something about the nature
+of the universe as a whole, and to give grounds for either optimism or
+pessimism. Both these expectations seem to me mistaken. I believe the
+conception of "the universe" to be, as its etymology indicates, a
+mere relic of pre-Copernican astronomy: and I believe the question of
+optimism and pessimism to be one which the philosopher will regard as
+outside his scope, except, possibly, to the extent of maintaining that
+it is insoluble.
+
+In the days before Copernicus, the conception of the "universe" was
+defensible on scientific grounds: the diurnal revolution of the
+heavenly bodies bound them together as all parts of one system, of
+which the earth was the centre. Round this apparent scientific fact,
+many human desires rallied: the wish to believe Man important in the
+scheme of things, the theoretical desire for a comprehensive
+understanding of the Whole, the hope that the course of nature might
+be guided by some sympathy with our wishes. In this way, an ethically
+inspired system of metaphysics grew up, whose anthropocentrism was
+apparently warranted by the geocentrism of astronomy. When Copernicus
+swept away the astronomical basis of this system of thought, it had
+grown so familiar, and had associated itself so intimately with men's
+aspirations, that it survived with scarcely diminished force--survived
+even Kant's "Copernican revolution," and is still now the unconscious
+premiss of most metaphysical systems.
+
+The oneness of the world is an almost undiscussed postulate of most
+metaphysics. "Reality is not merely one and self-consistent, but is a
+system of reciprocally determinate parts"[19]--such a statement would
+pass almost unnoticed as a mere truism. Yet I believe that it embodies
+a failure to effect thoroughly the "Copernican revolution," and that
+the apparent oneness of the world is merely the oneness of what is
+seen by a single spectator or apprehended by a single mind. The
+Critical Philosophy, although it intended to emphasise the subjective
+element in many apparent characteristics of the world, yet, by
+regarding the world in itself as unknowable, so concentrated attention
+upon the subjective representation that its subjectivity was soon
+forgotten. Having recognised the categories as the work of the mind,
+it was paralysed by its own recognition, and abandoned in despair the
+attempt to undo the work of subjective falsification. In part, no
+doubt, its despair was well founded, but not, I think, in any absolute
+or ultimate sense. Still less was it a ground for rejoicing, or for
+supposing that the nescience to which it ought to have given rise
+could be legitimately exchanged for a metaphysical dogmatism.
+
+
+I
+
+As regards our present question, namely, the question of the unity of
+the world, the right method, as I think, has been indicated by William
+James.[20] "Let us now turn our backs upon ineffable or unintelligible
+ways of accounting for the world's oneness, and inquire whether,
+instead of being a principle, the 'oneness' affirmed may not merely be
+a name like 'substance' descriptive of the fact that certain _specific
+and verifiable connections_ are found among the parts of the
+experiential flux.... We can easily conceive of things that shall have
+no connection whatever with each other. We may assume them to inhabit
+different times and spaces, as the dreams of different persons do even
+now. They may be so unlike and incommensurable, and so inert towards
+one another, as never to jostle or interfere. Even now there may
+actually be whole universes so disparate from ours that we who know
+ours have no means of perceiving that they exist. We conceive their
+diversity, however; and by that fact the whole lot of them form what
+is known in logic as 'a universe of discourse.' To form a universe of
+discourse argues, as this example shows, no further kind of connexion.
+The importance attached by certain monistic writers to the fact that
+any chaos may become a universe by merely being named, is to me
+incomprehensible." We are thus left with two kinds of unity in the
+experienced world; the one what we may call the epistemological unity,
+due merely to the fact that my experienced world is what _one_
+experience selects from the sum total of existence: the other that
+tentative and partial unity exhibited in the prevalence of scientific
+laws in those portions of the world which science has hitherto
+mastered. Now a generalisation based upon either of these kinds of
+unity would be fallacious. That the things which we experience have
+the common property of being experienced by us is a truism from which
+obviously nothing of importance can be deducible: it is clearly
+fallacious to draw from the fact that whatever we experience is
+experienced the conclusion that therefore everything must be
+experienced. The generalisation of the second kind of unity, namely,
+that derived from scientific laws, would be equally fallacious, though
+the fallacy is a trifle less elementary. In order to explain it let us
+consider for a moment what is called the reign of law. People often
+speak as though it were a remarkable fact that the physical world is
+subject to invariable laws. In fact, however, it is not easy to see
+how such a world could fail to obey general laws. Taking any arbitrary
+set of points in space, there is a function of the time corresponding
+to these points, i.e. expressing the motion of a particle which
+traverses these points: this function may be regarded as a general law
+to which the behaviour of such a particle is subject. Taking all such
+functions for all the particles in the universe, there will be
+theoretically some one formula embracing them all, and this formula
+may be regarded as the single and supreme law of the spatio-temporal
+world. Thus what is surprising in physics is not the existence of
+general laws, but their extreme simplicity. It is not the uniformity
+of nature that should surprise us, for, by sufficient analytic
+ingenuity, any conceivable course of nature might be shown to exhibit
+uniformity. What should surprise us is the fact that the uniformity is
+simple enough for us to be able to discover it. But it is just this
+characteristic of simplicity in the laws of nature hitherto discovered
+which it would be fallacious to generalise, for it is obvious that
+simplicity has been a part cause of their discovery, and can,
+therefore, give no ground for the supposition that other undiscovered
+laws are equally simple.
+
+The fallacies to which these two kinds of unity have given rise
+suggest a caution as regards all use in philosophy of general
+_results_ that science is supposed to have achieved. In the first
+place, in generalising these results beyond past experience, it is
+necessary to examine very carefully whether there is not some reason
+making it more probable that these results should hold of all that has
+been experienced than that they should hold of things universally. The
+sum total of what is experienced by mankind is a selection from the
+sum total of what exists, and any general character exhibited by this
+selection may be due to the manner of selecting rather than to the
+general character of that from which experience selects. In the second
+place, the most general results of science are the least certain and
+the most liable to be upset by subsequent research. In utilizing these
+results as the basis of a philosophy, we sacrifice the most valuable
+and remarkable characteristic of scientific method, namely, that,
+although almost everything in science is found sooner or later to
+require some correction, yet this correction is almost always such as
+to leave untouched, or only slightly modified, the greater part of the
+results which have been deduced from the premiss subsequently
+discovered to be faulty. The prudent man of science acquires a certain
+instinct as to the kind of uses which may be made of present
+scientific beliefs without incurring the danger of complete and utter
+refutation from the modifications likely to be introduced by
+subsequent discoveries. Unfortunately the use of scientific
+generalisations of a sweeping kind as the basis of philosophy is just
+that kind of use which an instinct of scientific caution would avoid,
+since, as a rule, it would only lead to true results if the
+generalisation upon which it is based stood in _no_ need of
+correction.
+
+We may illustrate these general considerations by means of two
+examples, namely, the conservation of energy and the principle of
+evolution.
+
+(1) Let us begin with the conservation of energy, or, as Herbert
+Spencer used to call it, the persistence of force. He says:[21]
+
+  "Before taking a first step in the rational interpretation of
+  Evolution, it is needful to recognise, not only the facts that
+  Matter is indestructible and Motion continuous, but also the fact
+  that Force persists. An attempt to assign the _causes_ of
+  Evolution would manifestly be absurd if that agency to which the
+  metamorphosis in general and in detail is due, could either come
+  into existence or cease to exist. The succession of phenomena
+  would in such case be altogether arbitrary, and deductive Science
+  impossible."
+
+This paragraph illustrates the kind of way in which the philosopher is
+tempted to give an air of absoluteness and necessity to empirical
+generalisations, of which only the approximate truth in the regions
+hitherto investigated can be guaranteed by the unaided methods of
+science. It is very often said that the persistence of something or
+other is a necessary presupposition of all scientific investigation,
+and this presupposition is then thought to be exemplified in some
+quantity which physics declares to be constant. There are here, as it
+seems to me, three distinct errors. First, the detailed scientific
+investigation of nature does not _presuppose_ any such general laws as
+its results are found to verify. Apart from particular observations,
+science need presuppose nothing except the general principles of
+logic, and these principles are not laws of nature, for they are
+merely hypothetical, and apply not only to the actual world but to
+whatever is _possible_. The second error consists in the
+identification of a constant quantity with a persistent entity. Energy
+is a certain function of a physical system, but is not a thing or
+substance persisting throughout the changes of the system. The same is
+true of mass, in spite of the fact that mass has often been defined as
+_quantity of matter_. The whole conception of quantity, involving, as
+it does, numerical measurement based largely upon conventions, is far
+more artificial, far more an embodiment of mathematical convenience,
+than is commonly believed by those who philosophise on physics. Thus
+even if (which I cannot for a moment admit) the persistence of some
+entity were among the necessary postulates of science, it would be a
+sheer error to infer from this the constancy of any physical quantity,
+or the _a priori_ necessity of any such constancy which may be
+empirically discovered. In the third place, it has become more and
+more evident with the progress of physics that large generalisations,
+such as the conservation of energy or mass, are far from certain and
+are very likely only approximate. Mass, which used to be regarded as
+the most indubitable of physical quantities, is now generally believed
+to vary according to velocity, and to be, in fact, a vector quantity
+which at a given moment is different in different directions. The
+detailed conclusions deduced from the supposed constancy of mass for
+such motions as used to be studied in physics will remain very nearly
+exact, and therefore over the field of the older investigations very
+little modification of the older results is required. But as soon as
+such a principle as the conservation of mass or of energy is erected
+into a universal _a priori_ law, the slightest failure in absolute
+exactness is fatal, and the whole philosophic structure raised upon
+this foundation is necessarily ruined. The prudent philosopher,
+therefore, though he may with advantage study the methods of physics,
+will be very chary of basing anything upon what happen at the moment
+to be the most general results apparently obtained by those methods.
+
+(2) The philosophy of evolution, which was to be our second example,
+illustrates the same tendency to hasty generalisation, and also
+another sort, namely, the undue preoccupation with ethical notions.
+There are two kinds of evolutionist philosophy, of which both Hegel
+and Spencer represent the older and less radical kind, while
+Pragmatism and Bergson represent the more modern and revolutionary
+variety. But both these sorts of evolutionism have in common the
+emphasis on _progress_, that is, upon a continual change from the
+worse to the better, or from the simpler to the more complex. It
+would be unfair to attribute to Hegel any scientific motive or
+foundation, but all the other evolutionists, including Hegel's modern
+disciples, have derived their impetus very largely from the history of
+biological development. To a philosophy which derives a law of
+universal progress from this history there are two objections. First,
+that this history itself is concerned with a very small selection of
+facts confined to an infinitesimal fragment of space and time, and
+even on scientific grounds probably not an average sample of events in
+the world at large. For we know that decay as well as growth is a
+normal occurrence in the world. An extra-terrestrial philosopher, who
+had watched a single youth up to the age of twenty-one and had never
+come across any other human being, might conclude that it is the
+nature of human beings to grow continually taller and wiser in an
+indefinite progress towards perfection; and this generalisation would
+be just as well founded as the generalisation which evolutionists base
+upon the previous history of this planet. Apart, however, from this
+scientific objection to evolutionism, there is another, derived from
+the undue admixture of ethical notions in the very idea of progress
+from which evolutionism derives its charm. Organic life, we are told,
+has developed gradually from the protozoon to the philosopher, and
+this development, we are assured, is indubitably an advance.
+Unfortunately it is the philosopher, not the protozoon, who gives us
+this assurance, and we can have no security that the impartial
+outsider would agree with the philosopher's self-complacent
+assumption. This point has been illustrated by the philosopher Chuang
+TzÅ­ in the following instructive anecdote:
+
+  "The Grand Augur, in his ceremonial robes, approached the shambles
+  and thus addressed the pigs: 'How can you object to die? I shall
+  fatten you for three months. I shall discipline myself for ten
+  days and fast for three. I shall strew fine grass, and place you
+  bodily upon a carved sacrificial dish. Does not this satisfy you?'
+
+  Then, speaking from the pigs' point of view, he continued: 'It is
+  better, perhaps, after all, to live on bran and escape the
+  shambles....'
+
+  'But then,' added he, speaking from his own point of view, 'to
+  enjoy honour when alive one would readily die on a war-shield or
+  in the headsman's basket.'
+
+  So he rejected the pigs' point of view and adopted his own point
+  of view. In what sense, then, was he different from the pigs?"
+
+I much fear that the evolutionists too often resemble the Grand Augur
+and the pigs.
+
+The ethical element which has been prominent in many of the most
+famous systems of philosophy is, in my opinion, one of the most
+serious obstacles to the victory of scientific method in the
+investigation of philosophical questions. Human ethical notions, as
+Chuang TzÅ­ perceived, are essentially anthropocentric, and involve,
+when used in metaphysics, an attempt, however veiled, to legislate for
+the universe on the basis of the present desires of men. In this way
+they interfere with that receptivity to fact which is the essence of
+the scientific attitude towards the world. To regard ethical notions
+as a key to the understanding of the world is essentially
+pre-Copernican. It is to make man, with the hopes and ideals which he
+happens to have at the present moment, the centre of the universe and
+the interpreter of its supposed aims and purposes. Ethical metaphysics
+is fundamentally an attempt, however disguised, to give legislative
+force to our own wishes. This may, of course, be questioned, but I
+think that it is confirmed by a consideration of the way in which
+ethical notions arise. Ethics is essentially a product of the
+gregarious instinct, that is to say, of the instinct to co-operate
+with those who are to form our own group against those who belong to
+other groups. Those who belong to our own group are good; those who
+belong to hostile groups are wicked. The ends which are pursued by our
+own group are desirable ends, the ends pursued by hostile groups are
+nefarious. The subjectivity of this situation is not apparent to the
+gregarious animal, which feels that the general principles of justice
+are on the side of its own herd. When the animal has arrived at the
+dignity of the metaphysician, it invents ethics as the embodiment of
+its belief in the justice of its own herd. So the Grand Augur invokes
+ethics as the justification of Augurs in their conflicts with pigs.
+But, it may be said, this view of ethics takes no account of such
+truly ethical notions as that of self-sacrifice. This, however, would
+be a mistake. The success of gregarious animals in the struggle for
+existence depends upon co-operation within the herd, and co-operation
+requires sacrifice, to some extent, of what would otherwise be the
+interest of the individual. Hence arises a conflict of desires and
+instincts, since both self-preservation and the preservation of the
+herd are biological ends to the individual. Ethics is in origin the
+art of recommending to others the sacrifices required for co-operation
+with oneself. Hence, by reflexion, it comes, through the operation of
+social justice, to recommend sacrifices by oneself, but all ethics,
+however refined, remains more or less subjective. Even vegetarians do
+not hesitate, for example, to save the life of a man in a fever,
+although in doing so they destroy the lives of many millions of
+microbes. The view of the world taken by the philosophy derived from
+ethical notions is thus never impartial and therefore never fully
+scientific. As compared with science, it fails to achieve the
+imaginative liberation from self which is necessary to such
+understanding of the world as man can hope to achieve, and the
+philosophy which it inspires is always more or less parochial, more or
+less infected with the prejudices of a time and a place.
+
+I do not deny the importance or value, within its own sphere, of the
+kind of philosophy which is inspired by ethical notions. The ethical
+work of Spinoza, for example, appears to me of the very highest
+significance, but what is valuable in such work is not any
+metaphysical theory as to the nature of the world to which it may give
+rise, nor indeed anything which can be proved or disproved by
+argument. What is valuable is the indication of some new way of
+feeling towards life and the world, some way of feeling by which our
+own existence can acquire more of the characteristics which we must
+deeply desire. The value of such work, however immeasurable it is,
+belongs with practice and not with theory. Such theoretic importance
+as it may possess is only in relation to human nature, not in relation
+to the world at large. The scientific philosophy, therefore, which
+aims only at understanding the world and not directly at any other
+improvement of human life, cannot take account of ethical notions
+without being turned aside from that submission to fact which is the
+essence of the scientific temper.
+
+
+II
+
+If the notion of the universe and the notion of good and evil are
+extruded from scientific philosophy, it may be asked what specific
+problems remain for the philosopher as opposed to the man of science?
+It would be difficult to give a precise answer to this question, but
+certain characteristics may be noted as distinguishing the province of
+philosophy from that of the special sciences.
+
+In the first place a philosophical proposition must be general. It
+must not deal specially with things on the surface of the earth, or
+with the solar system, or with any other portion of space and time. It
+is this need of generality which has led to the belief that philosophy
+deals with the universe as a whole. I do not believe that this belief
+is justified, but I do believe that a philosophical proposition must
+be applicable to everything that exists or may exist. It might be
+supposed that this admission would be scarcely distinguishable from
+the view which I wish to reject. This, however, would be an error, and
+an important one. The traditional view would make the universe itself
+the subject of various predicates which could not be applied to any
+particular thing in the universe, and the ascription of such peculiar
+predicates to the universe would be the special business of
+philosophy. I maintain, on the contrary, that there are no
+propositions of which the "universe" is the subject; in other words,
+that there is no such thing as the "universe." What I do maintain is
+that there are general propositions which may be asserted of each
+individual thing, such as the propositions of logic. This does not
+involve that all the things there are form a whole which could be
+regarded as another thing and be made the subject of predicates. It
+involves only the assertion that there are properties which belong to
+each separate thing, not that there are properties belonging to the
+whole of things collectively. The philosophy which I wish to advocate
+may be called logical atomism or absolute pluralism, because, while
+maintaining that there are many things, it denies that there is a
+whole composed of those things. We shall see, therefore, that
+philosophical propositions, instead of being concerned with the whole
+of things collectively, are concerned with all things distributively;
+and not only must they be concerned with all things, but they must be
+concerned with such properties of all things as do not depend upon the
+accidental nature of the things that there happen to be, but are true
+of any possible world, independently of such facts as can only be
+discovered by our senses.
+
+This brings us to a second characteristic of philosophical
+propositions, namely, that they must be _a priori_. A philosophical
+proposition must be such as can be neither proved nor disproved by
+empirical evidence. Too often we find in philosophical books arguments
+based upon the course of history, or the convolutions of the brain, or
+the eyes of shell-fish. Special and accidental facts of this kind are
+irrelevant to philosophy, which must make only such assertions as
+would be equally true however the actual world were constituted.
+
+We may sum up these two characteristics of philosophical propositions
+by saying that _philosophy is the science of the possible_. But this
+statement unexplained is liable to be misleading, since it may be
+thought that the possible is something other than the general, whereas
+in fact the two are indistinguishable.
+
+Philosophy, if what has been said is correct, becomes indistinguishable
+from logic as that word has now come to be used. The study of logic
+consists, broadly speaking, of two not very sharply distinguished
+portions. On the one hand it is concerned with those general statements
+which can be made concerning everything without mentioning any one
+thing or predicate or relation, such for example as "if _x_ is a member
+of the class α and every member of α is a member of β, then _x_ is a
+member of the class β, whatever _x_, α, and β may be." On the other
+hand, it is concerned with the analysis and enumeration of logical
+_forms_, i.e. with the kinds of propositions that may occur, with the
+various types of facts, and with the classification of the constituents
+of facts. In this way logic provides an inventory of possibilities, a
+repertory of abstractly tenable hypotheses.
+
+It might be thought that such a study would be too vague and too
+general to be of any very great importance, and that, if its problems
+became at any point sufficiently definite, they would be merged in the
+problems of some special science. It appears, however, that this is
+not the case. In some problems, for example, the analysis of space and
+time, the nature of perception, or the theory of judgment, the
+discovery of the logical form of the facts involved is the hardest
+part of the work and the part whose performance has been most lacking
+hitherto. It is chiefly for want of the right logical hypothesis that
+such problems have hitherto been treated in such an unsatisfactory
+manner, and have given rise to those contradictions or antinomies in
+which the enemies of reason among philosophers have at all times
+delighted.
+
+By concentrating attention upon the investigation of logical forms, it
+becomes possible at last for philosophy to deal with its problems
+piecemeal, and to obtain, as the sciences do, such partial and
+probably not wholly correct results as subsequent investigation can
+utilise even while it supplements and improves them. Most
+philosophies hitherto have been constructed all in one block, in such
+a way that, if they were not wholly correct, they were wholly
+incorrect, and could not be used as a basis for further
+investigations. It is chiefly owing to this fact that philosophy,
+unlike science, has hitherto been unprogressive, because each original
+philosopher has had to begin the work again from the beginning,
+without being able to accept anything definite from the work of his
+predecessors. A scientific philosophy such as I wish to recommend will
+be piecemeal and tentative like other sciences; above all, it will be
+able to invent hypotheses which, even if they are not wholly true,
+will yet remain fruitful after the necessary corrections have been
+made. This possibility of successive approximations to the truth is,
+more than anything else, the source of the triumphs of science, and to
+transfer this possibility to philosophy is to ensure a progress in
+method whose importance it would be almost impossible to exaggerate.
+
+The essence of philosophy as thus conceived is analysis, not
+synthesis. To build up systems of the world, like Heine's German
+professor who knit together fragments of life and made an intelligible
+system out of them, is not, I believe, any more feasible than the
+discovery of the philosopher's stone. What is feasible is the
+understanding of general forms, and the division of traditional
+problems into a number of separate and less baffling questions.
+"Divide and conquer" is the maxim of success here as elsewhere.
+
+Let us illustrate these somewhat general maxims by examining their
+application to the philosophy of space, for it is only in application
+that the meaning or importance of a method can be understood. Suppose
+we are confronted with the problem of space as presented in Kant's
+Transcendental Æsthetic, and suppose we wish to discover what are the
+elements of the problem and what hope there is of obtaining a solution
+of them. It will soon appear that three entirely distinct problems,
+belonging to different studies, and requiring different methods for
+their solution, have been confusedly combined in the supposed single
+problem with which Kant is concerned. There is a problem of logic, a
+problem of physics, and a problem of theory of knowledge. Of these
+three, the problem of logic can be solved exactly and perfectly; the
+problem of physics can probably be solved with as great a degree of
+certainty and as great an approach to exactness as can be hoped in an
+empirical region; the problem of theory of knowledge, however, remains
+very obscure and very difficult to deal with. Let us see how these
+three problems arise.
+
+(1) The logical problem has arisen through the suggestions of
+non-Euclidean geometry. Given a body of geometrical propositions, it
+is not difficult to find a minimum statement of the axioms from which
+this body of propositions can be deduced. It is also not difficult, by
+dropping or altering some of these axioms, to obtain a more general or
+a different geometry, having, from the point of view of pure
+mathematics, the same logical coherence and the same title to respect
+as the more familiar Euclidean geometry. The Euclidean geometry itself
+is true perhaps of actual space (though this is doubtful), but
+certainly of an infinite number of purely arithmetical systems, each
+of which, from the point of view of abstract logic, has an equal and
+indefeasible right to be called a Euclidean space. Thus space as an
+object of logical or mathematical study loses its uniqueness; not only
+are there many kinds of spaces, but there are an infinity of examples
+of each kind, though it is difficult to find any kind of which the
+space of physics may be an example, and it is impossible to find any
+kind of which the space of physics is certainly an example. As an
+illustration of one possible logical system of geometry we may
+consider all relations of three terms which are analogous in certain
+formal respects to the relation "between" as it appears to be in
+actual space. A space is then defined by means of one such three-term
+relation. The points of the space are all the terms which have this
+relation to something or other, and their order in the space in
+question is determined by this relation. The points of one space are
+necessarily also points of other spaces, since there are necessarily
+other three-term relations having those same points for their field.
+The space in fact is not determined by the class of its points, but by
+the ordering three-term relation. When enough abstract logical
+properties of such relations have been enumerated to determine the
+resulting kind of geometry, say, for example, Euclidean geometry, it
+becomes unnecessary for the pure geometer in his abstract capacity to
+distinguish between the various relations which have all these
+properties. He considers the whole class of such relations, not any
+single one among them. Thus in studying a given kind of geometry the
+pure mathematician is studying a certain class of relations defined by
+means of certain abstract logical properties which take the place of
+what used to be called axioms. The nature of geometrical _reasoning_
+therefore is purely deductive and purely logical; if any special
+epistemological peculiarities are to be found in geometry, it must not
+be in the reasoning, but in our knowledge concerning the axioms in
+some given space.
+
+(2) The physical problem of space is both more interesting and more
+difficult than the logical problem. The physical problem may be
+stated as follows: to find in the physical world, or to construct from
+physical materials, a space of one of the kinds enumerated by the
+logical treatment of geometry. This problem derives its difficulty
+from the attempt to accommodate to the roughness and vagueness of the
+real world some system possessing the logical clearness and exactitude
+of pure mathematics. That this can be done with a certain degree of
+approximation is fairly evident If I see three people _A_, _B_, and
+_C_ sitting in a row, I become aware of the fact which may be
+expressed by saying that _B_ is between _A_ and _C_ rather than that
+_A_ is between _B_ and _C_, or _C_ is between _A_ and _B_. This
+relation of "between" which is thus perceived to hold has some of the
+abstract logical properties of those three-term relations which, we
+saw, give rise to a geometry, but its properties fail to be exact, and
+are not, as empirically given, amenable to the kind of treatment at
+which geometry aims. In abstract geometry we deal with points,
+straight lines, and planes; but the three people _A_, _B_, and _C_
+whom I see sitting in a row are not exactly points, nor is the row
+exactly a straight line. Nevertheless physics, which formally assumes
+a space containing points, straight lines, and planes, is found
+empirically to give results applicable to the sensible world. It must
+therefore be possible to find an interpretation of the points,
+straight lines, and planes of physics in terms of physical data, or at
+any rate in terms of data together with such hypothetical additions as
+seem least open to question. Since all data suffer from a lack of
+mathematical precision through being of a certain size and somewhat
+vague in outline, it is plain that if such a notion as that of a point
+is to find any application to empirical material, the point must be
+neither a datum nor a hypothetical addition to data, but a
+_construction_ by means of data with their hypothetical additions. It
+is obvious that any hypothetical filling out of data is less dubious
+and unsatisfactory when the additions are closely analogous to data
+than when they are of a radically different sort. To assume, for
+example, that objects which we see continue, after we have turned away
+our eyes, to be more or less analogous to what they were while we were
+looking, is a less violent assumption than to assume that such objects
+are composed of an infinite number of mathematical points. Hence in
+the physical study of the geometry of physical space, points must not
+be assumed _ab initio_ as they are in the logical treatment of
+geometry, but must be constructed as systems composed of data and
+hypothetical analogues of data. We are thus led naturally to define a
+physical point as a certain class of those objects which are the
+ultimate constituents of the physical world. It will be the class of
+all those objects which, as one would naturally say, _contain_ the
+point. To secure a definition giving this result, without previously
+assuming that physical objects are composed of points, is an agreeable
+problem in mathematical logic. The solution of this problem and the
+perception of its importance are due to my friend Dr. Whitehead. The
+oddity of regarding a point as a class of physical entities wears off
+with familiarity, and ought in any case not to be felt by those who
+maintain, as practically every one does, that points are mathematical
+fictions. The word "fiction" is used glibly in such connexions by many
+men who seem not to feel the necessity of explaining how it can come
+about that a fiction can be so useful in the study of the actual world
+as the points of mathematical physics have been found to be. By our
+definition, which regards a point as a class of physical objects, it
+is explained both how the use of points can lead to important
+physical results, and how we can nevertheless avoid the assumption
+that points are themselves entities in the physical world.
+
+Many of the mathematically convenient properties of abstract logical
+spaces cannot be either known to belong or known not to belong to the
+space of physics. Such are all the properties connected with continuity.
+For to know that actual space has these properties would require an
+infinite exactness of sense-perception. If actual space is continuous,
+there are nevertheless many possible non-continuous spaces which will be
+empirically indistinguishable from it; and, conversely, actual space may
+be non-continuous and yet empirically indistinguishable from a possible
+continuous space. Continuity, therefore, though obtainable in the _a
+priori_ region of arithmetic, is not with certainty obtainable in the
+space or time of the physical world: whether these are continuous or not
+would seem to be a question not only unanswered but for ever
+unanswerable. From the point of view of philosophy, however, the
+discovery that a question is unanswerable is as complete an answer as
+any that could possibly be obtained. And from the point of view of
+physics, where no empirical means of distinction can be found, there can
+be no empirical objection to the mathematically simplest assumption,
+which is that of continuity.
+
+The subject of the physical theory of space is a very large one,
+hitherto little explored. It is associated with a similar theory of
+time, and both have been forced upon the attention of philosophically
+minded physicists by the discussions which have raged concerning the
+theory of relativity.
+
+(3) The problem with which Kant is concerned in the Transcendental
+Æsthetic is primarily the epistemological problem: "How do we come to
+have knowledge of geometry _a priori_?" By the distinction between the
+logical and physical problems of geometry, the bearing and scope of
+this question are greatly altered. Our knowledge of pure geometry is
+_a priori_ but is wholly logical. Our knowledge of physical geometry
+is synthetic, but is not _a priori_. Our knowledge of pure geometry is
+hypothetical, and does not enable us to assert, for example, that the
+axiom of parallels is true in the physical world. Our knowledge of
+physical geometry, while it does enable us to assert that this axiom
+is approximately verified, does not, owing to the inevitable
+inexactitude of observation, enable us to assert that it is verified
+_exactly_. Thus, with the separation which we have made between pure
+geometry and the geometry of physics, the Kantian problem collapses.
+To the question, "How is synthetic _a priori_ knowledge possible?" we
+can now reply, at any rate so far as geometry is concerned, "It is not
+possible," if "synthetic" means "not deducible from logic alone." Our
+knowledge of geometry, like the rest of our knowledge, is derived
+partly from logic, partly from sense, and the peculiar position which
+in Kant's day geometry appeared to occupy is seen now to be a
+delusion. There are still some philosophers, it is true, who maintain
+that our knowledge that the axiom of parallels, for example, is true
+of actual space, is not to be accounted for empirically, but is as
+Kant maintained derived from an _a priori_ intuition. This position is
+not logically refutable, but I think it loses all plausibility as soon
+as we realise how complicated and derivative is the notion of physical
+space. As we have seen, the application of geometry to the physical
+world in no way demands that there should really be points and
+straight lines among physical entities. The principle of economy,
+therefore, demands that we should abstain from assuming the existence
+of points and straight lines. As soon, however, as we accept the view
+that points and straight lines are complicated constructions by means
+of classes of physical entities, the hypothesis that we have an _a
+priori_ intuition enabling us to know what happens to straight lines
+when they are produced indefinitely becomes extremely strained and
+harsh; nor do I think that such an hypothesis would ever have arisen
+in the mind of a philosopher who had grasped the nature of physical
+space. Kant, under the influence of Newton, adopted, though with some
+vacillation, the hypothesis of absolute space, and this hypothesis,
+though logically unobjectionable, is removed by Occam's razor, since
+absolute space is an unnecessary entity in the explanation of the
+physical world. Although, therefore, we cannot refute the Kantian
+theory of an _a priori_ intuition, we can remove its grounds one by
+one through an analysis of the problem. Thus, here as in many other
+philosophical questions, the analytic method, while not capable of
+arriving at a demonstrative result, is nevertheless capable of showing
+that all the positive grounds in favour of a certain theory are
+fallacious and that a less unnatural theory is capable of accounting
+for the facts.
+
+Another question by which the capacity of the analytic method can be
+shown is the question of realism. Both those who advocate and those
+who combat realism seem to me to be far from clear as to the nature of
+the problem which they are discussing. If we ask: "Are our objects of
+perception _real_ and are they _independent_ of the percipient?" it
+must be supposed that we attach some meaning to the words "real" and
+"independent," and yet, if either side in the controversy of realism
+is asked to define these two words, their answer is pretty sure to
+embody confusions such as logical analysis will reveal.
+
+Let us begin with the word "real." There certainly are objects of
+perception, and therefore, if the question whether these objects are
+real is to be a substantial question, there must be in the world two
+sorts of objects, namely, the real and the unreal, and yet the unreal
+is supposed to be essentially what there is not. The question what
+properties must belong to an object in order to make it real is one to
+which an adequate answer is seldom if ever forthcoming. There is of
+course the Hegelian answer, that the real is the self-consistent and
+that nothing is self-consistent except the Whole; but this answer,
+true or false, is not relevant in our present discussion, which moves
+on a lower plane and is concerned with the status of objects of
+perception among other objects of equal fragmentariness. Objects of
+perception are contrasted, in the discussions concerning realism,
+rather with psychical states on the one hand and matter on the other
+hand than with the all-inclusive whole of things. The question we have
+therefore to consider is the question as to what can be meant by
+assigning "reality" to some but not all of the entities that make up
+the world. Two elements, I think, make up what is felt rather than
+thought when the word "reality" is used in this sense. A thing is real
+if it persists at times when it is not perceived; or again, a thing is
+real when it is correlated with other things in a way which experience
+has led us to expect. It will be seen that reality in either of these
+senses is by no means necessary to a thing, and that in fact there
+might be a whole world in which nothing was real in either of these
+senses. It might turn out that the objects of perception failed of
+reality in one or both of these respects, without its being in any way
+deducible that they are not parts of the external world with which
+physics deals. Similar remarks will apply to the word "independent."
+Most of the associations of this word are bound up with ideas as to
+causation which it is not now possible to maintain. _A_ is independent
+of _B_ when _B_ is not an indispensable part of the _cause_ of _A_.
+But when it is recognised that causation is nothing more than
+correlation, and that there are correlations of simultaneity as well
+as of succession, it becomes evident that there is no uniqueness in a
+series of casual antecedents of a given event, but that, at any point
+where there is a correlation of simultaneity, we can pass from one
+line of antecedents to another in order to obtain a new series of
+causal antecedents. It will be necessary to specify the causal law
+according to which the antecedents are to be considered. I received a
+letter the other day from a correspondent who had been puzzled by
+various philosophical questions. After enumerating them he says:
+"These questions led me from Bonn to Strassburg, where I found
+Professor Simmel." Now, it would be absurd to deny that these
+questions caused his body to move from Bonn to Strassburg, and yet it
+must be supposed that a set of purely mechanical antecedents could
+also be found which would account for this transfer of matter from one
+place to another. Owing to this plurality of causal series antecedent
+to a given event, the notion of _the_ cause becomes indefinite, and
+the question of independence becomes correspondingly ambiguous. Thus,
+instead of asking simply whether _A_ is independent of _B_, we ought
+to ask whether there is a series determined by such and such causal
+laws leading from _B_ to _A_. This point is important in connexion
+with the particular question of objects of perception. It may be that
+no objects quite like those which we perceive ever exist unperceived;
+in this case there will be a causal law according to which objects of
+perception are not independent of being perceived. But even if this be
+the case, it may nevertheless also happen that there are purely
+physical causal laws determining the occurrence of objects which are
+perceived by means of other objects which perhaps are not perceived.
+In that case, in regard to such causal laws objects of perception will
+be independent of being perceived. Thus the question whether objects
+of perception are independent of being perceived is, as it stands,
+indeterminate, and the answer will be yes or no according to the
+method adopted of making it determinate. I believe that this confusion
+has borne a very large part in prolonging the controversies on this
+subject, which might well have seemed capable of remaining for ever
+undecided. The view which I should wish to advocate is that objects of
+perception do not persist unchanged at times when they are not
+perceived, although probably objects more or less resembling them do
+exist at such times; that objects of perception are part, and the only
+empirically knowable part, of the actual subject-matter of physics,
+and are themselves properly to be called physical; that purely
+physical laws exist determining the character and duration of objects
+of perception without any reference to the fact that they are
+perceived; and that in the establishment of such laws the propositions
+of physics do not presuppose any propositions of psychology or even
+the existence of mind. I do not know whether realists would recognise
+such a view as realism. All that I should claim for it is, that it
+avoids difficulties which seem to me to beset both realism and
+idealism as hitherto advocated, and that it avoids the appeal which
+they have made to ideas which logical analysis shows to be ambiguous.
+A further defence and elaboration of the positions which I advocate,
+but for which time is lacking now, will be found indicated in my book
+on _Our Knowledge of the External World_.[22]
+
+The adoption of scientific method in philosophy, if I am not mistaken,
+compels us to abandon the hope of solving many of the more ambitious
+and humanly interesting problems of traditional philosophy. Some of
+these it relegates, though with little expectation of a successful
+solution, to special sciences, others it shows to be such as our
+capacities are essentially incapable of solving. But there remain a
+large number of the recognised problems of philosophy in regard to
+which the method advocated gives all those advantages of division into
+distinct questions, of tentative, partial, and progressive advance,
+and of appeal to principles with which, independently of temperament,
+all competent students must agree. The failure of philosophy hitherto
+has been due in the main to haste and ambition: patience and modesty,
+here as in other sciences, will open the road to solid and durable
+progress.
+
+FOOTNOTES:
+
+[19] Bosanquet, _Logic_, ii, p. 211.
+
+[20] _Some Problems of Philosophy_, p 124.
+
+[21] _First Principles_ (1862), Part II, beginning of chap. viii.
+
+[22] Open Court Company, 1914.
+
+
+
+
+VII
+
+THE ULTIMATE CONSTITUENTS OF MATTER[23]
+
+
+I wish to discuss in this article no less a question than the ancient
+metaphysical query, "What is matter?" The question, "What is matter?"
+in so far as it concerns philosophy, is, I think, already capable of
+an answer which in principle will be as complete as an answer can hope
+to be; that is to say, we can separate the problem into an essentially
+soluble and an essentially insoluble portion, and we can now see how
+to solve the essentially soluble portion, at least as regards its main
+outlines. It is these outlines which I wish to suggest in the present
+article. My main position, which is realistic, is, I hope and believe,
+not remote from that of Professor Alexander, by whose writings on this
+subject I have profited greatly.[24] It is also in close accord with
+that of Dr. Nunn.[25]
+
+Common sense is accustomed to the division of the world into mind and
+matter. It is supposed by all who have never studied philosophy that
+the distinction between mind and matter is perfectly clear and easy,
+that the two do not at any point overlap, and that only a fool or a
+philosopher could be in doubt as to whether any given entity is mental
+or material. This simple faith survives in Descartes and in a
+somewhat modified form in Spinoza, but with Leibniz it begins to
+disappear, and from his day to our own almost every philosopher of
+note has criticised and rejected the dualism of common sense. It is my
+intention in this article to defend this dualism; but before defending
+it we must spend a few moments on the reasons which have prompted its
+rejection.
+
+Our knowledge of the material world is obtained by means of the
+senses, of sight and touch and so on. At first it is supposed that
+things are just as they seem, but two opposite sophistications soon
+destroy this naïve belief. On the one hand the physicists cut up
+matter into molecules, atoms, corpuscles, and as many more such
+subdivisions as their future needs may make them postulate, and the
+units at which they arrive are uncommonly different from the visible,
+tangible objects of daily life. A unit of matter tends more and more
+to be something like an electromagnetic field filling all space,
+though having its greatest intensity in a small region. Matter
+consisting of such elements is as remote from daily life as any
+metaphysical theory. It differs from the theories of metaphysicians
+only in the fact that its practical efficacy proves that it contains
+some measure of truth and induces business men to invest money on the
+strength of it; but, in spite of its connection with the money market,
+it remains a metaphysical theory none the less.
+
+The second kind of sophistication to which the world of common sense
+has been subjected is derived from the psychologists and
+physiologists. The physiologists point out that what we see depends
+upon the eye, that what we hear depends upon the ear, and that all our
+senses are liable to be affected by anything which affects the brain,
+like alcohol or hasheesh. Psychologists point out how much of what we
+think we see is supplied by association or unconscious inference, how
+much is mental interpretation, and how doubtful is the residuum which
+can be regarded as crude datum. From these facts it is argued by the
+psychologists that the notion of a datum passively received by the
+mind is a delusion, and it is argued by the physiologists that even if
+a pure datum of sense could be obtained by the analysis of experience,
+still this datum could not belong, as common sense supposes, to the
+outer world, since its whole nature is conditioned by our nerves and
+sense organs, changing as they change in ways which it is thought
+impossible to connect with any change in the matter supposed to be
+perceived. This physiologist's argument is exposed to the rejoinder,
+more specious than solid, that our knowledge of the existence of the
+sense organs and nerves is obtained by that very process which the
+physiologist has been engaged in discrediting, since the existence of
+the nerves and sense organs is only known through the evidence of the
+senses themselves. This argument may prove that some reinterpretation
+of the results of physiology is necessary before they can acquire
+metaphysical validity. But it does not upset the physiological
+argument in so far as this constitutes merely a _reductio ad absurdum_
+of naïve realism.
+
+These various lines of argument prove, I think, that some part of the
+beliefs of common sense must be abandoned. They prove that, if we take
+these beliefs as a whole, we are forced into conclusions which are in
+part self-contradictory; but such arguments cannot of themselves
+decide what portion of our common-sense beliefs is in need of
+correction. Common sense believes that what we see is physical,
+outside the mind, and continuing to exist if we shut our eyes or turn
+them in another direction. I believe that common sense is right in
+regarding what we see as physical and (in one of several possible
+senses) outside the mind, but is probably wrong in supposing that it
+continues to exist when we are no longer looking at it. It seems to me
+that the whole discussion of matter has been obscured by two errors
+which support each other. The first of these is the error that what we
+see, or perceive through any of our other senses, is subjective: the
+second is the belief that what is physical must be persistent.
+Whatever physics may regard as the ultimate constituents of matter, it
+always supposes these constituents to be indestructible. Since the
+immediate data of sense are not indestructible but in a state of
+perpetual flux, it is argued that these data themselves cannot be
+among the ultimate constituents of matter. I believe this to be a
+sheer mistake. The persistent particles of mathematical physics I
+regard as logical constructions, symbolic fictions enabling us to
+express compendiously very complicated assemblages of facts; and, on
+the other hand, I believe that the actual data in sensation, the
+immediate objects of sight or touch or hearing, are extra-mental,
+purely physical, and among the ultimate constituents of matter.
+
+My meaning in regard to the impermanence of physical entities may
+perhaps be made clearer by the use of Bergson's favourite illustration
+of the cinematograph. When I first read Bergson's statement that the
+mathematician conceives the world after the analogy of a
+cinematograph, I had never seen a cinematograph, and my first visit to
+one was determined by the desire to verify Bergson's statement, which
+I found to be completely true, at least so far as I am concerned.
+When, in a picture palace, we see a man rolling down hill, or running
+away from the police, or falling into a river, or doing any of those
+other things to which men in such places are addicted, we know that
+there is not really only one man moving, but a succession of films,
+each with a different momentary man. The illusion of persistence
+arises only through the approach to continuity in the series of
+momentary men. Now what I wish to suggest is that in this respect the
+cinema is a better metaphysician than common sense, physics, or
+philosophy. The real man too, I believe, however the police may swear
+to his identity, is really a series of momentary men, each different
+one from the other, and bound together, not by a numerical identity,
+but by continuity and certain intrinsic causal laws. And what applies
+to men applies equally to tables and chairs, the sun, moon and stars.
+Each of these is to be regarded, not as one single persistent entity,
+but as a series of entities succeeding each other in time, each
+lasting for a very brief period, though probably not for a mere
+mathematical instant. In saying this I am only urging the same kind of
+division in time as we are accustomed to acknowledge in the case of
+space. A body which fills a cubic foot will be admitted to consist of
+many smaller bodies, each occupying only a very tiny volume; similarly
+a thing which persists for an hour is to be regarded as composed of
+many things of less duration. A true theory of matter requires a
+division of things into time-corpuscles as well as into
+space-corpuscles.
+
+The world may be conceived as consisting of a multitude of entities
+arranged in a certain pattern. The entities which are arranged I shall
+call "particulars." The arrangement or pattern results from relations
+among particulars. Classes or series of particulars, collected
+together on account of some property which makes it convenient to be
+able to speak of them as wholes, are what I call logical constructions
+or symbolic fictions. The particulars are to be conceived, not on the
+analogy of bricks in a building, but rather on the analogy of notes
+in a symphony. The ultimate constituents of a symphony (apart from
+relations) are the notes, each of which lasts only for a very short
+time. We may collect together all the notes played by one instrument:
+these may be regarded as the analogues of the successive particulars
+which common sense would regard as successive states of one "thing."
+But the "thing" ought to be regarded as no more "real" or
+"substantial" than, for example, the rôle of the trombone. As soon as
+"things" are conceived in this manner it will be found that the
+difficulties in the way of regarding immediate objects of sense as
+physical have largely disappeared.
+
+When people ask, "Is the object of sense mental or physical?" they
+seldom have any clear idea either what is meant by "mental" or
+"physical," or what criteria are to be applied for deciding whether a
+given entity belongs to one class or the other. I do not know how to
+give a sharp definition of the word "mental," but something may be
+done by enumerating occurrences which are indubitably mental:
+believing, doubting, wishing, willing, being pleased or pained, are
+certainly mental occurrences; so are what we may call experiences,
+seeing, hearing, smelling, perceiving generally. But it does not
+follow from this that what is seen, what is heard, what is smelt, what
+is perceived, must be mental. When I see a flash of lightning, my
+seeing of it is mental, but what I see, although it is not quite the
+same as what anybody else sees at the same moment, and although it
+seems very unlike what the physicist would describe as a flash of
+lightning, is not mental. I maintain, in fact, that if the physicist
+could describe truly and fully all that occurs in the physical world
+when there is a flash of lightning, it would contain as a constituent
+what I see, and also what is seen by anybody else who would commonly
+be said to see the same flash. What I mean may perhaps be made plainer
+by saying that if my body could remain in exactly the same state in
+which it is, although my mind had ceased to exist, precisely that
+object which I now see when I see the flash would exist, although of
+course I should not see it, since my seeing is mental. The principal
+reasons which have led people to reject this view have, I think, been
+two: first, that they did not adequately distinguish between my seeing
+and what I see; secondly, that the causal dependence of what I see
+upon my body has made people suppose that what I see cannot be
+"outside" me. The first of these reasons need not detain us, since the
+confusion only needs to be pointed out in order to be obviated; but
+the second requires some discussion, since it can only be answered by
+removing current misconceptions, on the one hand as to the nature of
+space, and on the other, as to the meaning of causal dependence.
+
+When people ask whether colours, for example, or other secondary
+qualities are inside or outside the mind, they seem to suppose that
+their meaning must be clear, and that it ought to be possible to say
+yes or no without any further discussion of the terms involved. In
+fact, however, such terms as "inside" or "outside" are very ambiguous.
+What is meant by asking whether this or that is "in" the mind? The
+mind is not like a bag or a pie; it does not occupy a certain region
+in space, or, if (in a sense) it does, what is in that region is
+presumably part of the brain, which would not be said to be in the
+mind. When people say that sensible qualities are in the mind, they do
+not mean "spatially contained in" in the sense in which the blackbirds
+were in the pie. We might regard the mind as an assemblage of
+particulars, namely, what would be called "states of mind," which
+would belong together in virtue of some specific common quality. The
+common quality of all states of mind would be the quality designated
+by the word "mental"; and besides this we should have to suppose that
+each separate person's states of mind have some common characteristic
+distinguishing them from the states of mind of other people. Ignoring
+this latter point, let us ask ourselves whether the quality designated
+by the word "mental" does, as a matter of observation, actually belong
+to objects of sense, such as colours or noises. I think any candid
+person must reply that, however difficult it may be to know what we
+mean by "mental," it is not difficult to see that colours and noises
+are not mental in the sense of having that intrinsic peculiarity which
+belongs to beliefs and wishes and volitions, but not to the physical
+world. Berkeley advances on this subject a plausible argument[26]
+which seems to me to rest upon an ambiguity in the word "pain." He
+argues that the realist supposes the heat which he feels in
+approaching a fire to be something outside his mind, but that as he
+approaches nearer and nearer to the fire the sensation of heat passes
+imperceptibly into pain, and that no one could regard pain as
+something outside the mind. In reply to this argument, it should be
+observed in the first place that the heat of which we are immediately
+aware is not in the fire but in our own body. It is only by inference
+that the fire is judged to be the cause of the heat which we feel in
+our body. In the second place (and this is the more important point),
+when we speak of pain we may mean one of two things: we may mean the
+object of the sensation or other experience which has the quality of
+being painful, or we may mean the quality of painfulness itself. When
+a man says he has a pain in his great toe, what he means is that he
+has a sensation associated with his great toe and having the quality
+of painfulness. The sensation itself, like every sensation, consists
+in experiencing a sensible object, and the experiencing has that
+quality of painfulness which only mental occurrences can have, but
+which may belong to thoughts or desires, as well as to sensations. But
+in common language we speak of the sensible object experienced in a
+painful sensation as a pain, and it is this way of speaking which
+causes the confusion upon which the plausibility of Berkeley's
+argument depends. It would be absurd to attribute the quality of
+painfulness to anything non-mental, and hence it comes to be thought
+that what we call a pain in the toe must be mental. In fact, however,
+it is not the sensible object in such a case which is painful, but the
+sensation, that is to say, the experience of the sensible object. As
+the heat which we experience from the fire grows greater, the
+experience passes gradually from being pleasant to being painful, but
+neither the pleasure nor the pain is a quality of the object
+experienced as opposed to the experience, and it is therefore a
+fallacy to argue that this object must be mental on the ground that
+painfulness can only be attributed to what is mental.
+
+If, then, when we say that something is in the mind we mean that it
+has a certain recognisable intrinsic characteristic such as belongs to
+thoughts and desires, it must be maintained on grounds of immediate
+inspection that objects of sense are not in any mind.
+
+A different meaning of "in the mind" is, however, to be inferred from
+the arguments advanced by those who regard sensible objects as being
+in the mind. The arguments used are, in the main, such as would prove
+the causal dependence of objects of sense upon the percipient. Now
+the notion of causal dependence is very obscure and difficult, much
+more so in fact than is generally realised by philosophers. I shall
+return to this point in a moment. For the present, however, accepting
+the notion of causal dependence without criticism, I wish to urge that
+the dependence in question is rather upon our bodies than upon our
+minds. The visual appearance of an object is altered if we shut one
+eye, or squint, or look previously at something dazzling; but all
+these are bodily acts, and the alterations which they effect are to be
+explained by physiology and optics, not by psychology.[27] They are in
+fact of exactly the same kind as the alterations effected by
+spectacles or a microscope. They belong therefore to the theory of the
+physical world, and can have no bearing upon the question whether what
+we see is causally dependent upon the mind. What they do tend to
+prove, and what I for my part have no wish to deny, is that what we
+see is causally dependent upon our body and is not, as crude common
+sense would suppose, something which would exist equally if our eyes
+and nerves and brain were absent, any more than the visual appearance
+presented by an object seen through a microscope would remain if the
+microscope were removed. So long as it is supposed that the physical
+world is composed of stable and more or less permanent constituents,
+the fact that what we see is changed by changes in our body appears to
+afford reason for regarding what we see as not an ultimate constituent
+of matter. But if it is recognised that the ultimate constituents of
+matter are as circumscribed in duration as in spatial extent, the
+whole of this difficulty vanishes.
+
+There remains, however, another difficulty, connected with space. When
+we look at the sun we wish to know something about the sun itself,
+which is ninety-three million miles away; but what we see is dependent
+upon our eyes, and it is difficult to suppose that our eyes can affect
+what happens at a distance of ninety-three million miles. Physics
+tells us that certain electromagnetic waves start from the sun, and
+reach our eyes after about eight minutes. They there produce
+disturbances in the rods and cones, thence in the optic nerve, thence
+in the brain. At the end of this purely physical series, by some odd
+miracle, comes the experience which we call "seeing the sun," and it
+is such experiences which form the whole and sole reason for our
+belief in the optic nerve, the rods and cones, the ninety-three
+million miles, the electromagnetic waves, and the sun itself. It is
+this curious oppositeness of direction between the order of causation
+as affirmed by physics, and the order of evidence as revealed by
+theory of knowledge, that causes the most serious perplexities in
+regard to the nature of physical reality. Anything that invalidates
+our seeing, as a source of knowledge concerning physical reality,
+invalidates also the whole of physics and physiology. And yet,
+starting from a common-sense acceptance of our seeing, physics has
+been led step by step to the construction of the causal chain in which
+our seeing is the last link, and the immediate object which we see
+cannot be regarded as that initial cause which we believe to be
+ninety-three million miles away, and which we are inclined to regard
+as the "real" sun.
+
+I have stated this difficulty as forcibly as I can, because I believe
+that it can only be answered by a radical analysis and reconstruction
+of all the conceptions upon whose employment it depends.
+
+Space, time, matter and cause, are the chief of these conceptions. Let
+us begin with the conception of cause.
+
+Causal dependence, as I observed a moment ago, is a conception which
+it is very dangerous to accept at its face value. There exists a
+notion that in regard to any event there is something which may be
+called _the_ cause of that event--some one definite occurrence,
+without which the event would have been impossible and with which it
+becomes necessary. An event is supposed to be dependent upon its cause
+in some way which in it is not dependent upon other things. Thus men
+will urge that the mind is dependent upon the brain, or, with equal
+plausibility, that the brain is dependent upon the mind. It seems not
+improbable that if we had sufficient knowledge we could infer the
+state of a man's mind from the state of his brain, or the state of his
+brain from the state of his mind. So long as the usual conception of
+causal dependence is retained, this state of affairs can be used by
+the materialist to urge that the state of our brain causes our
+thoughts, and by the idealist to urge that our thoughts cause the
+state of our brain. Either contention is equally valid or equally
+invalid. The fact seems to be that there are many correlations of the
+sort which may be called causal, and that, for example, either a
+physical or a mental event can be predicted, theoretically, either
+from a sufficient number of physical antecedents or from a sufficient
+number of mental antecedents. To speak of _the_ cause of an event is
+therefore misleading. Any set of antecedents from which the event can
+theoretically be inferred by means of correlations might be called a
+cause of the event. But to speak of _the_ cause is to imply a
+uniqueness which does not exist.
+
+The relevance of this to the experience which we call "seeing the sun"
+is obvious. The fact that there exists a chain of antecedents which
+makes our seeing dependent upon the eyes and nerves and brain does not
+even tend to show that there is not another chain of antecedents in
+which the eyes and nerves and brain as physical things are ignored. If
+we are to escape from the dilemma which seemed to arise out of the
+physiological causation of what we see when we say we see the sun, we
+must find, at least in theory, a way of stating causal laws for the
+physical world, in which the units are not material things, such as
+the eyes and nerves and brain, but momentary particulars of the same
+sort as our momentary visual object when we look at the sun. The sun
+itself and the eyes and nerves and brain must be regarded as
+assemblages of momentary particulars. Instead of supposing, as we
+naturally do when we start from an uncritical acceptance of the
+apparent dicta of physics, that _matter_ is what is "really real" in
+the physical world, and that the immediate objects of sense are mere
+phantasms, we must regard matter as a logical construction, of which
+the constituents will be just such evanescent particulars as may, when
+an observer happens to be present, become data of sense to that
+observer. What physics regards as the sun of eight minutes ago will be
+a whole assemblage of particulars, existing at different times,
+spreading out from a centre with the velocity of light, and containing
+among their number all those visual data which are seen by people who
+are now looking at the sun. Thus the sun of eight minutes ago is a
+class of particulars, and what I see when I now look at the sun is one
+member of this class. The various particulars constituting this class
+will be correlated with each other by a certain continuity and certain
+intrinsic laws of variation as we pass outwards from the centre,
+together with certain modifications correlated extrinsically with
+other particulars which are not members of this class. It is these
+extrinsic modifications which represent the sort of facts that, in our
+former account, appeared as the influence of the eyes and nerves in
+modifying the appearance of the sun.[28]
+
+The _prima facie_ difficulties in the way of this view are chiefly
+derived from an unduly conventional theory of space. It might seem at
+first sight as if we had packed the world much fuller than it could
+possibly hold. At every place between us and the sun, we said, there
+is to be a particular which is to be a member of the sun as it was a
+few minutes ago. There will also, of course, have to be a particular
+which is a member of any planet or fixed star that may happen to be
+visible from that place. At the place where I am, there will be
+particulars which will be members severally of all the "things" I am
+now said to be perceiving. Thus throughout the world, everywhere,
+there will be an enormous number of particulars coexisting in the same
+place. But these troubles result from contenting ourselves too readily
+with the merely three-dimensional space to which schoolmasters have
+accustomed us. The space of the real world is a space of six
+dimensions, and as soon as we realise this we see that there is plenty
+of room for all the particulars for which we want to find positions.
+In order to realise this we have only to return for a moment from the
+polished space of physics to the rough and untidy space of our
+immediate sensible experience. The space of one man's sensible objects
+is a three-dimensional space. It does not appear probable that two men
+ever both perceive at the same time any one sensible object; when they
+are said to see the same thing or hear the same noise, there will
+always be some difference, however slight, between the actual shapes
+seen or the actual sounds heard. If this is so, and if, as is
+generally assumed, position in space is purely relative, it follows
+that the space of one man's objects and the space of another man's
+objects have no place in common, that they are in fact different
+spaces, and not merely different parts of one space. I mean by this
+that such immediate spatial relations as are perceived to hold
+between the different parts of the sensible space perceived by one
+man, do not hold between parts of sensible spaces perceived by
+different men. There are therefore a multitude of three-dimensional
+spaces in the world: there are all those perceived by observers, and
+presumably also those which are not perceived, merely because no
+observer is suitably situated for perceiving them.
+
+But although these spaces do not have to one another the same kind of
+spatial relations as obtain between the parts of one of them, it is
+nevertheless possible to arrange these spaces themselves in a
+three-dimensional order. This is done by means of the correlated
+particulars which we regard as members (or aspects) of one physical
+thing. When a number of people are said to see the same object, those
+who would be said to be near to the object see a particular occupying
+a larger part of their field of vision than is occupied by the
+corresponding particular seen by people who would be said to be
+farther from the thing. By means of such considerations it is
+possible, in ways which need not now be further specified, to arrange
+all the different spaces in a three-dimensional series. Since each of
+the spaces is itself three-dimensional, the whole world of particulars
+is thus arranged in a six-dimensional space, that is to say, six
+co-ordinates will be required to assign completely the position of any
+given particular, namely, three to assign its position in its own
+space and three more to assign the position of its space among the
+other spaces.
+
+There are two ways of classifying particulars: we may take together
+all those that belong to a given "perspective," or all those that are,
+as common sense would say, different "aspects" of the same "thing."
+For example, if I am (as is said) seeing the sun, what I see belongs
+to two assemblages: (1) the assemblage of all my present objects of
+sense, which is what I call a "perspective"; (2) the assemblage of
+all the different particulars which would be called aspects of the sun
+of eight minutes ago--this assemblage is what I define as _being_ the
+sun of eight minutes ago. Thus "perspectives" and "things" are merely
+two different ways of classifying particulars. It is to be observed
+that there is no _a priori_ necessity for particulars to be
+susceptible of this double classification. There may be what might be
+called "wild" particulars, not having the usual relations by which the
+classification is effected; perhaps dreams and hallucinations are
+composed of particulars which are "wild" in this sense.
+
+The exact definition of what is meant by a perspective is not quite
+easy. So long as we confine ourselves to visible objects or to objects
+of touch we might define the perspective of a given particular as "all
+particulars which have a simple (direct) spatial relation to the given
+particular." Between two patches of colour which I see now, there is a
+direct spatial relation which I equally see. But between patches of
+colour seen by different men there is only an indirect constructed
+spatial relation by means of the placing of "things" in physical space
+(which is the same as the space composed of perspectives). Those
+particulars which have direct spatial relations to a given particular
+will belong to the same perspective. But if, for example, the sounds
+which I hear are to belong to the same perspective with the patches of
+colour which I see, there must be particulars which have no direct
+spatial relation and yet belong to the same perspective. We cannot
+define a perspective as all the data of one percipient at one time,
+because we wish to allow the possibility of perspectives which are not
+perceived by any one. There will be need, therefore, in defining a
+perspective, of some principle derived neither from psychology nor
+from space.
+
+Such a principle may be obtained from the consideration of _time_.
+The one all-embracing time, like the one all-embracing space, is a
+construction; there is no _direct_ time-relation between particulars
+belonging to my perspective and particulars belonging to another
+man's. On the other hand, any two particulars of which I am aware are
+either simultaneous or successive, and their simultaneity or
+successiveness is sometimes itself a datum to me. We may therefore
+define the perspective to which a given particular belongs as "all
+particulars simultaneous with the given particular," where
+"simultaneous" is to be understood as a direct simple relation, not
+the derivative constructed relation of physics. It may be observed
+that the introduction of "local time" suggested by the principle of
+relativity has effected, for purely scientific reasons, much the same
+multiplication of times as we have just been advocating.
+
+The sum-total of all the particulars that are (directly) either
+simultaneous with or before or after a given particular may be defined
+as the "biography" to which that particular belongs. It will be
+observed that, just as a perspective need not be actually perceived by
+any one, so a biography need not be actually lived by any one. Those
+biographies that are lived by no one are called "official."
+
+The definition of a "thing" is effected by means of continuity and of
+correlations which have a certain differential independence of other
+"things." That is to say, given a particular in one perspective, there
+will usually in a neighbouring perspective be a very similar
+particular, differing from the given particular, to the first order of
+small quantities, according to a law involving only the difference of
+position of the two perspectives in perspective space, and not any of
+the other "things" in the universe. It is this continuity and
+differential independence in the law of change as we pass from one
+perspective to another that defines the class of particulars which is
+to be called "one thing."
+
+Broadly speaking, we may say that the physicist finds it convenient to
+classify particulars into "things," while the psychologist finds it
+convenient to classify them into "perspectives" and "biographies,"
+since one perspective _may_ constitute the momentary data of one
+percipient, and one biography _may_ constitute the whole of the data
+of one percipient throughout his life.
+
+We may now sum up our discussion. Our object has been to discover as
+far as possible the nature of the ultimate constituents of the
+physical world. When I speak of the "physical world," I mean, to begin
+with, the world dealt with by physics. It is obvious that physics is
+an empirical science, giving us a certain amount of knowledge and
+based upon evidence obtained through the senses. But partly through
+the development of physics itself, partly through arguments derived
+from physiology, psychology or metaphysics, it has come to be thought
+that the immediate data of sense could not themselves form part of the
+ultimate constituents of the physical world, but were in some sense
+"mental," "in the mind," or "subjective." The grounds for this view,
+in so far as they depend upon physics, can only be adequately dealt
+with by rather elaborate constructions depending upon symbolic logic,
+showing that out of such materials as are provided by the senses it is
+possible to construct classes and series having the properties which
+physics assigns to matter. Since this argument is difficult and
+technical, I have not embarked upon it in this article. But in so far
+as the view that sense-data are "mental" rests upon physiology,
+psychology, or metaphysics, I have tried to show that it rests upon
+confusions and prejudices--prejudices in favour of permanence in the
+ultimate constituents of matter, and confusions derived from unduly
+simple notions as to space, from the causal correlation of sense-data
+with sense-organs, and from failure to distinguish between sense-data
+and sensations. If what we have said on these subjects is valid, the
+existence of sense-data is logically independent of the existence of
+mind, and is causally dependent upon the _body_ of the percipient
+rather than upon his mind. The causal dependence upon the body of the
+percipient, we found, is a more complicated matter than it appears to
+be, and, like all causal dependence, is apt to give rise to erroneous
+beliefs through misconceptions as to the nature of causal correlation.
+If we have been right in our contentions, sense-data are merely those
+among the ultimate constituents of the physical world, of which we
+happen to be immediately aware; they themselves are purely physical,
+and all that is mental in connection with them is our awareness of
+them, which is irrelevant to their nature and to their place in
+physics.
+
+Unduly simple notions as to space have been a great stumbling-block to
+realists. When two men look at the same table, it is supposed that
+what the one sees and what the other sees are in the same place. Since
+the shape and colour are not quite the same for the two men, this
+raises a difficulty, hastily solved, or rather covered up, by
+declaring what each sees to be purely "subjective"--though it would
+puzzle those who use this glib word to say what they mean by it. The
+truth seems to be that space--and time also--is much more complicated
+than it would appear to be from the finished structure of physics, and
+that the one all-embracing three-dimensional space is a logical
+construction, obtained by means of correlations from a crude space of
+six dimensions. The particulars occupying this six-dimensional space,
+classified in one way, form "things," from which with certain further
+manipulations we can obtain what physics can regard as matter;
+classified in another way, they form "perspectives" and "biographies,"
+which may, if a suitable percipient happens to exist, form
+respectively the sense-data of a momentary or of a total experience.
+It is only when physical "things" have been dissected into series of
+classes of particulars, as we have done, that the conflict between the
+point of view of physics and the point of view of psychology can be
+overcome. This conflict, if what has been said is not mistaken, flows
+from different methods of classification, and vanishes as soon as its
+source is discovered.
+
+In favour of the theory which I have briefly outlined, I do not claim
+that it is _certainly_ true. Apart from the likelihood of mistakes,
+much of it is avowedly hypothetical. What I do claim for the theory is
+that it _may_ be true, and that this is more than can be said for any
+other theory except the closely analogous theory of Leibniz. The
+difficulties besetting realism, the confusions obstructing any
+philosophical account of physics, the dilemma resulting from
+discrediting sense-data, which yet remain the sole source of our
+knowledge of the outer world--all these are avoided by the theory
+which I advocate. This does not prove the theory to be true, since
+probably many other theories might be invented which would have the
+same merits. But it does prove that the theory has a better chance of
+being true than any of its present competitors, and it suggests that
+what can be known with certainty is likely to be discoverable by
+taking our theory as a starting-point, and gradually freeing it from
+all such assumptions as seem irrelevant, unnecessary, or unfounded. On
+these grounds, I recommend it to attention as a hypothesis and a basis
+for further work, though not as itself a finished or adequate solution
+of the problem with which it deals.
+
+FOOTNOTES:
+
+[23] An address delivered to the Philosophical Society of Manchester
+in February, 1915. Reprinted from _The Monist_, July, 1915.
+
+[24] Cf. especially Samuel Alexander, "The Basis of Realism," _British
+Academy_, Vol. VI.
+
+[25] "Are Secondary Qualities Independent of Perception?" _Proc.
+Arist. Soc._, 1909-10, pp. 191-218.
+
+[26] First dialogue between Hylas and Philonous, _Works_ (Fraser's
+edition 1901). I. p. 384.
+
+[27] This point has been well urged by the American realists.
+
+[28] Cf. T.P. Nunn, "Are Secondary Qualities Independent of
+Perception?" _Proc. Arist. Soc._, 1909-1910.
+
+
+
+
+VIII
+
+THE RELATION OF SENSE-DATA TO PHYSICS
+
+
+I. THE PROBLEM STATED
+
+Physics is said to be an empirical science, based upon observation and
+experiment.
+
+It is supposed to be verifiable, i.e. capable of calculating
+beforehand results subsequently confirmed by observation and
+experiment.
+
+What can we learn by observation and experiment?
+
+Nothing, so far as physics is concerned, except immediate data of
+sense: certain patches of colour, sounds, tastes, smells, etc., with
+certain spatio-temporal relations.
+
+The supposed contents of the physical world are _prima facie_ very
+different from these: molecules have no colour, atoms make no noise,
+electrons have no taste, and corpuscles do not even smell.
+
+If such objects are to be verified, it must be solely through their
+relation to sense-data: they must have some kind of correlation with
+sense-data, and must be verifiable through their correlation _alone_.
+
+But how is the correlation itself ascertained? A correlation can only
+be ascertained empirically by the correlated objects being constantly
+_found_ together. But in our case, only one term of the correlation,
+namely, the sensible term, is ever _found_: the other term seems
+essentially incapable of being found. Therefore, it would seem, the
+correlation with objects of sense, by which physics was to be
+verified, is itself utterly and for ever unverifiable.
+
+There are two ways of avoiding this result.
+
+(1) We may say that we know some principle _a priori_, without the
+need of empirical verification, e.g. that our sense-data have _causes_
+other than themselves, and that something can be known about these
+causes by inference from their effects. This way has been often
+adopted by philosophers. It may be necessary to adopt this way to some
+extent, but in so far as it is adopted physics ceases to be empirical
+or based upon experiment and observation alone. Therefore this way is
+to be avoided as much as possible.
+
+(2) We may succeed in actually defining the objects of physics as
+functions of sense-data. Just in so far as physics leads to
+expectations, this _must_ be possible, since we can only _expect_ what
+can be experienced. And in so far as the physical state of affairs is
+inferred from sense-data, it must be capable of expression as a
+function of sense-data. The problem of accomplishing this expression
+leads to much interesting logico-mathematical work.
+
+In physics as commonly set forth, sense-data appear as functions of
+physical objects: when such-and-such waves impinge upon the eye, we
+see such-and-such colours, and so on. But the waves are in fact
+inferred from the colours, not vice versa. Physics cannot be regarded
+as validly based upon empirical data until the waves have been
+expressed as functions of the colours and other sense-data.
+
+Thus if physics is to be verifiable we are faced with the following
+problem: Physics exhibits sense-data as functions of physical objects,
+but verification is only possible if physical objects can be exhibited
+as functions of sense-data. We have therefore to solve the equations
+giving sense-data in terms of physical objects, so as to make them
+instead give physical objects in terms of sense-data.
+
+
+II. CHARACTERISTICS OF SENSE-DATA
+
+When I speak of a "sense-datum," I do not mean the whole of what is
+given in sense at one time. I mean rather such a part of the whole as
+might be singled out by attention: particular patches of colour,
+particular noises, and so on. There is some difficulty in deciding
+what is to be considered _one_ sense-datum: often attention causes
+divisions to appear where, so far as can be discovered, there were no
+divisions before. An observed complex fact, such as that this patch of
+red is to the left of that patch of blue, is also to be regarded as a
+datum from our present point of view: epistemologically, it does not
+differ greatly from a simple sense-datum as regards its function in
+giving knowledge. Its _logical_ structure is very different, however,
+from that of sense: _sense_ gives acquaintance with particulars, and
+is thus a two-term relation in which the object can be _named_ but not
+_asserted_, and is inherently incapable of truth or falsehood, whereas
+the observation of a complex fact, which may be suitably called
+perception, is not a two-term relation, but involves the propositional
+form on the object-side, and gives knowledge of a truth, not mere
+acquaintance with a particular. This logical difference, important as
+it is, is not very relevant to our present problem; and it will be
+convenient to regard data of perception as included among sense-data
+for the purposes of this paper. It is to be observed that the
+particulars which are constituents of a datum of perception are always
+sense-data in the strict sense.
+
+Concerning sense-data, we know that they are there while they are
+data, and this is the epistemological basis of all our knowledge of
+external particulars. (The meaning of the word "external" of course
+raises problems which will concern us later.) We do not know, except
+by means of more or less precarious inferences, whether the objects
+which are at one time sense-data continue to exist at times when they
+are not data. Sense-data at the times when they are data are all that
+we directly and primitively know of the external world; hence in
+epistemology the fact that they are _data_ is all-important. But the
+fact that they are all that we directly know gives, of course, no
+presumption that they are all that there is. If we could construct an
+impersonal metaphysic, independent of the accidents of our knowledge
+and ignorance, the privileged position of the actual data would
+probably disappear, and they would probably appear as a rather
+haphazard selection from a mass of objects more or less like them. In
+saying this, I assume only that it is probable that there are
+particulars with which we are not acquainted. Thus the special
+importance of sense-data is in relation to epistemology, not to
+metaphysics. In this respect, physics is to be reckoned as
+metaphysics: it is impersonal, and nominally pays no special attention
+to sense-data. It is only when we ask how physics can be _known_ that
+the importance of sense-data re-emerges.
+
+
+III. SENSIBILIA
+
+I shall give the name _sensibilia_ to those objects which have the
+same metaphysical and physical status as sense-data, without
+necessarily being data to any mind. Thus the relation of a _sensibile_
+to a sense-datum is like that of a man to a husband: a man becomes a
+husband by entering into the relation of marriage, and similarly a
+_sensibile_ becomes a sense-datum by entering into the relation of
+acquaintance. It is important to have both terms; for we wish to
+discuss whether an object which is at one time a sense-datum can still
+exist at a time when it is not a sense-datum. We cannot ask "Can
+sense-data exist without being given?" for that is like asking "Can
+husbands exist without being married?" We must ask "Can _sensibilia_
+exist without being given?" and also "Can a particular _sensibile_ be
+at one time a sense-datum, and at another not?" Unless we have the
+word _sensibile_ as well as the word "sense-datum," such questions are
+apt to entangle us in trivial logical puzzles.
+
+It will be seen that all sense-data are _sensibilia_. It is a
+metaphysical question whether all _sensibilia_ are sense-data, and an
+epistemological question whether there exist means of inferring
+_sensibilia_ which are not data from those that are.
+
+A few preliminary remarks, to be amplified as we proceed, will serve
+to elucidate the use which I propose to make of _sensibilia_.
+
+I regard sense-data as not mental, and as being, in fact, part of the
+actual subject-matter of physics. There are arguments, shortly to be
+examined, for their subjectivity, but these arguments seem to me only
+to prove _physiological_ subjectivity, i.e. causal dependence on the
+sense-organs, nerves, and brain. The appearance which a thing presents
+to us is causally dependent upon these, in exactly the same way as it
+is dependent upon intervening fog or smoke or coloured glass. Both
+dependences are contained in the statement that the appearance which a
+piece of matter presents when viewed from a given place is a function
+not only of the piece of matter, but also of the intervening medium.
+(The terms used in this statement--"matter," "view from a given
+place," "appearance," "intervening medium"--will all be defined in the
+course of the present paper.) We have not the means of ascertaining
+how things appear from places not surrounded by brain and nerves and
+sense-organs, because we cannot leave the body; but continuity makes
+it not unreasonable to suppose that they present _some_ appearance at
+such places. Any such appearance would be included among _sensibilia_.
+If--_per impossibile_--there were a complete human body with no mind
+inside it, all those _sensibilia_ would exist, in relation to that
+body, which would be sense-data if there were a mind in the body. What
+the mind adds to _sensibilia_, in fact, is _merely_ awareness:
+everything else is physical or physiological.
+
+
+IV. SENSE-DATA ARE PHYSICAL
+
+Before discussing this question it will be well to define the sense in
+which the terms "mental" and "physical" are to be used. The word
+"physical," in all preliminary discussions, is to be understood as
+meaning "what is dealt with by physics." Physics, it is plain, tells
+us something about some of the constituents of the actual world; what
+these constituents are may be doubtful, but it is they that are to be
+called physical, whatever their nature may prove to be.
+
+The definition of the term "mental" is more difficult, and can only be
+satisfactorily given after many difficult controversies have been
+discussed and decided. For present purposes therefore I must content
+myself with assuming a dogmatic answer to these controversies. I shall
+call a particular "mental" when it is aware of something, and I shall
+call a fact "mental" when it contains a mental particular as a
+constituent.
+
+It will be seen that the mental and the physical are not necessarily
+mutually exclusive, although I know of no reason to suppose that they
+overlap.
+
+The doubt as to the correctness of our definition of the "mental" is
+of little importance in our present discussion. For what I am
+concerned to maintain is that sense-data are physical, and this being
+granted it is a matter of indifference in our present inquiry whether
+or not they are also mental. Although I do not hold, with Mach and
+James and the "new realists," that the difference between the mental
+and the physical is _merely_ one of arrangement, yet what I have to
+say in the present paper is compatible with their doctrine and might
+have been reached from their standpoint.
+
+In discussions on sense-data, two questions are commonly confused,
+namely:
+
+(1) Do sensible objects persist when we are not sensible of them? in
+other words, do _sensibilia_ which are data at a certain time
+sometimes continue to exist at times when they are not data? And (2)
+are sense-data mental or physical?
+
+I propose to assert that sense-data are physical, while yet
+maintaining that they probably never persist unchanged after ceasing
+to be data. The view that they do not persist is often thought, quite
+erroneously in my opinion, to imply that they are mental; and this
+has, I believe, been a potent source of confusion in regard to our
+present problem. If there were, as some have held, a _logical
+impossibility_ in sense-data persisting after ceasing to be data, that
+certainly would tend to show that they were mental; but if, as I
+contend, their non-persistence is merely a probable inference from
+empirically ascertained causal laws, then it carries no such
+implication with it, and we are quite free to treat them as part of
+the subject-matter of physics.
+
+Logically a sense-datum is an object, a particular of which the
+subject is aware. It does not contain the subject as a part, as for
+example beliefs and volitions do. The existence of the sense-datum is
+therefore not logically dependent upon that of the subject; for the
+only way, so far as I know, in which the existence of _A_ can be
+_logically_ dependent upon the existence of _B_ is when _B_ is part of
+_A_. There is therefore no _a priori_ reason why a particular which is
+a sense-datum should not persist after it has ceased to be a datum,
+nor why other similar particulars should not exist without ever being
+data. The view that sense-data are mental is derived, no doubt, in
+part from their physiological subjectivity, but in part also from a
+failure to distinguish between sense-data and "sensations." By a
+sensation I mean the fact consisting in the subject's awareness of the
+sense-datum. Thus a sensation is a complex of which the subject is a
+constituent and which therefore is mental. The sense-datum, on the
+other hand, stands over against the subject as that external object of
+which in sensation the subject is aware. It is true that the
+sense-datum is in many cases in the subject's body, but the subject's
+body is as distinct from the subject as tables and chairs are, and is
+in fact merely a part of the material world. So soon, therefore, as
+sense-data are clearly distinguished from sensations, and as their
+subjectivity is recognised to be physiological not psychical, the
+chief obstacles in the way of regarding them as physical are removed.
+
+
+V. "SENSIBILIA" AND "THINGS"
+
+But if "sensibilia" are to be recognised as the ultimate constituents
+of the physical world, a long and difficult journey is to be performed
+before we can arrive either at the "thing" of common sense or at the
+"matter" of physics. The supposed impossibility of combining the
+different sense-data which are regarded as appearances of the same
+"thing" to different people has made it seem as though these
+"sensibilia" must be regarded as mere subjective phantasms. A given
+table will present to one man a rectangular appearance, while to
+another it appears to have two acute angles and two obtuse angles; to
+one man it appears brown, while to another, towards whom it reflects
+the light, it appears white and shiny. It is said, not wholly without
+plausibility, that these different shapes and different colours cannot
+co-exist simultaneously in the same place, and cannot therefore both
+be constituents of the physical world. This argument I must confess
+appeared to me until recently to be irrefutable. The contrary opinion
+has, however, been ably maintained by Dr. T.P. Nunn in an article
+entitled: "Are Secondary Qualities Independent of Perception?"[29] The
+supposed impossibility derives its apparent force from the phrase:
+"_in the same place_," and it is precisely in this phrase that its
+weakness lies. The conception of space is too often treated in
+philosophy--even by those who on reflection would not defend such
+treatment--as though it were as given, simple, and unambiguous as
+Kant, in his psychological innocence, supposed. It is the unperceived
+ambiguity of the word "place" which, as we shall shortly see, has
+caused the difficulties to realists and given an undeserved advantage
+to their opponents. Two "places" of different kinds are involved in
+every sense-datum, namely the place _at_ which it appears and the
+place _from_ which it appears. These belong to different spaces,
+although, as we shall see, it is possible, with certain limitations,
+to establish a correlation between them. What we call the different
+appearances of the same thing to different observers are each in a
+space private to the observer concerned. No place in the private world
+of one observer is identical with a place in the private world of
+another observer. There is therefore no question of combining the
+different appearances in the one place; and the fact that they cannot
+all exist in one place affords accordingly no ground whatever for
+questioning their physical reality. The "thing" of common sense may in
+fact be identified with the whole class of its appearances--where,
+however, we must include among appearances not only those which are
+actual sense-data, but also those "sensibilia," if any, which, on
+grounds of continuity and resemblance, are to be regarded as belonging
+to the same system of appearances, although there happen to be no
+observers to whom they are data.
+
+An example may make this clearer. Suppose there are a number of people
+in a room, all seeing, as they say, the same tables and chairs, walls
+and pictures. No two of these people have exactly the same sense-data,
+yet there is sufficient similarity among their data to enable them to
+group together certain of these data as appearances of one "thing" to
+the several spectators, and others as appearances of another "thing."
+Besides the appearances which a given thing in the room presents to
+the actual spectators, there are, we may suppose, other appearances
+which it would present to other possible spectators. If a man were to
+sit down between two others, the appearance which the room would
+present to him would be intermediate between the appearances which it
+presents to the two others: and although this appearance would not
+exist as it is without the sense organs, nerves and brain, of the
+newly arrived spectator, still it is not unnatural to suppose that,
+from the position which he now occupies, _some_ appearance of the
+room existed before his arrival. This supposition, however, need
+merely be noticed and not insisted upon.
+
+Since the "thing" cannot, without indefensible partiality, be
+identified with any single one of its appearances, it came to be
+thought of as something distinct from all of them and underlying them.
+But by the principle of Occam's razor, if the class of appearances
+will fulfil the purposes for the sake of which the thing was invented
+by the prehistoric metaphysicians to whom common sense is due, economy
+demands that we should identify the thing with the class of its
+appearances. It is not necessary to _deny_ a substance or substratum
+underlying these appearances; it is merely expedient to abstain from
+asserting this unnecessary entity. Our procedure here is precisely
+analogous to that which has swept away from the philosophy of
+mathematics the useless menagerie of metaphysical monsters with which
+it used to be infested.
+
+
+VI. CONSTRUCTIONS VERSUS INFERENCES
+
+Before proceeding to analyse and explain the ambiguities of the word
+"place," a few general remarks on method are desirable. The supreme
+maxim in scientific philosophising is this:
+
+  _Wherever possible, logical constructions are to be substituted
+  for inferred entities._
+
+Some examples of the substitution of construction for inference in the
+realm of mathematical philosophy may serve to elucidate the uses of
+this maxim. Take first the case of irrationals. In old days,
+irrationals were inferred as the supposed limits of series of
+rationals which had no rational limit; but the objection to this
+procedure was that it left the existence of irrationals merely
+optative, and for this reason the stricter methods of the present day
+no longer tolerate such a definition. We now define an irrational
+number as a certain class of ratios, thus constructing it logically by
+means of ratios, instead of arriving at it by a doubtful inference
+from them. Take again the case of cardinal numbers. Two equally
+numerous collections appear to have something in common: this
+something is supposed to be their cardinal number. But so long as the
+cardinal number is inferred from the collections, not constructed in
+terms of them, its existence must remain in doubt, unless in virtue of
+a metaphysical postulate _ad hoc_. By defining the cardinal number of
+a given collection as the class of all equally numerous collections,
+we avoid the necessity of this metaphysical postulate, and thereby
+remove a needless element of doubt from the philosophy of arithmetic.
+A similar method, as I have shown elsewhere, can be applied to classes
+themselves, which need not be supposed to have any metaphysical
+reality, but can be regarded as symbolically constructed fictions.
+
+The method by which the construction proceeds is closely analogous in
+these and all similar cases. Given a set of propositions nominally
+dealing with the supposed inferred entities, we observe the properties
+which are required of the supposed entities in order to make these
+propositions true. By dint of a little logical ingenuity, we then
+construct some logical function of less hypothetical entities which
+has the requisite properties. This constructed function we substitute
+for the supposed inferred entities, and thereby obtain a new and less
+doubtful interpretation of the body of propositions in question. This
+method, so fruitful in the philosophy of mathematics, will be found
+equally applicable in the philosophy of physics, where, I do not
+doubt, it would have been applied long ago but for the fact that all
+who have studied this subject hitherto have been completely ignorant
+of mathematical logic. I myself cannot claim originality in the
+application of this method to physics, since I owe the suggestion and
+the stimulus for its application entirely to my friend and
+collaborator Dr. Whitehead, who is engaged in applying it to the more
+mathematical portions of the region intermediate between sense-data
+and the points, instants and particles of physics.
+
+A complete application of the method which substitutes constructions
+for inferences would exhibit matter wholly in terms of sense-data, and
+even, we may add, of the sense-data of a single person, since the
+sense-data of others cannot be known without some element of
+inference. This, however, must remain for the present an ideal, to be
+approached as nearly as possible, but to be reached, if at all, only
+after a long preliminary labour of which as yet we can only see the
+very beginning. The inferences which are unavoidable can, however, be
+subjected to certain guiding principles. In the first place they
+should always be made perfectly explicit, and should be formulated in
+the most general manner possible. In the second place the inferred
+entities should, whenever this can be done, be similar to those whose
+existence is given, rather than, like the Kantian _Ding an sich_,
+something wholly remote from the data which nominally support the
+inference. The inferred entities which I shall allow myself are of two
+kinds: (_a_) the sense-data of other people, in favour of which there
+is the evidence of testimony, resting ultimately upon the analogical
+argument in favour of minds other than my own; (_b_) the "sensibilia"
+which would appear from places where there happen to be no minds, and
+which I suppose to be real although they are no one's data. Of these
+two classes of inferred entities, the first will probably be allowed
+to pass unchallenged. It would give me the greatest satisfaction to be
+able to dispense with it, and thus establish physics upon a
+solipsistic basis; but those--and I fear they are the majority--in
+whom the human affections are stronger than the desire for logical
+economy, will, no doubt, not share my desire to render solipsism
+scientifically satisfactory. The second class of inferred entities
+raises much more serious questions. It may be thought monstrous to
+maintain that a thing can present any appearance at all in a place
+where no sense organs and nervous structure exist through which it
+could appear. I do not myself feel the monstrosity; nevertheless I
+should regard these supposed appearances only in the light of a
+hypothetical scaffolding, to be used while the edifice of physics is
+being raised, though possibly capable of being removed as soon as the
+edifice is completed. These "sensibilia" which are not data to anyone
+are therefore to be taken rather as an illustrative hypothesis and as
+an aid in preliminary statement than as a dogmatic part of the
+philosophy of physics in its final form.
+
+
+VII. PRIVATE SPACE AND THE SPACE OF PERSPECTIVES
+
+We have now to explain the ambiguity in the word "place," and how it
+comes that two places of different sorts are associated with every
+sense-datum, namely the place _at_ which it is and the place _from_
+which it is perceived. The theory to be advocated is closely analogous
+to Leibniz's monadology, from which it differs chiefly in being less
+smooth and tidy.
+
+The first fact to notice is that, so far as can be discovered, no
+sensibile is ever a datum to two people at once. The things seen by
+two different people are often closely similar, so similar that the
+same _words_ can be used to denote them, without which communication
+with others concerning sensible objects would be impossible. But, in
+spite of this similarity, it would seem that some difference always
+arises from difference in the point of view. Thus each person, so far
+as his sense-data are concerned, lives in a private world. This
+private world contains its own space, or rather spaces, for it would
+seem that only experience teaches us to correlate the space of sight
+with the space of touch and with the various other spaces of other
+senses. This multiplicity of private spaces, however, though
+interesting to the psychologist, is of no great importance in regard
+to our present problem, since a merely solipsistic experience enables
+us to correlate them into the one private space which embraces all our
+own sense-data. The place _at_ which a sense-datum is, is a place in
+private space. This place therefore is different from any place in the
+private space of another percipient. For if we assume, as logical
+economy demands, that all position is relative, a place is only
+definable by the things in or around it, and therefore the same place
+cannot occur in two private worlds which have no common constituent.
+The question, therefore, of combining what we call different
+appearances of the same thing in the same place does not arise, and
+the fact that a given object appears to different spectators to have
+different shapes and colours affords no argument against the physical
+reality of all these shapes and colours.
+
+In addition to the private spaces belonging to the private worlds of
+different percipients, there is, however, another space, in which one
+whole private world counts as a point, or at least as a spatial unit.
+This might be described as the space of points of view, since each
+private world may be regarded as the appearance which the universe
+presents from a certain point of view. I prefer, however, to speak of
+it as the space of _perspectives_, in order to obviate the suggestion
+that a private world is only real when someone views it. And for the
+same reason, when I wish to speak of a private world without assuming
+a percipient, I shall call it a "perspective."
+
+We have now to explain how the different perspectives are ordered in
+one space. This is effected by means of the correlated "sensibilia"
+which are regarded as the appearances, in different perspectives, of
+one and the same thing. By moving, and by testimony, we discover that
+two different perspectives, though they cannot both contain the same
+"sensibilia," may nevertheless contain very similar ones; and the
+spatial order of a certain group of "sensibilia" in a private space of
+one perspective is found to be identical with, or very similar to, the
+spatial order of the correlated "sensibilia" in the private space of
+another perspective. In this way one "sensibile" in one perspective is
+correlated with one "sensibile" in another. Such correlated
+"sensibilia" will be called "appearances of one thing." In Leibniz's
+monadology, since each monad mirrored the whole universe, there was in
+each perspective a "sensibile" which was an appearance of each thing.
+In our system of perspectives, we make no such assumption of
+completeness. A given thing will have appearances in some
+perspectives, but presumably not in certain others. The "thing" being
+defined as the class of its appearances, if κ is the class of
+perspectives in which a certain thing θ appears, then θ is a member of
+the multiplicative class of κ, κ being a class of mutually exclusive
+classes of "sensibilia." And similarly a perspective is a member of
+the multiplicative class of the things which appear in it.
+
+The arrangement of perspectives in a space is effected by means of the
+differences between the appearances of a given thing in the various
+perspectives. Suppose, say, that a certain penny appears in a number
+of different perspectives; in some it looks larger and in some
+smaller, in some it looks circular, in others it presents the
+appearance of an ellipse of varying eccentricity. We may collect
+together all those perspectives in which the appearance of the penny
+is circular. These we will place on one straight line, ordering them
+in a series by the variations in the apparent size of the penny. Those
+perspectives in which the penny appears as a straight line of a
+certain thickness will similarly be placed upon a plane (though in
+this case there will be many different perspectives in which the penny
+is of the same size; when one arrangement is completed these will form
+a circle concentric with the penny), and ordered as before by the
+apparent size of the penny. By such means, all those perspectives in
+which the penny presents a visual appearance can be arranged in a
+three-dimensional spatial order. Experience shows that the same
+spatial order of perspectives would have resulted if, instead of the
+penny, we had chosen any other thing which appeared in all the
+perspectives in question, or any other method of utilising the
+differences between the appearances of the same things in different
+perspectives. It is this empirical fact which has made it possible to
+construct the one all-embracing space of physics.
+
+The space whose construction has just been explained, and whose
+elements are whole perspectives, will be called "perspective-space."
+
+
+VIII. THE PLACING OF "THINGS" AND "SENSIBILIA" IN PERSPECTIVE SPACE
+
+The world which we have so far constructed is a world of six
+dimensions, since it is a three-dimensional series of perspectives,
+each of which is itself three-dimensional. We have now to explain the
+correlation between the perspective space and the various private
+spaces contained within the various perspectives severally. It is by
+means of this correlation that the one three-dimensional space of
+physics is constructed; and it is because of the unconscious
+performance of this correlation that the distinction between
+perspective space and the percipient's private space has been blurred,
+with disastrous results for the philosophy of physics. Let us revert
+to our penny: the perspectives in which the penny appears larger are
+regarded as being nearer to the penny than those in which it appears
+smaller, but as far as experience goes the apparent size of the penny
+will not grow beyond a certain limit, namely, that where (as we say)
+the penny is so near the eye that if it were any nearer it could not
+be seen. By touch we may prolong the series until the penny touches
+the eye, but no further. If we have been travelling along a line of
+perspectives in the previously defined sense, we may, however, by
+imagining the penny removed, prolong the line of perspectives by
+means, say, of another penny; and the same may be done with any other
+line of perspectives defined by means of the penny. All these lines
+meet in a certain place, that is, in a certain perspective. This
+perspective will be defined as "the place where the penny is."
+
+It is now evident in what sense two places in constructed physical
+space are associated with a given "sensibile." There is first the
+place which is the perspective of which the "sensibile" is a member.
+This is the place _from_ which the "sensibile" appears. Secondly there
+is the place where the thing is of which the "sensibile" is a member,
+in other words an appearance; this is the place _at_ which the
+"sensibile" appears. The "sensibile" which is a member of one
+perspective is correlated with another perspective, namely, that which
+is the place where the thing is of which the "sensibile" is an
+appearance. To the psychologist the "place from which" is the more
+interesting, and the "sensibile" accordingly appears to him subjective
+and where the percipient is. To the physicist the "place at which" is
+the more interesting, and the "sensibile" accordingly appears to him
+physical and external. The causes, limits and partial justification of
+each of these two apparently incompatible views are evident from the
+above duplicity of places associated with a given "sensibile."
+
+We have seen that we can assign to a physical thing a place in the
+perspective space. In this way different parts of our body acquire
+positions in perspective space, and therefore there is a meaning
+(whether true or false need not much concern us) in saying that the
+perspective to which our sense-data belong is inside our head. Since
+our mind is correlated with the perspective to which our sense-data
+belong, we may regard this perspective as being the position of our
+mind in perspective space. If, therefore, this perspective is, in the
+above defined sense, inside our head, there is a good meaning for the
+statement that the mind is in the head. We can now say of the various
+appearances of a given thing that some of them are nearer to the thing
+than others; those are nearer which belong to perspectives that are
+nearer to "the place where the thing is." We can thus find a meaning,
+true or false, for the statement that more is to be learnt about a
+thing by examining it close to than by viewing it from a distance. We
+can also find a meaning for the phrase "the things which intervene
+between the subject and a thing of which an appearance is a datum to
+him." One reason often alleged for the subjectivity of sense-data is
+that the appearance of a thing may change when we find it hard to
+suppose that the thing itself has changed--for example, when the
+change is due to our shutting our eyes, or to our screwing them up so
+as to make the thing look double. If the thing is defined as the class
+of its appearances (which is the definition adopted above), there is
+of course necessarily _some_ change in the thing whenever any one of
+its appearances changes. Nevertheless there is a very important
+distinction between two different ways in which the appearances may
+change. If after looking at a thing I shut my eyes, the appearance of
+my eyes changes in every perspective in which there is such an
+appearance, whereas most of the appearances of the thing will remain
+unchanged. We may say, as a matter of definition, that a thing changes
+when, however near to the thing an appearance of it may be, there are
+changes in appearances as near as, or still nearer to, the thing. On
+the other hand we shall say that the change is in some other thing if
+all appearances of the thing which are at not more than a certain
+distance from the thing remain unchanged, while only comparatively
+distant appearances of the thing are altered. From this consideration
+we are naturally led to the consideration of _matter_, which must be
+our next topic.
+
+
+IX. THE DEFINITION OF MATTER
+
+We defined the "physical thing" as the class of its appearances, but
+this can hardly be taken as a definition of matter. We want to be able
+to express the fact that the appearance of a thing in a given
+perspective is causally affected by the matter between the thing and
+the perspective. We have found a meaning for "between a thing and a
+perspective." But we want matter to be something other than the whole
+class of appearances of a thing, in order to state the influence of
+matter on appearances.
+
+We commonly assume that the information we get about a thing is more
+accurate when the thing is nearer. Far off, we see it is a man; then
+we see it is Jones; then we see he is smiling. Complete accuracy would
+only be attainable as a limit: if the appearances of Jones as we
+approach him tend towards a limit, that limit may be taken to be what
+Jones really is. It is obvious that from the point of view of physics
+the appearances of a thing close to "count" more than the appearances
+far off. We may therefore set up the following tentative definition:
+
+The _matter_ of a given thing is the limit of its appearances as their
+distance from the thing diminishes.
+
+It seems probable that there is something in this definition, but it
+is not quite satisfactory, because empirically there is no such limit
+to be obtained from sense-data. The definition will have to be eked
+out by constructions and definitions. But probably it suggests the
+right direction in which to look.
+
+We are now in a position to understand in outline the reverse journey
+from matter to sense-data which is performed by physics. The
+appearance of a thing in a given perspective is a function of the
+matter composing the thing and of the intervening matter. The
+appearance of a thing is altered by intervening smoke or mist, by blue
+spectacles or by alterations in the sense-organs or nerves of the
+percipient (which also must be reckoned as part of the intervening
+medium). The nearer we approach to the thing, the less its appearance
+is affected by the intervening matter. As we travel further and
+further from the thing, its appearances diverge more and more from
+their initial character; and the causal laws of their divergence are
+to be stated in terms of the matter which lies between them and the
+thing. Since the appearances at very small distances are less affected
+by causes other than the thing itself, we come to think that the limit
+towards which these appearances tend as the distance diminishes is
+what the thing "really is," as opposed to what it merely seems to be.
+This, together with its necessity for the statement of causal laws,
+seems to be the source of the entirely erroneous feeling that matter
+is more "real" than sense-data.
+
+Consider for example the infinite divisibility of matter. In looking
+at a given thing and approaching it, one sense-datum will become
+several, and each of these will again divide. Thus _one_ appearance
+may represent _many_ things, and to this process there seems no end.
+Hence in the limit, when we approach indefinitely near to the thing
+there will be an indefinite number of units of matter corresponding to
+what, at a finite distance, is only one appearance. This is how
+infinite divisibility arises.
+
+The whole causal efficacy of a thing resides in its matter. This is in
+some sense an empirical fact, but it would be hard to state it
+precisely, because "causal efficacy" is difficult to define.
+
+What can be known empirically about the matter of a thing is only
+approximate, because we cannot get to know the appearances of the
+thing from very small distances, and cannot accurately infer the limit
+of these appearances. But it _is_ inferred _approximately_ by means of
+the appearances we can observe. It then turns out that these
+appearances can be exhibited by physics as a function of the matter
+in our immediate neighbourhood; e.g. the visual appearance of a
+distant object is a function of the light-waves that reach the eyes.
+This leads to confusions of thought, but offers no real difficulty.
+
+One appearance, of a visible object for example, is not sufficient to
+determine its other simultaneous appearances, although it goes a
+certain distance towards determining them. The determination of the
+hidden structure of a thing, so far as it is possible at all, can only
+be effected by means of elaborate dynamical inferences.
+
+
+X. TIME[30]
+
+It seems that the one all-embracing time is a construction, like the
+one all-embracing space. Physics itself has become conscious of this
+fact through the discussions connected with relativity.
+
+Between two perspectives which both belong to one person's experience,
+there will be a direct time-relation of before and after. This
+suggests a way of dividing history in the same sort of way as it is
+divided by different experiences, but without introducing experience
+or anything mental: we may define a "biography" as everything that is
+(directly) earlier or later than, or simultaneous with, a given
+"sensibile." This will give a series of perspectives, which _might_
+all form parts of one person's experience, though it is not necessary
+that all or any of them should actually do so. By this means, the
+history of the world is divided into a number of mutually exclusive
+biographies.
+
+We have now to correlate the times in the different biographies. The
+natural thing would be to say that the appearances of a given
+(momentary) thing in two different perspectives belonging to different
+biographies are to be taken as simultaneous; but this is not
+convenient. Suppose _A_ shouts to _B_, and _B_ replies as soon as he
+hears _A's_ shout. Then between _A's_ hearing of his own shout and his
+hearing of _B's_ there is an interval; thus if we made _A's_ and _B's_
+hearing of the same shout exactly simultaneous with each other, we
+should have events exactly simultaneous with a given event but not
+with each other. To obviate this, we assume a "velocity of sound."
+That is, we assume that the time when _B_ hears _A's_ shout is
+half-way between the time when _A_ hears his own shout and the time
+when he hears _B's_. In this way the correlation is effected.
+
+What has been said about sound applies of course equally to light. The
+general principle is that the appearances, in different perspectives,
+which are to be grouped together as constituting what a certain thing
+is at a certain moment, are not to be all regarded as being at that
+moment. On the contrary they spread outward from the thing with
+various velocities according to the nature of the appearances. Since
+no _direct_ means exist of correlating the time in one biography with
+the time in another, this temporal grouping of the appearances
+belonging to a given thing at a given moment is in part conventional.
+Its motive is partly to secure the verification of such maxims as that
+events which are exactly simultaneous with the same event are exactly
+simultaneous with one another, partly to secure convenience in the
+formulation of causal laws.
+
+
+XI. THE PERSISTENCE OF THINGS AND MATTER
+
+Apart from any of the fluctuating hypotheses of physics, three main
+problems arise in connecting the world of physics with the world of
+sense, namely:
+
+    1. the construction of a single space;
+    2. the construction of a single time;
+    3. the construction of permanent things or matter.
+
+We have already considered the first and second of these problems; it
+remains to consider the third.
+
+We have seen how correlated appearances in different perspectives are
+combined to form one "thing" at one moment in the all-embracing time
+of physics. We have now to consider how appearances at different times
+are combined as belonging to one "thing," and how we arrive at the
+persistent "matter" of physics. The assumption of permanent substance,
+which technically underlies the procedure of physics, cannot of course
+be regarded as metaphysically legitimate: just as the one thing
+simultaneously seen by many people is a construction, so the one thing
+seen at different times by the same or different people must be a
+construction, being in fact nothing but a certain grouping of certain
+"sensibilia."
+
+We have seen that the momentary state of a "thing" is an assemblage of
+"sensibilia," in different perspectives, not all simultaneous in the
+one constructed time, but spreading out from "the place where the
+thing is" with velocities depending upon the nature of the
+"sensibilia." The time _at_ which the "thing" is in this state is the
+lower limit of the times at which these appearances occur. We have now
+to consider what leads us to speak of another set of appearances as
+belonging to the same "thing" at a different time.
+
+For this purpose, we may, at least to begin with, confine ourselves
+within a single biography. If we can always say when two "sensibilia"
+in a given biography are appearances of one thing, then, since we have
+seen how to connect "sensibilia" in different biographies as
+appearances of the same momentary state of a thing, we shall have all
+that is necessary for the complete construction of the history of a
+thing.
+
+It is to be observed, to begin with, that the identity of a thing for
+common sense is not always correlated with the identity of matter for
+physics. A human body is one persisting thing for common sense, but
+for physics its matter is constantly changing. We may say, broadly,
+that the common-sense conception is based upon continuity in
+appearances at the ordinary distances of sense-data, while the
+physical conception is based upon the continuity of appearances at
+very small distances from the thing. It is probable that the
+common-sense conception is not capable of complete precision. Let us
+therefore concentrate our attention upon the conception of the
+persistence of matter in physics.
+
+The first characteristic of two appearances of the same piece of
+matter at different times is _continuity_. The two appearances must be
+connected by a series of intermediaries, which, if time and space form
+compact series, must themselves form a compact series. The colour of
+the leaves is different in autumn from what it is in summer; but we
+believe that the change occurs gradually, and that, if the colours are
+different at two given times, there are intermediate times at which
+the colours are intermediate between those at the given times.
+
+But there are two considerations that are important as regards
+continuity.
+
+First, it is largely hypothetical. We do not observe any one thing
+continuously, and it is merely a hypothesis to assume that, while we
+are not observing it, it passes through conditions intermediate
+between those in which it is perceived. During uninterrupted
+observation, it is true, continuity is nearly verified; but even here,
+when motions are very rapid, as in the case of explosions, the
+continuity is not actually capable of direct verification. Thus we can
+only say that the sense-data are found to _permit_ a hypothetical
+complement of "sensibilia" such as will preserve continuity, and that
+therefore there _may_ be such a complement. Since, however, we have
+already made such use of hypothetical "sensibilia," we will let this
+point pass, and admit such "sensibilia" as are required to preserve
+continuity.
+
+Secondly, continuity is not a sufficient criterion of material
+identity. It is true that in many cases, such as rocks, mountains,
+tables, chairs, etc., where the appearances change slowly, continuity
+is sufficient, but in other cases, such as the parts of an
+approximately homogeneous fluid, it fails us utterly. We can travel by
+sensibly continuous gradations from any one drop of the sea at any one
+time to any other drop at any other time. We infer the motions of
+sea-water from the effects of the current, but they cannot be inferred
+from direct sensible observation together with the assumption of
+continuity.
+
+The characteristic required in addition to continuity is conformity
+with the laws of dynamics. Starting from what common sense regards as
+persistent things, and making only such modifications as from time to
+time seem reasonable, we arrive at assemblages of "sensibilia" which
+are found to obey certain simple laws, namely those of dynamics. By
+regarding "sensibilia" at different times as belonging to the same
+piece of matter, we are able to define _motion_, which presupposes the
+assumption or construction of something persisting throughout the
+time of the motion. The motions which are regarded as occurring,
+during a period in which all the "sensibilia" and the times of their
+appearance are given, will be different according to the manner in
+which we combine "sensibilia" at different times as belonging to the
+same piece of matter. Thus even when the whole history of the world is
+given in every particular, the question what motions take place is
+still to a certain extent arbitrary even after the assumption of
+continuity. Experience shows that it is possible to determine motions
+in such a way as to satisfy the laws of dynamics, and that this
+determination, roughly and on the whole, is fairly in agreement with
+the common-sense opinions about persistent things. This determination,
+therefore, is adopted, and leads to a criterion by which we can
+determine, sometimes practically, sometimes only theoretically,
+whether two appearances at different times are to be regarded as
+belonging to the same piece of matter. The persistence of all matter
+throughout all time can, I imagine, be secured by definition.
+
+To recommend this conclusion, we must consider what it is that is
+proved by the empirical success of physics. What is proved is that its
+hypotheses, though unverifiable where they go beyond sense-data, are
+at no point in contradiction with sense-data, but, on the contrary,
+are ideally such as to render all sense-data calculable when a
+sufficient collection of "sensibilia" is given. Now physics has found
+it empirically possible to collect sense-data into series, each series
+being regarded as belonging to one "thing," and behaving, with regard
+to the laws of physics, in a way in which series not belonging to one
+thing would in general not behave. If it is to be unambiguous whether
+two appearances belong to the same thing or not, there must be only
+one way of grouping appearances so that the resulting things obey the
+laws of physics. It would be very difficult to prove that this is the
+case, but for our present purposes we may let this point pass, and
+assume that there is only one way. Thus we may lay down the following
+definition: _Physical things are those series of appearances whose
+matter obeys the laws of physics_. That such series exist is an
+empirical fact, which constitutes the verifiability of physics.
+
+
+XII. ILLUSIONS, HALLUCINATIONS, AND DREAMS
+
+It remains to ask how, in our system, we are to find a place for
+sense-data which apparently fail to have the usual connection with the
+world of physics. Such sense-data are of various kinds, requiring
+somewhat different treatment. But all are of the sort that would be
+called "unreal," and therefore, before embarking upon the discussion,
+certain logical remarks must be made upon the conceptions of reality
+and unreality.
+
+Mr. A. Wolf[31] says:
+
+  "The conception of mind as a system of transparent activities is,
+  I think, also untenable because of its failure to account for the
+  very possibility of dreams and hallucinations. It seems impossible
+  to realise how a bare, transparent activity can be directed to
+  what is not there, to apprehend what is not given."
+
+This statement is one which, probably, most people would endorse. But
+it is open to two objections. First it is difficult to see how an
+activity, however un-"transparent," can be directed towards a nothing:
+a term of a relation cannot be a mere nonentity. Secondly, no reason
+is given, and I am convinced that none can be given, for the assertion
+that dream-objects are not "there" and not "given." Let us take the
+second point first.
+
+(1) The belief that dream-objects are not given comes, I think, from
+failure to distinguish, as regards waking life, between the
+sense-datum and the corresponding "thing." In dreams, there is no such
+corresponding "thing" as the dreamer supposes; if, therefore, the
+"thing" were given in waking life, as e.g. Meinong maintains,[32] then
+there would be a difference in respect of givenness between dreams and
+waking life. But if, as we have maintained, what is given is never the
+thing, but merely one of the "sensibilia" which compose the thing,
+then what we apprehend in a dream is just as much given as what we
+apprehend in waking life.
+
+Exactly the same argument applies as to the dream-objects being
+"there." They have their position in the private space of the
+perspective of the dreamer; where they fail is in their correlation
+with other private spaces and therefore with perspective space. But in
+the only sense in which "there" can be a datum, they are "there" just
+as truly as any of the sense-data of waking life.
+
+(2) The conception of "illusion" or "unreality," and the correlative
+conception of "reality," are generally used in a way which embodies
+profound logical confusions. Words that go in pairs, such as "real"
+and "unreal," "existent" and "non-existent," "valid" and "invalid,"
+etc., are all derived from the one fundamental pair, "true" and
+"false." Now "true" and "false" are applicable only--except in
+derivative significations--to _propositions_. Thus wherever the above
+pairs can be significantly applied, we must be dealing either with
+propositions or with such incomplete phrases as only acquire meaning
+when put into a context which, with them, forms a proposition. Thus
+such pairs of words can be applied to _descriptions_,[33] but not to
+proper names: in other words, they have no application whatever to
+data, but only to entities or non-entities described in terms of data.
+
+Let us illustrate by the terms "existence" and "non-existence." Given
+any datum _x_, it is meaningless either to assert or to deny that _x_
+"exists." We might be tempted to say: "Of course _x_ exists, for
+otherwise it could not be a datum." But such a statement is really
+meaningless, although it is significant and true to say "My present
+sense-datum exists," and it may also be true that "_x_ is my present
+sense-datum." The inference from these two propositions to "_x_
+exists" is one which seems irresistible to people unaccustomed to
+logic; yet the apparent proposition inferred is not merely false, but
+strictly meaningless. To say "My present sense-datum exists" is to say
+(roughly): "There is an object of which 'my present sense-datum' is a
+description." But we cannot say: "There is an object of which '_x_' is
+a description," because '_x_' is (in the case we are supposing) a
+name, not a description. Dr. Whitehead and I have explained this point
+fully elsewhere (_loc. cit._) with the help of symbols, without which
+it is hard to understand; I shall not therefore here repeat the
+demonstration of the above propositions, but shall proceed with their
+application to our present problem.
+
+The fact that "existence" is only applicable to descriptions is
+concealed by the use of what are grammatically proper names in a way
+which really transforms them into descriptions. It is, for example, a
+legitimate question whether Homer existed; but here "Homer" means
+"the author of the Homeric poems," and is a description. Similarly we
+may ask whether God exists; but then "God" means "the Supreme Being"
+or "the _ens realissimum_" or whatever other description we may
+prefer. If "God" were a proper name, God would have to be a datum; and
+then no question could arise as to His existence. The distinction
+between existence and other predicates, which Kant obscurely felt, is
+brought to light by the theory of descriptions, and is seen to remove
+"existence" altogether from the fundamental notions of metaphysics.
+
+What has been said about "existence" applies equally to "reality,"
+which may, in fact, be taken as synonymous with "existence."
+Concerning the immediate objects in illusions, hallucinations, and
+dreams, it is meaningless to ask whether they "exist" or are "real."
+There they are, and that ends the matter. But we may legitimately
+inquire as to the existence or reality of "things" or other
+"sensibilia" inferred from such objects. It is the unreality of these
+"things" and other "sensibilia," together with a failure to notice
+that they are not data, which has led to the view that the objects of
+dreams are unreal.
+
+We may now apply these considerations in detail to the stock arguments
+against realism, though what is to be said will be mainly a repetition
+of what others have said before.
+
+(1) We have first the variety of normal appearances, supposed to be
+incompatible. This is the case of the different shapes and colours
+which a given thing presents to different spectators. Locke's water
+which seems both hot and cold belongs to this class of cases. Our
+system of different perspectives fully accounts for these cases, and
+shows that they afford no argument against realism.
+
+(2) We have cases where the correlation between different senses is
+unusual. The bent stick in water belongs here. People say it looks
+bent but is straight: this only means that it is straight to the
+touch, though bent to sight. There is no "illusion," but only a false
+inference, if we think that the stick would feel bent to the touch.
+The stick would look just as bent in a photograph, and, as Mr.
+Gladstone used to say, "the photograph cannot lie."[34] The case of
+seeing double also belongs here, though in this case the cause of the
+unusual correlation is physiological, and would therefore not operate
+in a photograph. It is a mistake to ask whether the "thing" is
+duplicated when we see it double. The "thing" is a whole system of
+"sensibilia," and it is only those visual "sensibilia" which are data
+to the percipient that are duplicated. The phenomenon has a purely
+physiological explanation; indeed, in view of our having two eyes, it
+is in less need of explanation than the single visual sense-datum
+which we normally obtain from the things on which we focus.
+
+(3) We come now to cases like dreams, which may, at the moment of
+dreaming, contain nothing to arouse suspicion, but are condemned on the
+ground of their supposed incompatibility with earlier and later data. Of
+course it often happens that dream-objects fail to behave in the
+accustomed manner: heavy objects fly, solid objects melt, babies turn
+into pigs or undergo even greater changes. But none of these unusual
+occurrences _need_ happen in a dream, and it is not on account of such
+occurrences that dream-objects are called "unreal." It is their lack of
+continuity with the dreamer's past and future that makes him, when he
+wakes, condemn them; and it is their lack of correlation with other
+private worlds that makes others condemn them. Omitting the latter
+ground, our reason for condemning them is that the "things" which we
+infer from them cannot be combined according to the laws of physics with
+the "things" inferred from waking sense-data. This might be used to
+condemn the "things" inferred from the data of dreams. Dream-data are no
+doubt appearances of "things," but not of such "things" as the dreamer
+supposes. I have no wish to combat psychological theories of dreams,
+such as those of the psycho-analysts. But there certainly are cases
+where (whatever psychological causes may contribute) the presence of
+physical causes also is very evident. For instance, a door banging may
+produce a dream of a naval engagement, with images of battleships and
+sea and smoke. The whole dream will be an appearance of the door
+banging, but owing to the peculiar condition of the body (especially the
+brain) during sleep, this appearance is not that expected to be produced
+by a door banging, and thus the dreamer is led to entertain false
+beliefs. But his sense-data are still physical, and are such as a
+completed physics would include and calculate.
+
+(4) The last class of illusions are those which cannot be discovered
+within one person's experience, except through the discovery of
+discrepancies with the experiences of others. Dreams might conceivably
+belong to this class, if they were jointed sufficiently neatly into
+waking life; but the chief instances are recurrent sensory
+hallucinations of the kind that lead to insanity. What makes the
+patient, in such cases, become what others call insane is the fact
+that, within his own experience, there is nothing to show that the
+hallucinatory sense-data do not have the usual kind of connection with
+"sensibilia" in other perspectives. Of course he may learn this
+through testimony, but he probably finds it simpler to suppose that
+the testimony is untrue and that he is being wilfully deceived. There
+is, so far as I can see, no theoretical criterion by which the patient
+can decide, in such a case, between the two equally satisfactory
+hypotheses of his madness and of his friends' mendacity.
+
+From the above instances it would appear that abnormal sense-data, of
+the kind which we regard as deceptive, have intrinsically just the
+same status as any others, but differ as regards their correlations or
+causal connections with other "sensibilia" and with "things." Since
+the usual correlations and connections become part of our unreflective
+expectations, and even seem, except to the psychologist, to form part
+of our data, it comes to be thought, mistakenly, that in such cases
+the data are unreal, whereas they are merely the causes of false
+inferences. The fact that correlations and connections of unusual
+kinds occur adds to the difficulty of inferring things from sense and
+of expressing physics in terms of sense-data. But the unusualness
+would seem to be always physically or physiologically explicable, and
+therefore raises only a complication, not a philosophical objection.
+
+I conclude, therefore, that no valid objection exists to the view
+which regards sense-data as part of the actual substance of the
+physical world, and that, on the other hand, this view is the only one
+which accounts for the empirical verifiability of physics. In the
+present paper, I have given only a rough preliminary sketch. In
+particular, the part played by _time_ in the construction of the
+physical world is, I think, more fundamental than would appear from
+the above account. I should hope that, with further elaboration, the
+part played by unperceived "sensibilia" could be indefinitely
+diminished, probably by invoking the history of a "thing" to eke out
+the inferences derivable from its momentary appearance.
+
+FOOTNOTES:
+
+[29] _Proc. Arist. Soc._, 1909-1910, pp. 191-218.
+
+[30] On this subject, compare _A Theory of Time and Space_, by Mr.
+A.A. Robb (Camb. Univ. Press), which first suggested to me the views
+advocated here, though I have, for present purposes, omitted what is
+most interesting and novel in his theory. Mr. Robb has given a sketch
+of his theory in a pamphlet with the same title (Heffer and Sons,
+Cambridge, 1913).
+
+[31] "Natural Realism and Present Tendencies in Philosophy," _Proc.
+Arist. Soc._, 1908-1909, p. 165.
+
+[32] _Die Erfahrungsgrundlagen unseres Wissens_, p. 28.
+
+[33] Cf. _Principia Mathematica_, Vol. I, * 14, and Introduction,
+Chap. III. For the definition of _existence_, cf. * 14. 02.
+
+[34] Cf. Edwin B. Holt, _The Place of Illusory Experience in a
+Realistic World._ "The New Realism," p. 303, both on this point and as
+regards _seeing double_.
+
+
+
+
+IX
+
+ON THE NOTION OF CAUSE
+
+
+In the following paper I wish, first, to maintain that the word
+"cause" is so inextricably bound up with misleading associations as to
+make its complete extrusion from the philosophical vocabulary
+desirable; secondly, to inquire what principle, if any, is employed in
+science in place of the supposed "law of causality" which philosophers
+imagine to be employed; thirdly, to exhibit certain confusions,
+especially in regard to teleology and determinism, which appear to me
+to be connected with erroneous notions as to causality.
+
+All philosophers, of every school, imagine that causation is one of
+the fundamental axioms or postulates of science, yet, oddly enough, in
+advanced sciences such as gravitational astronomy, the word "cause"
+never occurs. Dr. James Ward, in his _Naturalism and Agnosticism_,
+makes this a ground of complaint against physics: the business of
+those who wish to ascertain the ultimate truth about the world, he
+apparently thinks, should be the discovery of causes, yet physics
+never even seeks them. To me it seems that philosophy ought not to
+assume such legislative functions, and that the reason why physics has
+ceased to look for causes is that, in fact, there are no such things.
+The law of causality, I believe, like much that passes muster among
+philosophers, is a relic of a bygone age, surviving, like the
+monarchy, only because it is erroneously supposed to do no harm. In
+order to find out what philosophers commonly understand by "cause," I
+consulted Baldwin's _Dictionary_, and was rewarded beyond my
+expectations, for I found the following three mutually incompatible
+definitions:--
+
+  "CAUSALITY. (1) The necessary connection of events in the
+     time-series....
+
+  "CAUSE (notion of). Whatever may be included in the thought or
+     perception of a process as taking place in consequence of
+     another process....
+
+  "CAUSE AND EFFECT. (1) Cause and effect ... are correlative terms
+     denoting any two distinguishable things, phases, or aspects of
+     reality, which are so related to each other that whenever the
+     first ceases to exist the second comes into existence
+     immediately after, and whenever the second comes into existence
+     the first has ceased to exist immediately before."
+
+Let us consider these three definitions in turn. The first, obviously,
+is unintelligible without a definition of "necessary." Under this
+head, Baldwin's _Dictionary_ gives the following:--
+
+  "NECESSARY. That is necessary which not only is true, but would
+     be true under all circumstances. Something more than brute
+     compulsion is, therefore, involved in the conception; there is
+     a general law under which the thing takes place."
+
+The notion of cause is so intimately connected with that of necessity
+that it will be no digression to linger over the above definition,
+with a view to discovering, if possible, _some_ meaning of which it is
+capable; for, as it stands, it is very far from having any definite
+signification.
+
+The first point to notice is that, if any meaning is to be given to
+the phrase "would be true under all circumstances," the subject of it
+must be a propositional function, not a proposition.[35] A
+proposition is simply true or false, and that ends the matter: there
+can be no question of "circumstances." "Charles I's head was cut off"
+is just as true in summer as in winter, on Sundays as on Mondays. Thus
+when it is worth saying that something "would be true under all
+circumstances," the something in question must be a propositional
+function, i.e. an expression containing a variable, and becoming a
+proposition when a value is assigned to the variable; the varying
+"circumstances" alluded to are then the different values of which the
+variable is capable. Thus if "necessary" means "what is true under all
+circumstances," then "if _x_ is a man, _x_ is mortal" is necessary,
+because it is true for any possible value of _x_. Thus we should be
+led to the following definition:--
+
+  "NECESSARY is a predicate of a propositional function, meaning
+     that it is true for all possible values of its argument or
+     arguments."
+
+Unfortunately, however, the definition in Baldwin's _Dictionary_ says
+that what is necessary is not only "true under all circumstances" but
+is also "true." Now these two are incompatible. Only propositions can
+be "true," and only propositional functions can be "true under all
+circumstances." Hence the definition as it stands is nonsense. What is
+meant seems to be this: "A proposition is necessary when it is a value
+of a propositional function which is true under all circumstances,
+i.e. for all values of its argument or arguments." But if we adopt
+this definition, the same proposition will be necessary or contingent
+according as we choose one or other of its terms as the argument to
+our propositional function. For example, "if Socrates is a man,
+Socrates is mortal," is necessary if Socrates is chosen as argument,
+but not if _man_ or _mortal_ is chosen. Again, "if Socrates is a man,
+Plato is mortal," will be necessary if either Socrates or _man_ is
+chosen as argument, but not if Plato or _mortal_ is chosen. However,
+this difficulty can be overcome by specifying the constituent which is
+to be regarded as argument, and we thus arrive at the following
+definition:
+
+"A proposition is _necessary_ with respect to a given constituent if
+it remains true when that constituent is altered in any way compatible
+with the proposition remaining significant."
+
+We may now apply this definition to the definition of causality quoted
+above. It is obvious that the argument must be the time at which the
+earlier event occurs. Thus an instance of causality will be such as:
+"If the event [Math: e_{1}] occurs at the time [Math: t_{1}], it will
+be followed by the event [Math: e_{2}]." This proposition is intended
+to be necessary with respect to [Math: t_{1}], i.e. to remain true
+however [Math: t_{1}] may be varied. Causality, as a universal law,
+will then be the following: "Given any event [Math: t_{1}], there is
+an event [Math: e_{2}] such that, whenever [Math: t_{1}] occurs,
+[Math: e_{2}] occurs later." But before this can be considered
+precise, we must specify how much later [Math: e_{2}] is to occur.
+Thus the principle becomes:--
+
+"Given any event [Math: e_{1}], there is an event [Math: e_{2}] and a
+time-interval Ï„ such that, whenever [Math: e_{1}] occurs, [Math:
+e_{2}] follows after an interval Ï„."
+
+I am not concerned as yet to consider whether this law is true or
+false. For the present, I am merely concerned to discover what the law
+of causality is supposed to be. I pass, therefore, to the other
+definitions quoted above.
+
+The second definition need not detain us long, for two reasons. First,
+because it is psychological: not the "thought or perception" of a
+process, but the process itself, must be what concerns us in
+considering causality. Secondly, because it is circular: in speaking
+of a process as "taking place in consequence of" another process, it
+introduces the very notion of cause which was to be defined.
+
+The third definition is by far the most precise; indeed as regards
+clearness it leaves nothing to be desired. But a great difficulty is
+caused by the temporal contiguity of cause and effect which the
+definition asserts. No two instants are contiguous, since the
+time-series is compact; hence either the cause or the effect or both
+must, if the definition is correct, endure for a finite time; indeed,
+by the wording of the definition it is plain that both are assumed to
+endure for a finite time. But then we are faced with a dilemma: if the
+cause is a process involving change within itself, we shall require
+(if causality is universal) causal relations between its earlier and
+later parts; moreover, it would seem that only the later parts can be
+relevant to the effect, since the earlier parts are not contiguous to
+the effect, and therefore (by the definition) cannot influence the
+effect. Thus we shall be led to diminish the duration of the cause
+without limit, and however much we may diminish it, there will still
+remain an earlier part which might be altered without altering the
+effect, so that the true cause, as defined, will not have been
+reached, for it will be observed that the definition excludes
+plurality of causes. If, on the other hand, the cause is purely
+static, involving no change within itself, then, in the first place,
+no such cause is to be found in nature, and in the second place, it
+seems strange--too strange to be accepted, in spite of bare logical
+possibility--that the cause, after existing placidly for some time,
+should suddenly explode into the effect, when it might just as well
+have done so at any earlier time, or have gone on unchanged without
+producing its effect. This dilemma, therefore, is fatal to the view
+that cause and effect can be contiguous in time; if there are causes
+and effects, they must be separated by a finite time-interval Ï„, as
+was assumed in the above interpretation of the first definition.
+
+What is essentially the same statement of the law of causality as the
+one elicited above from the first of Baldwin's definitions is given by
+other philosophers. Thus John Stuart Mill says:--
+
+"The Law of Causation, the recognition of which is the main pillar of
+inductive science, is but the familiar truth, that invariability of
+succession is found by observation to obtain between every fact in
+nature and some other fact which has preceded it."[36]
+
+And Bergson, who has rightly perceived that the law as stated by
+philosophers is worthless, nevertheless continues to suppose that it
+is used in science. Thus he says:--
+
+"Now, it is argued, this law [the law of causality] means that every
+phenomenon is determined by its conditions, or, in other words, that
+the same causes produce the same effects."[37]
+
+And again:--
+
+"We perceive physical phenomena, and these phenomena obey laws. This
+means: (1) That phenomena _a_, _b_, _c_, _d_, previously perceived,
+can occur again in the same shape; (2) that a certain phenomenon P,
+which appeared after the conditions _a_, _b_, _c_, _d_, and after
+these conditions only, will not fail to recur as soon as the same
+conditions are again present."[38]
+
+A great part of Bergson's attack on science rests on the assumption
+that it employs this principle. In fact, it employs no such principle,
+but philosophers--even Bergson--are too apt to take their views on
+science from each other, not from science. As to what the principle
+is, there is a fair consensus among philosophers of different schools.
+There are, however, a number of difficulties which at once arise. I
+omit the question of plurality of causes for the present, since other
+graver questions have to be considered. Two of these, which are forced
+on our attention by the above statement of the law, are the
+following:--
+
+  (1) What is meant by an "event"?
+
+  (2) How long may the time-interval be between cause and effect?
+
+(1) An "event," in the statement of the law, is obviously intended to
+be something that is likely to recur since otherwise the law becomes
+trivial. It follows that an "event" is not a particular, but some
+universal of which there may be many instances. It follows also that
+an "event" must be something short of the whole state of the universe,
+since it is highly improbable that this will recur. What is meant by
+an "event" is something like striking a match, or dropping a penny
+into the slot of an automatic machine. If such an event is to recur,
+it must not be defined too narrowly: we must not state with what
+degree of force the match is to be struck, nor what is to be the
+temperature of the penny. For if such considerations were relevant,
+our "event" would occur at most once, and the law would cease to give
+information. An "event," then, is a universal defined sufficiently
+widely to admit of many particular occurrences in time being instances
+of it.
+
+(2) The next question concerns the time-interval. Philosophers, no
+doubt, think of cause and effect as contiguous in time, but this, for
+reasons already given, is impossible. Hence, since there are no
+infinitesimal time-intervals, there must be some finite lapse of time
+Ï„ between cause and effect. This, however, at once raises insuperable
+difficulties. However short we make the interval Ï„, something may
+happen during this interval which prevents the expected result. I put
+my penny in the slot, but before I can draw out my ticket there is an
+earthquake which upsets the machine and my calculations. In order to
+be sure of the expected effect, we must know that there is nothing in
+the environment to interfere with it. But this means that the supposed
+cause is not, by itself, adequate to insure the effect. And as soon as
+we include the environment, the probability of repetition is
+diminished, until at last, when the whole environment is included, the
+probability of repetition becomes almost _nil_.
+
+In spite of these difficulties, it must, of course, be admitted that
+many fairly dependable regularities of sequence occur in daily life.
+It is these regularities that have suggested the supposed law of
+causality; where they are found to fail, it is thought that a better
+formulation could have been found which would have never failed. I am
+far from denying that there may be such sequences which in fact never
+do fail. It may be that there will never be an exception to the rule
+that when a stone of more than a certain mass, moving with more than a
+certain velocity, comes in contact with a pane of glass of less than
+a certain thickness, the glass breaks. I also do not deny that the
+observation of such regularities, even when they are not without
+exceptions, is useful in the infancy of a science: the observation
+that unsupported bodies in air usually fall was a stage on the way to
+the law of gravitation. What I deny is that science assumes the
+existence of invariable uniformities of sequence of this kind, or that
+it aims at discovering them. All such uniformities, as we saw, depend
+upon a certain vagueness in the definition of the "events." That
+bodies fall is a vague qualitative statement; science wishes to know
+how fast they fall. This depends upon the shape of the bodies and the
+density of the air. It is true that there is more nearly uniformity
+when they fall in a vacuum; so far as Galileo could observe, the
+uniformity is then complete. But later it appeared that even there the
+latitude made a difference, and the altitude. Theoretically, the
+position of the sun and moon must make a difference. In short, every
+advance in a science takes us farther away from the crude uniformities
+which are first observed, into greater differentiation of antecedent
+and consequent, and into a continually wider circle of antecedents
+recognised as relevant.
+
+The principle "same cause, same effect," which philosophers imagine to
+be vital to science, is therefore utterly otiose. As soon as the
+antecedents have been given sufficiently fully to enable the
+consequent to be calculated with some exactitude, the antecedents have
+become so complicated that it is very unlikely they will ever recur.
+Hence, if this were the principle involved, science would remain
+utterly sterile.
+
+The importance of these considerations lies partly in the fact that
+they lead to a more correct account of scientific procedure, partly in
+the fact that they remove the analogy with human volition which makes
+the conception of cause such a fruitful source of fallacies. The
+latter point will become clearer by the help of some illustrations.
+For this purpose I shall consider a few maxims which have played a
+great part in the history of philosophy.
+
+(1) "Cause and effect must more or less resemble each other." This
+principle was prominent in the philosophy of occasionalism, and is
+still by no means extinct. It is still often thought, for example,
+that mind could not have grown up in a universe which previously
+contained nothing mental, and one ground for this belief is that
+matter is too dissimilar from mind to have been able to cause it. Or,
+more particularly, what are termed the nobler parts of our nature are
+supposed to be inexplicable, unless the universe always contained
+something at least equally noble which could cause them. All such
+views seem to depend upon assuming some unduly simplified law of
+causality; for, in any legitimate sense of "cause" and "effect,"
+science seems to show that they are usually very widely dissimilar,
+the "cause" being, in fact, two states of the whole universe, and the
+"effect" some particular event.
+
+(2) "Cause is analogous to volition, since there must be an
+intelligible _nexus_ between cause and effect." This maxim is, I
+think, often unconsciously in the imaginations of philosophers who
+would reject it when explicitly stated. It is probably operative in
+the view we have just been considering, that mind could not have
+resulted from a purely material world. I do not profess to know what
+is meant by "intelligible"; it seems to mean "familiar to
+imagination." Nothing is less "intelligible," in any other sense, than
+the connection between an act of will and its fulfilment. But
+obviously the sort of nexus desired between cause and effect is such
+as could only hold between the "events" which the supposed law of
+causality contemplates; the laws which replace causality in such a
+science as physics leave no room for any two events between which a
+nexus could be sought.
+
+(3) "The cause _compels_ the effect in some sense in which the effect
+does not compel the cause." This belief seems largely operative in the
+dislike of determinism; but, as a matter of fact, it is connected with
+our second maxim, and falls as soon as that is abandoned. We may
+define "compulsion" as follows: "Any set of circumstances is said to
+compel A when A desires to do something which the circumstances
+prevent, or to abstain from something which the circumstances cause."
+This presupposes that some meaning has been found for the word
+"cause"--a point to which I shall return later. What I want to make
+clear at present is that compulsion is a very complex notion,
+involving thwarted desire. So long as a person does what he wishes to
+do, there is no compulsion, however much his wishes may be calculable
+by the help of earlier events. And where desire does not come in,
+there can be no question of compulsion. Hence it is, in general,
+misleading to regard the cause as compelling the effect.
+
+A vaguer form of the same maxim substitutes the word "determine" for
+the word "compel"; we are told that the cause _determines_ the effect
+in a sense in which the effect does not _determine_ the cause. It is
+not quite clear what is meant by "determining"; the only precise
+sense, so far as I know, is that of a function or one-many relation.
+If we admit plurality of causes, but not of effects, that is, if we
+suppose that, given the cause, the effect must be such and such, but,
+given the effect, the cause may have been one of many alternatives,
+then we may say that the cause determines the effect, but not the
+effect the cause. Plurality of causes, however, results only from
+conceiving the effect vaguely and narrowly and the cause precisely and
+widely. Many antecedents may "cause" a man's death, because his death
+is vague and narrow. But if we adopt the opposite course, taking as
+the "cause" the drinking of a dose of arsenic, and as the "effect" the
+whole state of the world five minutes later, we shall have plurality
+of effects instead of plurality of causes. Thus the supposed lack of
+symmetry between "cause" and "effect" is illusory.
+
+(4) "A cause cannot operate when it has ceased to exist, because what
+has ceased to exist is nothing." This is a common maxim, and a still
+more common unexpressed prejudice. It has, I fancy, a good deal to do
+with the attractiveness of Bergson's "_durée_": since the past has
+effects now, it must still exist in some sense. The mistake in this
+maxim consists in the supposition that causes "operate" at all. A
+volition "operates" when what it wills takes place; but nothing can
+operate except a volition. The belief that causes "operate" results
+from assimilating them, consciously or unconsciously, to volitions. We
+have already seen that, if there are causes at all, they must be
+separated by a finite interval of time from their effects, and thus
+cause their effects after they have ceased to exist.
+
+It may be objected to the above definition of a volition "operating"
+that it only operates when it "causes" what it wills, not when it
+merely happens to be followed by what it wills. This certainly
+represents the usual view of what is meant by a volition "operating,"
+but as it involves the very view of causation which we are engaged in
+combating, it is not open to us as a definition. We may say that a
+volition "operates" when there is some law in virtue of which a
+similar volition in rather similar circumstances will usually be
+followed by what it wills. But this is a vague conception, and
+introduces ideas which we have not yet considered. What is chiefly
+important to notice is that the usual notion of "operating" is not
+open to us if we reject, as I contend that we should, the usual notion
+of causation.
+
+(5) "A cause cannot operate except where it is." This maxim is very
+widespread; it was urged against Newton, and has remained a source of
+prejudice against "action at a distance." In philosophy it has led to
+a denial of transient action, and thence to monism or Leibnizian
+monadism. Like the analogous maxim concerning temporal contiguity, it
+rests upon the assumption that causes "operate," i.e. that they are in
+some obscure way analogous to volitions. And, as in the case of
+temporal contiguity, the inferences drawn from this maxim are wholly
+groundless.
+
+I return now to the question, What law or laws can be found to take
+the place of the supposed law of causality?
+
+First, without passing beyond such uniformities of sequence as are
+contemplated by the traditional law, we may admit that, if any such
+sequence has been observed in a great many cases, and has never been
+found to fail, there is an inductive probability that it will be found
+to hold in future cases. If stones have hitherto been found to break
+windows, it is probable that they will continue to do so. This, of
+course, assumes the inductive principle, of which the truth may
+reasonably be questioned; but as this principle is not our present
+concern, I shall in this discussion treat it as indubitable. We may
+then say, in the case of any such frequently observed sequence, that
+the earlier event is the _cause_ and the later event the _effect_.
+
+Several considerations, however, make such special sequences very
+different from the traditional relation of cause and effect. In the
+first place, the sequence, in any hitherto unobserved instance, is no
+more than probable, whereas the relation of cause and effect was
+supposed to be necessary. I do not mean by this merely that we are not
+sure of having discovered a true case of cause and effect; I mean
+that, even when we have a case of cause and effect in our present
+sense, all that is meant is that on grounds of observation, it is
+probable that when one occurs the other will also occur. Thus in our
+present sense, A may be the cause of B even if there actually are
+cases where B does not follow A. Striking a match will be the cause of
+its igniting, in spite of the fact that some matches are damp and fail
+to ignite.
+
+In the second place, it will not be assumed that _every_ event has
+some antecedent which is its cause in this sense; we shall only
+believe in causal sequences where we find them, without any
+presumption that they always are to be found.
+
+In the third place, _any_ case of sufficiently frequent sequence will
+be causal in our present sense; for example, we shall not refuse to
+say that night is the cause of day. Our repugnance to saying this
+arises from the ease with which we can imagine the sequence to fail,
+but owing to the fact that cause and effect must be separated by a
+finite interval of time, _any_ such sequence _might_ fail through the
+interposition of other circumstances in the interval. Mill, discussing
+this instance of night and day, says:--
+
+"It is necessary to our using the word cause, that we should believe
+not only that the antecedent always _has_ been followed by the
+consequent, but that as long as the present constitution of things
+endures, it always _will_ be so."[39]
+
+In this sense, we shall have to give up the hope of finding causal
+laws such as Mill contemplated; any causal sequence which we have
+observed may at any moment be falsified without a falsification of any
+laws of the kind that the more advanced sciences aim at establishing.
+
+In the fourth place, such laws of probable sequence, though useful in
+daily life and in the infancy of a science, tend to be displaced by
+quite different laws as soon as a science is successful. The law of
+gravitation will illustrate what occurs in any advanced science. In
+the motions of mutually gravitating bodies, there is nothing that can
+be called a cause, and nothing that can be called an effect; there is
+merely a formula. Certain differential equations can be found, which
+hold at every instant for every particle of the system, and which,
+given the configuration and velocities at one instant, or the
+configurations at two instants, render the configuration at any other
+earlier or later instant theoretically calculable. That is to say, the
+configuration at any instant is a function of that instant and the
+configurations at two given instants. This statement holds throughout
+physics, and not only in the special case of gravitation. But there is
+nothing that could be properly called "cause" and nothing that could
+be properly called "effect" in such a system.
+
+No doubt the reason why the old "law of causality" has so long
+continued to pervade the books of philosophers is simply that the idea
+of a function is unfamiliar to most of them, and therefore they seek
+an unduly simplified statement. There is no question of repetitions of
+the "same" cause producing the "same" effect; it is not in any
+sameness of causes and effects that the constancy of scientific law
+consists, but in sameness of relations. And even "sameness of
+relations" is too simple a phrase; "sameness of differential
+equations" is the only correct phrase. It is impossible to state this
+accurately in non-mathematical language; the nearest approach would be
+as follows: "There is a constant relation between the state of the
+universe at any instant and the rate of change in the rate at which
+any part of the universe is changing at that instant, and this
+relation is many-one, i.e. such that the rate of change in the rate of
+change is determinate when the state of the universe is given." If the
+"law of causality" is to be something actually discoverable in the
+practice of science, the above proposition has a better right to the
+name than any "law of causality" to be found in the books of
+philosophers.
+
+In regard to the above principle, several observations must be made--
+
+(1) No one can pretend that the above principle is _a priori_ or
+self-evident or a "necessity of thought." Nor is it, in any sense, a
+premiss of science: it is an empirical generalisation from a number of
+laws which are themselves empirical generalisations.
+
+(2) The law makes no difference between past and future: the future
+"determines" the past in exactly the same sense in which the past
+"determines" the future. The word "determine," here, has a purely
+logical significance: a certain number of variables "determine"
+another variable if that other variable is a function of them.
+
+(3) The law will not be empirically verifiable unless the course of
+events within some sufficiently small volume will be approximately
+the same in any two states of the universe which only differ in regard
+to what is at a considerable distance from the small volume in
+question. For example, motions of planets in the solar system must be
+approximately the same however the fixed stars may be distributed,
+provided that all the fixed stars are very much farther from the sun
+than the planets are. If gravitation varied directly as the distance,
+so that the most remote stars made the most difference to the motions
+of the planets, the world might be just as regular and just as much
+subject to mathematical laws as it is at present, but we could never
+discover the fact.
+
+(4) Although the old "law of causality" is not assumed by science,
+something which we may call the "uniformity of nature" is assumed, or
+rather is accepted on inductive grounds. The uniformity of nature does
+not assert the trivial principle "same cause, same effect," but the
+principle of the permanence of laws. That is to say, when a law
+exhibiting, e.g. an acceleration as a function of the configuration
+has been found to hold throughout the observable past, it is expected
+that it will continue to hold in the future, or that, if it does not
+itself hold, there is some other law, agreeing with the supposed law
+as regards the past, which will hold for the future. The ground of
+this principle is simply the inductive ground that it has been found
+to be true in very many instances; hence the principle cannot be
+considered certain, but only probable to a degree which cannot be
+accurately estimated.
+
+The uniformity of nature, in the above sense, although it is assumed
+in the practice of science, must not, in its generality, be regarded
+as a kind of major premiss, without which all scientific reasoning
+would be in error. The assumption that _all_ laws of nature are
+permanent has, of course, less probability than the assumption that
+this or that particular law is permanent; and the assumption that a
+particular law is permanent for all time has less probability than the
+assumption that it will be valid up to such and such a date. Science,
+in any given case, will assume what the case requires, but no more. In
+constructing the _Nautical Almanac_ for 1915 it will assume that the
+law of gravitation will remain true up to the end of that year; but it
+will make no assumption as to 1916 until it comes to the next volume
+of the almanac. This procedure is, of course, dictated by the fact
+that the uniformity of nature is not known _a priori_, but is an
+empirical generalisation, like "all men are mortal." In all such
+cases, it is better to argue immediately from the given particular
+instances to the new instance, than to argue by way of a major
+premiss; the conclusion is only probable in either case, but acquires
+a higher probability by the former method than by the latter.
+
+In all science we have to distinguish two sorts of laws: first, those
+that are empirically verifiable but probably only approximate;
+secondly, those that are not verifiable, but may be exact. The law of
+gravitation, for example, in its applications to the solar system, is
+only empirically verifiable when it is assumed that matter outside the
+solar system may be ignored for such purposes; we believe this to be
+only approximately true, but we cannot empirically verify the law of
+universal gravitation which we believe to be exact. This point is very
+important in connection with what we may call "relatively isolated
+systems." These may be defined as follows:--
+
+A system relatively isolated during a given period is one which,
+within some assignable margin of error, will behave in the same way
+throughout that period, however the rest of the universe may be
+constituted.
+
+A system may be called "practically isolated" during a given period
+if, although there _might_ be states of the rest of the universe which
+would produce more than the assigned margin of error, there is reason
+to believe that such states do not in fact occur.
+
+Strictly speaking, we ought to specify the respect in which the system
+is relatively isolated. For example, the earth is relatively isolated
+as regards falling bodies, but not as regards tides; it is
+_practically_ isolated as regards economic phenomena, although, if
+Jevons' sunspot theory of commercial crises had been true, it would
+not have been even practically isolated in this respect.
+
+It will be observed that we cannot prove in advance that a system is
+isolated. This will be inferred from the observed fact that
+approximate uniformities can be stated for this system alone. If the
+complete laws for the whole universe were known, the isolation of a
+system could be deduced from them; assuming, for example, the law of
+universal gravitation, the practical isolation of the solar system in
+this respect can be deduced by the help of the fact that there is very
+little matter in its neighbourhood. But it should be observed that
+isolated systems are only important as providing a possibility of
+_discovering_ scientific laws; they have no theoretical importance in
+the finished structure of a science.
+
+The case where one event A is said to "cause" another event B, which
+philosophers take as fundamental, is really only the most simplified
+instance of a practically isolated system. It may happen that, as a
+result of general scientific laws, whenever A occurs throughout a
+certain period, it is followed by B; in that case, A and B form a
+system which is practically isolated throughout that period. It is,
+however, to be regarded as a piece of good fortune if this occurs; it
+will always be due to special circumstances, and would not have been
+true if the rest of the universe had been different though subject to
+the same laws.
+
+The essential function which causality has been supposed to perform is
+the possibility of inferring the future from the past, or, more
+generally, events at any time from events at certain assigned times.
+Any system in which such inference is possible may be called a
+"deterministic" system. We may define a deterministic system as
+follows:--
+
+  A system is said to be "deterministic" when, given certain data,
+  [Math: e_{1}, e_{2}, ..., e_{n}, at times t_{1}, t_{2}, ...,
+  t_{n}] respectively, concerning this system, if [Math: E_{t}] is
+  the state of the system at any time _t_, there is a functional
+  relation of the form
+
+[Math: E_{t} = f (e_{1}, t_{1}, e_{2}, t_{2}, ..., e_{n}, t_{n}, t)]. (A)
+
+  The system will be "deterministic throughout a given period" if
+  _t_, in the above formula, may be any time within that period,
+  though outside that period the formula may be no longer true. If
+  the universe, as a whole, is such a system, determinism is true of
+  the universe; if not, not. A system which is part of a
+  deterministic system I shall call "determined"; one which is not
+  part of any such system I shall call "capricious."
+
+The events [Math: e_{1}, e_{2}, ..., e_{n}] I shall call "determinants"
+of the system. It is to be observed that a system which has one set of
+determinants will in general have many. In the case of the motions of
+the planets, for example, the configurations of the solar system at any
+two given times will be determinants.
+
+We may take another illustration from the hypothesis of
+psycho-physical parallelism. Let us assume, for the purposes of this
+illustration, that to a given state of brain a given state of mind
+always corresponds, and vice versa, i.e. that there is a one-one
+relation between them, so that each is a function of the other. We may
+also assume, what is practically certain, that to a given state of a
+certain brain a given state of the whole material universe
+corresponds, since it is highly improbable that a given brain is ever
+twice in exactly the same state. Hence there will be a one-one
+relation between the state of a given person's mind and the state of
+the whole material universe. It follows that, if _n_ states of the
+material universe are determinants of the material universe, then _n_
+states of a given man's mind are determinants of the whole material
+and mental universe--assuming, that is to say, that psycho-physical
+parallelism is true.
+
+The above illustration is important in connection with a certain
+confusion which seems to have beset those who have philosophised on
+the relation of mind and matter. It is often thought that, if the
+state of the mind is determinate when the state of the brain is given,
+and if the material world forms a deterministic system, then mind is
+"subject" to matter in some sense in which matter is not "subject" to
+mind. But if the state of the brain is also determinate when the state
+of the mind is given, it must be exactly as true to regard matter as
+subject to mind as it would be to regard mind as subject to matter. We
+could, theoretically, work out the history of mind without ever
+mentioning matter, and then, at the end, deduce that matter must
+meanwhile have gone through the corresponding history. It is true that
+if the relation of brain to mind were many-one, not one-one, there
+would be a one-sided dependence of mind on brain, while conversely, if
+the relation were one-many, as Bergson supposes, there would be a
+one-aided dependence of brain on mind. But the dependence involved is,
+in any case, only logical; it does not mean that we shall be
+compelled to do things we desire not to do, which is what people
+instinctively imagine it to mean.
+
+As another illustration we may take the case of mechanism and
+teleology. A system may be defined as "mechanical" when it has a set
+of determinants that are purely material, such as the positions of
+certain pieces of matter at certain times. It is an open question
+whether the world of mind and matter, as we know it, is a mechanical
+system or not; let us suppose, for the sake of argument, that it is a
+mechanical system. This supposition--so I contend--throws no light
+whatever on the question whether the universe is or is not a
+"teleological" system. It is difficult to define accurately what is
+meant by a "teleological" system, but the argument is not much
+affected by the particular definition we adopt. Broadly, a
+teleological system is one in which purposes are realised, i.e. in
+which certain desires--those that are deeper or nobler or more
+fundamental or more universal or what not--are followed by their
+realisation. Now the fact--if it be a fact--that the universe is
+mechanical has no bearing whatever on the question whether it is
+teleological in the above sense. There might be a mechanical system in
+which all wishes were realised, and there might be one in which all
+wishes were thwarted. The question whether, or how far, our actual
+world is teleological, cannot, therefore, be settled by proving that
+it is mechanical, and the desire that it should be teleological is no
+ground for wishing it to be not mechanical.
+
+There is, in all these questions, a very great difficulty in avoiding
+confusion between what we can infer and what is in fact determined.
+Let us consider, for a moment, the various senses in which the future
+may be "determined." There is one sense--and a very important one--in
+which it is determined quite independently of scientific laws, namely,
+the sense that it will be what it will be. We all regard the past as
+determined simply by the fact that it has happened; but for the
+accident that memory works backward and not forward, we should regard
+the future as equally determined by the fact that it will happen.
+"But," we are told, "you cannot alter the past, while you can to some
+extent alter the future." This view seems to me to rest upon just
+those errors in regard to causation which it has been my object to
+remove. You cannot make the past other than it was--true, but this is
+a mere application of the law of contradiction. If you already know
+what the past was, obviously it is useless to wish it different. But
+also you cannot make the future other than it will be; this again is
+an application of the law of contradiction. And if you happen to know
+the future--e.g. in the case of a forthcoming eclipse--it is just as
+useless to wish it different as to wish the past different. "But," it
+will be rejoined, "our wishes can _cause_ the future, sometimes, to be
+different from what it would be if they did not exist, and they can
+have no such effect upon the past." This, again, is a mere tautology.
+An effect being _defined_ as something subsequent to its cause,
+obviously we can have no _effect_ upon the past. But that does not
+mean that the past would not have been different if our present wishes
+had been different. Obviously, our present wishes are conditioned by
+the past, and therefore could not have been different unless the past
+had been different; therefore, if our present wishes were different,
+the past would be different. Of course, the past cannot be different
+from what it was, but no more can our present wishes be different from
+what they are; this again is merely the law of contradiction. The
+facts seem to be merely (1) that wishing generally depends upon
+ignorance, and is therefore commoner in regard to the future than in
+regard to the past; (2) that where a wish concerns the future, it and
+its realisation very often form a "practically independent system,"
+i.e. many wishes regarding the future are realised. But there seems no
+doubt that the main difference in our feelings arises from the
+accidental fact that the past but not the future can be known by
+memory.
+
+Although the sense of "determined" in which the future is determined
+by the mere fact that it will be what it will be is sufficient (at
+least so it seems to me) to refute some opponents of determinism,
+notably M. Bergson and the pragmatists, yet it is not what most people
+have in mind when they speak of the future as determined. What they
+have in mind is a formula by means of which the future can be
+exhibited, and at least theoretically calculated, as a function of the
+past. But at this point we meet with a great difficulty, which besets
+what has been said above about deterministic systems, as well as what
+is said by others.
+
+If formulæ of any degree of complexity, however great, are admitted,
+it would seem that any system, whose state at a given moment is a
+function of certain measurable quantities, must be a deterministic
+system. Let us consider, in illustration, a single material particle,
+whose co-ordinates at time _t_ are [Math: x_{t}, y_{t}, z_{t}]. Then,
+however, the particle moves, there must be, theoretically, functions
+[Math: f_{1}, f_{2}, f_{3}], such that
+
+[Math: x_{t} = f_{t}(t), y_{t} = f_{2}(t), z_{t} = f_{3}(t).]
+
+It follows that, theoretically, the whole state of the material
+universe at time _t_ must be capable of being exhibited as a function
+of _t_. Hence our universe will be deterministic in the sense defined
+above. But if this be true, no information is conveyed about the
+universe in stating that it is deterministic. It is true that the
+formulæ involved may be of strictly infinite complexity, and therefore
+not practically capable of being written down or apprehended. But
+except from the point of view of our knowledge, this might seem to be
+a detail: in itself, if the above considerations are sound, the
+material universe _must_ be deterministic, _must_ be subject to laws.
+
+This, however, is plainly not what was intended. The difference
+between this view and the view intended may be seen as follows. Given
+some formula which fits the facts hitherto--say the law of
+gravitation--there will be an infinite number of other formulæ, not
+empirically distinguishable from it in the past, but diverging from it
+more and more in the future. Hence, even assuming that there are
+persistent laws, we shall have no reason for assuming that the law of
+the inverse square will hold in future; it may be some other hitherto
+indistinguishable law that will hold. We cannot say that _every_ law
+which has held hitherto must hold in the future, because past facts
+which obey one law will also obey others, hitherto indistinguishable
+but diverging in future. Hence there must, at every moment, be laws
+hitherto unbroken which are now broken for the first time. What
+science does, in fact, is to select the _simplest_ formula that will
+fit the facts. But this, quite obviously, is merely a methodological
+precept, not a law of Nature. If the simplest formula ceases, after a
+time, to be applicable, the simplest formula that remains applicable
+is selected, and science has no sense that an axiom has been
+falsified. We are thus left with the brute fact that, in many
+departments of science, quite simple laws have hitherto been found to
+hold. This fact cannot be regarded as having any _a priori_ ground,
+nor can it be used to support inductively the opinion that the same
+laws will continue; for at every moment laws hitherto true are being
+falsified, though in the advanced sciences these laws are less simple
+than those that have remained true. Moreover it would be fallacious to
+argue inductively from the state of the advanced sciences to the
+future state of the others, for it may well be that the advanced
+sciences are advanced simply because, hitherto, their subject-matter
+has obeyed simple and easily ascertainable laws, while the
+subject-matter of other sciences has not done so.
+
+The difficulty we have been considering seems to be met partly, if not
+wholly, by the principle that the _time_ must not enter explicitly
+into our formulæ. All mechanical laws exhibit acceleration as a
+function of configuration, not of configuration and time jointly; and
+this principle of the irrelevance of the time may be extended to all
+scientific laws. In fact we might interpret the "uniformity of nature"
+as meaning just this, that no scientific law involves the time as an
+argument, unless, of course, it is given in an integrated form, in
+which case _lapse_ of time, though not absolute time, may appear in
+our formulæ. Whether this consideration suffices to overcome our
+difficulty completely, I do not know; but in any case it does much to
+diminish it.
+
+It will serve to illustrate what has been said if we apply it to the
+question of free will.
+
+(1) Determinism in regard to the will is the doctrine that our
+volitions belong to some deterministic system, i.e. are "determined"
+in the sense defined above. Whether this doctrine is true or false, is
+a mere question of fact; no _a priori_ considerations (if our previous
+discussions have been correct) can exist on either side. On the one
+hand, there is no _a priori_ category of causality, but merely certain
+observed uniformities. As a matter of fact, there are observed
+uniformities in regard to volitions; thus there is some empirical
+evidence that volitions are determined. But it would be very rash to
+maintain that the evidence is overwhelming, and it is quite possible
+that some volitions, as well as some other things, are not determined,
+except in the sense in which we found that everything must be
+determined.
+
+(2) But, on the other hand, the subjective sense of freedom, sometimes
+alleged against determinism, has no bearing on the question whatever.
+The view that it has a bearing rests upon the belief that causes
+compel their effects, or that nature enforces obedience to its laws as
+governments do. These are mere anthropomorphic superstitions, due to
+assimilation of causes with volitions and of natural laws with human
+edicts. We feel that our will is not compelled, but that only means
+that it is not other than we choose it to be. It is one of the
+demerits of the traditional theory of causality that it has created an
+artificial opposition between determinism and the freedom of which we
+are introspectively conscious.
+
+(3) Besides the general question whether volitions are determined,
+there is the further question whether they are _mechanically_
+determined, i.e. whether they are part of what was above defined as a
+mechanical system. This is the question whether they form part of a
+system with purely material determinants, i.e. whether there are laws
+which, given certain material data, make all volitions functions of
+those data. Here again, there is empirical evidence up to a point, but
+it is not conclusive in regard to all volitions. It is important to
+observe, however that even if volitions are part of a mechanical
+system, this by no means implies any supremacy of matter over mind. It
+may well be that the same system which is susceptible of material
+determinants is also susceptible of mental determinants; thus a
+mechanical system may be determined by sets of volitions, as well as
+by sets of material facts. It would seem, therefore, that the reasons
+which make people dislike the view that volitions are mechanically
+determined are fallacious.
+
+(4) The notion of _necessity_, which is often associated with
+determinism, is a confused notion not legitimately deducible from
+determinism. Three meanings are commonly confounded when necessity is
+spoken of:--
+
+(α) An _action_ is necessary when it will be performed however much
+the agent may wish to do otherwise. Determinism does not imply that
+actions are necessary in this sense.
+
+(β) A _propositional function_ is necessary when all its values are
+true. This sense is not relevant to our present discussion.
+
+(γ) A _proposition_ is necessary with respect to a given constituent
+when it is the value, with that constituent as argument, of a
+necessary propositional function, in other words, when it remains true
+however that constituent may be varied. In this sense, in a
+deterministic system, the connection of a volition with its
+determinants is necessary, if the time at which the determinants occur
+be taken as the constituent to be varied, the time-interval between
+the determinants and the volition being kept constant. But this sense
+of necessity is purely logical, and has no emotional importance.
+
+We may now sum up our discussion of causality. We found first that the
+law of causality, as usually stated by philosophers, is false, and is
+not employed in science. We then considered the nature of scientific
+laws, and found that, instead of stating that one event A is always
+followed by another event B, they stated functional relations between
+certain events at certain times, which we called determinants, and
+other events at earlier or later times or at the same time. We were
+unable to find any _a priori_ category involved: the existence of
+scientific laws appeared as a purely empirical fact, not necessarily
+universal, except in a trivial and scientifically useless form. We
+found that a system with one set of determinants may very likely have
+other sets of a quite different kind, that, for example, a
+mechanically determined system may also be teleologically or
+volitionally determined. Finally we considered the problem of free
+will: here we found that the reasons for supposing volitions to be
+determined are strong but not conclusive, and we decided that even if
+volitions are mechanically determined, that is no reason for denying
+freedom in the sense revealed by introspection, or for supposing that
+mechanical events are not determined by volitions. The problem of free
+will _versus_ determinism is therefore, if we were right, mainly
+illusory, but in part not yet capable of being decisively solved.
+
+FOOTNOTES:
+
+[35] A propositional function is an expression containing a variable,
+or undetermined constituent, and becoming a proposition as soon as a
+definite value is assigned to the variable. Examples are: "A is A,"
+"_x_ is a number." The variable is called the _argument_ of the
+function.
+
+[36] _Logic_, Bk. III, Chap. V, § 2.
+
+[37] _Time and Free Will_, p. 199.
+
+[38] _Time and Free Will._ p. 202.
+
+[39] _Loc. cit._, § 6
+
+
+
+
+X
+
+KNOWLEDGE BY ACQUAINTANCE AND KNOWLEDGE BY DESCRIPTION
+
+
+The object of the following paper is to consider what it is that we
+know in cases where we know propositions about "the so-and-so" without
+knowing who or what the so-and-so is. For example, I know that the
+candidate who gets most votes will be elected, though I do not know
+who is the candidate who will get most votes. The problem I wish to
+consider is: What do we know in these cases, where the subject is
+merely described? I have considered this problem elsewhere[40] from a
+purely logical point of view; but in what follows I wish to consider
+the question in relation to theory of knowledge as well as in relation
+to logic, and in view of the above-mentioned logical discussions, I
+shall in this paper make the logical portion as brief as possible.
+
+In order to make clear the antithesis between "acquaintance" and
+"description," I shall first of all try to explain what I mean by
+"acquaintance." I say that I am _acquainted_ with an object when I
+have a direct cognitive relation to that object, i.e. when I am
+directly aware of the object itself. When I speak of a cognitive
+relation here, I do not mean the sort of relation which constitutes
+judgment, but the sort which constitutes presentation. In fact, I
+think the relation of subject and object which I call acquaintance is
+simply the converse of the relation of object and subject which
+constitutes presentation. That is, to say that S has acquaintance with
+O is essentially the same thing as to say that O is presented to S.
+But the associations and natural extensions of the word _acquaintance_
+are different from those of the word _presentation_. To begin with, as
+in most cognitive words, it is natural to say that I am acquainted
+with an object even at moments when it is not actually before my mind,
+provided it has been before my mind, and will be again whenever
+occasion arises. This is the same sense in which I am said to know
+that 2+2=4 even when I am thinking of something else. In the second
+place, the word _acquaintance_ is designed to emphasise, more than the
+word _presentation_, the relational character of the fact with which
+we are concerned. There is, to my mind, a danger that, in speaking of
+presentation, we may so emphasise the object as to lose sight of the
+subject. The result of this is either to lead to the view that there
+is no subject, whence we arrive at materialism; or to lead to the view
+that what is presented is part of the subject, whence we arrive at
+idealism, and should arrive at solipsism but for the most desperate
+contortions. Now I wish to preserve the dualism of subject and object
+in my terminology, because this dualism seems to me a fundamental fact
+concerning cognition. Hence I prefer the word _acquaintance_ because
+it emphasises the need of a subject which is acquainted.
+
+When we ask what are the kinds of objects with which we are
+acquainted, the first and most obvious example is _sense-data_. When I
+see a colour or hear a noise, I have direct acquaintance with the
+colour or the noise. The sense-datum with which I am acquainted in
+these cases is generally, if not always, complex. This is
+particularly obvious in the case of sight. I do not mean, of course,
+merely that the supposed physical object is complex, but that the
+direct sensible object is complex and contains parts with spatial
+relations. Whether it is possible to be aware of a complex without
+being aware of its constituents is not an easy question, but on the
+whole it would seem that there is no reason why it should not be
+possible. This question arises in an acute form in connection with
+self-consciousness, which we must now briefly consider.
+
+In introspection, we seem to be immediately aware of varying
+complexes, consisting of objects in various cognitive and conative
+relations to ourselves. When I see the sun, it often happens that I
+am aware of my seeing the sun, in addition to being aware of the sun;
+and when I desire food, it often happens that I am aware of my desire
+for food. But it is hard to discover any state of mind in which I am
+aware of myself alone, as opposed to a complex of which I am a
+constituent. The question of the nature of self-consciousness is too
+large and too slightly connected with our subject, to be argued at
+length here. It is difficult, but probably not impossible, to account
+for plain facts if we assume that we do not have acquaintance with
+ourselves. It is plain that we are not only _acquainted_ with the
+complex "Self-acquainted-with-A," but we also _know_ the proposition
+"I am acquainted with A." Now here the complex has been analysed, and
+if "I" does not stand for something which is a direct object of
+acquaintance, we shall have to suppose that "I" is something known by
+description. If we wished to maintain the view that there is no
+acquaintance with Self, we might argue as follows: We are acquainted
+with _acquaintance_, and we know that it is a relation. Also we are
+acquainted with a complex in which we perceive that acquaintance is
+the relating relation. Hence we know that this complex must have a
+constituent which is that which is acquainted, i.e. must have a
+subject-term as well as an object-term. This subject-term we define
+as "I." Thus "I" means "the subject-term in awarenesses of which _I_
+am aware." But as a definition this cannot be regarded as a happy
+effort. It would seem necessary, therefore, either to suppose that I
+am acquainted with myself, and that "I," therefore, requires no
+definition, being merely the proper name of a certain object, or to
+find some other analysis of self-consciousness. Thus self-consciousness
+cannot be regarded as throwing light on the question whether we can
+know a complex without knowing its constituents. This question,
+however, is not important for our present purposes, and I shall
+therefore not discuss it further.
+
+The awarenesses we have considered so far have all been awarenesses of
+particular existents, and might all in a large sense be called
+sense-data. For, from the point of view of theory of knowledge,
+introspective knowledge is exactly on a level with knowledge derived
+from sight or hearing. But, in addition to awareness of the above kind
+of objects, which may be called awareness of _particulars_; we have
+also (though not quite in the same sense) what may be called awareness
+of _universals_. Awareness of universals is called _conceiving_, and a
+universal of which we are aware is called a _concept_. Not only are we
+aware of particular yellows, but if we have seen a sufficient number
+of yellows and have sufficient intelligence, we are aware of the
+universal _yellow_; this universal is the subject in such judgments as
+"yellow differs from blue" or "yellow resembles blue less than green
+does." And the universal yellow is the predicate in such judgments as
+"this is yellow," where "this" is a particular sense-datum. And
+universal relations, too, are objects of awarenesses; up and down,
+before and after, resemblance, desire, awareness itself, and so on,
+would seem to be all of them objects of which we can be aware.
+
+In regard to relations, it might be urged that we are never aware of
+the universal relation itself, but only of complexes in which it is a
+constituent. For example, it may be said that we do not know directly
+such a relation as _before_, though we understand such a proposition
+as "this is before that," and may be directly aware of such a complex
+as "this being before that." This view, however, is difficult to
+reconcile with the fact that we often know propositions in which the
+relation is the subject, or in which the relata are not definite given
+objects, but "anything." For example, we know that if one thing is
+before another, and the other before a third, then the first is before
+the third; and here the things concerned are not definite things, but
+"anything." It is hard to see how we could know such a fact about
+"before" unless we were acquainted with "before," and not merely with
+actual particular cases of one given object being before another given
+object. And more directly: A judgment such as "this is before that,"
+where this judgment is derived from awareness of a complex,
+constitutes an analysis, and we should not understand the analysis if
+we were not acquainted with the meaning of the terms employed. Thus we
+must suppose that we are acquainted with the meaning of "before," and
+not merely with instances of it.
+
+There are thus at least two sorts of objects of which we are aware,
+namely, particulars and universals. Among particulars I include all
+existents, and all complexes of which one or more constituents are
+existents, such as this-before-that, this-above-that,
+the-yellowness-of-this. Among universals I include all objects of
+which no particular is a constituent. Thus the disjunction
+"universal-particular" includes all objects. We might also call it the
+disjunction "abstract-concrete." It is not quite parallel with the
+opposition "concept-percept," because things remembered or imagined
+belong with particulars, but can hardly be called percepts. (On the
+other hand, universals with which we are acquainted may be identified
+with concepts.)
+
+It will be seen that among the objects with which we are acquainted
+are not included physical objects (as opposed to sense-data), nor
+other people's minds. These things are known to us by what I call
+"knowledge by description," which we must now consider.
+
+By a "description" I mean any phrase of the form "a so-and-so" or "the
+so-and-so." A phrase of the form "a so-and-so" I shall call an
+"ambiguous" description; a phrase of the form "the so-and-so" (in the
+singular) I shall call a "definite" description. Thus "a man" is an
+ambiguous description, and "the man with the iron mask" is a definite
+description. There are various problems connected with ambiguous
+descriptions, but I pass them by, since they do not directly concern
+the matter I wish to discuss. What I wish to discuss is the nature of
+our knowledge concerning objects in cases where we know that there is
+an object answering to a definite description, though we are not
+_acquainted_ with any such object. This is a matter which is concerned
+exclusively with _definite_ descriptions. I shall, therefore, in the
+sequel, speak simply of "descriptions" when I mean "definite
+descriptions." Thus a description will mean any phrase of the form
+"the so-and-so" in the singular.
+
+I shall say that an object is "known by description" when we know that
+it is "_the_ so-and-so," i.e. when we know that there is one object,
+and no more, having a certain property; and it will generally be
+implied that we do not have knowledge of the same object by
+acquaintance. We know that the man with the iron mask existed, and
+many propositions are known about him; but we do not know who he was.
+We know that the candidate who gets most votes will be elected, and in
+this case we are very likely also acquainted (in the only sense in
+which one can be acquainted with some one else) with the man who is,
+in fact, the candidate who will get most votes, but we do not know
+which of the candidates he is, i.e. we do not know any proposition of
+the form "A is the candidate who will get most votes" where A is one
+of the candidates by name. We shall say that we have "_merely_
+descriptive knowledge" of the so-and-so when, although we know that
+the so-and-so exists, and although we may possibly be acquainted with
+the object which is, in fact, the so-and-so, yet we do not know any
+proposition "_a_ is the so-and-so," where _a_ is something with which
+we are acquainted.
+
+When we say "the so-and-so exists," we mean that there is just one
+object which is the so-and-so. The proposition "_a_ is the so-and-so"
+means that _a_ has the property so-and-so, and nothing else has. "Sir
+Joseph Larmor is the Unionist candidate" means "Sir Joseph Larmor is a
+Unionist candidate, and no one else is." "The Unionist candidate
+exists" means "some one is a Unionist candidate, and no one else is."
+Thus, when we are acquainted with an object which we know to be the
+so-and-so, we know that the so-and-so exists but we may know that the
+so-and-so exists when we are not acquainted with any object which we
+know to be the so-and-so, and even when we are not acquainted with any
+object which, in fact, is the so-and-so.
+
+Common words, even proper names, are usually really descriptions. That
+is to say, the thought in the mind of a person using a proper name
+correctly can generally only be expressed explicitly if we replace the
+proper name by a description. Moreover, the description required to
+express the thought will vary for different people, or for the same
+person at different times. The only thing constant (so long as the
+name is rightly used) is the object to which the name applies. But so
+long as this remains constant, the particular description involved
+usually makes no difference to the truth or falsehood of the
+proposition in which the name appears.
+
+Let us take some illustrations. Suppose some statement made about
+Bismarck. Assuming that there is such a thing as direct acquaintance
+with oneself, Bismarck himself might have used his name directly to
+designate the particular person with whom he was acquainted. In this
+case, if he made a judgment about himself, he himself might be a
+constituent of the judgment. Here the proper name has the direct use
+which it always wishes to have, as simply standing for a certain
+object, and not for a description of the object. But if a person who
+knew Bismarck made a judgment about him, the case is different. What
+this person was acquainted with were certain sense-data which he
+connected (rightly, we will suppose) with Bismarck's body. His body as
+a physical object, and still more his mind, were only known as the
+body and the mind connected with these sense-data. That is, they were
+known by description. It is, of course, very much a matter of chance
+which characteristics of a man's appearance will come into a friend's
+mind when he thinks of him; thus the description actually in the
+friend's mind is accidental. The essential point is that he knows that
+the various descriptions all apply to the same entity, in spite of
+not being acquainted with the entity in question.
+
+When we, who did not know Bismarck, make a judgment about him, the
+description in our minds will probably be some more or less vague mass
+of historical knowledge--far more, in most cases, than is required to
+identify him. But, for the sake of illustration, let us assume that we
+think of him as "the first Chancellor of the German Empire." Here all
+the words are abstract except "German." The word "German" will again
+have different meanings for different people. To some it will recall
+travels in Germany, to some the look of Germany on the map, and so on.
+But if we are to obtain a description which we know to be applicable,
+we shall be compelled, at some point, to bring in a reference to a
+particular with which we are acquainted. Such reference is involved in
+any mention of past, present, and future (as opposed to definite
+dates), or of here and there, or of what others have told us. Thus it
+would seem that, in some way or other, a description known to be
+applicable to a particular must involve some reference to a particular
+with which we are acquainted, if our knowledge about the thing
+described is not to be merely what follows logically from the
+description. For example, "the most long-lived of men" is a
+description which must apply to some man, but we can make no judgments
+concerning this man which involve knowledge about him beyond what the
+description gives. If, however, we say, "the first Chancellor of the
+German Empire was an astute diplomatist," we can only be assured of
+the truth of our judgment in virtue of something with which we are
+acquainted--usually a testimony heard or read. Considered
+psychologically, apart from the information we convey to others, apart
+from the fact about the actual Bismarck, which gives importance to
+our judgment, the thought we really have contains the one or more
+particulars involved, and otherwise consists wholly of concepts. All
+names of places--London, England, Europe, the earth, the Solar
+System--similarly involve, when used, descriptions which start from
+some one or more particulars with which we are acquainted. I suspect
+that even the Universe, as considered by metaphysics, involves such a
+connection with particulars. In logic, on the contrary, where we are
+concerned not merely with what does exist, but with whatever might or
+could exist or be, no reference to actual particulars is involved.
+
+It would seem that, when we make a statement about something only
+known by description, we often _intend_ to make our statement, not in
+the form involving the description, but about the actual thing
+described. That is to say, when we say anything about Bismarck, we
+should like, if we could, to make the judgment which Bismarck alone
+can make, namely, the judgment of which he himself is a constituent.
+In this we are necessarily defeated, since the actual Bismarck is
+unknown to us. But we know that there is an object B called Bismarck,
+and that B was an astute diplomatist. We can thus _describe_ the
+proposition we should like to affirm, namely, "B was an astute
+diplomatist," where B is the object which was Bismarck. What enables
+us to communicate in spite of the varying descriptions we employ is
+that we know there is a true proposition concerning the actual
+Bismarck, and that, however we may vary the description (so long as
+the description is correct), the proposition described is still the
+same. This proposition, which is described and is known to be true, is
+what interests us; but we are not acquainted with the proposition
+itself, and do not know _it_, though we know it is true.
+
+It will be seen that there are various stages in the removal from
+acquaintance with particulars: there is Bismarck to people who knew
+him, Bismarck to those who only know of him through history, the man
+with the iron mask, the longest-lived of men. These are progressively
+further removed from acquaintance with particulars, and there is a
+similar hierarchy in the region of universals. Many universals, like
+many particulars, are only known to us by description. But here, as in
+the case of particulars, knowledge concerning what is known by
+description is ultimately reducible to knowledge concerning what is
+known by acquaintance.
+
+The fundamental epistemological principle in the analysis of
+propositions containing descriptions is this: _Every proposition which
+we can understand must be composed wholly of constituents with which
+we are acquainted._ From what has been said already, it will be plain
+why I advocate this principle, and how I propose to meet the case of
+propositions which at first sight contravene it. Let us begin with the
+reasons for supposing the principle true.
+
+The chief reason for supposing the principle true is that it seems
+scarcely possible to believe that we can make a judgment or entertain
+a supposition without knowing what it is that we are judging or
+supposing about. If we make a judgment about (say) Julius Cæsar, it is
+plain that the actual person who was Julius Cæsar is not a constituent
+of the judgment. But before going further, it may be well to explain
+what I mean when I say that this or that is a constituent of a
+judgment, or of a proposition which we understand. To begin with
+judgments: a judgment, as an occurrence, I take to be a relation of a
+mind to several entities, namely, the entities which compose what is
+judged. If, e.g. I judge that A loves B, the judgment as an event
+consists in the existence, at a certain moment, of a specific
+four-term relation, called _judging_, between me and A and love and B.
+That is to say, at the time when I judge, there is a certain complex
+whose terms are myself and A and love and B, and whose relating
+relation is _judging_. My reasons for this view have been set forth
+elsewhere,[41] and I shall not repeat them here. Assuming this view of
+judgment, the constituents of the judgment are simply the constituents
+of the complex which is the judgment. Thus, in the above case, the
+constituents are myself and A and love and B and judging. But myself
+and judging are constituents shared by all my judgments; thus the
+_distinctive_ constituents of the particular judgment in question are
+A and love and B. Coming now to what is meant by "understanding a
+proposition," I should say that there is another relation possible
+between me and A and love and B, which is called my _supposing_ that A
+loves B.[42] When we can _suppose_ that A loves B, we "understand the
+proposition" _A loves B_. Thus we often understand a proposition in
+cases where we have not enough knowledge to make a judgment.
+Supposing, like judging, is a many-term relation, of which a mind is
+one term. The other terms of the relation are called the constituents
+of the proposition supposed. Thus the principle which I enunciated may
+be re-stated as follows: _Whenever a relation of supposing or judging
+occurs, the terms to which the supposing or judging mind is related by
+the relation of supposing or judging must be terms with which the mind
+in question is acquainted._ This is merely to say that we cannot make
+a judgment or a supposition without knowing what it is that we are
+making our judgment or supposition about. It seems to me that the
+truth of this principle is evident as soon as the principle is
+understood; I shall, therefore, in what follows, assume the principle,
+and use it as a guide in analysing judgments that contain
+descriptions.
+
+Returning now to Julius Cæsar, I assume that it will be admitted that
+he himself is not a constituent of any judgment which I can make. But
+at this point it is necessary to examine the view that judgments are
+composed of something called "ideas," and that it is the "idea" of
+Julius Cæsar that is a constituent of my judgment. I believe the
+plausibility of this view rests upon a failure to form a right theory
+of descriptions. We may mean by my "idea" of Julius Cæsar the things
+that I know about him, e.g. that he conquered Gaul, was assassinated
+on the Ides of March, and is a plague to schoolboys. Now I am
+admitting, and indeed contending, that in order to discover what is
+actually in my mind when I judge about Julius Cæsar, we must
+substitute for the proper name a description made up of some of the
+things I know about him. (A description which will often serve to
+express my thought is "the man whose name was _Julius Cæsar_." For
+whatever else I may have forgotten about him, it is plain that when I
+mention him I have not forgotten that that was his name.) But although
+I think the theory that judgments consist of ideas may have been
+suggested in some such way, yet I think the theory itself is
+fundamentally mistaken. The view seems to be that there is some
+mental existent which may be called the "idea" of something outside
+the mind of the person who has the idea, and that, since judgment is a
+mental event, its constituents must be constituents of the mind of the
+person judging. But in this view ideas become a veil between us and
+outside things--we never really, in knowledge, attain to the things we
+are supposed to be knowing about, but only to the ideas of those
+things. The relation of mind, idea, and object, on this view, is
+utterly obscure, and, so far as I can see, nothing discoverable by
+inspection warrants the intrusion of the idea between the mind and the
+object. I suspect that the view is fostered by the dislike of
+relations, and that it is felt the mind could not know objects unless
+there were something "in" the mind which could be called the state of
+knowing the object. Such a view, however, leads at once to a vicious
+endless regress, since the relation of idea to object will have to be
+explained by supposing that the idea itself has an idea of the object,
+and so on _ad infinitum_. I therefore see no reason to believe that,
+when we are acquainted with an object, there is in us something which
+can be called the "idea" of the object. On the contrary, I hold that
+acquaintance is wholly a relation, not demanding any such constituent
+of the mind as is supposed by advocates of "ideas." This is, of
+course, a large question, and one which would take us far from our
+subject if it were adequately discussed. I therefore content myself
+with the above indications, and with the corollary that, in judging,
+the actual objects concerning which we judge, rather than any supposed
+purely mental entities, are constituents of the complex which is the
+judgment.
+
+When, therefore, I say that we must substitute for "Julius Cæsar" some
+description of Julius Cæsar, in order to discover the meaning of a
+judgment nominally about him, I am not saying that we must substitute
+an idea. Suppose our description is "the man whose name was _Julius
+Cæsar_." Let our judgment be "Julius Cæsar was assassinated." Then it
+becomes "the man whose name was _Julius Cæsar_ was assassinated." Here
+_Julius Cæsar_ is a noise or shape with which we are acquainted, and
+all the other constituents of the judgment (neglecting the tense in
+"was") are _concepts_ with which we are acquainted. Thus our judgment
+is wholly reduced to constituents with which we are acquainted, but
+Julius Cæsar himself has ceased to be a constituent of our judgment.
+This, however, requires a proviso, to be further explained shortly,
+namely that "the man whose name was _Julius Cæsar_" must not, as a
+whole, be a constituent of our judgment, that is to say, this phrase
+must not, as a whole, have a meaning which enters into the judgment.
+Any right analysis of the judgment, therefore, must break up this
+phrase, and not treat it as a subordinate complex which is part of the
+judgment. The judgment "the man whose name was _Julius Cæsar_ was
+assassinated" may be interpreted as meaning "one and only one man was
+called _Julius Cæsar_, and that one was assassinated." Here it is
+plain that there is no constituent corresponding to the phrase "the
+man whose name was _Julius Cæsar_." Thus there is no reason to regard
+this phrase as expressing a constituent of the judgment, and we have
+seen that this phrase must be broken up if we are to be acquainted
+with all the constituents of the judgment. This conclusion, which we
+have reached from considerations concerned with the theory of
+knowledge, is also forced upon us by logical considerations, which
+must now be briefly reviewed.
+
+It is common to distinguish two aspects, _meaning_ and _denotation_,
+such phrases as "the author of Waverley." The meaning will be a
+certain complex, consisting (at least) of authorship and Waverley with
+some relation; the denotation will be Scott. Similarly "featherless
+bipeds" will have a complex meaning, containing as constituents the
+presence of two feet and the absence of feathers, while its denotation
+will be the class of men. Thus when we say "Scott is the author of
+Waverley" or "men are the same as featherless bipeds," we are
+asserting an identity of denotation, and this assertion is worth
+making because of the diversity of meaning.[43] I believe that the
+duality of meaning and denotation, though capable of a true
+interpretation, is misleading if taken as fundamental. The denotation,
+I believe, is not a constituent of the proposition, except in the case
+of proper names, i.e. of words which do not assign a property to an
+object, but merely and solely name it. And I should hold further that,
+in this sense, there are only two words which are strictly proper
+names of particulars, namely, "I" and "this."[44]
+
+One reason for not believing the denotation to be a constituent of the
+proposition is that we may know the proposition even when we are not
+acquainted with the denotation. The proposition "the author of
+Waverley is a novelist" was known to people who did not know that "the
+author of Waverley" denoted Scott. This reason has been already
+sufficiently emphasised.
+
+A second reason is that propositions concerning "the so-and-so" are
+possible even when "the so-and-so" has no denotation. Take, e.g. "the
+golden mountain does not exist" or "the round square is
+self-contradictory." If we are to preserve the duality of meaning and
+denotation, we have to say, with Meinong, that there are such objects
+as the golden mountain and the round square, although these objects do
+not have being. We even have to admit that the existent round square
+is existent, but does not exist.[45] Meinong does not regard this as a
+contradiction, but I fail to see that it is not one. Indeed, it seems
+to me evident that the judgment "there is no such object as the round
+square" does not presuppose that there is such an object. If this is
+admitted, however, we are led to the conclusion that, by parity of
+form, no judgment concerning "the so-and-so" actually involves the
+so-and-so as a constituent.
+
+Miss Jones[46] contends that there is no difficulty in admitting
+contradictory predicates concerning such an object as "the present
+King of France," on the ground that this object is in itself
+contradictory. Now it might, of course, be argued that this object,
+unlike the round square, is not self-contradictory, but merely
+non-existent. This, however, would not go to the root of the matter.
+The real objection to such an argument is that the law of
+contradiction ought not to be stated in the traditional form "A is not
+both B and not B," but in the form "no proposition is both true and
+false." The traditional form only applies to certain propositions,
+namely, to those which attribute a predicate to a subject. When the
+law is stated of propositions, instead of being stated concerning
+subjects and predicates, it is at once evident that propositions about
+the present King of France or the round square can form no exception,
+but are just as incapable of being both true and false as other
+propositions. Miss Jones[47] argues that "Scott is the author of
+Waverley" asserts identity of denotation between _Scott_ and _the
+author of Waverley_. But there is some difficulty in choosing among
+alternative meanings of this contention. In the first place, it should
+be observed that _the author of Waverley_ is not a _mere_ name, like
+_Scott_. _Scott_ is merely a noise or shape conventionally used to
+designate a certain person; it gives us no information about that
+person, and has nothing that can be called meaning as opposed to
+denotation. (I neglect the fact, considered above, that even proper
+names, as a rule, really stand for descriptions.) But _the author of
+Waverley_ is not merely conventionally a name for Scott; the element
+of mere convention belongs here to the separate words, _the_ and
+_author_ and _of_ and _Waverley_. Given what these words stand for,
+_the author of Waverley_ is no longer arbitrary. When it is said that
+Scott is the author of Waverley, we are not stating that these are two
+_names_ for one man, as we should be if we said "Scott is Sir Walter."
+A man's name is what he is called, but however much Scott had been
+called the author of Waverley, that would not have made him be the
+author; it was necessary for him actually to write Waverley, which was
+a fact having nothing to do with names.
+
+If, then, we are asserting identity of denotation, we must not mean by
+_denotation_ the mere relation of a name to the thing named. In fact,
+it would be nearer to the truth to say that the _meaning_ of "Scott"
+is the _denotation_ of "the author of Waverley." The relation of
+"Scott" to Scott is that "Scott" means Scott, just as the relation of
+"author" to the concept which is so called is that "author" means this
+concept. Thus if we distinguish meaning and denotation in "the author
+of Waverley," we shall have to say that "Scott" has meaning but not
+denotation. Also when we say "Scott is the author of Waverley," the
+_meaning_ of "the author of Waverley" is relevant to our assertion.
+For if the denotation alone were relevant, any other phrase with the
+same denotation would give the same proposition. Thus "Scott is the
+author of Marmion" would be the same proposition as "Scott is the
+author of Waverley." But this is plainly not the case, since from the
+first we learn that Scott wrote Marmion and from the second we learn
+that he wrote Waverley, but the first tells us nothing about Waverley
+and the second nothing about Marmion. Hence the meaning of "the author
+of Waverley," as opposed to the denotation, is certainly relevant to
+"Scott is the author of Waverley."
+
+We have thus agreed that "the author of Waverley" is not a mere name,
+and that its meaning is relevant in propositions in which it occurs.
+Thus if we are to say, as Miss Jones does, that "Scott is the author
+of Waverley" asserts an identity of denotation, we must regard the
+denotation of "the author of Waverley" as the denotation of what is
+_meant_ by "the author of Waverley." Let us call the meaning of "the
+author of Waverley" M. Thus M is what "the author of Waverley" means.
+Then we are to suppose that "Scott is the author of Waverley" means
+"Scott is the denotation of M." But here we are explaining our
+proposition by another of the same form, and thus we have made no
+progress towards a real explanation. "The denotation of M," like "the
+author of Waverley," has both meaning and denotation, on the theory we
+are examining. If we call its meaning M', our proposition becomes
+"Scott is the denotation of M'." But this leads at once to an endless
+regress. Thus the attempt to regard our proposition as asserting
+identity of denotation breaks down, and it becomes imperative to find
+some other analysis. When this analysis has been completed, we shall
+be able to reinterpret the phrase "identity of denotation," which
+remains obscure so long as it is taken as fundamental.
+
+The first point to observe is that, in any proposition about "the
+author of Waverley," provided Scott is not explicitly mentioned, the
+denotation itself, i.e. Scott, does not occur, but only the concept of
+denotation, which will be represented by a variable. Suppose we say
+"the author of Waverley was the author of Marmion," we are certainly
+not saying that both were Scott--we may have forgotten that there was
+such a person as Scott. We are saying that there is some man who was
+the author of Waverley and the author of Marmion. That is to say,
+there is some one who wrote Waverley and Marmion, and no one else
+wrote them. Thus the identity is that of a variable, i.e. of an
+indefinite subject, "some one." This is why we can understand
+propositions about "the author of Waverley," without knowing who he
+was. When we say "the author of Waverley was a poet," we mean "one and
+only one man wrote Waverley, and he was a poet"; when we say "the
+author of Waverley was Scott" we mean "one and only one man wrote
+Waverley, and he was Scott." Here the identity is between a variable,
+i.e. an indeterminate subject ("he"), and Scott; "the author of
+Waverley" has been analysed away, and no longer appears as a
+constituent of the proposition.[48]
+
+The reason why it is imperative to analyse away the phrase "the author
+of Waverley" may be stated as follows. It is plain that when we say
+"the author of Waverley is the author of Marmion," the _is_ expresses
+identity. We have seen also that the common _denotation_, namely
+Scott, is not a constituent of this proposition, while the _meanings_
+(if any) of "the author of Waverley" and "the author of Marmion" are
+not identical. We have seen also that, in any sense in which the
+meaning of a word is a constituent of a proposition in whose verbal
+expression the word occurs, "Scott" means the actual man Scott, in the
+same sense (so far as concerns our present discussion) in which
+"author" means a certain universal. Thus, if "the author of Waverley"
+were a subordinate complex in the above proposition, its _meaning_
+would have to be what was said to be identical with the _meaning_ of
+"the author of Marmion." This is plainly not the case; and the only
+escape is to say that "the author of Waverley" does not, by itself,
+have a meaning, though phrases of which it is part do have a meaning.
+That is, in a right analysis of the above proposition, "the author of
+Waverley" must disappear. This is effected when the above proposition
+is analysed as meaning: "Some one wrote Waverley and no one else did,
+and that some one also wrote Marmion and no one else did." This may be
+more simply expressed by saying that the propositional function "_x_
+wrote Waverley and Marmion, and no one else did" is capable of truth,
+i.e. some value of _x_ makes it true, but no other value does. Thus
+the true subject of our judgment is a propositional function, i.e. a
+complex containing an undetermined constituent, and becoming a
+proposition as soon as this constituent is determined.
+
+We may now define the denotation of a phrase. If we know that the
+proposition "_a_ is the so-and-so" is true, i.e. that _a_ is so-and-so
+and nothing else is, we call _a_ the denotation of the phrase "the
+so-and-so." A very great many of the propositions we naturally make
+about "the so-and-so" will remain true or remain false if we
+substitute _a_ for "the so-and-so," where _a_ is the denotation of
+"the so-and-so." Such propositions will also remain true or remain
+false if we substitute for "the so-and-so" any other phrase having the
+same denotation. Hence, as practical men, we become interested in the
+denotation more than in the description, since the denotation decides
+as to the truth or falsehood of so many statements in which the
+description occurs. Moreover, as we saw earlier in considering the
+relations of description and acquaintance, we often wish to reach the
+denotation, and are only hindered by lack of acquaintance: in such
+cases the description is merely the means we employ to get as near as
+possible to the denotation. Hence it naturally comes to be supposed
+that the denotation is part of the proposition in which the
+description occurs. But we have seen, both on logical and on
+epistemological grounds, that this is an error. The actual object (if
+any) which is the denotation is not (unless it is explicitly
+mentioned) a constituent of propositions in which descriptions occur;
+and this is the reason why, in order to understand such propositions,
+we need acquaintance with the constituents of the description, but do
+not need acquaintance with its denotation. The first result of
+analysis, when applied to propositions whose grammatical subject is
+"the so-and-so," is to substitute a variable as subject; i.e. we
+obtain a proposition of the form: "There is _something_ which alone is
+so-and-so, and that _something_ is such-and-such." The further
+analysis of propositions concerning "the so-and-so" is thus merged in
+the problem of the nature of the variable, i.e. of the meanings of
+_some_, _any_, and _all_. This is a difficult problem, concerning
+which I do not intend to say anything at present.
+
+To sum up our whole discussion. We began by distinguishing two sorts
+of knowledge of objects, namely, knowledge by _acquaintance_ and
+knowledge by _description_. Of these it is only the former that brings
+the object itself before the mind. We have acquaintance with
+sense-data, with many universals, and possibly with ourselves, but not
+with physical objects or other minds. We have _descriptive_ knowledge
+of an object when we know that it is _the_ object having some property
+or properties with which we are acquainted; that is to say, when we
+know that the property or properties in question belong to one object
+and no more, we are said to have knowledge of that one object by
+description, whether or not we are acquainted with the object. Our
+knowledge of physical objects and of other minds is only knowledge by
+description, the descriptions involved being usually such as involve
+sense-data. All propositions intelligible to us, whether or not they
+primarily concern things only known to us by description, are composed
+wholly of constituents with which we are acquainted, for a constituent
+with which we are not acquainted is unintelligible to us. A judgment,
+we found, is not composed of mental constituents called "ideas," but
+consists of an occurrence whose constituents are a mind[49] and
+certain objects, particulars or universals. (One at least must be a
+universal.) When a judgment is rightly analysed, the objects which are
+constituents of it must all be objects with which the mind which is a
+constituent of it is acquainted. This conclusion forces us to analyse
+descriptive phrases occurring in propositions, and to say that the
+objects denoted by such phrases are not constituents of judgments in
+which such phrases occur (unless these objects are explicitly
+mentioned). This leads us to the view (recommended also on purely
+logical grounds) that when we say "the author of Marmion was the
+author of Waverley," Scott himself is not a constituent of our
+judgment, and that the judgment cannot be explained by saying that it
+affirms identity of denotation with diversity of meaning. It also,
+plainly, does not assert identity of meaning. Such judgments,
+therefore, can only be analysed by breaking up the descriptive
+phrases, introducing a variable, and making propositional functions
+the ultimate subjects. In fact, "the so-and-so is such-and-such" will
+mean that "_x_ is so-and-so and nothing else is, and _x_ is
+such-and-such" is capable of truth. The analysis of such judgments
+involves many fresh problems, but the discussion of these problems is
+not undertaken in the present paper.
+
+FOOTNOTES:
+
+[40] See references later.
+
+[41] _Philosophical Essays_, "The Nature of Truth." I have been
+persuaded by Mr. Wittgenstein that this theory is somewhat unduly
+simple, but the modification which I believe it to require does not
+affect the above argument [1917].
+
+[42] Cf. Meinong, _Ueber Annahmen_, _passim_. I formerly supposed,
+contrary to Meinong's view, that the relationship of supposing might
+be merely that of presentation. In this view I now think I was
+mistaken, and Meinong is right. But my present view depends upon the
+theory that both in judgment and in assumption there is no single
+Objective, but the several constituents of the judgment or assumption
+are in a many-term relation to the mind.
+
+[43] This view has been recently advocated by Miss E.E.C. Jones. "A
+New Law of Thought and its Implications," _Mind_, January, 1911.
+
+[44] I should now exclude "I" from proper names in the strict sense,
+and retain only "this" [1917].
+
+[45] Meinong, _Ueber Annahmen_, 2nd ed., Leipzig, 1910, p. 141.
+
+[46] _Mind_, July, 1910, p. 380.
+
+[47] _Mind_, July, 1910, p. 379.
+
+[48] The theory which I am advocating is set forth fully, with the
+logical grounds in its favour, in _Principia Mathematica_, Vol. I.
+Introduction, Chap. III; also, less fully, in _Mind_, October, 1905.
+
+[49] I use this phrase merely to denote the something psychological
+which enters into judgment, without intending to prejudge the question
+as to what this something is.
+
+
+
+
+INDEX
+
+
+Achilles and the tortoise, 80 ff, 89 ff
+
+Acquaintance, the relation of, 209 ff
+
+Alexander, 125
+
+American Realists, the, 134
+
+Aristotle, 42, 76, 97
+
+
+Bacon, 41
+
+Bergson, 14 ff, 22, 105, 128, 185 ff, 203
+
+Berkeley, 97, 132
+
+Blake, 1
+
+Bosanquet, 99
+
+Broad, 89 _n_
+
+
+Calculus, the, 82
+
+Cantor, Georg, 64, 81 ff, 85, 91
+
+Carlyle, 50, 82
+
+Cause, the conception of, 135 _n_, 180 ff
+
+Christianity and renunciation, 51
+
+Chuang TzÅ­, 106
+
+Construction of permanent things and matter, 169 ff
+
+Constructions, logical, 155 ff
+
+
+Darwin, 15, 23, 43
+
+Dedekind, 64, 81 ff, 85
+
+Descartes, 97, 126
+
+Descriptions, 175, 214 ff
+
+
+Education, 37 ff
+
+Euclid, 62, 92, 94
+
+Evolutionism, 23 ff, 28
+
+
+Fano, 93
+
+Faraday, 34
+
+Free will, 205 ff
+
+Frege, 78 _n_
+
+
+Galileo, 42
+
+Gladstone, 177
+
+Good and evil, 26 ff
+
+
+Hegel, 8, 10, 18, 85, 97, 105 ff
+
+Heine, 113
+
+Heraclitus, 1 ff, 10
+
+Hertz, 34
+
+Holt, 177 _n_
+
+Hume, 1, 97
+
+
+Infinite, the mathematical, 84 ff
+
+
+James, William, 100
+
+Jones, Miss E.E.C., 224 _n_, 225
+
+Judgment, 219 ff
+
+
+Kant, 85, 96, 97, 99, 118 ff
+
+Knowledge by acquaintance, 209 ff;
+  by description, 214 ff
+
+
+Laplace, 23
+
+Leibniz, 76, 79, 82 ff, 97, 126, 144, 160
+
+Locke, 97
+
+Logic, the laws of, 68 ff
+
+
+Macaulay and Taylor's theorem, 95
+
+Malthus, 43
+
+Mathematics, 58 ff;
+  and the Metaphysicians, 74 ff;
+  and logic, 75 ff;
+  and the infinitesimal, 82 ff
+
+Matter, the nature of, 125 ff;
+  definition of, 164 ff
+
+Maxwell, 34
+
+Meaning and denotation, 223 ff
+
+Meinong, 174, 220 _n_, 225
+
+Militarism, 50
+
+Mill, 185, 193 ff
+
+Mysticism and logic, 1 ff
+
+
+Necessity, the notion of, 207 ff
+
+Nietzsche, 22, 50
+
+Nunn, 125, 137 _n_, 153
+
+
+Parmenides, 7 ff, 18, 21
+
+Particulars, awareness of, 210 ff
+
+Peano, 78 ff, 93 ff
+
+Perspectives, 139 ff;
+  the space of, 158 ff
+
+Philosophy and logic, 111
+
+Physics, sense-data and, 145 ff
+
+Pierce, 76 _n_
+
+Plato, 1 ff, 10, 30, 60, 97
+
+Pragmatism, 22, 105
+
+
+Realism and the analytic method, 120 ff
+
+Reason and intuition, 12 ff
+
+Relatives, the logic of, 76
+
+Robb, 167 _n_
+
+
+Santayana, 20
+
+Sense-data, 147, 210 ff;
+  and physics, 145 ff
+
+Sensibilia, 148 ff
+
+Space, 138 ff;
+  private, 158 ff;
+  the logical problem, 114 ff;
+  the problem in physics, 115 ff;
+  the epistemological problem, 118 ff
+
+Systems, deterministic, 199;
+  practically isolated, 198;
+  relatively isolated, 197;
+  mechanical, 201
+
+
+Time, 10, 21 ff, 141 ff, 167 ff
+
+Tristram Shandy, the paradox of, 90 ff
+
+
+Unity and Plurality, 18 ff
+
+Universals, awareness of, 212 ff
+
+
+Ward, 180
+
+Weierstrass, 80, 82, 95
+
+Whitehead, 117, 157, 175
+
+Wolf, 173
+
+
+Zeno the Eleatic, 64, 80, 84, 89 ff
+
+
+
+
+[Illustration]
+
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+       *       *       *       *       *
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diff --git a/25447-0.zip b/25447-0.zip
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+Project Gutenberg's Mysticism and Logic and Other Essays, by Bertrand Russell
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Mysticism and Logic and Other Essays
+
+Author: Bertrand Russell
+
+Release Date: May 12, 2008 [EBook #25447]
+[Last updated: May 5, 2012]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK MYSTICISM AND LOGIC ***
+
+
+
+
+Produced by Jeannie Howse, Adrian Mastronardi and the
+Online Distributed Proofreading Team at http://www.pgdp.net
+(This file was produced from images generously made
+available by The Internet Archive/Canadian Libraries)
+
+
+
+
+
+
+       *       *       *       *       *
+
+    +-----------------------------------------------------------+
+    | Transcriber's Note:                                       |
+    |                                                           |
+    | Inconsistent hyphenation in the original document has     |
+    | been preserved.                                           |
+    |                                                           |
+    | Mathematical equations and variables are marked with      |
+    | [Math:] to reduce confusion between underscores used for  |
+    | italics and underscores used to indicate subscripts.      |
+    | Subscripts are indicated with underscores, with the       |
+    | subscripted character marked with {}'s, i.e.: x_{t}       |
+    |                                                           |
+    | Greek letters have been transliterated and marked with    |
+    | []'s, i.e.: [alpha]                                       |
+    |                                                           |
+    | Obvious typographical errors have been corrected. For     |
+    | a complete list, please see the end of this document.     |
+    |                                                           |
+    +-----------------------------------------------------------+
+
+       *       *       *       *       *
+
+
+
+
+BERTRAND RUSSELL
+
+MYSTICISM AND
+LOGIC
+
+AND OTHER ESSAYS
+
+
+
+
+_LONDON_
+GEORGE ALLEN & UNWIN LTD
+RUSKIN HOUSE MUSEUM STREET
+
+
+
+
+MYSTICISM AND LOGIC
+AND OTHER ESSAYS
+
+
+
+
+BY BERTRAND RUSSELL
+
+_The ABC of Relativity_
+_The Analysis of Matter_
+_Human Society in Ethics and Politics_
+_The Impact of Science on Society_
+_New Hopes for a Changing World_
+_Authority and the Individual_
+_Human Knowledge_
+_History of Western Philosophy_
+_The Principles of Mathematics_
+_Introduction to Mathematical Philosophy_
+_The Analysis of Mind_
+_Our Knowledge of the External World_
+_An Outline of Philosophy_
+_The Philosophy of Leibniz_
+_An Inquiry into Meaning and Truth_
+_Logic and Knowledge_
+_The Problems of Philosophy_
+_Principia Mathematica_
+
+_Common Sense and Nuclear Warfare_
+_Why I am Not a Christian_
+_Portraits from Memory_
+_My Philosophical Development_
+_Unpopular Essays_
+_Power_
+_In Praise of Idleness_
+_The Conquest of Happiness_
+_Sceptical Essays_
+_The Scientific Outlook_
+_Marriage and Morals_
+_Education and the Social Order_
+_On Education_
+
+_Freedom and Organization_
+_Principles of Social Reconstruction_
+_Roads to Freedom_
+_Practice and Theory of Bolshevism_
+
+_Satan in The Suburbs_
+_Nightmares of Eminent Persons_
+
+
+
+
+_First published as "Philosophical Essays"_      _October 1910_
+_Second Edition as "Mysticism and Logic"_       _December 1917_
+_Third Impression_                                 _April 1918_
+_Fourth Impression_                             _February 1919_
+_Fifth Impression_                               _October 1921_
+_Sixth Impression_                                _August 1925_
+_Seventh Impression_                             _January 1932_
+_Eighth Impression_                                      _1949_
+_Ninth Impression_                                       _1950_
+_Tenth Impression_                                       _1951_
+_Eleventh Impression_                                    _1959_
+
+  _This book is copyright under the Berne Convention. Apart from any
+  fair dealing for the purpose of private study, research, criticism
+  or review, as permitted under the Copyright Act, 1956, no portion
+  may be reproduced by any process without written permission.
+  Enquiry should be made to the publisher._
+
+
+PRINTED IN GREAT BRITAIN
+_by Taylor Garnett Evans & Co. Ltd.,
+Watford, Herts._
+
+
+
+
+PREFACE
+
+
+The following essays have been written and published at various times,
+and my thanks are due to the previous publishers for the permission to
+reprint them.
+
+The essay on "Mysticism and Logic" appeared in the _Hibbert Journal_
+for July, 1914. "The Place of Science in a Liberal Education" appeared
+in two numbers of _The New Statesman_, May 24 and 31, 1913. "The Free
+Man's Worship" and "The Study of Mathematics" were included in a
+former collection (now out of print), _Philosophical Essays_, also
+published by Messrs. Longmans, Green & Co. Both were written in 1902;
+the first appeared originally in the _Independent Review_ for 1903,
+the second in the _New Quarterly_, November, 1907. In theoretical
+Ethics, the position advocated in "The Free Man's Worship" is not
+quite identical with that which I hold now: I feel less convinced than
+I did then of the objectivity of good and evil. But the general
+attitude towards life which is suggested in that essay still seems to
+me, in the main, the one which must be adopted in times of stress and
+difficulty by those who have no dogmatic religious beliefs, if inward
+defeat is to be avoided.
+
+The essay on "Mathematics and the Metaphysicians" was written in 1901,
+and appeared in an American magazine, _The International Monthly_,
+under the title "Recent Work in the Philosophy of Mathematics." Some
+points in this essay require modification in view of later work.
+These are indicated in footnotes. Its tone is partly explained by the
+fact that the editor begged me to make the article "as romantic as
+possible."
+
+All the above essays are entirely popular, but those that follow are
+somewhat more technical. "On Scientific Method in Philosophy" was the
+Herbert Spencer lecture at Oxford in 1914, and was published by the
+Clarendon Press, which has kindly allowed me to include it in this
+collection. "The Ultimate Constituents of Matter" was an address to
+the Manchester Philosophical Society, early in 1915, and was published
+in the _Monist_ in July of that year. The essay on "The Relation of
+Sense-data to Physics" was written in January, 1914, and first
+appeared in No. 4 of that year's volume of _Scientia_, an
+International Review of Scientific Synthesis, edited by M. Eugenio
+Rignano, published monthly by Messrs. Williams and Norgate, London,
+Nicola Zanichelli, Bologna, and Félix Alcan, Paris. The essay "On the
+Notion of Cause" was the presidential address to the Aristotelian
+Society in November, 1912, and was published in their _Proceedings_
+for 1912-13. "Knowledge by Acquaintance and Knowledge by Description"
+was also a paper read before the Aristotelian Society, and published
+in their _Proceedings_ for 1910-11.
+
+  LONDON,
+    _September, 1917_
+
+
+
+
+CONTENTS
+
+
+_Chapter_                                                  _Page_
+
+   I. _Mysticism and Logic_                                     1
+
+  II. _The Place of Science in a Liberal Education_            33
+
+ III. _A Free Man's Worship_                                   46
+
+  IV. _The Study of Mathematics_                               58
+
+   V. _Mathematics and the Metaphysicians_                     74
+
+  VI. _On Scientific Method in Philosophy_                     97
+
+ VII. _The Ultimate Constituents of Matter_                   125
+
+VIII. _The Relation of Sense-data to Physics_                 145
+
+  IX. _On the Notion of Cause_                                180
+
+   X. _Knowledge by Acquaintance and Knowledge by
+       Description_                                           209
+
+
+
+
+MYSTICISM AND LOGIC AND OTHER ESSAYS
+
+
+
+
+I
+
+MYSTICISM AND LOGIC
+
+
+Metaphysics, or the attempt to conceive the world as a whole by means
+of thought, has been developed, from the first, by the union and
+conflict of two very different human impulses, the one urging men
+towards mysticism, the other urging them towards science. Some men
+have achieved greatness through one of these impulses alone, others
+through the other alone: in Hume, for example, the scientific impulse
+reigns quite unchecked, while in Blake a strong hostility to science
+co-exists with profound mystic insight. But the greatest men who have
+been philosophers have felt the need both of science and of mysticism:
+the attempt to harmonise the two was what made their life, and what
+always must, for all its arduous uncertainty, make philosophy, to some
+minds, a greater thing than either science or religion.
+
+Before attempting an explicit characterisation of the scientific and
+the mystical impulses, I will illustrate them by examples from two
+philosophers whose greatness lies in the very intimate blending which
+they achieved. The two philosophers I mean are Heraclitus and Plato.
+
+Heraclitus, as every one knows, was a believer in universal flux: time
+builds and destroys all things. From the few fragments that remain, it
+is not easy to discover how he arrived at his opinions, but there are
+some sayings that strongly suggest scientific observation as the
+source.
+
+"The things that can be seen, heard, and learned," he says, "are what
+I prize the most." This is the language of the empiricist, to whom
+observation is the sole guarantee of truth. "The sun is new every
+day," is another fragment; and this opinion, in spite of its
+paradoxical character, is obviously inspired by scientific reflection,
+and no doubt seemed to him to obviate the difficulty of understanding
+how the sun can work its way underground from west to east during the
+night. Actual observation must also have suggested to him his central
+doctrine, that Fire is the one permanent substance, of which all
+visible things are passing phases. In combustion we see things change
+utterly, while their flame and heat rise up into the air and vanish.
+
+"This world, which is the same for all," he says, "no one of gods or
+men has made; but it was ever, is now, and ever shall be, an
+ever-living Fire, with measures kindling, and measures going out."
+
+"The transformations of Fire are, first of all, sea; and half of the
+sea is earth, half whirlwind."
+
+This theory, though no longer one which science can accept, is
+nevertheless scientific in spirit. Science, too, might have inspired
+the famous saying to which Plato alludes: "You cannot step twice into
+the same rivers; for fresh waters are ever flowing in upon you." But
+we find also another statement among the extant fragments: "We step
+and do not step into the same rivers; we are and are not."
+
+The comparison of this statement, which is mystical, with the one
+quoted by Plato, which is scientific, shows how intimately the two
+tendencies are blended in the system of Heraclitus. Mysticism is, in
+essence, little more than a certain intensity and depth of feeling in
+regard to what is believed about the universe; and this kind of
+feeling leads Heraclitus, on the basis of his science, to strangely
+poignant sayings concerning life and the world, such as:
+
+"Time is a child playing draughts, the kingly power is a child's."
+
+It is poetic imagination, not science, which presents Time as despotic
+lord of the world, with all the irresponsible frivolity of a child. It
+is mysticism, too, which leads Heraclitus to assert the identity of
+opposites: "Good and ill are one," he says; and again: "To God all
+things are fair and good and right, but men hold some things wrong and
+some right."
+
+Much of mysticism underlies the ethics of Heraclitus. It is true that
+a scientific determinism alone might have inspired the statement:
+"Man's character is his fate"; but only a mystic would have said:
+
+"Every beast is driven to the pasture with blows"; and again:
+
+"It is hard to fight with one's heart's desire. Whatever it wishes to
+get, it purchases at the cost of soul"; and again:
+
+"Wisdom is one thing. It is to know the thought by which all things
+are steered through all things."[1]
+
+Examples might be multiplied, but those that have been given are
+enough to show the character of the man: the facts of science, as they
+appeared to him, fed the flame in his soul, and in its light he saw
+into the depths of the world by the reflection of his own dancing
+swiftly penetrating fire. In such a nature we see the true union of
+the mystic and the man of science--the highest eminence, as I think,
+that it is possible to achieve in the world of thought.
+
+In Plato, the same twofold impulse exists, though the mystic impulse
+is distinctly the stronger of the two, and secures ultimate victory
+whenever the conflict is sharp. His description of the cave is the
+classical statement of belief in a knowledge and reality truer and
+more real than that of the senses:
+
+  "Imagine[2] a number of men living in an underground cavernous
+  chamber, with an entrance open to the light, extending along the
+  entire length of the cavern, in which they have been confined, from
+  their childhood, with their legs and necks so shackled that they
+  are obliged to sit still and look straight forwards, because their
+  chains render it impossible for them to turn their heads round: and
+  imagine a bright fire burning some way off, above and behind them,
+  and an elevated roadway passing between the fire and the prisoners,
+  with a low wall built along it, like the screens which conjurors
+  put up in front of their audience, and above which they exhibit
+  their wonders.
+
+  I have it, he replied.
+
+  Also figure to yourself a number of persons walking behind this
+  wall, and carrying with them statues of men, and images of other
+  animals, wrought in wood and stone and all kinds of materials,
+  together with various other articles, which overtop the wall; and,
+  as you might expect, let some of the passers-by be talking, and
+  others silent.
+
+  You are describing a strange scene, and strange prisoners.
+
+  They resemble us, I replied.
+
+  Now consider what would happen if the course of nature brought them
+  a release from their fetters, and a remedy for their foolishness,
+  in the following manner. Let us suppose that one of them has been
+  released, and compelled suddenly to stand up, and turn his neck
+  round and walk with open eyes towards the light; and let us suppose
+  that he goes through all these actions with pain, and that the
+  dazzling splendour renders him incapable of discerning those
+  objects of which he used formerly to see the shadows. What answer
+  should you expect him to make, if some one were to tell him that in
+  those days he was watching foolish phantoms, but that now he is
+  somewhat nearer to reality, and is turned towards things more real,
+  and sees more correctly; above all, if he were to point out to him
+  the several objects that are passing by, and question him, and
+  compel him to answer what they are? Should you not expect him to be
+  puzzled, and to regard his old visions as truer than the objects
+  now forced upon his notice?
+
+  Yes, much truer....
+
+  Hence, I suppose, habit will be necessary to enable him to perceive
+  objects in that upper world. At first he will be most successful in
+  distinguishing shadows; then he will discern the reflections of men
+  and other things in water, and afterwards the realities; and after
+  this he will raise his eyes to encounter the light of the moon and
+  stars, finding it less difficult to study the heavenly bodies and
+  the heaven itself by night, than the sun and the sun's light by
+  day.
+
+  Doubtless.
+
+  Last of all, I imagine, he will be able to observe and contemplate
+  the nature of the sun, not as it _appears_ in water or on alien
+  ground, but as it is in itself in its own territory.
+
+  Of course.
+
+  His next step will be to draw the conclusion, that the sun is the
+  author of the seasons and the years, and the guardian of all things
+  in the visible world, and in a manner the cause of all those things
+  which he and his companions used to see.
+
+  Obviously, this will be his next step....
+
+  Now this imaginary case, my dear Glancon, you must apply in all its
+  parts to our former statements, by comparing the region which the
+  eye reveals to the prison house, and the light of the fire therein
+  to the power of the sun: and if, by the upward ascent and the
+  contemplation of the upper world, you understand the mounting of
+  the soul into the intellectual region, you will hit the tendency of
+  my own surmises, since you desire to be told what they are; though,
+  indeed, God only knows whether they are correct. But, be that as it
+  may, the view which I take of the subject is to the following
+  effect. In the world of knowledge, the essential Form of Good is
+  the limit of our enquiries, and can barely be perceived; but, when
+  perceived, we cannot help concluding that it is in every case the
+  source of all that is bright and beautiful,--in the visible world
+  giving birth to light and its master, and in the intellectual world
+  dispensing, immediately and with full authority, truth and
+  reason;--and that whosoever would act wisely, either in private or
+  in public, must set this Form of Good before his eyes."
+
+But in this passage, as throughout most of Plato's teaching, there is
+an identification of the good with the truly real, which became
+embodied in the philosophical tradition, and is still largely
+operative in our own day. In thus allowing a legislative function to
+the good, Plato produced a divorce between philosophy and science,
+from which, in my opinion, both have suffered ever since and are still
+suffering. The man of science, whatever his hopes may be, must lay
+them aside while he studies nature; and the philosopher, if he is to
+achieve truth, must do the same. Ethical considerations can only
+legitimately appear when the truth has been ascertained: they can and
+should appear as determining our feeling towards the truth, and our
+manner of ordering our lives in view of the truth, but not as
+themselves dictating what the truth is to be.
+
+There are passages in Plato--among those which illustrate the
+scientific side of his mind--where he seems clearly aware of this. The
+most noteworthy is the one in which Socrates, as a young man, is
+explaining the theory of ideas to Parmenides.
+
+After Socrates has explained that there is an idea of the good, but
+not of such things as hair and mud and dirt, Parmenides advises him
+"not to despise even the meanest things," and this advice shows the
+genuine scientific temper. It is with this impartial temper that the
+mystic's apparent insight into a higher reality and a hidden good has
+to be combined if philosophy is to realise its greatest possibilities.
+And it is failure in this respect that has made so much of idealistic
+philosophy thin, lifeless, and insubstantial. It is only in marriage
+with the world that our ideals can bear fruit: divorced from it, they
+remain barren. But marriage with the world is not to be achieved by an
+ideal which shrinks from fact, or demands in advance that the world
+shall conform to its desires.
+
+Parmenides himself is the source of a peculiarly interesting strain
+of mysticism which pervades Plato's thought--the mysticism which may
+be called "logical" because it is embodied in theories on logic. This
+form of mysticism, which appears, so far as the West is concerned, to
+have originated with Parmenides, dominates the reasonings of all the
+great mystical metaphysicians from his day to that of Hegel and his
+modern disciples. Reality, he says, is uncreated, indestructible,
+unchanging, indivisible; it is "immovable in the bonds of mighty
+chains, without beginning and without end; since coming into being and
+passing away have been driven afar, and true belief has cast them
+away." The fundamental principle of his inquiry is stated in a
+sentence which would not be out of place in Hegel: "Thou canst not
+know what is not--that is impossible--nor utter it; for it is the same
+thing that can be thought and that can be." And again: "It needs must
+be that what can be thought and spoken of is; for it is possible for
+it to be, and it is not possible for what is nothing to be." The
+impossibility of change follows from this principle; for what is past
+can be spoken of, and therefore, by the principle, still is.
+
+Mystical philosophy, in all ages and in all parts of the world, is
+characterised by certain beliefs which are illustrated by the
+doctrines we have been considering.
+
+There is, first, the belief in insight as against discursive analytic
+knowledge: the belief in a way of wisdom, sudden, penetrating,
+coercive, which is contrasted with the slow and fallible study of
+outward appearance by a science relying wholly upon the senses. All
+who are capable of absorption in an inward passion must have
+experienced at times the strange feeling of unreality in common
+objects, the loss of contact with daily things, in which the solidity
+of the outer world is lost, and the soul seems, in utter loneliness,
+to bring forth, out of its own depths, the mad dance of fantastic
+phantoms which have hitherto appeared as independently real and
+living. This is the negative side of the mystic's initiation: the
+doubt concerning common knowledge, preparing the way for the reception
+of what seems a higher wisdom. Many men to whom this negative
+experience is familiar do not pass beyond it, but for the mystic it is
+merely the gateway to an ampler world.
+
+The mystic insight begins with the sense of a mystery unveiled, of a
+hidden wisdom now suddenly become certain beyond the possibility of a
+doubt. The sense of certainty and revelation comes earlier than any
+definite belief. The definite beliefs at which mystics arrive are the
+result of reflection upon the inarticulate experience gained in the
+moment of insight. Often, beliefs which have no real connection with
+this moment become subsequently attracted into the central nucleus;
+thus in addition to the convictions which all mystics share, we find,
+in many of them, other convictions of a more local and temporary
+character, which no doubt become amalgamated with what was essentially
+mystical in virtue of their subjective certainty. We may ignore such
+inessential accretions, and confine ourselves to the beliefs which all
+mystics share.
+
+The first and most direct outcome of the moment of illumination is
+belief in the possibility of a way of knowledge which may be called
+revelation or insight or intuition, as contrasted with sense, reason,
+and analysis, which are regarded as blind guides leading to the morass
+of illusion. Closely connected with this belief is the conception of a
+Reality behind the world of appearance and utterly different from it.
+This Reality is regarded with an admiration often amounting to
+worship; it is felt to be always and everywhere close at hand, thinly
+veiled by the shows of sense, ready, for the receptive mind, to shine
+in its glory even through the apparent folly and wickedness of Man.
+The poet, the artist, and the lover are seekers after that glory: the
+haunting beauty that they pursue is the faint reflection of its sun.
+But the mystic lives in the full light of the vision: what others
+dimly seek he knows, with a knowledge beside which all other knowledge
+is ignorance.
+
+The second characteristic of mysticism is its belief in unity, and its
+refusal to admit opposition or division anywhere. We found Heraclitus
+saying "good and ill are one"; and again he says, "the way up and the
+way down is one and the same." The same attitude appears in the
+simultaneous assertion of contradictory propositions, such as: "We
+step and do not step into the same rivers; we are and are not." The
+assertion of Parmenides, that reality is one and indivisible, comes
+from the same impulse towards unity. In Plato, this impulse is less
+prominent, being held in check by his theory of ideas; but it
+reappears, so far as his logic permits, in the doctrine of the primacy
+of the Good.
+
+A third mark of almost all mystical metaphysics is the denial of the
+reality of Time. This is an outcome of the denial of division; if all
+is one, the distinction of past and future must be illusory. We have
+seen this doctrine prominent in Parmenides; and among moderns it is
+fundamental in the systems of Spinoza and Hegel.
+
+The last of the doctrines of mysticism which we have to consider is
+its belief that all evil is mere appearance, an illusion produced by
+the divisions and oppositions of the analytic intellect. Mysticism
+does not maintain that such things as cruelty, for example, are good,
+but it denies that they are real: they belong to that lower world of
+phantoms from which we are to be liberated by the insight of the
+vision. Sometimes--for example in Hegel, and at least verbally in
+Spinoza--not only evil, but good also, is regarded as illusory, though
+nevertheless the emotional attitude towards what is held to be Reality
+is such as would naturally be associated with the belief that Reality
+is good. What is, in all cases, ethically characteristic of mysticism
+is absence of indignation or protest, acceptance with joy, disbelief
+in the ultimate truth of the division into two hostile camps, the good
+and the bad. This attitude is a direct outcome of the nature of the
+mystical experience: with its sense of unity is associated a feeling
+of infinite peace. Indeed it may be suspected that the feeling of
+peace produces, as feelings do in dreams, the whole system of
+associated beliefs which make up the body of mystic doctrine. But this
+is a difficult question, and one on which it cannot be hoped that
+mankind will reach agreement.
+
+Four questions thus arise in considering the truth or falsehood of
+mysticism, namely:
+
+  I. Are there two ways of knowing, which may be called respectively
+  reason and intuition? And if so, is either to be preferred to the
+  other?
+
+  II. Is all plurality and division illusory?
+
+  III. Is time unreal?
+
+  IV. What kind of reality belongs to good and evil?
+
+On all four of these questions, while fully developed mysticism seems
+to me mistaken, I yet believe that, by sufficient restraint, there is
+an element of wisdom to be learned from the mystical way of feeling,
+which does not seem to be attainable in any other manner. If this is
+the truth, mysticism is to be commended as an attitude towards life,
+not as a creed about the world. The meta-physical creed, I shall
+maintain, is a mistaken outcome of the emotion, although this emotion,
+as colouring and informing all other thoughts and feelings, is the
+inspirer of whatever is best in Man. Even the cautious and patient
+investigation of truth by science, which seems the very antithesis of
+the mystic's swift certainty, may be fostered and nourished by that
+very spirit of reverence in which mysticism lives and moves.
+
+
+I. REASON AND INTUITION[3]
+
+Of the reality or unreality of the mystic's world I know nothing. I
+have no wish to deny it, nor even to declare that the insight which
+reveals it is not a genuine insight. What I do wish to maintain--and
+it is here that the scientific attitude becomes imperative--is that
+insight, untested and unsupported, is an insufficient guarantee of
+truth, in spite of the fact that much of the most important truth is
+first suggested by its means. It is common to speak of an opposition
+between instinct and reason; in the eighteenth century, the opposition
+was drawn in favour of reason, but under the influence of Rousseau and
+the romantic movement instinct was given the preference, first by
+those who rebelled against artificial forms of government and thought,
+and then, as the purely rationalistic defence of traditional theology
+became increasingly difficult, by all who felt in science a menace to
+creeds which they associated with a spiritual outlook on life and the
+world. Bergson, under the name of "intuition," has raised instinct to
+the position of sole arbiter of metaphysical truth. But in fact the
+opposition of instinct and reason is mainly illusory. Instinct,
+intuition, or insight is what first leads to the beliefs which
+subsequent reason confirms or confutes; but the confirmation, where it
+is possible, consists, in the last analysis, of agreement with other
+beliefs no less instinctive. Reason is a harmonising, controlling
+force rather than a creative one. Even in the most purely logical
+realm, it is insight that first arrives at what is new.
+
+Where instinct and reason do sometimes conflict is in regard to single
+beliefs, held instinctively, and held with such determination that no
+degree of inconsistency with other beliefs leads to their abandonment.
+Instinct, like all human faculties, is liable to error. Those in whom
+reason is weak are often unwilling to admit this as regards
+themselves, though all admit it in regard to others. Where instinct is
+least liable to error is in practical matters as to which right
+judgment is a help to survival: friendship and hostility in others,
+for instance, are often felt with extraordinary discrimination through
+very careful disguises. But even in such matters a wrong impression
+may be given by reserve or flattery; and in matters less directly
+practical, such as philosophy deals with, very strong instinctive
+beliefs are sometimes wholly mistaken, as we may come to know through
+their perceived inconsistency with other equally strong beliefs. It is
+such considerations that necessitate the harmonising mediation of
+reason, which tests our beliefs by their mutual compatibility, and
+examines, in doubtful cases, the possible sources of error on the one
+side and on the other. In this there is no opposition to instinct as a
+whole, but only to blind reliance upon some one interesting aspect of
+instinct to the exclusion of other more commonplace but not less
+trustworthy aspects. It is such one-sidedness, not instinct itself,
+that reason aims at correcting.
+
+These more or less trite maxims may be illustrated by application to
+Bergson's advocacy of "intuition" as against "intellect." There are,
+he says, "two profoundly different ways of knowing a thing. The first
+implies that we move round the object: the second that we enter into
+it. The first depends on the point of view at which we are placed and
+on the symbols by which we express ourselves. The second neither
+depends on a point of view nor relies on any symbol. The first kind of
+knowledge may be said to stop at the _relative_; the second, in those
+cases where it is possible, to attain the _absolute_."[4] The second
+of these, which is intuition, is, he says, "the kind of _intellectual
+sympathy_ by which one places oneself within an object in order to
+coincide with what is unique in it and therefore inexpressible" (p.
+6). In illustration, he mentions self-knowledge: "there is one
+reality, at least, which we all seize from within, by intuition and
+not by simple analysis. It is our own personality in its flowing
+through time--our self which endures" (p. 8). The rest of Bergson's
+philosophy consists in reporting, through the imperfect medium of
+words, the knowledge gained by intuition, and the consequent complete
+condemnation of all the pretended knowledge derived from science and
+common sense.
+
+This procedure, since it takes sides in a conflict of instinctive
+beliefs, stands in need of justification by proving the greater
+trustworthiness of the beliefs on one side than of those on the other.
+Bergson attempts this justification in two ways, first by explaining
+that intellect is a purely practical faculty to secure biological
+success, secondly by mentioning remarkable feats of instinct in
+animals and by pointing out characteristics of the world which, though
+intuition can apprehend them, are baffling to intellect as he
+interprets it.
+
+Of Bergson's theory that intellect is a purely practical faculty,
+developed in the struggle for survival, and not a source of true
+beliefs, we may say, first, that it is only through intellect that we
+know of the struggle for survival and of the biological ancestry of
+man: if the intellect is misleading, the whole of this merely inferred
+history is presumably untrue. If, on the other hand, we agree with him
+in thinking that evolution took place as Darwin believed, then it is
+not only intellect, but all our faculties, that have been developed
+under the stress of practical utility. Intuition is seen at its best
+where it is directly useful, for example in regard to other people's
+characters and dispositions. Bergson apparently holds that capacity
+for this kind of knowledge is less explicable by the struggle for
+existence than, for example, capacity for pure mathematics. Yet the
+savage deceived by false friendship is likely to pay for his mistake
+with his life; whereas even in the most civilised societies men are
+not put to death for mathematical incompetence. All the most striking
+of his instances of intuition in animals have a very direct survival
+value. The fact is, of course, that both intuition and intellect have
+been developed because they are useful, and that, speaking broadly,
+they are useful when they give truth and become harmful when they give
+falsehood. Intellect, in civilised man, like artistic capacity, has
+occasionally been developed beyond the point where it is useful to the
+individual; intuition, on the other hand, seems on the whole to
+diminish as civilisation increases. It is greater, as a rule, in
+children than in adults, in the uneducated than in the educated.
+Probably in dogs it exceeds anything to be found in human beings. But
+those who see in these facts a recommendation of intuition ought to
+return to running wild in the woods, dyeing themselves with woad and
+living on hips and haws.
+
+Let us next examine whether intuition possesses any such infallibility
+as Bergson claims for it. The best instance of it, according to him,
+is our acquaintance with ourselves; yet self-knowledge is proverbially
+rare and difficult. Most men, for example, have in their nature
+meannesses, vanities, and envies of which they are quite unconscious,
+though even their best friends can perceive them without any
+difficulty. It is true that intuition has a convincingness which is
+lacking to intellect: while it is present, it is almost impossible to
+doubt its truth. But if it should appear, on examination, to be at
+least as fallible as intellect, its greater subjective certainty
+becomes a demerit, making it only the more irresistibly deceptive.
+Apart from self-knowledge, one of the most notable examples of
+intuition is the knowledge people believe themselves to possess of
+those with whom they are in love: the wall between different
+personalities seems to become transparent, and people think they see
+into another soul as into their own. Yet deception in such cases is
+constantly practised with success; and even where there is no
+intentional deception, experience gradually proves, as a rule, that
+the supposed insight was illusory, and that the slower more groping
+methods of the intellect are in the long run more reliable.
+
+Bergson maintains that intellect can only deal with things in so far
+as they resemble what has been experienced in the past, while
+intuition has the power of apprehending the uniqueness and novelty
+that always belong to each fresh moment. That there is something
+unique and new at every moment, is certainly true; it is also true
+that this cannot be fully expressed by means of intellectual concepts.
+Only direct acquaintance can give knowledge of what is unique and new.
+But direct acquaintance of this kind is given fully in sensation, and
+does not require, so far as I can see, any special faculty of
+intuition for its apprehension. It is neither intellect nor intuition,
+but sensation, that supplies new data; but when the data are new in
+any remarkable manner, intellect is much more capable of dealing with
+them than intuition would be. The hen with a brood of ducklings no
+doubt has intuition which seems to place her inside them, and not
+merely to know them analytically; but when the ducklings take to the
+water, the whole apparent intuition is seen to be illusory, and the
+hen is left helpless on the shore. Intuition, in fact, is an aspect
+and development of instinct, and, like all instinct, is admirable in
+those customary surroundings which have moulded the habits of the
+animal in question, but totally incompetent as soon as the
+surroundings are changed in a way which demands some non-habitual mode
+of action.
+
+The theoretical understanding of the world, which is the aim of
+philosophy, is not a matter of great practical importance to animals,
+or to savages, or even to most civilised men. It is hardly to be
+supposed, therefore, that the rapid, rough and ready methods of
+instinct or intuition will find in this field a favourable ground for
+their application. It is the older kinds of activity, which bring out
+our kinship with remote generations of animal and semi-human
+ancestors, that show intuition at its best. In such matters as
+self-preservation and love, intuition will act sometimes (though not
+always) with a swiftness and precision which are astonishing to the
+critical intellect. But philosophy is not one of the pursuits which
+illustrate our affinity with the past: it is a highly refined, highly
+civilised pursuit, demanding, for its success, a certain liberation
+from the life of instinct, and even, at times, a certain aloofness
+from all mundane hopes and fears. It is not in philosophy, therefore,
+that we can hope to see intuition at its best. On the contrary, since
+the true objects of philosophy, and the habit of thought demanded for
+their apprehension, are strange, unusual, and remote, it is here, more
+almost than anywhere else, that intellect proves superior to
+intuition, and that quick unanalysed convictions are least deserving
+of uncritical acceptance.
+
+In advocating the scientific restraint and balance, as against the
+self-assertion of a confident reliance upon intuition, we are only
+urging, in the sphere of knowledge, that largeness of contemplation,
+that impersonal disinterestedness, and that freedom from practical
+preoccupations which have been inculcated by all the great religions
+of the world. Thus our conclusion, however it may conflict with the
+explicit beliefs of many mystics, is, in essence, not contrary to the
+spirit which inspires those beliefs, but rather the outcome of this
+very spirit as applied in the realm of thought.
+
+
+II. UNITY AND PLURALITY
+
+One of the most convincing aspects of the mystic illumination is the
+apparent revelation of the oneness of all things, giving rise to
+pantheism in religion and to monism in philosophy. An elaborate logic,
+beginning with Parmenides, and culminating in Hegel and his followers,
+has been gradually developed, to prove that the universe is one
+indivisible Whole, and that what seem to be its parts, if considered
+as substantial and self-existing, are mere illusion. The conception
+of a Reality quite other than the world of appearance, a reality one,
+indivisible, and unchanging, was introduced into Western philosophy by
+Parmenides, not, nominally at least, for mystical or religious
+reasons, but on the basis of a logical argument as to the
+impossibility of not-being, and most subsequent metaphysical systems
+are the outcome of this fundamental idea.
+
+The logic used in defence of mysticism seems to be faulty as logic,
+and open to technical criticisms, which I have explained elsewhere. I
+shall not here repeat these criticisms, since they are lengthy and
+difficult, but shall instead attempt an analysis of the state of mind
+from which mystical logic has arisen.
+
+Belief in a reality quite different from what appears to the senses
+arises with irresistible force in certain moods, which are the source
+of most mysticism, and of most metaphysics. While such a mood is
+dominant, the need of logic is not felt, and accordingly the more
+thoroughgoing mystics do not employ logic, but appeal directly to the
+immediate deliverance of their insight. But such fully developed
+mysticism is rare in the West. When the intensity of emotional
+conviction subsides, a man who is in the habit of reasoning will
+search for logical grounds in favour of the belief which he finds in
+himself. But since the belief already exists, he will be very
+hospitable to any ground that suggests itself. The paradoxes
+apparently proved by his logic are really the paradoxes of mysticism,
+and are the goal which he feels his logic must reach if it is to be in
+accordance with insight. The resulting logic has rendered most
+philosophers incapable of giving any account of the world of science
+and daily life. If they had been anxious to give such an account, they
+would probably have discovered the errors of their logic; but most of
+them were less anxious to understand the world of science and daily
+life than to convict it of unreality in the interests of a
+super-sensible "real" world.
+
+It is in this way that logic has been pursued by those of the great
+philosophers who were mystics. But since they usually took for granted
+the supposed insight of the mystic emotion, their logical doctrines
+were presented with a certain dryness, and were believed by their
+disciples to be quite independent of the sudden illumination from
+which they sprang. Nevertheless their origin clung to them, and they
+remained--to borrow a useful word from Mr. Santayana--"malicious" in
+regard to the world of science and common sense. It is only so that we
+can account for the complacency with which philosophers have accepted
+the inconsistency of their doctrines with all the common and
+scientific facts which seem best established and most worthy of
+belief.
+
+The logic of mysticism shows, as is natural, the defects which are
+inherent in anything malicious. The impulse to logic, not felt while
+the mystic mood is dominant, reasserts itself as the mood fades, but
+with a desire to retain the vanishing insight, or at least to prove
+that it _was_ insight, and that what seems to contradict it is
+illusion. The logic which thus arises is not quite disinterested or
+candid, and is inspired by a certain hatred of the daily world to
+which it is to be applied. Such an attitude naturally does not tend to
+the best results. Everyone knows that to read an author simply in
+order to refute him is not the way to understand him; and to read the
+book of Nature with a conviction that it is all illusion is just as
+unlikely to lead to understanding. If our logic is to find the common
+world intelligible, it must not be hostile, but must be inspired by a
+genuine acceptance such as is not usually to be found among
+metaphysicians.
+
+
+III. TIME
+
+The unreality of time is a cardinal doctrine of many metaphysical
+systems, often nominally based, as already by Parmenides, upon logical
+arguments, but originally derived, at any rate in the founders of new
+systems, from the certainty which is born in the moment of mystic
+insight. As a Persian Sufi poet says:
+
+    "Past and future are what veil God from our sight.
+    Burn up both of them with fire! How long
+    Wilt thou be partitioned by these segments as a reed?"[5]
+
+The belief that what is ultimately real must be immutable is a very
+common one: it gave rise to the metaphysical notion of substance, and
+finds, even now, a wholly illegitimate satisfaction in such scientific
+doctrines as the conservation of energy and mass.
+
+It is difficult to disentangle the truth and the error in this view.
+The arguments for the contention that time is unreal and that the
+world of sense is illusory must, I think, be regarded as fallacious.
+Nevertheless there is some sense--easier to feel than to state--in
+which time is an unimportant and superficial characteristic of
+reality. Past and future must be acknowledged to be as real as the
+present, and a certain emancipation from slavery to time is essential
+to philosophic thought. The importance of time is rather practical
+than theoretical, rather in relation to our desires than in relation
+to truth. A truer image of the world, I think, is obtained by
+picturing things as entering into the stream of time from an eternal
+world outside, than from a view which regards time as the devouring
+tyrant of all that is. Both in thought and in feeling, even though
+time be real, to realise the unimportance of time is the gate of
+wisdom.
+
+That this is the case may be seen at once by asking ourselves why our
+feelings towards the past are so different from our feelings towards
+the future. The reason for this difference is wholly practical: our
+wishes can affect the future but not the past, the future is to some
+extent subject to our power, while the past is unalterably fixed. But
+every future will some day be past: if we see the past truly now, it
+must, when it was still future, have been just what we now see it to
+be, and what is now future must be just what we shall see it to be
+when it has become past. The felt difference of quality between past
+and future, therefore, is not an intrinsic difference, but only a
+difference in relation to us: to impartial contemplation, it ceases to
+exist. And impartiality of contemplation is, in the intellectual
+sphere, that very same virtue of disinterestedness which, in the
+sphere of action, appears as justice and unselfishness. Whoever wishes
+to see the world truly, to rise in thought above the tyranny of
+practical desires, must learn to overcome the difference of attitude
+towards past and future, and to survey the whole stream of time in one
+comprehensive vision.
+
+The kind of way in which, as it seems to me, time ought not to enter
+into our theoretic philosophical thought, may be illustrated by the
+philosophy which has become associated with the idea of evolution, and
+which is exemplified by Nietzsche, pragmatism, and Bergson. This
+philosophy, on the basis of the development which has led from the
+lowest forms of life up to man, sees in _progress_ the fundamental law
+of the universe, and thus admits the difference between _earlier_ and
+_later_ into the very citadel of its contemplative outlook. With its
+past and future history of the world, conjectural as it is, I do not
+wish to quarrel. But I think that, in the intoxication of a quick
+success, much that is required for a true understanding of the
+universe has been forgotten. Something of Hellenism, something, too,
+of Oriental resignation, must be combined with its hurrying Western
+self-assertion before it can emerge from the ardour of youth into the
+mature wisdom of manhood. In spite of its appeals to science, the true
+scientific philosophy, I think, is something more arduous and more
+aloof, appealing to less mundane hopes, and requiring a severer
+discipline for its successful practice.
+
+Darwin's _Origin of Species_ persuaded the world that the difference
+between different species of animals and plants is not the fixed
+immutable difference that it appears to be. The doctrine of natural
+kinds, which had rendered classification easy and definite, which was
+enshrined in the Aristotelian tradition, and protected by its supposed
+necessity for orthodox dogma, was suddenly swept away for ever out of
+the biological world. The difference between man and the lower
+animals, which to our human conceit appears enormous, was shown to be
+a gradual achievement, involving intermediate being who could not with
+certainty be placed either within or without the human family. The sun
+and the planets had already been shown by Laplace to be very probably
+derived from a primitive more or less undifferentiated nebula. Thus
+the old fixed landmarks became wavering and indistinct, and all sharp
+outlines were blurred. Things and species lost their boundaries, and
+none could say where they began or where they ended.
+
+But if human conceit was staggered for a moment by its kinship with
+the ape, it soon found a way to reassert itself, and that way is the
+"philosophy" of evolution. A process which led from the amoeba to Man
+appeared to the philosophers to be obviously a progress--though
+whether the amoeba would agree with this opinion is not known. Hence
+the cycle of changes which science had shown to be the probable
+history of the past was welcomed as revealing a law of development
+towards good in the universe--an evolution or unfolding of an idea
+slowly embodying itself in the actual. But such a view, though it
+might satisfy Spencer and those whom we may call Hegelian
+evolutionists, could not be accepted as adequate by the more
+whole-hearted votaries of change. An ideal to which the world
+continuously approaches is, to these minds, too dead and static to be
+inspiring. Not only the aspiration, but the ideal too, must change and
+develop with the course of evolution: there must be no fixed goal, but
+a continual fashioning of fresh needs by the impulse which is life and
+which alone gives unity to the process.
+
+Life, in this philosophy, is a continuous stream, in which all
+divisions are artificial and unreal. Separate things, beginnings and
+endings, are mere convenient fictions: there is only smooth unbroken
+transition. The beliefs of to-day may count as true to-day, if they
+carry us along the stream; but to-morrow they will be false, and must
+be replaced by new beliefs to meet the new situation. All our thinking
+consists of convenient fictions, imaginary congealings of the stream:
+reality flows on in spite of all our fictions, and though it can be
+lived, it cannot be conceived in thought. Somehow, without explicit
+statement, the assurance is slipped in that the future, though we
+cannot foresee it, will be better than the past or the present: the
+reader is like the child which expects a sweet because it has been
+told to open its mouth and shut its eyes. Logic, mathematics, physics
+disappear in this philosophy, because they are too "static"; what is
+real is no impulse and movement towards a goal which, like the
+rainbow, recedes as we advance, and makes every place different when
+it reaches it from what it appeared to be at a distance.
+
+I do not propose to enter upon a technical examination of this
+philosophy. I wish only to maintain that the motives and interests
+which inspire it are so exclusively practical, and the problems with
+which it deals are so special, that it can hardly be regarded as
+touching any of the questions that, to my mind, constitute genuine
+philosophy.
+
+The predominant interest of evolutionism is in the question of human
+destiny, or at least of the destiny of Life. It is more interested in
+morality and happiness than in knowledge for its own sake. It must be
+admitted that the same may be said of many other philosophies, and
+that a desire for the kind of knowledge which philosophy can give is
+very rare. But if philosophy is to attain truth, it is necessary first
+and foremost that philosophers should acquire the disinterested
+intellectual curiosity which characterises the genuine man of science.
+Knowledge concerning the future--which is the kind of knowledge that
+must be sought if we are to know about human destiny--is possible
+within certain narrow limits. It is impossible to say how much the
+limits may be enlarged with the progress of science. But what is
+evident is that any proposition about the future belongs by its
+subject-matter to some particular science, and is to be ascertained,
+if at all, by the methods of that science. Philosophy is not a short
+cut to the same kind of results as those of the other sciences: if it
+is to be a genuine study, it must have a province of its own, and aim
+at results which the other sciences can neither prove nor disprove.
+
+Evolutionism, in basing itself upon the notion of _progress_, which is
+change from the worse to the better, allows the notion of time, as it
+seems to me, to become its tyrant rather than its servant, and thereby
+loses that impartiality of contemplation which is the source of all
+that is best in philosophic thought and feeling. Metaphysicians, as we
+saw, have frequently denied altogether the reality of time. I do not
+wish to do this; I wish only to preserve the mental outlook which
+inspired the denial, the attitude which, in thought, regards the past
+as having the same reality as the present and the same importance as
+the future. "In so far," says Spinoza,[6] "as the mind conceives a
+thing according to the dictate of reason, it will be equally affected
+whether the idea is that of a future, past, or present thing." It is
+this "conceiving according to the dictate of reason" that I find
+lacking in the philosophy which is based on evolution.
+
+
+IV. GOOD AND EVIL
+
+Mysticism maintains that all evil is illusory, and sometimes maintains
+the same view as regards good, but more often holds that all Reality
+is good. Both views are to be found in Heraclitus: "Good and ill are
+one," he says, but again, "To God all things are fair and good and
+right, but men hold some things wrong and some right." A similar
+twofold position is to be found in Spinoza, but he uses the word
+"perfection" when he means to speak of the good that is not merely
+human. "By reality and perfection I mean the same thing," he says;[7]
+but elsewhere we find the definition: "By _good_ I shall mean that
+which we certainly know to be useful to us."[8] Thus perfection
+belongs to Reality in its own nature, but goodness is relative to
+ourselves and our needs, and disappears in an impartial survey. Some
+such distinction, I think, is necessary in order to understand the
+ethical outlook of mysticism: there is a lower mundane kind of good
+and evil, which divides the world of appearance into what seem to be
+conflicting parts; but there is also a higher, mystical kind of good,
+which belongs to Reality and is not opposed by any correlative kind of
+evil.
+
+It is difficult to give a logically tenable account of this position
+without recognising that good and evil are subjective, that what is
+good is merely that towards which we have one kind of feeling, and
+what is evil is merely that towards which we have another kind of
+feeling. In our active life, where we have to exercise choice, and to
+prefer this to that of two possible acts, it is necessary to have a
+distinction of good and evil, or at least of better and worse. But
+this distinction, like everything pertaining to action, belongs to
+what mysticism regards as the world of illusion, if only because it is
+essentially concerned with time. In our contemplative life, where
+action is not called for, it is possible to be impartial, and to
+overcome the ethical dualism which action requires. So long as we
+remain _merely_ impartial, we may be content to say that both the good
+and the evil of action are illusions. But if, as we must do if we have
+the mystic vision, we find the whole world worthy of love and worship,
+if we see
+
+    "The earth, and every common sight....
+    Apparell'd in celestial light,"
+
+we shall say that there is a higher good than that of action, and that
+this higher good belongs to the whole world as it is in reality. In
+this way the twofold attitude and the apparent vacillation of
+mysticism are explained and justified.
+
+The possibility of this universal love and joy in all that exists is
+of supreme importance for the conduct and happiness of life, and gives
+inestimable value to the mystic emotion, apart from any creeds which
+may be built upon it. But if we are not to be led into false beliefs,
+it is necessary to realise exactly _what_ the mystic emotion reveals.
+It reveals a possibility of human nature--a possibility of a nobler,
+happier, freer life than any that can be otherwise achieved. But it
+does not reveal anything about the non-human, or about the nature of
+the universe in general. Good and bad, and even the higher good that
+mysticism finds everywhere, are the reflections of our own emotions on
+other things, not part of the substance of things as they are in
+themselves. And therefore an impartial contemplation, freed from all
+pre-occupation with Self, will not judge things good or bad, although
+it is very easily combined with that feeling of universal love which
+leads the mystic to say that the whole world is good.
+
+The philosophy of evolution, through the notion of progress, is bound
+up with the ethical dualism of the worse and the better, and is thus
+shut out, not only from the kind of survey which discards good and
+evil altogether from its view, but also from the mystical belief in
+the goodness of everything. In this way the distinction of good and
+evil, like time, becomes a tyrant in this philosophy, and introduces
+into thought the restless selectiveness of action. Good and evil, like
+time, are, it would seem, not general or fundamental in the world of
+thought, but late and highly specialised members of the intellectual
+hierarchy.
+
+Although, as we saw, mysticism can be interpreted so as to agree with
+the view that good and evil are not intellectually fundamental, it
+must be admitted that here we are no longer in verbal agreement with
+most of the great philosophers and religious teachers of the past. I
+believe, however, that the elimination of ethical considerations from
+philosophy is both scientifically necessary and--though this may seem
+a paradox--an ethical advance. Both these contentions must be briefly
+defended.
+
+The hope of satisfaction to our more human desires--the hope of
+demonstrating that the world has this or that desirable ethical
+characteristic--is not one which, so far as I can see, a scientific
+philosophy can do anything whatever to satisfy. The difference between
+a good world and a bad one is a difference in the particular
+characteristics of the particular things that exist in these worlds:
+it is not a sufficiently abstract difference to come within the
+province of philosophy. Love and hate, for example, are ethical
+opposites, but to philosophy they are closely analogous attitudes
+towards objects. The general form and structure of those attitudes
+towards objects which constitute mental phenomena is a problem for
+philosophy, but the difference between love and hate is not a
+difference of form or structure, and therefore belongs rather to the
+special science of psychology than to philosophy. Thus the ethical
+interests which have often inspired philosophers must remain in the
+background: some kind of ethical interest may inspire the whole study,
+but none must obtrude in the detail or be expected in the special
+results which are sought.
+
+If this view seems at first sight disappointing, we may remind
+ourselves that a similar change has been found necessary in all the
+other sciences. The physicist or chemist is not now required to prove
+the ethical importance of his ions or atoms; the biologist is not
+expected to prove the utility of the plants or animals which he
+dissects. In pre-scientific ages this was not the case. Astronomy, for
+example, was studied because men believed in astrology: it was thought
+that the movements of the planets had the most direct and important
+bearing upon the lives of human beings. Presumably, when this belief
+decayed and the disinterested study of astronomy began, many who had
+found astrology absorbingly interesting decided that astronomy had too
+little human interest to be worthy of study. Physics, as it appears in
+Plato's Timæus for example, is full of ethical notions: it is an
+essential part of its purpose to show that the earth is worthy of
+admiration. The modern physicist, on the contrary, though he has no
+wish to deny that the earth is admirable, is not concerned, as
+physicist, with its ethical attributes: he is merely concerned to find
+out facts, not to consider whether they are good or bad. In
+psychology, the scientific attitude is even more recent and more
+difficult than in the physical sciences: it is natural to consider
+that human nature is either good or bad, and to suppose that the
+difference between good and bad, so all-important in practice, must be
+important in theory also. It is only during the last century that an
+ethically neutral psychology has grown up; and here too, ethical
+neutrality has been essential to scientific success.
+
+In philosophy, hitherto, ethical neutrality has been seldom sought and
+hardly ever achieved. Men have remembered their wishes, and have
+judged philosophies in relation to their wishes. Driven from the
+particular sciences, the belief that the notions of good and evil must
+afford a key to the understanding of the world has sought a refuge in
+philosophy. But even from this last refuge, if philosophy is not to
+remain a set of pleasing dreams, this belief must be driven forth. It
+is a commonplace that happiness is not best achieved by those who
+seek it directly; and it would seem that the same is true of the good.
+In thought, at any rate, those who forget good and evil and seek only
+to know the facts are more likely to achieve good than those who view
+the world through the distorting medium of their own desires.
+
+We are thus brought back to our seeming paradox, that a philosophy
+which does not seek to impose upon the world its own conceptions of
+good and evil is not only more likely to achieve truth, but is also
+the outcome of a higher ethical standpoint than one which, like
+evolutionism and most traditional systems, is perpetually appraising
+the universe and seeking to find in it an embodiment of present
+ideals. In religion, and in every deeply serious view of the world and
+of human destiny, there is an element of submission, a realisation of
+the limits of human power, which is somewhat lacking in the modern
+world, with its quick material successes and its insolent belief in
+the boundless possibilities of progress. "He that loveth his life
+shall lose it"; and there is danger lest, through a too confident love
+of life, life itself should lose much of what gives it its highest
+worth. The submission which religion inculcates in action is
+essentially the same in spirit as that which science teaches in
+thought; and the ethical neutrality by which its victories have been
+achieved is the outcome of that submission.
+
+The good which it concerns us to remember is the good which it lies in
+our power to create--the good in our own lives and in our attitude
+towards the world. Insistence on belief in an external realisation of
+the good is a form of self-assertion, which, while it cannot secure
+the external good which it desires, can seriously impair the inward
+good which lies within our power, and destroy that reverence towards
+fact which constitutes both what is valuable in humility and what is
+fruitful in the scientific temper.
+
+Human beings cannot, of course, wholly transcend human nature;
+something subjective, if only the interest that determines the
+direction of our attention, must remain in all our thought. But
+scientific philosophy comes nearer to objectivity than any other human
+pursuit, and gives us, therefore, the closest constant and the most
+intimate relation with the outer world that it is possible to achieve.
+To the primitive mind, everything is either friendly or hostile; but
+experience has shown that friendliness and hostility are not the
+conceptions by which the world is to be understood. Scientific
+philosophy thus represents, though as yet only in a nascent condition,
+a higher form of thought than any pre-scientific belief or
+imagination, and, like every approach to self-transcendence, it brings
+with it a rich reward in increase of scope and breadth and
+comprehension. Evolutionism, in spite of its appeals to particular
+scientific facts, fails to be a truly scientific philosophy because of
+its slavery to time, its ethical preoccupations, and its predominant
+interest in our mundane concerns and destiny. A truly scientific
+philosophy will be more humble, more piecemeal, more arduous, offering
+less glitter of outward mirage to flatter fallacious hopes, but more
+indifferent to fate, and more capable of accepting the world without
+the tyrannous imposition of our human and temporary demands.
+
+FOOTNOTES:
+
+[1] All the above quotations are from Burnet's _Early Greek
+Philosophy_, (2nd ed., 1908), pp. 146-156.
+
+[2] _Republic_, 514, translated by Davies and Vaughan.
+
+[3] This section, and also one or two pages in later sections, have
+been printed in a course of Lowell lectures _On our knowledge of the
+external world_, published by the Open Court Publishing Company. But I
+have left them here, as this is the context for which they were
+originally written.
+
+[4] _Introduction to Metaphysics_, p. 1.
+
+[5] Whinfield's translation of the _Masnavi_ (Trübner, 1887), p. 34.
+
+[6] _Ethics_, Bk. IV, Prop. LXII.
+
+[7] Ib., Pt. IV, Df. I.
+
+[8] _Ethics_. Pt. II. Df. VI.
+
+
+
+
+II
+
+THE PLACE OF SCIENCE IN A LIBERAL EDUCATION
+
+
+I
+
+Science, to the ordinary reader of newspapers, is represented by a
+varying selection of sensational triumphs, such as wireless telegraphy
+and aeroplanes, radio-activity and the marvels of modern alchemy. It is
+not of this aspect of science that I wish to speak. Science, in this
+aspect, consists of detached up-to-date fragments, interesting only
+until they are replaced by something newer and more up-to-date,
+displaying nothing of the systems of patiently constructed knowledge
+out of which, almost as a casual incident, have come the practically
+useful results which interest the man in the street. The increased
+command over the forces of nature which is derived from science is
+undoubtedly an amply sufficient reason for encouraging scientific
+research, but this reason has been so often urged and is so easily
+appreciated that other reasons, to my mind quite as important, are apt
+to be overlooked. It is with these other reasons, especially with the
+intrinsic value of a scientific habit of mind in forming our outlook
+on the world, that I shall be concerned in what follows.
+
+The instance of wireless telegraphy will serve to illustrate the
+difference between the two points of view. Almost all the serious
+intellectual labour required for the possibility of this invention is
+due to three men--Faraday, Maxwell, and Hertz. In alternating layers
+of experiment and theory these three men built up the modern theory of
+electromagnetism, and demonstrated the identity of light with
+electromagnetic waves. The system which they discovered is one of
+profound intellectual interest, bringing together and unifying an
+endless variety of apparently detached phenomena, and displaying a
+cumulative mental power which cannot but afford delight to every
+generous spirit. The mechanical details which remained to be adjusted
+in order to utilise their discoveries for a practical system of
+telegraphy demanded, no doubt, very considerable ingenuity, but had
+not that broad sweep and that universality which could give them
+intrinsic interest as an object of disinterested contemplation.
+
+From the point of view of training the mind, of giving that
+well-informed, impersonal outlook which constitutes culture in the
+good sense of this much-misused word, it seems to be generally held
+indisputable that a literary education is superior to one based on
+science. Even the warmest advocates of science are apt to rest their
+claims on the contention that culture ought to be sacrificed to
+utility. Those men of science who respect culture, when they associate
+with men learned in the classics, are apt to admit, not merely
+politely, but sincerely, a certain inferiority on their side,
+compensated doubtless by the services which science renders to
+humanity, but none the less real. And so long as this attitude exists
+among men of science, it tends to verify itself: the intrinsically
+valuable aspects of science tend to be sacrificed to the merely
+useful, and little attempt is made to preserve that leisurely,
+systematic survey by which the finer quality of mind is formed and
+nourished.
+
+But even if there be, in present fact, any such inferiority as is
+supposed in the educational value of science, this is, I believe, not
+the fault of science itself, but the fault of the spirit in which
+science is taught. If its full possibilities were realised by those
+who teach it, I believe that its capacity of producing those habits of
+mind which constitute the highest mental excellence would be at least
+as great as that of literature, and more particularly of Greek and
+Latin literature. In saying this I have no wish whatever to disparage
+a classical education. I have not myself enjoyed its benefits, and my
+knowledge of Greek and Latin authors is derived almost wholly from
+translations. But I am firmly persuaded that the Greeks fully deserve
+all the admiration that is bestowed upon them, and that it is a very
+great and serious loss to be unacquainted with their writings. It is
+not by attacking them, but by drawing attention to neglected
+excellences in science, that I wish to conduct my argument.
+
+One defect, however, does seem inherent in a purely classical
+education--namely, a too exclusive emphasis on the past. By the study
+of what is absolutely ended and can never be renewed, a habit of
+criticism towards the present and the future is engendered. The
+qualities in which the present excels are qualities to which the study
+of the past does not direct attention, and to which, therefore, the
+student of Greek civilisation may easily become blind. In what is new
+and growing there is apt to be something crude, insolent, even a
+little vulgar, which is shocking to the man of sensitive taste;
+quivering from the rough contact, he retires to the trim gardens of a
+polished past, forgetting that they were reclaimed from the wilderness
+by men as rough and earth-soiled as those from whom he shrinks in his
+own day. The habit of being unable to recognise merit until it is
+dead is too apt to be the result of a purely bookish life, and a
+culture based wholly on the past will seldom be able to pierce through
+everyday surroundings to the essential splendour of contemporary
+things, or to the hope of still greater splendour in the future.
+
+    "My eyes saw not the men of old;
+    And now their age away has rolled.
+    I weep--to think I shall not see
+    The heroes of posterity."
+
+So says the Chinese poet; but such impartiality is rare in the more
+pugnacious atmosphere of the West, where the champions of past and
+future fight a never-ending battle, instead of combining to seek out
+the merits of both.
+
+This consideration, which militates not only against the exclusive
+study of the classics, but against every form of culture which has
+become static, traditional, and academic, leads inevitably to the
+fundamental question: What is the true end of education? But before
+attempting to answer this question it will be well to define the sense
+in which we are to use the word "education." For this purpose I shall
+distinguish the sense in which I mean to use it from two others, both
+perfectly legitimate, the one broader and the other narrower than the
+sense in which I mean to use the word.
+
+In the broader sense, education will include not only what we learn
+through instruction, but all that we learn through personal
+experience--the formation of character through the education of life.
+Of this aspect of education, vitally important as it is, I will say
+nothing, since its consideration would introduce topics quite foreign
+to the question with which we are concerned.
+
+In the narrower sense, education may be confined to instruction, the
+imparting of definite information on various subjects, because such
+information, in and for itself, is useful in daily life. Elementary
+education--reading, writing, and arithmetic--is almost wholly of this
+kind. But instruction, necessary as it is, does not _per se_
+constitute education in the sense in which I wish to consider it.
+
+Education, in the sense in which I mean it, may be defined as _the
+formation, by means of instruction, of certain mental habits and a
+certain outlook on life and the world_. It remains to ask ourselves,
+what mental habits, and what sort of outlook, can be hoped for as the
+result of instruction? When we have answered this question we can
+attempt to decide what science has to contribute to the formation of
+the habits and outlook which we desire.
+
+Our whole life is built about a certain number--not a very small
+number--of primary instincts and impulses. Only what is in some way
+connected with these instincts and impulses appears to us desirable or
+important; there is no faculty, whether "reason" or "virtue" or
+whatever it may be called, that can take our active life and our hopes
+and fears outside the region controlled by these first movers of all
+desire. Each of them is like a queen-bee, aided by a hive of workers
+gathering honey; but when the queen is gone the workers languish and
+die, and the cells remain empty of their expected sweetness. So with
+each primary impulse in civilised man: it is surrounded and protected
+by a busy swarm of attendant derivative desires, which store up in its
+service whatever honey the surrounding world affords. But if the
+queen-impulse dies, the death-dealing influence, though retarded a
+little by habit, spreads slowly through all the subsidiary impulses,
+and a whole tract of life becomes inexplicably colourless. What was
+formerly full of zest, and so obviously worth doing that it raised no
+questions, has now grown dreary and purposeless: with a sense of
+disillusion we inquire the meaning of life, and decide, perhaps, that
+all is vanity. The search for an outside meaning that can _compel_ an
+inner response must always be disappointed: all "meaning" must be at
+bottom related to our primary desires, and when they are extinct no
+miracle can restore to the world the value which they reflected upon
+it.
+
+The purpose of education, therefore, cannot be to create any primary
+impulse which is lacking in the uneducated; the purpose can only be to
+enlarge the scope of those that human nature provides, by increasing
+the number and variety of attendant thoughts, and by showing where the
+most permanent satisfaction is to be found. Under the impulse of a
+Calvinistic horror of the "natural man," this obvious truth has been
+too often misconceived in the training of the young; "nature" has been
+falsely regarded as excluding all that is best in what is natural, and
+the endeavour to teach virtue has led to the production of stunted and
+contorted hypocrites instead of full-grown human beings. From such
+mistakes in education a better psychology or a kinder heart is
+beginning to preserve the present generation; we need, therefore,
+waste no more words on the theory that the purpose of education is to
+thwart or eradicate nature.
+
+But although nature must supply the initial force of desire, nature is
+not, in the civilised man, the spasmodic, fragmentary, and yet violent
+set of impulses that it is in the savage. Each impulse has its
+constitutional ministry of thought and knowledge and reflection,
+through which possible conflicts of impulses are foreseen, and
+temporary impulses are controlled by the unifying impulse which may be
+called wisdom. In this way education destroys the crudity of
+instinct, and increases through knowledge the wealth and variety of
+the individual's contacts with the outside world, making him no longer
+an isolated fighting unit, but a citizen of the universe, embracing
+distant countries, remote regions of space, and vast stretches of past
+and future within the circle of his interests. It is this simultaneous
+softening in the insistence of desire and enlargement of its scope
+that is the chief moral end of education.
+
+Closely connected with this moral end is the more purely intellectual
+aim of education, the endeavour to make us see and imagine the world
+in an objective manner, as far as possible as it is in itself, and not
+merely through the distorting medium of personal desire. The complete
+attainment of such an objective view is no doubt an ideal,
+indefinitely approachable, but not actually and fully realisable.
+Education, considered as a process of forming our mental habits and
+our outlook on the world, is to be judged successful in proportion as
+its outcome approximates to this ideal; in proportion, that is to say,
+as it gives us a true view of our place in society, of the relation of
+the whole human society to its non-human environment, and of the
+nature of the non-human world as it is in itself apart from our
+desires and interests. If this standard is admitted, we can return to
+the consideration of science, inquiring how far science contributes to
+such an aim, and whether it is in any respect superior to its rivals
+in educational practice.
+
+
+II
+
+Two opposite and at first sight conflicting merits belong to science
+as against literature and art. The one, which is not inherently
+necessary, but is certainly true at the present day, is hopefulness
+as to the future of human achievement, and in particular as to the
+useful work that may be accomplished by any intelligent student. This
+merit and the cheerful outlook which it engenders prevent what might
+otherwise be the depressing effect of another aspect of science, to my
+mind also a merit, and perhaps its greatest merit--I mean the
+irrelevance of human passions and of the whole subjective apparatus
+where scientific truth is concerned. Each of these reasons for
+preferring the study of science requires some amplification. Let us
+begin with the first.
+
+In the study of literature or art our attention is perpetually riveted
+upon the past: the men of Greece or of the Renaissance did better than
+any men do now; the triumphs of former ages, so far from facilitating
+fresh triumphs in our own age, actually increase the difficulty of
+fresh triumphs by rendering originality harder of attainment; not only
+is artistic achievement not cumulative, but it seems even to depend
+upon a certain freshness and _naïveté_ of impulse and vision which
+civilisation tends to destroy. Hence comes, to those who have been
+nourished on the literary and artistic productions of former ages, a
+certain peevishness and undue fastidiousness towards the present, from
+which there seems no escape except into the deliberate vandalism which
+ignores tradition and in the search after originality achieves only
+the eccentric. But in such vandalism there is none of the simplicity
+and spontaneity out of which great art springs: theory is still the
+canker in its core, and insincerity destroys the advantages of a
+merely pretended ignorance.
+
+The despair thus arising from an education which suggests no
+pre-eminent mental activity except that of artistic creation is wholly
+absent from an education which gives the knowledge of scientific
+method. The discovery of scientific method, except in pure
+mathematics, is a thing of yesterday; speaking broadly, we may say
+that it dates from Galileo. Yet already it has transformed the world,
+and its success proceeds with ever-accelerating velocity. In science
+men have discovered an activity of the very highest value in which
+they are no longer, as in art, dependent for progress upon the
+appearance of continually greater genius, for in science the
+successors stand upon the shoulders of their predecessors; where one
+man of supreme genius has invented a method, a thousand lesser men can
+apply it. No transcendent ability is required in order to make useful
+discoveries in science; the edifice of science needs its masons,
+bricklayers, and common labourers as well as its foremen,
+master-builders, and architects. In art nothing worth doing can be
+done without genius; in science even a very moderate capacity can
+contribute to a supreme achievement.
+
+In science the man of real genius is the man who invents a new method.
+The notable discoveries are often made by his successors, who can
+apply the method with fresh vigour, unimpaired by the previous labour
+of perfecting it; but the mental calibre of the thought required for
+their work, however brilliant, is not so great as that required by the
+first inventor of the method. There are in science immense numbers of
+different methods, appropriate to different classes of problems; but
+over and above them all, there is something not easily definable,
+which may be called _the_ method of science. It was formerly customary
+to identify this with the inductive method, and to associate it with
+the name of Bacon. But the true inductive method was not discovered by
+Bacon, and the true method of science is something which includes
+deduction as much as induction, logic and mathematics as much as
+botany and geology. I shall not attempt the difficult task of stating
+what the scientific method is, but I will try to indicate the temper
+of mind out of which the scientific method grows, which is the second
+of the two merits that were mentioned above as belonging to a
+scientific education.
+
+The kernel of the scientific outlook is a thing so simple, so obvious,
+so seemingly trivial, that the mention of it may almost excite
+derision. The kernel of the scientific outlook is the refusal to
+regard our own desires, tastes, and interests as affording a key to
+the understanding of the world. Stated thus baldly, this may seem no
+more than a trite truism. But to remember it consistently in matters
+arousing our passionate partisanship is by no means easy, especially
+where the available evidence is uncertain and inconclusive. A few
+illustrations will make this clear.
+
+Aristotle, I understand, considered that the stars must move in
+circles because the circle is the most perfect curve. In the absence
+of evidence to the contrary, he allowed himself to decide a question
+of fact by an appeal to æsthetico-moral considerations. In such a case
+it is at once obvious to us that this appeal was unjustifiable. We
+know now how to ascertain as a fact the way in which the heavenly
+bodies move, and we know that they do not move in circles, or even in
+accurate ellipses, or in any other kind of simply describable curve.
+This may be painful to a certain hankering after simplicity of pattern
+in the universe, but we know that in astronomy such feelings are
+irrelevant. Easy as this knowledge seems now, we owe it to the courage
+and insight of the first inventors of scientific method, and more
+especially of Galileo.
+
+We may take as another illustration Malthus's doctrine of population.
+This illustration is all the better for the fact that his actual
+doctrine is now known to be largely erroneous. It is not his
+conclusions that are valuable, but the temper and method of his
+inquiry. As everyone knows, it was to him that Darwin owed an
+essential part of his theory of natural selection, and this was only
+possible because Malthus's outlook was truly scientific. His great
+merit lies in considering man not as the object of praise or blame,
+but as a part of nature, a thing with a certain characteristic
+behaviour from which certain consequences must follow. If the
+behaviour is not quite what Malthus supposed, if the consequences are
+not quite what he inferred, that may falsify his conclusions, but does
+not impair the value of his method. The objections which were made
+when his doctrine was new--that it was horrible and depressing, that
+people ought not to act as he said they did, and so on--were all such
+as implied an unscientific attitude of mind; as against all of them,
+his calm determination to treat man as a natural phenomenon marks an
+important advance over the reformers of the eighteenth century and the
+Revolution.
+
+Under the influence of Darwinism the scientific attitude towards man
+has now become fairly common, and is to some people quite natural,
+though to most it is still a difficult and artificial intellectual
+contortion. There is however, one study which is as yet almost wholly
+untouched by the scientific spirit--I mean the study of philosophy.
+Philosophers and the public imagine that the scientific spirit must
+pervade pages that bristle with allusions to ions, germ-plasms, and
+the eyes of shell-fish. But as the devil can quote Scripture, so the
+philosopher can quote science. The scientific spirit is not an affair
+of quotation, of externally acquired information, any more than
+manners are an affair of the etiquette-book. The scientific attitude
+of mind involves a sweeping away of all other desires in the interests
+of the desire to know--it involves suppression of hopes and fears,
+loves and hates, and the whole subjective emotional life, until we
+become subdued to the material, able to see it frankly, without
+preconceptions, without bias, without any wish except to see it as it
+is, and without any belief that what it is must be determined by some
+relation, positive or negative, to what we should like it to be, or to
+what we can easily imagine it to be.
+
+Now in philosophy this attitude of mind has not as yet been achieved.
+A certain self-absorption, not personal, but human, has marked almost
+all attempts to conceive the universe as a whole. Mind, or some aspect
+of it--thought or will or sentience--has been regarded as the pattern
+after which the universe is to be conceived, for no better reason, at
+bottom, than that such a universe would not seem strange, and would
+give us the cosy feeling that every place is like home. To conceive
+the universe as essentially progressive or essentially deteriorating,
+for example, is to give to our hopes and fears a cosmic importance
+which _may_, of course, be justified, but which we have as yet no
+reason to suppose justified. Until we have learnt to think of it in
+ethically neutral terms, we have not arrived at a scientific attitude
+in philosophy; and until we have arrived at such an attitude, it is
+hardly to be hoped that philosophy will achieve any solid results.
+
+I have spoken so far largely of the negative aspect of the scientific
+spirit, but it is from the positive aspect that its value is derived.
+The instinct of constructiveness, which is one of the chief incentives
+to artistic creation, can find in scientific systems a satisfaction
+more massive than any epic poem. Disinterested curiosity, which is the
+source of almost all intellectual effort, finds with astonished
+delight that science can unveil secrets which might well have seemed
+for ever undiscoverable. The desire for a larger life and wider
+interests, for an escape from private circumstances, and even from the
+whole recurring human cycle of birth and death, is fulfilled by the
+impersonal cosmic outlook of science as by nothing else. To all these
+must be added, as contributing to the happiness of the man of science,
+the admiration of splendid achievement, and the consciousness of
+inestimable utility to the human race. A life devoted to science is
+therefore a happy life, and its happiness is derived from the very
+best sources that are open to dwellers on this troubled and passionate
+planet.
+
+
+
+
+III
+
+A FREE MAN'S WORSHIP[9]
+
+
+To Dr. Faustus in his study Mephistopheles told the history of the
+Creation, saying:
+
+"The endless praises of the choirs of angels had begun to grow
+wearisome; for, after all, did he not deserve their praise? Had he not
+given them endless joy? Would it not be more amusing to obtain
+undeserved praise, to be worshipped by beings whom he tortured? He
+smiled inwardly, and resolved that the great drama should be
+performed.
+
+"For countless ages the hot nebula whirled aimlessly through space. At
+length it began to take shape, the central mass threw off planets, the
+planets cooled, boiling seas and burning mountains heaved and tossed,
+from black masses of cloud hot sheets of rain deluged the barely solid
+crust. And now the first germ of life grew in the depths of the ocean,
+and developed rapidly in the fructifying warmth into vast forest
+trees, huge ferns springing from the damp mould, sea monsters
+breeding, fighting, devouring, and passing away. And from the
+monsters, as the play unfolded itself, Man was born, with the power of
+thought, the knowledge of good and evil, and the cruel thirst for
+worship. And Man saw that all is passing in this mad, monstrous world,
+that all is struggling to snatch, at any cost, a few brief moments of
+life before Death's inexorable decree. And Man said: 'There is a
+hidden purpose, could we but fathom it, and the purpose is good; for
+we must reverence something, and in the visible world there is nothing
+worthy of reverence.' And Man stood aside from the struggle, resolving
+that God intended harmony to come out of chaos by human efforts. And
+when he followed the instincts which God had transmitted to him from
+his ancestry of beasts of prey, he called it Sin, and asked God to
+forgive him. But he doubted whether he could be justly forgiven, until
+he invented a divine Plan by which God's wrath was to have been
+appeased. And seeing the present was bad, he made it yet worse, that
+thereby the future might be better. And he gave God thanks for the
+strength that enabled him to forgo even the joys that were possible.
+And God smiled; and when he saw that Man had become perfect in
+renunciation and worship, he sent another sun through the sky, which
+crashed into Man's sun; and all returned again to nebula.
+
+"'Yes,' he murmured, 'it was a good play; I will have it performed
+again.'"
+
+Such, in outline, but even more purposeless, more void of meaning, is
+the world which Science presents for our belief. Amid such a world, if
+anywhere, our ideals henceforward must find a home. That Man is the
+product of causes which had no prevision of the end they were
+achieving; that his origin, his growth, his hopes and fears, his loves
+and his beliefs, are but the outcome of accidental collocations of
+atoms; that no fire, no heroism, no intensity of thought and feeling,
+can preserve an individual life beyond the grave; that all the labours
+of the ages, all the devotion, all the inspiration, all the noonday
+brightness of human genius, are destined to extinction in the vast
+death of the solar system, and that the whole temple of Man's
+achievement must inevitably be buried beneath the débris of a universe
+in ruins--all these things, if not quite beyond dispute, are yet so
+nearly certain, that no philosophy which rejects them can hope to
+stand. Only within the scaffolding of these truths, only on the firm
+foundation of unyielding despair, can the soul's habitation henceforth
+be safely built.
+
+How, in such an alien and inhuman world, can so powerless a creature
+as Man preserve his aspirations untarnished? A strange mystery it is
+that Nature, omnipotent but blind, in the revolutions of her secular
+hurryings through the abysses of space, has brought forth at last a
+child, subject still to her power, but gifted with sight, with
+knowledge of good and evil, with the capacity of judging all the works
+of his unthinking Mother. In spite of Death, the mark and seal of the
+parental control, Man is yet free, during his brief years, to examine,
+to criticise, to know, and in imagination to create. To him alone, in
+the world with which he is acquainted, this freedom belongs; and in
+this lies his superiority to the resistless forces that control his
+outward life.
+
+The savage, like ourselves, feels the oppression of his impotence
+before the powers of Nature; but having in himself nothing that he
+respects more than Power, he is willing to prostrate himself before
+his gods, without inquiring whether they are worthy of his worship.
+Pathetic and very terrible is the long history of cruelty and torture,
+of degradation and human sacrifice, endured in the hope of placating
+the jealous gods: surely, the trembling believer thinks, when what is
+most precious has been freely given, their lust for blood must be
+appeased, and more will not be required. The religion of Moloch--as
+such creeds may be generically called--is in essence the cringing
+submission of the slave, who dare not, even in his heart, allow the
+thought that his master deserves no adulation. Since the independence
+of ideals is not yet acknowledged, Power may be freely worshipped, and
+receive an unlimited respect, despite its wanton infliction of pain.
+
+But gradually, as morality grows bolder, the claim of the ideal world
+begins to be felt; and worship, if it is not to cease, must be given
+to gods of another kind than those created by the savage. Some, though
+they feel the demands of the ideal, will still consciously reject
+them, still urging that naked Power is worthy of worship. Such is the
+attitude inculcated in God's answer to Job out of the whirlwind: the
+divine power and knowledge are paraded, but of the divine goodness
+there is no hint. Such also is the attitude of those who, in our own
+day, base their morality upon the struggle for survival, maintaining
+that the survivors are necessarily the fittest. But others, not
+content with an answer so repugnant to the moral sense, will adopt the
+position which we have become accustomed to regard as specially
+religious, maintaining that, in some hidden manner, the world of fact
+is really harmonious with the world of ideals. Thus Man creates God,
+all-powerful and all-good, the mystic unity of what is and what should
+be.
+
+But the world of fact, after all, is not good; and, in submitting our
+judgment to it, there is an element of slavishness from which our
+thoughts must be purged. For in all things it is well to exalt the
+dignity of Man, by freeing him as far as possible from the tyranny of
+non-human Power. When we have realised that Power is largely bad, that
+man, with his knowledge of good and evil, is but a helpless atom in a
+world which has no such knowledge, the choice is again presented to
+us: Shall we worship Force, or shall we worship Goodness? Shall our
+God exist and be evil, or shall he be recognised as the creation of
+our own conscience?
+
+The answer to this question is very momentous, and affects profoundly
+our whole morality. The worship of Force, to which Carlyle and
+Nietzsche and the creed of Militarism have accustomed us, is the
+result of failure to maintain our own ideals against a hostile
+universe: it is itself a prostrate submission to evil, a sacrifice of
+our best to Moloch. If strength indeed is to be respected, let us
+respect rather the strength of those who refuse that false
+"recognition of facts" which fails to recognise that facts are often
+bad. Let us admit that, in the world we know, there are many things
+that would be better otherwise, and that the ideals to which we do and
+must adhere are not realised in the realm of matter. Let us preserve
+our respect for truth, for beauty, for the ideal of perfection which
+life does not permit us to attain, though none of these things meet
+with the approval of the unconscious universe. If Power is bad, as it
+seems to be, let us reject it from our hearts. In this lies Man's true
+freedom: in determination to worship only the God created by our own
+love of the good, to respect only the heaven which inspires the
+insight of our best moments. In action, in desire, we must submit
+perpetually to the tyranny of outside forces; but in thought, in
+aspiration, we are free, free from our fellow-men, free from the petty
+planet on which our bodies impotently crawl, free even, while we live,
+from the tyranny of death. Let us learn, then, that energy of faith
+which enables us to live constantly in the vision of the good; and let
+us descend, in action, into the world of fact, with that vision always
+before us.
+
+When first the opposition of fact and ideal grows fully visible, a
+spirit of fiery revolt, of fierce hatred of the gods, seems necessary
+to the assertion of freedom. To defy with Promethean constancy a
+hostile universe, to keep its evil always in view, always actively
+hated, to refuse no pain that the malice of Power can invent, appears
+to be the duty of all who will not bow before the inevitable. But
+indignation is still a bondage, for it compels our thoughts to be
+occupied with an evil world; and in the fierceness of desire from
+which rebellion springs there is a kind of self-assertion which it is
+necessary for the wise to overcome. Indignation is a submission of our
+thoughts, but not of our desires; the Stoic freedom in which wisdom
+consists is found in the submission of our desires, but not of our
+thoughts. From the submission of our desires springs the virtue of
+resignation; from the freedom of our thoughts springs the whole world
+of art and philosophy, and the vision of beauty by which, at last, we
+half reconquer the reluctant world. But the vision of beauty is
+possible only to unfettered contemplation, to thoughts not weighted by
+the load of eager wishes; and thus Freedom comes only to those who no
+longer ask of life that it shall yield them any of those personal
+goods that are subject to the mutations of Time.
+
+Although the necessity of renunciation is evidence of the existence of
+evil, yet Christianity, in preaching it, has shown a wisdom exceeding
+that of the Promethean philosophy of rebellion. It must be admitted
+that, of the things we desire, some, though they prove impossible, are
+yet real goods; others, however, as ardently longed for, do not form
+part of a fully purified ideal. The belief that what must be renounced
+is bad, though sometimes false, is far less often false than untamed
+passion supposes; and the creed of religion, by providing a reason
+for proving that it is never false, has been the means of purifying
+our hopes by the discovery of many austere truths.
+
+But there is in resignation a further good element: even real goods,
+when they are unattainable, ought not to be fretfully desired. To
+every man comes, sooner or later, the great renunciation. For the
+young, there is nothing unattainable; a good thing desired with the
+whole force of a passionate will, and yet impossible, is to them not
+credible. Yet, by death, by illness, by poverty, or by the voice of
+duty, we must learn, each one of us, that the world was not made for
+us, and that, however beautiful may be the things we crave, Fate may
+nevertheless forbid them. It is the part of courage, when misfortune
+comes, to bear without repining the ruin of our hopes, to turn away
+our thoughts from vain regrets. This degree of submission to Power is
+not only just and right: it is the very gate of wisdom.
+
+But passive renunciation is not the whole of wisdom; for not by
+renunciation alone can we build a temple for the worship of our own
+ideals. Haunting foreshadowings of the temple appear in the realm of
+imagination, in music, in architecture, in the untroubled kingdom of
+reason, and in the golden sunset magic of lyrics, where beauty shines
+and glows, remote from the touch of sorrow, remote from the fear of
+change, remote from the failures and disenchantments of the world of
+fact. In the contemplation of these things the vision of heaven will
+shape itself in our hearts, giving at once a touchstone to judge the
+world about us, and an inspiration by which to fashion to our needs
+whatever is not incapable of serving as a stone in the sacred temple.
+
+Except for those rare spirits that are born without sin, there is a
+cavern of darkness to be traversed before that temple can be entered.
+The gate of the cavern is despair, and its floor is paved with the
+gravestones of abandoned hopes. There Self must die; there the
+eagerness, the greed of untamed desire must be slain, for only so can
+the soul be freed from the empire of Fate. But out of the cavern the
+Gate of Renunciation leads again to the daylight of wisdom, by whose
+radiance a new insight, a new joy, a new tenderness, shine forth to
+gladden the pilgrim's heart.
+
+When, without the bitterness of impotent rebellion, we have learnt
+both to resign ourselves to the outward rule of Fate and to recognise
+that the non-human world is unworthy of our worship, it becomes
+possible at last so to transform and refashion the unconscious
+universe, so to transmute it in the crucible of imagination, that a
+new image of shining gold replaces the old idol of clay. In all the
+multiform facts of the world--in the visual shapes of trees and
+mountains and clouds, in the events of the life of man, even in the
+very omnipotence of Death--the insight of creative idealism can find
+the reflection of a beauty which its own thoughts first made. In this
+way mind asserts its subtle mastery over the thoughtless forces of
+Nature. The more evil the material with which it deals, the more
+thwarting to untrained desire, the greater is its achievement in
+inducing the reluctant rock to yield up its hidden treasures, the
+prouder its victory in compelling the opposing forces to swell the
+pageant of its triumph. Of all the arts, Tragedy is the proudest, the
+most triumphant; for it builds its shining citadel in the very centre
+of the enemy's country, on the very summit of his highest mountain;
+from its impregnable watchtowers, his camps and arsenals, his columns
+and forts, are all revealed; within its walls the free life continues,
+while the legions of Death and Pain and Despair, and all the servile
+captains of tyrant Fate, afford the burghers of that dauntless city
+new spectacles of beauty. Happy those sacred ramparts, thrice happy
+the dwellers on that all-seeing eminence. Honour to those brave
+warriors who, through countless ages of warfare, have preserved for us
+the priceless heritage of liberty, and have kept undefiled by
+sacrilegious invaders the home of the unsubdued.
+
+But the beauty of Tragedy does but make visible a quality which, in
+more or less obvious shapes, is present always and everywhere in life.
+In the spectacle of Death, in the endurance of intolerable pain, and
+in the irrevocableness of a vanished past, there is a sacredness, an
+overpowering awe, a feeling of the vastness, the depth, the
+inexhaustible mystery of existence, in which, as by some strange
+marriage of pain, the sufferer is bound to the world by bonds of
+sorrow. In these moments of insight, we lose all eagerness of
+temporary desire, all struggling and striving for petty ends, all care
+for the little trivial things that, to a superficial view, make up the
+common life of day by day; we see, surrounding the narrow raft
+illumined by the flickering light of human comradeship, the dark ocean
+on whose rolling waves we toss for a brief hour; from the great night
+without, a chill blast breaks in upon our refuge; all the loneliness
+of humanity amid hostile forces is concentrated upon the individual
+soul, which must struggle alone, with what of courage it can command,
+against the whole weight of a universe that cares nothing for its
+hopes and fears. Victory, in this struggle with the powers of
+darkness, is the true baptism into the glorious company of heroes, the
+true initiation into the overmastering beauty of human existence. From
+that awful encounter of the soul with the outer world, renunciation,
+wisdom, and charity are born; and with their birth a new life begins.
+To take into the inmost shrine of the soul the irresistible forces
+whose puppets we seem to be--Death and change, the irrevocableness of
+the past, and the powerlessness of man before the blind hurry of the
+universe from vanity to vanity--to feel these things and know them is
+to conquer them.
+
+This is the reason why the Past has such magical power. The beauty of
+its motionless and silent pictures is like the enchanted purity of
+late autumn, when the leaves, though one breath would make them fall,
+still glow against the sky in golden glory. The Past does not change
+or strive; like Duncan, after life's fitful fever it sleeps well; what
+was eager and grasping, what was petty and transitory, has faded away,
+the things that were beautiful and eternal shine out of it like stars
+in the night. Its beauty, to a soul not worthy of it, is unendurable;
+but to a soul which has conquered Fate it is the key of religion.
+
+The life of Man, viewed outwardly, is but a small thing in comparison
+with the forces of Nature. The slave is doomed to worship Time and
+Fate and Death, because they are greater than anything he finds in
+himself, and because all his thoughts are of things which they devour.
+But, great as they are, to think of them greatly, to feel their
+passionless splendour, is greater still. And such thought makes us
+free men; we no longer bow before the inevitable in Oriental
+subjection, but we absorb it, and make it a part of ourselves. To
+abandon the struggle for private happiness, to expel all eagerness of
+temporary desire, to burn with passion for eternal things--this is
+emancipation, and this is the free man's worship. And this liberation
+is effected by a contemplation of Fate; for Fate itself is subdued by
+the mind which leaves nothing to be purged by the purifying fire of
+Time.
+
+United with his fellow-men by the strongest of all ties, the tie of a
+common doom, the free man finds that a new vision is with him always,
+shedding over every daily task the light of love. The life of Man is a
+long march through the night, surrounded by invisible foes, tortured
+by weariness and pain, towards a goal that few can hope to reach, and
+where none may tarry long. One by one, as they march, our comrades
+vanish from our sight, seized by the silent orders of omnipotent
+Death. Very brief is the time in which we can help them, in which
+their happiness or misery is decided. Be it ours to shed sunshine on
+their path, to lighten their sorrows by the balm of sympathy, to give
+them the pure joy of a never-tiring affection, to strengthen failing
+courage, to instil faith in hours of despair. Let us not weigh in
+grudging scales their merits and demerits, but let us think only of
+their need--of the sorrows, the difficulties, perhaps the blindnesses,
+that make the misery of their lives; let us remember that they are
+fellow-sufferers in the same darkness, actors in the same tragedy with
+ourselves. And so, when their day is over, when their good and their
+evil have become eternal by the immortality of the past, be it ours to
+feel that, where they suffered, where they failed, no deed of ours was
+the cause; but wherever a spark of the divine fire kindled in their
+hearts, we were ready with encouragement, with sympathy, with brave
+words in which high courage glowed.
+
+Brief and powerless is Man's life; on him and all his race the slow,
+sure doom falls pitiless and dark. Blind to good and evil, reckless of
+destruction, omnipotent matter rolls on its relentless way; for Man,
+condemned to-day to lose his dearest, to-morrow himself to pass
+through the gate of darkness, it remains only to cherish, ere yet the
+blow falls, the lofty thoughts that ennoble his little day; disdaining
+the coward terrors of the slave of Fate, to worship at the shrine that
+his own hands have built; undismayed by the empire of chance, to
+preserve a mind free from the wanton tyranny that rules his outward
+life; proudly defiant of the irresistible forces that tolerate, for a
+moment, his knowledge and his condemnation, to sustain alone, a weary
+but unyielding Atlas, the world that his own ideals have fashioned
+despite the trampling march of unconscious power.
+
+FOOTNOTES:
+
+[9] Reprinted from the _Independent Review_, December, 1903.
+
+
+
+
+IV
+
+THE STUDY OF MATHEMATICS
+
+
+In regard to every form of human activity it is necessary that the
+question should be asked from time to time, What is its purpose and
+ideal? In what way does it contribute to the beauty of human
+existence? As respects those pursuits which contribute only remotely,
+by providing the mechanism of life, it is well to be reminded that not
+the mere fact of living is to be desired, but the art of living in the
+contemplation of great things. Still more in regard to those
+avocations which have no end outside themselves, which are to be
+justified, if at all, as actually adding to the sum of the world's
+permanent possessions, it is necessary to keep alive a knowledge of
+their aims, a clear prefiguring vision of the temple in which creative
+imagination is to be embodied.
+
+The fulfilment of this need, in what concerns the studies forming the
+material upon which custom has decided to train the youthful mind, is
+indeed sadly remote--so remote as to make the mere statement of such a
+claim appear preposterous. Great men, fully alive to the beauty of the
+contemplations to whose service their lives are devoted, desiring that
+others may share in their joys, persuade mankind to impart to the
+successive generations the mechanical knowledge without which it is
+impossible to cross the threshold. Dry pedants possess themselves of
+the privilege of instilling this knowledge: they forget that it is to
+serve but as a key to open the doors of the temple; though they spend
+their lives on the steps leading up to those sacred doors, they turn
+their backs upon the temple so resolutely that its very existence is
+forgotten, and the eager youth, who would press forward to be
+initiated to its domes and arches, is bidden to turn back and count
+the steps.
+
+Mathematics, perhaps more even than the study of Greece and Rome, has
+suffered from this oblivion of its due place in civilisation. Although
+tradition has decreed that the great bulk of educated men shall know
+at least the elements of the subject, the reasons for which the
+tradition arose are forgotten, buried beneath a great rubbish-heap of
+pedantries and trivialities. To those who inquire as to the purpose of
+mathematics, the usual answer will be that it facilitates the making
+of machines, the travelling from place to place, and the victory over
+foreign nations, whether in war or commerce. If it be objected that
+these ends--all of which are of doubtful value--are not furthered by
+the merely elementary study imposed upon those who do not become
+expert mathematicians, the reply, it is true, will probably be that
+mathematics trains the reasoning faculties. Yet the very men who make
+this reply are, for the most part, unwilling to abandon the teaching
+of definite fallacies, known to be such, and instinctively rejected by
+the unsophisticated mind of every intelligent learner. And the
+reasoning faculty itself is generally conceived, by those who urge its
+cultivation, as merely a means for the avoidance of pitfalls and a
+help in the discovery of rules for the guidance of practical life. All
+these are undeniably important achievements to the credit of
+mathematics; yet it is none of these that entitles mathematics to a
+place in every liberal education. Plato, we know, regarded the
+contemplation of mathematical truths as worthy of the Deity; and
+Plato realised, more perhaps than any other single man, what those
+elements are in human life which merit a place in heaven. There is in
+mathematics, he says, "something which is _necessary_ and cannot be
+set aside ... and, if I mistake not, of divine necessity; for as to
+the human necessities of which the Many talk in this connection,
+nothing can be more ridiculous than such an application of the words.
+_Cleinias._ And what are these necessities of knowledge, Stranger,
+which are divine and not human? _Athenian._ Those things without some
+use or knowledge of which a man cannot become a God to the world, nor
+a spirit, nor yet a hero, nor able earnestly to think and care for
+man" (_Laws_, p. 818).[10] Such was Plato's judgment of mathematics;
+but the mathematicians do not read Plato, while those who read him
+know no mathematics, and regard his opinion upon this question as
+merely a curious aberration.
+
+Mathematics, rightly viewed, possesses not only truth, but supreme
+beauty--a beauty cold and austere, like that of sculpture, without
+appeal to any part of our weaker nature, without the gorgeous
+trappings of painting or music, yet sublimely pure, and capable of a
+stern perfection such as only the greatest art can show. The true
+spirit of delight, the exaltation, the sense of being more than man,
+which is the touchstone of the highest excellence, is to be found in
+mathematics as surely as in poetry. What is best in mathematics
+deserves not merely to be learnt as a task, but to be assimilated as a
+part of daily thought, and brought again and again before the mind
+with ever-renewed encouragement. Real life is, to most men, a long
+second-best, a perpetual compromise between the ideal and the
+possible; but the world of pure reason knows no compromise, no
+practical limitations, no barrier to the creative activity embodying
+in splendid edifices the passionate aspiration after the perfect from
+which all great work springs. Remote from human passions, remote even
+from the pitiful facts of nature, the generations have gradually
+created an ordered cosmos, where pure thought can dwell as in its
+natural home, and where one, at least, of our nobler impulses can
+escape from the dreary exile of the actual world.
+
+So little, however, have mathematicians aimed at beauty, that hardly
+anything in their work has had this conscious purpose. Much, owing to
+irrepressible instincts, which were better than avowed beliefs, has
+been moulded by an unconscious taste; but much also has been spoilt by
+false notions of what was fitting. The characteristic excellence of
+mathematics is only to be found where the reasoning is rigidly
+logical: the rules of logic are to mathematics what those of structure
+are to architecture. In the most beautiful work, a chain of argument
+is presented in which every link is important on its own account, in
+which there is an air of ease and lucidity throughout, and the
+premises achieve more than would have been thought possible, by means
+which appear natural and inevitable. Literature embodies what is
+general in particular circumstances whose universal significance
+shines through their individual dress; but mathematics endeavours to
+present whatever is most general in its purity, without any irrelevant
+trappings.
+
+How should the teaching of mathematics be conducted so as to
+communicate to the learner as much as possible of this high ideal?
+Here experience must, in a great measure, be our guide; but some
+maxims may result from our consideration of the ultimate purpose to be
+achieved.
+
+One of the chief ends served by mathematics, when rightly taught, is
+to awaken the learner's belief in reason, his confidence in the truth
+of what has been demonstrated, and in the value of demonstration. This
+purpose is not served by existing instruction; but it is easy to see
+ways in which it might be served. At present, in what concerns
+arithmetic, the boy or girl is given a set of rules, which present
+themselves as neither true nor false, but as merely the will of the
+teacher, the way in which, for some unfathomable reason, the teacher
+prefers to have the game played. To some degree, in a study of such
+definite practical utility, this is no doubt unavoidable; but as soon
+as possible, the reasons of rules should be set forth by whatever
+means most readily appeal to the childish mind. In geometry, instead
+of the tedious apparatus of fallacious proofs for obvious truisms
+which constitutes the beginning of Euclid, the learner should be
+allowed at first to assume the truth of everything obvious, and should
+be instructed in the demonstrations of theorems which are at once
+startling and easily verifiable by actual drawing, such as those in
+which it is shown that three or more lines meet in a point. In this
+way belief is generated; it is seen that reasoning may lead to
+startling conclusions, which nevertheless the facts will verify; and
+thus the instinctive distrust of whatever is abstract or rational is
+gradually overcome. Where theorems are difficult, they should be first
+taught as exercises in geometrical drawing, until the figure has
+become thoroughly familiar; it will then be an agreeable advance to be
+taught the logical connections of the various lines or circles that
+occur. It is desirable also that the figure illustrating a theorem
+should be drawn in all possible cases and shapes, that so the abstract
+relations with which geometry is concerned may of themselves emerge
+as the residue of similarity amid such great apparent diversity. In
+this way the abstract demonstrations should form but a small part of
+the instruction, and should be given when, by familiarity with
+concrete illustrations, they have come to be felt as the natural
+embodiment of visible fact. In this early stage proofs should not be
+given with pedantic fullness; definitely fallacious methods, such as
+that of superposition, should be rigidly excluded from the first, but
+where, without such methods, the proof would be very difficult, the
+result should be rendered acceptable by arguments and illustrations
+which are explicitly contrasted with demonstrations.
+
+In the beginning of algebra, even the most intelligent child finds, as
+a rule, very great difficulty. The use of letters is a mystery, which
+seems to have no purpose except mystification. It is almost
+impossible, at first, not to think that every letter stands for some
+particular number, if only the teacher would reveal _what_ number it
+stands for. The fact is, that in algebra the mind is first taught to
+consider general truths, truths which are not asserted to hold only of
+this or that particular thing, but of any one of a whole group of
+things. It is in the power of understanding and discovering such
+truths that the mastery of the intellect over the whole world of
+things actual and possible resides; and ability to deal with the
+general as such is one of the gifts that a mathematical education
+should bestow. But how little, as a rule, is the teacher of algebra
+able to explain the chasm which divides it from arithmetic, and how
+little is the learner assisted in his groping efforts at
+comprehension! Usually the method that has been adopted in arithmetic
+is continued: rules are set forth, with no adequate explanation of
+their grounds; the pupil learns to use the rules blindly, and
+presently, when he is able to obtain the answer that the teacher
+desires, he feels that he has mastered the difficulties of the
+subject. But of inner comprehension of the processes employed he has
+probably acquired almost nothing.
+
+When algebra has been learnt, all goes smoothly until we reach those
+studies in which the notion of infinity is employed--the infinitesimal
+calculus and the whole of higher mathematics. The solution of the
+difficulties which formerly surrounded the mathematical infinite is
+probably the greatest achievement of which our own age has to boast.
+Since the beginnings of Greek thought these difficulties have been
+known; in every age the finest intellects have vainly endeavoured to
+answer the apparently unanswerable questions that had been asked by
+Zeno the Eleatic. At last Georg Cantor has found the answer, and has
+conquered for the intellect a new and vast province which had been
+given over to Chaos and old Night. It was assumed as self-evident,
+until Cantor and Dedekind established the opposite, that if, from any
+collection of things, some were taken away, the number of things left
+must always be less than the original number of things. This
+assumption, as a matter of fact, holds only of finite collections; and
+the rejection of it, where the infinite is concerned, has been shown
+to remove all the difficulties that had hitherto baffled human reason
+in this matter, and to render possible the creation of an exact
+science of the infinite. This stupendous fact ought to produce a
+revolution in the higher teaching of mathematics; it has itself added
+immeasurably to the educational value of the subject, and it has at
+last given the means of treating with logical precision many studies
+which, until lately, were wrapped in fallacy and obscurity. By those
+who were educated on the old lines, the new work is considered to be
+appallingly difficult, abstruse, and obscure; and it must be confessed
+that the discoverer, as is so often the case, has hardly himself
+emerged from the mists which the light of his intellect is dispelling.
+But inherently, the new doctrine of the infinite, to all candid and
+inquiring minds, has facilitated the mastery of higher mathematics;
+for hitherto, it has been necessary to learn, by a long process of
+sophistication, to give assent to arguments which, on first
+acquaintance, were rightly judged to be confused and erroneous. So far
+from producing a fearless belief in reason, a bold rejection of
+whatever failed to fulfil the strictest requirements of logic, a
+mathematical training, during the past two centuries, encouraged the
+belief that many things, which a rigid inquiry would reject as
+fallacious, must yet be accepted because they work in what the
+mathematician calls "practice." By this means, a timid, compromising
+spirit, or else a sacerdotal belief in mysteries not intelligible to
+the profane, has been bred where reason alone should have ruled. All
+this it is now time to sweep away; let those who wish to penetrate
+into the arcana of mathematics be taught at once the true theory in
+all its logical purity, and in the concatenation established by the
+very essence of the entities concerned.
+
+If we are considering mathematics as an end in itself, and not as a
+technical training for engineers, it is very desirable to preserve the
+purity and strictness of its reasoning. Accordingly those who have
+attained a sufficient familiarity with its easier portions should be
+led backward from propositions to which they have assented as
+self-evident to more and more fundamental principles from which what
+had previously appeared as premises can be deduced. They should be
+taught--what the theory of infinity very aptly illustrates--that many
+propositions seem self-evident to the untrained mind which,
+nevertheless, a nearer scrutiny shows to be false. By this means they
+will be led to a sceptical inquiry into first principles, an
+examination of the foundations upon which the whole edifice of
+reasoning is built, or, to take perhaps a more fitting metaphor, the
+great trunk from which the spreading branches spring. At this stage,
+it is well to study afresh the elementary portions of mathematics,
+asking no longer merely whether a given proposition is true, but also
+how it grows out of the central principles of logic. Questions of this
+nature can now be answered with a precision and certainty which were
+formerly quite impossible; and in the chains of reasoning that the
+answer requires the unity of all mathematical studies at last unfolds
+itself.
+
+In the great majority of mathematical text-books there is a total lack
+of unity in method and of systematic development of a central theme.
+Propositions of very diverse kinds are proved by whatever means are
+thought most easily intelligible, and much space is devoted to mere
+curiosities which in no way contribute to the main argument. But in
+the greatest works, unity and inevitability are felt as in the
+unfolding of a drama; in the premisses a subject is proposed for
+consideration, and in every subsequent step some definite advance is
+made towards mastery of its nature. The love of system, of
+interconnection, which is perhaps the inmost essence of the
+intellectual impulse, can find free play in mathematics as nowhere
+else. The learner who feels this impulse must not be repelled by an
+array of meaningless examples or distracted by amusing oddities, but
+must be encouraged to dwell upon central principles, to become
+familiar with the structure of the various subjects which are put
+before him, to travel easily over the steps of the more important
+deductions. In this way a good tone of mind is cultivated, and
+selective attention is taught to dwell by preference upon what is
+weighty and essential.
+
+When the separate studies into which mathematics is divided have each
+been viewed as a logical whole, as a natural growth from the
+propositions which constitute their principles, the learner will be
+able to understand the fundamental science which unifies and
+systematises the whole of deductive reasoning. This is symbolic
+logic--a study which, though it owes its inception to Aristotle, is
+yet, in its wider developments, a product, almost wholly, of the
+nineteenth century, and is indeed, in the present day, still growing
+with great rapidity. The true method of discovery in symbolic logic,
+and probably also the best method for introducing the study to a
+learner acquainted with other parts of mathematics, is the analysis of
+actual examples of deductive reasoning, with a view to the discovery
+of the principles employed. These principles, for the most part, are
+so embedded in our ratiocinative instincts, that they are employed
+quite unconsciously, and can be dragged to light only by much patient
+effort. But when at last they have been found, they are seen to be few
+in number, and to be the sole source of everything in pure
+mathematics. The discovery that all mathematics follows inevitably
+from a small collection of fundamental laws is one which immeasurably
+enhances the intellectual beauty of the whole; to those who have been
+oppressed by the fragmentary and incomplete nature of most existing
+chains of deduction this discovery comes with all the overwhelming
+force of a revelation; like a palace emerging from the autumn mist as
+the traveller ascends an Italian hill-side, the stately storeys of the
+mathematical edifice appear in their due order and proportion, with a
+new perfection in every part.
+
+Until symbolic logic had acquired its present development, the
+principles upon which mathematics depends were always supposed to be
+philosophical, and discoverable only by the uncertain, unprogressive
+methods hitherto employed by philosophers. So long as this was
+thought, mathematics seemed to be not autonomous, but dependent upon a
+study which had quite other methods than its own. Moreover, since the
+nature of the postulates from which arithmetic, analysis, and geometry
+are to be deduced was wrapped in all the traditional obscurities of
+metaphysical discussion, the edifice built upon such dubious
+foundations began to be viewed as no better than a castle in the air.
+In this respect, the discovery that the true principles are as much a
+part of mathematics as any of their consequences has very greatly
+increased the intellectual satisfaction to be obtained. This
+satisfaction ought not to be refused to learners capable of enjoying
+it, for it is of a kind to increase our respect for human powers and
+our knowledge of the beauties belonging to the abstract world.
+
+Philosophers have commonly held that the laws of logic, which underlie
+mathematics, are laws of thought, laws regulating the operations of
+our minds. By this opinion the true dignity of reason is very greatly
+lowered: it ceases to be an investigation into the very heart and
+immutable essence of all things actual and possible, becoming,
+instead, an inquiry into something more or less human and subject to
+our limitations. The contemplation of what is non-human, the discovery
+that our minds are capable of dealing with material not created by
+them, above all, the realisation that beauty belongs to the outer
+world as to the inner, are the chief means of overcoming the terrible
+sense of impotence, of weakness, of exile amid hostile powers, which
+is too apt to result from acknowledging the all-but omnipotence of
+alien forces. To reconcile us, by the exhibition of its awful beauty,
+to the reign of Fate--which is merely the literary personification of
+these forces--is the task of tragedy. But mathematics takes us still
+further from what is human, into the region of absolute necessity, to
+which not only the actual world, but every possible world, must
+conform; and even here it builds a habitation, or rather finds a
+habitation eternally standing, where our ideals are fully satisfied
+and our best hopes are not thwarted. It is only when we thoroughly
+understand the entire independence of ourselves, which belongs to this
+world that reason finds, that we can adequately realise the profound
+importance of its beauty.
+
+Not only is mathematics independent of us and our thoughts, but in
+another sense we and the whole universe of existing things are
+independent of mathematics. The apprehension of this purely ideal
+character is indispensable, if we are to understand rightly the place
+of mathematics as one among the arts. It was formerly supposed that
+pure reason could decide, in some respects, as to the nature of the
+actual world: geometry, at least, was thought to deal with the space
+in which we live. But we now know that pure mathematics can never
+pronounce upon questions of actual existence: the world of reason, in
+a sense, controls the world of fact, but it is not at any point
+creative of fact, and in the application of its results to the world
+in time and space, its certainty and precision are lost among
+approximations and working hypotheses. The objects considered by
+mathematicians have, in the past, been mainly of a kind suggested by
+phenomena; but from such restrictions the abstract imagination should
+be wholly free. A reciprocal liberty must thus be accorded: reason
+cannot dictate to the world of facts, but the facts cannot restrict
+reason's privilege of dealing with whatever objects its love of beauty
+may cause to seem worthy of consideration. Here, as elsewhere, we
+build up our own ideals out of the fragments to be found in the world;
+and in the end it is hard to say whether the result is a creation or a
+discovery.
+
+It is very desirable, in instruction, not merely to persuade the
+student of the accuracy of important theorems, but to persuade him in
+the way which itself has, of all possible ways, the most beauty. The
+true interest of a demonstration is not, as traditional modes of
+exposition suggest, concentrated wholly in the result; where this does
+occur, it must be viewed as a defect, to be remedied, if possible, by
+so generalising the steps of the proof that each becomes important in
+and for itself. An argument which serves only to prove a conclusion is
+like a story subordinated to some moral which it is meant to teach:
+for æsthetic perfection no part of the whole should be merely a means.
+A certain practical spirit, a desire for rapid progress, for conquest
+of new realms, is responsible for the undue emphasis upon results
+which prevails in mathematical instruction. The better way is to
+propose some theme for consideration--in geometry, a figure having
+important properties; in analysis, a function of which the study is
+illuminating, and so on. Whenever proofs depend upon some only of the
+marks by which we define the object to be studied, these marks should
+be isolated and investigated on their own account. For it is a defect,
+in an argument, to employ more premisses than the conclusion demands:
+what mathematicians call elegance results from employing only the
+essential principles in virtue of which the thesis is true. It is a
+merit in Euclid that he advances as far as he is able to go without
+employing the axiom of parallels--not, as is often said, because this
+axiom is inherently objectionable, but because, in mathematics, every
+new axiom diminishes the generality of the resulting theorems, and the
+greatest possible generality is before all things to be sought.
+
+Of the effects of mathematics outside its own sphere more has been
+written than on the subject of its own proper ideal. The effect upon
+philosophy has, in the past, been most notable, but most varied; in
+the seventeenth century, idealism and rationalism, in the eighteenth,
+materialism and sensationalism, seemed equally its offspring. Of the
+effect which it is likely to have in the future it would be very rash
+to say much; but in one respect a good result appears probable.
+Against that kind of scepticism which abandons the pursuit of ideals
+because the road is arduous and the goal not certainly attainable,
+mathematics, within its own sphere, is a complete answer. Too often it
+is said that there is no absolute truth, but only opinion and private
+judgment; that each of us is conditioned, in his view of the world, by
+his own peculiarities, his own taste and bias; that there is no
+external kingdom of truth to which, by patience and discipline, we may
+at last obtain admittance, but only truth for me, for you, for every
+separate person. By this habit of mind one of the chief ends of human
+effort is denied, and the supreme virtue of candour, of fearless
+acknowledgment of what is, disappears from our moral vision. Of such
+scepticism mathematics is a perpetual reproof; for its edifice of
+truths stands unshakable and inexpungable to all the weapons of
+doubting cynicism.
+
+The effects of mathematics upon practical life, though they should not
+be regarded as the motive of our studies, may be used to answer a
+doubt to which the solitary student must always be liable. In a world
+so full of evil and suffering, retirement into the cloister of
+contemplation, to the enjoyment of delights which, however noble, must
+always be for the few only, cannot but appear as a somewhat selfish
+refusal to share the burden imposed upon others by accidents in which
+justice plays no part. Have any of us the right, we ask, to withdraw
+from present evils, to leave our fellow-men unaided, while we live a
+life which, though arduous and austere, is yet plainly good in its own
+nature? When these questions arise, the true answer is, no doubt, that
+some must keep alive the sacred fire, some must preserve, in every
+generation, the haunting vision which shadows forth the goal of so
+much striving. But when, as must sometimes occur, this answer seems
+too cold, when we are almost maddened by the spectacle of sorrows to
+which we bring no help, then we may reflect that indirectly the
+mathematician often does more for human happiness than any of his more
+practically active contemporaries. The history of science abundantly
+proves that a body of abstract propositions--even if, as in the case
+of conic sections, it remains two thousand years without effect upon
+daily life--may yet, at any moment, be used to cause a revolution in
+the habitual thoughts and occupations of every citizen. The use of
+steam and electricity--to take striking instances--is rendered
+possible only by mathematics. In the results of abstract thought the
+world possesses a capital of which the employment in enriching the
+common round has no hitherto discoverable limits. Nor does experience
+give any means of deciding what parts of mathematics will be found
+useful. Utility, therefore, can be only a consolation in moments of
+discouragement, not a guide in directing our studies.
+
+For the health of the moral life, for ennobling the tone of an age or
+a nation, the austerer virtues have a strange power, exceeding the
+power of those not informed and purified by thought. Of these austerer
+virtues the love of truth is the chief, and in mathematics, more than
+elsewhere, the love of truth may find encouragement for waning faith.
+Every great study is not only an end in itself, but also a means of
+creating and sustaining a lofty habit of mind; and this purpose should
+be kept always in view throughout the teaching and learning of
+mathematics.
+
+FOOTNOTES:
+
+[10] This passage was pointed out to me by Professor Gilbert Murray.
+
+
+
+
+V
+
+MATHEMATICS AND THE METAPHYSICIANS
+
+
+The nineteenth century, which prided itself upon the invention of
+steam and evolution, might have derived a more legitimate title to
+fame from the discovery of pure mathematics. This science, like most
+others, was baptised long before it was born; and thus we find writers
+before the nineteenth century alluding to what they called pure
+mathematics. But if they had been asked what this subject was, they
+would only have been able to say that it consisted of Arithmetic,
+Algebra, Geometry, and so on. As to what these studies had in common,
+and as to what distinguished them from applied mathematics, our
+ancestors were completely in the dark.
+
+Pure mathematics was discovered by Boole, in a work which he called
+the _Laws of Thought_ (1854). This work abounds in asseverations that
+it is not mathematical, the fact being that Boole was too modest to
+suppose his book the first ever written on mathematics. He was also
+mistaken in supposing that he was dealing with the laws of thought:
+the question how people actually think was quite irrelevant to him,
+and if his book had really contained the laws of thought, it was
+curious that no one should ever have thought in such a way before. His
+book was in fact concerned with formal logic, and this is the same
+thing as mathematics.
+
+Pure mathematics consists entirely of assertions to the effect that,
+if such and such a proposition is true of _anything_, then such and
+such another proposition is true of that thing. It is essential not to
+discuss whether the first proposition is really true, and not to
+mention what the anything is, of which it is supposed to be true. Both
+these points would belong to applied mathematics. We start, in pure
+mathematics, from certain rules of inference, by which we can infer
+that _if_ one proposition is true, then so is some other proposition.
+These rules of inference constitute the major part of the principles
+of formal logic. We then take any hypothesis that seems amusing, and
+deduce its consequences. _If_ our hypothesis is about _anything_, and
+not about some one or more particular things, then our deductions
+constitute mathematics. Thus mathematics may be defined as the subject
+in which we never know what we are talking about, nor whether what we
+are saying is true. People who have been puzzled by the beginnings of
+mathematics will, I hope, find comfort in this definition, and will
+probably agree that it is accurate.
+
+As one of the chief triumphs of modern mathematics consists in having
+discovered what mathematics really is, a few more words on this
+subject may not be amiss. It is common to start any branch of
+mathematics--for instance, Geometry--with a certain number of
+primitive ideas, supposed incapable of definition, and a certain
+number of primitive propositions or axioms, supposed incapable of
+proof. Now the fact is that, though there are indefinables and
+indemonstrables in every branch of applied mathematics, there are none
+in pure mathematics except such as belong to general logic. Logic,
+broadly speaking, is distinguished by the fact that its propositions
+can be put into a form in which they apply to anything whatever. All
+pure mathematics--Arithmetic, Analysis, and Geometry--is built up by
+combinations of the primitive ideas of logic, and its propositions are
+deduced from the general axioms of logic, such as the syllogism and
+the other rules of inference. And this is no longer a dream or an
+aspiration. On the contrary, over the greater and more difficult part
+of the domain of mathematics, it has been already accomplished; in the
+few remaining cases, there is no special difficulty, and it is now
+being rapidly achieved. Philosophers have disputed for ages whether
+such deduction was possible; mathematicians have sat down and made the
+deduction. For the philosophers there is now nothing left but graceful
+acknowledgments.
+
+The subject of formal logic, which has thus at last shown itself to be
+identical with mathematics, was, as every one knows, invented by
+Aristotle, and formed the chief study (other than theology) of the
+Middle Ages. But Aristotle never got beyond the syllogism, which is a
+very small part of the subject, and the schoolmen never got beyond
+Aristotle. If any proof were required of our superiority to the
+mediæval doctors, it might be found in this. Throughout the Middle
+Ages, almost all the best intellects devoted themselves to formal
+logic, whereas in the nineteenth century only an infinitesimal
+proportion of the world's thought went into this subject.
+Nevertheless, in each decade since 1850 more has been done to advance
+the subject than in the whole period from Aristotle to Leibniz. People
+have discovered how to make reasoning symbolic, as it is in Algebra,
+so that deductions are effected by mathematical rules. They have
+discovered many rules besides the syllogism, and a new branch of
+logic, called the Logic of Relatives,[11] has been invented to deal
+with topics that wholly surpassed the powers of the old logic, though
+they form the chief contents of mathematics.
+
+It is not easy for the lay mind to realise the importance of symbolism
+in discussing the foundations of mathematics, and the explanation may
+perhaps seem strangely paradoxical. The fact is that symbolism is
+useful because it makes things difficult. (This is not true of the
+advanced parts of mathematics, but only of the beginnings.) What we
+wish to know is, what can be deduced from what. Now, in the
+beginnings, everything is self-evident; and it is very hard to see
+whether one self-evident proposition follows from another or not.
+Obviousness is always the enemy to correctness. Hence we invent some
+new and difficult symbolism, in which nothing seems obvious. Then we
+set up certain rules for operating on the symbols, and the whole thing
+becomes mechanical. In this way we find out what must be taken as
+premiss and what can be demonstrated or defined. For instance, the
+whole of Arithmetic and Algebra has been shown to require three
+indefinable notions and five indemonstrable propositions. But without
+a symbolism it would have been very hard to find this out. It is so
+obvious that two and two are four, that we can hardly make ourselves
+sufficiently sceptical to doubt whether it can be proved. And the same
+holds in other cases where self-evident things are to be proved.
+
+But the proof of self-evident propositions may seem, to the
+uninitiated, a somewhat frivolous occupation. To this we might reply
+that it is often by no means self-evident that one obvious proposition
+follows from another obvious proposition; so that we are really
+discovering new truths when we prove what is evident by a method which
+is not evident. But a more interesting retort is, that since people
+have tried to prove obvious propositions, they have found that many of
+them are false. Self-evidence is often a mere will-o'-the-wisp, which
+is sure to lead us astray if we take it as our guide. For instance,
+nothing is plainer than that a whole always has more terms than a
+part, or that a number is increased by adding one to it. But these
+propositions are now known to be usually false. Most numbers are
+infinite, and if a number is infinite you may add ones to it as long
+as you like without disturbing it in the least. One of the merits of a
+proof is that it instils a certain doubt as to the result proved; and
+when what is obvious can be proved in some cases, but not in others,
+it becomes possible to suppose that in these other cases it is false.
+
+The great master of the art of formal reasoning, among the men of our
+own day, is an Italian, Professor Peano, of the University of
+Turin.[12] He has reduced the greater part of mathematics (and he or
+his followers will, in time, have reduced the whole) to strict
+symbolic form, in which there are no words at all. In the ordinary
+mathematical books, there are no doubt fewer words than most readers
+would wish. Still, little phrases occur, such as _therefore, let us
+assume, consider_, or _hence it follows_. All these, however, are a
+concession, and are swept away by Professor Peano. For instance, if we
+wish to learn the whole of Arithmetic, Algebra, the Calculus, and
+indeed all that is usually called pure mathematics (except Geometry),
+we must start with a dictionary of three words. One symbol stands for
+_zero_, another for _number_, and a third for _next after_. What these
+ideas mean, it is necessary to know if you wish to become an
+arithmetician. But after symbols have been invented for these three
+ideas, not another word is required in the whole development. All
+future symbols are symbolically explained by means of these three.
+Even these three can be explained by means of the notions of
+_relation_ and _class_; but this requires the Logic of Relations,
+which Professor Peano has never taken up. It must be admitted that
+what a mathematician has to know to begin with is not much. There are
+at most a dozen notions out of which all the notions in all pure
+mathematics (including Geometry) are compounded. Professor Peano, who
+is assisted by a very able school of young Italian disciples, has
+shown how this may be done; and although the method which he has
+invented is capable of being carried a good deal further than he has
+carried it, the honour of the pioneer must belong to him.
+
+Two hundred years ago, Leibniz foresaw the science which Peano has
+perfected, and endeavoured to create it. He was prevented from
+succeeding by respect for the authority of Aristotle, whom he could
+not believe guilty of definite, formal fallacies; but the subject
+which he desired to create now exists, in spite of the patronising
+contempt with which his schemes have been treated by all superior
+persons. From this "Universal Characteristic," as he called it, he
+hoped for a solution of all problems, and an end to all disputes. "If
+controversies were to arise," he says, "there would be no more need of
+disputation between two philosophers than between two accountants. For
+it would suffice to take their pens in their hands, to sit down to
+their desks, and to say to each other (with a friend as witness, if
+they liked), 'Let us calculate.'" This optimism has now appeared to be
+somewhat excessive; there still are problems whose solution is
+doubtful, and disputes which calculation cannot decide. But over an
+enormous field of what was formerly controversial, Leibniz's dream has
+become sober fact. In the whole philosophy of mathematics, which used
+to be at least as full of doubt as any other part of philosophy, order
+and certainty have replaced the confusion and hesitation which
+formerly reigned. Philosophers, of course, have not yet discovered
+this fact, and continue to write on such subjects in the old way. But
+mathematicians, at least in Italy, have now the power of treating the
+principles of mathematics in an exact and masterly manner, by means of
+which the certainty of mathematics extends also to mathematical
+philosophy. Hence many of the topics which used to be placed among the
+great mysteries--for example, the natures of infinity, of continuity,
+of space, time and motion--are now no longer in any degree open to
+doubt or discussion. Those who wish to know the nature of these things
+need only read the works of such men as Peano or Georg Cantor; they
+will there find exact and indubitable expositions of all these quondam
+mysteries.
+
+In this capricious world, nothing is more capricious than posthumous
+fame. One of the most notable examples of posterity's lack of judgment
+is the Eleatic Zeno. This man, who may be regarded as the founder of
+the philosophy of infinity, appears in Plato's Parmenides in the
+privileged position of instructor to Socrates. He invented four
+arguments, all immeasurably subtle and profound, to prove that motion
+is impossible, that Achilles can never overtake the tortoise, and that
+an arrow in flight is really at rest. After being refuted by
+Aristotle, and by every subsequent philosopher from that day to our
+own, these arguments were reinstated, and made the basis of a
+mathematical renaissance, by a German professor, who probably never
+dreamed of any connection between himself and Zeno. Weierstrass,[13]
+by strictly banishing from mathematics the use of infinitesimals, has
+at last shown that we live in an unchanging world, and that the arrow
+in its flight is truly at rest. Zeno's only error lay in inferring (if
+he did infer) that, because there is no such thing as a state of
+change, therefore the world is in the same state at any one time as at
+any other. This is a consequence which by no means follows; and in
+this respect, the German mathematician is more constructive than the
+ingenious Greek. Weierstrass has been able, by embodying his views in
+mathematics, where familiarity with truth eliminates the vulgar
+prejudices of common sense, to invest Zeno's paradoxes with the
+respectable air of platitudes; and if the result is less delightful to
+the lover of reason than Zeno's bold defiance, it is at any rate more
+calculated to appease the mass of academic mankind.
+
+Zeno was concerned, as a matter of fact, with three problems, each
+presented by motion, but each more abstract than motion, and capable
+of a purely arithmetical treatment. These are the problems of the
+infinitesimal, the infinite, and continuity. To state clearly the
+difficulties involved, was to accomplish perhaps the hardest part of
+the philosopher's task. This was done by Zeno. From him to our own
+day, the finest intellects of each generation in turn attacked the
+problems, but achieved, broadly speaking, nothing. In our own time,
+however, three men--Weierstrass, Dedekind, and Cantor--have not merely
+advanced the three problems, but have completely solved them. The
+solutions, for those acquainted with mathematics, are so clear as to
+leave no longer the slightest doubt or difficulty. This achievement is
+probably the greatest of which our age has to boast; and I know of no
+age (except perhaps the golden age of Greece) which has a more
+convincing proof to offer of the transcendent genius of its great men.
+Of the three problems, that of the infinitesimal was solved by
+Weierstrass; the solution of the other two was begun by Dedekind, and
+definitively accomplished by Cantor.
+
+The infinitesimal played formerly a great part in mathematics. It was
+introduced by the Greeks, who regarded a circle as differing
+infinitesimally from a polygon with a very large number of very small
+equal sides. It gradually grew in importance, until, when Leibniz
+invented the Infinitesimal Calculus, it seemed to become the
+fundamental notion of all higher mathematics. Carlyle tells, in his
+_Frederick the Great_, how Leibniz used to discourse to Queen Sophia
+Charlotte of Prussia concerning the infinitely little, and how she
+would reply that on that subject she needed no instruction--the
+behaviour of courtiers had made her thoroughly familiar with it. But
+philosophers and mathematicians--who for the most part had less
+acquaintance with courts--continued to discuss this topic, though
+without making any advance. The Calculus required continuity, and
+continuity was supposed to require the infinitely little; but nobody
+could discover what the infinitely little might be. It was plainly not
+quite zero, because a sufficiently large number of infinitesimals,
+added together, were seen to make up a finite whole. But nobody could
+point out any fraction which was not zero, and yet not finite. Thus
+there was a deadlock. But at last Weierstrass discovered that the
+infinitesimal was not needed at all, and that everything could be
+accomplished without it. Thus there was no longer any need to suppose
+that there was such a thing. Nowadays, therefore, mathematicians are
+more dignified than Leibniz: instead of talking about the infinitely
+small, they talk about the infinitely great--a subject which, however
+appropriate to monarchs, seems, unfortunately, to interest them even
+less than the infinitely little interested the monarchs to whom
+Leibniz discoursed.
+
+The banishment of the infinitesimal has all sorts of odd consequences,
+to which one has to become gradually accustomed. For example, there is
+no such thing as the next moment. The interval between one moment and
+the next would have to be infinitesimal, since, if we take two moments
+with a finite interval between them, there are always other moments in
+the interval. Thus if there are to be no infinitesimals, no two
+moments are quite consecutive, but there are always other moments
+between any two. Hence there must be an infinite number of moments
+between any two; because if there were a finite number one would be
+nearest the first of the two moments, and therefore next to it. This
+might be thought to be a difficulty; but, as a matter of fact, it is
+here that the philosophy of the infinite comes in, and makes all
+straight.
+
+The same sort of thing happens in space. If any piece of matter be cut
+in two, and then each part be halved, and so on, the bits will become
+smaller and smaller, and can theoretically be made as small as we
+please. However small they may be, they can still be cut up and made
+smaller still. But they will always have _some_ finite size, however
+small they may be. We never reach the infinitesimal in this way, and
+no finite number of divisions will bring us to points. Nevertheless
+there _are_ points, only these are not to be reached by successive
+divisions. Here again, the philosophy of the infinite shows us how
+this is possible, and why points are not infinitesimal lengths.
+
+As regards motion and change, we get similarly curious results. People
+used to think that when a thing changes, it must be in a state of
+change, and that when a thing moves, it is in a state of motion. This
+is now known to be a mistake. When a body moves, all that can be said
+is that it is in one place at one time and in another at another. We
+must not say that it will be in a neighbouring place at the next
+instant, since there is no next instant. Philosophers often tell us
+that when a body is in motion, it changes its position within the
+instant. To this view Zeno long ago made the fatal retort that every
+body always is where it is; but a retort so simple and brief was not
+of the kind to which philosophers are accustomed to give weight, and
+they have continued down to our own day to repeat the same phrases
+which roused the Eleatic's destructive ardour. It was only recently
+that it became possible to explain motion in detail in accordance with
+Zeno's platitude, and in opposition to the philosopher's paradox. We
+may now at last indulge the comfortable belief that a body in motion
+is just as truly where it is as a body at rest. Motion consists merely
+in the fact that bodies are sometimes in one place and sometimes in
+another, and that they are at intermediate places at intermediate
+times. Only those who have waded through the quagmire of philosophic
+speculation on this subject can realise what a liberation from antique
+prejudices is involved in this simple and straightforward commonplace.
+
+The philosophy of the infinitesimal, as we have just seen, is mainly
+negative. People used to believe in it, and now they have found out
+their mistake. The philosophy of the infinite, on the other hand, is
+wholly positive. It was formerly supposed that infinite numbers, and
+the mathematical infinite generally, were self-contradictory. But as
+it was obvious that there were infinities--for example, the number of
+numbers--the contradictions of infinity seemed unavoidable, and
+philosophy seemed to have wandered into a "cul-de-sac." This
+difficulty led to Kant's antinomies, and hence, more or less
+indirectly, to much of Hegel's dialectic method. Almost all current
+philosophy is upset by the fact (of which very few philosophers are as
+yet aware) that all the ancient and respectable contradictions in the
+notion of the infinite have been once for all disposed of. The method
+by which this has been done is most interesting and instructive. In
+the first place, though people had talked glibly about infinity ever
+since the beginnings of Greek thought, nobody had ever thought of
+asking, What is infinity? If any philosopher had been asked for a
+definition of infinity, he might have produced some unintelligible
+rigmarole, but he would certainly not have been able to give a
+definition that had any meaning at all. Twenty years ago, roughly
+speaking, Dedekind and Cantor asked this question, and, what is more
+remarkable, they answered it. They found, that is to say, a perfectly
+precise definition of an infinite number or an infinite collection of
+things. This was the first and perhaps the greatest step. It then
+remained to examine the supposed contradictions in this notion. Here
+Cantor proceeded in the only proper way. He took pairs of
+contradictory propositions, in which both sides of the contradiction
+would be usually regarded as demonstrable, and he strictly examined
+the supposed proofs. He found that all proofs adverse to infinity
+involved a certain principle, at first sight obviously true, but
+destructive, in its consequences, of almost all mathematics. The
+proofs favourable to infinity, on the other hand, involved no
+principle that had evil consequences. It thus appeared that common
+sense had allowed itself to be taken in by a specious maxim, and that,
+when once this maxim was rejected, all went well.
+
+The maxim in question is, that if one collection is part of another,
+the one which is a part has fewer terms than the one of which it is a
+part. This maxim is true of finite numbers. For example, Englishmen
+are only some among Europeans, and there are fewer Englishmen than
+Europeans. But when we come to infinite numbers, this is no longer
+true. This breakdown of the maxim gives us the precise definition of
+infinity. A collection of terms is infinite when it contains as parts
+other collections which have just as many terms as it has. If you can
+take away some of the terms of a collection, without diminishing the
+number of terms, then there are an infinite number of terms in the
+collection. For example, there are just as many even numbers as there
+are numbers altogether, since every number can be doubled. This may be
+seen by putting odd and even numbers together in one row, and even
+numbers alone in a row below:--
+
+          1, 2, 3, 4, 5, _ad infinitum_.
+          2, 4, 6, 8, 10, _ad infinitum_.
+
+There are obviously just as many numbers in the row below as in the
+row above, because there is one below for each one above. This
+property, which was formerly thought to be a contradiction, is now
+transformed into a harmless definition of infinity, and shows, in the
+above case, that the number of finite numbers is infinite.
+
+But the uninitiated may wonder how it is possible to deal with a
+number which cannot be counted. It is impossible to count up _all_ the
+numbers, one by one, because, however many we may count, there are
+always more to follow. The fact is that counting is a very vulgar and
+elementary way of finding out how many terms there are in a
+collection. And in any case, counting gives us what mathematicians
+call the _ordinal_ number of our terms; that is to say, it arranges
+our terms in an order or series, and its result tells us what type of
+series results from this arrangement. In other words, it is impossible
+to count things without counting some first and others afterwards, so
+that counting always has to do with order. Now when there are only a
+finite number of terms, we can count them in any order we like; but
+when there are an infinite number, what corresponds to counting will
+give us quite different results according to the way in which we carry
+out the operation. Thus the ordinal number, which results from what,
+in a general sense may be called counting, depends not only upon how
+many terms we have, but also (where the number of terms is infinite)
+upon the way in which the terms are arranged.
+
+The fundamental infinite numbers are not ordinal, but are what is
+called _cardinal_. They are not obtained by putting our terms in order
+and counting them, but by a different method, which tells us, to begin
+with, whether two collections have the same number of terms, or, if
+not, which is the greater.[14] It does not tell us, in the way in
+which counting does, _what_ number of terms a collection has; but if
+we define a number as the number of terms in such and such a
+collection, then this method enables us to discover whether some other
+collection that may be mentioned has more or fewer terms. An
+illustration will show how this is done. If there existed some country
+in which, for one reason or another, it was impossible to take a
+census, but in which it was known that every man had a wife and every
+woman a husband, then (provided polygamy was not a national
+institution) we should know, without counting, that there were exactly
+as many men as there were women in that country, neither more nor
+less. This method can be applied generally. If there is some relation
+which, like marriage, connects the things in one collection each with
+one of the things in another collection, and vice versa, then the two
+collections have the same number of terms. This was the way in which
+we found that there are as many even numbers as there are numbers.
+Every number can be doubled, and every even number can be halved, and
+each process gives just one number corresponding to the one that is
+doubled or halved. And in this way we can find any number of
+collections each of which has just as many terms as there are finite
+numbers. If every term of a collection can be hooked on to a number,
+and all the finite numbers are used once, and only once, in the
+process, then our collection must have just as many terms as there are
+finite numbers. This is the general method by which the numbers of
+infinite collections are defined.
+
+But it must not be supposed that all infinite numbers are equal. On
+the contrary, there are infinitely more infinite numbers than finite
+ones. There are more ways of arranging the finite numbers in different
+types of series than there are finite numbers. There are probably more
+points in space and more moments in time than there are finite
+numbers. There are exactly as many fractions as whole numbers,
+although there are an infinite number of fractions between any two
+whole numbers. But there are more irrational numbers than there are
+whole numbers or fractions. There are probably exactly as many points
+in space as there are irrational numbers, and exactly as many points
+on a line a millionth of an inch long as in the whole of infinite
+space. There is a greatest of all infinite numbers, which is the
+number of things altogether, of every sort and kind. It is obvious
+that there cannot be a greater number than this, because, if
+everything has been taken, there is nothing left to add. Cantor has a
+proof that there is no greatest number, and if this proof were valid,
+the contradictions of infinity would reappear in a sublimated form.
+But in this one point, the master has been guilty of a very subtle
+fallacy, which I hope to explain in some future work.[15]
+
+We can now understand why Zeno believed that Achilles cannot overtake
+the tortoise and why as a matter of fact he can overtake it. We shall
+see that all the people who disagreed with Zeno had no right to do so,
+because they all accepted premises from which his conclusion followed.
+The argument is this: Let Achilles and the tortoise start along a road
+at the same time, the tortoise (as is only fair) being allowed a
+handicap. Let Achilles go twice as fast as the tortoise, or ten times
+or a hundred times as fast. Then he will never reach the tortoise. For
+at every moment the tortoise is somewhere and Achilles is somewhere;
+and neither is ever twice in the same place while the race is going
+on. Thus the tortoise goes to just as many places as Achilles does,
+because each is in one place at one moment, and in another at any
+other moment. But if Achilles were to catch up with the tortoise, the
+places where the tortoise would have been would be only part of the
+places where Achilles would have been. Here, we must suppose, Zeno
+appealed to the maxim that the whole has more terms than the part.[16]
+Thus if Achilles were to overtake the tortoise, he would have been in
+more places than the tortoise; but we saw that he must, in any period,
+be in exactly as many places as the tortoise. Hence we infer that he
+can never catch the tortoise. This argument is strictly correct, if we
+allow the axiom that the whole has more terms than the part. As the
+conclusion is absurd, the axiom must be rejected, and then all goes
+well. But there is no good word to be said for the philosophers of the
+past two thousand years and more, who have all allowed the axiom and
+denied the conclusion.
+
+The retention of this axiom leads to absolute contradictions, while
+its rejection leads only to oddities. Some of these oddities, it must
+be confessed, are very odd. One of them, which I call the paradox of
+Tristram Shandy, is the converse of the Achilles, and shows that the
+tortoise, if you give him time, will go just as far as Achilles.
+Tristram Shandy, as we know, employed two years in chronicling the
+first two days of his life, and lamented that, at this rate, material
+would accumulate faster than he could deal with it, so that, as years
+went by, he would be farther and farther from the end of his history.
+Now I maintain that, if he had lived for ever, and had not wearied of
+his task, then, even if his life had continued as event fully as it
+began, no part of his biography would have remained unwritten. For
+consider: the hundredth day will be described in the hundredth year,
+the thousandth in the thousandth year, and so on. Whatever day we may
+choose as so far on that he cannot hope to reach it, that day will be
+described in the corresponding year. Thus any day that may be
+mentioned will be written up sooner or later, and therefore no part of
+the biography will remain permanently unwritten. This paradoxical but
+perfectly true proposition depends upon the fact that the number of
+days in all time is no greater than the number of years.
+
+Thus on the subject of infinity it is impossible to avoid conclusions
+which at first sight appear paradoxical, and this is the reason why so
+many philosophers have supposed that there were inherent
+contradictions in the infinite. But a little practice enables one to
+grasp the true principles of Cantor's doctrine, and to acquire new and
+better instincts as to the true and the false. The oddities then
+become no odder than the people at the antipodes, who used to be
+thought impossible because they would find it so inconvenient to stand
+on their heads.
+
+The solution of the problems concerning infinity has enabled Cantor to
+solve also the problems of continuity. Of this, as of infinity, he has
+given a perfectly precise definition, and has shown that there are no
+contradictions in the notion so defined. But this subject is so
+technical that it is impossible to give any account of it here.
+
+The notion of continuity depends upon that of _order_, since
+continuity is merely a particular type of order. Mathematics has, in
+modern times, brought order into greater and greater prominence. In
+former days, it was supposed (and philosophers are still apt to
+suppose) that quantity was the fundamental notion of mathematics. But
+nowadays, quantity is banished altogether, except from one little
+corner of Geometry, while order more and more reigns supreme. The
+investigation of different kinds of series and their relations is now
+a very large part of mathematics, and it has been found that this
+investigation can be conducted without any reference to quantity, and,
+for the most part, without any reference to number. All types of
+series are capable of formal definition, and their properties can be
+deduced from the principles of symbolic logic by means of the Algebra
+of Relatives. The notion of a limit, which is fundamental in the
+greater part of higher mathematics, used to be defined by means of
+quantity, as a term to which the terms of some series approximate as
+nearly as we please. But nowadays the limit is defined quite
+differently, and the series which it limits may not approximate to it
+at all. This improvement also is due to Cantor, and it is one which
+has revolutionised mathematics. Only order is now relevant to limits.
+Thus, for instance, the smallest of the infinite integers is the limit
+of the finite integers, though all finite integers are at an infinite
+distance from it. The study of different types of series is a general
+subject of which the study of ordinal numbers (mentioned above) is a
+special and very interesting branch. But the unavoidable
+technicalities of this subject render it impossible to explain to any
+but professed mathematicians.
+
+Geometry, like Arithmetic, has been subsumed, in recent times, under
+the general study of order. It was formerly supposed that Geometry was
+the study of the nature of the space in which we live, and accordingly
+it was urged, by those who held that what exists can only be known
+empirically, that Geometry should really be regarded as belonging to
+applied mathematics. But it has gradually appeared, by the increase of
+non-Euclidean systems, that Geometry throws no more light upon the
+nature of space than Arithmetic throws upon the population of the
+United States. Geometry is a whole collection of deductive sciences
+based on a corresponding collection of sets of axioms. One set of
+axioms is Euclid's; other equally good sets of axioms lead to other
+results. Whether Euclid's axioms are true, is a question as to which
+the pure mathematician is indifferent; and, what is more, it is a
+question which it is theoretically impossible to answer with certainty
+in the affirmative. It might possibly be shown, by very careful
+measurements, that Euclid's axioms are false; but no measurements
+could ever assure us (owing to the errors of observation) that they
+are exactly true. Thus the geometer leaves to the man of science to
+decide, as best he may, what axioms are most nearly true in the actual
+world. The geometer takes any set of axioms that seem interesting, and
+deduces their consequences. What defines Geometry, in this sense, is
+that the axioms must give rise to a series of more than one dimension.
+And it is thus that Geometry becomes a department in the study of
+order.
+
+In Geometry, as in other parts of mathematics, Peano and his disciples
+have done work of the very greatest merit as regards principles.
+Formerly, it was held by philosophers and mathematicians alike that
+the proofs in Geometry depended on the figure; nowadays, this is known
+to be false. In the best books there are no figures at all. The
+reasoning proceeds by the strict rules of formal logic from a set of
+axioms laid down to begin with. If a figure is used, all sorts of
+things seem obviously to follow, which no formal reasoning can prove
+from the explicit axioms, and which, as a matter of fact, are only
+accepted because they are obvious. By banishing the figure, it becomes
+possible to discover _all_ the axioms that are needed; and in this way
+all sorts of possibilities, which would have otherwise remained
+undetected, are brought to light.
+
+One great advance, from the point of view of correctness, has been
+made by introducing points as they are required, and not starting, as
+was formerly done, by assuming the whole of space. This method is due
+partly to Peano, partly to another Italian named Fano. To those
+unaccustomed to it, it has an air of somewhat wilful pedantry. In this
+way, we begin with the following axioms: (1) There is a class of
+entities called _points_. (2) There is at least one point. (3) If _a_
+be a point, there is at least one other point besides _a_. Then we
+bring in the straight line joining two points, and begin again with
+(4), namely, on the straight line joining _a_ and _b_, there is at
+least one other point besides _a_ and _b_. (5) There is at least one
+point not on the line _ab_. And so we go on, till we have the means of
+obtaining as many points as we require. But the word _space_, as Peano
+humorously remarks, is one for which Geometry has no use at all.
+
+The rigid methods employed by modern geometers have deposed Euclid
+from his pinnacle of correctness. It was thought, until recent times,
+that, as Sir Henry Savile remarked in 1621, there were only two
+blemishes in Euclid, the theory of parallels and the theory of
+proportion. It is now known that these are almost the only points in
+which Euclid is free from blemish. Countless errors are involved in
+his first eight propositions. That is to say, not only is it doubtful
+whether his axioms are true, which is a comparatively trivial matter,
+but it is certain that his propositions do not follow from the axioms
+which he enunciates. A vastly greater number of axioms, which Euclid
+unconsciously employs, are required for the proof of his propositions.
+Even in the first proposition of all, where he constructs an
+equilateral triangle on a given base, he uses two circles which are
+assumed to intersect. But no explicit axiom assures us that they do
+so, and in some kinds of spaces they do not always intersect. It is
+quite doubtful whether our space belongs to one of these kinds or not.
+Thus Euclid fails entirely to prove his point in the very first
+proposition. As he is certainly not an easy author, and is terribly
+long-winded, he has no longer any but an historical interest. Under
+these circumstances, it is nothing less than a scandal that he should
+still be taught to boys in England.[17] A book should have either
+intelligibility or correctness; to combine the two is impossible, but
+to lack both is to be unworthy of such a place as Euclid has occupied
+in education.
+
+The most remarkable result of modern methods in mathematics is the
+importance of symbolic logic and of rigid formalism. Mathematicians,
+under the influence of Weierstrass, have shown in modern times a care
+for accuracy, and an aversion to slipshod reasoning, such as had not
+been known among them previously since the time of the Greeks. The
+great inventions of the seventeenth century--Analytical Geometry and
+the Infinitesimal Calculus--were so fruitful in new results that
+mathematicians had neither time nor inclination to examine their
+foundations. Philosophers, who should have taken up the task, had too
+little mathematical ability to invent the new branches of mathematics
+which have now been found necessary for any adequate discussion. Thus
+mathematicians were only awakened from their "dogmatic slumbers" when
+Weierstrass and his followers showed that many of their most cherished
+propositions are in general false. Macaulay, contrasting the certainty
+of mathematics with the uncertainty of philosophy, asks who ever heard
+of a reaction against Taylor's theorem? If he had lived now, he
+himself might have heard of such a reaction, for this is precisely one
+of the theorems which modern investigations have overthrown. Such rude
+shocks to mathematical faith have produced that love of formalism
+which appears, to those who are ignorant of its motive, to be mere
+outrageous pedantry.
+
+The proof that all pure mathematics, including Geometry, is nothing
+but formal logic, is a fatal blow to the Kantian philosophy. Kant,
+rightly perceiving that Euclid's propositions could not be deduced
+from Euclid's axioms without the help of the figures, invented a
+theory of knowledge to account for this fact; and it accounted so
+successfully that, when the fact is shown to be a mere defect in
+Euclid, and not a result of the nature of geometrical reasoning,
+Kant's theory also has to be abandoned. The whole doctrine of _a
+priori_ intuitions, by which Kant explained the possibility of pure
+mathematics, is wholly inapplicable to mathematics in its present
+form. The Aristotelian doctrines of the schoolmen come nearer in
+spirit to the doctrines which modern mathematics inspire; but the
+schoolmen were hampered by the fact that their formal logic was very
+defective, and that the philosophical logic based upon the syllogism
+showed a corresponding narrowness. What is now required is to give the
+greatest possible development to mathematical logic, to allow to the
+full the importance of relations, and then to found upon this secure
+basis a new philosophical logic, which may hope to borrow some of the
+exactitude and certainty of its mathematical foundation. If this can
+be successfully accomplished, there is every reason to hope that the
+near future will be as great an epoch in pure philosophy as the
+immediate past has been in the principles of mathematics. Great
+triumphs inspire great hopes; and pure thought may achieve, within our
+generation, such results as will place our time, in this respect, on a
+level with the greatest age of Greece.[18]
+
+FOOTNOTES:
+
+[11] This subject is due in the main to Mr. C.S. Peirce.
+
+[12] I ought to have added Frege, but his writings were unknown to me
+when this article was written. [Note added in 1917.]
+
+[13] Professor of Mathematics in the University of Berlin. He died in
+1897.
+
+[14] [Note added in 1917.] Although some infinite numbers are greater
+than some others, it cannot be proved that of any two infinite numbers
+one must be the greater.
+
+[15] Cantor was not guilty of a fallacy on this point. His proof that
+there is no greatest number is valid. The solution of the puzzle is
+complicated and depends upon the theory of types, which is explained
+in _Principia Mathematica_, Vol. I (Camb. Univ. Press, 1910). [Note
+added in 1917.]
+
+[16] This must not be regarded as a historically correct account of
+what Zeno actually had in mind. It is a new argument for his
+conclusion, not the argument which influenced him. On this point, see
+e.g. C.D. Broad, "Note on Achilles and the Tortoise," _Mind_, N.S.,
+Vol. XXII, pp. 318-19. Much valuable work on the interpretation of
+Zeno has been done since this article was written. [Note added in
+1917.]
+
+[17] Since the above was written, he has ceased to be used as a
+textbook. But I fear many of the books now used are so bad that the
+change is no great improvement. [Note added in 1917.]
+
+[18] The greatest age of Greece was brought to an end by the
+Peloponnesian War. [Note added in 1917.]
+
+
+
+
+VI
+
+ON SCIENTIFIC METHOD IN PHILOSOPHY
+
+
+When we try to ascertain the motives which have led men to the
+investigation of philosophical questions, we find that, broadly
+speaking, they can be divided into two groups, often antagonistic, and
+leading to very divergent systems. These two groups of motives are, on
+the one hand, those derived from religion and ethics, and, on the
+other hand, those derived from science. Plato, Spinoza, and Hegel may
+be taken as typical of the philosophers whose interests are mainly
+religious and ethical, while Leibniz, Locke, and Hume may be taken as
+representatives of the scientific wing. In Aristotle, Descartes,
+Berkeley, and Kant we find both groups of motives strongly present.
+
+Herbert Spencer, in whose honour we are assembled to-day, would
+naturally be classed among scientific philosophers: it was mainly from
+science that he drew his data, his formulation of problems, and his
+conception of method. But his strong religious sense is obvious in
+much of his writing, and his ethical pre-occupations are what make him
+value the conception of evolution--that conception in which, as a
+whole generation has believed, science and morals are to be united in
+fruitful and indissoluble marriage.
+
+It is my belief that the ethical and religious motives in spite of
+the splendidly imaginative systems to which they have given rise, have
+been on the whole a hindrance to the progress of philosophy, and ought
+now to be consciously thrust aside by those who wish to discover
+philosophical truth. Science, originally, was entangled in similar
+motives, and was thereby hindered in its advances. It is, I maintain,
+from science, rather than from ethics and religion, that philosophy
+should draw its inspiration.
+
+But there are two different ways in which a philosophy may seek to
+base itself upon science. It may emphasise the most general _results_
+of science, and seek to give even greater generality and unity to
+these results. Or it may study the _methods_ of science, and seek to
+apply these methods, with the necessary adaptations, to its own
+peculiar province. Much philosophy inspired by science has gone astray
+through preoccupation with the _results_ momentarily supposed to have
+been achieved. It is not results, but _methods_ that can be
+transferred with profit from the sphere of the special sciences to the
+sphere of philosophy. What I wish to bring to your notice is the
+possibility and importance of applying to philosophical problems
+certain broad principles of method which have been found successful in
+the study of scientific questions.
+
+The opposition between a philosophy guided by scientific method and a
+philosophy dominated by religious and ethical ideas may be illustrated
+by two notions which are very prevalent in the works of philosophers,
+namely the notion of _the universe_, and the notion of _good and
+evil_. A philosopher is expected to tell us something about the nature
+of the universe as a whole, and to give grounds for either optimism or
+pessimism. Both these expectations seem to me mistaken. I believe the
+conception of "the universe" to be, as its etymology indicates, a
+mere relic of pre-Copernican astronomy: and I believe the question of
+optimism and pessimism to be one which the philosopher will regard as
+outside his scope, except, possibly, to the extent of maintaining that
+it is insoluble.
+
+In the days before Copernicus, the conception of the "universe" was
+defensible on scientific grounds: the diurnal revolution of the
+heavenly bodies bound them together as all parts of one system, of
+which the earth was the centre. Round this apparent scientific fact,
+many human desires rallied: the wish to believe Man important in the
+scheme of things, the theoretical desire for a comprehensive
+understanding of the Whole, the hope that the course of nature might
+be guided by some sympathy with our wishes. In this way, an ethically
+inspired system of metaphysics grew up, whose anthropocentrism was
+apparently warranted by the geocentrism of astronomy. When Copernicus
+swept away the astronomical basis of this system of thought, it had
+grown so familiar, and had associated itself so intimately with men's
+aspirations, that it survived with scarcely diminished force--survived
+even Kant's "Copernican revolution," and is still now the unconscious
+premiss of most metaphysical systems.
+
+The oneness of the world is an almost undiscussed postulate of most
+metaphysics. "Reality is not merely one and self-consistent, but is a
+system of reciprocally determinate parts"[19]--such a statement would
+pass almost unnoticed as a mere truism. Yet I believe that it embodies
+a failure to effect thoroughly the "Copernican revolution," and that
+the apparent oneness of the world is merely the oneness of what is
+seen by a single spectator or apprehended by a single mind. The
+Critical Philosophy, although it intended to emphasise the subjective
+element in many apparent characteristics of the world, yet, by
+regarding the world in itself as unknowable, so concentrated attention
+upon the subjective representation that its subjectivity was soon
+forgotten. Having recognised the categories as the work of the mind,
+it was paralysed by its own recognition, and abandoned in despair the
+attempt to undo the work of subjective falsification. In part, no
+doubt, its despair was well founded, but not, I think, in any absolute
+or ultimate sense. Still less was it a ground for rejoicing, or for
+supposing that the nescience to which it ought to have given rise
+could be legitimately exchanged for a metaphysical dogmatism.
+
+
+I
+
+As regards our present question, namely, the question of the unity of
+the world, the right method, as I think, has been indicated by William
+James.[20] "Let us now turn our backs upon ineffable or unintelligible
+ways of accounting for the world's oneness, and inquire whether,
+instead of being a principle, the 'oneness' affirmed may not merely be
+a name like 'substance' descriptive of the fact that certain _specific
+and verifiable connections_ are found among the parts of the
+experiential flux.... We can easily conceive of things that shall have
+no connection whatever with each other. We may assume them to inhabit
+different times and spaces, as the dreams of different persons do even
+now. They may be so unlike and incommensurable, and so inert towards
+one another, as never to jostle or interfere. Even now there may
+actually be whole universes so disparate from ours that we who know
+ours have no means of perceiving that they exist. We conceive their
+diversity, however; and by that fact the whole lot of them form what
+is known in logic as 'a universe of discourse.' To form a universe of
+discourse argues, as this example shows, no further kind of connexion.
+The importance attached by certain monistic writers to the fact that
+any chaos may become a universe by merely being named, is to me
+incomprehensible." We are thus left with two kinds of unity in the
+experienced world; the one what we may call the epistemological unity,
+due merely to the fact that my experienced world is what _one_
+experience selects from the sum total of existence: the other that
+tentative and partial unity exhibited in the prevalence of scientific
+laws in those portions of the world which science has hitherto
+mastered. Now a generalisation based upon either of these kinds of
+unity would be fallacious. That the things which we experience have
+the common property of being experienced by us is a truism from which
+obviously nothing of importance can be deducible: it is clearly
+fallacious to draw from the fact that whatever we experience is
+experienced the conclusion that therefore everything must be
+experienced. The generalisation of the second kind of unity, namely,
+that derived from scientific laws, would be equally fallacious, though
+the fallacy is a trifle less elementary. In order to explain it let us
+consider for a moment what is called the reign of law. People often
+speak as though it were a remarkable fact that the physical world is
+subject to invariable laws. In fact, however, it is not easy to see
+how such a world could fail to obey general laws. Taking any arbitrary
+set of points in space, there is a function of the time corresponding
+to these points, i.e. expressing the motion of a particle which
+traverses these points: this function may be regarded as a general law
+to which the behaviour of such a particle is subject. Taking all such
+functions for all the particles in the universe, there will be
+theoretically some one formula embracing them all, and this formula
+may be regarded as the single and supreme law of the spatio-temporal
+world. Thus what is surprising in physics is not the existence of
+general laws, but their extreme simplicity. It is not the uniformity
+of nature that should surprise us, for, by sufficient analytic
+ingenuity, any conceivable course of nature might be shown to exhibit
+uniformity. What should surprise us is the fact that the uniformity is
+simple enough for us to be able to discover it. But it is just this
+characteristic of simplicity in the laws of nature hitherto discovered
+which it would be fallacious to generalise, for it is obvious that
+simplicity has been a part cause of their discovery, and can,
+therefore, give no ground for the supposition that other undiscovered
+laws are equally simple.
+
+The fallacies to which these two kinds of unity have given rise
+suggest a caution as regards all use in philosophy of general
+_results_ that science is supposed to have achieved. In the first
+place, in generalising these results beyond past experience, it is
+necessary to examine very carefully whether there is not some reason
+making it more probable that these results should hold of all that has
+been experienced than that they should hold of things universally. The
+sum total of what is experienced by mankind is a selection from the
+sum total of what exists, and any general character exhibited by this
+selection may be due to the manner of selecting rather than to the
+general character of that from which experience selects. In the second
+place, the most general results of science are the least certain and
+the most liable to be upset by subsequent research. In utilizing these
+results as the basis of a philosophy, we sacrifice the most valuable
+and remarkable characteristic of scientific method, namely, that,
+although almost everything in science is found sooner or later to
+require some correction, yet this correction is almost always such as
+to leave untouched, or only slightly modified, the greater part of the
+results which have been deduced from the premiss subsequently
+discovered to be faulty. The prudent man of science acquires a certain
+instinct as to the kind of uses which may be made of present
+scientific beliefs without incurring the danger of complete and utter
+refutation from the modifications likely to be introduced by
+subsequent discoveries. Unfortunately the use of scientific
+generalisations of a sweeping kind as the basis of philosophy is just
+that kind of use which an instinct of scientific caution would avoid,
+since, as a rule, it would only lead to true results if the
+generalisation upon which it is based stood in _no_ need of
+correction.
+
+We may illustrate these general considerations by means of two
+examples, namely, the conservation of energy and the principle of
+evolution.
+
+(1) Let us begin with the conservation of energy, or, as Herbert
+Spencer used to call it, the persistence of force. He says:[21]
+
+  "Before taking a first step in the rational interpretation of
+  Evolution, it is needful to recognise, not only the facts that
+  Matter is indestructible and Motion continuous, but also the fact
+  that Force persists. An attempt to assign the _causes_ of
+  Evolution would manifestly be absurd if that agency to which the
+  metamorphosis in general and in detail is due, could either come
+  into existence or cease to exist. The succession of phenomena
+  would in such case be altogether arbitrary, and deductive Science
+  impossible."
+
+This paragraph illustrates the kind of way in which the philosopher is
+tempted to give an air of absoluteness and necessity to empirical
+generalisations, of which only the approximate truth in the regions
+hitherto investigated can be guaranteed by the unaided methods of
+science. It is very often said that the persistence of something or
+other is a necessary presupposition of all scientific investigation,
+and this presupposition is then thought to be exemplified in some
+quantity which physics declares to be constant. There are here, as it
+seems to me, three distinct errors. First, the detailed scientific
+investigation of nature does not _presuppose_ any such general laws as
+its results are found to verify. Apart from particular observations,
+science need presuppose nothing except the general principles of
+logic, and these principles are not laws of nature, for they are
+merely hypothetical, and apply not only to the actual world but to
+whatever is _possible_. The second error consists in the
+identification of a constant quantity with a persistent entity. Energy
+is a certain function of a physical system, but is not a thing or
+substance persisting throughout the changes of the system. The same is
+true of mass, in spite of the fact that mass has often been defined as
+_quantity of matter_. The whole conception of quantity, involving, as
+it does, numerical measurement based largely upon conventions, is far
+more artificial, far more an embodiment of mathematical convenience,
+than is commonly believed by those who philosophise on physics. Thus
+even if (which I cannot for a moment admit) the persistence of some
+entity were among the necessary postulates of science, it would be a
+sheer error to infer from this the constancy of any physical quantity,
+or the _a priori_ necessity of any such constancy which may be
+empirically discovered. In the third place, it has become more and
+more evident with the progress of physics that large generalisations,
+such as the conservation of energy or mass, are far from certain and
+are very likely only approximate. Mass, which used to be regarded as
+the most indubitable of physical quantities, is now generally believed
+to vary according to velocity, and to be, in fact, a vector quantity
+which at a given moment is different in different directions. The
+detailed conclusions deduced from the supposed constancy of mass for
+such motions as used to be studied in physics will remain very nearly
+exact, and therefore over the field of the older investigations very
+little modification of the older results is required. But as soon as
+such a principle as the conservation of mass or of energy is erected
+into a universal _a priori_ law, the slightest failure in absolute
+exactness is fatal, and the whole philosophic structure raised upon
+this foundation is necessarily ruined. The prudent philosopher,
+therefore, though he may with advantage study the methods of physics,
+will be very chary of basing anything upon what happen at the moment
+to be the most general results apparently obtained by those methods.
+
+(2) The philosophy of evolution, which was to be our second example,
+illustrates the same tendency to hasty generalisation, and also
+another sort, namely, the undue preoccupation with ethical notions.
+There are two kinds of evolutionist philosophy, of which both Hegel
+and Spencer represent the older and less radical kind, while
+Pragmatism and Bergson represent the more modern and revolutionary
+variety. But both these sorts of evolutionism have in common the
+emphasis on _progress_, that is, upon a continual change from the
+worse to the better, or from the simpler to the more complex. It
+would be unfair to attribute to Hegel any scientific motive or
+foundation, but all the other evolutionists, including Hegel's modern
+disciples, have derived their impetus very largely from the history of
+biological development. To a philosophy which derives a law of
+universal progress from this history there are two objections. First,
+that this history itself is concerned with a very small selection of
+facts confined to an infinitesimal fragment of space and time, and
+even on scientific grounds probably not an average sample of events in
+the world at large. For we know that decay as well as growth is a
+normal occurrence in the world. An extra-terrestrial philosopher, who
+had watched a single youth up to the age of twenty-one and had never
+come across any other human being, might conclude that it is the
+nature of human beings to grow continually taller and wiser in an
+indefinite progress towards perfection; and this generalisation would
+be just as well founded as the generalisation which evolutionists base
+upon the previous history of this planet. Apart, however, from this
+scientific objection to evolutionism, there is another, derived from
+the undue admixture of ethical notions in the very idea of progress
+from which evolutionism derives its charm. Organic life, we are told,
+has developed gradually from the protozoon to the philosopher, and
+this development, we are assured, is indubitably an advance.
+Unfortunately it is the philosopher, not the protozoon, who gives us
+this assurance, and we can have no security that the impartial
+outsider would agree with the philosopher's self-complacent
+assumption. This point has been illustrated by the philosopher Chuang
+Tz[)u] in the following instructive anecdote:
+
+  "The Grand Augur, in his ceremonial robes, approached the shambles
+  and thus addressed the pigs: 'How can you object to die? I shall
+  fatten you for three months. I shall discipline myself for ten
+  days and fast for three. I shall strew fine grass, and place you
+  bodily upon a carved sacrificial dish. Does not this satisfy you?'
+
+  Then, speaking from the pigs' point of view, he continued: 'It is
+  better, perhaps, after all, to live on bran and escape the
+  shambles....'
+
+  'But then,' added he, speaking from his own point of view, 'to
+  enjoy honour when alive one would readily die on a war-shield or
+  in the headsman's basket.'
+
+  So he rejected the pigs' point of view and adopted his own point
+  of view. In what sense, then, was he different from the pigs?"
+
+I much fear that the evolutionists too often resemble the Grand Augur
+and the pigs.
+
+The ethical element which has been prominent in many of the most
+famous systems of philosophy is, in my opinion, one of the most
+serious obstacles to the victory of scientific method in the
+investigation of philosophical questions. Human ethical notions, as
+Chuang Tz[)u] perceived, are essentially anthropocentric, and involve,
+when used in metaphysics, an attempt, however veiled, to legislate for
+the universe on the basis of the present desires of men. In this way
+they interfere with that receptivity to fact which is the essence of
+the scientific attitude towards the world. To regard ethical notions
+as a key to the understanding of the world is essentially
+pre-Copernican. It is to make man, with the hopes and ideals which he
+happens to have at the present moment, the centre of the universe and
+the interpreter of its supposed aims and purposes. Ethical metaphysics
+is fundamentally an attempt, however disguised, to give legislative
+force to our own wishes. This may, of course, be questioned, but I
+think that it is confirmed by a consideration of the way in which
+ethical notions arise. Ethics is essentially a product of the
+gregarious instinct, that is to say, of the instinct to co-operate
+with those who are to form our own group against those who belong to
+other groups. Those who belong to our own group are good; those who
+belong to hostile groups are wicked. The ends which are pursued by our
+own group are desirable ends, the ends pursued by hostile groups are
+nefarious. The subjectivity of this situation is not apparent to the
+gregarious animal, which feels that the general principles of justice
+are on the side of its own herd. When the animal has arrived at the
+dignity of the metaphysician, it invents ethics as the embodiment of
+its belief in the justice of its own herd. So the Grand Augur invokes
+ethics as the justification of Augurs in their conflicts with pigs.
+But, it may be said, this view of ethics takes no account of such
+truly ethical notions as that of self-sacrifice. This, however, would
+be a mistake. The success of gregarious animals in the struggle for
+existence depends upon co-operation within the herd, and co-operation
+requires sacrifice, to some extent, of what would otherwise be the
+interest of the individual. Hence arises a conflict of desires and
+instincts, since both self-preservation and the preservation of the
+herd are biological ends to the individual. Ethics is in origin the
+art of recommending to others the sacrifices required for co-operation
+with oneself. Hence, by reflexion, it comes, through the operation of
+social justice, to recommend sacrifices by oneself, but all ethics,
+however refined, remains more or less subjective. Even vegetarians do
+not hesitate, for example, to save the life of a man in a fever,
+although in doing so they destroy the lives of many millions of
+microbes. The view of the world taken by the philosophy derived from
+ethical notions is thus never impartial and therefore never fully
+scientific. As compared with science, it fails to achieve the
+imaginative liberation from self which is necessary to such
+understanding of the world as man can hope to achieve, and the
+philosophy which it inspires is always more or less parochial, more or
+less infected with the prejudices of a time and a place.
+
+I do not deny the importance or value, within its own sphere, of the
+kind of philosophy which is inspired by ethical notions. The ethical
+work of Spinoza, for example, appears to me of the very highest
+significance, but what is valuable in such work is not any
+metaphysical theory as to the nature of the world to which it may give
+rise, nor indeed anything which can be proved or disproved by
+argument. What is valuable is the indication of some new way of
+feeling towards life and the world, some way of feeling by which our
+own existence can acquire more of the characteristics which we must
+deeply desire. The value of such work, however immeasurable it is,
+belongs with practice and not with theory. Such theoretic importance
+as it may possess is only in relation to human nature, not in relation
+to the world at large. The scientific philosophy, therefore, which
+aims only at understanding the world and not directly at any other
+improvement of human life, cannot take account of ethical notions
+without being turned aside from that submission to fact which is the
+essence of the scientific temper.
+
+
+II
+
+If the notion of the universe and the notion of good and evil are
+extruded from scientific philosophy, it may be asked what specific
+problems remain for the philosopher as opposed to the man of science?
+It would be difficult to give a precise answer to this question, but
+certain characteristics may be noted as distinguishing the province of
+philosophy from that of the special sciences.
+
+In the first place a philosophical proposition must be general. It
+must not deal specially with things on the surface of the earth, or
+with the solar system, or with any other portion of space and time. It
+is this need of generality which has led to the belief that philosophy
+deals with the universe as a whole. I do not believe that this belief
+is justified, but I do believe that a philosophical proposition must
+be applicable to everything that exists or may exist. It might be
+supposed that this admission would be scarcely distinguishable from
+the view which I wish to reject. This, however, would be an error, and
+an important one. The traditional view would make the universe itself
+the subject of various predicates which could not be applied to any
+particular thing in the universe, and the ascription of such peculiar
+predicates to the universe would be the special business of
+philosophy. I maintain, on the contrary, that there are no
+propositions of which the "universe" is the subject; in other words,
+that there is no such thing as the "universe." What I do maintain is
+that there are general propositions which may be asserted of each
+individual thing, such as the propositions of logic. This does not
+involve that all the things there are form a whole which could be
+regarded as another thing and be made the subject of predicates. It
+involves only the assertion that there are properties which belong to
+each separate thing, not that there are properties belonging to the
+whole of things collectively. The philosophy which I wish to advocate
+may be called logical atomism or absolute pluralism, because, while
+maintaining that there are many things, it denies that there is a
+whole composed of those things. We shall see, therefore, that
+philosophical propositions, instead of being concerned with the whole
+of things collectively, are concerned with all things distributively;
+and not only must they be concerned with all things, but they must be
+concerned with such properties of all things as do not depend upon the
+accidental nature of the things that there happen to be, but are true
+of any possible world, independently of such facts as can only be
+discovered by our senses.
+
+This brings us to a second characteristic of philosophical
+propositions, namely, that they must be _a priori_. A philosophical
+proposition must be such as can be neither proved nor disproved by
+empirical evidence. Too often we find in philosophical books arguments
+based upon the course of history, or the convolutions of the brain, or
+the eyes of shell-fish. Special and accidental facts of this kind are
+irrelevant to philosophy, which must make only such assertions as
+would be equally true however the actual world were constituted.
+
+We may sum up these two characteristics of philosophical propositions
+by saying that _philosophy is the science of the possible_. But this
+statement unexplained is liable to be misleading, since it may be
+thought that the possible is something other than the general, whereas
+in fact the two are indistinguishable.
+
+Philosophy, if what has been said is correct, becomes
+indistinguishable from logic as that word has now come to be used.
+The study of logic consists, broadly speaking, of two not very sharply
+distinguished portions. On the one hand it is concerned with those
+general statements which can be made concerning everything without
+mentioning any one thing or predicate or relation, such for example as
+"if _x_ is a member of the class [alpha] and every member of [alpha]
+is a member of [beta], then _x_ is a member of the class [beta],
+whatever _x_, [alpha], and [beta] may be." On the other hand, it is
+concerned with the analysis and enumeration of logical _forms_, i.e.
+with the kinds of propositions that may occur, with the various types
+of facts, and with the classification of the constituents of facts. In
+this way logic provides an inventory of possibilities, a repertory of
+abstractly tenable hypotheses.
+
+It might be thought that such a study would be too vague and too
+general to be of any very great importance, and that, if its problems
+became at any point sufficiently definite, they would be merged in the
+problems of some special science. It appears, however, that this is
+not the case. In some problems, for example, the analysis of space and
+time, the nature of perception, or the theory of judgment, the
+discovery of the logical form of the facts involved is the hardest
+part of the work and the part whose performance has been most lacking
+hitherto. It is chiefly for want of the right logical hypothesis that
+such problems have hitherto been treated in such an unsatisfactory
+manner, and have given rise to those contradictions or antinomies in
+which the enemies of reason among philosophers have at all times
+delighted.
+
+By concentrating attention upon the investigation of logical forms, it
+becomes possible at last for philosophy to deal with its problems
+piecemeal, and to obtain, as the sciences do, such partial and
+probably not wholly correct results as subsequent investigation can
+utilise even while it supplements and improves them. Most
+philosophies hitherto have been constructed all in one block, in such
+a way that, if they were not wholly correct, they were wholly
+incorrect, and could not be used as a basis for further
+investigations. It is chiefly owing to this fact that philosophy,
+unlike science, has hitherto been unprogressive, because each original
+philosopher has had to begin the work again from the beginning,
+without being able to accept anything definite from the work of his
+predecessors. A scientific philosophy such as I wish to recommend will
+be piecemeal and tentative like other sciences; above all, it will be
+able to invent hypotheses which, even if they are not wholly true,
+will yet remain fruitful after the necessary corrections have been
+made. This possibility of successive approximations to the truth is,
+more than anything else, the source of the triumphs of science, and to
+transfer this possibility to philosophy is to ensure a progress in
+method whose importance it would be almost impossible to exaggerate.
+
+The essence of philosophy as thus conceived is analysis, not
+synthesis. To build up systems of the world, like Heine's German
+professor who knit together fragments of life and made an intelligible
+system out of them, is not, I believe, any more feasible than the
+discovery of the philosopher's stone. What is feasible is the
+understanding of general forms, and the division of traditional
+problems into a number of separate and less baffling questions.
+"Divide and conquer" is the maxim of success here as elsewhere.
+
+Let us illustrate these somewhat general maxims by examining their
+application to the philosophy of space, for it is only in application
+that the meaning or importance of a method can be understood. Suppose
+we are confronted with the problem of space as presented in Kant's
+Transcendental Æsthetic, and suppose we wish to discover what are the
+elements of the problem and what hope there is of obtaining a solution
+of them. It will soon appear that three entirely distinct problems,
+belonging to different studies, and requiring different methods for
+their solution, have been confusedly combined in the supposed single
+problem with which Kant is concerned. There is a problem of logic, a
+problem of physics, and a problem of theory of knowledge. Of these
+three, the problem of logic can be solved exactly and perfectly; the
+problem of physics can probably be solved with as great a degree of
+certainty and as great an approach to exactness as can be hoped in an
+empirical region; the problem of theory of knowledge, however, remains
+very obscure and very difficult to deal with. Let us see how these
+three problems arise.
+
+(1) The logical problem has arisen through the suggestions of
+non-Euclidean geometry. Given a body of geometrical propositions, it
+is not difficult to find a minimum statement of the axioms from which
+this body of propositions can be deduced. It is also not difficult, by
+dropping or altering some of these axioms, to obtain a more general or
+a different geometry, having, from the point of view of pure
+mathematics, the same logical coherence and the same title to respect
+as the more familiar Euclidean geometry. The Euclidean geometry itself
+is true perhaps of actual space (though this is doubtful), but
+certainly of an infinite number of purely arithmetical systems, each
+of which, from the point of view of abstract logic, has an equal and
+indefeasible right to be called a Euclidean space. Thus space as an
+object of logical or mathematical study loses its uniqueness; not only
+are there many kinds of spaces, but there are an infinity of examples
+of each kind, though it is difficult to find any kind of which the
+space of physics may be an example, and it is impossible to find any
+kind of which the space of physics is certainly an example. As an
+illustration of one possible logical system of geometry we may
+consider all relations of three terms which are analogous in certain
+formal respects to the relation "between" as it appears to be in
+actual space. A space is then defined by means of one such three-term
+relation. The points of the space are all the terms which have this
+relation to something or other, and their order in the space in
+question is determined by this relation. The points of one space are
+necessarily also points of other spaces, since there are necessarily
+other three-term relations having those same points for their field.
+The space in fact is not determined by the class of its points, but by
+the ordering three-term relation. When enough abstract logical
+properties of such relations have been enumerated to determine the
+resulting kind of geometry, say, for example, Euclidean geometry, it
+becomes unnecessary for the pure geometer in his abstract capacity to
+distinguish between the various relations which have all these
+properties. He considers the whole class of such relations, not any
+single one among them. Thus in studying a given kind of geometry the
+pure mathematician is studying a certain class of relations defined by
+means of certain abstract logical properties which take the place of
+what used to be called axioms. The nature of geometrical _reasoning_
+therefore is purely deductive and purely logical; if any special
+epistemological peculiarities are to be found in geometry, it must not
+be in the reasoning, but in our knowledge concerning the axioms in
+some given space.
+
+(2) The physical problem of space is both more interesting and more
+difficult than the logical problem. The physical problem may be
+stated as follows: to find in the physical world, or to construct from
+physical materials, a space of one of the kinds enumerated by the
+logical treatment of geometry. This problem derives its difficulty
+from the attempt to accommodate to the roughness and vagueness of the
+real world some system possessing the logical clearness and exactitude
+of pure mathematics. That this can be done with a certain degree of
+approximation is fairly evident If I see three people _A_, _B_, and
+_C_ sitting in a row, I become aware of the fact which may be
+expressed by saying that _B_ is between _A_ and _C_ rather than that
+_A_ is between _B_ and _C_, or _C_ is between _A_ and _B_. This
+relation of "between" which is thus perceived to hold has some of the
+abstract logical properties of those three-term relations which, we
+saw, give rise to a geometry, but its properties fail to be exact, and
+are not, as empirically given, amenable to the kind of treatment at
+which geometry aims. In abstract geometry we deal with points,
+straight lines, and planes; but the three people _A_, _B_, and _C_
+whom I see sitting in a row are not exactly points, nor is the row
+exactly a straight line. Nevertheless physics, which formally assumes
+a space containing points, straight lines, and planes, is found
+empirically to give results applicable to the sensible world. It must
+therefore be possible to find an interpretation of the points,
+straight lines, and planes of physics in terms of physical data, or at
+any rate in terms of data together with such hypothetical additions as
+seem least open to question. Since all data suffer from a lack of
+mathematical precision through being of a certain size and somewhat
+vague in outline, it is plain that if such a notion as that of a point
+is to find any application to empirical material, the point must be
+neither a datum nor a hypothetical addition to data, but a
+_construction_ by means of data with their hypothetical additions. It
+is obvious that any hypothetical filling out of data is less dubious
+and unsatisfactory when the additions are closely analogous to data
+than when they are of a radically different sort. To assume, for
+example, that objects which we see continue, after we have turned away
+our eyes, to be more or less analogous to what they were while we were
+looking, is a less violent assumption than to assume that such objects
+are composed of an infinite number of mathematical points. Hence in
+the physical study of the geometry of physical space, points must not
+be assumed _ab initio_ as they are in the logical treatment of
+geometry, but must be constructed as systems composed of data and
+hypothetical analogues of data. We are thus led naturally to define a
+physical point as a certain class of those objects which are the
+ultimate constituents of the physical world. It will be the class of
+all those objects which, as one would naturally say, _contain_ the
+point. To secure a definition giving this result, without previously
+assuming that physical objects are composed of points, is an agreeable
+problem in mathematical logic. The solution of this problem and the
+perception of its importance are due to my friend Dr. Whitehead. The
+oddity of regarding a point as a class of physical entities wears off
+with familiarity, and ought in any case not to be felt by those who
+maintain, as practically every one does, that points are mathematical
+fictions. The word "fiction" is used glibly in such connexions by many
+men who seem not to feel the necessity of explaining how it can come
+about that a fiction can be so useful in the study of the actual world
+as the points of mathematical physics have been found to be. By our
+definition, which regards a point as a class of physical objects, it
+is explained both how the use of points can lead to important
+physical results, and how we can nevertheless avoid the assumption
+that points are themselves entities in the physical world.
+
+Many of the mathematically convenient properties of abstract logical
+spaces cannot be either known to belong or known not to belong to the
+space of physics. Such are all the properties connected with continuity.
+For to know that actual space has these properties would require an
+infinite exactness of sense-perception. If actual space is continuous,
+there are nevertheless many possible non-continuous spaces which will be
+empirically indistinguishable from it; and, conversely, actual space may
+be non-continuous and yet empirically indistinguishable from a possible
+continuous space. Continuity, therefore, though obtainable in the _a
+priori_ region of arithmetic, is not with certainty obtainable in the
+space or time of the physical world: whether these are continuous or not
+would seem to be a question not only unanswered but for ever
+unanswerable. From the point of view of philosophy, however, the
+discovery that a question is unanswerable is as complete an answer as
+any that could possibly be obtained. And from the point of view of
+physics, where no empirical means of distinction can be found, there can
+be no empirical objection to the mathematically simplest assumption,
+which is that of continuity.
+
+The subject of the physical theory of space is a very large one,
+hitherto little explored. It is associated with a similar theory of
+time, and both have been forced upon the attention of philosophically
+minded physicists by the discussions which have raged concerning the
+theory of relativity.
+
+(3) The problem with which Kant is concerned in the Transcendental
+Æsthetic is primarily the epistemological problem: "How do we come to
+have knowledge of geometry _a priori_?" By the distinction between the
+logical and physical problems of geometry, the bearing and scope of
+this question are greatly altered. Our knowledge of pure geometry is
+_a priori_ but is wholly logical. Our knowledge of physical geometry
+is synthetic, but is not _a priori_. Our knowledge of pure geometry is
+hypothetical, and does not enable us to assert, for example, that the
+axiom of parallels is true in the physical world. Our knowledge of
+physical geometry, while it does enable us to assert that this axiom
+is approximately verified, does not, owing to the inevitable
+inexactitude of observation, enable us to assert that it is verified
+_exactly_. Thus, with the separation which we have made between pure
+geometry and the geometry of physics, the Kantian problem collapses.
+To the question, "How is synthetic _a priori_ knowledge possible?" we
+can now reply, at any rate so far as geometry is concerned, "It is not
+possible," if "synthetic" means "not deducible from logic alone." Our
+knowledge of geometry, like the rest of our knowledge, is derived
+partly from logic, partly from sense, and the peculiar position which
+in Kant's day geometry appeared to occupy is seen now to be a
+delusion. There are still some philosophers, it is true, who maintain
+that our knowledge that the axiom of parallels, for example, is true
+of actual space, is not to be accounted for empirically, but is as
+Kant maintained derived from an _a priori_ intuition. This position is
+not logically refutable, but I think it loses all plausibility as soon
+as we realise how complicated and derivative is the notion of physical
+space. As we have seen, the application of geometry to the physical
+world in no way demands that there should really be points and
+straight lines among physical entities. The principle of economy,
+therefore, demands that we should abstain from assuming the existence
+of points and straight lines. As soon, however, as we accept the view
+that points and straight lines are complicated constructions by means
+of classes of physical entities, the hypothesis that we have an _a
+priori_ intuition enabling us to know what happens to straight lines
+when they are produced indefinitely becomes extremely strained and
+harsh; nor do I think that such an hypothesis would ever have arisen
+in the mind of a philosopher who had grasped the nature of physical
+space. Kant, under the influence of Newton, adopted, though with some
+vacillation, the hypothesis of absolute space, and this hypothesis,
+though logically unobjectionable, is removed by Occam's razor, since
+absolute space is an unnecessary entity in the explanation of the
+physical world. Although, therefore, we cannot refute the Kantian
+theory of an _a priori_ intuition, we can remove its grounds one by
+one through an analysis of the problem. Thus, here as in many other
+philosophical questions, the analytic method, while not capable of
+arriving at a demonstrative result, is nevertheless capable of showing
+that all the positive grounds in favour of a certain theory are
+fallacious and that a less unnatural theory is capable of accounting
+for the facts.
+
+Another question by which the capacity of the analytic method can be
+shown is the question of realism. Both those who advocate and those
+who combat realism seem to me to be far from clear as to the nature of
+the problem which they are discussing. If we ask: "Are our objects of
+perception _real_ and are they _independent_ of the percipient?" it
+must be supposed that we attach some meaning to the words "real" and
+"independent," and yet, if either side in the controversy of realism
+is asked to define these two words, their answer is pretty sure to
+embody confusions such as logical analysis will reveal.
+
+Let us begin with the word "real." There certainly are objects of
+perception, and therefore, if the question whether these objects are
+real is to be a substantial question, there must be in the world two
+sorts of objects, namely, the real and the unreal, and yet the unreal
+is supposed to be essentially what there is not. The question what
+properties must belong to an object in order to make it real is one to
+which an adequate answer is seldom if ever forthcoming. There is of
+course the Hegelian answer, that the real is the self-consistent and
+that nothing is self-consistent except the Whole; but this answer,
+true or false, is not relevant in our present discussion, which moves
+on a lower plane and is concerned with the status of objects of
+perception among other objects of equal fragmentariness. Objects of
+perception are contrasted, in the discussions concerning realism,
+rather with psychical states on the one hand and matter on the other
+hand than with the all-inclusive whole of things. The question we have
+therefore to consider is the question as to what can be meant by
+assigning "reality" to some but not all of the entities that make up
+the world. Two elements, I think, make up what is felt rather than
+thought when the word "reality" is used in this sense. A thing is real
+if it persists at times when it is not perceived; or again, a thing is
+real when it is correlated with other things in a way which experience
+has led us to expect. It will be seen that reality in either of these
+senses is by no means necessary to a thing, and that in fact there
+might be a whole world in which nothing was real in either of these
+senses. It might turn out that the objects of perception failed of
+reality in one or both of these respects, without its being in any way
+deducible that they are not parts of the external world with which
+physics deals. Similar remarks will apply to the word "independent."
+Most of the associations of this word are bound up with ideas as to
+causation which it is not now possible to maintain. _A_ is independent
+of _B_ when _B_ is not an indispensable part of the _cause_ of _A_.
+But when it is recognised that causation is nothing more than
+correlation, and that there are correlations of simultaneity as well
+as of succession, it becomes evident that there is no uniqueness in a
+series of casual antecedents of a given event, but that, at any point
+where there is a correlation of simultaneity, we can pass from one
+line of antecedents to another in order to obtain a new series of
+causal antecedents. It will be necessary to specify the causal law
+according to which the antecedents are to be considered. I received a
+letter the other day from a correspondent who had been puzzled by
+various philosophical questions. After enumerating them he says:
+"These questions led me from Bonn to Strassburg, where I found
+Professor Simmel." Now, it would be absurd to deny that these
+questions caused his body to move from Bonn to Strassburg, and yet it
+must be supposed that a set of purely mechanical antecedents could
+also be found which would account for this transfer of matter from one
+place to another. Owing to this plurality of causal series antecedent
+to a given event, the notion of _the_ cause becomes indefinite, and
+the question of independence becomes correspondingly ambiguous. Thus,
+instead of asking simply whether _A_ is independent of _B_, we ought
+to ask whether there is a series determined by such and such causal
+laws leading from _B_ to _A_. This point is important in connexion
+with the particular question of objects of perception. It may be that
+no objects quite like those which we perceive ever exist unperceived;
+in this case there will be a causal law according to which objects of
+perception are not independent of being perceived. But even if this be
+the case, it may nevertheless also happen that there are purely
+physical causal laws determining the occurrence of objects which are
+perceived by means of other objects which perhaps are not perceived.
+In that case, in regard to such causal laws objects of perception will
+be independent of being perceived. Thus the question whether objects
+of perception are independent of being perceived is, as it stands,
+indeterminate, and the answer will be yes or no according to the
+method adopted of making it determinate. I believe that this confusion
+has borne a very large part in prolonging the controversies on this
+subject, which might well have seemed capable of remaining for ever
+undecided. The view which I should wish to advocate is that objects of
+perception do not persist unchanged at times when they are not
+perceived, although probably objects more or less resembling them do
+exist at such times; that objects of perception are part, and the only
+empirically knowable part, of the actual subject-matter of physics,
+and are themselves properly to be called physical; that purely
+physical laws exist determining the character and duration of objects
+of perception without any reference to the fact that they are
+perceived; and that in the establishment of such laws the propositions
+of physics do not presuppose any propositions of psychology or even
+the existence of mind. I do not know whether realists would recognise
+such a view as realism. All that I should claim for it is, that it
+avoids difficulties which seem to me to beset both realism and
+idealism as hitherto advocated, and that it avoids the appeal which
+they have made to ideas which logical analysis shows to be ambiguous.
+A further defence and elaboration of the positions which I advocate,
+but for which time is lacking now, will be found indicated in my book
+on _Our Knowledge of the External World_.[22]
+
+The adoption of scientific method in philosophy, if I am not mistaken,
+compels us to abandon the hope of solving many of the more ambitious
+and humanly interesting problems of traditional philosophy. Some of
+these it relegates, though with little expectation of a successful
+solution, to special sciences, others it shows to be such as our
+capacities are essentially incapable of solving. But there remain a
+large number of the recognised problems of philosophy in regard to
+which the method advocated gives all those advantages of division into
+distinct questions, of tentative, partial, and progressive advance,
+and of appeal to principles with which, independently of temperament,
+all competent students must agree. The failure of philosophy hitherto
+has been due in the main to haste and ambition: patience and modesty,
+here as in other sciences, will open the road to solid and durable
+progress.
+
+FOOTNOTES:
+
+[19] Bosanquet, _Logic_, ii, p. 211.
+
+[20] _Some Problems of Philosophy_, p 124.
+
+[21] _First Principles_ (1862), Part II, beginning of chap. viii.
+
+[22] Open Court Company, 1914.
+
+
+
+
+VII
+
+THE ULTIMATE CONSTITUENTS OF MATTER[23]
+
+
+I wish to discuss in this article no less a question than the ancient
+metaphysical query, "What is matter?" The question, "What is matter?"
+in so far as it concerns philosophy, is, I think, already capable of
+an answer which in principle will be as complete as an answer can hope
+to be; that is to say, we can separate the problem into an essentially
+soluble and an essentially insoluble portion, and we can now see how
+to solve the essentially soluble portion, at least as regards its main
+outlines. It is these outlines which I wish to suggest in the present
+article. My main position, which is realistic, is, I hope and believe,
+not remote from that of Professor Alexander, by whose writings on this
+subject I have profited greatly.[24] It is also in close accord with
+that of Dr. Nunn.[25]
+
+Common sense is accustomed to the division of the world into mind and
+matter. It is supposed by all who have never studied philosophy that
+the distinction between mind and matter is perfectly clear and easy,
+that the two do not at any point overlap, and that only a fool or a
+philosopher could be in doubt as to whether any given entity is mental
+or material. This simple faith survives in Descartes and in a
+somewhat modified form in Spinoza, but with Leibniz it begins to
+disappear, and from his day to our own almost every philosopher of
+note has criticised and rejected the dualism of common sense. It is my
+intention in this article to defend this dualism; but before defending
+it we must spend a few moments on the reasons which have prompted its
+rejection.
+
+Our knowledge of the material world is obtained by means of the
+senses, of sight and touch and so on. At first it is supposed that
+things are just as they seem, but two opposite sophistications soon
+destroy this naïve belief. On the one hand the physicists cut up
+matter into molecules, atoms, corpuscles, and as many more such
+subdivisions as their future needs may make them postulate, and the
+units at which they arrive are uncommonly different from the visible,
+tangible objects of daily life. A unit of matter tends more and more
+to be something like an electromagnetic field filling all space,
+though having its greatest intensity in a small region. Matter
+consisting of such elements is as remote from daily life as any
+metaphysical theory. It differs from the theories of metaphysicians
+only in the fact that its practical efficacy proves that it contains
+some measure of truth and induces business men to invest money on the
+strength of it; but, in spite of its connection with the money market,
+it remains a metaphysical theory none the less.
+
+The second kind of sophistication to which the world of common sense
+has been subjected is derived from the psychologists and
+physiologists. The physiologists point out that what we see depends
+upon the eye, that what we hear depends upon the ear, and that all our
+senses are liable to be affected by anything which affects the brain,
+like alcohol or hasheesh. Psychologists point out how much of what we
+think we see is supplied by association or unconscious inference, how
+much is mental interpretation, and how doubtful is the residuum which
+can be regarded as crude datum. From these facts it is argued by the
+psychologists that the notion of a datum passively received by the
+mind is a delusion, and it is argued by the physiologists that even if
+a pure datum of sense could be obtained by the analysis of experience,
+still this datum could not belong, as common sense supposes, to the
+outer world, since its whole nature is conditioned by our nerves and
+sense organs, changing as they change in ways which it is thought
+impossible to connect with any change in the matter supposed to be
+perceived. This physiologist's argument is exposed to the rejoinder,
+more specious than solid, that our knowledge of the existence of the
+sense organs and nerves is obtained by that very process which the
+physiologist has been engaged in discrediting, since the existence of
+the nerves and sense organs is only known through the evidence of the
+senses themselves. This argument may prove that some reinterpretation
+of the results of physiology is necessary before they can acquire
+metaphysical validity. But it does not upset the physiological
+argument in so far as this constitutes merely a _reductio ad absurdum_
+of naïve realism.
+
+These various lines of argument prove, I think, that some part of the
+beliefs of common sense must be abandoned. They prove that, if we take
+these beliefs as a whole, we are forced into conclusions which are in
+part self-contradictory; but such arguments cannot of themselves
+decide what portion of our common-sense beliefs is in need of
+correction. Common sense believes that what we see is physical,
+outside the mind, and continuing to exist if we shut our eyes or turn
+them in another direction. I believe that common sense is right in
+regarding what we see as physical and (in one of several possible
+senses) outside the mind, but is probably wrong in supposing that it
+continues to exist when we are no longer looking at it. It seems to me
+that the whole discussion of matter has been obscured by two errors
+which support each other. The first of these is the error that what we
+see, or perceive through any of our other senses, is subjective: the
+second is the belief that what is physical must be persistent.
+Whatever physics may regard as the ultimate constituents of matter, it
+always supposes these constituents to be indestructible. Since the
+immediate data of sense are not indestructible but in a state of
+perpetual flux, it is argued that these data themselves cannot be
+among the ultimate constituents of matter. I believe this to be a
+sheer mistake. The persistent particles of mathematical physics I
+regard as logical constructions, symbolic fictions enabling us to
+express compendiously very complicated assemblages of facts; and, on
+the other hand, I believe that the actual data in sensation, the
+immediate objects of sight or touch or hearing, are extra-mental,
+purely physical, and among the ultimate constituents of matter.
+
+My meaning in regard to the impermanence of physical entities may
+perhaps be made clearer by the use of Bergson's favourite illustration
+of the cinematograph. When I first read Bergson's statement that the
+mathematician conceives the world after the analogy of a
+cinematograph, I had never seen a cinematograph, and my first visit to
+one was determined by the desire to verify Bergson's statement, which
+I found to be completely true, at least so far as I am concerned.
+When, in a picture palace, we see a man rolling down hill, or running
+away from the police, or falling into a river, or doing any of those
+other things to which men in such places are addicted, we know that
+there is not really only one man moving, but a succession of films,
+each with a different momentary man. The illusion of persistence
+arises only through the approach to continuity in the series of
+momentary men. Now what I wish to suggest is that in this respect the
+cinema is a better metaphysician than common sense, physics, or
+philosophy. The real man too, I believe, however the police may swear
+to his identity, is really a series of momentary men, each different
+one from the other, and bound together, not by a numerical identity,
+but by continuity and certain intrinsic causal laws. And what applies
+to men applies equally to tables and chairs, the sun, moon and stars.
+Each of these is to be regarded, not as one single persistent entity,
+but as a series of entities succeeding each other in time, each
+lasting for a very brief period, though probably not for a mere
+mathematical instant. In saying this I am only urging the same kind of
+division in time as we are accustomed to acknowledge in the case of
+space. A body which fills a cubic foot will be admitted to consist of
+many smaller bodies, each occupying only a very tiny volume; similarly
+a thing which persists for an hour is to be regarded as composed of
+many things of less duration. A true theory of matter requires a
+division of things into time-corpuscles as well as into
+space-corpuscles.
+
+The world may be conceived as consisting of a multitude of entities
+arranged in a certain pattern. The entities which are arranged I shall
+call "particulars." The arrangement or pattern results from relations
+among particulars. Classes or series of particulars, collected
+together on account of some property which makes it convenient to be
+able to speak of them as wholes, are what I call logical constructions
+or symbolic fictions. The particulars are to be conceived, not on the
+analogy of bricks in a building, but rather on the analogy of notes
+in a symphony. The ultimate constituents of a symphony (apart from
+relations) are the notes, each of which lasts only for a very short
+time. We may collect together all the notes played by one instrument:
+these may be regarded as the analogues of the successive particulars
+which common sense would regard as successive states of one "thing."
+But the "thing" ought to be regarded as no more "real" or
+"substantial" than, for example, the rôle of the trombone. As soon as
+"things" are conceived in this manner it will be found that the
+difficulties in the way of regarding immediate objects of sense as
+physical have largely disappeared.
+
+When people ask, "Is the object of sense mental or physical?" they
+seldom have any clear idea either what is meant by "mental" or
+"physical," or what criteria are to be applied for deciding whether a
+given entity belongs to one class or the other. I do not know how to
+give a sharp definition of the word "mental," but something may be
+done by enumerating occurrences which are indubitably mental:
+believing, doubting, wishing, willing, being pleased or pained, are
+certainly mental occurrences; so are what we may call experiences,
+seeing, hearing, smelling, perceiving generally. But it does not
+follow from this that what is seen, what is heard, what is smelt, what
+is perceived, must be mental. When I see a flash of lightning, my
+seeing of it is mental, but what I see, although it is not quite the
+same as what anybody else sees at the same moment, and although it
+seems very unlike what the physicist would describe as a flash of
+lightning, is not mental. I maintain, in fact, that if the physicist
+could describe truly and fully all that occurs in the physical world
+when there is a flash of lightning, it would contain as a constituent
+what I see, and also what is seen by anybody else who would commonly
+be said to see the same flash. What I mean may perhaps be made plainer
+by saying that if my body could remain in exactly the same state in
+which it is, although my mind had ceased to exist, precisely that
+object which I now see when I see the flash would exist, although of
+course I should not see it, since my seeing is mental. The principal
+reasons which have led people to reject this view have, I think, been
+two: first, that they did not adequately distinguish between my seeing
+and what I see; secondly, that the causal dependence of what I see
+upon my body has made people suppose that what I see cannot be
+"outside" me. The first of these reasons need not detain us, since the
+confusion only needs to be pointed out in order to be obviated; but
+the second requires some discussion, since it can only be answered by
+removing current misconceptions, on the one hand as to the nature of
+space, and on the other, as to the meaning of causal dependence.
+
+When people ask whether colours, for example, or other secondary
+qualities are inside or outside the mind, they seem to suppose that
+their meaning must be clear, and that it ought to be possible to say
+yes or no without any further discussion of the terms involved. In
+fact, however, such terms as "inside" or "outside" are very ambiguous.
+What is meant by asking whether this or that is "in" the mind? The
+mind is not like a bag or a pie; it does not occupy a certain region
+in space, or, if (in a sense) it does, what is in that region is
+presumably part of the brain, which would not be said to be in the
+mind. When people say that sensible qualities are in the mind, they do
+not mean "spatially contained in" in the sense in which the blackbirds
+were in the pie. We might regard the mind as an assemblage of
+particulars, namely, what would be called "states of mind," which
+would belong together in virtue of some specific common quality. The
+common quality of all states of mind would be the quality designated
+by the word "mental"; and besides this we should have to suppose that
+each separate person's states of mind have some common characteristic
+distinguishing them from the states of mind of other people. Ignoring
+this latter point, let us ask ourselves whether the quality designated
+by the word "mental" does, as a matter of observation, actually belong
+to objects of sense, such as colours or noises. I think any candid
+person must reply that, however difficult it may be to know what we
+mean by "mental," it is not difficult to see that colours and noises
+are not mental in the sense of having that intrinsic peculiarity which
+belongs to beliefs and wishes and volitions, but not to the physical
+world. Berkeley advances on this subject a plausible argument[26]
+which seems to me to rest upon an ambiguity in the word "pain." He
+argues that the realist supposes the heat which he feels in
+approaching a fire to be something outside his mind, but that as he
+approaches nearer and nearer to the fire the sensation of heat passes
+imperceptibly into pain, and that no one could regard pain as
+something outside the mind. In reply to this argument, it should be
+observed in the first place that the heat of which we are immediately
+aware is not in the fire but in our own body. It is only by inference
+that the fire is judged to be the cause of the heat which we feel in
+our body. In the second place (and this is the more important point),
+when we speak of pain we may mean one of two things: we may mean the
+object of the sensation or other experience which has the quality of
+being painful, or we may mean the quality of painfulness itself. When
+a man says he has a pain in his great toe, what he means is that he
+has a sensation associated with his great toe and having the quality
+of painfulness. The sensation itself, like every sensation, consists
+in experiencing a sensible object, and the experiencing has that
+quality of painfulness which only mental occurrences can have, but
+which may belong to thoughts or desires, as well as to sensations. But
+in common language we speak of the sensible object experienced in a
+painful sensation as a pain, and it is this way of speaking which
+causes the confusion upon which the plausibility of Berkeley's
+argument depends. It would be absurd to attribute the quality of
+painfulness to anything non-mental, and hence it comes to be thought
+that what we call a pain in the toe must be mental. In fact, however,
+it is not the sensible object in such a case which is painful, but the
+sensation, that is to say, the experience of the sensible object. As
+the heat which we experience from the fire grows greater, the
+experience passes gradually from being pleasant to being painful, but
+neither the pleasure nor the pain is a quality of the object
+experienced as opposed to the experience, and it is therefore a
+fallacy to argue that this object must be mental on the ground that
+painfulness can only be attributed to what is mental.
+
+If, then, when we say that something is in the mind we mean that it
+has a certain recognisable intrinsic characteristic such as belongs to
+thoughts and desires, it must be maintained on grounds of immediate
+inspection that objects of sense are not in any mind.
+
+A different meaning of "in the mind" is, however, to be inferred from
+the arguments advanced by those who regard sensible objects as being
+in the mind. The arguments used are, in the main, such as would prove
+the causal dependence of objects of sense upon the percipient. Now
+the notion of causal dependence is very obscure and difficult, much
+more so in fact than is generally realised by philosophers. I shall
+return to this point in a moment. For the present, however, accepting
+the notion of causal dependence without criticism, I wish to urge that
+the dependence in question is rather upon our bodies than upon our
+minds. The visual appearance of an object is altered if we shut one
+eye, or squint, or look previously at something dazzling; but all
+these are bodily acts, and the alterations which they effect are to be
+explained by physiology and optics, not by psychology.[27] They are in
+fact of exactly the same kind as the alterations effected by
+spectacles or a microscope. They belong therefore to the theory of the
+physical world, and can have no bearing upon the question whether what
+we see is causally dependent upon the mind. What they do tend to
+prove, and what I for my part have no wish to deny, is that what we
+see is causally dependent upon our body and is not, as crude common
+sense would suppose, something which would exist equally if our eyes
+and nerves and brain were absent, any more than the visual appearance
+presented by an object seen through a microscope would remain if the
+microscope were removed. So long as it is supposed that the physical
+world is composed of stable and more or less permanent constituents,
+the fact that what we see is changed by changes in our body appears to
+afford reason for regarding what we see as not an ultimate constituent
+of matter. But if it is recognised that the ultimate constituents of
+matter are as circumscribed in duration as in spatial extent, the
+whole of this difficulty vanishes.
+
+There remains, however, another difficulty, connected with space. When
+we look at the sun we wish to know something about the sun itself,
+which is ninety-three million miles away; but what we see is dependent
+upon our eyes, and it is difficult to suppose that our eyes can affect
+what happens at a distance of ninety-three million miles. Physics
+tells us that certain electromagnetic waves start from the sun, and
+reach our eyes after about eight minutes. They there produce
+disturbances in the rods and cones, thence in the optic nerve, thence
+in the brain. At the end of this purely physical series, by some odd
+miracle, comes the experience which we call "seeing the sun," and it
+is such experiences which form the whole and sole reason for our
+belief in the optic nerve, the rods and cones, the ninety-three
+million miles, the electromagnetic waves, and the sun itself. It is
+this curious oppositeness of direction between the order of causation
+as affirmed by physics, and the order of evidence as revealed by
+theory of knowledge, that causes the most serious perplexities in
+regard to the nature of physical reality. Anything that invalidates
+our seeing, as a source of knowledge concerning physical reality,
+invalidates also the whole of physics and physiology. And yet,
+starting from a common-sense acceptance of our seeing, physics has
+been led step by step to the construction of the causal chain in which
+our seeing is the last link, and the immediate object which we see
+cannot be regarded as that initial cause which we believe to be
+ninety-three million miles away, and which we are inclined to regard
+as the "real" sun.
+
+I have stated this difficulty as forcibly as I can, because I believe
+that it can only be answered by a radical analysis and reconstruction
+of all the conceptions upon whose employment it depends.
+
+Space, time, matter and cause, are the chief of these conceptions. Let
+us begin with the conception of cause.
+
+Causal dependence, as I observed a moment ago, is a conception which
+it is very dangerous to accept at its face value. There exists a
+notion that in regard to any event there is something which may be
+called _the_ cause of that event--some one definite occurrence,
+without which the event would have been impossible and with which it
+becomes necessary. An event is supposed to be dependent upon its cause
+in some way which in it is not dependent upon other things. Thus men
+will urge that the mind is dependent upon the brain, or, with equal
+plausibility, that the brain is dependent upon the mind. It seems not
+improbable that if we had sufficient knowledge we could infer the
+state of a man's mind from the state of his brain, or the state of his
+brain from the state of his mind. So long as the usual conception of
+causal dependence is retained, this state of affairs can be used by
+the materialist to urge that the state of our brain causes our
+thoughts, and by the idealist to urge that our thoughts cause the
+state of our brain. Either contention is equally valid or equally
+invalid. The fact seems to be that there are many correlations of the
+sort which may be called causal, and that, for example, either a
+physical or a mental event can be predicted, theoretically, either
+from a sufficient number of physical antecedents or from a sufficient
+number of mental antecedents. To speak of _the_ cause of an event is
+therefore misleading. Any set of antecedents from which the event can
+theoretically be inferred by means of correlations might be called a
+cause of the event. But to speak of _the_ cause is to imply a
+uniqueness which does not exist.
+
+The relevance of this to the experience which we call "seeing the sun"
+is obvious. The fact that there exists a chain of antecedents which
+makes our seeing dependent upon the eyes and nerves and brain does not
+even tend to show that there is not another chain of antecedents in
+which the eyes and nerves and brain as physical things are ignored. If
+we are to escape from the dilemma which seemed to arise out of the
+physiological causation of what we see when we say we see the sun, we
+must find, at least in theory, a way of stating causal laws for the
+physical world, in which the units are not material things, such as
+the eyes and nerves and brain, but momentary particulars of the same
+sort as our momentary visual object when we look at the sun. The sun
+itself and the eyes and nerves and brain must be regarded as
+assemblages of momentary particulars. Instead of supposing, as we
+naturally do when we start from an uncritical acceptance of the
+apparent dicta of physics, that _matter_ is what is "really real" in
+the physical world, and that the immediate objects of sense are mere
+phantasms, we must regard matter as a logical construction, of which
+the constituents will be just such evanescent particulars as may, when
+an observer happens to be present, become data of sense to that
+observer. What physics regards as the sun of eight minutes ago will be
+a whole assemblage of particulars, existing at different times,
+spreading out from a centre with the velocity of light, and containing
+among their number all those visual data which are seen by people who
+are now looking at the sun. Thus the sun of eight minutes ago is a
+class of particulars, and what I see when I now look at the sun is one
+member of this class. The various particulars constituting this class
+will be correlated with each other by a certain continuity and certain
+intrinsic laws of variation as we pass outwards from the centre,
+together with certain modifications correlated extrinsically with
+other particulars which are not members of this class. It is these
+extrinsic modifications which represent the sort of facts that, in our
+former account, appeared as the influence of the eyes and nerves in
+modifying the appearance of the sun.[28]
+
+The _prima facie_ difficulties in the way of this view are chiefly
+derived from an unduly conventional theory of space. It might seem at
+first sight as if we had packed the world much fuller than it could
+possibly hold. At every place between us and the sun, we said, there
+is to be a particular which is to be a member of the sun as it was a
+few minutes ago. There will also, of course, have to be a particular
+which is a member of any planet or fixed star that may happen to be
+visible from that place. At the place where I am, there will be
+particulars which will be members severally of all the "things" I am
+now said to be perceiving. Thus throughout the world, everywhere,
+there will be an enormous number of particulars coexisting in the same
+place. But these troubles result from contenting ourselves too readily
+with the merely three-dimensional space to which schoolmasters have
+accustomed us. The space of the real world is a space of six
+dimensions, and as soon as we realise this we see that there is plenty
+of room for all the particulars for which we want to find positions.
+In order to realise this we have only to return for a moment from the
+polished space of physics to the rough and untidy space of our
+immediate sensible experience. The space of one man's sensible objects
+is a three-dimensional space. It does not appear probable that two men
+ever both perceive at the same time any one sensible object; when they
+are said to see the same thing or hear the same noise, there will
+always be some difference, however slight, between the actual shapes
+seen or the actual sounds heard. If this is so, and if, as is
+generally assumed, position in space is purely relative, it follows
+that the space of one man's objects and the space of another man's
+objects have no place in common, that they are in fact different
+spaces, and not merely different parts of one space. I mean by this
+that such immediate spatial relations as are perceived to hold
+between the different parts of the sensible space perceived by one
+man, do not hold between parts of sensible spaces perceived by
+different men. There are therefore a multitude of three-dimensional
+spaces in the world: there are all those perceived by observers, and
+presumably also those which are not perceived, merely because no
+observer is suitably situated for perceiving them.
+
+But although these spaces do not have to one another the same kind of
+spatial relations as obtain between the parts of one of them, it is
+nevertheless possible to arrange these spaces themselves in a
+three-dimensional order. This is done by means of the correlated
+particulars which we regard as members (or aspects) of one physical
+thing. When a number of people are said to see the same object, those
+who would be said to be near to the object see a particular occupying
+a larger part of their field of vision than is occupied by the
+corresponding particular seen by people who would be said to be
+farther from the thing. By means of such considerations it is
+possible, in ways which need not now be further specified, to arrange
+all the different spaces in a three-dimensional series. Since each of
+the spaces is itself three-dimensional, the whole world of particulars
+is thus arranged in a six-dimensional space, that is to say, six
+co-ordinates will be required to assign completely the position of any
+given particular, namely, three to assign its position in its own
+space and three more to assign the position of its space among the
+other spaces.
+
+There are two ways of classifying particulars: we may take together
+all those that belong to a given "perspective," or all those that are,
+as common sense would say, different "aspects" of the same "thing."
+For example, if I am (as is said) seeing the sun, what I see belongs
+to two assemblages: (1) the assemblage of all my present objects of
+sense, which is what I call a "perspective"; (2) the assemblage of
+all the different particulars which would be called aspects of the sun
+of eight minutes ago--this assemblage is what I define as _being_ the
+sun of eight minutes ago. Thus "perspectives" and "things" are merely
+two different ways of classifying particulars. It is to be observed
+that there is no _a priori_ necessity for particulars to be
+susceptible of this double classification. There may be what might be
+called "wild" particulars, not having the usual relations by which the
+classification is effected; perhaps dreams and hallucinations are
+composed of particulars which are "wild" in this sense.
+
+The exact definition of what is meant by a perspective is not quite
+easy. So long as we confine ourselves to visible objects or to objects
+of touch we might define the perspective of a given particular as "all
+particulars which have a simple (direct) spatial relation to the given
+particular." Between two patches of colour which I see now, there is a
+direct spatial relation which I equally see. But between patches of
+colour seen by different men there is only an indirect constructed
+spatial relation by means of the placing of "things" in physical space
+(which is the same as the space composed of perspectives). Those
+particulars which have direct spatial relations to a given particular
+will belong to the same perspective. But if, for example, the sounds
+which I hear are to belong to the same perspective with the patches of
+colour which I see, there must be particulars which have no direct
+spatial relation and yet belong to the same perspective. We cannot
+define a perspective as all the data of one percipient at one time,
+because we wish to allow the possibility of perspectives which are not
+perceived by any one. There will be need, therefore, in defining a
+perspective, of some principle derived neither from psychology nor
+from space.
+
+Such a principle may be obtained from the consideration of _time_.
+The one all-embracing time, like the one all-embracing space, is a
+construction; there is no _direct_ time-relation between particulars
+belonging to my perspective and particulars belonging to another
+man's. On the other hand, any two particulars of which I am aware are
+either simultaneous or successive, and their simultaneity or
+successiveness is sometimes itself a datum to me. We may therefore
+define the perspective to which a given particular belongs as "all
+particulars simultaneous with the given particular," where
+"simultaneous" is to be understood as a direct simple relation, not
+the derivative constructed relation of physics. It may be observed
+that the introduction of "local time" suggested by the principle of
+relativity has effected, for purely scientific reasons, much the same
+multiplication of times as we have just been advocating.
+
+The sum-total of all the particulars that are (directly) either
+simultaneous with or before or after a given particular may be defined
+as the "biography" to which that particular belongs. It will be
+observed that, just as a perspective need not be actually perceived by
+any one, so a biography need not be actually lived by any one. Those
+biographies that are lived by no one are called "official."
+
+The definition of a "thing" is effected by means of continuity and of
+correlations which have a certain differential independence of other
+"things." That is to say, given a particular in one perspective, there
+will usually in a neighbouring perspective be a very similar
+particular, differing from the given particular, to the first order of
+small quantities, according to a law involving only the difference of
+position of the two perspectives in perspective space, and not any of
+the other "things" in the universe. It is this continuity and
+differential independence in the law of change as we pass from one
+perspective to another that defines the class of particulars which is
+to be called "one thing."
+
+Broadly speaking, we may say that the physicist finds it convenient to
+classify particulars into "things," while the psychologist finds it
+convenient to classify them into "perspectives" and "biographies,"
+since one perspective _may_ constitute the momentary data of one
+percipient, and one biography _may_ constitute the whole of the data
+of one percipient throughout his life.
+
+We may now sum up our discussion. Our object has been to discover as
+far as possible the nature of the ultimate constituents of the
+physical world. When I speak of the "physical world," I mean, to begin
+with, the world dealt with by physics. It is obvious that physics is
+an empirical science, giving us a certain amount of knowledge and
+based upon evidence obtained through the senses. But partly through
+the development of physics itself, partly through arguments derived
+from physiology, psychology or metaphysics, it has come to be thought
+that the immediate data of sense could not themselves form part of the
+ultimate constituents of the physical world, but were in some sense
+"mental," "in the mind," or "subjective." The grounds for this view,
+in so far as they depend upon physics, can only be adequately dealt
+with by rather elaborate constructions depending upon symbolic logic,
+showing that out of such materials as are provided by the senses it is
+possible to construct classes and series having the properties which
+physics assigns to matter. Since this argument is difficult and
+technical, I have not embarked upon it in this article. But in so far
+as the view that sense-data are "mental" rests upon physiology,
+psychology, or metaphysics, I have tried to show that it rests upon
+confusions and prejudices--prejudices in favour of permanence in the
+ultimate constituents of matter, and confusions derived from unduly
+simple notions as to space, from the causal correlation of sense-data
+with sense-organs, and from failure to distinguish between sense-data
+and sensations. If what we have said on these subjects is valid, the
+existence of sense-data is logically independent of the existence of
+mind, and is causally dependent upon the _body_ of the percipient
+rather than upon his mind. The causal dependence upon the body of the
+percipient, we found, is a more complicated matter than it appears to
+be, and, like all causal dependence, is apt to give rise to erroneous
+beliefs through misconceptions as to the nature of causal correlation.
+If we have been right in our contentions, sense-data are merely those
+among the ultimate constituents of the physical world, of which we
+happen to be immediately aware; they themselves are purely physical,
+and all that is mental in connection with them is our awareness of
+them, which is irrelevant to their nature and to their place in
+physics.
+
+Unduly simple notions as to space have been a great stumbling-block to
+realists. When two men look at the same table, it is supposed that
+what the one sees and what the other sees are in the same place. Since
+the shape and colour are not quite the same for the two men, this
+raises a difficulty, hastily solved, or rather covered up, by
+declaring what each sees to be purely "subjective"--though it would
+puzzle those who use this glib word to say what they mean by it. The
+truth seems to be that space--and time also--is much more complicated
+than it would appear to be from the finished structure of physics, and
+that the one all-embracing three-dimensional space is a logical
+construction, obtained by means of correlations from a crude space of
+six dimensions. The particulars occupying this six-dimensional space,
+classified in one way, form "things," from which with certain further
+manipulations we can obtain what physics can regard as matter;
+classified in another way, they form "perspectives" and "biographies,"
+which may, if a suitable percipient happens to exist, form
+respectively the sense-data of a momentary or of a total experience.
+It is only when physical "things" have been dissected into series of
+classes of particulars, as we have done, that the conflict between the
+point of view of physics and the point of view of psychology can be
+overcome. This conflict, if what has been said is not mistaken, flows
+from different methods of classification, and vanishes as soon as its
+source is discovered.
+
+In favour of the theory which I have briefly outlined, I do not claim
+that it is _certainly_ true. Apart from the likelihood of mistakes,
+much of it is avowedly hypothetical. What I do claim for the theory is
+that it _may_ be true, and that this is more than can be said for any
+other theory except the closely analogous theory of Leibniz. The
+difficulties besetting realism, the confusions obstructing any
+philosophical account of physics, the dilemma resulting from
+discrediting sense-data, which yet remain the sole source of our
+knowledge of the outer world--all these are avoided by the theory
+which I advocate. This does not prove the theory to be true, since
+probably many other theories might be invented which would have the
+same merits. But it does prove that the theory has a better chance of
+being true than any of its present competitors, and it suggests that
+what can be known with certainty is likely to be discoverable by
+taking our theory as a starting-point, and gradually freeing it from
+all such assumptions as seem irrelevant, unnecessary, or unfounded. On
+these grounds, I recommend it to attention as a hypothesis and a basis
+for further work, though not as itself a finished or adequate solution
+of the problem with which it deals.
+
+FOOTNOTES:
+
+[23] An address delivered to the Philosophical Society of Manchester
+in February, 1915. Reprinted from _The Monist_, July, 1915.
+
+[24] Cf. especially Samuel Alexander, "The Basis of Realism," _British
+Academy_, Vol. VI.
+
+[25] "Are Secondary Qualities Independent of Perception?" _Proc.
+Arist. Soc._, 1909-10, pp. 191-218.
+
+[26] First dialogue between Hylas and Philonous, _Works_ (Fraser's
+edition 1901). I. p. 384.
+
+[27] This point has been well urged by the American realists.
+
+[28] Cf. T.P. Nunn, "Are Secondary Qualities Independent of
+Perception?" _Proc. Arist. Soc._, 1909-1910.
+
+
+
+
+VIII
+
+THE RELATION OF SENSE-DATA TO PHYSICS
+
+
+I. THE PROBLEM STATED
+
+Physics is said to be an empirical science, based upon observation and
+experiment.
+
+It is supposed to be verifiable, i.e. capable of calculating
+beforehand results subsequently confirmed by observation and
+experiment.
+
+What can we learn by observation and experiment?
+
+Nothing, so far as physics is concerned, except immediate data of
+sense: certain patches of colour, sounds, tastes, smells, etc., with
+certain spatio-temporal relations.
+
+The supposed contents of the physical world are _prima facie_ very
+different from these: molecules have no colour, atoms make no noise,
+electrons have no taste, and corpuscles do not even smell.
+
+If such objects are to be verified, it must be solely through their
+relation to sense-data: they must have some kind of correlation with
+sense-data, and must be verifiable through their correlation _alone_.
+
+But how is the correlation itself ascertained? A correlation can only
+be ascertained empirically by the correlated objects being constantly
+_found_ together. But in our case, only one term of the correlation,
+namely, the sensible term, is ever _found_: the other term seems
+essentially incapable of being found. Therefore, it would seem, the
+correlation with objects of sense, by which physics was to be
+verified, is itself utterly and for ever unverifiable.
+
+There are two ways of avoiding this result.
+
+(1) We may say that we know some principle _a priori_, without the
+need of empirical verification, e.g. that our sense-data have _causes_
+other than themselves, and that something can be known about these
+causes by inference from their effects. This way has been often
+adopted by philosophers. It may be necessary to adopt this way to some
+extent, but in so far as it is adopted physics ceases to be empirical
+or based upon experiment and observation alone. Therefore this way is
+to be avoided as much as possible.
+
+(2) We may succeed in actually defining the objects of physics as
+functions of sense-data. Just in so far as physics leads to
+expectations, this _must_ be possible, since we can only _expect_ what
+can be experienced. And in so far as the physical state of affairs is
+inferred from sense-data, it must be capable of expression as a
+function of sense-data. The problem of accomplishing this expression
+leads to much interesting logico-mathematical work.
+
+In physics as commonly set forth, sense-data appear as functions of
+physical objects: when such-and-such waves impinge upon the eye, we
+see such-and-such colours, and so on. But the waves are in fact
+inferred from the colours, not vice versa. Physics cannot be regarded
+as validly based upon empirical data until the waves have been
+expressed as functions of the colours and other sense-data.
+
+Thus if physics is to be verifiable we are faced with the following
+problem: Physics exhibits sense-data as functions of physical objects,
+but verification is only possible if physical objects can be exhibited
+as functions of sense-data. We have therefore to solve the equations
+giving sense-data in terms of physical objects, so as to make them
+instead give physical objects in terms of sense-data.
+
+
+II. CHARACTERISTICS OF SENSE-DATA
+
+When I speak of a "sense-datum," I do not mean the whole of what is
+given in sense at one time. I mean rather such a part of the whole as
+might be singled out by attention: particular patches of colour,
+particular noises, and so on. There is some difficulty in deciding
+what is to be considered _one_ sense-datum: often attention causes
+divisions to appear where, so far as can be discovered, there were no
+divisions before. An observed complex fact, such as that this patch of
+red is to the left of that patch of blue, is also to be regarded as a
+datum from our present point of view: epistemologically, it does not
+differ greatly from a simple sense-datum as regards its function in
+giving knowledge. Its _logical_ structure is very different, however,
+from that of sense: _sense_ gives acquaintance with particulars, and
+is thus a two-term relation in which the object can be _named_ but not
+_asserted_, and is inherently incapable of truth or falsehood, whereas
+the observation of a complex fact, which may be suitably called
+perception, is not a two-term relation, but involves the propositional
+form on the object-side, and gives knowledge of a truth, not mere
+acquaintance with a particular. This logical difference, important as
+it is, is not very relevant to our present problem; and it will be
+convenient to regard data of perception as included among sense-data
+for the purposes of this paper. It is to be observed that the
+particulars which are constituents of a datum of perception are always
+sense-data in the strict sense.
+
+Concerning sense-data, we know that they are there while they are
+data, and this is the epistemological basis of all our knowledge of
+external particulars. (The meaning of the word "external" of course
+raises problems which will concern us later.) We do not know, except
+by means of more or less precarious inferences, whether the objects
+which are at one time sense-data continue to exist at times when they
+are not data. Sense-data at the times when they are data are all that
+we directly and primitively know of the external world; hence in
+epistemology the fact that they are _data_ is all-important. But the
+fact that they are all that we directly know gives, of course, no
+presumption that they are all that there is. If we could construct an
+impersonal metaphysic, independent of the accidents of our knowledge
+and ignorance, the privileged position of the actual data would
+probably disappear, and they would probably appear as a rather
+haphazard selection from a mass of objects more or less like them. In
+saying this, I assume only that it is probable that there are
+particulars with which we are not acquainted. Thus the special
+importance of sense-data is in relation to epistemology, not to
+metaphysics. In this respect, physics is to be reckoned as
+metaphysics: it is impersonal, and nominally pays no special attention
+to sense-data. It is only when we ask how physics can be _known_ that
+the importance of sense-data re-emerges.
+
+
+III. SENSIBILIA
+
+I shall give the name _sensibilia_ to those objects which have the
+same metaphysical and physical status as sense-data, without
+necessarily being data to any mind. Thus the relation of a _sensibile_
+to a sense-datum is like that of a man to a husband: a man becomes a
+husband by entering into the relation of marriage, and similarly a
+_sensibile_ becomes a sense-datum by entering into the relation of
+acquaintance. It is important to have both terms; for we wish to
+discuss whether an object which is at one time a sense-datum can still
+exist at a time when it is not a sense-datum. We cannot ask "Can
+sense-data exist without being given?" for that is like asking "Can
+husbands exist without being married?" We must ask "Can _sensibilia_
+exist without being given?" and also "Can a particular _sensibile_ be
+at one time a sense-datum, and at another not?" Unless we have the
+word _sensibile_ as well as the word "sense-datum," such questions are
+apt to entangle us in trivial logical puzzles.
+
+It will be seen that all sense-data are _sensibilia_. It is a
+metaphysical question whether all _sensibilia_ are sense-data, and an
+epistemological question whether there exist means of inferring
+_sensibilia_ which are not data from those that are.
+
+A few preliminary remarks, to be amplified as we proceed, will serve
+to elucidate the use which I propose to make of _sensibilia_.
+
+I regard sense-data as not mental, and as being, in fact, part of the
+actual subject-matter of physics. There are arguments, shortly to be
+examined, for their subjectivity, but these arguments seem to me only
+to prove _physiological_ subjectivity, i.e. causal dependence on the
+sense-organs, nerves, and brain. The appearance which a thing presents
+to us is causally dependent upon these, in exactly the same way as it
+is dependent upon intervening fog or smoke or coloured glass. Both
+dependences are contained in the statement that the appearance which a
+piece of matter presents when viewed from a given place is a function
+not only of the piece of matter, but also of the intervening medium.
+(The terms used in this statement--"matter," "view from a given
+place," "appearance," "intervening medium"--will all be defined in the
+course of the present paper.) We have not the means of ascertaining
+how things appear from places not surrounded by brain and nerves and
+sense-organs, because we cannot leave the body; but continuity makes
+it not unreasonable to suppose that they present _some_ appearance at
+such places. Any such appearance would be included among _sensibilia_.
+If--_per impossibile_--there were a complete human body with no mind
+inside it, all those _sensibilia_ would exist, in relation to that
+body, which would be sense-data if there were a mind in the body. What
+the mind adds to _sensibilia_, in fact, is _merely_ awareness:
+everything else is physical or physiological.
+
+
+IV. SENSE-DATA ARE PHYSICAL
+
+Before discussing this question it will be well to define the sense in
+which the terms "mental" and "physical" are to be used. The word
+"physical," in all preliminary discussions, is to be understood as
+meaning "what is dealt with by physics." Physics, it is plain, tells
+us something about some of the constituents of the actual world; what
+these constituents are may be doubtful, but it is they that are to be
+called physical, whatever their nature may prove to be.
+
+The definition of the term "mental" is more difficult, and can only be
+satisfactorily given after many difficult controversies have been
+discussed and decided. For present purposes therefore I must content
+myself with assuming a dogmatic answer to these controversies. I shall
+call a particular "mental" when it is aware of something, and I shall
+call a fact "mental" when it contains a mental particular as a
+constituent.
+
+It will be seen that the mental and the physical are not necessarily
+mutually exclusive, although I know of no reason to suppose that they
+overlap.
+
+The doubt as to the correctness of our definition of the "mental" is
+of little importance in our present discussion. For what I am
+concerned to maintain is that sense-data are physical, and this being
+granted it is a matter of indifference in our present inquiry whether
+or not they are also mental. Although I do not hold, with Mach and
+James and the "new realists," that the difference between the mental
+and the physical is _merely_ one of arrangement, yet what I have to
+say in the present paper is compatible with their doctrine and might
+have been reached from their standpoint.
+
+In discussions on sense-data, two questions are commonly confused,
+namely:
+
+(1) Do sensible objects persist when we are not sensible of them? in
+other words, do _sensibilia_ which are data at a certain time
+sometimes continue to exist at times when they are not data? And (2)
+are sense-data mental or physical?
+
+I propose to assert that sense-data are physical, while yet
+maintaining that they probably never persist unchanged after ceasing
+to be data. The view that they do not persist is often thought, quite
+erroneously in my opinion, to imply that they are mental; and this
+has, I believe, been a potent source of confusion in regard to our
+present problem. If there were, as some have held, a _logical
+impossibility_ in sense-data persisting after ceasing to be data, that
+certainly would tend to show that they were mental; but if, as I
+contend, their non-persistence is merely a probable inference from
+empirically ascertained causal laws, then it carries no such
+implication with it, and we are quite free to treat them as part of
+the subject-matter of physics.
+
+Logically a sense-datum is an object, a particular of which the
+subject is aware. It does not contain the subject as a part, as for
+example beliefs and volitions do. The existence of the sense-datum is
+therefore not logically dependent upon that of the subject; for the
+only way, so far as I know, in which the existence of _A_ can be
+_logically_ dependent upon the existence of _B_ is when _B_ is part of
+_A_. There is therefore no _a priori_ reason why a particular which is
+a sense-datum should not persist after it has ceased to be a datum,
+nor why other similar particulars should not exist without ever being
+data. The view that sense-data are mental is derived, no doubt, in
+part from their physiological subjectivity, but in part also from a
+failure to distinguish between sense-data and "sensations." By a
+sensation I mean the fact consisting in the subject's awareness of the
+sense-datum. Thus a sensation is a complex of which the subject is a
+constituent and which therefore is mental. The sense-datum, on the
+other hand, stands over against the subject as that external object of
+which in sensation the subject is aware. It is true that the
+sense-datum is in many cases in the subject's body, but the subject's
+body is as distinct from the subject as tables and chairs are, and is
+in fact merely a part of the material world. So soon, therefore, as
+sense-data are clearly distinguished from sensations, and as their
+subjectivity is recognised to be physiological not psychical, the
+chief obstacles in the way of regarding them as physical are removed.
+
+
+V. "SENSIBILIA" AND "THINGS"
+
+But if "sensibilia" are to be recognised as the ultimate constituents
+of the physical world, a long and difficult journey is to be performed
+before we can arrive either at the "thing" of common sense or at the
+"matter" of physics. The supposed impossibility of combining the
+different sense-data which are regarded as appearances of the same
+"thing" to different people has made it seem as though these
+"sensibilia" must be regarded as mere subjective phantasms. A given
+table will present to one man a rectangular appearance, while to
+another it appears to have two acute angles and two obtuse angles; to
+one man it appears brown, while to another, towards whom it reflects
+the light, it appears white and shiny. It is said, not wholly without
+plausibility, that these different shapes and different colours cannot
+co-exist simultaneously in the same place, and cannot therefore both
+be constituents of the physical world. This argument I must confess
+appeared to me until recently to be irrefutable. The contrary opinion
+has, however, been ably maintained by Dr. T.P. Nunn in an article
+entitled: "Are Secondary Qualities Independent of Perception?"[29] The
+supposed impossibility derives its apparent force from the phrase:
+"_in the same place_," and it is precisely in this phrase that its
+weakness lies. The conception of space is too often treated in
+philosophy--even by those who on reflection would not defend such
+treatment--as though it were as given, simple, and unambiguous as
+Kant, in his psychological innocence, supposed. It is the unperceived
+ambiguity of the word "place" which, as we shall shortly see, has
+caused the difficulties to realists and given an undeserved advantage
+to their opponents. Two "places" of different kinds are involved in
+every sense-datum, namely the place _at_ which it appears and the
+place _from_ which it appears. These belong to different spaces,
+although, as we shall see, it is possible, with certain limitations,
+to establish a correlation between them. What we call the different
+appearances of the same thing to different observers are each in a
+space private to the observer concerned. No place in the private world
+of one observer is identical with a place in the private world of
+another observer. There is therefore no question of combining the
+different appearances in the one place; and the fact that they cannot
+all exist in one place affords accordingly no ground whatever for
+questioning their physical reality. The "thing" of common sense may in
+fact be identified with the whole class of its appearances--where,
+however, we must include among appearances not only those which are
+actual sense-data, but also those "sensibilia," if any, which, on
+grounds of continuity and resemblance, are to be regarded as belonging
+to the same system of appearances, although there happen to be no
+observers to whom they are data.
+
+An example may make this clearer. Suppose there are a number of people
+in a room, all seeing, as they say, the same tables and chairs, walls
+and pictures. No two of these people have exactly the same sense-data,
+yet there is sufficient similarity among their data to enable them to
+group together certain of these data as appearances of one "thing" to
+the several spectators, and others as appearances of another "thing."
+Besides the appearances which a given thing in the room presents to
+the actual spectators, there are, we may suppose, other appearances
+which it would present to other possible spectators. If a man were to
+sit down between two others, the appearance which the room would
+present to him would be intermediate between the appearances which it
+presents to the two others: and although this appearance would not
+exist as it is without the sense organs, nerves and brain, of the
+newly arrived spectator, still it is not unnatural to suppose that,
+from the position which he now occupies, _some_ appearance of the
+room existed before his arrival. This supposition, however, need
+merely be noticed and not insisted upon.
+
+Since the "thing" cannot, without indefensible partiality, be
+identified with any single one of its appearances, it came to be
+thought of as something distinct from all of them and underlying them.
+But by the principle of Occam's razor, if the class of appearances
+will fulfil the purposes for the sake of which the thing was invented
+by the prehistoric metaphysicians to whom common sense is due, economy
+demands that we should identify the thing with the class of its
+appearances. It is not necessary to _deny_ a substance or substratum
+underlying these appearances; it is merely expedient to abstain from
+asserting this unnecessary entity. Our procedure here is precisely
+analogous to that which has swept away from the philosophy of
+mathematics the useless menagerie of metaphysical monsters with which
+it used to be infested.
+
+
+VI. CONSTRUCTIONS VERSUS INFERENCES
+
+Before proceeding to analyse and explain the ambiguities of the word
+"place," a few general remarks on method are desirable. The supreme
+maxim in scientific philosophising is this:
+
+  _Wherever possible, logical constructions are to be substituted
+  for inferred entities._
+
+Some examples of the substitution of construction for inference in the
+realm of mathematical philosophy may serve to elucidate the uses of
+this maxim. Take first the case of irrationals. In old days,
+irrationals were inferred as the supposed limits of series of
+rationals which had no rational limit; but the objection to this
+procedure was that it left the existence of irrationals merely
+optative, and for this reason the stricter methods of the present day
+no longer tolerate such a definition. We now define an irrational
+number as a certain class of ratios, thus constructing it logically by
+means of ratios, instead of arriving at it by a doubtful inference
+from them. Take again the case of cardinal numbers. Two equally
+numerous collections appear to have something in common: this
+something is supposed to be their cardinal number. But so long as the
+cardinal number is inferred from the collections, not constructed in
+terms of them, its existence must remain in doubt, unless in virtue of
+a metaphysical postulate _ad hoc_. By defining the cardinal number of
+a given collection as the class of all equally numerous collections,
+we avoid the necessity of this metaphysical postulate, and thereby
+remove a needless element of doubt from the philosophy of arithmetic.
+A similar method, as I have shown elsewhere, can be applied to classes
+themselves, which need not be supposed to have any metaphysical
+reality, but can be regarded as symbolically constructed fictions.
+
+The method by which the construction proceeds is closely analogous in
+these and all similar cases. Given a set of propositions nominally
+dealing with the supposed inferred entities, we observe the properties
+which are required of the supposed entities in order to make these
+propositions true. By dint of a little logical ingenuity, we then
+construct some logical function of less hypothetical entities which
+has the requisite properties. This constructed function we substitute
+for the supposed inferred entities, and thereby obtain a new and less
+doubtful interpretation of the body of propositions in question. This
+method, so fruitful in the philosophy of mathematics, will be found
+equally applicable in the philosophy of physics, where, I do not
+doubt, it would have been applied long ago but for the fact that all
+who have studied this subject hitherto have been completely ignorant
+of mathematical logic. I myself cannot claim originality in the
+application of this method to physics, since I owe the suggestion and
+the stimulus for its application entirely to my friend and
+collaborator Dr. Whitehead, who is engaged in applying it to the more
+mathematical portions of the region intermediate between sense-data
+and the points, instants and particles of physics.
+
+A complete application of the method which substitutes constructions
+for inferences would exhibit matter wholly in terms of sense-data, and
+even, we may add, of the sense-data of a single person, since the
+sense-data of others cannot be known without some element of
+inference. This, however, must remain for the present an ideal, to be
+approached as nearly as possible, but to be reached, if at all, only
+after a long preliminary labour of which as yet we can only see the
+very beginning. The inferences which are unavoidable can, however, be
+subjected to certain guiding principles. In the first place they
+should always be made perfectly explicit, and should be formulated in
+the most general manner possible. In the second place the inferred
+entities should, whenever this can be done, be similar to those whose
+existence is given, rather than, like the Kantian _Ding an sich_,
+something wholly remote from the data which nominally support the
+inference. The inferred entities which I shall allow myself are of two
+kinds: (_a_) the sense-data of other people, in favour of which there
+is the evidence of testimony, resting ultimately upon the analogical
+argument in favour of minds other than my own; (_b_) the "sensibilia"
+which would appear from places where there happen to be no minds, and
+which I suppose to be real although they are no one's data. Of these
+two classes of inferred entities, the first will probably be allowed
+to pass unchallenged. It would give me the greatest satisfaction to be
+able to dispense with it, and thus establish physics upon a
+solipsistic basis; but those--and I fear they are the majority--in
+whom the human affections are stronger than the desire for logical
+economy, will, no doubt, not share my desire to render solipsism
+scientifically satisfactory. The second class of inferred entities
+raises much more serious questions. It may be thought monstrous to
+maintain that a thing can present any appearance at all in a place
+where no sense organs and nervous structure exist through which it
+could appear. I do not myself feel the monstrosity; nevertheless I
+should regard these supposed appearances only in the light of a
+hypothetical scaffolding, to be used while the edifice of physics is
+being raised, though possibly capable of being removed as soon as the
+edifice is completed. These "sensibilia" which are not data to anyone
+are therefore to be taken rather as an illustrative hypothesis and as
+an aid in preliminary statement than as a dogmatic part of the
+philosophy of physics in its final form.
+
+
+VII. PRIVATE SPACE AND THE SPACE OF PERSPECTIVES
+
+We have now to explain the ambiguity in the word "place," and how it
+comes that two places of different sorts are associated with every
+sense-datum, namely the place _at_ which it is and the place _from_
+which it is perceived. The theory to be advocated is closely analogous
+to Leibniz's monadology, from which it differs chiefly in being less
+smooth and tidy.
+
+The first fact to notice is that, so far as can be discovered, no
+sensibile is ever a datum to two people at once. The things seen by
+two different people are often closely similar, so similar that the
+same _words_ can be used to denote them, without which communication
+with others concerning sensible objects would be impossible. But, in
+spite of this similarity, it would seem that some difference always
+arises from difference in the point of view. Thus each person, so far
+as his sense-data are concerned, lives in a private world. This
+private world contains its own space, or rather spaces, for it would
+seem that only experience teaches us to correlate the space of sight
+with the space of touch and with the various other spaces of other
+senses. This multiplicity of private spaces, however, though
+interesting to the psychologist, is of no great importance in regard
+to our present problem, since a merely solipsistic experience enables
+us to correlate them into the one private space which embraces all our
+own sense-data. The place _at_ which a sense-datum is, is a place in
+private space. This place therefore is different from any place in the
+private space of another percipient. For if we assume, as logical
+economy demands, that all position is relative, a place is only
+definable by the things in or around it, and therefore the same place
+cannot occur in two private worlds which have no common constituent.
+The question, therefore, of combining what we call different
+appearances of the same thing in the same place does not arise, and
+the fact that a given object appears to different spectators to have
+different shapes and colours affords no argument against the physical
+reality of all these shapes and colours.
+
+In addition to the private spaces belonging to the private worlds of
+different percipients, there is, however, another space, in which one
+whole private world counts as a point, or at least as a spatial unit.
+This might be described as the space of points of view, since each
+private world may be regarded as the appearance which the universe
+presents from a certain point of view. I prefer, however, to speak of
+it as the space of _perspectives_, in order to obviate the suggestion
+that a private world is only real when someone views it. And for the
+same reason, when I wish to speak of a private world without assuming
+a percipient, I shall call it a "perspective."
+
+We have now to explain how the different perspectives are ordered in
+one space. This is effected by means of the correlated "sensibilia"
+which are regarded as the appearances, in different perspectives, of
+one and the same thing. By moving, and by testimony, we discover that
+two different perspectives, though they cannot both contain the same
+"sensibilia," may nevertheless contain very similar ones; and the
+spatial order of a certain group of "sensibilia" in a private space of
+one perspective is found to be identical with, or very similar to, the
+spatial order of the correlated "sensibilia" in the private space of
+another perspective. In this way one "sensibile" in one perspective is
+correlated with one "sensibile" in another. Such correlated
+"sensibilia" will be called "appearances of one thing." In Leibniz's
+monadology, since each monad mirrored the whole universe, there was in
+each perspective a "sensibile" which was an appearance of each thing.
+In our system of perspectives, we make no such assumption of
+completeness. A given thing will have appearances in some
+perspectives, but presumably not in certain others. The "thing" being
+defined as the class of its appearances, if [kappa] is the class of
+perspectives in which a certain thing [theta] appears, then [theta] is
+a member of the multiplicative class of [kappa], [kappa] being a class
+of mutually exclusive classes of "sensibilia." And similarly a
+perspective is a member of the multiplicative class of the things
+which appear in it.
+
+The arrangement of perspectives in a space is effected by means of the
+differences between the appearances of a given thing in the various
+perspectives. Suppose, say, that a certain penny appears in a number
+of different perspectives; in some it looks larger and in some
+smaller, in some it looks circular, in others it presents the
+appearance of an ellipse of varying eccentricity. We may collect
+together all those perspectives in which the appearance of the penny
+is circular. These we will place on one straight line, ordering them
+in a series by the variations in the apparent size of the penny. Those
+perspectives in which the penny appears as a straight line of a
+certain thickness will similarly be placed upon a plane (though in
+this case there will be many different perspectives in which the penny
+is of the same size; when one arrangement is completed these will form
+a circle concentric with the penny), and ordered as before by the
+apparent size of the penny. By such means, all those perspectives in
+which the penny presents a visual appearance can be arranged in a
+three-dimensional spatial order. Experience shows that the same
+spatial order of perspectives would have resulted if, instead of the
+penny, we had chosen any other thing which appeared in all the
+perspectives in question, or any other method of utilising the
+differences between the appearances of the same things in different
+perspectives. It is this empirical fact which has made it possible to
+construct the one all-embracing space of physics.
+
+The space whose construction has just been explained, and whose
+elements are whole perspectives, will be called "perspective-space."
+
+
+VIII. THE PLACING OF "THINGS" AND "SENSIBILIA" IN PERSPECTIVE SPACE
+
+The world which we have so far constructed is a world of six
+dimensions, since it is a three-dimensional series of perspectives,
+each of which is itself three-dimensional. We have now to explain the
+correlation between the perspective space and the various private
+spaces contained within the various perspectives severally. It is by
+means of this correlation that the one three-dimensional space of
+physics is constructed; and it is because of the unconscious
+performance of this correlation that the distinction between
+perspective space and the percipient's private space has been blurred,
+with disastrous results for the philosophy of physics. Let us revert
+to our penny: the perspectives in which the penny appears larger are
+regarded as being nearer to the penny than those in which it appears
+smaller, but as far as experience goes the apparent size of the penny
+will not grow beyond a certain limit, namely, that where (as we say)
+the penny is so near the eye that if it were any nearer it could not
+be seen. By touch we may prolong the series until the penny touches
+the eye, but no further. If we have been travelling along a line of
+perspectives in the previously defined sense, we may, however, by
+imagining the penny removed, prolong the line of perspectives by
+means, say, of another penny; and the same may be done with any other
+line of perspectives defined by means of the penny. All these lines
+meet in a certain place, that is, in a certain perspective. This
+perspective will be defined as "the place where the penny is."
+
+It is now evident in what sense two places in constructed physical
+space are associated with a given "sensibile." There is first the
+place which is the perspective of which the "sensibile" is a member.
+This is the place _from_ which the "sensibile" appears. Secondly there
+is the place where the thing is of which the "sensibile" is a member,
+in other words an appearance; this is the place _at_ which the
+"sensibile" appears. The "sensibile" which is a member of one
+perspective is correlated with another perspective, namely, that which
+is the place where the thing is of which the "sensibile" is an
+appearance. To the psychologist the "place from which" is the more
+interesting, and the "sensibile" accordingly appears to him subjective
+and where the percipient is. To the physicist the "place at which" is
+the more interesting, and the "sensibile" accordingly appears to him
+physical and external. The causes, limits and partial justification of
+each of these two apparently incompatible views are evident from the
+above duplicity of places associated with a given "sensibile."
+
+We have seen that we can assign to a physical thing a place in the
+perspective space. In this way different parts of our body acquire
+positions in perspective space, and therefore there is a meaning
+(whether true or false need not much concern us) in saying that the
+perspective to which our sense-data belong is inside our head. Since
+our mind is correlated with the perspective to which our sense-data
+belong, we may regard this perspective as being the position of our
+mind in perspective space. If, therefore, this perspective is, in the
+above defined sense, inside our head, there is a good meaning for the
+statement that the mind is in the head. We can now say of the various
+appearances of a given thing that some of them are nearer to the thing
+than others; those are nearer which belong to perspectives that are
+nearer to "the place where the thing is." We can thus find a meaning,
+true or false, for the statement that more is to be learnt about a
+thing by examining it close to than by viewing it from a distance. We
+can also find a meaning for the phrase "the things which intervene
+between the subject and a thing of which an appearance is a datum to
+him." One reason often alleged for the subjectivity of sense-data is
+that the appearance of a thing may change when we find it hard to
+suppose that the thing itself has changed--for example, when the
+change is due to our shutting our eyes, or to our screwing them up so
+as to make the thing look double. If the thing is defined as the class
+of its appearances (which is the definition adopted above), there is
+of course necessarily _some_ change in the thing whenever any one of
+its appearances changes. Nevertheless there is a very important
+distinction between two different ways in which the appearances may
+change. If after looking at a thing I shut my eyes, the appearance of
+my eyes changes in every perspective in which there is such an
+appearance, whereas most of the appearances of the thing will remain
+unchanged. We may say, as a matter of definition, that a thing changes
+when, however near to the thing an appearance of it may be, there are
+changes in appearances as near as, or still nearer to, the thing. On
+the other hand we shall say that the change is in some other thing if
+all appearances of the thing which are at not more than a certain
+distance from the thing remain unchanged, while only comparatively
+distant appearances of the thing are altered. From this consideration
+we are naturally led to the consideration of _matter_, which must be
+our next topic.
+
+
+IX. THE DEFINITION OF MATTER
+
+We defined the "physical thing" as the class of its appearances, but
+this can hardly be taken as a definition of matter. We want to be able
+to express the fact that the appearance of a thing in a given
+perspective is causally affected by the matter between the thing and
+the perspective. We have found a meaning for "between a thing and a
+perspective." But we want matter to be something other than the whole
+class of appearances of a thing, in order to state the influence of
+matter on appearances.
+
+We commonly assume that the information we get about a thing is more
+accurate when the thing is nearer. Far off, we see it is a man; then
+we see it is Jones; then we see he is smiling. Complete accuracy would
+only be attainable as a limit: if the appearances of Jones as we
+approach him tend towards a limit, that limit may be taken to be what
+Jones really is. It is obvious that from the point of view of physics
+the appearances of a thing close to "count" more than the appearances
+far off. We may therefore set up the following tentative definition:
+
+The _matter_ of a given thing is the limit of its appearances as their
+distance from the thing diminishes.
+
+It seems probable that there is something in this definition, but it
+is not quite satisfactory, because empirically there is no such limit
+to be obtained from sense-data. The definition will have to be eked
+out by constructions and definitions. But probably it suggests the
+right direction in which to look.
+
+We are now in a position to understand in outline the reverse journey
+from matter to sense-data which is performed by physics. The
+appearance of a thing in a given perspective is a function of the
+matter composing the thing and of the intervening matter. The
+appearance of a thing is altered by intervening smoke or mist, by blue
+spectacles or by alterations in the sense-organs or nerves of the
+percipient (which also must be reckoned as part of the intervening
+medium). The nearer we approach to the thing, the less its appearance
+is affected by the intervening matter. As we travel further and
+further from the thing, its appearances diverge more and more from
+their initial character; and the causal laws of their divergence are
+to be stated in terms of the matter which lies between them and the
+thing. Since the appearances at very small distances are less affected
+by causes other than the thing itself, we come to think that the limit
+towards which these appearances tend as the distance diminishes is
+what the thing "really is," as opposed to what it merely seems to be.
+This, together with its necessity for the statement of causal laws,
+seems to be the source of the entirely erroneous feeling that matter
+is more "real" than sense-data.
+
+Consider for example the infinite divisibility of matter. In looking
+at a given thing and approaching it, one sense-datum will become
+several, and each of these will again divide. Thus _one_ appearance
+may represent _many_ things, and to this process there seems no end.
+Hence in the limit, when we approach indefinitely near to the thing
+there will be an indefinite number of units of matter corresponding to
+what, at a finite distance, is only one appearance. This is how
+infinite divisibility arises.
+
+The whole causal efficacy of a thing resides in its matter. This is in
+some sense an empirical fact, but it would be hard to state it
+precisely, because "causal efficacy" is difficult to define.
+
+What can be known empirically about the matter of a thing is only
+approximate, because we cannot get to know the appearances of the
+thing from very small distances, and cannot accurately infer the limit
+of these appearances. But it _is_ inferred _approximately_ by means of
+the appearances we can observe. It then turns out that these
+appearances can be exhibited by physics as a function of the matter
+in our immediate neighbourhood; e.g. the visual appearance of a
+distant object is a function of the light-waves that reach the eyes.
+This leads to confusions of thought, but offers no real difficulty.
+
+One appearance, of a visible object for example, is not sufficient to
+determine its other simultaneous appearances, although it goes a
+certain distance towards determining them. The determination of the
+hidden structure of a thing, so far as it is possible at all, can only
+be effected by means of elaborate dynamical inferences.
+
+
+X. TIME[30]
+
+It seems that the one all-embracing time is a construction, like the
+one all-embracing space. Physics itself has become conscious of this
+fact through the discussions connected with relativity.
+
+Between two perspectives which both belong to one person's experience,
+there will be a direct time-relation of before and after. This
+suggests a way of dividing history in the same sort of way as it is
+divided by different experiences, but without introducing experience
+or anything mental: we may define a "biography" as everything that is
+(directly) earlier or later than, or simultaneous with, a given
+"sensibile." This will give a series of perspectives, which _might_
+all form parts of one person's experience, though it is not necessary
+that all or any of them should actually do so. By this means, the
+history of the world is divided into a number of mutually exclusive
+biographies.
+
+We have now to correlate the times in the different biographies. The
+natural thing would be to say that the appearances of a given
+(momentary) thing in two different perspectives belonging to different
+biographies are to be taken as simultaneous; but this is not
+convenient. Suppose _A_ shouts to _B_, and _B_ replies as soon as he
+hears _A's_ shout. Then between _A's_ hearing of his own shout and his
+hearing of _B's_ there is an interval; thus if we made _A's_ and _B's_
+hearing of the same shout exactly simultaneous with each other, we
+should have events exactly simultaneous with a given event but not
+with each other. To obviate this, we assume a "velocity of sound."
+That is, we assume that the time when _B_ hears _A's_ shout is
+half-way between the time when _A_ hears his own shout and the time
+when he hears _B's_. In this way the correlation is effected.
+
+What has been said about sound applies of course equally to light. The
+general principle is that the appearances, in different perspectives,
+which are to be grouped together as constituting what a certain thing
+is at a certain moment, are not to be all regarded as being at that
+moment. On the contrary they spread outward from the thing with
+various velocities according to the nature of the appearances. Since
+no _direct_ means exist of correlating the time in one biography with
+the time in another, this temporal grouping of the appearances
+belonging to a given thing at a given moment is in part conventional.
+Its motive is partly to secure the verification of such maxims as that
+events which are exactly simultaneous with the same event are exactly
+simultaneous with one another, partly to secure convenience in the
+formulation of causal laws.
+
+
+XI. THE PERSISTENCE OF THINGS AND MATTER
+
+Apart from any of the fluctuating hypotheses of physics, three main
+problems arise in connecting the world of physics with the world of
+sense, namely:
+
+    1. the construction of a single space;
+    2. the construction of a single time;
+    3. the construction of permanent things or matter.
+
+We have already considered the first and second of these problems; it
+remains to consider the third.
+
+We have seen how correlated appearances in different perspectives are
+combined to form one "thing" at one moment in the all-embracing time
+of physics. We have now to consider how appearances at different times
+are combined as belonging to one "thing," and how we arrive at the
+persistent "matter" of physics. The assumption of permanent substance,
+which technically underlies the procedure of physics, cannot of course
+be regarded as metaphysically legitimate: just as the one thing
+simultaneously seen by many people is a construction, so the one thing
+seen at different times by the same or different people must be a
+construction, being in fact nothing but a certain grouping of certain
+"sensibilia."
+
+We have seen that the momentary state of a "thing" is an assemblage of
+"sensibilia," in different perspectives, not all simultaneous in the
+one constructed time, but spreading out from "the place where the
+thing is" with velocities depending upon the nature of the
+"sensibilia." The time _at_ which the "thing" is in this state is the
+lower limit of the times at which these appearances occur. We have now
+to consider what leads us to speak of another set of appearances as
+belonging to the same "thing" at a different time.
+
+For this purpose, we may, at least to begin with, confine ourselves
+within a single biography. If we can always say when two "sensibilia"
+in a given biography are appearances of one thing, then, since we have
+seen how to connect "sensibilia" in different biographies as
+appearances of the same momentary state of a thing, we shall have all
+that is necessary for the complete construction of the history of a
+thing.
+
+It is to be observed, to begin with, that the identity of a thing for
+common sense is not always correlated with the identity of matter for
+physics. A human body is one persisting thing for common sense, but
+for physics its matter is constantly changing. We may say, broadly,
+that the common-sense conception is based upon continuity in
+appearances at the ordinary distances of sense-data, while the
+physical conception is based upon the continuity of appearances at
+very small distances from the thing. It is probable that the
+common-sense conception is not capable of complete precision. Let us
+therefore concentrate our attention upon the conception of the
+persistence of matter in physics.
+
+The first characteristic of two appearances of the same piece of
+matter at different times is _continuity_. The two appearances must be
+connected by a series of intermediaries, which, if time and space form
+compact series, must themselves form a compact series. The colour of
+the leaves is different in autumn from what it is in summer; but we
+believe that the change occurs gradually, and that, if the colours are
+different at two given times, there are intermediate times at which
+the colours are intermediate between those at the given times.
+
+But there are two considerations that are important as regards
+continuity.
+
+First, it is largely hypothetical. We do not observe any one thing
+continuously, and it is merely a hypothesis to assume that, while we
+are not observing it, it passes through conditions intermediate
+between those in which it is perceived. During uninterrupted
+observation, it is true, continuity is nearly verified; but even here,
+when motions are very rapid, as in the case of explosions, the
+continuity is not actually capable of direct verification. Thus we can
+only say that the sense-data are found to _permit_ a hypothetical
+complement of "sensibilia" such as will preserve continuity, and that
+therefore there _may_ be such a complement. Since, however, we have
+already made such use of hypothetical "sensibilia," we will let this
+point pass, and admit such "sensibilia" as are required to preserve
+continuity.
+
+Secondly, continuity is not a sufficient criterion of material
+identity. It is true that in many cases, such as rocks, mountains,
+tables, chairs, etc., where the appearances change slowly, continuity
+is sufficient, but in other cases, such as the parts of an
+approximately homogeneous fluid, it fails us utterly. We can travel by
+sensibly continuous gradations from any one drop of the sea at any one
+time to any other drop at any other time. We infer the motions of
+sea-water from the effects of the current, but they cannot be inferred
+from direct sensible observation together with the assumption of
+continuity.
+
+The characteristic required in addition to continuity is conformity
+with the laws of dynamics. Starting from what common sense regards as
+persistent things, and making only such modifications as from time to
+time seem reasonable, we arrive at assemblages of "sensibilia" which
+are found to obey certain simple laws, namely those of dynamics. By
+regarding "sensibilia" at different times as belonging to the same
+piece of matter, we are able to define _motion_, which presupposes the
+assumption or construction of something persisting throughout the
+time of the motion. The motions which are regarded as occurring,
+during a period in which all the "sensibilia" and the times of their
+appearance are given, will be different according to the manner in
+which we combine "sensibilia" at different times as belonging to the
+same piece of matter. Thus even when the whole history of the world is
+given in every particular, the question what motions take place is
+still to a certain extent arbitrary even after the assumption of
+continuity. Experience shows that it is possible to determine motions
+in such a way as to satisfy the laws of dynamics, and that this
+determination, roughly and on the whole, is fairly in agreement with
+the common-sense opinions about persistent things. This determination,
+therefore, is adopted, and leads to a criterion by which we can
+determine, sometimes practically, sometimes only theoretically,
+whether two appearances at different times are to be regarded as
+belonging to the same piece of matter. The persistence of all matter
+throughout all time can, I imagine, be secured by definition.
+
+To recommend this conclusion, we must consider what it is that is
+proved by the empirical success of physics. What is proved is that its
+hypotheses, though unverifiable where they go beyond sense-data, are
+at no point in contradiction with sense-data, but, on the contrary,
+are ideally such as to render all sense-data calculable when a
+sufficient collection of "sensibilia" is given. Now physics has found
+it empirically possible to collect sense-data into series, each series
+being regarded as belonging to one "thing," and behaving, with regard
+to the laws of physics, in a way in which series not belonging to one
+thing would in general not behave. If it is to be unambiguous whether
+two appearances belong to the same thing or not, there must be only
+one way of grouping appearances so that the resulting things obey the
+laws of physics. It would be very difficult to prove that this is the
+case, but for our present purposes we may let this point pass, and
+assume that there is only one way. Thus we may lay down the following
+definition: _Physical things are those series of appearances whose
+matter obeys the laws of physics_. That such series exist is an
+empirical fact, which constitutes the verifiability of physics.
+
+
+XII. ILLUSIONS, HALLUCINATIONS, AND DREAMS
+
+It remains to ask how, in our system, we are to find a place for
+sense-data which apparently fail to have the usual connection with the
+world of physics. Such sense-data are of various kinds, requiring
+somewhat different treatment. But all are of the sort that would be
+called "unreal," and therefore, before embarking upon the discussion,
+certain logical remarks must be made upon the conceptions of reality
+and unreality.
+
+Mr. A. Wolf[31] says:
+
+  "The conception of mind as a system of transparent activities is,
+  I think, also untenable because of its failure to account for the
+  very possibility of dreams and hallucinations. It seems impossible
+  to realise how a bare, transparent activity can be directed to
+  what is not there, to apprehend what is not given."
+
+This statement is one which, probably, most people would endorse. But
+it is open to two objections. First it is difficult to see how an
+activity, however un-"transparent," can be directed towards a nothing:
+a term of a relation cannot be a mere nonentity. Secondly, no reason
+is given, and I am convinced that none can be given, for the assertion
+that dream-objects are not "there" and not "given." Let us take the
+second point first.
+
+(1) The belief that dream-objects are not given comes, I think, from
+failure to distinguish, as regards waking life, between the
+sense-datum and the corresponding "thing." In dreams, there is no such
+corresponding "thing" as the dreamer supposes; if, therefore, the
+"thing" were given in waking life, as e.g. Meinong maintains,[32] then
+there would be a difference in respect of givenness between dreams and
+waking life. But if, as we have maintained, what is given is never the
+thing, but merely one of the "sensibilia" which compose the thing,
+then what we apprehend in a dream is just as much given as what we
+apprehend in waking life.
+
+Exactly the same argument applies as to the dream-objects being
+"there." They have their position in the private space of the
+perspective of the dreamer; where they fail is in their correlation
+with other private spaces and therefore with perspective space. But in
+the only sense in which "there" can be a datum, they are "there" just
+as truly as any of the sense-data of waking life.
+
+(2) The conception of "illusion" or "unreality," and the correlative
+conception of "reality," are generally used in a way which embodies
+profound logical confusions. Words that go in pairs, such as "real"
+and "unreal," "existent" and "non-existent," "valid" and "invalid,"
+etc., are all derived from the one fundamental pair, "true" and
+"false." Now "true" and "false" are applicable only--except in
+derivative significations--to _propositions_. Thus wherever the above
+pairs can be significantly applied, we must be dealing either with
+propositions or with such incomplete phrases as only acquire meaning
+when put into a context which, with them, forms a proposition. Thus
+such pairs of words can be applied to _descriptions_,[33] but not to
+proper names: in other words, they have no application whatever to
+data, but only to entities or non-entities described in terms of data.
+
+Let us illustrate by the terms "existence" and "non-existence." Given
+any datum _x_, it is meaningless either to assert or to deny that _x_
+"exists." We might be tempted to say: "Of course _x_ exists, for
+otherwise it could not be a datum." But such a statement is really
+meaningless, although it is significant and true to say "My present
+sense-datum exists," and it may also be true that "_x_ is my present
+sense-datum." The inference from these two propositions to "_x_
+exists" is one which seems irresistible to people unaccustomed to
+logic; yet the apparent proposition inferred is not merely false, but
+strictly meaningless. To say "My present sense-datum exists" is to say
+(roughly): "There is an object of which 'my present sense-datum' is a
+description." But we cannot say: "There is an object of which '_x_' is
+a description," because '_x_' is (in the case we are supposing) a
+name, not a description. Dr. Whitehead and I have explained this point
+fully elsewhere (_loc. cit._) with the help of symbols, without which
+it is hard to understand; I shall not therefore here repeat the
+demonstration of the above propositions, but shall proceed with their
+application to our present problem.
+
+The fact that "existence" is only applicable to descriptions is
+concealed by the use of what are grammatically proper names in a way
+which really transforms them into descriptions. It is, for example, a
+legitimate question whether Homer existed; but here "Homer" means
+"the author of the Homeric poems," and is a description. Similarly we
+may ask whether God exists; but then "God" means "the Supreme Being"
+or "the _ens realissimum_" or whatever other description we may
+prefer. If "God" were a proper name, God would have to be a datum; and
+then no question could arise as to His existence. The distinction
+between existence and other predicates, which Kant obscurely felt, is
+brought to light by the theory of descriptions, and is seen to remove
+"existence" altogether from the fundamental notions of metaphysics.
+
+What has been said about "existence" applies equally to "reality,"
+which may, in fact, be taken as synonymous with "existence."
+Concerning the immediate objects in illusions, hallucinations, and
+dreams, it is meaningless to ask whether they "exist" or are "real."
+There they are, and that ends the matter. But we may legitimately
+inquire as to the existence or reality of "things" or other
+"sensibilia" inferred from such objects. It is the unreality of these
+"things" and other "sensibilia," together with a failure to notice
+that they are not data, which has led to the view that the objects of
+dreams are unreal.
+
+We may now apply these considerations in detail to the stock arguments
+against realism, though what is to be said will be mainly a repetition
+of what others have said before.
+
+(1) We have first the variety of normal appearances, supposed to be
+incompatible. This is the case of the different shapes and colours
+which a given thing presents to different spectators. Locke's water
+which seems both hot and cold belongs to this class of cases. Our
+system of different perspectives fully accounts for these cases, and
+shows that they afford no argument against realism.
+
+(2) We have cases where the correlation between different senses is
+unusual. The bent stick in water belongs here. People say it looks
+bent but is straight: this only means that it is straight to the
+touch, though bent to sight. There is no "illusion," but only a false
+inference, if we think that the stick would feel bent to the touch.
+The stick would look just as bent in a photograph, and, as Mr.
+Gladstone used to say, "the photograph cannot lie."[34] The case of
+seeing double also belongs here, though in this case the cause of the
+unusual correlation is physiological, and would therefore not operate
+in a photograph. It is a mistake to ask whether the "thing" is
+duplicated when we see it double. The "thing" is a whole system of
+"sensibilia," and it is only those visual "sensibilia" which are data
+to the percipient that are duplicated. The phenomenon has a purely
+physiological explanation; indeed, in view of our having two eyes, it
+is in less need of explanation than the single visual sense-datum
+which we normally obtain from the things on which we focus.
+
+(3) We come now to cases like dreams, which may, at the moment of
+dreaming, contain nothing to arouse suspicion, but are condemned on the
+ground of their supposed incompatibility with earlier and later data. Of
+course it often happens that dream-objects fail to behave in the
+accustomed manner: heavy objects fly, solid objects melt, babies turn
+into pigs or undergo even greater changes. But none of these unusual
+occurrences _need_ happen in a dream, and it is not on account of such
+occurrences that dream-objects are called "unreal." It is their lack of
+continuity with the dreamer's past and future that makes him, when he
+wakes, condemn them; and it is their lack of correlation with other
+private worlds that makes others condemn them. Omitting the latter
+ground, our reason for condemning them is that the "things" which we
+infer from them cannot be combined according to the laws of physics with
+the "things" inferred from waking sense-data. This might be used to
+condemn the "things" inferred from the data of dreams. Dream-data are no
+doubt appearances of "things," but not of such "things" as the dreamer
+supposes. I have no wish to combat psychological theories of dreams,
+such as those of the psycho-analysts. But there certainly are cases
+where (whatever psychological causes may contribute) the presence of
+physical causes also is very evident. For instance, a door banging may
+produce a dream of a naval engagement, with images of battleships and
+sea and smoke. The whole dream will be an appearance of the door
+banging, but owing to the peculiar condition of the body (especially the
+brain) during sleep, this appearance is not that expected to be produced
+by a door banging, and thus the dreamer is led to entertain false
+beliefs. But his sense-data are still physical, and are such as a
+completed physics would include and calculate.
+
+(4) The last class of illusions are those which cannot be discovered
+within one person's experience, except through the discovery of
+discrepancies with the experiences of others. Dreams might conceivably
+belong to this class, if they were jointed sufficiently neatly into
+waking life; but the chief instances are recurrent sensory
+hallucinations of the kind that lead to insanity. What makes the
+patient, in such cases, become what others call insane is the fact
+that, within his own experience, there is nothing to show that the
+hallucinatory sense-data do not have the usual kind of connection with
+"sensibilia" in other perspectives. Of course he may learn this
+through testimony, but he probably finds it simpler to suppose that
+the testimony is untrue and that he is being wilfully deceived. There
+is, so far as I can see, no theoretical criterion by which the patient
+can decide, in such a case, between the two equally satisfactory
+hypotheses of his madness and of his friends' mendacity.
+
+From the above instances it would appear that abnormal sense-data, of
+the kind which we regard as deceptive, have intrinsically just the
+same status as any others, but differ as regards their correlations or
+causal connections with other "sensibilia" and with "things." Since
+the usual correlations and connections become part of our unreflective
+expectations, and even seem, except to the psychologist, to form part
+of our data, it comes to be thought, mistakenly, that in such cases
+the data are unreal, whereas they are merely the causes of false
+inferences. The fact that correlations and connections of unusual
+kinds occur adds to the difficulty of inferring things from sense and
+of expressing physics in terms of sense-data. But the unusualness
+would seem to be always physically or physiologically explicable, and
+therefore raises only a complication, not a philosophical objection.
+
+I conclude, therefore, that no valid objection exists to the view
+which regards sense-data as part of the actual substance of the
+physical world, and that, on the other hand, this view is the only one
+which accounts for the empirical verifiability of physics. In the
+present paper, I have given only a rough preliminary sketch. In
+particular, the part played by _time_ in the construction of the
+physical world is, I think, more fundamental than would appear from
+the above account. I should hope that, with further elaboration, the
+part played by unperceived "sensibilia" could be indefinitely
+diminished, probably by invoking the history of a "thing" to eke out
+the inferences derivable from its momentary appearance.
+
+FOOTNOTES:
+
+[29] _Proc. Arist. Soc._, 1909-1910, pp. 191-218.
+
+[30] On this subject, compare _A Theory of Time and Space_, by Mr.
+A.A. Robb (Camb. Univ. Press), which first suggested to me the views
+advocated here, though I have, for present purposes, omitted what is
+most interesting and novel in his theory. Mr. Robb has given a sketch
+of his theory in a pamphlet with the same title (Heffer and Sons,
+Cambridge, 1913).
+
+[31] "Natural Realism and Present Tendencies in Philosophy," _Proc.
+Arist. Soc._, 1908-1909, p. 165.
+
+[32] _Die Erfahrungsgrundlagen unseres Wissens_, p. 28.
+
+[33] Cf. _Principia Mathematica_, Vol. I, * 14, and Introduction,
+Chap. III. For the definition of _existence_, cf. * 14. 02.
+
+[34] Cf. Edwin B. Holt, _The Place of Illusory Experience in a
+Realistic World._ "The New Realism," p. 303, both on this point and as
+regards _seeing double_.
+
+
+
+
+IX
+
+ON THE NOTION OF CAUSE
+
+
+In the following paper I wish, first, to maintain that the word
+"cause" is so inextricably bound up with misleading associations as to
+make its complete extrusion from the philosophical vocabulary
+desirable; secondly, to inquire what principle, if any, is employed in
+science in place of the supposed "law of causality" which philosophers
+imagine to be employed; thirdly, to exhibit certain confusions,
+especially in regard to teleology and determinism, which appear to me
+to be connected with erroneous notions as to causality.
+
+All philosophers, of every school, imagine that causation is one of
+the fundamental axioms or postulates of science, yet, oddly enough, in
+advanced sciences such as gravitational astronomy, the word "cause"
+never occurs. Dr. James Ward, in his _Naturalism and Agnosticism_,
+makes this a ground of complaint against physics: the business of
+those who wish to ascertain the ultimate truth about the world, he
+apparently thinks, should be the discovery of causes, yet physics
+never even seeks them. To me it seems that philosophy ought not to
+assume such legislative functions, and that the reason why physics has
+ceased to look for causes is that, in fact, there are no such things.
+The law of causality, I believe, like much that passes muster among
+philosophers, is a relic of a bygone age, surviving, like the
+monarchy, only because it is erroneously supposed to do no harm. In
+order to find out what philosophers commonly understand by "cause," I
+consulted Baldwin's _Dictionary_, and was rewarded beyond my
+expectations, for I found the following three mutually incompatible
+definitions:--
+
+  "CAUSALITY. (1) The necessary connection of events in the
+     time-series....
+
+  "CAUSE (notion of). Whatever may be included in the thought or
+     perception of a process as taking place in consequence of
+     another process....
+
+  "CAUSE AND EFFECT. (1) Cause and effect ... are correlative terms
+     denoting any two distinguishable things, phases, or aspects of
+     reality, which are so related to each other that whenever the
+     first ceases to exist the second comes into existence
+     immediately after, and whenever the second comes into existence
+     the first has ceased to exist immediately before."
+
+Let us consider these three definitions in turn. The first, obviously,
+is unintelligible without a definition of "necessary." Under this
+head, Baldwin's _Dictionary_ gives the following:--
+
+  "NECESSARY. That is necessary which not only is true, but would
+     be true under all circumstances. Something more than brute
+     compulsion is, therefore, involved in the conception; there is
+     a general law under which the thing takes place."
+
+The notion of cause is so intimately connected with that of necessity
+that it will be no digression to linger over the above definition,
+with a view to discovering, if possible, _some_ meaning of which it is
+capable; for, as it stands, it is very far from having any definite
+signification.
+
+The first point to notice is that, if any meaning is to be given to
+the phrase "would be true under all circumstances," the subject of it
+must be a propositional function, not a proposition.[35] A
+proposition is simply true or false, and that ends the matter: there
+can be no question of "circumstances." "Charles I's head was cut off"
+is just as true in summer as in winter, on Sundays as on Mondays. Thus
+when it is worth saying that something "would be true under all
+circumstances," the something in question must be a propositional
+function, i.e. an expression containing a variable, and becoming a
+proposition when a value is assigned to the variable; the varying
+"circumstances" alluded to are then the different values of which the
+variable is capable. Thus if "necessary" means "what is true under all
+circumstances," then "if _x_ is a man, _x_ is mortal" is necessary,
+because it is true for any possible value of _x_. Thus we should be
+led to the following definition:--
+
+  "NECESSARY is a predicate of a propositional function, meaning
+     that it is true for all possible values of its argument or
+     arguments."
+
+Unfortunately, however, the definition in Baldwin's _Dictionary_ says
+that what is necessary is not only "true under all circumstances" but
+is also "true." Now these two are incompatible. Only propositions can
+be "true," and only propositional functions can be "true under all
+circumstances." Hence the definition as it stands is nonsense. What is
+meant seems to be this: "A proposition is necessary when it is a value
+of a propositional function which is true under all circumstances,
+i.e. for all values of its argument or arguments." But if we adopt
+this definition, the same proposition will be necessary or contingent
+according as we choose one or other of its terms as the argument to
+our propositional function. For example, "if Socrates is a man,
+Socrates is mortal," is necessary if Socrates is chosen as argument,
+but not if _man_ or _mortal_ is chosen. Again, "if Socrates is a man,
+Plato is mortal," will be necessary if either Socrates or _man_ is
+chosen as argument, but not if Plato or _mortal_ is chosen. However,
+this difficulty can be overcome by specifying the constituent which is
+to be regarded as argument, and we thus arrive at the following
+definition:
+
+"A proposition is _necessary_ with respect to a given constituent if
+it remains true when that constituent is altered in any way compatible
+with the proposition remaining significant."
+
+We may now apply this definition to the definition of causality quoted
+above. It is obvious that the argument must be the time at which the
+earlier event occurs. Thus an instance of causality will be such as:
+"If the event [Math: e_{1}] occurs at the time [Math: t_{1}], it will
+be followed by the event [Math: e_{2}]." This proposition is intended
+to be necessary with respect to [Math: t_{1}], i.e. to remain true
+however [Math: t_{1}] may be varied. Causality, as a universal law,
+will then be the following: "Given any event [Math: t_{1}], there is
+an event [Math: e_{2}] such that, whenever [Math: t_{1}] occurs,
+[Math: e_{2}] occurs later." But before this can be considered
+precise, we must specify how much later [Math: e_{2}] is to occur.
+Thus the principle becomes:--
+
+"Given any event [Math: e_{1}], there is an event [Math: e_{2}] and a
+time-interval [tau] such that, whenever [Math: e_{1}] occurs, [Math:
+e_{2}] follows after an interval [tau]."
+
+I am not concerned as yet to consider whether this law is true or
+false. For the present, I am merely concerned to discover what the law
+of causality is supposed to be. I pass, therefore, to the other
+definitions quoted above.
+
+The second definition need not detain us long, for two reasons. First,
+because it is psychological: not the "thought or perception" of a
+process, but the process itself, must be what concerns us in
+considering causality. Secondly, because it is circular: in speaking
+of a process as "taking place in consequence of" another process, it
+introduces the very notion of cause which was to be defined.
+
+The third definition is by far the most precise; indeed as regards
+clearness it leaves nothing to be desired. But a great difficulty is
+caused by the temporal contiguity of cause and effect which the
+definition asserts. No two instants are contiguous, since the
+time-series is compact; hence either the cause or the effect or both
+must, if the definition is correct, endure for a finite time; indeed,
+by the wording of the definition it is plain that both are assumed to
+endure for a finite time. But then we are faced with a dilemma: if the
+cause is a process involving change within itself, we shall require
+(if causality is universal) causal relations between its earlier and
+later parts; moreover, it would seem that only the later parts can be
+relevant to the effect, since the earlier parts are not contiguous to
+the effect, and therefore (by the definition) cannot influence the
+effect. Thus we shall be led to diminish the duration of the cause
+without limit, and however much we may diminish it, there will still
+remain an earlier part which might be altered without altering the
+effect, so that the true cause, as defined, will not have been
+reached, for it will be observed that the definition excludes
+plurality of causes. If, on the other hand, the cause is purely
+static, involving no change within itself, then, in the first place,
+no such cause is to be found in nature, and in the second place, it
+seems strange--too strange to be accepted, in spite of bare logical
+possibility--that the cause, after existing placidly for some time,
+should suddenly explode into the effect, when it might just as well
+have done so at any earlier time, or have gone on unchanged without
+producing its effect. This dilemma, therefore, is fatal to the view
+that cause and effect can be contiguous in time; if there are causes
+and effects, they must be separated by a finite time-interval [tau],
+as was assumed in the above interpretation of the first definition.
+
+What is essentially the same statement of the law of causality as the
+one elicited above from the first of Baldwin's definitions is given by
+other philosophers. Thus John Stuart Mill says:--
+
+"The Law of Causation, the recognition of which is the main pillar of
+inductive science, is but the familiar truth, that invariability of
+succession is found by observation to obtain between every fact in
+nature and some other fact which has preceded it."[36]
+
+And Bergson, who has rightly perceived that the law as stated by
+philosophers is worthless, nevertheless continues to suppose that it
+is used in science. Thus he says:--
+
+"Now, it is argued, this law [the law of causality] means that every
+phenomenon is determined by its conditions, or, in other words, that
+the same causes produce the same effects."[37]
+
+And again:--
+
+"We perceive physical phenomena, and these phenomena obey laws. This
+means: (1) That phenomena _a_, _b_, _c_, _d_, previously perceived,
+can occur again in the same shape; (2) that a certain phenomenon P,
+which appeared after the conditions _a_, _b_, _c_, _d_, and after
+these conditions only, will not fail to recur as soon as the same
+conditions are again present."[38]
+
+A great part of Bergson's attack on science rests on the assumption
+that it employs this principle. In fact, it employs no such principle,
+but philosophers--even Bergson--are too apt to take their views on
+science from each other, not from science. As to what the principle
+is, there is a fair consensus among philosophers of different schools.
+There are, however, a number of difficulties which at once arise. I
+omit the question of plurality of causes for the present, since other
+graver questions have to be considered. Two of these, which are forced
+on our attention by the above statement of the law, are the
+following:--
+
+  (1) What is meant by an "event"?
+
+  (2) How long may the time-interval be between cause and effect?
+
+(1) An "event," in the statement of the law, is obviously intended to
+be something that is likely to recur since otherwise the law becomes
+trivial. It follows that an "event" is not a particular, but some
+universal of which there may be many instances. It follows also that
+an "event" must be something short of the whole state of the universe,
+since it is highly improbable that this will recur. What is meant by
+an "event" is something like striking a match, or dropping a penny
+into the slot of an automatic machine. If such an event is to recur,
+it must not be defined too narrowly: we must not state with what
+degree of force the match is to be struck, nor what is to be the
+temperature of the penny. For if such considerations were relevant,
+our "event" would occur at most once, and the law would cease to give
+information. An "event," then, is a universal defined sufficiently
+widely to admit of many particular occurrences in time being instances
+of it.
+
+(2) The next question concerns the time-interval. Philosophers, no
+doubt, think of cause and effect as contiguous in time, but this, for
+reasons already given, is impossible. Hence, since there are no
+infinitesimal time-intervals, there must be some finite lapse of time
+[tau] between cause and effect. This, however, at once raises
+insuperable difficulties. However short we make the interval [tau],
+something may happen during this interval which prevents the expected
+result. I put my penny in the slot, but before I can draw out my
+ticket there is an earthquake which upsets the machine and my
+calculations. In order to be sure of the expected effect, we must know
+that there is nothing in the environment to interfere with it. But
+this means that the supposed cause is not, by itself, adequate to
+insure the effect. And as soon as we include the environment, the
+probability of repetition is diminished, until at last, when the whole
+environment is included, the probability of repetition becomes almost
+_nil_.
+
+In spite of these difficulties, it must, of course, be admitted that
+many fairly dependable regularities of sequence occur in daily life.
+It is these regularities that have suggested the supposed law of
+causality; where they are found to fail, it is thought that a better
+formulation could have been found which would have never failed. I am
+far from denying that there may be such sequences which in fact never
+do fail. It may be that there will never be an exception to the rule
+that when a stone of more than a certain mass, moving with more than a
+certain velocity, comes in contact with a pane of glass of less than
+a certain thickness, the glass breaks. I also do not deny that the
+observation of such regularities, even when they are not without
+exceptions, is useful in the infancy of a science: the observation
+that unsupported bodies in air usually fall was a stage on the way to
+the law of gravitation. What I deny is that science assumes the
+existence of invariable uniformities of sequence of this kind, or that
+it aims at discovering them. All such uniformities, as we saw, depend
+upon a certain vagueness in the definition of the "events." That
+bodies fall is a vague qualitative statement; science wishes to know
+how fast they fall. This depends upon the shape of the bodies and the
+density of the air. It is true that there is more nearly uniformity
+when they fall in a vacuum; so far as Galileo could observe, the
+uniformity is then complete. But later it appeared that even there the
+latitude made a difference, and the altitude. Theoretically, the
+position of the sun and moon must make a difference. In short, every
+advance in a science takes us farther away from the crude uniformities
+which are first observed, into greater differentiation of antecedent
+and consequent, and into a continually wider circle of antecedents
+recognised as relevant.
+
+The principle "same cause, same effect," which philosophers imagine to
+be vital to science, is therefore utterly otiose. As soon as the
+antecedents have been given sufficiently fully to enable the
+consequent to be calculated with some exactitude, the antecedents have
+become so complicated that it is very unlikely they will ever recur.
+Hence, if this were the principle involved, science would remain
+utterly sterile.
+
+The importance of these considerations lies partly in the fact that
+they lead to a more correct account of scientific procedure, partly in
+the fact that they remove the analogy with human volition which makes
+the conception of cause such a fruitful source of fallacies. The
+latter point will become clearer by the help of some illustrations.
+For this purpose I shall consider a few maxims which have played a
+great part in the history of philosophy.
+
+(1) "Cause and effect must more or less resemble each other." This
+principle was prominent in the philosophy of occasionalism, and is
+still by no means extinct. It is still often thought, for example,
+that mind could not have grown up in a universe which previously
+contained nothing mental, and one ground for this belief is that
+matter is too dissimilar from mind to have been able to cause it. Or,
+more particularly, what are termed the nobler parts of our nature are
+supposed to be inexplicable, unless the universe always contained
+something at least equally noble which could cause them. All such
+views seem to depend upon assuming some unduly simplified law of
+causality; for, in any legitimate sense of "cause" and "effect,"
+science seems to show that they are usually very widely dissimilar,
+the "cause" being, in fact, two states of the whole universe, and the
+"effect" some particular event.
+
+(2) "Cause is analogous to volition, since there must be an
+intelligible _nexus_ between cause and effect." This maxim is, I
+think, often unconsciously in the imaginations of philosophers who
+would reject it when explicitly stated. It is probably operative in
+the view we have just been considering, that mind could not have
+resulted from a purely material world. I do not profess to know what
+is meant by "intelligible"; it seems to mean "familiar to
+imagination." Nothing is less "intelligible," in any other sense, than
+the connection between an act of will and its fulfilment. But
+obviously the sort of nexus desired between cause and effect is such
+as could only hold between the "events" which the supposed law of
+causality contemplates; the laws which replace causality in such a
+science as physics leave no room for any two events between which a
+nexus could be sought.
+
+(3) "The cause _compels_ the effect in some sense in which the effect
+does not compel the cause." This belief seems largely operative in the
+dislike of determinism; but, as a matter of fact, it is connected with
+our second maxim, and falls as soon as that is abandoned. We may
+define "compulsion" as follows: "Any set of circumstances is said to
+compel A when A desires to do something which the circumstances
+prevent, or to abstain from something which the circumstances cause."
+This presupposes that some meaning has been found for the word
+"cause"--a point to which I shall return later. What I want to make
+clear at present is that compulsion is a very complex notion,
+involving thwarted desire. So long as a person does what he wishes to
+do, there is no compulsion, however much his wishes may be calculable
+by the help of earlier events. And where desire does not come in,
+there can be no question of compulsion. Hence it is, in general,
+misleading to regard the cause as compelling the effect.
+
+A vaguer form of the same maxim substitutes the word "determine" for
+the word "compel"; we are told that the cause _determines_ the effect
+in a sense in which the effect does not _determine_ the cause. It is
+not quite clear what is meant by "determining"; the only precise
+sense, so far as I know, is that of a function or one-many relation.
+If we admit plurality of causes, but not of effects, that is, if we
+suppose that, given the cause, the effect must be such and such, but,
+given the effect, the cause may have been one of many alternatives,
+then we may say that the cause determines the effect, but not the
+effect the cause. Plurality of causes, however, results only from
+conceiving the effect vaguely and narrowly and the cause precisely and
+widely. Many antecedents may "cause" a man's death, because his death
+is vague and narrow. But if we adopt the opposite course, taking as
+the "cause" the drinking of a dose of arsenic, and as the "effect" the
+whole state of the world five minutes later, we shall have plurality
+of effects instead of plurality of causes. Thus the supposed lack of
+symmetry between "cause" and "effect" is illusory.
+
+(4) "A cause cannot operate when it has ceased to exist, because what
+has ceased to exist is nothing." This is a common maxim, and a still
+more common unexpressed prejudice. It has, I fancy, a good deal to do
+with the attractiveness of Bergson's "_durée_": since the past has
+effects now, it must still exist in some sense. The mistake in this
+maxim consists in the supposition that causes "operate" at all. A
+volition "operates" when what it wills takes place; but nothing can
+operate except a volition. The belief that causes "operate" results
+from assimilating them, consciously or unconsciously, to volitions. We
+have already seen that, if there are causes at all, they must be
+separated by a finite interval of time from their effects, and thus
+cause their effects after they have ceased to exist.
+
+It may be objected to the above definition of a volition "operating"
+that it only operates when it "causes" what it wills, not when it
+merely happens to be followed by what it wills. This certainly
+represents the usual view of what is meant by a volition "operating,"
+but as it involves the very view of causation which we are engaged in
+combating, it is not open to us as a definition. We may say that a
+volition "operates" when there is some law in virtue of which a
+similar volition in rather similar circumstances will usually be
+followed by what it wills. But this is a vague conception, and
+introduces ideas which we have not yet considered. What is chiefly
+important to notice is that the usual notion of "operating" is not
+open to us if we reject, as I contend that we should, the usual notion
+of causation.
+
+(5) "A cause cannot operate except where it is." This maxim is very
+widespread; it was urged against Newton, and has remained a source of
+prejudice against "action at a distance." In philosophy it has led to
+a denial of transient action, and thence to monism or Leibnizian
+monadism. Like the analogous maxim concerning temporal contiguity, it
+rests upon the assumption that causes "operate," i.e. that they are in
+some obscure way analogous to volitions. And, as in the case of
+temporal contiguity, the inferences drawn from this maxim are wholly
+groundless.
+
+I return now to the question, What law or laws can be found to take
+the place of the supposed law of causality?
+
+First, without passing beyond such uniformities of sequence as are
+contemplated by the traditional law, we may admit that, if any such
+sequence has been observed in a great many cases, and has never been
+found to fail, there is an inductive probability that it will be found
+to hold in future cases. If stones have hitherto been found to break
+windows, it is probable that they will continue to do so. This, of
+course, assumes the inductive principle, of which the truth may
+reasonably be questioned; but as this principle is not our present
+concern, I shall in this discussion treat it as indubitable. We may
+then say, in the case of any such frequently observed sequence, that
+the earlier event is the _cause_ and the later event the _effect_.
+
+Several considerations, however, make such special sequences very
+different from the traditional relation of cause and effect. In the
+first place, the sequence, in any hitherto unobserved instance, is no
+more than probable, whereas the relation of cause and effect was
+supposed to be necessary. I do not mean by this merely that we are not
+sure of having discovered a true case of cause and effect; I mean
+that, even when we have a case of cause and effect in our present
+sense, all that is meant is that on grounds of observation, it is
+probable that when one occurs the other will also occur. Thus in our
+present sense, A may be the cause of B even if there actually are
+cases where B does not follow A. Striking a match will be the cause of
+its igniting, in spite of the fact that some matches are damp and fail
+to ignite.
+
+In the second place, it will not be assumed that _every_ event has
+some antecedent which is its cause in this sense; we shall only
+believe in causal sequences where we find them, without any
+presumption that they always are to be found.
+
+In the third place, _any_ case of sufficiently frequent sequence will
+be causal in our present sense; for example, we shall not refuse to
+say that night is the cause of day. Our repugnance to saying this
+arises from the ease with which we can imagine the sequence to fail,
+but owing to the fact that cause and effect must be separated by a
+finite interval of time, _any_ such sequence _might_ fail through the
+interposition of other circumstances in the interval. Mill, discussing
+this instance of night and day, says:--
+
+"It is necessary to our using the word cause, that we should believe
+not only that the antecedent always _has_ been followed by the
+consequent, but that as long as the present constitution of things
+endures, it always _will_ be so."[39]
+
+In this sense, we shall have to give up the hope of finding causal
+laws such as Mill contemplated; any causal sequence which we have
+observed may at any moment be falsified without a falsification of any
+laws of the kind that the more advanced sciences aim at establishing.
+
+In the fourth place, such laws of probable sequence, though useful in
+daily life and in the infancy of a science, tend to be displaced by
+quite different laws as soon as a science is successful. The law of
+gravitation will illustrate what occurs in any advanced science. In
+the motions of mutually gravitating bodies, there is nothing that can
+be called a cause, and nothing that can be called an effect; there is
+merely a formula. Certain differential equations can be found, which
+hold at every instant for every particle of the system, and which,
+given the configuration and velocities at one instant, or the
+configurations at two instants, render the configuration at any other
+earlier or later instant theoretically calculable. That is to say, the
+configuration at any instant is a function of that instant and the
+configurations at two given instants. This statement holds throughout
+physics, and not only in the special case of gravitation. But there is
+nothing that could be properly called "cause" and nothing that could
+be properly called "effect" in such a system.
+
+No doubt the reason why the old "law of causality" has so long
+continued to pervade the books of philosophers is simply that the idea
+of a function is unfamiliar to most of them, and therefore they seek
+an unduly simplified statement. There is no question of repetitions of
+the "same" cause producing the "same" effect; it is not in any
+sameness of causes and effects that the constancy of scientific law
+consists, but in sameness of relations. And even "sameness of
+relations" is too simple a phrase; "sameness of differential
+equations" is the only correct phrase. It is impossible to state this
+accurately in non-mathematical language; the nearest approach would be
+as follows: "There is a constant relation between the state of the
+universe at any instant and the rate of change in the rate at which
+any part of the universe is changing at that instant, and this
+relation is many-one, i.e. such that the rate of change in the rate of
+change is determinate when the state of the universe is given." If the
+"law of causality" is to be something actually discoverable in the
+practice of science, the above proposition has a better right to the
+name than any "law of causality" to be found in the books of
+philosophers.
+
+In regard to the above principle, several observations must be made--
+
+(1) No one can pretend that the above principle is _a priori_ or
+self-evident or a "necessity of thought." Nor is it, in any sense, a
+premiss of science: it is an empirical generalisation from a number of
+laws which are themselves empirical generalisations.
+
+(2) The law makes no difference between past and future: the future
+"determines" the past in exactly the same sense in which the past
+"determines" the future. The word "determine," here, has a purely
+logical significance: a certain number of variables "determine"
+another variable if that other variable is a function of them.
+
+(3) The law will not be empirically verifiable unless the course of
+events within some sufficiently small volume will be approximately
+the same in any two states of the universe which only differ in regard
+to what is at a considerable distance from the small volume in
+question. For example, motions of planets in the solar system must be
+approximately the same however the fixed stars may be distributed,
+provided that all the fixed stars are very much farther from the sun
+than the planets are. If gravitation varied directly as the distance,
+so that the most remote stars made the most difference to the motions
+of the planets, the world might be just as regular and just as much
+subject to mathematical laws as it is at present, but we could never
+discover the fact.
+
+(4) Although the old "law of causality" is not assumed by science,
+something which we may call the "uniformity of nature" is assumed, or
+rather is accepted on inductive grounds. The uniformity of nature does
+not assert the trivial principle "same cause, same effect," but the
+principle of the permanence of laws. That is to say, when a law
+exhibiting, e.g. an acceleration as a function of the configuration
+has been found to hold throughout the observable past, it is expected
+that it will continue to hold in the future, or that, if it does not
+itself hold, there is some other law, agreeing with the supposed law
+as regards the past, which will hold for the future. The ground of
+this principle is simply the inductive ground that it has been found
+to be true in very many instances; hence the principle cannot be
+considered certain, but only probable to a degree which cannot be
+accurately estimated.
+
+The uniformity of nature, in the above sense, although it is assumed
+in the practice of science, must not, in its generality, be regarded
+as a kind of major premiss, without which all scientific reasoning
+would be in error. The assumption that _all_ laws of nature are
+permanent has, of course, less probability than the assumption that
+this or that particular law is permanent; and the assumption that a
+particular law is permanent for all time has less probability than the
+assumption that it will be valid up to such and such a date. Science,
+in any given case, will assume what the case requires, but no more. In
+constructing the _Nautical Almanac_ for 1915 it will assume that the
+law of gravitation will remain true up to the end of that year; but it
+will make no assumption as to 1916 until it comes to the next volume
+of the almanac. This procedure is, of course, dictated by the fact
+that the uniformity of nature is not known _a priori_, but is an
+empirical generalisation, like "all men are mortal." In all such
+cases, it is better to argue immediately from the given particular
+instances to the new instance, than to argue by way of a major
+premiss; the conclusion is only probable in either case, but acquires
+a higher probability by the former method than by the latter.
+
+In all science we have to distinguish two sorts of laws: first, those
+that are empirically verifiable but probably only approximate;
+secondly, those that are not verifiable, but may be exact. The law of
+gravitation, for example, in its applications to the solar system, is
+only empirically verifiable when it is assumed that matter outside the
+solar system may be ignored for such purposes; we believe this to be
+only approximately true, but we cannot empirically verify the law of
+universal gravitation which we believe to be exact. This point is very
+important in connection with what we may call "relatively isolated
+systems." These may be defined as follows:--
+
+A system relatively isolated during a given period is one which,
+within some assignable margin of error, will behave in the same way
+throughout that period, however the rest of the universe may be
+constituted.
+
+A system may be called "practically isolated" during a given period
+if, although there _might_ be states of the rest of the universe which
+would produce more than the assigned margin of error, there is reason
+to believe that such states do not in fact occur.
+
+Strictly speaking, we ought to specify the respect in which the system
+is relatively isolated. For example, the earth is relatively isolated
+as regards falling bodies, but not as regards tides; it is
+_practically_ isolated as regards economic phenomena, although, if
+Jevons' sunspot theory of commercial crises had been true, it would
+not have been even practically isolated in this respect.
+
+It will be observed that we cannot prove in advance that a system is
+isolated. This will be inferred from the observed fact that
+approximate uniformities can be stated for this system alone. If the
+complete laws for the whole universe were known, the isolation of a
+system could be deduced from them; assuming, for example, the law of
+universal gravitation, the practical isolation of the solar system in
+this respect can be deduced by the help of the fact that there is very
+little matter in its neighbourhood. But it should be observed that
+isolated systems are only important as providing a possibility of
+_discovering_ scientific laws; they have no theoretical importance in
+the finished structure of a science.
+
+The case where one event A is said to "cause" another event B, which
+philosophers take as fundamental, is really only the most simplified
+instance of a practically isolated system. It may happen that, as a
+result of general scientific laws, whenever A occurs throughout a
+certain period, it is followed by B; in that case, A and B form a
+system which is practically isolated throughout that period. It is,
+however, to be regarded as a piece of good fortune if this occurs; it
+will always be due to special circumstances, and would not have been
+true if the rest of the universe had been different though subject to
+the same laws.
+
+The essential function which causality has been supposed to perform is
+the possibility of inferring the future from the past, or, more
+generally, events at any time from events at certain assigned times.
+Any system in which such inference is possible may be called a
+"deterministic" system. We may define a deterministic system as
+follows:--
+
+  A system is said to be "deterministic" when, given certain data,
+  [Math: e_{1}, e_{2}, ..., e_{n}, at times t_{1}, t_{2}, ...,
+  t_{n}] respectively, concerning this system, if [Math: E_{t}] is
+  the state of the system at any time _t_, there is a functional
+  relation of the form
+
+[Math: E_{t} = f (e_{1}, t_{1}, e_{2}, t_{2}, ..., e_{n}, t_{n}, t)]. (A)
+
+  The system will be "deterministic throughout a given period" if
+  _t_, in the above formula, may be any time within that period,
+  though outside that period the formula may be no longer true. If
+  the universe, as a whole, is such a system, determinism is true of
+  the universe; if not, not. A system which is part of a
+  deterministic system I shall call "determined"; one which is not
+  part of any such system I shall call "capricious."
+
+The events [Math: e_{1}, e_{2}, ..., e_{n}] I shall call "determinants"
+of the system. It is to be observed that a system which has one set of
+determinants will in general have many. In the case of the motions of
+the planets, for example, the configurations of the solar system at any
+two given times will be determinants.
+
+We may take another illustration from the hypothesis of
+psycho-physical parallelism. Let us assume, for the purposes of this
+illustration, that to a given state of brain a given state of mind
+always corresponds, and vice versa, i.e. that there is a one-one
+relation between them, so that each is a function of the other. We may
+also assume, what is practically certain, that to a given state of a
+certain brain a given state of the whole material universe
+corresponds, since it is highly improbable that a given brain is ever
+twice in exactly the same state. Hence there will be a one-one
+relation between the state of a given person's mind and the state of
+the whole material universe. It follows that, if _n_ states of the
+material universe are determinants of the material universe, then _n_
+states of a given man's mind are determinants of the whole material
+and mental universe--assuming, that is to say, that psycho-physical
+parallelism is true.
+
+The above illustration is important in connection with a certain
+confusion which seems to have beset those who have philosophised on
+the relation of mind and matter. It is often thought that, if the
+state of the mind is determinate when the state of the brain is given,
+and if the material world forms a deterministic system, then mind is
+"subject" to matter in some sense in which matter is not "subject" to
+mind. But if the state of the brain is also determinate when the state
+of the mind is given, it must be exactly as true to regard matter as
+subject to mind as it would be to regard mind as subject to matter. We
+could, theoretically, work out the history of mind without ever
+mentioning matter, and then, at the end, deduce that matter must
+meanwhile have gone through the corresponding history. It is true that
+if the relation of brain to mind were many-one, not one-one, there
+would be a one-sided dependence of mind on brain, while conversely, if
+the relation were one-many, as Bergson supposes, there would be a
+one-aided dependence of brain on mind. But the dependence involved is,
+in any case, only logical; it does not mean that we shall be
+compelled to do things we desire not to do, which is what people
+instinctively imagine it to mean.
+
+As another illustration we may take the case of mechanism and
+teleology. A system may be defined as "mechanical" when it has a set
+of determinants that are purely material, such as the positions of
+certain pieces of matter at certain times. It is an open question
+whether the world of mind and matter, as we know it, is a mechanical
+system or not; let us suppose, for the sake of argument, that it is a
+mechanical system. This supposition--so I contend--throws no light
+whatever on the question whether the universe is or is not a
+"teleological" system. It is difficult to define accurately what is
+meant by a "teleological" system, but the argument is not much
+affected by the particular definition we adopt. Broadly, a
+teleological system is one in which purposes are realised, i.e. in
+which certain desires--those that are deeper or nobler or more
+fundamental or more universal or what not--are followed by their
+realisation. Now the fact--if it be a fact--that the universe is
+mechanical has no bearing whatever on the question whether it is
+teleological in the above sense. There might be a mechanical system in
+which all wishes were realised, and there might be one in which all
+wishes were thwarted. The question whether, or how far, our actual
+world is teleological, cannot, therefore, be settled by proving that
+it is mechanical, and the desire that it should be teleological is no
+ground for wishing it to be not mechanical.
+
+There is, in all these questions, a very great difficulty in avoiding
+confusion between what we can infer and what is in fact determined.
+Let us consider, for a moment, the various senses in which the future
+may be "determined." There is one sense--and a very important one--in
+which it is determined quite independently of scientific laws, namely,
+the sense that it will be what it will be. We all regard the past as
+determined simply by the fact that it has happened; but for the
+accident that memory works backward and not forward, we should regard
+the future as equally determined by the fact that it will happen.
+"But," we are told, "you cannot alter the past, while you can to some
+extent alter the future." This view seems to me to rest upon just
+those errors in regard to causation which it has been my object to
+remove. You cannot make the past other than it was--true, but this is
+a mere application of the law of contradiction. If you already know
+what the past was, obviously it is useless to wish it different. But
+also you cannot make the future other than it will be; this again is
+an application of the law of contradiction. And if you happen to know
+the future--e.g. in the case of a forthcoming eclipse--it is just as
+useless to wish it different as to wish the past different. "But," it
+will be rejoined, "our wishes can _cause_ the future, sometimes, to be
+different from what it would be if they did not exist, and they can
+have no such effect upon the past." This, again, is a mere tautology.
+An effect being _defined_ as something subsequent to its cause,
+obviously we can have no _effect_ upon the past. But that does not
+mean that the past would not have been different if our present wishes
+had been different. Obviously, our present wishes are conditioned by
+the past, and therefore could not have been different unless the past
+had been different; therefore, if our present wishes were different,
+the past would be different. Of course, the past cannot be different
+from what it was, but no more can our present wishes be different from
+what they are; this again is merely the law of contradiction. The
+facts seem to be merely (1) that wishing generally depends upon
+ignorance, and is therefore commoner in regard to the future than in
+regard to the past; (2) that where a wish concerns the future, it and
+its realisation very often form a "practically independent system,"
+i.e. many wishes regarding the future are realised. But there seems no
+doubt that the main difference in our feelings arises from the
+accidental fact that the past but not the future can be known by
+memory.
+
+Although the sense of "determined" in which the future is determined
+by the mere fact that it will be what it will be is sufficient (at
+least so it seems to me) to refute some opponents of determinism,
+notably M. Bergson and the pragmatists, yet it is not what most people
+have in mind when they speak of the future as determined. What they
+have in mind is a formula by means of which the future can be
+exhibited, and at least theoretically calculated, as a function of the
+past. But at this point we meet with a great difficulty, which besets
+what has been said above about deterministic systems, as well as what
+is said by others.
+
+If formulæ of any degree of complexity, however great, are admitted,
+it would seem that any system, whose state at a given moment is a
+function of certain measurable quantities, must be a deterministic
+system. Let us consider, in illustration, a single material particle,
+whose co-ordinates at time _t_ are [Math: x_{t}, y_{t}, z_{t}]. Then,
+however, the particle moves, there must be, theoretically, functions
+[Math: f_{1}, f_{2}, f_{3}], such that
+
+[Math: x_{t} = f_{t}(t), y_{t} = f_{2}(t), z_{t} = f_{3}(t).]
+
+It follows that, theoretically, the whole state of the material
+universe at time _t_ must be capable of being exhibited as a function
+of _t_. Hence our universe will be deterministic in the sense defined
+above. But if this be true, no information is conveyed about the
+universe in stating that it is deterministic. It is true that the
+formulæ involved may be of strictly infinite complexity, and therefore
+not practically capable of being written down or apprehended. But
+except from the point of view of our knowledge, this might seem to be
+a detail: in itself, if the above considerations are sound, the
+material universe _must_ be deterministic, _must_ be subject to laws.
+
+This, however, is plainly not what was intended. The difference
+between this view and the view intended may be seen as follows. Given
+some formula which fits the facts hitherto--say the law of
+gravitation--there will be an infinite number of other formulæ, not
+empirically distinguishable from it in the past, but diverging from it
+more and more in the future. Hence, even assuming that there are
+persistent laws, we shall have no reason for assuming that the law of
+the inverse square will hold in future; it may be some other hitherto
+indistinguishable law that will hold. We cannot say that _every_ law
+which has held hitherto must hold in the future, because past facts
+which obey one law will also obey others, hitherto indistinguishable
+but diverging in future. Hence there must, at every moment, be laws
+hitherto unbroken which are now broken for the first time. What
+science does, in fact, is to select the _simplest_ formula that will
+fit the facts. But this, quite obviously, is merely a methodological
+precept, not a law of Nature. If the simplest formula ceases, after a
+time, to be applicable, the simplest formula that remains applicable
+is selected, and science has no sense that an axiom has been
+falsified. We are thus left with the brute fact that, in many
+departments of science, quite simple laws have hitherto been found to
+hold. This fact cannot be regarded as having any _a priori_ ground,
+nor can it be used to support inductively the opinion that the same
+laws will continue; for at every moment laws hitherto true are being
+falsified, though in the advanced sciences these laws are less simple
+than those that have remained true. Moreover it would be fallacious to
+argue inductively from the state of the advanced sciences to the
+future state of the others, for it may well be that the advanced
+sciences are advanced simply because, hitherto, their subject-matter
+has obeyed simple and easily ascertainable laws, while the
+subject-matter of other sciences has not done so.
+
+The difficulty we have been considering seems to be met partly, if not
+wholly, by the principle that the _time_ must not enter explicitly
+into our formulæ. All mechanical laws exhibit acceleration as a
+function of configuration, not of configuration and time jointly; and
+this principle of the irrelevance of the time may be extended to all
+scientific laws. In fact we might interpret the "uniformity of nature"
+as meaning just this, that no scientific law involves the time as an
+argument, unless, of course, it is given in an integrated form, in
+which case _lapse_ of time, though not absolute time, may appear in
+our formulæ. Whether this consideration suffices to overcome our
+difficulty completely, I do not know; but in any case it does much to
+diminish it.
+
+It will serve to illustrate what has been said if we apply it to the
+question of free will.
+
+(1) Determinism in regard to the will is the doctrine that our
+volitions belong to some deterministic system, i.e. are "determined"
+in the sense defined above. Whether this doctrine is true or false, is
+a mere question of fact; no _a priori_ considerations (if our previous
+discussions have been correct) can exist on either side. On the one
+hand, there is no _a priori_ category of causality, but merely certain
+observed uniformities. As a matter of fact, there are observed
+uniformities in regard to volitions; thus there is some empirical
+evidence that volitions are determined. But it would be very rash to
+maintain that the evidence is overwhelming, and it is quite possible
+that some volitions, as well as some other things, are not determined,
+except in the sense in which we found that everything must be
+determined.
+
+(2) But, on the other hand, the subjective sense of freedom, sometimes
+alleged against determinism, has no bearing on the question whatever.
+The view that it has a bearing rests upon the belief that causes
+compel their effects, or that nature enforces obedience to its laws as
+governments do. These are mere anthropomorphic superstitions, due to
+assimilation of causes with volitions and of natural laws with human
+edicts. We feel that our will is not compelled, but that only means
+that it is not other than we choose it to be. It is one of the
+demerits of the traditional theory of causality that it has created an
+artificial opposition between determinism and the freedom of which we
+are introspectively conscious.
+
+(3) Besides the general question whether volitions are determined,
+there is the further question whether they are _mechanically_
+determined, i.e. whether they are part of what was above defined as a
+mechanical system. This is the question whether they form part of a
+system with purely material determinants, i.e. whether there are laws
+which, given certain material data, make all volitions functions of
+those data. Here again, there is empirical evidence up to a point, but
+it is not conclusive in regard to all volitions. It is important to
+observe, however that even if volitions are part of a mechanical
+system, this by no means implies any supremacy of matter over mind. It
+may well be that the same system which is susceptible of material
+determinants is also susceptible of mental determinants; thus a
+mechanical system may be determined by sets of volitions, as well as
+by sets of material facts. It would seem, therefore, that the reasons
+which make people dislike the view that volitions are mechanically
+determined are fallacious.
+
+(4) The notion of _necessity_, which is often associated with
+determinism, is a confused notion not legitimately deducible from
+determinism. Three meanings are commonly confounded when necessity is
+spoken of:--
+
+([alpha]) An _action_ is necessary when it will be performed
+however much the agent may wish to do otherwise. Determinism does not
+imply that actions are necessary in this sense.
+
+([beta]) A _propositional function_ is necessary when all its
+values are true. This sense is not relevant to our present discussion.
+
+([gamma]) A _proposition_ is necessary with respect to a given
+constituent when it is the value, with that constituent as argument,
+of a necessary propositional function, in other words, when it remains
+true however that constituent may be varied. In this sense, in a
+deterministic system, the connection of a volition with its
+determinants is necessary, if the time at which the determinants occur
+be taken as the constituent to be varied, the time-interval between
+the determinants and the volition being kept constant. But this sense
+of necessity is purely logical, and has no emotional importance.
+
+We may now sum up our discussion of causality. We found first that the
+law of causality, as usually stated by philosophers, is false, and is
+not employed in science. We then considered the nature of scientific
+laws, and found that, instead of stating that one event A is always
+followed by another event B, they stated functional relations between
+certain events at certain times, which we called determinants, and
+other events at earlier or later times or at the same time. We were
+unable to find any _a priori_ category involved: the existence of
+scientific laws appeared as a purely empirical fact, not necessarily
+universal, except in a trivial and scientifically useless form. We
+found that a system with one set of determinants may very likely have
+other sets of a quite different kind, that, for example, a
+mechanically determined system may also be teleologically or
+volitionally determined. Finally we considered the problem of free
+will: here we found that the reasons for supposing volitions to be
+determined are strong but not conclusive, and we decided that even if
+volitions are mechanically determined, that is no reason for denying
+freedom in the sense revealed by introspection, or for supposing that
+mechanical events are not determined by volitions. The problem of free
+will _versus_ determinism is therefore, if we were right, mainly
+illusory, but in part not yet capable of being decisively solved.
+
+FOOTNOTES:
+
+[35] A propositional function is an expression containing a variable,
+or undetermined constituent, and becoming a proposition as soon as a
+definite value is assigned to the variable. Examples are: "A is A,"
+"_x_ is a number." The variable is called the _argument_ of the
+function.
+
+[36] _Logic_, Bk. III, Chap. V, § 2.
+
+[37] _Time and Free Will_, p. 199.
+
+[38] _Time and Free Will._ p. 202.
+
+[39] _Loc. cit._, § 6
+
+
+
+
+X
+
+KNOWLEDGE BY ACQUAINTANCE AND KNOWLEDGE BY DESCRIPTION
+
+
+The object of the following paper is to consider what it is that we
+know in cases where we know propositions about "the so-and-so" without
+knowing who or what the so-and-so is. For example, I know that the
+candidate who gets most votes will be elected, though I do not know
+who is the candidate who will get most votes. The problem I wish to
+consider is: What do we know in these cases, where the subject is
+merely described? I have considered this problem elsewhere[40] from a
+purely logical point of view; but in what follows I wish to consider
+the question in relation to theory of knowledge as well as in relation
+to logic, and in view of the above-mentioned logical discussions, I
+shall in this paper make the logical portion as brief as possible.
+
+In order to make clear the antithesis between "acquaintance" and
+"description," I shall first of all try to explain what I mean by
+"acquaintance." I say that I am _acquainted_ with an object when I
+have a direct cognitive relation to that object, i.e. when I am
+directly aware of the object itself. When I speak of a cognitive
+relation here, I do not mean the sort of relation which constitutes
+judgment, but the sort which constitutes presentation. In fact, I
+think the relation of subject and object which I call acquaintance is
+simply the converse of the relation of object and subject which
+constitutes presentation. That is, to say that S has acquaintance with
+O is essentially the same thing as to say that O is presented to S.
+But the associations and natural extensions of the word _acquaintance_
+are different from those of the word _presentation_. To begin with, as
+in most cognitive words, it is natural to say that I am acquainted
+with an object even at moments when it is not actually before my mind,
+provided it has been before my mind, and will be again whenever
+occasion arises. This is the same sense in which I am said to know
+that 2+2=4 even when I am thinking of something else. In the second
+place, the word _acquaintance_ is designed to emphasise, more than the
+word _presentation_, the relational character of the fact with which
+we are concerned. There is, to my mind, a danger that, in speaking of
+presentation, we may so emphasise the object as to lose sight of the
+subject. The result of this is either to lead to the view that there
+is no subject, whence we arrive at materialism; or to lead to the view
+that what is presented is part of the subject, whence we arrive at
+idealism, and should arrive at solipsism but for the most desperate
+contortions. Now I wish to preserve the dualism of subject and object
+in my terminology, because this dualism seems to me a fundamental fact
+concerning cognition. Hence I prefer the word _acquaintance_ because
+it emphasises the need of a subject which is acquainted.
+
+When we ask what are the kinds of objects with which we are
+acquainted, the first and most obvious example is _sense-data_. When I
+see a colour or hear a noise, I have direct acquaintance with the
+colour or the noise. The sense-datum with which I am acquainted in
+these cases is generally, if not always, complex. This is
+particularly obvious in the case of sight. I do not mean, of course,
+merely that the supposed physical object is complex, but that the
+direct sensible object is complex and contains parts with spatial
+relations. Whether it is possible to be aware of a complex without
+being aware of its constituents is not an easy question, but on the
+whole it would seem that there is no reason why it should not be
+possible. This question arises in an acute form in connection with
+self-consciousness, which we must now briefly consider.
+
+In introspection, we seem to be immediately aware of varying
+complexes, consisting of objects in various cognitive and conative
+relations to ourselves. When I see the sun, it often happens that I
+am aware of my seeing the sun, in addition to being aware of the sun;
+and when I desire food, it often happens that I am aware of my desire
+for food. But it is hard to discover any state of mind in which I am
+aware of myself alone, as opposed to a complex of which I am a
+constituent. The question of the nature of self-consciousness is too
+large and too slightly connected with our subject, to be argued at
+length here. It is difficult, but probably not impossible, to account
+for plain facts if we assume that we do not have acquaintance with
+ourselves. It is plain that we are not only _acquainted_ with the
+complex "Self-acquainted-with-A," but we also _know_ the proposition
+"I am acquainted with A." Now here the complex has been analysed, and
+if "I" does not stand for something which is a direct object of
+acquaintance, we shall have to suppose that "I" is something known by
+description. If we wished to maintain the view that there is no
+acquaintance with Self, we might argue as follows: We are acquainted
+with _acquaintance_, and we know that it is a relation. Also we are
+acquainted with a complex in which we perceive that acquaintance is
+the relating relation. Hence we know that this complex must have a
+constituent which is that which is acquainted, i.e. must have a
+subject-term as well as an object-term. This subject-term we define
+as "I." Thus "I" means "the subject-term in awarenesses of which _I_
+am aware." But as a definition this cannot be regarded as a happy
+effort. It would seem necessary, therefore, either to suppose that I
+am acquainted with myself, and that "I," therefore, requires no
+definition, being merely the proper name of a certain object, or to
+find some other analysis of self-consciousness. Thus self-consciousness
+cannot be regarded as throwing light on the question whether we can
+know a complex without knowing its constituents. This question,
+however, is not important for our present purposes, and I shall
+therefore not discuss it further.
+
+The awarenesses we have considered so far have all been awarenesses of
+particular existents, and might all in a large sense be called
+sense-data. For, from the point of view of theory of knowledge,
+introspective knowledge is exactly on a level with knowledge derived
+from sight or hearing. But, in addition to awareness of the above kind
+of objects, which may be called awareness of _particulars_; we have
+also (though not quite in the same sense) what may be called awareness
+of _universals_. Awareness of universals is called _conceiving_, and a
+universal of which we are aware is called a _concept_. Not only are we
+aware of particular yellows, but if we have seen a sufficient number
+of yellows and have sufficient intelligence, we are aware of the
+universal _yellow_; this universal is the subject in such judgments as
+"yellow differs from blue" or "yellow resembles blue less than green
+does." And the universal yellow is the predicate in such judgments as
+"this is yellow," where "this" is a particular sense-datum. And
+universal relations, too, are objects of awarenesses; up and down,
+before and after, resemblance, desire, awareness itself, and so on,
+would seem to be all of them objects of which we can be aware.
+
+In regard to relations, it might be urged that we are never aware of
+the universal relation itself, but only of complexes in which it is a
+constituent. For example, it may be said that we do not know directly
+such a relation as _before_, though we understand such a proposition
+as "this is before that," and may be directly aware of such a complex
+as "this being before that." This view, however, is difficult to
+reconcile with the fact that we often know propositions in which the
+relation is the subject, or in which the relata are not definite given
+objects, but "anything." For example, we know that if one thing is
+before another, and the other before a third, then the first is before
+the third; and here the things concerned are not definite things, but
+"anything." It is hard to see how we could know such a fact about
+"before" unless we were acquainted with "before," and not merely with
+actual particular cases of one given object being before another given
+object. And more directly: A judgment such as "this is before that,"
+where this judgment is derived from awareness of a complex,
+constitutes an analysis, and we should not understand the analysis if
+we were not acquainted with the meaning of the terms employed. Thus we
+must suppose that we are acquainted with the meaning of "before," and
+not merely with instances of it.
+
+There are thus at least two sorts of objects of which we are aware,
+namely, particulars and universals. Among particulars I include all
+existents, and all complexes of which one or more constituents are
+existents, such as this-before-that, this-above-that,
+the-yellowness-of-this. Among universals I include all objects of
+which no particular is a constituent. Thus the disjunction
+"universal-particular" includes all objects. We might also call it the
+disjunction "abstract-concrete." It is not quite parallel with the
+opposition "concept-percept," because things remembered or imagined
+belong with particulars, but can hardly be called percepts. (On the
+other hand, universals with which we are acquainted may be identified
+with concepts.)
+
+It will be seen that among the objects with which we are acquainted
+are not included physical objects (as opposed to sense-data), nor
+other people's minds. These things are known to us by what I call
+"knowledge by description," which we must now consider.
+
+By a "description" I mean any phrase of the form "a so-and-so" or "the
+so-and-so." A phrase of the form "a so-and-so" I shall call an
+"ambiguous" description; a phrase of the form "the so-and-so" (in the
+singular) I shall call a "definite" description. Thus "a man" is an
+ambiguous description, and "the man with the iron mask" is a definite
+description. There are various problems connected with ambiguous
+descriptions, but I pass them by, since they do not directly concern
+the matter I wish to discuss. What I wish to discuss is the nature of
+our knowledge concerning objects in cases where we know that there is
+an object answering to a definite description, though we are not
+_acquainted_ with any such object. This is a matter which is concerned
+exclusively with _definite_ descriptions. I shall, therefore, in the
+sequel, speak simply of "descriptions" when I mean "definite
+descriptions." Thus a description will mean any phrase of the form
+"the so-and-so" in the singular.
+
+I shall say that an object is "known by description" when we know that
+it is "_the_ so-and-so," i.e. when we know that there is one object,
+and no more, having a certain property; and it will generally be
+implied that we do not have knowledge of the same object by
+acquaintance. We know that the man with the iron mask existed, and
+many propositions are known about him; but we do not know who he was.
+We know that the candidate who gets most votes will be elected, and in
+this case we are very likely also acquainted (in the only sense in
+which one can be acquainted with some one else) with the man who is,
+in fact, the candidate who will get most votes, but we do not know
+which of the candidates he is, i.e. we do not know any proposition of
+the form "A is the candidate who will get most votes" where A is one
+of the candidates by name. We shall say that we have "_merely_
+descriptive knowledge" of the so-and-so when, although we know that
+the so-and-so exists, and although we may possibly be acquainted with
+the object which is, in fact, the so-and-so, yet we do not know any
+proposition "_a_ is the so-and-so," where _a_ is something with which
+we are acquainted.
+
+When we say "the so-and-so exists," we mean that there is just one
+object which is the so-and-so. The proposition "_a_ is the so-and-so"
+means that _a_ has the property so-and-so, and nothing else has. "Sir
+Joseph Larmor is the Unionist candidate" means "Sir Joseph Larmor is a
+Unionist candidate, and no one else is." "The Unionist candidate
+exists" means "some one is a Unionist candidate, and no one else is."
+Thus, when we are acquainted with an object which we know to be the
+so-and-so, we know that the so-and-so exists but we may know that the
+so-and-so exists when we are not acquainted with any object which we
+know to be the so-and-so, and even when we are not acquainted with any
+object which, in fact, is the so-and-so.
+
+Common words, even proper names, are usually really descriptions. That
+is to say, the thought in the mind of a person using a proper name
+correctly can generally only be expressed explicitly if we replace the
+proper name by a description. Moreover, the description required to
+express the thought will vary for different people, or for the same
+person at different times. The only thing constant (so long as the
+name is rightly used) is the object to which the name applies. But so
+long as this remains constant, the particular description involved
+usually makes no difference to the truth or falsehood of the
+proposition in which the name appears.
+
+Let us take some illustrations. Suppose some statement made about
+Bismarck. Assuming that there is such a thing as direct acquaintance
+with oneself, Bismarck himself might have used his name directly to
+designate the particular person with whom he was acquainted. In this
+case, if he made a judgment about himself, he himself might be a
+constituent of the judgment. Here the proper name has the direct use
+which it always wishes to have, as simply standing for a certain
+object, and not for a description of the object. But if a person who
+knew Bismarck made a judgment about him, the case is different. What
+this person was acquainted with were certain sense-data which he
+connected (rightly, we will suppose) with Bismarck's body. His body as
+a physical object, and still more his mind, were only known as the
+body and the mind connected with these sense-data. That is, they were
+known by description. It is, of course, very much a matter of chance
+which characteristics of a man's appearance will come into a friend's
+mind when he thinks of him; thus the description actually in the
+friend's mind is accidental. The essential point is that he knows that
+the various descriptions all apply to the same entity, in spite of
+not being acquainted with the entity in question.
+
+When we, who did not know Bismarck, make a judgment about him, the
+description in our minds will probably be some more or less vague mass
+of historical knowledge--far more, in most cases, than is required to
+identify him. But, for the sake of illustration, let us assume that we
+think of him as "the first Chancellor of the German Empire." Here all
+the words are abstract except "German." The word "German" will again
+have different meanings for different people. To some it will recall
+travels in Germany, to some the look of Germany on the map, and so on.
+But if we are to obtain a description which we know to be applicable,
+we shall be compelled, at some point, to bring in a reference to a
+particular with which we are acquainted. Such reference is involved in
+any mention of past, present, and future (as opposed to definite
+dates), or of here and there, or of what others have told us. Thus it
+would seem that, in some way or other, a description known to be
+applicable to a particular must involve some reference to a particular
+with which we are acquainted, if our knowledge about the thing
+described is not to be merely what follows logically from the
+description. For example, "the most long-lived of men" is a
+description which must apply to some man, but we can make no judgments
+concerning this man which involve knowledge about him beyond what the
+description gives. If, however, we say, "the first Chancellor of the
+German Empire was an astute diplomatist," we can only be assured of
+the truth of our judgment in virtue of something with which we are
+acquainted--usually a testimony heard or read. Considered
+psychologically, apart from the information we convey to others, apart
+from the fact about the actual Bismarck, which gives importance to
+our judgment, the thought we really have contains the one or more
+particulars involved, and otherwise consists wholly of concepts. All
+names of places--London, England, Europe, the earth, the Solar
+System--similarly involve, when used, descriptions which start from
+some one or more particulars with which we are acquainted. I suspect
+that even the Universe, as considered by metaphysics, involves such a
+connection with particulars. In logic, on the contrary, where we are
+concerned not merely with what does exist, but with whatever might or
+could exist or be, no reference to actual particulars is involved.
+
+It would seem that, when we make a statement about something only
+known by description, we often _intend_ to make our statement, not in
+the form involving the description, but about the actual thing
+described. That is to say, when we say anything about Bismarck, we
+should like, if we could, to make the judgment which Bismarck alone
+can make, namely, the judgment of which he himself is a constituent.
+In this we are necessarily defeated, since the actual Bismarck is
+unknown to us. But we know that there is an object B called Bismarck,
+and that B was an astute diplomatist. We can thus _describe_ the
+proposition we should like to affirm, namely, "B was an astute
+diplomatist," where B is the object which was Bismarck. What enables
+us to communicate in spite of the varying descriptions we employ is
+that we know there is a true proposition concerning the actual
+Bismarck, and that, however we may vary the description (so long as
+the description is correct), the proposition described is still the
+same. This proposition, which is described and is known to be true, is
+what interests us; but we are not acquainted with the proposition
+itself, and do not know _it_, though we know it is true.
+
+It will be seen that there are various stages in the removal from
+acquaintance with particulars: there is Bismarck to people who knew
+him, Bismarck to those who only know of him through history, the man
+with the iron mask, the longest-lived of men. These are progressively
+further removed from acquaintance with particulars, and there is a
+similar hierarchy in the region of universals. Many universals, like
+many particulars, are only known to us by description. But here, as in
+the case of particulars, knowledge concerning what is known by
+description is ultimately reducible to knowledge concerning what is
+known by acquaintance.
+
+The fundamental epistemological principle in the analysis of
+propositions containing descriptions is this: _Every proposition which
+we can understand must be composed wholly of constituents with which
+we are acquainted._ From what has been said already, it will be plain
+why I advocate this principle, and how I propose to meet the case of
+propositions which at first sight contravene it. Let us begin with the
+reasons for supposing the principle true.
+
+The chief reason for supposing the principle true is that it seems
+scarcely possible to believe that we can make a judgment or entertain
+a supposition without knowing what it is that we are judging or
+supposing about. If we make a judgment about (say) Julius Cæsar, it is
+plain that the actual person who was Julius Cæsar is not a constituent
+of the judgment. But before going further, it may be well to explain
+what I mean when I say that this or that is a constituent of a
+judgment, or of a proposition which we understand. To begin with
+judgments: a judgment, as an occurrence, I take to be a relation of a
+mind to several entities, namely, the entities which compose what is
+judged. If, e.g. I judge that A loves B, the judgment as an event
+consists in the existence, at a certain moment, of a specific
+four-term relation, called _judging_, between me and A and love and B.
+That is to say, at the time when I judge, there is a certain complex
+whose terms are myself and A and love and B, and whose relating
+relation is _judging_. My reasons for this view have been set forth
+elsewhere,[41] and I shall not repeat them here. Assuming this view of
+judgment, the constituents of the judgment are simply the constituents
+of the complex which is the judgment. Thus, in the above case, the
+constituents are myself and A and love and B and judging. But myself
+and judging are constituents shared by all my judgments; thus the
+_distinctive_ constituents of the particular judgment in question are
+A and love and B. Coming now to what is meant by "understanding a
+proposition," I should say that there is another relation possible
+between me and A and love and B, which is called my _supposing_ that A
+loves B.[42] When we can _suppose_ that A loves B, we "understand the
+proposition" _A loves B_. Thus we often understand a proposition in
+cases where we have not enough knowledge to make a judgment.
+Supposing, like judging, is a many-term relation, of which a mind is
+one term. The other terms of the relation are called the constituents
+of the proposition supposed. Thus the principle which I enunciated may
+be re-stated as follows: _Whenever a relation of supposing or judging
+occurs, the terms to which the supposing or judging mind is related by
+the relation of supposing or judging must be terms with which the mind
+in question is acquainted._ This is merely to say that we cannot make
+a judgment or a supposition without knowing what it is that we are
+making our judgment or supposition about. It seems to me that the
+truth of this principle is evident as soon as the principle is
+understood; I shall, therefore, in what follows, assume the principle,
+and use it as a guide in analysing judgments that contain
+descriptions.
+
+Returning now to Julius Cæsar, I assume that it will be admitted that
+he himself is not a constituent of any judgment which I can make. But
+at this point it is necessary to examine the view that judgments are
+composed of something called "ideas," and that it is the "idea" of
+Julius Cæsar that is a constituent of my judgment. I believe the
+plausibility of this view rests upon a failure to form a right theory
+of descriptions. We may mean by my "idea" of Julius Cæsar the things
+that I know about him, e.g. that he conquered Gaul, was assassinated
+on the Ides of March, and is a plague to schoolboys. Now I am
+admitting, and indeed contending, that in order to discover what is
+actually in my mind when I judge about Julius Cæsar, we must
+substitute for the proper name a description made up of some of the
+things I know about him. (A description which will often serve to
+express my thought is "the man whose name was _Julius Cæsar_." For
+whatever else I may have forgotten about him, it is plain that when I
+mention him I have not forgotten that that was his name.) But although
+I think the theory that judgments consist of ideas may have been
+suggested in some such way, yet I think the theory itself is
+fundamentally mistaken. The view seems to be that there is some
+mental existent which may be called the "idea" of something outside
+the mind of the person who has the idea, and that, since judgment is a
+mental event, its constituents must be constituents of the mind of the
+person judging. But in this view ideas become a veil between us and
+outside things--we never really, in knowledge, attain to the things we
+are supposed to be knowing about, but only to the ideas of those
+things. The relation of mind, idea, and object, on this view, is
+utterly obscure, and, so far as I can see, nothing discoverable by
+inspection warrants the intrusion of the idea between the mind and the
+object. I suspect that the view is fostered by the dislike of
+relations, and that it is felt the mind could not know objects unless
+there were something "in" the mind which could be called the state of
+knowing the object. Such a view, however, leads at once to a vicious
+endless regress, since the relation of idea to object will have to be
+explained by supposing that the idea itself has an idea of the object,
+and so on _ad infinitum_. I therefore see no reason to believe that,
+when we are acquainted with an object, there is in us something which
+can be called the "idea" of the object. On the contrary, I hold that
+acquaintance is wholly a relation, not demanding any such constituent
+of the mind as is supposed by advocates of "ideas." This is, of
+course, a large question, and one which would take us far from our
+subject if it were adequately discussed. I therefore content myself
+with the above indications, and with the corollary that, in judging,
+the actual objects concerning which we judge, rather than any supposed
+purely mental entities, are constituents of the complex which is the
+judgment.
+
+When, therefore, I say that we must substitute for "Julius Cæsar" some
+description of Julius Cæsar, in order to discover the meaning of a
+judgment nominally about him, I am not saying that we must substitute
+an idea. Suppose our description is "the man whose name was _Julius
+Cæsar_." Let our judgment be "Julius Cæsar was assassinated." Then it
+becomes "the man whose name was _Julius Cæsar_ was assassinated." Here
+_Julius Cæsar_ is a noise or shape with which we are acquainted, and
+all the other constituents of the judgment (neglecting the tense in
+"was") are _concepts_ with which we are acquainted. Thus our judgment
+is wholly reduced to constituents with which we are acquainted, but
+Julius Cæsar himself has ceased to be a constituent of our judgment.
+This, however, requires a proviso, to be further explained shortly,
+namely that "the man whose name was _Julius Cæsar_" must not, as a
+whole, be a constituent of our judgment, that is to say, this phrase
+must not, as a whole, have a meaning which enters into the judgment.
+Any right analysis of the judgment, therefore, must break up this
+phrase, and not treat it as a subordinate complex which is part of the
+judgment. The judgment "the man whose name was _Julius Cæsar_ was
+assassinated" may be interpreted as meaning "one and only one man was
+called _Julius Cæsar_, and that one was assassinated." Here it is
+plain that there is no constituent corresponding to the phrase "the
+man whose name was _Julius Cæsar_." Thus there is no reason to regard
+this phrase as expressing a constituent of the judgment, and we have
+seen that this phrase must be broken up if we are to be acquainted
+with all the constituents of the judgment. This conclusion, which we
+have reached from considerations concerned with the theory of
+knowledge, is also forced upon us by logical considerations, which
+must now be briefly reviewed.
+
+It is common to distinguish two aspects, _meaning_ and _denotation_,
+such phrases as "the author of Waverley." The meaning will be a
+certain complex, consisting (at least) of authorship and Waverley with
+some relation; the denotation will be Scott. Similarly "featherless
+bipeds" will have a complex meaning, containing as constituents the
+presence of two feet and the absence of feathers, while its denotation
+will be the class of men. Thus when we say "Scott is the author of
+Waverley" or "men are the same as featherless bipeds," we are
+asserting an identity of denotation, and this assertion is worth
+making because of the diversity of meaning.[43] I believe that the
+duality of meaning and denotation, though capable of a true
+interpretation, is misleading if taken as fundamental. The denotation,
+I believe, is not a constituent of the proposition, except in the case
+of proper names, i.e. of words which do not assign a property to an
+object, but merely and solely name it. And I should hold further that,
+in this sense, there are only two words which are strictly proper
+names of particulars, namely, "I" and "this."[44]
+
+One reason for not believing the denotation to be a constituent of the
+proposition is that we may know the proposition even when we are not
+acquainted with the denotation. The proposition "the author of
+Waverley is a novelist" was known to people who did not know that "the
+author of Waverley" denoted Scott. This reason has been already
+sufficiently emphasised.
+
+A second reason is that propositions concerning "the so-and-so" are
+possible even when "the so-and-so" has no denotation. Take, e.g. "the
+golden mountain does not exist" or "the round square is
+self-contradictory." If we are to preserve the duality of meaning and
+denotation, we have to say, with Meinong, that there are such objects
+as the golden mountain and the round square, although these objects do
+not have being. We even have to admit that the existent round square
+is existent, but does not exist.[45] Meinong does not regard this as a
+contradiction, but I fail to see that it is not one. Indeed, it seems
+to me evident that the judgment "there is no such object as the round
+square" does not presuppose that there is such an object. If this is
+admitted, however, we are led to the conclusion that, by parity of
+form, no judgment concerning "the so-and-so" actually involves the
+so-and-so as a constituent.
+
+Miss Jones[46] contends that there is no difficulty in admitting
+contradictory predicates concerning such an object as "the present
+King of France," on the ground that this object is in itself
+contradictory. Now it might, of course, be argued that this object,
+unlike the round square, is not self-contradictory, but merely
+non-existent. This, however, would not go to the root of the matter.
+The real objection to such an argument is that the law of
+contradiction ought not to be stated in the traditional form "A is not
+both B and not B," but in the form "no proposition is both true and
+false." The traditional form only applies to certain propositions,
+namely, to those which attribute a predicate to a subject. When the
+law is stated of propositions, instead of being stated concerning
+subjects and predicates, it is at once evident that propositions about
+the present King of France or the round square can form no exception,
+but are just as incapable of being both true and false as other
+propositions. Miss Jones[47] argues that "Scott is the author of
+Waverley" asserts identity of denotation between _Scott_ and _the
+author of Waverley_. But there is some difficulty in choosing among
+alternative meanings of this contention. In the first place, it should
+be observed that _the author of Waverley_ is not a _mere_ name, like
+_Scott_. _Scott_ is merely a noise or shape conventionally used to
+designate a certain person; it gives us no information about that
+person, and has nothing that can be called meaning as opposed to
+denotation. (I neglect the fact, considered above, that even proper
+names, as a rule, really stand for descriptions.) But _the author of
+Waverley_ is not merely conventionally a name for Scott; the element
+of mere convention belongs here to the separate words, _the_ and
+_author_ and _of_ and _Waverley_. Given what these words stand for,
+_the author of Waverley_ is no longer arbitrary. When it is said that
+Scott is the author of Waverley, we are not stating that these are two
+_names_ for one man, as we should be if we said "Scott is Sir Walter."
+A man's name is what he is called, but however much Scott had been
+called the author of Waverley, that would not have made him be the
+author; it was necessary for him actually to write Waverley, which was
+a fact having nothing to do with names.
+
+If, then, we are asserting identity of denotation, we must not mean by
+_denotation_ the mere relation of a name to the thing named. In fact,
+it would be nearer to the truth to say that the _meaning_ of "Scott"
+is the _denotation_ of "the author of Waverley." The relation of
+"Scott" to Scott is that "Scott" means Scott, just as the relation of
+"author" to the concept which is so called is that "author" means this
+concept. Thus if we distinguish meaning and denotation in "the author
+of Waverley," we shall have to say that "Scott" has meaning but not
+denotation. Also when we say "Scott is the author of Waverley," the
+_meaning_ of "the author of Waverley" is relevant to our assertion.
+For if the denotation alone were relevant, any other phrase with the
+same denotation would give the same proposition. Thus "Scott is the
+author of Marmion" would be the same proposition as "Scott is the
+author of Waverley." But this is plainly not the case, since from the
+first we learn that Scott wrote Marmion and from the second we learn
+that he wrote Waverley, but the first tells us nothing about Waverley
+and the second nothing about Marmion. Hence the meaning of "the author
+of Waverley," as opposed to the denotation, is certainly relevant to
+"Scott is the author of Waverley."
+
+We have thus agreed that "the author of Waverley" is not a mere name,
+and that its meaning is relevant in propositions in which it occurs.
+Thus if we are to say, as Miss Jones does, that "Scott is the author
+of Waverley" asserts an identity of denotation, we must regard the
+denotation of "the author of Waverley" as the denotation of what is
+_meant_ by "the author of Waverley." Let us call the meaning of "the
+author of Waverley" M. Thus M is what "the author of Waverley" means.
+Then we are to suppose that "Scott is the author of Waverley" means
+"Scott is the denotation of M." But here we are explaining our
+proposition by another of the same form, and thus we have made no
+progress towards a real explanation. "The denotation of M," like "the
+author of Waverley," has both meaning and denotation, on the theory we
+are examining. If we call its meaning M', our proposition becomes
+"Scott is the denotation of M'." But this leads at once to an endless
+regress. Thus the attempt to regard our proposition as asserting
+identity of denotation breaks down, and it becomes imperative to find
+some other analysis. When this analysis has been completed, we shall
+be able to reinterpret the phrase "identity of denotation," which
+remains obscure so long as it is taken as fundamental.
+
+The first point to observe is that, in any proposition about "the
+author of Waverley," provided Scott is not explicitly mentioned, the
+denotation itself, i.e. Scott, does not occur, but only the concept of
+denotation, which will be represented by a variable. Suppose we say
+"the author of Waverley was the author of Marmion," we are certainly
+not saying that both were Scott--we may have forgotten that there was
+such a person as Scott. We are saying that there is some man who was
+the author of Waverley and the author of Marmion. That is to say,
+there is some one who wrote Waverley and Marmion, and no one else
+wrote them. Thus the identity is that of a variable, i.e. of an
+indefinite subject, "some one." This is why we can understand
+propositions about "the author of Waverley," without knowing who he
+was. When we say "the author of Waverley was a poet," we mean "one and
+only one man wrote Waverley, and he was a poet"; when we say "the
+author of Waverley was Scott" we mean "one and only one man wrote
+Waverley, and he was Scott." Here the identity is between a variable,
+i.e. an indeterminate subject ("he"), and Scott; "the author of
+Waverley" has been analysed away, and no longer appears as a
+constituent of the proposition.[48]
+
+The reason why it is imperative to analyse away the phrase "the author
+of Waverley" may be stated as follows. It is plain that when we say
+"the author of Waverley is the author of Marmion," the _is_ expresses
+identity. We have seen also that the common _denotation_, namely
+Scott, is not a constituent of this proposition, while the _meanings_
+(if any) of "the author of Waverley" and "the author of Marmion" are
+not identical. We have seen also that, in any sense in which the
+meaning of a word is a constituent of a proposition in whose verbal
+expression the word occurs, "Scott" means the actual man Scott, in the
+same sense (so far as concerns our present discussion) in which
+"author" means a certain universal. Thus, if "the author of Waverley"
+were a subordinate complex in the above proposition, its _meaning_
+would have to be what was said to be identical with the _meaning_ of
+"the author of Marmion." This is plainly not the case; and the only
+escape is to say that "the author of Waverley" does not, by itself,
+have a meaning, though phrases of which it is part do have a meaning.
+That is, in a right analysis of the above proposition, "the author of
+Waverley" must disappear. This is effected when the above proposition
+is analysed as meaning: "Some one wrote Waverley and no one else did,
+and that some one also wrote Marmion and no one else did." This may be
+more simply expressed by saying that the propositional function "_x_
+wrote Waverley and Marmion, and no one else did" is capable of truth,
+i.e. some value of _x_ makes it true, but no other value does. Thus
+the true subject of our judgment is a propositional function, i.e. a
+complex containing an undetermined constituent, and becoming a
+proposition as soon as this constituent is determined.
+
+We may now define the denotation of a phrase. If we know that the
+proposition "_a_ is the so-and-so" is true, i.e. that _a_ is so-and-so
+and nothing else is, we call _a_ the denotation of the phrase "the
+so-and-so." A very great many of the propositions we naturally make
+about "the so-and-so" will remain true or remain false if we
+substitute _a_ for "the so-and-so," where _a_ is the denotation of
+"the so-and-so." Such propositions will also remain true or remain
+false if we substitute for "the so-and-so" any other phrase having the
+same denotation. Hence, as practical men, we become interested in the
+denotation more than in the description, since the denotation decides
+as to the truth or falsehood of so many statements in which the
+description occurs. Moreover, as we saw earlier in considering the
+relations of description and acquaintance, we often wish to reach the
+denotation, and are only hindered by lack of acquaintance: in such
+cases the description is merely the means we employ to get as near as
+possible to the denotation. Hence it naturally comes to be supposed
+that the denotation is part of the proposition in which the
+description occurs. But we have seen, both on logical and on
+epistemological grounds, that this is an error. The actual object (if
+any) which is the denotation is not (unless it is explicitly
+mentioned) a constituent of propositions in which descriptions occur;
+and this is the reason why, in order to understand such propositions,
+we need acquaintance with the constituents of the description, but do
+not need acquaintance with its denotation. The first result of
+analysis, when applied to propositions whose grammatical subject is
+"the so-and-so," is to substitute a variable as subject; i.e. we
+obtain a proposition of the form: "There is _something_ which alone is
+so-and-so, and that _something_ is such-and-such." The further
+analysis of propositions concerning "the so-and-so" is thus merged in
+the problem of the nature of the variable, i.e. of the meanings of
+_some_, _any_, and _all_. This is a difficult problem, concerning
+which I do not intend to say anything at present.
+
+To sum up our whole discussion. We began by distinguishing two sorts
+of knowledge of objects, namely, knowledge by _acquaintance_ and
+knowledge by _description_. Of these it is only the former that brings
+the object itself before the mind. We have acquaintance with
+sense-data, with many universals, and possibly with ourselves, but not
+with physical objects or other minds. We have _descriptive_ knowledge
+of an object when we know that it is _the_ object having some property
+or properties with which we are acquainted; that is to say, when we
+know that the property or properties in question belong to one object
+and no more, we are said to have knowledge of that one object by
+description, whether or not we are acquainted with the object. Our
+knowledge of physical objects and of other minds is only knowledge by
+description, the descriptions involved being usually such as involve
+sense-data. All propositions intelligible to us, whether or not they
+primarily concern things only known to us by description, are composed
+wholly of constituents with which we are acquainted, for a constituent
+with which we are not acquainted is unintelligible to us. A judgment,
+we found, is not composed of mental constituents called "ideas," but
+consists of an occurrence whose constituents are a mind[49] and
+certain objects, particulars or universals. (One at least must be a
+universal.) When a judgment is rightly analysed, the objects which are
+constituents of it must all be objects with which the mind which is a
+constituent of it is acquainted. This conclusion forces us to analyse
+descriptive phrases occurring in propositions, and to say that the
+objects denoted by such phrases are not constituents of judgments in
+which such phrases occur (unless these objects are explicitly
+mentioned). This leads us to the view (recommended also on purely
+logical grounds) that when we say "the author of Marmion was the
+author of Waverley," Scott himself is not a constituent of our
+judgment, and that the judgment cannot be explained by saying that it
+affirms identity of denotation with diversity of meaning. It also,
+plainly, does not assert identity of meaning. Such judgments,
+therefore, can only be analysed by breaking up the descriptive
+phrases, introducing a variable, and making propositional functions
+the ultimate subjects. In fact, "the so-and-so is such-and-such" will
+mean that "_x_ is so-and-so and nothing else is, and _x_ is
+such-and-such" is capable of truth. The analysis of such judgments
+involves many fresh problems, but the discussion of these problems is
+not undertaken in the present paper.
+
+FOOTNOTES:
+
+[40] See references later.
+
+[41] _Philosophical Essays_, "The Nature of Truth." I have been
+persuaded by Mr. Wittgenstein that this theory is somewhat unduly
+simple, but the modification which I believe it to require does not
+affect the above argument [1917].
+
+[42] Cf. Meinong, _Ueber Annahmen_, _passim_. I formerly supposed,
+contrary to Meinong's view, that the relationship of supposing might
+be merely that of presentation. In this view I now think I was
+mistaken, and Meinong is right. But my present view depends upon the
+theory that both in judgment and in assumption there is no single
+Objective, but the several constituents of the judgment or assumption
+are in a many-term relation to the mind.
+
+[43] This view has been recently advocated by Miss E.E.C. Jones. "A
+New Law of Thought and its Implications," _Mind_, January, 1911.
+
+[44] I should now exclude "I" from proper names in the strict sense,
+and retain only "this" [1917].
+
+[45] Meinong, _Ueber Annahmen_, 2nd ed., Leipzig, 1910, p. 141.
+
+[46] _Mind_, July, 1910, p. 380.
+
+[47] _Mind_, July, 1910, p. 379.
+
+[48] The theory which I am advocating is set forth fully, with the
+logical grounds in its favour, in _Principia Mathematica_, Vol. I.
+Introduction, Chap. III; also, less fully, in _Mind_, October, 1905.
+
+[49] I use this phrase merely to denote the something psychological
+which enters into judgment, without intending to prejudge the question
+as to what this something is.
+
+
+
+
+INDEX
+
+
+Achilles and the tortoise, 80 ff, 89 ff
+
+Acquaintance, the relation of, 209 ff
+
+Alexander, 125
+
+American Realists, the, 134
+
+Aristotle, 42, 76, 97
+
+
+Bacon, 41
+
+Bergson, 14 ff, 22, 105, 128, 185 ff, 203
+
+Berkeley, 97, 132
+
+Blake, 1
+
+Bosanquet, 99
+
+Broad, 89 _n_
+
+
+Calculus, the, 82
+
+Cantor, Georg, 64, 81 ff, 85, 91
+
+Carlyle, 50, 82
+
+Cause, the conception of, 135 _n_, 180 ff
+
+Christianity and renunciation, 51
+
+Chuang Tz[)u], 106
+
+Construction of permanent things and matter, 169 ff
+
+Constructions, logical, 155 ff
+
+
+Darwin, 15, 23, 43
+
+Dedekind, 64, 81 ff, 85
+
+Descartes, 97, 126
+
+Descriptions, 175, 214 ff
+
+
+Education, 37 ff
+
+Euclid, 62, 92, 94
+
+Evolutionism, 23 ff, 28
+
+
+Fano, 93
+
+Faraday, 34
+
+Free will, 205 ff
+
+Frege, 78 _n_
+
+
+Galileo, 42
+
+Gladstone, 177
+
+Good and evil, 26 ff
+
+
+Hegel, 8, 10, 18, 85, 97, 105 ff
+
+Heine, 113
+
+Heraclitus, 1 ff, 10
+
+Hertz, 34
+
+Holt, 177 _n_
+
+Hume, 1, 97
+
+
+Infinite, the mathematical, 84 ff
+
+
+James, William, 100
+
+Jones, Miss E.E.C., 224 _n_, 225
+
+Judgment, 219 ff
+
+
+Kant, 85, 96, 97, 99, 118 ff
+
+Knowledge by acquaintance, 209 ff;
+  by description, 214 ff
+
+
+Laplace, 23
+
+Leibniz, 76, 79, 82 ff, 97, 126, 144, 160
+
+Locke, 97
+
+Logic, the laws of, 68 ff
+
+
+Macaulay and Taylor's theorem, 95
+
+Malthus, 43
+
+Mathematics, 58 ff;
+  and the Metaphysicians, 74 ff;
+  and logic, 75 ff;
+  and the infinitesimal, 82 ff
+
+Matter, the nature of, 125 ff;
+  definition of, 164 ff
+
+Maxwell, 34
+
+Meaning and denotation, 223 ff
+
+Meinong, 174, 220 _n_, 225
+
+Militarism, 50
+
+Mill, 185, 193 ff
+
+Mysticism and logic, 1 ff
+
+
+Necessity, the notion of, 207 ff
+
+Nietzsche, 22, 50
+
+Nunn, 125, 137 _n_, 153
+
+
+Parmenides, 7 ff, 18, 21
+
+Particulars, awareness of, 210 ff
+
+Peano, 78 ff, 93 ff
+
+Perspectives, 139 ff;
+  the space of, 158 ff
+
+Philosophy and logic, 111
+
+Physics, sense-data and, 145 ff
+
+Pierce, 76 _n_
+
+Plato, 1 ff, 10, 30, 60, 97
+
+Pragmatism, 22, 105
+
+
+Realism and the analytic method, 120 ff
+
+Reason and intuition, 12 ff
+
+Relatives, the logic of, 76
+
+Robb, 167 _n_
+
+
+Santayana, 20
+
+Sense-data, 147, 210 ff;
+  and physics, 145 ff
+
+Sensibilia, 148 ff
+
+Space, 138 ff;
+  private, 158 ff;
+  the logical problem, 114 ff;
+  the problem in physics, 115 ff;
+  the epistemological problem, 118 ff
+
+Systems, deterministic, 199;
+  practically isolated, 198;
+  relatively isolated, 197;
+  mechanical, 201
+
+
+Time, 10, 21 ff, 141 ff, 167 ff
+
+Tristram Shandy, the paradox of, 90 ff
+
+
+Unity and Plurality, 18 ff
+
+Universals, awareness of, 212 ff
+
+
+Ward, 180
+
+Weierstrass, 80, 82, 95
+
+Whitehead, 117, 157, 175
+
+Wolf, 173
+
+
+Zeno the Eleatic, 64, 80, 84, 89 ff
+
+
+
+
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+
+Project Gutenberg's Mysticism and Logic and Other Essays, by Bertrand Russell
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Mysticism and Logic and Other Essays
+
+Author: Bertrand Russell
+
+Release Date: May 12, 2008 [EBook #25447]
+[Last updated: May 24, 2012]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK MYSTICISM AND LOGIC ***
+
+
+
+
+Produced by Jeannie Howse, Adrian Mastronardi and the
+Online Distributed Proofreading Team at http://www.pgdp.net
+(This file was produced from images generously made
+available by The Internet Archive/Canadian Libraries)
+
+
+
+
+
+
+</pre>
+
+
+<br />
+<hr />
+<br />
+
+<div class="tr">
+<p class="cen" style="font-weight: bold;">Transcriber's Note:</p>
+<br />
+<p class="noin">Inconsistent hyphenation in the original document has been preserved.</p>
+<p class="noin">The link to the Index has been added for the benefit of easy access.</p>
+<p class="noin" style="text-align: left;">Obvious typographical errors have been corrected.
+For a complete list, please see the <span style="white-space: nowrap;"><a href="#TN">end of this document</a>.</span></p>
+</div>
+
+<br />
+<hr />
+<br />
+<br />
+<br />
+
+
+<h2>BERTRAND RUSSELL</h2>
+
+<h1>MYSTICISM AND
+LOGIC</h1>
+
+<h2>AND OTHER ESSAYS</h2>
+
+<br />
+<br />
+<br />
+<br />
+<br />
+<br />
+<br />
+<br />
+<br />
+<br />
+<br />
+<br />
+<br />
+<br />
+<br />
+
+<h4><i>LONDON</i><br />
+GEORGE ALLEN &amp; UNWIN LTD<br />
+RUSKIN HOUSE MUSEUM STREET</h4>
+
+<br />
+<br />
+<br />
+<hr />
+<br />
+<br />
+<br />
+<br />
+
+<h4>MYSTICISM AND LOGIC<br />
+AND OTHER ESSAYS</h4>
+
+<br />
+<br />
+<br />
+<br />
+<hr />
+<br />
+
+<h4>BY BERTRAND RUSSELL</h4>
+
+<p class="cen"><i>The ABC of Relativity</i><br />
+<i>The Analysis of Matter</i><br />
+<i>Human Society in Ethics and Politics</i><br />
+<i>The Impact of Science on Society</i><br />
+<i>New Hopes for a Changing World</i><br />
+<i>Authority and the Individual</i><br />
+<i>Human Knowledge</i><br />
+<i>History of Western Philosophy</i><br />
+<i>The Principles of Mathematics</i><br />
+<i>Introduction to Mathematical Philosophy</i><br />
+<i>The Analysis of Mind</i><br />
+<i>Our Knowledge of the External World</i><br />
+<i>An Outline of Philosophy</i><br />
+<i>The Philosophy of Leibniz</i><br />
+<i>An Inquiry into Meaning and Truth</i><br />
+<i>Logic and Knowledge</i><br />
+<i>The Problems of Philosophy</i><br />
+<i>Principia Mathematica</i></p>
+
+<p class="cen"><i>Common Sense and Nuclear Warfare</i><br />
+<i>Why I am Not a Christian</i><br />
+<i>Portraits from Memory</i><br />
+<i>My Philosophical Development</i><br />
+<i>Unpopular Essays</i><br />
+<i>Power</i><br />
+<i>In Praise of Idleness</i><br />
+<i>The Conquest of Happiness</i><br />
+<i>Sceptical Essays</i><br />
+<i>The Scientific Outlook</i><br />
+<i>Marriage and Morals</i><br />
+<i>Education and the Social Order</i><br />
+<i>On Education</i></p>
+
+<p class="cen"><i>Freedom and Organization</i><br />
+<i>Principles of Social Reconstruction</i><br />
+<i>Roads to Freedom</i><br />
+<i>Practice and Theory of Bolshevism</i></p>
+
+<p class="cen"><i>Satan in The Suburbs</i><br />
+<i>Nightmares of Eminent Persons</i></p>
+
+<br />
+<hr />
+<br />
+
+<div class="centered">
+<table border="0" cellpadding="0" cellspacing="0" width="60%" summary="dates published">
+  <tr>
+  <td class="tdl" width="70%"><i>First published as "Philosophical Essays"</i></td>
+  <td class="tdr" width="30%"><i>October 1910</i></td>
+  </tr>
+  <tr>
+  <td class="tdl"><i>Second Edition as "Mysticism and Logic"</i></td>
+  <td class="tdr"><i>December 1917</i></td>
+  </tr>
+  <tr>
+  <td class="tdl"><i>Third Impression</i></td>
+  <td class="tdr"><i>April 1918</i></td>
+  </tr>
+  <tr>
+  <td class="tdl"><i>Fourth Impression</i></td>
+  <td class="tdr"><i>February 1919</i></td>
+  </tr>
+  <tr>
+  <td class="tdl"><i>Fifth Impression</i></td>
+  <td class="tdr"><i>October 1921</i></td>
+  </tr>
+  <tr>
+  <td class="tdl"><i>Sixth Impression</i></td>
+  <td class="tdr"><i>August 1925</i></td>
+  </tr>
+  <tr>
+  <td class="tdl"><i>Seventh Impression</i></td>
+  <td class="tdr"><i>January 1932</i></td>
+  </tr>
+  <tr>
+  <td class="tdl"><i>Eighth Impression</i></td>
+  <td class="tdr"><i>1949</i></td>
+  </tr>
+  <tr>
+  <td class="tdl"><i>Ninth Impression</i></td>
+  <td class="tdr"><i>1950</i></td>
+  </tr>
+  <tr>
+  <td class="tdl"><i>Tenth Impression</i></td>
+  <td class="tdr"><i>1951</i></td>
+  </tr>
+  <tr>
+  <td class="tdl"><i>Eleventh Impression</i></td>
+  <td class="tdr"><i>1959</i></td>
+  </tr>
+</table>
+</div>
+
+<br />
+
+<div class="block2"><p><i>This book is copyright under the Berne Convention. Apart from any
+fair dealing for the purpose of private study, research, criticism
+or review, as permitted under the Copyright Act, 1956, no portion
+may be reproduced by any process without written permission.
+Enquiry should be made to the publisher.</i></p></div>
+
+
+<h5>PRINTED IN GREAT BRITAIN<br />
+<i>by Taylor Garnett Evans &amp; Co. Ltd.,<br />
+Watford, Herts.</i></h5>
+
+<br />
+<br />
+<br />
+<br />
+<hr />
+<span class='pagenum'><a name="Page_v" id="Page_v">[v]</a></span><br />
+
+<h3>PREFACE</h3>
+<br />
+
+<p>The following essays have been written and published at various times,
+and my thanks are due to the previous publishers for the permission to
+reprint them.</p>
+
+<p>The essay on "Mysticism and Logic" appeared in the <i>Hibbert Journal</i>
+for July, 1914. "The Place of Science in a Liberal Education" appeared
+in two numbers of <i>The New Statesman</i>, May 24 and 31, 1913. "The Free
+Man's Worship" and "The Study of Mathematics" were included in a
+former collection (now out of print), <i>Philosophical Essays</i>, also
+published by Messrs. Longmans, Green &amp; Co. Both were written in 1902;
+the first appeared originally in the <i>Independent Review</i> for 1903,
+the second in the <i>New Quarterly</i>, November, 1907. In theoretical
+Ethics, the position advocated in "The Free Man's Worship" is not
+quite identical with that which I hold now: I feel less convinced than
+I did then of the objectivity of good and evil. But the general
+attitude towards life which is suggested in that essay still seems to
+me, in the main, the one which must be adopted in times of stress and
+difficulty by those who have no dogmatic religious beliefs, if inward
+defeat is to be avoided.</p>
+
+<p>The essay on "Mathematics and the Metaphysicians" was written in 1901,
+and appeared in an American magazine, <i>The International Monthly</i>,
+under the title "Recent Work in the Philosophy of Mathematics." Some
+points <span class='pagenum'><a name="Page_vi" id="Page_vi">[vi]</a></span>in this essay require modification in view of later work.
+These are indicated in footnotes. Its tone is partly explained by the
+fact that the editor begged me to make the article "as romantic as
+possible."</p>
+
+<p>All the above essays are entirely popular, but those that follow are
+somewhat more technical. "On Scientific Method in Philosophy" was the
+Herbert Spencer lecture at Oxford in 1914, and was published by the
+Clarendon Press, which has kindly allowed me to include it in this
+collection. "The Ultimate Constituents of Matter" was an address to
+the Manchester Philosophical Society, early in 1915, and was published
+in the <i>Monist</i> in July of that year. The essay on "The Relation of
+Sense-data to Physics" was written in January, 1914, and first
+appeared in No. 4 of that year's volume of <i>Scientia</i>, an
+International Review of Scientific Synthesis, edited by M. Eugenio
+Rignano, published monthly by Messrs. Williams and Norgate, London,
+Nicola Zanichelli, Bologna, and F&eacute;lix Alcan, Paris. The essay "On the
+Notion of Cause" was the presidential address to the Aristotelian
+Society in November, 1912, and was published in their <i>Proceedings</i>
+for 1912-13. "Knowledge by Acquaintance and Knowledge by Description"
+was also a paper read before the Aristotelian Society, and published
+in their <i>Proceedings</i> for 1910-11.</p>
+
+<p><span class="sc">London,</span><br />
+<span style="margin-left: 2em;"><i>September, 1917</i></span></p>
+
+<br />
+<br />
+<br />
+<br />
+<a name="toc" id="toc"></a><hr />
+<span class='pagenum'><a name="Page_vii" id="Page_vii">[vii]</a></span><br />
+
+<h3>CONTENTS</h3>
+<br />
+
+<div class="centered">
+<table border="0" cellpadding="2" cellspacing="0" width="70%" summary="Table of Contents">
+  <tr>
+  <td class="tdr" width="10%" style="font-size: 90%;"><i>Chapter</i></td>
+  <td class="tdl" width="70%">&nbsp;</td>
+  <td class="tdr" width="20%" style="font-size: 90%;"><i>Page</i></td>
+  </tr>
+  <tr>
+  <td class="tdr">I.</td>
+  <td class="tdl"><a href="#I"><i>Mysticism and Logic</i></a></td>
+  <td class="tdr">1</td>
+  </tr>
+  <tr>
+  <td class="tdr">II.</td>
+  <td class="tdl"><a href="#II"><i>The Place of Science in a Liberal Education</i></a></td>
+  <td class="tdr">33</td>
+  </tr>
+  <tr>
+  <td class="tdr">III.</td>
+  <td class="tdl"><a href="#III"><i>A Free Man's Worship</i></a></td>
+  <td class="tdr">46</td>
+  </tr>
+  <tr>
+  <td class="tdr">IV.</td>
+  <td class="tdl"><a href="#IV"><i>The Study of Mathematics</i></a></td>
+  <td class="tdr">58</td>
+  </tr>
+  <tr>
+  <td class="tdr">V.</td>
+  <td class="tdl"><a href="#V"><i>Mathematics and the Metaphysicians</i></a></td>
+  <td class="tdr">74</td>
+  </tr>
+  <tr>
+  <td class="tdr">VI.</td>
+  <td class="tdl"><a href="#VI"><i>On Scientific Method in Philosophy</i></a></td>
+  <td class="tdr">97</td>
+  </tr>
+  <tr>
+  <td class="tdr">VII.</td>
+  <td class="tdl"><a href="#VII"><i>The Ultimate Constituents of Matter</i></a></td>
+  <td class="tdr">125</td>
+  </tr>
+  <tr>
+  <td class="tdr">VIII.</td>
+  <td class="tdl"><a href="#VIII"><i>The Relation of Sense-data to Physics</i></a></td>
+  <td class="tdr">145</td>
+  </tr>
+  <tr>
+  <td class="tdr">IX.</td>
+  <td class="tdl"><a href="#IX"><i>On the Notion of Cause</i></a></td>
+  <td class="tdr">180</td>
+  </tr>
+  <tr>
+  <td class="tdr">X.</td>
+  <td class="tdl"><a href="#X"><i>Knowledge by Acquaintance and Knowledge by Description</i></a></td>
+  <td class="tdr">209</td>
+  </tr>
+  <tr>
+  <td class="tdr">&nbsp;</td>
+  <td class="tdl"><a href="#INDEX">Index</a></td>
+  <td class="tdr">233</td>
+  </tr>
+</table>
+</div>
+
+<br />
+<br />
+<br />
+<br />
+<a name="I" id="I"></a><hr />
+<span class='pagenum'><a name="Page_1" id="Page_1">[1]</a></span><br />
+<br />
+<br />
+<br />
+
+<h1>MYSTICISM AND LOGIC<br /> AND OTHER ESSAYS</h1>
+
+<br />
+<br />
+
+<h3>I<span class="totoc"><a href="#toc">ToC</a></span></h3>
+
+<h4>MYSTICISM AND LOGIC</h4>
+<br />
+
+<p>Metaphysics, or the attempt to conceive the world as a whole by means
+of thought, has been developed, from the first, by the union and
+conflict of two very different human impulses, the one urging men
+towards mysticism, the other urging them towards science. Some men
+have achieved greatness through one of these impulses alone, others
+through the other alone: in Hume, for example, the scientific impulse
+reigns quite unchecked, while in Blake a strong hostility to science
+co-exists with profound mystic insight. But the greatest men who have
+been philosophers have felt the need both of science and of mysticism:
+the attempt to harmonise the two was what made their life, and what
+always must, for all its arduous uncertainty, make philosophy, to some
+minds, a greater thing than either science or religion.</p>
+
+<p>Before attempting an explicit characterisation of the scientific and
+the mystical impulses, I will illustrate them by examples from two
+philosophers whose greatness lies in the very intimate blending which
+they achieved. The two philosophers I mean are Heraclitus and Plato.</p>
+
+<p><span class='pagenum'><a name="Page_2" id="Page_2">[2]</a></span>Heraclitus, as every one knows, was a believer in universal flux: time
+builds and destroys all things. From the few fragments that remain, it
+is not easy to discover how he arrived at his opinions, but there are
+some sayings that strongly suggest scientific observation as the
+source.</p>
+
+<p>"The things that can be seen, heard, and learned," he says, "are what
+I prize the most." This is the language of the empiricist, to whom
+observation is the sole guarantee of truth. "The sun is new every
+day," is another fragment; and this opinion, in spite of its
+paradoxical character, is obviously inspired by scientific reflection,
+and no doubt seemed to him to obviate the difficulty of understanding
+how the sun can work its way underground from west to east during the
+night. Actual observation must also have suggested to him his central
+doctrine, that Fire is the one permanent substance, of which all
+visible things are passing phases. In combustion we see things change
+utterly, while their flame and heat rise up into the air and vanish.</p>
+
+<p>"This world, which is the same for all," he says, "no one of gods or
+men has made; but it was ever, is now, and ever shall be, an
+ever-living Fire, with measures kindling, and measures going out."</p>
+
+<p>"The transformations of Fire are, first of all, sea; and half of the
+sea is earth, half whirlwind."</p>
+
+<p>This theory, though no longer one which science can accept, is
+nevertheless scientific in spirit. Science, too, might have inspired
+the famous saying to which Plato alludes: "You cannot step twice into
+the same rivers; for fresh waters are ever flowing in upon you." But
+we find also another statement among the extant fragments: "We step
+and do not step into the same rivers; we are and are not."</p>
+
+<p><span class='pagenum'><a name="Page_3" id="Page_3">[3]</a></span>The comparison of this statement, which is mystical, with the one
+quoted by Plato, which is scientific, shows how intimately the two
+tendencies are blended in the system of Heraclitus. Mysticism is, in
+essence, little more than a certain intensity and depth of feeling in
+regard to what is believed about the universe; and this kind of
+feeling leads Heraclitus, on the basis of his science, to strangely
+poignant sayings concerning life and the world, such as:</p>
+
+<p>"Time is a child playing draughts, the kingly power is a child's."</p>
+
+<p>It is poetic imagination, not science, which presents Time as despotic
+lord of the world, with all the irresponsible frivolity of a child. It
+is mysticism, too, which leads Heraclitus to assert the identity of
+opposites: "Good and ill are one," he says; and again: "To God all
+things are fair and good and right, but men hold some things wrong and
+some right."</p>
+
+<p>Much of mysticism underlies the ethics of Heraclitus. It is true that
+a scientific determinism alone might have inspired the statement:
+"Man's character is his fate"; but only a mystic would have said:</p>
+
+<p>"Every beast is driven to the pasture with blows"; and again:</p>
+
+<p>"It is hard to fight with one's heart's desire. Whatever it wishes to
+get, it purchases at the cost of soul"; and again:</p>
+
+<p>"Wisdom is one thing. It is to know the thought by which all things
+are steered through all things."<a name="FNanchor_1_1" id="FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a></p>
+
+<p>Examples might be multiplied, but those that have been given are
+enough to show the character of the man: the facts of science, as they
+appeared to him, fed the <span class='pagenum'><a name="Page_4" id="Page_4">[4]</a></span>flame in his soul, and in its light he saw
+into the depths of the world by the reflection of his own dancing
+swiftly penetrating fire. In such a nature we see the true union of
+the mystic and the man of science&mdash;the highest eminence, as I think,
+that it is possible to achieve in the world of thought.</p>
+
+<p>In Plato, the same twofold impulse exists, though the mystic impulse
+is distinctly the stronger of the two, and secures ultimate victory
+whenever the conflict is sharp. His description of the cave is the
+classical statement of belief in a knowledge and reality truer and
+more real than that of the senses:</p>
+
+<div class="block">
+<p>"Imagine<a name="FNanchor_2_2" id="FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a> a number of men living in an underground cavernous
+chamber, with an entrance open to the light, extending along the
+entire length of the cavern, in which they have been confined, from
+their childhood, with their legs and necks so shackled that they are
+obliged to sit still and look straight forwards, because their chains
+render it impossible for them to turn their heads round: and imagine a
+bright fire burning some way off, above and behind them, and an
+elevated roadway passing between the fire and the prisoners, with a
+low wall built along it, like the screens which conjurors put up in
+front of their audience, and above which they exhibit their wonders.</p>
+
+<p>I have it, he replied.</p>
+
+<p>Also figure to yourself a number of persons walking behind this wall,
+and carrying with them statues of men, and images of other animals,
+wrought in wood and stone and all kinds of materials, together with
+various other articles, which overtop the wall; and, as you might
+expect, let some of the passers-by be talking, and others silent.</p>
+
+<p><span class='pagenum'><a name="Page_5" id="Page_5">[5]</a></span>You are describing a strange scene, and strange prisoners.</p>
+
+<p>They resemble us, I replied.</p>
+
+<p>Now consider what would happen if the course of nature brought them a
+release from their fetters, and a remedy for their foolishness, in the
+following manner. Let us suppose that one of them has been released,
+and compelled suddenly to stand up, and turn his neck round and walk
+with open eyes towards the light; and let us suppose that he goes
+through all these actions with pain, and that the dazzling splendour
+renders him incapable of discerning those objects of which he used
+formerly to see the shadows. What answer should you expect him to
+make, if some one were to tell him that in those days he was watching
+foolish phantoms, but that now he is somewhat nearer to reality, and
+is turned towards things more real, and sees more correctly; above
+all, if he were to point out to him the several objects that are
+passing by, and question him, and compel him to answer what they are?
+Should you not expect him to be puzzled, and to regard his old visions
+as truer than the objects now forced upon his notice?</p>
+
+<p>Yes, much truer....</p>
+
+<p>Hence, I suppose, habit will be necessary to enable him to perceive
+objects in that upper world. At first he will be most successful in
+distinguishing shadows; then he will discern the reflections of men
+and other things in water, and afterwards the realities; and after
+this he will raise his eyes to encounter the light of the moon and
+stars, finding it less difficult to study the heavenly bodies and the
+heaven itself by night, than the sun and the sun's light by day.</p>
+
+<p>Doubtless.</p>
+
+<p>Last of all, I imagine, he will be able to observe and <span class='pagenum'><a name="Page_6" id="Page_6">[6]</a></span>contemplate
+the nature of the sun, not as it <i>appears</i> in water or on alien
+ground, but as it is in itself in its own territory.</p>
+
+<p>Of course.</p>
+
+<p>His next step will be to draw the conclusion, that the sun is the
+author of the seasons and the years, and the guardian of all things in
+the visible world, and in a manner the cause of all those things which
+he and his companions used to see.</p>
+
+<p>Obviously, this will be his next step....</p>
+
+<p>Now this imaginary case, my dear Glancon, you must apply in all its
+parts to our former statements, by comparing the region which the eye
+reveals to the prison house, and the light of the fire therein to the
+power of the sun: and if, by the upward ascent and the contemplation
+of the upper world, you understand the mounting of the soul into the
+intellectual region, you will hit the tendency of my own surmises,
+since you desire to be told what they are; though, indeed, God only
+knows whether they are correct. But, be that as it may, the view which
+I take of the subject is to the following effect. In the world of
+knowledge, the essential Form of Good is the limit of our enquiries,
+and can barely be perceived; but, when perceived, we cannot help
+concluding that it is in every case the source of all that is bright
+and beautiful,&mdash;in the visible world giving birth to light and its
+master, and in the intellectual world dispensing, immediately and with
+full authority, truth and reason;&mdash;and that whosoever would act
+wisely, either in private or in public, must set this Form of Good
+before his eyes."</p>
+</div>
+
+<p>But in this passage, as throughout most of Plato's teaching, there is
+an identification of the good with the truly real, which became
+embodied in the philosophical <span class='pagenum'><a name="Page_7" id="Page_7">[7]</a></span>tradition, and is still largely
+operative in our own day. In thus allowing a legislative function to
+the good, Plato produced a divorce between philosophy and science,
+from which, in my opinion, both have suffered ever since and are still
+suffering. The man of science, whatever his hopes may be, must lay
+them aside while he studies nature; and the philosopher, if he is to
+achieve truth, must do the same. Ethical considerations can only
+legitimately appear when the truth has been ascertained: they can and
+should appear as determining our feeling towards the truth, and our
+manner of ordering our lives in view of the truth, but not as
+themselves dictating what the truth is to be.</p>
+
+<p>There are passages in Plato&mdash;among those which illustrate the
+scientific side of his mind&mdash;where he seems clearly aware of this. The
+most noteworthy is the one in which Socrates, as a young man, is
+explaining the theory of ideas to Parmenides.</p>
+
+<p>After Socrates has explained that there is an idea of the good, but
+not of such things as hair and mud and dirt, Parmenides advises him
+"not to despise even the meanest things," and this advice shows the
+genuine scientific temper. It is with this impartial temper that the
+mystic's apparent insight into a higher reality and a hidden good has
+to be combined if philosophy is to realise its greatest possibilities.
+And it is failure in this respect that has made so much of idealistic
+philosophy thin, lifeless, and insubstantial. It is only in marriage
+with the world that our ideals can bear fruit: divorced from it, they
+remain barren. But marriage with the world is not to be achieved by an
+ideal which shrinks from fact, or demands in advance that the world
+shall conform to its desires.</p>
+
+<p>Parmenides himself is the source of a peculiarly <span class='pagenum'><a name="Page_8" id="Page_8">[8]</a></span>interesting strain
+of mysticism which pervades Plato's thought&mdash;the mysticism which may
+be called "logical" because it is embodied in theories on logic. This
+form of mysticism, which appears, so far as the West is concerned, to
+have originated with Parmenides, dominates the reasonings of all the
+great mystical metaphysicians from his day to that of Hegel and his
+modern disciples. Reality, he says, is uncreated, indestructible,
+unchanging, indivisible; it is "immovable in the bonds of mighty
+chains, without beginning and without end; since coming into being and
+passing away have been driven afar, and true belief has cast them
+away." The fundamental principle of his inquiry is stated in a
+sentence which would not be out of place in Hegel: "Thou canst not
+know what is not&mdash;that is impossible&mdash;nor utter it; for it is the same
+thing that can be thought and that can be." And again: "It needs must
+be that what can be thought and spoken of is; for it is possible for
+it to be, and it is not possible for what is nothing to be." The
+impossibility of change follows from this principle; for what is past
+can be spoken of, and therefore, by the principle, still is.</p>
+
+<p>Mystical philosophy, in all ages and in all parts of the world, is
+characterised by certain beliefs which are illustrated by the
+doctrines we have been considering.</p>
+
+<p>There is, first, the belief in insight as against discursive analytic
+knowledge: the belief in a way of wisdom, sudden, penetrating,
+coercive, which is contrasted with the slow and fallible study of
+outward appearance by a science relying wholly upon the senses. All
+who are capable of absorption in an inward passion must have
+experienced at times the strange feeling of unreality in common
+objects, the loss of contact with daily things, in which the solidity
+of the outer world is lost, and the soul <span class='pagenum'><a name="Page_9" id="Page_9">[9]</a></span>seems, in utter loneliness,
+to bring forth, out of its own depths, the mad dance of fantastic
+phantoms which have hitherto appeared as independently real and
+living. This is the negative side of the mystic's initiation: the
+doubt concerning common knowledge, preparing the way for the reception
+of what seems a higher wisdom. Many men to whom this negative
+experience is familiar do not pass beyond it, but for the mystic it is
+merely the gateway to an ampler world.</p>
+
+<p>The mystic insight begins with the sense of a mystery unveiled, of a
+hidden wisdom now suddenly become certain beyond the possibility of a
+doubt. The sense of certainty and revelation comes earlier than any
+definite belief. The definite beliefs at which mystics arrive are the
+result of reflection upon the inarticulate experience gained in the
+moment of insight. Often, beliefs which have no real connection with
+this moment become subsequently attracted into the central nucleus;
+thus in addition to the convictions which all mystics share, we find,
+in many of them, other convictions of a more local and temporary
+character, which no doubt become amalgamated with what was essentially
+mystical in virtue of their subjective certainty. We may ignore such
+inessential accretions, and confine ourselves to the beliefs which all
+mystics share.</p>
+
+<p>The first and most direct outcome of the moment of illumination is
+belief in the possibility of a way of knowledge which may be called
+revelation or insight or intuition, as contrasted with sense, reason,
+and analysis, which are regarded as blind guides leading to the morass
+of illusion. Closely connected with this belief is the conception of a
+Reality behind the world of appearance and utterly different from it.
+This Reality is regarded with an admiration often amounting to
+worship; it is <span class='pagenum'><a name="Page_10" id="Page_10">[10]</a></span>felt to be always and everywhere close at hand, thinly
+veiled by the shows of sense, ready, for the receptive mind, to shine
+in its glory even through the apparent folly and wickedness of Man.
+The poet, the artist, and the lover are seekers after that glory: the
+haunting beauty that they pursue is the faint reflection of its sun.
+But the mystic lives in the full light of the vision: what others
+dimly seek he knows, with a knowledge beside which all other knowledge
+is ignorance.</p>
+
+<p>The second characteristic of mysticism is its belief in unity, and its
+refusal to admit opposition or division anywhere. We found Heraclitus
+saying "good and ill are one"; and again he says, "the way up and the
+way down is one and the same." The same attitude appears in the
+simultaneous assertion of contradictory propositions, such as: "We
+step and do not step into the same rivers; we are and are not." The
+assertion of Parmenides, that reality is one and indivisible, comes
+from the same impulse towards unity. In Plato, this impulse is less
+prominent, being held in check by his theory of ideas; but it
+reappears, so far as his logic permits, in the doctrine of the primacy
+of the Good.</p>
+
+<p>A third mark of almost all mystical metaphysics is the denial of the
+reality of Time. This is an outcome of the denial of division; if all
+is one, the distinction of past and future must be illusory. We have
+seen this doctrine prominent in Parmenides; and among moderns it is
+fundamental in the systems of Spinoza and Hegel.</p>
+
+<p>The last of the doctrines of mysticism which we have to consider is
+its belief that all evil is mere appearance, an illusion produced by
+the divisions and oppositions of the analytic intellect. Mysticism
+does not maintain that such things as cruelty, for example, are good,
+but it denies that they are real: they belong to that lower <span class='pagenum'><a name="Page_11" id="Page_11">[11]</a></span>world of
+phantoms from which we are to be liberated by the insight of the
+vision. Sometimes&mdash;for example in Hegel, and at least verbally in
+Spinoza&mdash;not only evil, but good also, is regarded as illusory, though
+nevertheless the emotional attitude towards what is held to be Reality
+is such as would naturally be associated with the belief that Reality
+is good. What is, in all cases, ethically characteristic of mysticism
+is absence of indignation or protest, acceptance with joy, disbelief
+in the ultimate truth of the division into two hostile camps, the good
+and the bad. This attitude is a direct outcome of the nature of the
+mystical experience: with its sense of unity is associated a feeling
+of infinite peace. Indeed it may be suspected that the feeling of
+peace produces, as feelings do in dreams, the whole system of
+associated beliefs which make up the body of mystic doctrine. But this
+is a difficult question, and one on which it cannot be hoped that
+mankind will reach agreement.</p>
+
+<p>Four questions thus arise in considering the truth or falsehood of
+mysticism, namely:</p>
+
+<div class="block"><p>I. Are there two ways of knowing, which may be called respectively
+reason and intuition? And if so, is either to be preferred to the
+other?</p>
+
+<p>II. Is all plurality and division illusory?</p>
+
+<p>III. Is time unreal?</p>
+
+<p>IV. What kind of reality belongs to good and evil?</p></div>
+
+<p>On all four of these questions, while fully developed mysticism seems
+to me mistaken, I yet believe that, by sufficient restraint, there is
+an element of wisdom to be learned from the mystical way of feeling,
+which does not seem to be attainable in any other manner. If this is
+the truth, mysticism is to be commended as an attitude towards life,
+not as a creed about the world. The <span class='pagenum'><a name="Page_12" id="Page_12">[12]</a></span>meta-physical creed, I shall
+maintain, is a mistaken outcome of the emotion, although this emotion,
+as colouring and informing all other thoughts and feelings, is the
+inspirer of whatever is best in Man. Even the cautious and patient
+investigation of truth by science, which seems the very antithesis of
+the mystic's swift certainty, may be fostered and nourished by that
+very spirit of reverence in which mysticism lives and moves.</p>
+
+<br />
+
+<h4>I. REASON AND INTUITION<a name="FNanchor_3_3" id="FNanchor_3_3"></a><a href="#Footnote_3_3" class="fnanchor">[3]</a></h4>
+
+<p>Of the reality or unreality of the mystic's world I know nothing. I
+have no wish to deny it, nor even to declare that the insight which
+reveals it is not a genuine insight. What I do wish to maintain&mdash;and
+it is here that the scientific attitude becomes imperative&mdash;is that
+insight, untested and unsupported, is an insufficient guarantee of
+truth, in spite of the fact that much of the most important truth is
+first suggested by its means. It is common to speak of an opposition
+between instinct and reason; in the eighteenth century, the opposition
+was drawn in favour of reason, but under the influence of Rousseau and
+the romantic movement instinct was given the preference, first by
+those who rebelled against artificial forms of government and thought,
+and then, as the purely rationalistic defence of traditional theology
+became increasingly difficult, by all who felt in science a menace to
+creeds which they associated with a spiritual outlook on life and the
+world. Bergson, under the name of "intuition," has raised instinct to
+the position of sole <span class='pagenum'><a name="Page_13" id="Page_13">[13]</a></span>arbiter of metaphysical truth. But in fact the
+opposition of instinct and reason is mainly illusory. Instinct,
+intuition, or insight is what first leads to the beliefs which
+subsequent reason confirms or confutes; but the confirmation, where it
+is possible, consists, in the last analysis, of agreement with other
+beliefs no less instinctive. Reason is a harmonising, controlling
+force rather than a creative one. Even in the most purely logical
+realm, it is insight that first arrives at what is new.</p>
+
+<p>Where instinct and reason do sometimes conflict is in regard to single
+beliefs, held instinctively, and held with such determination that no
+degree of inconsistency with other beliefs leads to their abandonment.
+Instinct, like all human faculties, is liable to error. Those in whom
+reason is weak are often unwilling to admit this as regards
+themselves, though all admit it in regard to others. Where instinct is
+least liable to error is in practical matters as to which right
+judgment is a help to survival: friendship and hostility in others,
+for instance, are often felt with extraordinary discrimination through
+very careful disguises. But even in such matters a wrong impression
+may be given by reserve or flattery; and in matters less directly
+practical, such as philosophy deals with, very strong instinctive
+beliefs are sometimes wholly mistaken, as we may come to know through
+their perceived inconsistency with other equally strong beliefs. It is
+such considerations that necessitate the harmonising mediation of
+reason, which tests our beliefs by their mutual compatibility, and
+examines, in doubtful cases, the possible sources of error on the one
+side and on the other. In this there is no opposition to instinct as a
+whole, but only to blind reliance upon some one interesting aspect of
+instinct to the exclusion of other more <span class='pagenum'><a name="Page_14" id="Page_14">[14]</a></span>commonplace but not less
+trustworthy aspects. It is such one-sidedness, not instinct itself,
+that reason aims at correcting.</p>
+
+<p>These more or less trite maxims may be illustrated by application to
+Bergson's advocacy of "intuition" as against "intellect." There are,
+he says, "two profoundly different ways of knowing a thing. The first
+implies that we move round the object: the second that we enter into
+it. The first depends on the point of view at which we are placed and
+on the symbols by which we express ourselves. The second neither
+depends on a point of view nor relies on any symbol. The first kind of
+knowledge may be said to stop at the <i>relative</i>; the second, in those
+cases where it is possible, to attain the <i>absolute</i>."<a name="FNanchor_4_4" id="FNanchor_4_4"></a><a href="#Footnote_4_4" class="fnanchor">[4]</a> The second
+of these, which is intuition, is, he says, "the kind of <i>intellectual
+sympathy</i> by which one places oneself within an object in order to
+coincide with what is unique in it and therefore inexpressible" (p.
+6). In illustration, he mentions self-knowledge: "there is one
+reality, at least, which we all seize from within, by intuition and
+not by simple analysis. It is our own personality in its flowing
+through time&mdash;our self which endures" (p. 8). The rest of Bergson's
+philosophy consists in reporting, through the imperfect medium of
+words, the knowledge gained by intuition, and the consequent complete
+condemnation of all the pretended knowledge derived from science and
+common sense.</p>
+
+<p>This procedure, since it takes sides in a conflict of instinctive
+beliefs, stands in need of justification by proving the greater
+trustworthiness of the beliefs on one side than of those on the other.
+Bergson attempts this justification in two ways, first by explaining
+that intellect is a purely practical faculty to secure biological
+success, <span class='pagenum'><a name="Page_15" id="Page_15">[15]</a></span>secondly by mentioning remarkable feats of instinct in
+animals and by pointing out characteristics of the world which, though
+intuition can apprehend them, are baffling to intellect as he
+interprets it.</p>
+
+<p>Of Bergson's theory that intellect is a purely practical faculty,
+developed in the struggle for survival, and not a source of true
+beliefs, we may say, first, that it is only through intellect that we
+know of the struggle for survival and of the biological ancestry of
+man: if the intellect is misleading, the whole of this merely inferred
+history is presumably untrue. If, on the other hand, we agree with him
+in thinking that evolution took place as Darwin believed, then it is
+not only intellect, but all our faculties, that have been developed
+under the stress of practical utility. Intuition is seen at its best
+where it is directly useful, for example in regard to other people's
+characters and dispositions. Bergson apparently holds that capacity
+for this kind of knowledge is less explicable by the struggle for
+existence than, for example, capacity for pure mathematics. Yet the
+savage deceived by false friendship is likely to pay for his mistake
+with his life; whereas even in the most civilised societies men are
+not put to death for mathematical incompetence. All the most striking
+of his instances of intuition in animals have a very direct survival
+value. The fact is, of course, that both intuition and intellect have
+been developed because they are useful, and that, speaking broadly,
+they are useful when they give truth and become harmful when they give
+falsehood. Intellect, in civilised man, like artistic capacity, has
+occasionally been developed beyond the point where it is useful to the
+individual; intuition, on the other hand, seems on the whole to
+diminish as civilisation increases. It is greater, as a rule, in
+children than in adults, in the uneducated than in the educated.
+<span class='pagenum'><a name="Page_16" id="Page_16">[16]</a></span>Probably in dogs it exceeds anything to be found in human beings. But
+those who see in these facts a recommendation of intuition ought to
+return to running wild in the woods, dyeing themselves with woad and
+living on hips and haws.</p>
+
+<p>Let us next examine whether intuition possesses any such infallibility
+as Bergson claims for it. The best instance of it, according to him,
+is our acquaintance with ourselves; yet self-knowledge is proverbially
+rare and difficult. Most men, for example, have in their nature
+meannesses, vanities, and envies of which they are quite unconscious,
+though even their best friends can perceive them without any
+difficulty. It is true that intuition has a convincingness which is
+lacking to intellect: while it is present, it is almost impossible to
+doubt its truth. But if it should appear, on examination, to be at
+least as fallible as intellect, its greater subjective certainty
+becomes a demerit, making it only the more irresistibly deceptive.
+Apart from self-knowledge, one of the most notable examples of
+intuition is the knowledge people believe themselves to possess of
+those with whom they are in love: the wall between different
+personalities seems to become transparent, and people think they see
+into another soul as into their own. Yet deception in such cases is
+constantly practised with success; and even where there is no
+intentional deception, experience gradually proves, as a rule, that
+the supposed insight was illusory, and that the slower more groping
+methods of the intellect are in the long run more reliable.</p>
+
+<p>Bergson maintains that intellect can only deal with things in so far
+as they resemble what has been experienced in the past, while
+intuition has the power of apprehending the uniqueness and novelty
+that always belong to each fresh moment. That there is something
+unique <span class='pagenum'><a name="Page_17" id="Page_17">[17]</a></span>and new at every moment, is certainly true; it is also true
+that this cannot be fully expressed by means of intellectual concepts.
+Only direct acquaintance can give knowledge of what is unique and new.
+But direct acquaintance of this kind is given fully in sensation, and
+does not require, so far as I can see, any special faculty of
+intuition for its apprehension. It is neither intellect nor intuition,
+but sensation, that supplies new data; but when the data are new in
+any remarkable manner, intellect is much more capable of dealing with
+them than intuition would be. The hen with a brood of ducklings no
+doubt has intuition which seems to place her inside them, and not
+merely to know them analytically; but when the ducklings take to the
+water, the whole apparent intuition is seen to be illusory, and the
+hen is left helpless on the shore. Intuition, in fact, is an aspect
+and development of instinct, and, like all instinct, is admirable in
+those customary surroundings which have moulded the habits of the
+animal in question, but totally incompetent as soon as the
+surroundings are changed in a way which demands some non-habitual mode
+of action.</p>
+
+<p>The theoretical understanding of the world, which is the aim of
+philosophy, is not a matter of great practical importance to animals,
+or to savages, or even to most civilised men. It is hardly to be
+supposed, therefore, that the rapid, rough and ready methods of
+instinct or intuition will find in this field a favourable ground for
+their application. It is the older kinds of activity, which bring out
+our kinship with remote generations of animal and semi-human
+ancestors, that show intuition at its best. In such matters as
+self-preservation and love, intuition will act sometimes (though not
+always) with a swiftness and precision which are astonishing to the
+critical intellect. But philosophy is not one of the <span class='pagenum'><a name="Page_18" id="Page_18">[18]</a></span>pursuits which
+illustrate our affinity with the past: it is a highly refined, highly
+civilised pursuit, demanding, for its success, a certain liberation
+from the life of instinct, and even, at times, a certain aloofness
+from all mundane hopes and fears. It is not in philosophy, therefore,
+that we can hope to see intuition at its best. On the contrary, since
+the true objects of philosophy, and the habit of thought demanded for
+their apprehension, are strange, unusual, and remote, it is here, more
+almost than anywhere else, that intellect proves superior to
+intuition, and that quick unanalysed convictions are least deserving
+of uncritical acceptance.</p>
+
+<p>In advocating the scientific restraint and balance, as against the
+self-assertion of a confident reliance upon intuition, we are only
+urging, in the sphere of knowledge, that largeness of contemplation,
+that impersonal disinterestedness, and that freedom from practical
+preoccupations which have been inculcated by all the great religions
+of the world. Thus our conclusion, however it may conflict with the
+explicit beliefs of many mystics, is, in essence, not contrary to the
+spirit which inspires those beliefs, but rather the outcome of this
+very spirit as applied in the realm of thought.</p>
+
+<br />
+<h4>II. UNITY AND PLURALITY</h4>
+
+<p>One of the most convincing aspects of the mystic illumination is the
+apparent revelation of the oneness of all things, giving rise to
+pantheism in religion and to monism in philosophy. An elaborate logic,
+beginning with Parmenides, and culminating in Hegel and his followers,
+has been gradually developed, to prove that the universe is one
+indivisible Whole, and that what seem to be its parts, if considered
+as substantial and <span class='pagenum'><a name="Page_19" id="Page_19">[19]</a></span>self-existing, are mere illusion. The conception
+of a Reality quite other than the world of appearance, a reality one,
+indivisible, and unchanging, was introduced into Western philosophy by
+Parmenides, not, nominally at least, for mystical or religious
+reasons, but on the basis of a logical argument as to the
+impossibility of not-being, and most subsequent metaphysical systems
+are the outcome of this fundamental idea.</p>
+
+<p>The logic used in defence of mysticism seems to be faulty as logic,
+and open to technical criticisms, which I have explained elsewhere. I
+shall not here repeat these criticisms, since they are lengthy and
+difficult, but shall instead attempt an analysis of the state of mind
+from which mystical logic has arisen.</p>
+
+<p>Belief in a reality quite different from what appears to the senses
+arises with irresistible force in certain moods, which are the source
+of most mysticism, and of most metaphysics. While such a mood is
+dominant, the need of logic is not felt, and accordingly the more
+thoroughgoing mystics do not employ logic, but appeal directly to the
+immediate deliverance of their insight. But such fully developed
+mysticism is rare in the West. When the intensity of emotional
+conviction subsides, a man who is in the habit of reasoning will
+search for logical grounds in favour of the belief which he finds in
+himself. But since the belief already exists, he will be very
+hospitable to any ground that suggests itself. The paradoxes
+apparently proved by his logic are really the paradoxes of mysticism,
+and are the goal which he feels his logic must reach if it is to be in
+accordance with insight. The resulting logic has rendered most
+philosophers incapable of giving any account of the world of science
+and daily life. If they had been anxious to give such an account, they
+would probably have discovered the errors of their <span class='pagenum'><a name="Page_20" id="Page_20">[20]</a></span>logic; but most of
+them were less anxious to understand the world of science and daily
+life than to convict it of unreality in the interests of a
+super-sensible "real" world.</p>
+
+<p>It is in this way that logic has been pursued by those of the great
+philosophers who were mystics. But since they usually took for granted
+the supposed insight of the mystic emotion, their logical doctrines
+were presented with a certain dryness, and were believed by their
+disciples to be quite independent of the sudden illumination from
+which they sprang. Nevertheless their origin clung to them, and they
+remained&mdash;to borrow a useful word from Mr. Santayana&mdash;"malicious" in
+regard to the world of science and common sense. It is only so that we
+can account for the complacency with which philosophers have accepted
+the inconsistency of their doctrines with all the common and
+scientific facts which seem best established and most worthy of
+belief.</p>
+
+<p>The logic of mysticism shows, as is natural, the defects which are
+inherent in anything malicious. The impulse to logic, not felt while
+the mystic mood is dominant, reasserts itself as the mood fades, but
+with a desire to retain the vanishing insight, or at least to prove
+that it <i>was</i> insight, and that what seems to contradict it is
+illusion. The logic which thus arises is not quite disinterested or
+candid, and is inspired by a certain hatred of the daily world to
+which it is to be applied. Such an attitude naturally does not tend to
+the best results. Everyone knows that to read an author simply in
+order to refute him is not the way to understand him; and to read the
+book of Nature with a conviction that it is all illusion is just as
+unlikely to lead to understanding. If our logic is to find the common
+world intelligible, it must not be hostile, but must be inspired by a
+genuine <span class='pagenum'><a name="Page_21" id="Page_21">[21]</a></span>acceptance such as is not usually to be found among
+metaphysicians.</p>
+
+<br />
+<h4>III. TIME</h4>
+
+<p>The unreality of time is a cardinal doctrine of many metaphysical
+systems, often nominally based, as already by Parmenides, upon logical
+arguments, but originally derived, at any rate in the founders of new
+systems, from the certainty which is born in the moment of mystic
+insight. As a Persian Sufi poet says:</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"Past and future are what veil God from our sight.<br /></span>
+<span class="i0">Burn up both of them with fire! How long<br /></span>
+<span class="i0">Wilt thou be partitioned by these segments as a reed?"<a name="FNanchor_5_5" id="FNanchor_5_5"></a><a href="#Footnote_5_5" class="fnanchor">[5]</a><br /></span>
+</div></div>
+
+<p>The belief that what is ultimately real must be immutable is a very
+common one: it gave rise to the metaphysical notion of substance, and
+finds, even now, a wholly illegitimate satisfaction in such scientific
+doctrines as the conservation of energy and mass.</p>
+
+<p>It is difficult to disentangle the truth and the error in this view.
+The arguments for the contention that time is unreal and that the
+world of sense is illusory must, I think, be regarded as fallacious.
+Nevertheless there is some sense&mdash;easier to feel than to state&mdash;in
+which time is an unimportant and superficial characteristic of
+reality. Past and future must be acknowledged to be as real as the
+present, and a certain emancipation from slavery to time is essential
+to philosophic thought. The importance of time is rather practical
+than theoretical, rather in relation to our desires than in relation
+to truth. A truer image of the world, I think, is obtained by
+picturing things as entering into the stream of time from an eternal
+world outside, than from a view which regards time as the devouring
+tyrant of all that is. Both in <span class='pagenum'><a name="Page_22" id="Page_22">[22]</a></span>thought and in feeling, even though
+time be real, to realise the unimportance of time is the gate of
+wisdom.</p>
+
+<p>That this is the case may be seen at once by asking ourselves why our
+feelings towards the past are so different from our feelings towards
+the future. The reason for this difference is wholly practical: our
+wishes can affect the future but not the past, the future is to some
+extent subject to our power, while the past is unalterably fixed. But
+every future will some day be past: if we see the past truly now, it
+must, when it was still future, have been just what we now see it to
+be, and what is now future must be just what we shall see it to be
+when it has become past. The felt difference of quality between past
+and future, therefore, is not an intrinsic difference, but only a
+difference in relation to us: to impartial contemplation, it ceases to
+exist. And impartiality of contemplation is, in the intellectual
+sphere, that very same virtue of disinterestedness which, in the
+sphere of action, appears as justice and unselfishness. Whoever wishes
+to see the world truly, to rise in thought above the tyranny of
+practical desires, must learn to overcome the difference of attitude
+towards past and future, and to survey the whole stream of time in one
+comprehensive vision.</p>
+
+<p>The kind of way in which, as it seems to me, time ought not to enter
+into our theoretic philosophical thought, may be illustrated by the
+philosophy which has become associated with the idea of evolution, and
+which is exemplified by Nietzsche, pragmatism, and Bergson. This
+philosophy, on the basis of the development which has led from the
+lowest forms of life up to man, sees in <i>progress</i> the fundamental law
+of the universe, and thus admits the difference between <i>earlier</i> and
+<i>later</i> into the very citadel of its contemplative outlook. With its
+past and future <span class='pagenum'><a name="Page_23" id="Page_23">[23]</a></span>history of the world, conjectural as it is, I do not
+wish to quarrel. But I think that, in the intoxication of a quick
+success, much that is required for a true understanding of the
+universe has been forgotten. Something of Hellenism, something, too,
+of Oriental resignation, must be combined with its hurrying Western
+self-assertion before it can emerge from the ardour of youth into the
+mature wisdom of manhood. In spite of its appeals to science, the true
+scientific philosophy, I think, is something more arduous and more
+aloof, appealing to less mundane hopes, and requiring a severer
+discipline for its successful practice.</p>
+
+<p>Darwin's <i>Origin of Species</i> persuaded the world that the difference
+between different species of animals and plants is not the fixed
+immutable difference that it appears to be. The doctrine of natural
+kinds, which had rendered classification easy and definite, which was
+enshrined in the Aristotelian tradition, and protected by its supposed
+necessity for orthodox dogma, was suddenly swept away for ever out of
+the biological world. The difference between man and the lower
+animals, which to our human conceit appears enormous, was shown to be
+a gradual achievement, involving intermediate being who could not with
+certainty be placed either within or without the human family. The sun
+and the planets had already been shown by Laplace to be very probably
+derived from a primitive more or less undifferentiated nebula. Thus
+the old fixed landmarks became wavering and indistinct, and all sharp
+outlines were blurred. Things and species lost their boundaries, and
+none could say where they began or where they ended.</p>
+
+<p>But if human conceit was staggered for a moment by its kinship with
+the ape, it soon found a way to reassert itself, and that way is the
+"philosophy" of evolution. <span class='pagenum'><a name="Page_24" id="Page_24">[24]</a></span>A process which led from the am[oe]ba to
+Man appeared to the philosophers to be obviously a progress&mdash;though
+whether the am[oe]ba would agree with this opinion is not known. Hence
+the cycle of changes which science had shown to be the probable
+history of the past was welcomed as revealing a law of development
+towards good in the universe&mdash;an evolution or unfolding of an idea
+slowly embodying itself in the actual. But such a view, though it
+might satisfy Spencer and those whom we may call Hegelian
+evolutionists, could not be accepted as adequate by the more
+whole-hearted votaries of change. An ideal to which the world
+continuously approaches is, to these minds, too dead and static to be
+inspiring. Not only the aspiration, but the ideal too, must change and
+develop with the course of evolution: there must be no fixed goal, but
+a continual fashioning of fresh needs by the impulse which is life and
+which alone gives unity to the process.</p>
+
+<p>Life, in this philosophy, is a continuous stream, in which all
+divisions are artificial and unreal. Separate things, beginnings and
+endings, are mere convenient fictions: there is only smooth unbroken
+transition. The beliefs of to-day may count as true to-day, if they
+carry us along the stream; but to-morrow they will be false, and must
+be replaced by new beliefs to meet the new situation. All our thinking
+consists of convenient fictions, imaginary congealings of the stream:
+reality flows on in spite of all our fictions, and though it can be
+lived, it cannot be conceived in thought. Somehow, without explicit
+statement, the assurance is slipped in that the future, though we
+cannot foresee it, will be better than the past or the present: the
+reader is like the child which expects a sweet because it has been
+told to open its mouth and shut its eyes. Logic, mathematics, <span class='pagenum'><a name="Page_25" id="Page_25">[25]</a></span>physics
+disappear in this philosophy, because they are too "static"; what is
+real is no impulse and movement towards a goal which, like the
+rainbow, recedes as we advance, and makes every place different when
+it reaches it from what it appeared to be at a distance.</p>
+
+<p>I do not propose to enter upon a technical examination of this
+philosophy. I wish only to maintain that the motives and interests
+which inspire it are so exclusively practical, and the problems with
+which it deals are so special, that it can hardly be regarded as
+touching any of the questions that, to my mind, constitute genuine
+philosophy.</p>
+
+<p>The predominant interest of evolutionism is in the question of human
+destiny, or at least of the destiny of Life. It is more interested in
+morality and happiness than in knowledge for its own sake. It must be
+admitted that the same may be said of many other philosophies, and
+that a desire for the kind of knowledge which philosophy can give is
+very rare. But if philosophy is to attain truth, it is necessary first
+and foremost that philosophers should acquire the disinterested
+intellectual curiosity which characterises the genuine man of science.
+Knowledge concerning the future&mdash;which is the kind of knowledge that
+must be sought if we are to know about human destiny&mdash;is possible
+within certain narrow limits. It is impossible to say how much the
+limits may be enlarged with the progress of science. But what is
+evident is that any proposition about the future belongs by its
+subject-matter to some particular science, and is to be ascertained,
+if at all, by the methods of that science. Philosophy is not a short
+cut to the same kind of results as those of the other sciences: if it
+is to be a genuine study, it must have a province of its own, and aim
+at results which the other sciences can neither prove nor disprove.</p>
+
+<p><span class='pagenum'><a name="Page_26" id="Page_26">[26]</a></span>Evolutionism, in basing itself upon the notion of <i>progress</i>, which is
+change from the worse to the better, allows the notion of time, as it
+seems to me, to become its tyrant rather than its servant, and thereby
+loses that impartiality of contemplation which is the source of all
+that is best in philosophic thought and feeling. Metaphysicians, as we
+saw, have frequently denied altogether the reality of time. I do not
+wish to do this; I wish only to preserve the mental outlook which
+inspired the denial, the attitude which, in thought, regards the past
+as having the same reality as the present and the same importance as
+the future. "In so far," says Spinoza,<a name="FNanchor_6_6" id="FNanchor_6_6"></a><a href="#Footnote_6_6" class="fnanchor">[6]</a> "as the mind conceives a
+thing according to the dictate of reason, it will be equally affected
+whether the idea is that of a future, past, or present thing." It is
+this "conceiving according to the dictate of reason" that I find
+lacking in the philosophy which is based on evolution.</p>
+
+<br />
+<h4>IV. GOOD AND EVIL</h4>
+
+<p>Mysticism maintains that all evil is illusory, and sometimes maintains
+the same view as regards good, but more often holds that all Reality
+is good. Both views are to be found in Heraclitus: "Good and ill are
+one," he says, but again, "To God all things are fair and good and
+right, but men hold some things wrong and some right." A similar
+twofold position is to be found in Spinoza, but he uses the word
+"perfection" when he means to speak of the good that is not merely
+human. "By reality and perfection I mean the same thing," he says;<a name="FNanchor_7_7" id="FNanchor_7_7"></a><a href="#Footnote_7_7" class="fnanchor">[7]</a>
+but elsewhere we find the definition: "By <i>good</i> I shall mean that
+which we certainly know to be useful to us."<a name="FNanchor_8_8" id="FNanchor_8_8"></a><a href="#Footnote_8_8" class="fnanchor">[8]</a> Thus perfection
+belongs to Reality in its own nature, but <span class='pagenum'><a name="Page_27" id="Page_27">[27]</a></span>goodness is relative to
+ourselves and our needs, and disappears in an impartial survey. Some
+such distinction, I think, is necessary in order to understand the
+ethical outlook of mysticism: there is a lower mundane kind of good
+and evil, which divides the world of appearance into what seem to be
+conflicting parts; but there is also a higher, mystical kind of good,
+which belongs to Reality and is not opposed by any correlative kind of
+evil.</p>
+
+<p>It is difficult to give a logically tenable account of this position
+without recognising that good and evil are subjective, that what is
+good is merely that towards which we have one kind of feeling, and
+what is evil is merely that towards which we have another kind of
+feeling. In our active life, where we have to exercise choice, and to
+prefer this to that of two possible acts, it is necessary to have a
+distinction of good and evil, or at least of better and worse. But
+this distinction, like everything pertaining to action, belongs to
+what mysticism regards as the world of illusion, if only because it is
+essentially concerned with time. In our contemplative life, where
+action is not called for, it is possible to be impartial, and to
+overcome the ethical dualism which action requires. So long as we
+remain <i>merely</i> impartial, we may be content to say that both the good
+and the evil of action are illusions. But if, as we must do if we have
+the mystic vision, we find the whole world worthy of love and worship,
+if we see</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"The earth, and every common sight....<br /></span>
+<span class="i0">Apparell'd in celestial light,"<br /></span>
+</div></div>
+
+<p class="noin">we shall say that there is a higher good than that of action, and that
+this higher good belongs to the whole world as it is in reality. In
+this way the twofold attitude and the apparent vacillation of
+mysticism are explained and justified.</p>
+
+<p><span class='pagenum'><a name="Page_28" id="Page_28">[28]</a></span>The possibility of this universal love and joy in all that exists is
+of supreme importance for the conduct and happiness of life, and gives
+inestimable value to the mystic emotion, apart from any creeds which
+may be built upon it. But if we are not to be led into false beliefs,
+it is necessary to realise exactly <i>what</i> the mystic emotion reveals.
+It reveals a possibility of human nature&mdash;a possibility of a nobler,
+happier, freer life than any that can be otherwise achieved. But it
+does not reveal anything about the non-human, or about the nature of
+the universe in general. Good and bad, and even the higher good that
+mysticism finds everywhere, are the reflections of our own emotions on
+other things, not part of the substance of things as they are in
+themselves. And therefore an impartial contemplation, freed from all
+pre-occupation with Self, will not judge things good or bad, although
+it is very easily combined with that feeling of universal love which
+leads the mystic to say that the whole world is good.</p>
+
+<p>The philosophy of evolution, through the notion of progress, is bound
+up with the ethical dualism of the worse and the better, and is thus
+shut out, not only from the kind of survey which discards good and
+evil altogether from its view, but also from the mystical belief in
+the goodness of everything. In this way the distinction of good and
+evil, like time, becomes a tyrant in this philosophy, and introduces
+into thought the restless selectiveness of action. Good and evil, like
+time, are, it would seem, not general or fundamental in the world of
+thought, but late and highly specialised members of the intellectual
+hierarchy.</p>
+
+<p>Although, as we saw, mysticism can be interpreted so as to agree with
+the view that good and evil are not intellectually fundamental, it
+must be admitted that here <span class='pagenum'><a name="Page_29" id="Page_29">[29]</a></span>we are no longer in verbal agreement with
+most of the great philosophers and religious teachers of the past. I
+believe, however, that the elimination of ethical considerations from
+philosophy is both scientifically necessary and&mdash;though this may seem
+a paradox&mdash;an ethical advance. Both these contentions must be briefly
+defended.</p>
+
+<p>The hope of satisfaction to our more human desires&mdash;the hope of
+demonstrating that the world has this or that desirable ethical
+characteristic&mdash;is not one which, so far as I can see, a scientific
+philosophy can do anything whatever to satisfy. The difference between
+a good world and a bad one is a difference in the particular
+characteristics of the particular things that exist in these worlds:
+it is not a sufficiently abstract difference to come within the
+province of philosophy. Love and hate, for example, are ethical
+opposites, but to philosophy they are closely analogous attitudes
+towards objects. The general form and structure of those attitudes
+towards objects which constitute mental phenomena is a problem for
+philosophy, but the difference between love and hate is not a
+difference of form or structure, and therefore belongs rather to the
+special science of psychology than to philosophy. Thus the ethical
+interests which have often inspired philosophers must remain in the
+background: some kind of ethical interest may inspire the whole study,
+but none must obtrude in the detail or be expected in the special
+results which are sought.</p>
+
+<p>If this view seems at first sight disappointing, we may remind
+ourselves that a similar change has been found necessary in all the
+other sciences. The physicist or chemist is not now required to prove
+the ethical importance of his ions or atoms; the biologist is not
+expected to prove the utility of the plants or animals <span class='pagenum'><a name="Page_30" id="Page_30">[30]</a></span>which he
+dissects. In pre-scientific ages this was not the case. Astronomy, for
+example, was studied because men believed in astrology: it was thought
+that the movements of the planets had the most direct and important
+bearing upon the lives of human beings. Presumably, when this belief
+decayed and the disinterested study of astronomy began, many who had
+found astrology absorbingly interesting decided that astronomy had too
+little human interest to be worthy of study. Physics, as it appears in
+Plato's Tim&aelig;us for example, is full of ethical notions: it is an
+essential part of its purpose to show that the earth is worthy of
+admiration. The modern physicist, on the contrary, though he has no
+wish to deny that the earth is admirable, is not concerned, as
+physicist, with its ethical attributes: he is merely concerned to find
+out facts, not to consider whether they are good or bad. In
+psychology, the scientific attitude is even more recent and more
+difficult than in the physical sciences: it is natural to consider
+that human nature is either good or bad, and to suppose that the
+difference between good and bad, so all-important in practice, must be
+important in theory also. It is only during the last century that an
+ethically neutral psychology has grown up; and here too, ethical
+neutrality has been essential to scientific success.</p>
+
+<p>In philosophy, hitherto, ethical neutrality has been seldom sought and
+hardly ever achieved. Men have remembered their wishes, and have
+judged philosophies in relation to their wishes. Driven from the
+particular sciences, the belief that the notions of good and evil must
+afford a key to the understanding of the world has sought a refuge in
+philosophy. But even from this last refuge, if philosophy is not to
+remain a set of pleasing dreams, this belief must be driven forth. It
+is a commonplace that <span class='pagenum'><a name="Page_31" id="Page_31">[31]</a></span>happiness is not best achieved by those who
+seek it directly; and it would seem that the same is true of the good.
+In thought, at any rate, those who forget good and evil and seek only
+to know the facts are more likely to achieve good than those who view
+the world through the distorting medium of their own desires.</p>
+
+<p>We are thus brought back to our seeming paradox, that a philosophy
+which does not seek to impose upon the world its own conceptions of
+good and evil is not only more likely to achieve truth, but is also
+the outcome of a higher ethical standpoint than one which, like
+evolutionism and most traditional systems, is perpetually appraising
+the universe and seeking to find in it an embodiment of present
+ideals. In religion, and in every deeply serious view of the world and
+of human destiny, there is an element of submission, a realisation of
+the limits of human power, which is somewhat lacking in the modern
+world, with its quick material successes and its insolent belief in
+the boundless possibilities of progress. "He that loveth his life
+shall lose it"; and there is danger lest, through a too confident love
+of life, life itself should lose much of what gives it its highest
+worth. The submission which religion inculcates in action is
+essentially the same in spirit as that which science teaches in
+thought; and the ethical neutrality by which its victories have been
+achieved is the outcome of that submission.</p>
+
+<p>The good which it concerns us to remember is the good which it lies in
+our power to create&mdash;the good in our own lives and in our attitude
+towards the world. Insistence on belief in an external realisation of
+the good is a form of self-assertion, which, while it cannot secure
+the external good which it desires, can seriously impair the inward
+good which lies within our power, and destroy that reverence towards
+fact which constitutes both what is <span class='pagenum'><a name="Page_32" id="Page_32">[32]</a></span>valuable in humility and what is
+fruitful in the scientific temper.</p>
+
+<p>Human beings cannot, of course, wholly transcend human nature;
+something subjective, if only the interest that determines the
+direction of our attention, must remain in all our thought. But
+scientific philosophy comes nearer to objectivity than any other human
+pursuit, and gives us, therefore, the closest constant and the most
+intimate relation with the outer world that it is possible to achieve.
+To the primitive mind, everything is either friendly or hostile; but
+experience has shown that friendliness and hostility are not the
+conceptions by which the world is to be understood. Scientific
+philosophy thus represents, though as yet only in a nascent condition,
+a higher form of thought than any pre-scientific belief or
+imagination, and, like every approach to self-transcendence, it brings
+with it a rich reward in increase of scope and breadth and
+comprehension. Evolutionism, in spite of its appeals to particular
+scientific facts, fails to be a truly scientific philosophy because of
+its slavery to time, its ethical preoccupations, and its predominant
+interest in our mundane concerns and destiny. A truly scientific
+philosophy will be more humble, more piecemeal, more arduous, offering
+less glitter of outward mirage to flatter fallacious hopes, but more
+indifferent to fate, and more capable of accepting the world without
+the tyrannous imposition of our human and temporary demands.</p>
+
+<br />
+<hr style="width: 15%;" />
+<br />
+
+<h4>FOOTNOTES:</h4>
+
+<div class="footnote"><p class="noin"><a name="Footnote_1_1" id="Footnote_1_1"></a><a href="#FNanchor_1_1"><span class="label">[1]</span></a> All the above quotations are from Burnet's <i>Early Greek
+Philosophy</i>, (2nd ed., 1908), pp. 146-156.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_2_2" id="Footnote_2_2"></a><a href="#FNanchor_2_2"><span class="label">[2]</span></a> <i>Republic</i>, 514, translated by Davies and Vaughan.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_3_3" id="Footnote_3_3"></a><a href="#FNanchor_3_3"><span class="label">[3]</span></a> This section, and also one or two pages in later
+sections, have been printed in a course of Lowell lectures <i>On our
+knowledge of the external world</i>, published by the Open Court
+Publishing Company. But I have left them here, as this is the context
+for which they were originally written.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_4_4" id="Footnote_4_4"></a><a href="#FNanchor_4_4"><span class="label">[4]</span></a> <i>Introduction to Metaphysics</i>, p. 1.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_5_5" id="Footnote_5_5"></a><a href="#FNanchor_5_5"><span class="label">[5]</span></a> Whinfield's translation of the <i>Masnavi</i> (Tr&uuml;bner, 1887),
+p. 34.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_6_6" id="Footnote_6_6"></a><a href="#FNanchor_6_6"><span class="label">[6]</span></a> <i>Ethics</i>, Bk. IV, Prop. LXII.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_7_7" id="Footnote_7_7"></a><a href="#FNanchor_7_7"><span class="label">[7]</span></a> Ib., Pt. IV, Df. I.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_8_8" id="Footnote_8_8"></a><a href="#FNanchor_8_8"><span class="label">[8]</span></a> <i>Ethics</i>. Pt. II. Df. VI.</p></div>
+
+
+<br />
+<br />
+<br />
+<br />
+<a name="II" id="II"></a><hr />
+<span class='pagenum'><a name="Page_33" id="Page_33">[33]</a></span><br />
+
+<h3>II<span class="totoc"><a href="#toc">ToC</a></span></h3>
+
+<h4>THE PLACE OF SCIENCE IN A LIBERAL EDUCATION</h4>
+<br />
+
+<h4>I</h4>
+
+<p>Science, to the ordinary reader of newspapers, is represented by a
+varying selection of sensational triumphs, such as wireless telegraphy
+and aeroplanes, radio-activity and the marvels of modern alchemy. It is
+not of this aspect of science that I wish to speak. Science, in this
+aspect, consists of detached up-to-date fragments, interesting only
+until they are replaced by something newer and more up-to-date,
+displaying nothing of the systems of patiently constructed knowledge
+out of which, almost as a casual incident, have come the practically
+useful results which interest the man in the street. The increased
+command over the forces of nature which is derived from science is
+undoubtedly an amply sufficient reason for encouraging scientific
+research, but this reason has been so often urged and is so easily
+appreciated that other reasons, to my mind quite as important, are apt
+to be overlooked. It is with these other reasons, especially with the
+intrinsic value of a scientific habit of mind in forming our outlook
+on the world, that I shall be concerned in what follows.</p>
+
+<p>The instance of wireless telegraphy will serve to illustrate the
+difference between the two points of view. Almost all the serious
+intellectual labour required for the <span class='pagenum'><a name="Page_34" id="Page_34">[34]</a></span>possibility of this invention is
+due to three men&mdash;Faraday, Maxwell, and Hertz. In alternating layers
+of experiment and theory these three men built up the modern theory of
+electromagnetism, and demonstrated the identity of light with
+electromagnetic waves. The system which they discovered is one of
+profound intellectual interest, bringing together and unifying an
+endless variety of apparently detached phenomena, and displaying a
+cumulative mental power which cannot but afford delight to every
+generous spirit. The mechanical details which remained to be adjusted
+in order to utilise their discoveries for a practical system of
+telegraphy demanded, no doubt, very considerable ingenuity, but had
+not that broad sweep and that universality which could give them
+intrinsic interest as an object of disinterested contemplation.</p>
+
+<p>From the point of view of training the mind, of giving that
+well-informed, impersonal outlook which constitutes culture in the
+good sense of this much-misused word, it seems to be generally held
+indisputable that a literary education is superior to one based on
+science. Even the warmest advocates of science are apt to rest their
+claims on the contention that culture ought to be sacrificed to
+utility. Those men of science who respect culture, when they associate
+with men learned in the classics, are apt to admit, not merely
+politely, but sincerely, a certain inferiority on their side,
+compensated doubtless by the services which science renders to
+humanity, but none the less real. And so long as this attitude exists
+among men of science, it tends to verify itself: the intrinsically
+valuable aspects of science tend to be sacrificed to the merely
+useful, and little attempt is made to preserve that leisurely,
+systematic survey by which the finer quality of mind is formed and
+nourished.</p>
+
+<p><span class='pagenum'><a name="Page_35" id="Page_35">[35]</a></span>But even if there be, in present fact, any such inferiority as is
+supposed in the educational value of science, this is, I believe, not
+the fault of science itself, but the fault of the spirit in which
+science is taught. If its full possibilities were realised by those
+who teach it, I believe that its capacity of producing those habits of
+mind which constitute the highest mental excellence would be at least
+as great as that of literature, and more particularly of Greek and
+Latin literature. In saying this I have no wish whatever to disparage
+a classical education. I have not myself enjoyed its benefits, and my
+knowledge of Greek and Latin authors is derived almost wholly from
+translations. But I am firmly persuaded that the Greeks fully deserve
+all the admiration that is bestowed upon them, and that it is a very
+great and serious loss to be unacquainted with their writings. It is
+not by attacking them, but by drawing attention to neglected
+excellences in science, that I wish to conduct my argument.</p>
+
+<p>One defect, however, does seem inherent in a purely classical
+education&mdash;namely, a too exclusive emphasis on the past. By the study
+of what is absolutely ended and can never be renewed, a habit of
+criticism towards the present and the future is engendered. The
+qualities in which the present excels are qualities to which the study
+of the past does not direct attention, and to which, therefore, the
+student of Greek civilisation may easily become blind. In what is new
+and growing there is apt to be something crude, insolent, even a
+little vulgar, which is shocking to the man of sensitive taste;
+quivering from the rough contact, he retires to the trim gardens of a
+polished past, forgetting that they were reclaimed from the wilderness
+by men as rough and earth-soiled as those from whom he shrinks in his
+own day. The habit of being unable to recognise merit <span class='pagenum'><a name="Page_36" id="Page_36">[36]</a></span>until it is
+dead is too apt to be the result of a purely bookish life, and a
+culture based wholly on the past will seldom be able to pierce through
+everyday surroundings to the essential splendour of contemporary
+things, or to the hope of still greater splendour in the future.</p>
+
+<div class="poem"><div class="stanza">
+<span class="i0">"My eyes saw not the men of old;<br /></span>
+<span class="i0">And now their age away has rolled.<br /></span>
+<span class="i0">I weep&mdash;to think I shall not see<br /></span>
+<span class="i0">The heroes of posterity."<br /></span>
+</div></div>
+
+<p class="noin">So says the Chinese poet; but such impartiality is rare in the more
+pugnacious atmosphere of the West, where the champions of past and
+future fight a never-ending battle, instead of combining to seek out
+the merits of both.</p>
+
+<p>This consideration, which militates not only against the exclusive
+study of the classics, but against every form of culture which has
+become static, traditional, and academic, leads inevitably to the
+fundamental question: What is the true end of education? But before
+attempting to answer this question it will be well to define the sense
+in which we are to use the word "education." For this purpose I shall
+distinguish the sense in which I mean to use it from two others, both
+perfectly legitimate, the one broader and the other narrower than the
+sense in which I mean to use the word.</p>
+
+<p>In the broader sense, education will include not only what we learn
+through instruction, but all that we learn through personal
+experience&mdash;the formation of character through the education of life.
+Of this aspect of education, vitally important as it is, I will say
+nothing, since its consideration would introduce topics quite foreign
+to the question with which we are concerned.</p>
+
+<p>In the narrower sense, education may be confined to instruction, the
+imparting of definite information on <span class='pagenum'><a name="Page_37" id="Page_37">[37]</a></span>various subjects, because such
+information, in and for itself, is useful in daily life. Elementary
+education&mdash;reading, writing, and arithmetic&mdash;is almost wholly of this
+kind. But instruction, necessary as it is, does not <i>per se</i>
+constitute education in the sense in which I wish to consider it.</p>
+
+<p>Education, in the sense in which I mean it, may be defined as <i>the
+formation, by means of instruction, of certain mental habits and a
+certain outlook on life and the world</i>. It remains to ask ourselves,
+what mental habits, and what sort of outlook, can be hoped for as the
+result of instruction? When we have answered this question we can
+attempt to decide what science has to contribute to the formation of
+the habits and outlook which we desire.</p>
+
+<p>Our whole life is built about a certain number&mdash;not a very small
+number&mdash;of primary instincts and impulses. Only what is in some way
+connected with these instincts and impulses appears to us desirable or
+important; there is no faculty, whether "reason" or "virtue" or
+whatever it may be called, that can take our active life and our hopes
+and fears outside the region controlled by these first movers of all
+desire. Each of them is like a queen-bee, aided by a hive of workers
+gathering honey; but when the queen is gone the workers languish and
+die, and the cells remain empty of their expected sweetness. So with
+each primary impulse in civilised man: it is surrounded and protected
+by a busy swarm of attendant derivative desires, which store up in its
+service whatever honey the surrounding world affords. But if the
+queen-impulse dies, the death-dealing influence, though retarded a
+little by habit, spreads slowly through all the subsidiary impulses,
+and a whole tract of life becomes inexplicably colourless. What was
+formerly full of zest, and so obviously worth doing that it raised <span class='pagenum'><a name="Page_38" id="Page_38">[38]</a></span>no
+questions, has now grown dreary and purposeless: with a sense of
+disillusion we inquire the meaning of life, and decide, perhaps, that
+all is vanity. The search for an outside meaning that can <i>compel</i> an
+inner response must always be disappointed: all "meaning" must be at
+bottom related to our primary desires, and when they are extinct no
+miracle can restore to the world the value which they reflected upon
+it.</p>
+
+<p>The purpose of education, therefore, cannot be to create any primary
+impulse which is lacking in the uneducated; the purpose can only be to
+enlarge the scope of those that human nature provides, by increasing
+the number and variety of attendant thoughts, and by showing where the
+most permanent satisfaction is to be found. Under the impulse of a
+Calvinistic horror of the "natural man," this obvious truth has been
+too often misconceived in the training of the young; "nature" has been
+falsely regarded as excluding all that is best in what is natural, and
+the endeavour to teach virtue has led to the production of stunted and
+contorted hypocrites instead of full-grown human beings. From such
+mistakes in education a better psychology or a kinder heart is
+beginning to preserve the present generation; we need, therefore,
+waste no more words on the theory that the purpose of education is to
+thwart or eradicate nature.</p>
+
+<p>But although nature must supply the initial force of desire, nature is
+not, in the civilised man, the spasmodic, fragmentary, and yet violent
+set of impulses that it is in the savage. Each impulse has its
+constitutional ministry of thought and knowledge and reflection,
+through which possible conflicts of impulses are foreseen, and
+temporary impulses are controlled by the unifying impulse which may be
+called wisdom. In this way <span class='pagenum'><a name="Page_39" id="Page_39">[39]</a></span>education destroys the crudity of
+instinct, and increases through knowledge the wealth and variety of
+the individual's contacts with the outside world, making him no longer
+an isolated fighting unit, but a citizen of the universe, embracing
+distant countries, remote regions of space, and vast stretches of past
+and future within the circle of his interests. It is this simultaneous
+softening in the insistence of desire and enlargement of its scope
+that is the chief moral end of education.</p>
+
+<p>Closely connected with this moral end is the more purely intellectual
+aim of education, the endeavour to make us see and imagine the world
+in an objective manner, as far as possible as it is in itself, and not
+merely through the distorting medium of personal desire. The complete
+attainment of such an objective view is no doubt an ideal,
+indefinitely approachable, but not actually and fully realisable.
+Education, considered as a process of forming our mental habits and
+our outlook on the world, is to be judged successful in proportion as
+its outcome approximates to this ideal; in proportion, that is to say,
+as it gives us a true view of our place in society, of the relation of
+the whole human society to its non-human environment, and of the
+nature of the non-human world as it is in itself apart from our
+desires and interests. If this standard is admitted, we can return to
+the consideration of science, inquiring how far science contributes to
+such an aim, and whether it is in any respect superior to its rivals
+in educational practice.</p>
+
+<br />
+
+<h4>II</h4>
+
+<p>Two opposite and at first sight conflicting merits belong to science
+as against literature and art. The one, which is not inherently
+necessary, but is certainly true <span class='pagenum'><a name="Page_40" id="Page_40">[40]</a></span>at the present day, is hopefulness
+as to the future of human achievement, and in particular as to the
+useful work that may be accomplished by any intelligent student. This
+merit and the cheerful outlook which it engenders prevent what might
+otherwise be the depressing effect of another aspect of science, to my
+mind also a merit, and perhaps its greatest merit&mdash;I mean the
+irrelevance of human passions and of the whole subjective apparatus
+where scientific truth is concerned. Each of these reasons for
+preferring the study of science requires some amplification. Let us
+begin with the first.</p>
+
+<p>In the study of literature or art our attention is perpetually riveted
+upon the past: the men of Greece or of the Renaissance did better than
+any men do now; the triumphs of former ages, so far from facilitating
+fresh triumphs in our own age, actually increase the difficulty of
+fresh triumphs by rendering originality harder of attainment; not only
+is artistic achievement not cumulative, but it seems even to depend
+upon a certain freshness and <i>na&iuml;vet&eacute;</i> of impulse and vision which
+civilisation tends to destroy. Hence comes, to those who have been
+nourished on the literary and artistic productions of former ages, a
+certain peevishness and undue fastidiousness towards the present, from
+which there seems no escape except into the deliberate vandalism which
+ignores tradition and in the search after originality achieves only
+the eccentric. But in such vandalism there is none of the simplicity
+and spontaneity out of which great art springs: theory is still the
+canker in its core, and insincerity destroys the advantages of a
+merely pretended ignorance.</p>
+
+<p>The despair thus arising from an education which suggests no
+pre-eminent mental activity except that of artistic creation is wholly
+absent from an education <span class='pagenum'><a name="Page_41" id="Page_41">[41]</a></span>which gives the knowledge of scientific
+method. The discovery of scientific method, except in pure
+mathematics, is a thing of yesterday; speaking broadly, we may say
+that it dates from Galileo. Yet already it has transformed the world,
+and its success proceeds with ever-accelerating velocity. In science
+men have discovered an activity of the very highest value in which
+they are no longer, as in art, dependent for progress upon the
+appearance of continually greater genius, for in science the
+successors stand upon the shoulders of their predecessors; where one
+man of supreme genius has invented a method, a thousand lesser men can
+apply it. No transcendent ability is required in order to make useful
+discoveries in science; the edifice of science needs its masons,
+bricklayers, and common labourers as well as its foremen,
+master-builders, and architects. In art nothing worth doing can be
+done without genius; in science even a very moderate capacity can
+contribute to a supreme achievement.</p>
+
+<p>In science the man of real genius is the man who invents a new method.
+The notable discoveries are often made by his successors, who can
+apply the method with fresh vigour, unimpaired by the previous labour
+of perfecting it; but the mental calibre of the thought required for
+their work, however brilliant, is not so great as that required by the
+first inventor of the method. There are in science immense numbers of
+different methods, appropriate to different classes of problems; but
+over and above them all, there is something not easily definable,
+which may be called <i>the</i> method of science. It was formerly customary
+to identify this with the inductive method, and to associate it with
+the name of Bacon. But the true inductive method was not discovered by
+Bacon, and the true method of science <span class='pagenum'><a name="Page_42" id="Page_42">[42]</a></span>is something which includes
+deduction as much as induction, logic and mathematics as much as
+botany and geology. I shall not attempt the difficult task of stating
+what the scientific method is, but I will try to indicate the temper
+of mind out of which the scientific method grows, which is the second
+of the two merits that were mentioned above as belonging to a
+scientific education.</p>
+
+<p>The kernel of the scientific outlook is a thing so simple, so obvious,
+so seemingly trivial, that the mention of it may almost excite
+derision. The kernel of the scientific outlook is the refusal to
+regard our own desires, tastes, and interests as affording a key to
+the understanding of the world. Stated thus baldly, this may seem no
+more than a trite truism. But to remember it consistently in matters
+arousing our passionate partisanship is by no means easy, especially
+where the available evidence is uncertain and inconclusive. A few
+illustrations will make this clear.</p>
+
+<p>Aristotle, I understand, considered that the stars must move in
+circles because the circle is the most perfect curve. In the absence
+of evidence to the contrary, he allowed himself to decide a question
+of fact by an appeal to &aelig;sthetico-moral considerations. In such a case
+it is at once obvious to us that this appeal was unjustifiable. We
+know now how to ascertain as a fact the way in which the heavenly
+bodies move, and we know that they do not move in circles, or even in
+accurate ellipses, or in any other kind of simply describable curve.
+This may be painful to a certain hankering after simplicity of pattern
+in the universe, but we know that in astronomy such feelings are
+irrelevant. Easy as this knowledge seems now, we owe it to the courage
+and insight of the first inventors of scientific method, and more
+especially of Galileo.</p>
+
+<p><span class='pagenum'><a name="Page_43" id="Page_43">[43]</a></span>We may take as another illustration Malthus's doctrine of population.
+This illustration is all the better for the fact that his actual
+doctrine is now known to be largely erroneous. It is not his
+conclusions that are valuable, but the temper and method of his
+inquiry. As everyone knows, it was to him that Darwin owed an
+essential part of his theory of natural selection, and this was only
+possible because Malthus's outlook was truly scientific. His great
+merit lies in considering man not as the object of praise or blame,
+but as a part of nature, a thing with a certain characteristic
+behaviour from which certain consequences must follow. If the
+behaviour is not quite what Malthus supposed, if the consequences are
+not quite what he inferred, that may falsify his conclusions, but does
+not impair the value of his method. The objections which were made
+when his doctrine was new&mdash;that it was horrible and depressing, that
+people ought not to act as he said they did, and so on&mdash;were all such
+as implied an unscientific attitude of mind; as against all of them,
+his calm determination to treat man as a natural phenomenon marks an
+important advance over the reformers of the eighteenth century and the
+Revolution.</p>
+
+<p>Under the influence of Darwinism the scientific attitude towards man
+has now become fairly common, and is to some people quite natural,
+though to most it is still a difficult and artificial intellectual
+contortion. There is however, one study which is as yet almost wholly
+untouched by the scientific spirit&mdash;I mean the study of philosophy.
+Philosophers and the public imagine that the scientific spirit must
+pervade pages that bristle with allusions to ions, germ-plasms, and
+the eyes of shell-fish. But as the devil can quote Scripture, so the
+philosopher can quote science. The scientific spirit is not an affair
+of <span class='pagenum'><a name="Page_44" id="Page_44">[44]</a></span>quotation, of externally acquired information, any more than
+manners are an affair of the etiquette-book. The scientific attitude
+of mind involves a sweeping away of all other desires in the interests
+of the desire to know&mdash;it involves suppression of hopes and fears,
+loves and hates, and the whole subjective emotional life, until we
+become subdued to the material, able to see it frankly, without
+preconceptions, without bias, without any wish except to see it as it
+is, and without any belief that what it is must be determined by some
+relation, positive or negative, to what we should like it to be, or to
+what we can easily imagine it to be.</p>
+
+<p>Now in philosophy this attitude of mind has not as yet been achieved.
+A certain self-absorption, not personal, but human, has marked almost
+all attempts to conceive the universe as a whole. Mind, or some aspect
+of it&mdash;thought or will or sentience&mdash;has been regarded as the pattern
+after which the universe is to be conceived, for no better reason, at
+bottom, than that such a universe would not seem strange, and would
+give us the cosy feeling that every place is like home. To conceive
+the universe as essentially progressive or essentially deteriorating,
+for example, is to give to our hopes and fears a cosmic importance
+which <i>may</i>, of course, be justified, but which we have as yet no
+reason to suppose justified. Until we have learnt to think of it in
+ethically neutral terms, we have not arrived at a scientific attitude
+in philosophy; and until we have arrived at such an attitude, it is
+hardly to be hoped that philosophy will achieve any solid results.</p>
+
+<p>I have spoken so far largely of the negative aspect of the scientific
+spirit, but it is from the positive aspect that its value is derived.
+The instinct of constructiveness, which is one of the chief incentives
+to artistic creation, can find <span class='pagenum'><a name="Page_45" id="Page_45">[45]</a></span>in scientific systems a satisfaction
+more massive than any epic poem. Disinterested curiosity, which is the
+source of almost all intellectual effort, finds with astonished
+delight that science can unveil secrets which might well have seemed
+for ever undiscoverable. The desire for a larger life and wider
+interests, for an escape from private circumstances, and even from the
+whole recurring human cycle of birth and death, is fulfilled by the
+impersonal cosmic outlook of science as by nothing else. To all these
+must be added, as contributing to the happiness of the man of science,
+the admiration of splendid achievement, and the consciousness of
+inestimable utility to the human race. A life devoted to science is
+therefore a happy life, and its happiness is derived from the very
+best sources that are open to dwellers on this troubled and passionate
+planet.</p>
+
+<br />
+<br />
+<br />
+<br />
+<a name="III" id="III"></a><hr />
+<span class='pagenum'><a name="Page_46" id="Page_46">[46]</a></span><br />
+
+<h3>III<span class="totoc"><a href="#toc">ToC</a></span></h3>
+
+<h4>A FREE MAN'S WORSHIP<a name="FNanchor_9_9" id="FNanchor_9_9"></a><a href="#Footnote_9_9" class="fnanchor">[9]</a></h4>
+<br />
+
+<p>To Dr. Faustus in his study Mephistopheles told the history of the
+Creation, saying:</p>
+
+<p>"The endless praises of the choirs of angels had begun to grow
+wearisome; for, after all, did he not deserve their praise? Had he not
+given them endless joy? Would it not be more amusing to obtain
+undeserved praise, to be worshipped by beings whom he tortured? He
+smiled inwardly, and resolved that the great drama should be
+performed.</p>
+
+<p>"For countless ages the hot nebula whirled aimlessly through space. At
+length it began to take shape, the central mass threw off planets, the
+planets cooled, boiling seas and burning mountains heaved and tossed,
+from black masses of cloud hot sheets of rain deluged the barely solid
+crust. And now the first germ of life grew in the depths of the ocean,
+and developed rapidly in the fructifying warmth into vast forest
+trees, huge ferns springing from the damp mould, sea monsters
+breeding, fighting, devouring, and passing away. And from the
+monsters, as the play unfolded itself, Man was born, with the power of
+thought, the knowledge of good and evil, and the cruel thirst for
+worship. And Man saw that all is passing in this mad, monstrous world,
+that all is struggling to snatch, at any cost, a few brief moments of
+life before Death's inexorable decree. And <span class='pagenum'><a name="Page_47" id="Page_47">[47]</a></span>Man said: 'There is a
+hidden purpose, could we but fathom it, and the purpose is good; for
+we must reverence something, and in the visible world there is nothing
+worthy of reverence.' And Man stood aside from the struggle, resolving
+that God intended harmony to come out of chaos by human efforts. And
+when he followed the instincts which God had transmitted to him from
+his ancestry of beasts of prey, he called it Sin, and asked God to
+forgive him. But he doubted whether he could be justly forgiven, until
+he invented a divine Plan by which God's wrath was to have been
+appeased. And seeing the present was bad, he made it yet worse, that
+thereby the future might be better. And he gave God thanks for the
+strength that enabled him to forgo even the joys that were possible.
+And God smiled; and when he saw that Man had become perfect in
+renunciation and worship, he sent another sun through the sky, which
+crashed into Man's sun; and all returned again to nebula.</p>
+
+<p>"'Yes,' he murmured, 'it was a good play; I will have it performed
+again.'"</p>
+
+<p>Such, in outline, but even more purposeless, more void of meaning, is
+the world which Science presents for our belief. Amid such a world, if
+anywhere, our ideals henceforward must find a home. That Man is the
+product of causes which had no prevision of the end they were
+achieving; that his origin, his growth, his hopes and fears, his loves
+and his beliefs, are but the outcome of accidental collocations of
+atoms; that no fire, no heroism, no intensity of thought and feeling,
+can preserve an individual life beyond the grave; that all the labours
+of the ages, all the devotion, all the inspiration, all the noonday
+brightness of human genius, are destined to extinction in the vast
+death of the solar <span class='pagenum'><a name="Page_48" id="Page_48">[48]</a></span>system, and that the whole temple of Man's
+achievement must inevitably be buried beneath the d&eacute;bris of a universe
+in ruins&mdash;all these things, if not quite beyond dispute, are yet so
+nearly certain, that no philosophy which rejects them can hope to
+stand. Only within the scaffolding of these truths, only on the firm
+foundation of unyielding despair, can the soul's habitation henceforth
+be safely built.</p>
+
+<p>How, in such an alien and inhuman world, can so powerless a creature
+as Man preserve his aspirations untarnished? A strange mystery it is
+that Nature, omnipotent but blind, in the revolutions of her secular
+hurryings through the abysses of space, has brought forth at last a
+child, subject still to her power, but gifted with sight, with
+knowledge of good and evil, with the capacity of judging all the works
+of his unthinking Mother. In spite of Death, the mark and seal of the
+parental control, Man is yet free, during his brief years, to examine,
+to criticise, to know, and in imagination to create. To him alone, in
+the world with which he is acquainted, this freedom belongs; and in
+this lies his superiority to the resistless forces that control his
+outward life.</p>
+
+<p>The savage, like ourselves, feels the oppression of his impotence
+before the powers of Nature; but having in himself nothing that he
+respects more than Power, he is willing to prostrate himself before
+his gods, without inquiring whether they are worthy of his worship.
+Pathetic and very terrible is the long history of cruelty and torture,
+of degradation and human sacrifice, endured in the hope of placating
+the jealous gods: surely, the trembling believer thinks, when what is
+most precious has been freely given, their lust for blood must be
+appeased, and more will not be required. The religion of <span class='pagenum'><a name="Page_49" id="Page_49">[49]</a></span>Moloch&mdash;as
+such creeds may be generically called&mdash;is in essence the cringing
+submission of the slave, who dare not, even in his heart, allow the
+thought that his master deserves no adulation. Since the independence
+of ideals is not yet acknowledged, Power may be freely worshipped, and
+receive an unlimited respect, despite its wanton infliction of pain.</p>
+
+<p>But gradually, as morality grows bolder, the claim of the ideal world
+begins to be felt; and worship, if it is not to cease, must be given
+to gods of another kind than those created by the savage. Some, though
+they feel the demands of the ideal, will still consciously reject
+them, still urging that naked Power is worthy of worship. Such is the
+attitude inculcated in God's answer to Job out of the whirlwind: the
+divine power and knowledge are paraded, but of the divine goodness
+there is no hint. Such also is the attitude of those who, in our own
+day, base their morality upon the struggle for survival, maintaining
+that the survivors are necessarily the fittest. But others, not
+content with an answer so repugnant to the moral sense, will adopt the
+position which we have become accustomed to regard as specially
+religious, maintaining that, in some hidden manner, the world of fact
+is really harmonious with the world of ideals. Thus Man creates God,
+all-powerful and all-good, the mystic unity of what is and what should
+be.</p>
+
+<p>But the world of fact, after all, is not good; and, in submitting our
+judgment to it, there is an element of slavishness from which our
+thoughts must be purged. For in all things it is well to exalt the
+dignity of Man, by freeing him as far as possible from the tyranny of
+non-human Power. When we have realised that Power is largely bad, that
+man, with his knowledge of good and evil, is but a helpless atom in a
+world which has no such <span class='pagenum'><a name="Page_50" id="Page_50">[50]</a></span>knowledge, the choice is again presented to
+us: Shall we worship Force, or shall we worship Goodness? Shall our
+God exist and be evil, or shall he be recognised as the creation of
+our own conscience?</p>
+
+<p>The answer to this question is very momentous, and affects profoundly
+our whole morality. The worship of Force, to which Carlyle and
+Nietzsche and the creed of Militarism have accustomed us, is the
+result of failure to maintain our own ideals against a hostile
+universe: it is itself a prostrate submission to evil, a sacrifice of
+our best to Moloch. If strength indeed is to be respected, let us
+respect rather the strength of those who refuse that false
+"recognition of facts" which fails to recognise that facts are often
+bad. Let us admit that, in the world we know, there are many things
+that would be better otherwise, and that the ideals to which we do and
+must adhere are not realised in the realm of matter. Let us preserve
+our respect for truth, for beauty, for the ideal of perfection which
+life does not permit us to attain, though none of these things meet
+with the approval of the unconscious universe. If Power is bad, as it
+seems to be, let us reject it from our hearts. In this lies Man's true
+freedom: in determination to worship only the God created by our own
+love of the good, to respect only the heaven which inspires the
+insight of our best moments. In action, in desire, we must submit
+perpetually to the tyranny of outside forces; but in thought, in
+aspiration, we are free, free from our fellow-men, free from the petty
+planet on which our bodies impotently crawl, free even, while we live,
+from the tyranny of death. Let us learn, then, that energy of faith
+which enables us to live constantly in the vision of the good; and let
+us descend, in action, into the world of fact, with that vision always
+before us.</p>
+
+<p><span class='pagenum'><a name="Page_51" id="Page_51">[51]</a></span>When first the opposition of fact and ideal grows fully visible, a
+spirit of fiery revolt, of fierce hatred of the gods, seems necessary
+to the assertion of freedom. To defy with Promethean constancy a
+hostile universe, to keep its evil always in view, always actively
+hated, to refuse no pain that the malice of Power can invent, appears
+to be the duty of all who will not bow before the inevitable. But
+indignation is still a bondage, for it compels our thoughts to be
+occupied with an evil world; and in the fierceness of desire from
+which rebellion springs there is a kind of self-assertion which it is
+necessary for the wise to overcome. Indignation is a submission of our
+thoughts, but not of our desires; the Stoic freedom in which wisdom
+consists is found in the submission of our desires, but not of our
+thoughts. From the submission of our desires springs the virtue of
+resignation; from the freedom of our thoughts springs the whole world
+of art and philosophy, and the vision of beauty by which, at last, we
+half reconquer the reluctant world. But the vision of beauty is
+possible only to unfettered contemplation, to thoughts not weighted by
+the load of eager wishes; and thus Freedom comes only to those who no
+longer ask of life that it shall yield them any of those personal
+goods that are subject to the mutations of Time.</p>
+
+<p>Although the necessity of renunciation is evidence of the existence of
+evil, yet Christianity, in preaching it, has shown a wisdom exceeding
+that of the Promethean philosophy of rebellion. It must be admitted
+that, of the things we desire, some, though they prove impossible, are
+yet real goods; others, however, as ardently longed for, do not form
+part of a fully purified ideal. The belief that what must be renounced
+is bad, though sometimes false, is far less often false than untamed
+passion supposes; and the creed of religion, by providing a reason
+<span class='pagenum'><a name="Page_52" id="Page_52">[52]</a></span>for proving that it is never false, has been the means of purifying
+our hopes by the discovery of many austere truths.</p>
+
+<p>But there is in resignation a further good element: even real goods,
+when they are unattainable, ought not to be fretfully desired. To
+every man comes, sooner or later, the great renunciation. For the
+young, there is nothing unattainable; a good thing desired with the
+whole force of a passionate will, and yet impossible, is to them not
+credible. Yet, by death, by illness, by poverty, or by the voice of
+duty, we must learn, each one of us, that the world was not made for
+us, and that, however beautiful may be the things we crave, Fate may
+nevertheless forbid them. It is the part of courage, when misfortune
+comes, to bear without repining the ruin of our hopes, to turn away
+our thoughts from vain regrets. This degree of submission to Power is
+not only just and right: it is the very gate of wisdom.</p>
+
+<p>But passive renunciation is not the whole of wisdom; for not by
+renunciation alone can we build a temple for the worship of our own
+ideals. Haunting foreshadowings of the temple appear in the realm of
+imagination, in music, in architecture, in the untroubled kingdom of
+reason, and in the golden sunset magic of lyrics, where beauty shines
+and glows, remote from the touch of sorrow, remote from the fear of
+change, remote from the failures and disenchantments of the world of
+fact. In the contemplation of these things the vision of heaven will
+shape itself in our hearts, giving at once a touchstone to judge the
+world about us, and an inspiration by which to fashion to our needs
+whatever is not incapable of serving as a stone in the sacred temple.</p>
+
+<p>Except for those rare spirits that are born without sin, there is a
+cavern of darkness to be traversed before that <span class='pagenum'><a name="Page_53" id="Page_53">[53]</a></span>temple can be entered.
+The gate of the cavern is despair, and its floor is paved with the
+gravestones of abandoned hopes. There Self must die; there the
+eagerness, the greed of untamed desire must be slain, for only so can
+the soul be freed from the empire of Fate. But out of the cavern the
+Gate of Renunciation leads again to the daylight of wisdom, by whose
+radiance a new insight, a new joy, a new tenderness, shine forth to
+gladden the pilgrim's heart.</p>
+
+<p>When, without the bitterness of impotent rebellion, we have learnt
+both to resign ourselves to the outward rule of Fate and to recognise
+that the non-human world is unworthy of our worship, it becomes
+possible at last so to transform and refashion the unconscious
+universe, so to transmute it in the crucible of imagination, that a
+new image of shining gold replaces the old idol of clay. In all the
+multiform facts of the world&mdash;in the visual shapes of trees and
+mountains and clouds, in the events of the life of man, even in the
+very omnipotence of Death&mdash;the insight of creative idealism can find
+the reflection of a beauty which its own thoughts first made. In this
+way mind asserts its subtle mastery over the thoughtless forces of
+Nature. The more evil the material with which it deals, the more
+thwarting to untrained desire, the greater is its achievement in
+inducing the reluctant rock to yield up its hidden treasures, the
+prouder its victory in compelling the opposing forces to swell the
+pageant of its triumph. Of all the arts, Tragedy is the proudest, the
+most triumphant; for it builds its shining citadel in the very centre
+of the enemy's country, on the very summit of his highest mountain;
+from its impregnable watchtowers, his camps and arsenals, his columns
+and forts, are all revealed; within its walls the free life continues,
+while the legions of Death and Pain and Despair, and all <span class='pagenum'><a name="Page_54" id="Page_54">[54]</a></span>the servile
+captains of tyrant Fate, afford the burghers of that dauntless city
+new spectacles of beauty. Happy those sacred ramparts, thrice happy
+the dwellers on that all-seeing eminence. Honour to those brave
+warriors who, through countless ages of warfare, have preserved for us
+the priceless heritage of liberty, and have kept undefiled by
+sacrilegious invaders the home of the unsubdued.</p>
+
+<p>But the beauty of Tragedy does but make visible a quality which, in
+more or less obvious shapes, is present always and everywhere in life.
+In the spectacle of Death, in the endurance of intolerable pain, and
+in the irrevocableness of a vanished past, there is a sacredness, an
+overpowering awe, a feeling of the vastness, the depth, the
+inexhaustible mystery of existence, in which, as by some strange
+marriage of pain, the sufferer is bound to the world by bonds of
+sorrow. In these moments of insight, we lose all eagerness of
+temporary desire, all struggling and striving for petty ends, all care
+for the little trivial things that, to a superficial view, make up the
+common life of day by day; we see, surrounding the narrow raft
+illumined by the flickering light of human comradeship, the dark ocean
+on whose rolling waves we toss for a brief hour; from the great night
+without, a chill blast breaks in upon our refuge; all the loneliness
+of humanity amid hostile forces is concentrated upon the individual
+soul, which must struggle alone, with what of courage it can command,
+against the whole weight of a universe that cares nothing for its
+hopes and fears. Victory, in this struggle with the powers of
+darkness, is the true baptism into the glorious company of heroes, the
+true initiation into the overmastering beauty of human existence. From
+that awful encounter of the soul with the outer world, renunciation,
+wisdom, and charity are born; and with <span class='pagenum'><a name="Page_55" id="Page_55">[55]</a></span>their birth a new life begins.
+To take into the inmost shrine of the soul the irresistible forces
+whose puppets we seem to be&mdash;Death and change, the irrevocableness of
+the past, and the powerlessness of man before the blind hurry of the
+universe from vanity to vanity&mdash;to feel these things and know them is
+to conquer them.</p>
+
+<p>This is the reason why the Past has such magical power. The beauty of
+its motionless and silent pictures is like the enchanted purity of
+late autumn, when the leaves, though one breath would make them fall,
+still glow against the sky in golden glory. The Past does not change
+or strive; like Duncan, after life's fitful fever it sleeps well; what
+was eager and grasping, what was petty and transitory, has faded away,
+the things that were beautiful and eternal shine out of it like stars
+in the night. Its beauty, to a soul not worthy of it, is unendurable;
+but to a soul which has conquered Fate it is the key of religion.</p>
+
+<p>The life of Man, viewed outwardly, is but a small thing in comparison
+with the forces of Nature. The slave is doomed to worship Time and
+Fate and Death, because they are greater than anything he finds in
+himself, and because all his thoughts are of things which they devour.
+But, great as they are, to think of them greatly, to feel their
+passionless splendour, is greater still. And such thought makes us
+free men; we no longer bow before the inevitable in Oriental
+subjection, but we absorb it, and make it a part of ourselves. To
+abandon the struggle for private happiness, to expel all eagerness of
+temporary desire, to burn with passion for eternal things&mdash;this is
+emancipation, and this is the free man's worship. And this liberation
+is effected by a contemplation of Fate; for Fate itself is subdued by
+the <span class='pagenum'><a name="Page_56" id="Page_56">[56]</a></span>mind which leaves nothing to be purged by the purifying fire of
+Time.</p>
+
+<p>United with his fellow-men by the strongest of all ties, the tie of a
+common doom, the free man finds that a new vision is with him always,
+shedding over every daily task the light of love. The life of Man is a
+long march through the night, surrounded by invisible foes, tortured
+by weariness and pain, towards a goal that few can hope to reach, and
+where none may tarry long. One by one, as they march, our comrades
+vanish from our sight, seized by the silent orders of omnipotent
+Death. Very brief is the time in which we can help them, in which
+their happiness or misery is decided. Be it ours to shed sunshine on
+their path, to lighten their sorrows by the balm of sympathy, to give
+them the pure joy of a never-tiring affection, to strengthen failing
+courage, to instil faith in hours of despair. Let us not weigh in
+grudging scales their merits and demerits, but let us think only of
+their need&mdash;of the sorrows, the difficulties, perhaps the blindnesses,
+that make the misery of their lives; let us remember that they are
+fellow-sufferers in the same darkness, actors in the same tragedy with
+ourselves. And so, when their day is over, when their good and their
+evil have become eternal by the immortality of the past, be it ours to
+feel that, where they suffered, where they failed, no deed of ours was
+the cause; but wherever a spark of the divine fire kindled in their
+hearts, we were ready with encouragement, with sympathy, with brave
+words in which high courage glowed.</p>
+
+<p>Brief and powerless is Man's life; on him and all his race the slow,
+sure doom falls pitiless and dark. Blind to good and evil, reckless of
+destruction, omnipotent matter rolls on its relentless way; for Man,
+condemned to-day to lose his dearest, to-morrow himself to pass
+<span class='pagenum'><a name="Page_57" id="Page_57">[57]</a></span>through the gate of darkness, it remains only to cherish, ere yet the
+blow falls, the lofty thoughts that ennoble his little day; disdaining
+the coward terrors of the slave of Fate, to worship at the shrine that
+his own hands have built; undismayed by the empire of chance, to
+preserve a mind free from the wanton tyranny that rules his outward
+life; proudly defiant of the irresistible forces that tolerate, for a
+moment, his knowledge and his condemnation, to sustain alone, a weary
+but unyielding Atlas, the world that his own ideals have fashioned
+despite the trampling march of unconscious power.</p>
+
+<br />
+<hr style="width: 15%;" />
+<br />
+
+<h4>FOOTNOTES:</h4>
+
+<div class="footnote"><p class="noin"><a name="Footnote_9_9" id="Footnote_9_9"></a><a href="#FNanchor_9_9"><span class="label">[9]</span></a> Reprinted from the <i>Independent Review</i>, December,
+1903.</p></div>
+
+
+<br />
+<br />
+<br />
+<br />
+<a name="IV" id="IV"></a><hr />
+<span class='pagenum'><a name="Page_58" id="Page_58">[58]</a></span><br />
+
+<h3>IV<span class="totoc"><a href="#toc">ToC</a></span></h3>
+
+<h4>THE STUDY OF MATHEMATICS</h4>
+<br />
+
+<p>In regard to every form of human activity it is necessary that the
+question should be asked from time to time, What is its purpose and
+ideal? In what way does it contribute to the beauty of human
+existence? As respects those pursuits which contribute only remotely,
+by providing the mechanism of life, it is well to be reminded that not
+the mere fact of living is to be desired, but the art of living in the
+contemplation of great things. Still more in regard to those
+avocations which have no end outside themselves, which are to be
+justified, if at all, as actually adding to the sum of the world's
+permanent possessions, it is necessary to keep alive a knowledge of
+their aims, a clear prefiguring vision of the temple in which creative
+imagination is to be embodied.</p>
+
+<p>The fulfilment of this need, in what concerns the studies forming the
+material upon which custom has decided to train the youthful mind, is
+indeed sadly remote&mdash;so remote as to make the mere statement of such a
+claim appear preposterous. Great men, fully alive to the beauty of the
+contemplations to whose service their lives are devoted, desiring that
+others may share in their joys, persuade mankind to impart to the
+successive generations the mechanical knowledge without which it is
+impossible to cross the threshold. Dry pedants possess themselves of
+the privilege of instilling this knowledge: they forget that it is to
+serve but as a <span class='pagenum'><a name="Page_59" id="Page_59">[59]</a></span>key to open the doors of the temple; though they spend
+their lives on the steps leading up to those sacred doors, they turn
+their backs upon the temple so resolutely that its very existence is
+forgotten, and the eager youth, who would press forward to be
+initiated to its domes and arches, is bidden to turn back and count
+the steps.</p>
+
+<p>Mathematics, perhaps more even than the study of Greece and Rome, has
+suffered from this oblivion of its due place in civilisation. Although
+tradition has decreed that the great bulk of educated men shall know
+at least the elements of the subject, the reasons for which the
+tradition arose are forgotten, buried beneath a great rubbish-heap of
+pedantries and trivialities. To those who inquire as to the purpose of
+mathematics, the usual answer will be that it facilitates the making
+of machines, the travelling from place to place, and the victory over
+foreign nations, whether in war or commerce. If it be objected that
+these ends&mdash;all of which are of doubtful value&mdash;are not furthered by
+the merely elementary study imposed upon those who do not become
+expert mathematicians, the reply, it is true, will probably be that
+mathematics trains the reasoning faculties. Yet the very men who make
+this reply are, for the most part, unwilling to abandon the teaching
+of definite fallacies, known to be such, and instinctively rejected by
+the unsophisticated mind of every intelligent learner. And the
+reasoning faculty itself is generally conceived, by those who urge its
+cultivation, as merely a means for the avoidance of pitfalls and a
+help in the discovery of rules for the guidance of practical life. All
+these are undeniably important achievements to the credit of
+mathematics; yet it is none of these that entitles mathematics to a
+place in every liberal education. Plato, we know, regarded the
+contemplation of mathematical truths as worthy of the <span class='pagenum'><a name="Page_60" id="Page_60">[60]</a></span>Deity; and
+Plato realised, more perhaps than any other single man, what those
+elements are in human life which merit a place in heaven. There is in
+mathematics, he says, "something which is <i>necessary</i> and cannot be
+set aside ... and, if I mistake not, of divine necessity; for as to
+the human necessities of which the Many talk in this connection,
+nothing can be more ridiculous than such an application of the words.
+<i>Cleinias.</i> And what are these necessities of knowledge, Stranger,
+which are divine and not human? <i>Athenian.</i> Those things without some
+use or knowledge of which a man cannot become a God to the world, nor
+a spirit, nor yet a hero, nor able earnestly to think and care for
+man" (<i>Laws</i>, p. 818).<a name="FNanchor_10_10" id="FNanchor_10_10"></a><a href="#Footnote_10_10" class="fnanchor">[10]</a> Such was Plato's judgment of mathematics;
+but the mathematicians do not read Plato, while those who read him
+know no mathematics, and regard his opinion upon this question as
+merely a curious aberration.</p>
+
+<p>Mathematics, rightly viewed, possesses not only truth, but supreme
+beauty&mdash;a beauty cold and austere, like that of sculpture, without
+appeal to any part of our weaker nature, without the gorgeous
+trappings of painting or music, yet sublimely pure, and capable of a
+stern perfection such as only the greatest art can show. The true
+spirit of delight, the exaltation, the sense of being more than man,
+which is the touchstone of the highest excellence, is to be found in
+mathematics as surely as in poetry. What is best in mathematics
+deserves not merely to be learnt as a task, but to be assimilated as a
+part of daily thought, and brought again and again before the mind
+with ever-renewed encouragement. Real life is, to most men, a long
+second-best, a perpetual compromise between the ideal and the
+possible; but the world of pure reason knows no compromise, no
+practical <span class='pagenum'><a name="Page_61" id="Page_61">[61]</a></span>limitations, no barrier to the creative activity embodying
+in splendid edifices the passionate aspiration after the perfect from
+which all great work springs. Remote from human passions, remote even
+from the pitiful facts of nature, the generations have gradually
+created an ordered cosmos, where pure thought can dwell as in its
+natural home, and where one, at least, of our nobler impulses can
+escape from the dreary exile of the actual world.</p>
+
+<p>So little, however, have mathematicians aimed at beauty, that hardly
+anything in their work has had this conscious purpose. Much, owing to
+irrepressible instincts, which were better than avowed beliefs, has
+been moulded by an unconscious taste; but much also has been spoilt by
+false notions of what was fitting. The characteristic excellence of
+mathematics is only to be found where the reasoning is rigidly
+logical: the rules of logic are to mathematics what those of structure
+are to architecture. In the most beautiful work, a chain of argument
+is presented in which every link is important on its own account, in
+which there is an air of ease and lucidity throughout, and the
+premises achieve more than would have been thought possible, by means
+which appear natural and inevitable. Literature embodies what is
+general in particular circumstances whose universal significance
+shines through their individual dress; but mathematics endeavours to
+present whatever is most general in its purity, without any irrelevant
+trappings.</p>
+
+<p>How should the teaching of mathematics be conducted so as to
+communicate to the learner as much as possible of this high ideal?
+Here experience must, in a great measure, be our guide; but some
+maxims may result from our consideration of the ultimate purpose to be
+achieved.</p>
+
+<p><span class='pagenum'><a name="Page_62" id="Page_62">[62]</a></span>One of the chief ends served by mathematics, when rightly taught, is
+to awaken the learner's belief in reason, his confidence in the truth
+of what has been demonstrated, and in the value of demonstration. This
+purpose is not served by existing instruction; but it is easy to see
+ways in which it might be served. At present, in what concerns
+arithmetic, the boy or girl is given a set of rules, which present
+themselves as neither true nor false, but as merely the will of the
+teacher, the way in which, for some unfathomable reason, the teacher
+prefers to have the game played. To some degree, in a study of such
+definite practical utility, this is no doubt unavoidable; but as soon
+as possible, the reasons of rules should be set forth by whatever
+means most readily appeal to the childish mind. In geometry, instead
+of the tedious apparatus of fallacious proofs for obvious truisms
+which constitutes the beginning of Euclid, the learner should be
+allowed at first to assume the truth of everything obvious, and should
+be instructed in the demonstrations of theorems which are at once
+startling and easily verifiable by actual drawing, such as those in
+which it is shown that three or more lines meet in a point. In this
+way belief is generated; it is seen that reasoning may lead to
+startling conclusions, which nevertheless the facts will verify; and
+thus the instinctive distrust of whatever is abstract or rational is
+gradually overcome. Where theorems are difficult, they should be first
+taught as exercises in geometrical drawing, until the figure has
+become thoroughly familiar; it will then be an agreeable advance to be
+taught the logical connections of the various lines or circles that
+occur. It is desirable also that the figure illustrating a theorem
+should be drawn in all possible cases and shapes, that so the abstract
+relations with which geometry is concerned may of themselves <span class='pagenum'><a name="Page_63" id="Page_63">[63]</a></span>emerge
+as the residue of similarity amid such great apparent diversity. In
+this way the abstract demonstrations should form but a small part of
+the instruction, and should be given when, by familiarity with
+concrete illustrations, they have come to be felt as the natural
+embodiment of visible fact. In this early stage proofs should not be
+given with pedantic fullness; definitely fallacious methods, such as
+that of superposition, should be rigidly excluded from the first, but
+where, without such methods, the proof would be very difficult, the
+result should be rendered acceptable by arguments and illustrations
+which are explicitly contrasted with demonstrations.</p>
+
+<p>In the beginning of algebra, even the most intelligent child finds, as
+a rule, very great difficulty. The use of letters is a mystery, which
+seems to have no purpose except mystification. It is almost
+impossible, at first, not to think that every letter stands for some
+particular number, if only the teacher would reveal <i>what</i> number it
+stands for. The fact is, that in algebra the mind is first taught to
+consider general truths, truths which are not asserted to hold only of
+this or that particular thing, but of any one of a whole group of
+things. It is in the power of understanding and discovering such
+truths that the mastery of the intellect over the whole world of
+things actual and possible resides; and ability to deal with the
+general as such is one of the gifts that a mathematical education
+should bestow. But how little, as a rule, is the teacher of algebra
+able to explain the chasm which divides it from arithmetic, and how
+little is the learner assisted in his groping efforts at
+comprehension! Usually the method that has been adopted in arithmetic
+is continued: rules are set forth, with no adequate explanation of
+their grounds; the pupil learns to use the rules blindly, <span class='pagenum'><a name="Page_64" id="Page_64">[64]</a></span>and
+presently, when he is able to obtain the answer that the teacher
+desires, he feels that he has mastered the difficulties of the
+subject. But of inner comprehension of the processes employed he has
+probably acquired almost nothing.</p>
+
+<p>When algebra has been learnt, all goes smoothly until we reach those
+studies in which the notion of infinity is employed&mdash;the infinitesimal
+calculus and the whole of higher mathematics. The solution of the
+difficulties which formerly surrounded the mathematical infinite is
+probably the greatest achievement of which our own age has to boast.
+Since the beginnings of Greek thought these difficulties have been
+known; in every age the finest intellects have vainly endeavoured to
+answer the apparently unanswerable questions that had been asked by
+Zeno the Eleatic. At last Georg Cantor has found the answer, and has
+conquered for the intellect a new and vast province which had been
+given over to Chaos and old Night. It was assumed as self-evident,
+until Cantor and Dedekind established the opposite, that if, from any
+collection of things, some were taken away, the number of things left
+must always be less than the original number of things. This
+assumption, as a matter of fact, holds only of finite collections; and
+the rejection of it, where the infinite is concerned, has been shown
+to remove all the difficulties that had hitherto baffled human reason
+in this matter, and to render possible the creation of an exact
+science of the infinite. This stupendous fact ought to produce a
+revolution in the higher teaching of mathematics; it has itself added
+immeasurably to the educational value of the subject, and it has at
+last given the means of treating with logical precision many studies
+which, until lately, were wrapped in fallacy and obscurity. By those
+who were educated on the <span class='pagenum'><a name="Page_65" id="Page_65">[65]</a></span>old lines, the new work is considered to be
+appallingly difficult, abstruse, and obscure; and it must be confessed
+that the discoverer, as is so often the case, has hardly himself
+emerged from the mists which the light of his intellect is dispelling.
+But inherently, the new doctrine of the infinite, to all candid and
+inquiring minds, has facilitated the mastery of higher mathematics;
+for hitherto, it has been necessary to learn, by a long process of
+sophistication, to give assent to arguments which, on first
+acquaintance, were rightly judged to be confused and erroneous. So far
+from producing a fearless belief in reason, a bold rejection of
+whatever failed to fulfil the strictest requirements of logic, a
+mathematical training, during the past two centuries, encouraged the
+belief that many things, which a rigid inquiry would reject as
+fallacious, must yet be accepted because they work in what the
+mathematician calls "practice." By this means, a timid, compromising
+spirit, or else a sacerdotal belief in mysteries not intelligible to
+the profane, has been bred where reason alone should have ruled. All
+this it is now time to sweep away; let those who wish to penetrate
+into the arcana of mathematics be taught at once the true theory in
+all its logical purity, and in the concatenation established by the
+very essence of the entities concerned.</p>
+
+<p>If we are considering mathematics as an end in itself, and not as a
+technical training for engineers, it is very desirable to preserve the
+purity and strictness of its reasoning. Accordingly those who have
+attained a sufficient familiarity with its easier portions should be
+led backward from propositions to which they have assented as
+self-evident to more and more fundamental principles from which what
+had previously appeared as premises can be deduced. They should be
+<span class='pagenum'><a name="Page_66" id="Page_66">[66]</a></span>taught&mdash;what the theory of infinity very aptly illustrates&mdash;that many
+propositions seem self-evident to the untrained mind which,
+nevertheless, a nearer scrutiny shows to be false. By this means they
+will be led to a sceptical inquiry into first principles, an
+examination of the foundations upon which the whole edifice of
+reasoning is built, or, to take perhaps a more fitting metaphor, the
+great trunk from which the spreading branches spring. At this stage,
+it is well to study afresh the elementary portions of mathematics,
+asking no longer merely whether a given proposition is true, but also
+how it grows out of the central principles of logic. Questions of this
+nature can now be answered with a precision and certainty which were
+formerly quite impossible; and in the chains of reasoning that the
+answer requires the unity of all mathematical studies at last unfolds
+itself.</p>
+
+<p>In the great majority of mathematical text-books there is a total lack
+of unity in method and of systematic development of a central theme.
+Propositions of very diverse kinds are proved by whatever means are
+thought most easily intelligible, and much space is devoted to mere
+curiosities which in no way contribute to the main argument. But in
+the greatest works, unity and inevitability are felt as in the
+unfolding of a drama; in the premisses a subject is proposed for
+consideration, and in every subsequent step some definite advance is
+made towards mastery of its nature. The love of system, of
+interconnection, which is perhaps the inmost essence of the
+intellectual impulse, can find free play in mathematics as nowhere
+else. The learner who feels this impulse must not be repelled by an
+array of meaningless examples or distracted by amusing oddities, but
+must be encouraged to dwell upon central principles, to become
+familiar with the structure of the various subjects which are put
+before <span class='pagenum'><a name="Page_67" id="Page_67">[67]</a></span>him, to travel easily over the steps of the more important
+deductions. In this way a good tone of mind is cultivated, and
+selective attention is taught to dwell by preference upon what is
+weighty and essential.</p>
+
+<p>When the separate studies into which mathematics is divided have each
+been viewed as a logical whole, as a natural growth from the
+propositions which constitute their principles, the learner will be
+able to understand the fundamental science which unifies and
+systematises the whole of deductive reasoning. This is symbolic
+logic&mdash;a study which, though it owes its inception to Aristotle, is
+yet, in its wider developments, a product, almost wholly, of the
+nineteenth century, and is indeed, in the present day, still growing
+with great rapidity. The true method of discovery in symbolic logic,
+and probably also the best method for introducing the study to a
+learner acquainted with other parts of mathematics, is the analysis of
+actual examples of deductive reasoning, with a view to the discovery
+of the principles employed. These principles, for the most part, are
+so embedded in our ratiocinative instincts, that they are employed
+quite unconsciously, and can be dragged to light only by much patient
+effort. But when at last they have been found, they are seen to be few
+in number, and to be the sole source of everything in pure
+mathematics. The discovery that all mathematics follows inevitably
+from a small collection of fundamental laws is one which immeasurably
+enhances the intellectual beauty of the whole; to those who have been
+oppressed by the fragmentary and incomplete nature of most existing
+chains of deduction this discovery comes with all the overwhelming
+force of a revelation; like a palace emerging from the autumn mist as
+the traveller ascends an Italian hill-side, the stately storeys of the
+mathematical edifice appear in their <span class='pagenum'><a name="Page_68" id="Page_68">[68]</a></span>due order and proportion, with a
+new perfection in every part.</p>
+
+<p>Until symbolic logic had acquired its present development, the
+principles upon which mathematics depends were always supposed to be
+philosophical, and discoverable only by the uncertain, unprogressive
+methods hitherto employed by philosophers. So long as this was
+thought, mathematics seemed to be not autonomous, but dependent upon a
+study which had quite other methods than its own. Moreover, since the
+nature of the postulates from which arithmetic, analysis, and geometry
+are to be deduced was wrapped in all the traditional obscurities of
+metaphysical discussion, the edifice built upon such dubious
+foundations began to be viewed as no better than a castle in the air.
+In this respect, the discovery that the true principles are as much a
+part of mathematics as any of their consequences has very greatly
+increased the intellectual satisfaction to be obtained. This
+satisfaction ought not to be refused to learners capable of enjoying
+it, for it is of a kind to increase our respect for human powers and
+our knowledge of the beauties belonging to the abstract world.</p>
+
+<p>Philosophers have commonly held that the laws of logic, which underlie
+mathematics, are laws of thought, laws regulating the operations of
+our minds. By this opinion the true dignity of reason is very greatly
+lowered: it ceases to be an investigation into the very heart and
+immutable essence of all things actual and possible, becoming,
+instead, an inquiry into something more or less human and subject to
+our limitations. The contemplation of what is non-human, the discovery
+that our minds are capable of dealing with material not created by
+them, above all, the realisation that beauty belongs to the outer
+world as to the inner, are the chief means of overcoming <span class='pagenum'><a name="Page_69" id="Page_69">[69]</a></span>the terrible
+sense of impotence, of weakness, of exile amid hostile powers, which
+is too apt to result from acknowledging the all-but omnipotence of
+alien forces. To reconcile us, by the exhibition of its awful beauty,
+to the reign of Fate&mdash;which is merely the literary personification of
+these forces&mdash;is the task of tragedy. But mathematics takes us still
+further from what is human, into the region of absolute necessity, to
+which not only the actual world, but every possible world, must
+conform; and even here it builds a habitation, or rather finds a
+habitation eternally standing, where our ideals are fully satisfied
+and our best hopes are not thwarted. It is only when we thoroughly
+understand the entire independence of ourselves, which belongs to this
+world that reason finds, that we can adequately realise the profound
+importance of its beauty.</p>
+
+<p>Not only is mathematics independent of us and our thoughts, but in
+another sense we and the whole universe of existing things are
+independent of mathematics. The apprehension of this purely ideal
+character is indispensable, if we are to understand rightly the place
+of mathematics as one among the arts. It was formerly supposed that
+pure reason could decide, in some respects, as to the nature of the
+actual world: geometry, at least, was thought to deal with the space
+in which we live. But we now know that pure mathematics can never
+pronounce upon questions of actual existence: the world of reason, in
+a sense, controls the world of fact, but it is not at any point
+creative of fact, and in the application of its results to the world
+in time and space, its certainty and precision are lost among
+approximations and working hypotheses. The objects considered by
+mathematicians have, in the past, been mainly of a kind suggested by
+phenomena; but from such restrictions the abstract imagination <span class='pagenum'><a name="Page_70" id="Page_70">[70]</a></span>should
+be wholly free. A reciprocal liberty must thus be accorded: reason
+cannot dictate to the world of facts, but the facts cannot restrict
+reason's privilege of dealing with whatever objects its love of beauty
+may cause to seem worthy of consideration. Here, as elsewhere, we
+build up our own ideals out of the fragments to be found in the world;
+and in the end it is hard to say whether the result is a creation or a
+discovery.</p>
+
+<p>It is very desirable, in instruction, not merely to persuade the
+student of the accuracy of important theorems, but to persuade him in
+the way which itself has, of all possible ways, the most beauty. The
+true interest of a demonstration is not, as traditional modes of
+exposition suggest, concentrated wholly in the result; where this does
+occur, it must be viewed as a defect, to be remedied, if possible, by
+so generalising the steps of the proof that each becomes important in
+and for itself. An argument which serves only to prove a conclusion is
+like a story subordinated to some moral which it is meant to teach:
+for &aelig;sthetic perfection no part of the whole should be merely a means.
+A certain practical spirit, a desire for rapid progress, for conquest
+of new realms, is responsible for the undue emphasis upon results
+which prevails in mathematical instruction. The better way is to
+propose some theme for consideration&mdash;in geometry, a figure having
+important properties; in analysis, a function of which the study is
+illuminating, and so on. Whenever proofs depend upon some only of the
+marks by which we define the object to be studied, these marks should
+be isolated and investigated on their own account. For it is a defect,
+in an argument, to employ more premisses than the conclusion demands:
+what mathematicians call elegance results from employing only the
+essential principles in virtue of which the thesis is true. It is a
+merit in <span class='pagenum'><a name="Page_71" id="Page_71">[71]</a></span>Euclid that he advances as far as he is able to go without
+employing the axiom of parallels&mdash;not, as is often said, because this
+axiom is inherently objectionable, but because, in mathematics, every
+new axiom diminishes the generality of the resulting theorems, and the
+greatest possible generality is before all things to be sought.</p>
+
+<p>Of the effects of mathematics outside its own sphere more has been
+written than on the subject of its own proper ideal. The effect upon
+philosophy has, in the past, been most notable, but most varied; in
+the seventeenth century, idealism and rationalism, in the eighteenth,
+materialism and sensationalism, seemed equally its offspring. Of the
+effect which it is likely to have in the future it would be very rash
+to say much; but in one respect a good result appears probable.
+Against that kind of scepticism which abandons the pursuit of ideals
+because the road is arduous and the goal not certainly attainable,
+mathematics, within its own sphere, is a complete answer. Too often it
+is said that there is no absolute truth, but only opinion and private
+judgment; that each of us is conditioned, in his view of the world, by
+his own peculiarities, his own taste and bias; that there is no
+external kingdom of truth to which, by patience and discipline, we may
+at last obtain admittance, but only truth for me, for you, for every
+separate person. By this habit of mind one of the chief ends of human
+effort is denied, and the supreme virtue of candour, of fearless
+acknowledgment of what is, disappears from our moral vision. Of such
+scepticism mathematics is a perpetual reproof; for its edifice of
+truths stands unshakable and inexpungable to all the weapons of
+doubting cynicism.</p>
+
+<p>The effects of mathematics upon practical life, though they should not
+be regarded as the motive of our studies, may be used to answer a
+doubt to which the solitary <span class='pagenum'><a name="Page_72" id="Page_72">[72]</a></span>student must always be liable. In a world
+so full of evil and suffering, retirement into the cloister of
+contemplation, to the enjoyment of delights which, however noble, must
+always be for the few only, cannot but appear as a somewhat selfish
+refusal to share the burden imposed upon others by accidents in which
+justice plays no part. Have any of us the right, we ask, to withdraw
+from present evils, to leave our fellow-men unaided, while we live a
+life which, though arduous and austere, is yet plainly good in its own
+nature? When these questions arise, the true answer is, no doubt, that
+some must keep alive the sacred fire, some must preserve, in every
+generation, the haunting vision which shadows forth the goal of so
+much striving. But when, as must sometimes occur, this answer seems
+too cold, when we are almost maddened by the spectacle of sorrows to
+which we bring no help, then we may reflect that indirectly the
+mathematician often does more for human happiness than any of his more
+practically active contemporaries. The history of science abundantly
+proves that a body of abstract propositions&mdash;even if, as in the case
+of conic sections, it remains two thousand years without effect upon
+daily life&mdash;may yet, at any moment, be used to cause a revolution in
+the habitual thoughts and occupations of every citizen. The use of
+steam and electricity&mdash;to take striking instances&mdash;is rendered
+possible only by mathematics. In the results of abstract thought the
+world possesses a capital of which the employment in enriching the
+common round has no hitherto discoverable limits. Nor does experience
+give any means of deciding what parts of mathematics will be found
+useful. Utility, therefore, can be only a consolation in moments of
+discouragement, not a guide in directing our studies.</p>
+
+<p>For the health of the moral life, for ennobling the tone <span class='pagenum'><a name="Page_73" id="Page_73">[73]</a></span>of an age or
+a nation, the austerer virtues have a strange power, exceeding the
+power of those not informed and purified by thought. Of these austerer
+virtues the love of truth is the chief, and in mathematics, more than
+elsewhere, the love of truth may find encouragement for waning faith.
+Every great study is not only an end in itself, but also a means of
+creating and sustaining a lofty habit of mind; and this purpose should
+be kept always in view throughout the teaching and learning of
+mathematics.</p>
+
+<br />
+<hr style="width: 15%;" />
+<br />
+
+<h4>FOOTNOTES:</h4>
+
+<div class="footnote"><p class="noin"><a name="Footnote_10_10" id="Footnote_10_10"></a><a href="#FNanchor_10_10"><span class="label">[10]</span></a> This passage was pointed out to me by Professor Gilbert
+Murray.</p></div>
+
+
+<br />
+<br />
+<br />
+<br />
+<a name="V" id="V"></a><hr />
+<span class='pagenum'><a name="Page_74" id="Page_74">[74]</a></span><br />
+
+<h3>V<span class="totoc"><a href="#toc">ToC</a></span></h3>
+
+<h4>MATHEMATICS AND THE METAPHYSICIANS</h4>
+<br />
+
+<p>The nineteenth century, which prided itself upon the invention of
+steam and evolution, might have derived a more legitimate title to
+fame from the discovery of pure mathematics. This science, like most
+others, was baptised long before it was born; and thus we find writers
+before the nineteenth century alluding to what they called pure
+mathematics. But if they had been asked what this subject was, they
+would only have been able to say that it consisted of Arithmetic,
+Algebra, Geometry, and so on. As to what these studies had in common,
+and as to what distinguished them from applied mathematics, our
+ancestors were completely in the dark.</p>
+
+<p>Pure mathematics was discovered by Boole, in a work which he called
+the <i>Laws of Thought</i> (1854). This work abounds in asseverations that
+it is not mathematical, the fact being that Boole was too modest to
+suppose his book the first ever written on mathematics. He was also
+mistaken in supposing that he was dealing with the laws of thought:
+the question how people actually think was quite irrelevant to him,
+and if his book had really contained the laws of thought, it was
+curious that no one should ever have thought in such a way before. His
+book was in fact concerned with formal logic, and this is the same
+thing as mathematics.</p>
+
+<p><span class='pagenum'><a name="Page_75" id="Page_75">[75]</a></span>Pure mathematics consists entirely of assertions to the effect that,
+if such and such a proposition is true of <i>anything</i>, then such and
+such another proposition is true of that thing. It is essential not to
+discuss whether the first proposition is really true, and not to
+mention what the anything is, of which it is supposed to be true. Both
+these points would belong to applied mathematics. We start, in pure
+mathematics, from certain rules of inference, by which we can infer
+that <i>if</i> one proposition is true, then so is some other proposition.
+These rules of inference constitute the major part of the principles
+of formal logic. We then take any hypothesis that seems amusing, and
+deduce its consequences. <i>If</i> our hypothesis is about <i>anything</i>, and
+not about some one or more particular things, then our deductions
+constitute mathematics. Thus mathematics may be defined as the subject
+in which we never know what we are talking about, nor whether what we
+are saying is true. People who have been puzzled by the beginnings of
+mathematics will, I hope, find comfort in this definition, and will
+probably agree that it is accurate.</p>
+
+<p>As one of the chief triumphs of modern mathematics consists in having
+discovered what mathematics really is, a few more words on this
+subject may not be amiss. It is common to start any branch of
+mathematics&mdash;for instance, Geometry&mdash;with a certain number of
+primitive ideas, supposed incapable of definition, and a certain
+number of primitive propositions or axioms, supposed incapable of
+proof. Now the fact is that, though there are indefinables and
+indemonstrables in every branch of applied mathematics, there are none
+in pure mathematics except such as belong to general logic. Logic,
+broadly speaking, is distinguished by the fact that its propositions
+can be put into a form in which they apply to anything whatever. All
+pure mathematics&mdash;Arithmetic, Analysis, <span class='pagenum'><a name="Page_76" id="Page_76">[76]</a></span>and Geometry&mdash;is built up by
+combinations of the primitive ideas of logic, and its propositions are
+deduced from the general axioms of logic, such as the syllogism and
+the other rules of inference. And this is no longer a dream or an
+aspiration. On the contrary, over the greater and more difficult part
+of the domain of mathematics, it has been already accomplished; in the
+few remaining cases, there is no special difficulty, and it is now
+being rapidly achieved. Philosophers have disputed for ages whether
+such deduction was possible; mathematicians have sat down and made the
+deduction. For the philosophers there is now nothing left but graceful
+acknowledgments.</p>
+
+<p>The subject of formal logic, which has thus at last shown itself to be
+identical with mathematics, was, as every one knows, invented by
+Aristotle, and formed the chief study (other than theology) of the
+Middle Ages. But Aristotle never got beyond the syllogism, which is a
+very small part of the subject, and the schoolmen never got beyond
+Aristotle. If any proof were required of our superiority to the
+medi&aelig;val doctors, it might be found in this. Throughout the Middle
+Ages, almost all the best intellects devoted themselves to formal
+logic, whereas in the nineteenth century only an infinitesimal
+proportion of the world's thought went into this subject.
+Nevertheless, in each decade since 1850 more has been done to advance
+the subject than in the whole period from Aristotle to Leibniz. People
+have discovered how to make reasoning symbolic, as it is in Algebra,
+so that deductions are effected by mathematical rules. They have
+discovered many rules besides the syllogism, and a new branch of
+logic, called the Logic of Relatives,<a name="FNanchor_11_11" id="FNanchor_11_11"></a><a href="#Footnote_11_11" class="fnanchor">[11]</a> has been invented to deal
+with topics that wholly surpassed the powers of <span class='pagenum'><a name="Page_77" id="Page_77">[77]</a></span>the old logic, though
+they form the chief contents of mathematics.</p>
+
+<p>It is not easy for the lay mind to realise the importance of symbolism
+in discussing the foundations of mathematics, and the explanation may
+perhaps seem strangely paradoxical. The fact is that symbolism is
+useful because it makes things difficult. (This is not true of the
+advanced parts of mathematics, but only of the beginnings.) What we
+wish to know is, what can be deduced from what. Now, in the
+beginnings, everything is self-evident; and it is very hard to see
+whether one self-evident proposition follows from another or not.
+Obviousness is always the enemy to correctness. Hence we invent some
+new and difficult symbolism, in which nothing seems obvious. Then we
+set up certain rules for operating on the symbols, and the whole thing
+becomes mechanical. In this way we find out what must be taken as
+premiss and what can be demonstrated or defined. For instance, the
+whole of Arithmetic and Algebra has been shown to require three
+indefinable notions and five indemonstrable propositions. But without
+a symbolism it would have been very hard to find this out. It is so
+obvious that two and two are four, that we can hardly make ourselves
+sufficiently sceptical to doubt whether it can be proved. And the same
+holds in other cases where self-evident things are to be proved.</p>
+
+<p>But the proof of self-evident propositions may seem, to the
+uninitiated, a somewhat frivolous occupation. To this we might reply
+that it is often by no means self-evident that one obvious proposition
+follows from another obvious proposition; so that we are really
+discovering new truths when we prove what is evident by a method which
+is not evident. But a more interesting retort is, that since people
+have tried to prove obvious propositions, they have found that many of
+them are false. <span class='pagenum'><a name="Page_78" id="Page_78">[78]</a></span>Self-evidence is often a mere will-o'-the-wisp, which
+is sure to lead us astray if we take it as our guide. For instance,
+nothing is plainer than that a whole always has more terms than a
+part, or that a number is increased by adding one to it. But these
+propositions are now known to be usually false. Most numbers are
+infinite, and if a number is infinite you may add ones to it as long
+as you like without disturbing it in the least. One of the merits of a
+proof is that it instils a certain doubt as to the result proved; and
+when what is obvious can be proved in some cases, but not in others,
+it becomes possible to suppose that in these other cases it is false.</p>
+
+<p>The great master of the art of formal reasoning, among the men of our
+own day, is an Italian, Professor Peano, of the University of
+Turin.<a name="FNanchor_12_12" id="FNanchor_12_12"></a><a href="#Footnote_12_12" class="fnanchor">[12]</a> He has reduced the greater part of mathematics (and he or
+his followers will, in time, have reduced the whole) to strict
+symbolic form, in which there are no words at all. In the ordinary
+mathematical books, there are no doubt fewer words than most readers
+would wish. Still, little phrases occur, such as <i>therefore, let us
+assume, consider</i>, or <i>hence it follows</i>. All these, however, are a
+concession, and are swept away by Professor Peano. For instance, if we
+wish to learn the whole of Arithmetic, Algebra, the Calculus, and
+indeed all that is usually called pure mathematics (except Geometry),
+we must start with a dictionary of three words. One symbol stands for
+<i>zero</i>, another for <i>number</i>, and a third for <i>next after</i>. What these
+ideas mean, it is necessary to know if you wish to become an
+arithmetician. But after symbols have been invented for these three
+ideas, not another word is required in the whole development. All
+future symbols are symbolically explained by means of these <span class='pagenum'><a name="Page_79" id="Page_79">[79]</a></span>three.
+Even these three can be explained by means of the notions of
+<i>relation</i> and <i>class</i>; but this requires the Logic of Relations,
+which Professor Peano has never taken up. It must be admitted that
+what a mathematician has to know to begin with is not much. There are
+at most a dozen notions out of which all the notions in all pure
+mathematics (including Geometry) are compounded. Professor Peano, who
+is assisted by a very able school of young Italian disciples, has
+shown how this may be done; and although the method which he has
+invented is capable of being carried a good deal further than he has
+carried it, the honour of the pioneer must belong to him.</p>
+
+<p>Two hundred years ago, Leibniz foresaw the science which Peano has
+perfected, and endeavoured to create it. He was prevented from
+succeeding by respect for the authority of Aristotle, whom he could
+not believe guilty of definite, formal fallacies; but the subject
+which he desired to create now exists, in spite of the patronising
+contempt with which his schemes have been treated by all superior
+persons. From this "Universal Characteristic," as he called it, he
+hoped for a solution of all problems, and an end to all disputes. "If
+controversies were to arise," he says, "there would be no more need of
+disputation between two philosophers than between two accountants. For
+it would suffice to take their pens in their hands, to sit down to
+their desks, and to say to each other (with a friend as witness, if
+they liked), 'Let us calculate.'" This optimism has now appeared to be
+somewhat excessive; there still are problems whose solution is
+doubtful, and disputes which calculation cannot decide. But over an
+enormous field of what was formerly controversial, Leibniz's dream has
+become sober fact. In the whole philosophy of mathematics, which <span class='pagenum'><a name="Page_80" id="Page_80">[80]</a></span>used
+to be at least as full of doubt as any other part of philosophy, order
+and certainty have replaced the confusion and hesitation which
+formerly reigned. Philosophers, of course, have not yet discovered
+this fact, and continue to write on such subjects in the old way. But
+mathematicians, at least in Italy, have now the power of treating the
+principles of mathematics in an exact and masterly manner, by means of
+which the certainty of mathematics extends also to mathematical
+philosophy. Hence many of the topics which used to be placed among the
+great mysteries&mdash;for example, the natures of infinity, of continuity,
+of space, time and motion&mdash;are now no longer in any degree open to
+doubt or discussion. Those who wish to know the nature of these things
+need only read the works of such men as Peano or Georg Cantor; they
+will there find exact and indubitable expositions of all these quondam
+mysteries.</p>
+
+<p>In this capricious world, nothing is more capricious than posthumous
+fame. One of the most notable examples of posterity's lack of judgment
+is the Eleatic Zeno. This man, who may be regarded as the founder of
+the philosophy of infinity, appears in Plato's Parmenides in the
+privileged position of instructor to Socrates. He invented four
+arguments, all immeasurably subtle and profound, to prove that motion
+is impossible, that Achilles can never overtake the tortoise, and that
+an arrow in flight is really at rest. After being refuted by
+Aristotle, and by every subsequent philosopher from that day to our
+own, these arguments were reinstated, and made the basis of a
+mathematical renaissance, by a German professor, who probably never
+dreamed of any connection between himself and Zeno. Weierstrass,<a name="FNanchor_13_13" id="FNanchor_13_13"></a><a href="#Footnote_13_13" class="fnanchor">[13]</a>
+by strictly <span class='pagenum'><a name="Page_81" id="Page_81">[81]</a></span>banishing from mathematics the use of infinitesimals, has
+at last shown that we live in an unchanging world, and that the arrow
+in its flight is truly at rest. Zeno's only error lay in inferring (if
+he did infer) that, because there is no such thing as a state of
+change, therefore the world is in the same state at any one time as at
+any other. This is a consequence which by no means follows; and in
+this respect, the German mathematician is more constructive than the
+ingenious Greek. Weierstrass has been able, by embodying his views in
+mathematics, where familiarity with truth eliminates the vulgar
+prejudices of common sense, to invest Zeno's paradoxes with the
+respectable air of platitudes; and if the result is less delightful to
+the lover of reason than Zeno's bold defiance, it is at any rate more
+calculated to appease the mass of academic mankind.</p>
+
+<p>Zeno was concerned, as a matter of fact, with three problems, each
+presented by motion, but each more abstract than motion, and capable
+of a purely arithmetical treatment. These are the problems of the
+infinitesimal, the infinite, and continuity. To state clearly the
+difficulties involved, was to accomplish perhaps the hardest part of
+the philosopher's task. This was done by Zeno. From him to our own
+day, the finest intellects of each generation in turn attacked the
+problems, but achieved, broadly speaking, nothing. In our own time,
+however, three men&mdash;Weierstrass, Dedekind, and Cantor&mdash;have not merely
+advanced the three problems, but have completely solved them. The
+solutions, for those acquainted with mathematics, are so clear as to
+leave no longer the slightest doubt or difficulty. This achievement is
+probably the greatest of which our age has to boast; and I know of no
+age (except perhaps the golden <span class='pagenum'><a name="Page_82" id="Page_82">[82]</a></span>age of Greece) which has a more
+convincing proof to offer of the transcendent genius of its great men.
+Of the three problems, that of the infinitesimal was solved by
+Weierstrass; the solution of the other two was begun by Dedekind, and
+definitively accomplished by Cantor.</p>
+
+<p>The infinitesimal played formerly a great part in mathematics. It was
+introduced by the Greeks, who regarded a circle as differing
+infinitesimally from a polygon with a very large number of very small
+equal sides. It gradually grew in importance, until, when Leibniz
+invented the Infinitesimal Calculus, it seemed to become the
+fundamental notion of all higher mathematics. Carlyle tells, in his
+<i>Frederick the Great</i>, how Leibniz used to discourse to Queen Sophia
+Charlotte of Prussia concerning the infinitely little, and how she
+would reply that on that subject she needed no instruction&mdash;the
+behaviour of courtiers had made her thoroughly familiar with it. But
+philosophers and mathematicians&mdash;who for the most part had less
+acquaintance with courts&mdash;continued to discuss this topic, though
+without making any advance. The Calculus required continuity, and
+continuity was supposed to require the infinitely little; but nobody
+could discover what the infinitely little might be. It was plainly not
+quite zero, because a sufficiently large number of infinitesimals,
+added together, were seen to make up a finite whole. But nobody could
+point out any fraction which was not zero, and yet not finite. Thus
+there was a deadlock. But at last Weierstrass discovered that the
+infinitesimal was not needed at all, and that everything could be
+accomplished without it. Thus there was no longer any need to suppose
+that there was such a thing. Nowadays, therefore, mathematicians are
+more dignified than Leibniz: instead of talking about the infinitely
+small, they talk about the infinitely great&mdash;a subject <span class='pagenum'><a name="Page_83" id="Page_83">[83]</a></span>which, however
+appropriate to monarchs, seems, unfortunately, to interest them even
+less than the infinitely little interested the monarchs to whom
+Leibniz discoursed.</p>
+
+<p>The banishment of the infinitesimal has all sorts of odd consequences,
+to which one has to become gradually accustomed. For example, there is
+no such thing as the next moment. The interval between one moment and
+the next would have to be infinitesimal, since, if we take two moments
+with a finite interval between them, there are always other moments in
+the interval. Thus if there are to be no infinitesimals, no two
+moments are quite consecutive, but there are always other moments
+between any two. Hence there must be an infinite number of moments
+between any two; because if there were a finite number one would be
+nearest the first of the two moments, and therefore next to it. This
+might be thought to be a difficulty; but, as a matter of fact, it is
+here that the philosophy of the infinite comes in, and makes all
+straight.</p>
+
+<p>The same sort of thing happens in space. If any piece of matter be cut
+in two, and then each part be halved, and so on, the bits will become
+smaller and smaller, and can theoretically be made as small as we
+please. However small they may be, they can still be cut up and made
+smaller still. But they will always have <i>some</i> finite size, however
+small they may be. We never reach the infinitesimal in this way, and
+no finite number of divisions will bring us to points. Nevertheless
+there <i>are</i> points, only these are not to be reached by successive
+divisions. Here again, the philosophy of the infinite shows us how
+this is possible, and why points are not infinitesimal lengths.</p>
+
+<p>As regards motion and change, we get similarly curious results. People
+used to think that when a thing changes, it must be in a state of
+change, and that when a thing <span class='pagenum'><a name="Page_84" id="Page_84">[84]</a></span>moves, it is in a state of motion. This
+is now known to be a mistake. When a body moves, all that can be said
+is that it is in one place at one time and in another at another. We
+must not say that it will be in a neighbouring place at the next
+instant, since there is no next instant. Philosophers often tell us
+that when a body is in motion, it changes its position within the
+instant. To this view Zeno long ago made the fatal retort that every
+body always is where it is; but a retort so simple and brief was not
+of the kind to which philosophers are accustomed to give weight, and
+they have continued down to our own day to repeat the same phrases
+which roused the Eleatic's destructive ardour. It was only recently
+that it became possible to explain motion in detail in accordance with
+Zeno's platitude, and in opposition to the philosopher's paradox. We
+may now at last indulge the comfortable belief that a body in motion
+is just as truly where it is as a body at rest. Motion consists merely
+in the fact that bodies are sometimes in one place and sometimes in
+another, and that they are at intermediate places at intermediate
+times. Only those who have waded through the quagmire of philosophic
+speculation on this subject can realise what a liberation from antique
+prejudices is involved in this simple and straightforward commonplace.</p>
+
+<p>The philosophy of the infinitesimal, as we have just seen, is mainly
+negative. People used to believe in it, and now they have found out
+their mistake. The philosophy of the infinite, on the other hand, is
+wholly positive. It was formerly supposed that infinite numbers, and
+the mathematical infinite generally, were self-contradictory. But as
+it was obvious that there were infinities&mdash;for example, the number of
+numbers&mdash;the contradictions of infinity seemed unavoidable, and
+philosophy seemed to <span class='pagenum'><a name="Page_85" id="Page_85">[85]</a></span>have wandered into a "cul-de-sac." This
+difficulty led to Kant's antinomies, and hence, more or less
+indirectly, to much of Hegel's dialectic method. Almost all current
+philosophy is upset by the fact (of which very few philosophers are as
+yet aware) that all the ancient and respectable contradictions in the
+notion of the infinite have been once for all disposed of. The method
+by which this has been done is most interesting and instructive. In
+the first place, though people had talked glibly about infinity ever
+since the beginnings of Greek thought, nobody had ever thought of
+asking, What is infinity? If any philosopher had been asked for a
+definition of infinity, he might have produced some unintelligible
+rigmarole, but he would certainly not have been able to give a
+definition that had any meaning at all. Twenty years ago, roughly
+speaking, Dedekind and Cantor asked this question, and, what is more
+remarkable, they answered it. They found, that is to say, a perfectly
+precise definition of an infinite number or an infinite collection of
+things. This was the first and perhaps the greatest step. It then
+remained to examine the supposed contradictions in this notion. Here
+Cantor proceeded in the only proper way. He took pairs of
+contradictory propositions, in which both sides of the contradiction
+would be usually regarded as demonstrable, and he strictly examined
+the supposed proofs. He found that all proofs adverse to infinity
+involved a certain principle, at first sight obviously true, but
+destructive, in its consequences, of almost all mathematics. The
+proofs favourable to infinity, on the other hand, involved no
+principle that had evil consequences. It thus appeared that common
+sense had allowed itself to be taken in by a specious maxim, and that,
+when once this maxim was rejected, all went well.</p>
+
+<p>The maxim in question is, that if one collection is part <span class='pagenum'><a name="Page_86" id="Page_86">[86]</a></span>of another,
+the one which is a part has fewer terms than the one of which it is a
+part. This maxim is true of finite numbers. For example, Englishmen
+are only some among Europeans, and there are fewer Englishmen than
+Europeans. But when we come to infinite numbers, this is no longer
+true. This breakdown of the maxim gives us the precise definition of
+infinity. A collection of terms is infinite when it contains as parts
+other collections which have just as many terms as it has. If you can
+take away some of the terms of a collection, without diminishing the
+number of terms, then there are an infinite number of terms in the
+collection. For example, there are just as many even numbers as there
+are numbers altogether, since every number can be doubled. This may be
+seen by putting odd and even numbers together in one row, and even
+numbers alone in a row below:&mdash;</p>
+
+<div class="block">
+<p class="noin">1, 2, 3, 4, 5, <i>ad infinitum</i>.<br />
+2, 4, 6, 8, 10, <i>ad infinitum</i>.</p>
+</div>
+
+<p class="noin">There are obviously just as many numbers in the row below as in the
+row above, because there is one below for each one above. This
+property, which was formerly thought to be a contradiction, is now
+transformed into a harmless definition of infinity, and shows, in the
+above case, that the number of finite numbers is infinite.</p>
+
+<p>But the uninitiated may wonder how it is possible to deal with a
+number which cannot be counted. It is impossible to count up <i>all</i> the
+numbers, one by one, because, however many we may count, there are
+always more to follow. The fact is that counting is a very vulgar and
+elementary way of finding out how many terms there are in a
+collection. And in any case, counting gives us what mathematicians
+call the <i>ordinal</i> number of our terms; that is to say, it arranges
+our terms in an order or <span class='pagenum'><a name="Page_87" id="Page_87">[87]</a></span>series, and its result tells us what type of
+series results from this arrangement. In other words, it is impossible
+to count things without counting some first and others afterwards, so
+that counting always has to do with order. Now when there are only a
+finite number of terms, we can count them in any order we like; but
+when there are an infinite number, what corresponds to counting will
+give us quite different results according to the way in which we carry
+out the operation. Thus the ordinal number, which results from what,
+in a general sense may be called counting, depends not only upon how
+many terms we have, but also (where the number of terms is infinite)
+upon the way in which the terms are arranged.</p>
+
+<p>The fundamental infinite numbers are not ordinal, but are what is
+called <i>cardinal</i>. They are not obtained by putting our terms in order
+and counting them, but by a different method, which tells us, to begin
+with, whether two collections have the same number of terms, or, if
+not, which is the greater.<a name="FNanchor_14_14" id="FNanchor_14_14"></a><a href="#Footnote_14_14" class="fnanchor">[14]</a> It does not tell us, in the way in
+which counting does, <i>what</i> number of terms a collection has; but if
+we define a number as the number of terms in such and such a
+collection, then this method enables us to discover whether some other
+collection that may be mentioned has more or fewer terms. An
+illustration will show how this is done. If there existed some country
+in which, for one reason or another, it was impossible to take a
+census, but in which it was known that every man had a wife and every
+woman a husband, then (provided polygamy was not a national
+institution) we should know, without counting, that there were exactly
+as many men as there were women in that country, neither more nor
+<span class='pagenum'><a name="Page_88" id="Page_88">[88]</a></span>less. This method can be applied generally. If there is some relation
+which, like marriage, connects the things in one collection each with
+one of the things in another collection, and vice versa, then the two
+collections have the same number of terms. This was the way in which
+we found that there are as many even numbers as there are numbers.
+Every number can be doubled, and every even number can be halved, and
+each process gives just one number corresponding to the one that is
+doubled or halved. And in this way we can find any number of
+collections each of which has just as many terms as there are finite
+numbers. If every term of a collection can be hooked on to a number,
+and all the finite numbers are used once, and only once, in the
+process, then our collection must have just as many terms as there are
+finite numbers. This is the general method by which the numbers of
+infinite collections are defined.</p>
+
+<p>But it must not be supposed that all infinite numbers are equal. On
+the contrary, there are infinitely more infinite numbers than finite
+ones. There are more ways of arranging the finite numbers in different
+types of series than there are finite numbers. There are probably more
+points in space and more moments in time than there are finite
+numbers. There are exactly as many fractions as whole numbers,
+although there are an infinite number of fractions between any two
+whole numbers. But there are more irrational numbers than there are
+whole numbers or fractions. There are probably exactly as many points
+in space as there are irrational numbers, and exactly as many points
+on a line a millionth of an inch long as in the whole of infinite
+space. There is a greatest of all infinite numbers, which is the
+number of things altogether, of every sort and kind. It is obvious
+that there cannot be a greater number than this, because, <span class='pagenum'><a name="Page_89" id="Page_89">[89]</a></span>if
+everything has been taken, there is nothing left to add. Cantor has a
+proof that there is no greatest number, and if this proof were valid,
+the contradictions of infinity would reappear in a sublimated form.
+But in this one point, the master has been guilty of a very subtle
+fallacy, which I hope to explain in some future work.<a name="FNanchor_15_15" id="FNanchor_15_15"></a><a href="#Footnote_15_15" class="fnanchor">[15]</a></p>
+
+<p>We can now understand why Zeno believed that Achilles cannot overtake
+the tortoise and why as a matter of fact he can overtake it. We shall
+see that all the people who disagreed with Zeno had no right to do so,
+because they all accepted premises from which his conclusion followed.
+The argument is this: Let Achilles and the tortoise start along a road
+at the same time, the tortoise (as is only fair) being allowed a
+handicap. Let Achilles go twice as fast as the tortoise, or ten times
+or a hundred times as fast. Then he will never reach the tortoise. For
+at every moment the tortoise is somewhere and Achilles is somewhere;
+and neither is ever twice in the same place while the race is going
+on. Thus the tortoise goes to just as many places as Achilles does,
+because each is in one place at one moment, and in another at any
+other moment. But if Achilles were to catch up with the tortoise, the
+places where the tortoise would have been would be only part of the
+places where Achilles would have been. Here, we must suppose, Zeno
+appealed to the maxim that the whole has more terms than the part.<a name="FNanchor_16_16" id="FNanchor_16_16"></a><a href="#Footnote_16_16" class="fnanchor">[16]</a>
+Thus if Achilles were <span class='pagenum'><a name="Page_90" id="Page_90">[90]</a></span>to overtake the tortoise, he would have been in
+more places than the tortoise; but we saw that he must, in any period,
+be in exactly as many places as the tortoise. Hence we infer that he
+can never catch the tortoise. This argument is strictly correct, if we
+allow the axiom that the whole has more terms than the part. As the
+conclusion is absurd, the axiom must be rejected, and then all goes
+well. But there is no good word to be said for the philosophers of the
+past two thousand years and more, who have all allowed the axiom and
+denied the conclusion.</p>
+
+<p>The retention of this axiom leads to absolute contradictions, while
+its rejection leads only to oddities. Some of these oddities, it must
+be confessed, are very odd. One of them, which I call the paradox of
+Tristram Shandy, is the converse of the Achilles, and shows that the
+tortoise, if you give him time, will go just as far as Achilles.
+Tristram Shandy, as we know, employed two years in chronicling the
+first two days of his life, and lamented that, at this rate, material
+would accumulate faster than he could deal with it, so that, as years
+went by, he would be farther and farther from the end of his history.
+Now I maintain that, if he had lived for ever, and had not wearied of
+his task, then, even if his life had continued as event fully as it
+began, no part of his biography would have remained unwritten. For
+consider: the hundredth day will be described in the hundredth year,
+the thousandth in the thousandth year, and so on. Whatever day we may
+choose as so far on that he cannot hope to reach it, that day will be
+described in the corresponding year. Thus any day that may be
+mentioned will be written up sooner or later, and therefore no part of
+the biography will remain permanently unwritten. This paradoxical but
+perfectly true proposition depends upon the fact <span class='pagenum'><a name="Page_91" id="Page_91">[91]</a></span>that the number of
+days in all time is no greater than the number of years.</p>
+
+<p>Thus on the subject of infinity it is impossible to avoid conclusions
+which at first sight appear paradoxical, and this is the reason why so
+many philosophers have supposed that there were inherent
+contradictions in the infinite. But a little practice enables one to
+grasp the true principles of Cantor's doctrine, and to acquire new and
+better instincts as to the true and the false. The oddities then
+become no odder than the people at the antipodes, who used to be
+thought impossible because they would find it so inconvenient to stand
+on their heads.</p>
+
+<p>The solution of the problems concerning infinity has enabled Cantor to
+solve also the problems of continuity. Of this, as of infinity, he has
+given a perfectly precise definition, and has shown that there are no
+contradictions in the notion so defined. But this subject is so
+technical that it is impossible to give any account of it here.</p>
+
+<p>The notion of continuity depends upon that of <i>order</i>, since
+continuity is merely a particular type of order. Mathematics has, in
+modern times, brought order into greater and greater prominence. In
+former days, it was supposed (and philosophers are still apt to
+suppose) that quantity was the fundamental notion of mathematics. But
+nowadays, quantity is banished altogether, except from one little
+corner of Geometry, while order more and more reigns supreme. The
+investigation of different kinds of series and their relations is now
+a very large part of mathematics, and it has been found that this
+investigation can be conducted without any reference to quantity, and,
+for the most part, without any reference to number. All types of
+series are capable of formal definition, and their properties can be
+deduced from the principles of symbolic logic by means of the Algebra
+of Relatives. <span class='pagenum'><a name="Page_92" id="Page_92">[92]</a></span>The notion of a limit, which is fundamental in the
+greater part of higher mathematics, used to be defined by means of
+quantity, as a term to which the terms of some series approximate as
+nearly as we please. But nowadays the limit is defined quite
+differently, and the series which it limits may not approximate to it
+at all. This improvement also is due to Cantor, and it is one which
+has revolutionised mathematics. Only order is now relevant to limits.
+Thus, for instance, the smallest of the infinite integers is the limit
+of the finite integers, though all finite integers are at an infinite
+distance from it. The study of different types of series is a general
+subject of which the study of ordinal numbers (mentioned above) is a
+special and very interesting branch. But the unavoidable
+technicalities of this subject render it impossible to explain to any
+but professed mathematicians.</p>
+
+<p>Geometry, like Arithmetic, has been subsumed, in recent times, under
+the general study of order. It was formerly supposed that Geometry was
+the study of the nature of the space in which we live, and accordingly
+it was urged, by those who held that what exists can only be known
+empirically, that Geometry should really be regarded as belonging to
+applied mathematics. But it has gradually appeared, by the increase of
+non-Euclidean systems, that Geometry throws no more light upon the
+nature of space than Arithmetic throws upon the population of the
+United States. Geometry is a whole collection of deductive sciences
+based on a corresponding collection of sets of axioms. One set of
+axioms is Euclid's; other equally good sets of axioms lead to other
+results. Whether Euclid's axioms are true, is a question as to which
+the pure mathematician is indifferent; and, what is more, it is a
+question which it is theoretically impossible to answer with certainty
+in the affirmative. It might <span class='pagenum'><a name="Page_93" id="Page_93">[93]</a></span>possibly be shown, by very careful
+measurements, that Euclid's axioms are false; but no measurements
+could ever assure us (owing to the errors of observation) that they
+are exactly true. Thus the geometer leaves to the man of science to
+decide, as best he may, what axioms are most nearly true in the actual
+world. The geometer takes any set of axioms that seem interesting, and
+deduces their consequences. What defines Geometry, in this sense, is
+that the axioms must give rise to a series of more than one dimension.
+And it is thus that Geometry becomes a department in the study of
+order.</p>
+
+<p>In Geometry, as in other parts of mathematics, Peano and his disciples
+have done work of the very greatest merit as regards principles.
+Formerly, it was held by philosophers and mathematicians alike that
+the proofs in Geometry depended on the figure; nowadays, this is known
+to be false. In the best books there are no figures at all. The
+reasoning proceeds by the strict rules of formal logic from a set of
+axioms laid down to begin with. If a figure is used, all sorts of
+things seem obviously to follow, which no formal reasoning can prove
+from the explicit axioms, and which, as a matter of fact, are only
+accepted because they are obvious. By banishing the figure, it becomes
+possible to discover <i>all</i> the axioms that are needed; and in this way
+all sorts of possibilities, which would have otherwise remained
+undetected, are brought to light.</p>
+
+<p>One great advance, from the point of view of correctness, has been
+made by introducing points as they are required, and not starting, as
+was formerly done, by assuming the whole of space. This method is due
+partly to Peano, partly to another Italian named Fano. To those
+unaccustomed to it, it has an air of somewhat wilful pedantry. In this
+way, we begin with the following <span class='pagenum'><a name="Page_94" id="Page_94">[94]</a></span>axioms: (1) There is a class of
+entities called <i>points</i>. (2) There is at least one point. (3) If <i>a</i>
+be a point, there is at least one other point besides <i>a</i>. Then we
+bring in the straight line joining two points, and begin again with
+(4), namely, on the straight line joining <i>a</i> and <i>b</i>, there is at
+least one other point besides <i>a</i> and <i>b</i>. (5) There is at least one
+point not on the line <i>ab</i>. And so we go on, till we have the means of
+obtaining as many points as we require. But the word <i>space</i>, as Peano
+humorously remarks, is one for which Geometry has no use at all.</p>
+
+<p>The rigid methods employed by modern geometers have deposed Euclid
+from his pinnacle of correctness. It was thought, until recent times,
+that, as Sir Henry Savile remarked in 1621, there were only two
+blemishes in Euclid, the theory of parallels and the theory of
+proportion. It is now known that these are almost the only points in
+which Euclid is free from blemish. Countless errors are involved in
+his first eight propositions. That is to say, not only is it doubtful
+whether his axioms are true, which is a comparatively trivial matter,
+but it is certain that his propositions do not follow from the axioms
+which he enunciates. A vastly greater number of axioms, which Euclid
+unconsciously employs, are required for the proof of his propositions.
+Even in the first proposition of all, where he constructs an
+equilateral triangle on a given base, he uses two circles which are
+assumed to intersect. But no explicit axiom assures us that they do
+so, and in some kinds of spaces they do not always intersect. It is
+quite doubtful whether our space belongs to one of these kinds or not.
+Thus Euclid fails entirely to prove his point in the very first
+proposition. As he is certainly not an easy author, and is terribly
+long-winded, he has no longer any but an historical interest. Under
+these circumstances, it is nothing less than a <span class='pagenum'><a name="Page_95" id="Page_95">[95]</a></span>scandal that he should
+still be taught to boys in England.<a name="FNanchor_17_17" id="FNanchor_17_17"></a><a href="#Footnote_17_17" class="fnanchor">[17]</a> A book should have either
+intelligibility or correctness; to combine the two is impossible, but
+to lack both is to be unworthy of such a place as Euclid has occupied
+in education.</p>
+
+<p>The most remarkable result of modern methods in mathematics is the
+importance of symbolic logic and of rigid formalism. Mathematicians,
+under the influence of Weierstrass, have shown in modern times a care
+for accuracy, and an aversion to slipshod reasoning, such as had not
+been known among them previously since the time of the Greeks. The
+great inventions of the seventeenth century&mdash;Analytical Geometry and
+the Infinitesimal Calculus&mdash;were so fruitful in new results that
+mathematicians had neither time nor inclination to examine their
+foundations. Philosophers, who should have taken up the task, had too
+little mathematical ability to invent the new branches of mathematics
+which have now been found necessary for any adequate discussion. Thus
+mathematicians were only awakened from their "dogmatic slumbers" when
+Weierstrass and his followers showed that many of their most cherished
+propositions are in general false. Macaulay, contrasting the certainty
+of mathematics with the uncertainty of philosophy, asks who ever heard
+of a reaction against Taylor's theorem? If he had lived now, he
+himself might have heard of such a reaction, for this is precisely one
+of the theorems which modern investigations have overthrown. Such rude
+shocks to mathematical faith have produced that love of formalism
+which appears, to those who are ignorant of its motive, to be mere
+outrageous pedantry.</p>
+
+<p><span class='pagenum'><a name="Page_96" id="Page_96">[96]</a></span>The proof that all pure mathematics, including Geometry, is nothing
+but formal logic, is a fatal blow to the Kantian philosophy. Kant,
+rightly perceiving that Euclid's propositions could not be deduced
+from Euclid's axioms without the help of the figures, invented a
+theory of knowledge to account for this fact; and it accounted so
+successfully that, when the fact is shown to be a mere defect in
+Euclid, and not a result of the nature of geometrical reasoning,
+Kant's theory also has to be abandoned. The whole doctrine of <i>a
+priori</i> intuitions, by which Kant explained the possibility of pure
+mathematics, is wholly inapplicable to mathematics in its present
+form. The Aristotelian doctrines of the schoolmen come nearer in
+spirit to the doctrines which modern mathematics inspire; but the
+schoolmen were hampered by the fact that their formal logic was very
+defective, and that the philosophical logic based upon the syllogism
+showed a corresponding narrowness. What is now required is to give the
+greatest possible development to mathematical logic, to allow to the
+full the importance of relations, and then to found upon this secure
+basis a new philosophical logic, which may hope to borrow some of the
+exactitude and certainty of its mathematical foundation. If this can
+be successfully accomplished, there is every reason to hope that the
+near future will be as great an epoch in pure philosophy as the
+immediate past has been in the principles of mathematics. Great
+triumphs inspire great hopes; and pure thought may achieve, within our
+generation, such results as will place our time, in this respect, on a
+level with the greatest age of Greece.<a name="FNanchor_18_18" id="FNanchor_18_18"></a><a href="#Footnote_18_18" class="fnanchor">[18]</a></p>
+
+<br />
+<hr style="width: 15%;" />
+<br />
+
+<h4>FOOTNOTES:</h4>
+
+<div class="footnote"><p class="noin"><a name="Footnote_11_11" id="Footnote_11_11"></a><a href="#FNanchor_11_11"><span class="label">[11]</span></a> This subject is due in the main to Mr. C.S. Peirce.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_12_12" id="Footnote_12_12"></a><a href="#FNanchor_12_12"><span class="label">[12]</span></a> I ought to have added Frege, but his writings were
+unknown to me when this article was written. [Note added in 1917.]</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_13_13" id="Footnote_13_13"></a><a href="#FNanchor_13_13"><span class="label">[13]</span></a> Professor of Mathematics in the University of Berlin. He
+died in 1897.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_14_14" id="Footnote_14_14"></a><a href="#FNanchor_14_14"><span class="label">[14]</span></a> [Note added in 1917.] Although some infinite numbers are
+greater than some others, it cannot be proved that of any two infinite
+numbers one must be the greater.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_15_15" id="Footnote_15_15"></a><a href="#FNanchor_15_15"><span class="label">[15]</span></a> Cantor was not guilty of a fallacy on this point. His
+proof that there is no greatest number is valid. The solution of the
+puzzle is complicated and depends upon the theory of types, which is
+explained in <i>Principia Mathematica</i>, Vol. I (Camb. Univ. Press,
+1910). [Note added in 1917.]</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_16_16" id="Footnote_16_16"></a><a href="#FNanchor_16_16"><span class="label">[16]</span></a> This must not be regarded as a historically correct
+account of what Zeno actually had in mind. It is a new argument for
+his conclusion, not the argument which influenced him. On this point,
+see e.g. C.D. Broad, "Note on Achilles and the Tortoise," <i>Mind</i>,
+N.S., Vol. XXII, pp. 318-19. Much valuable work on the interpretation
+of Zeno has been done since this article was written. [Note added in
+1917.]</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_17_17" id="Footnote_17_17"></a><a href="#FNanchor_17_17"><span class="label">[17]</span></a> Since the above was written, he has ceased to be used as
+a textbook. But I fear many of the books now used are so bad that the
+change is no great improvement. [Note added in 1917.]</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_18_18" id="Footnote_18_18"></a><a href="#FNanchor_18_18"><span class="label">[18]</span></a> The greatest age of Greece was brought to an end by the
+Peloponnesian War. [Note added in 1917.]</p></div>
+
+
+<br />
+<br />
+<br />
+<br />
+<a name="VI" id="VI"></a><hr />
+<span class='pagenum'><a name="Page_97" id="Page_97">[97]</a></span><br />
+
+<h3>VI<span class="totoc"><a href="#toc">ToC</a></span></h3>
+
+<h4>ON SCIENTIFIC METHOD IN PHILOSOPHY</h4>
+<br />
+
+<p>When we try to ascertain the motives which have led men to the
+investigation of philosophical questions, we find that, broadly
+speaking, they can be divided into two groups, often antagonistic, and
+leading to very divergent systems. These two groups of motives are, on
+the one hand, those derived from religion and ethics, and, on the
+other hand, those derived from science. Plato, Spinoza, and Hegel may
+be taken as typical of the philosophers whose interests are mainly
+religious and ethical, while Leibniz, Locke, and Hume may be taken as
+representatives of the scientific wing. In Aristotle, Descartes,
+Berkeley, and Kant we find both groups of motives strongly present.</p>
+
+<p>Herbert Spencer, in whose honour we are assembled to-day, would
+naturally be classed among scientific philosophers: it was mainly from
+science that he drew his data, his formulation of problems, and his
+conception of method. But his strong religious sense is obvious in
+much of his writing, and his ethical pre-occupations are what make him
+value the conception of evolution&mdash;that conception in which, as a
+whole generation has believed, science and morals are to be united in
+fruitful and indissoluble marriage.</p>
+
+<p>It is my belief that the ethical and religious motives <span class='pagenum'><a name="Page_98" id="Page_98">[98]</a></span>in spite of
+the splendidly imaginative systems to which they have given rise, have
+been on the whole a hindrance to the progress of philosophy, and ought
+now to be consciously thrust aside by those who wish to discover
+philosophical truth. Science, originally, was entangled in similar
+motives, and was thereby hindered in its advances. It is, I maintain,
+from science, rather than from ethics and religion, that philosophy
+should draw its inspiration.</p>
+
+<p>But there are two different ways in which a philosophy may seek to
+base itself upon science. It may emphasise the most general <i>results</i>
+of science, and seek to give even greater generality and unity to
+these results. Or it may study the <i>methods</i> of science, and seek to
+apply these methods, with the necessary adaptations, to its own
+peculiar province. Much philosophy inspired by science has gone astray
+through preoccupation with the <i>results</i> momentarily supposed to have
+been achieved. It is not results, but <i>methods</i> that can be
+transferred with profit from the sphere of the special sciences to the
+sphere of philosophy. What I wish to bring to your notice is the
+possibility and importance of applying to philosophical problems
+certain broad principles of method which have been found successful in
+the study of scientific questions.</p>
+
+<p>The opposition between a philosophy guided by scientific method and a
+philosophy dominated by religious and ethical ideas may be illustrated
+by two notions which are very prevalent in the works of philosophers,
+namely the notion of <i>the universe</i>, and the notion of <i>good and
+evil</i>. A philosopher is expected to tell us something about the nature
+of the universe as a whole, and to give grounds for either optimism or
+pessimism. Both these expectations seem to me mistaken. I believe the
+conception of "the universe" to be, as its etymology indicates, a
+<span class='pagenum'><a name="Page_99" id="Page_99">[99]</a></span>mere relic of pre-Copernican astronomy: and I believe the question of
+optimism and pessimism to be one which the philosopher will regard as
+outside his scope, except, possibly, to the extent of maintaining that
+it is insoluble.</p>
+
+<p>In the days before Copernicus, the conception of the "universe" was
+defensible on scientific grounds: the diurnal revolution of the
+heavenly bodies bound them together as all parts of one system, of
+which the earth was the centre. Round this apparent scientific fact,
+many human desires rallied: the wish to believe Man important in the
+scheme of things, the theoretical desire for a comprehensive
+understanding of the Whole, the hope that the course of nature might
+be guided by some sympathy with our wishes. In this way, an ethically
+inspired system of metaphysics grew up, whose anthropocentrism was
+apparently warranted by the geocentrism of astronomy. When Copernicus
+swept away the astronomical basis of this system of thought, it had
+grown so familiar, and had associated itself so intimately with men's
+aspirations, that it survived with scarcely diminished force&mdash;survived
+even Kant's "Copernican revolution," and is still now the unconscious
+premiss of most metaphysical systems.</p>
+
+<p>The oneness of the world is an almost undiscussed postulate of most
+metaphysics. "Reality is not merely one and self-consistent, but is a
+system of reciprocally determinate parts"<a name="FNanchor_19_19" id="FNanchor_19_19"></a><a href="#Footnote_19_19" class="fnanchor">[19]</a>&mdash;such a statement would
+pass almost unnoticed as a mere truism. Yet I believe that it embodies
+a failure to effect thoroughly the "Copernican revolution," and that
+the apparent oneness of the world is merely the oneness of what is
+seen by a single spectator or apprehended by a single mind. The
+Critical Philosophy, although it intended to emphasise the subjective
+element <span class='pagenum'><a name="Page_100" id="Page_100">[100]</a></span>in many apparent characteristics of the world, yet, by
+regarding the world in itself as unknowable, so concentrated attention
+upon the subjective representation that its subjectivity was soon
+forgotten. Having recognised the categories as the work of the mind,
+it was paralysed by its own recognition, and abandoned in despair the
+attempt to undo the work of subjective falsification. In part, no
+doubt, its despair was well founded, but not, I think, in any absolute
+or ultimate sense. Still less was it a ground for rejoicing, or for
+supposing that the nescience to which it ought to have given rise
+could be legitimately exchanged for a metaphysical dogmatism.</p>
+
+<br />
+<h4>I</h4>
+
+<p>As regards our present question, namely, the question of the unity of
+the world, the right method, as I think, has been indicated by William
+James.<a name="FNanchor_20_20" id="FNanchor_20_20"></a><a href="#Footnote_20_20" class="fnanchor">[20]</a> "Let us now turn our backs upon ineffable or unintelligible
+ways of accounting for the world's oneness, and inquire whether,
+instead of being a principle, the 'oneness' affirmed may not merely be
+a name like 'substance' descriptive of the fact that certain <i>specific
+and verifiable connections</i> are found among the parts of the
+experiential flux.... We can easily conceive of things that shall have
+no connection whatever with each other. We may assume them to inhabit
+different times and spaces, as the dreams of different persons do even
+now. They may be so unlike and incommensurable, and so inert towards
+one another, as never to jostle or interfere. Even now there may
+actually be whole universes so disparate from ours that we who know
+ours have no means of perceiving that they exist. We conceive their
+diversity, however; and by that <span class='pagenum'><a name="Page_101" id="Page_101">[101]</a></span>fact the whole lot of them form what
+is known in logic as 'a universe of discourse.' To form a universe of
+discourse argues, as this example shows, no further kind of connexion.
+The importance attached by certain monistic writers to the fact that
+any chaos may become a universe by merely being named, is to me
+incomprehensible." We are thus left with two kinds of unity in the
+experienced world; the one what we may call the epistemological unity,
+due merely to the fact that my experienced world is what <i>one</i>
+experience selects from the sum total of existence: the other that
+tentative and partial unity exhibited in the prevalence of scientific
+laws in those portions of the world which science has hitherto
+mastered. Now a generalisation based upon either of these kinds of
+unity would be fallacious. That the things which we experience have
+the common property of being experienced by us is a truism from which
+obviously nothing of importance can be deducible: it is clearly
+fallacious to draw from the fact that whatever we experience is
+experienced the conclusion that therefore everything must be
+experienced. The generalisation of the second kind of unity, namely,
+that derived from scientific laws, would be equally fallacious, though
+the fallacy is a trifle less elementary. In order to explain it let us
+consider for a moment what is called the reign of law. People often
+speak as though it were a remarkable fact that the physical world is
+subject to invariable laws. In fact, however, it is not easy to see
+how such a world could fail to obey general laws. Taking any arbitrary
+set of points in space, there is a function of the time corresponding
+to these points, i.e. expressing the motion of a particle which
+traverses these points: this function may be regarded as a general law
+to which the behaviour of such a particle is subject. Taking all such
+functions for <span class='pagenum'><a name="Page_102" id="Page_102">[102]</a></span>all the particles in the universe, there will be
+theoretically some one formula embracing them all, and this formula
+may be regarded as the single and supreme law of the spatio-temporal
+world. Thus what is surprising in physics is not the existence of
+general laws, but their extreme simplicity. It is not the uniformity
+of nature that should surprise us, for, by sufficient analytic
+ingenuity, any conceivable course of nature might be shown to exhibit
+uniformity. What should surprise us is the fact that the uniformity is
+simple enough for us to be able to discover it. But it is just this
+characteristic of simplicity in the laws of nature hitherto discovered
+which it would be fallacious to generalise, for it is obvious that
+simplicity has been a part cause of their discovery, and can,
+therefore, give no ground for the supposition that other undiscovered
+laws are equally simple.</p>
+
+<p>The fallacies to which these two kinds of unity have given rise
+suggest a caution as regards all use in philosophy of general
+<i>results</i> that science is supposed to have achieved. In the first
+place, in generalising these results beyond past experience, it is
+necessary to examine very carefully whether there is not some reason
+making it more probable that these results should hold of all that has
+been experienced than that they should hold of things universally. The
+sum total of what is experienced by mankind is a selection from the
+sum total of what exists, and any general character exhibited by this
+selection may be due to the manner of selecting rather than to the
+general character of that from which experience selects. In the second
+place, the most general results of science are the least certain and
+the most liable to be upset by subsequent research. In utilizing these
+results as the basis of a philosophy, we sacrifice the most valuable
+and remarkable characteristic of scientific method, <span class='pagenum'><a name="Page_103" id="Page_103">[103]</a></span>namely, that,
+although almost everything in science is found sooner or later to
+require some correction, yet this correction is almost always such as
+to leave untouched, or only slightly modified, the greater part of the
+results which have been deduced from the premiss subsequently
+discovered to be faulty. The prudent man of science acquires a certain
+instinct as to the kind of uses which may be made of present
+scientific beliefs without incurring the danger of complete and utter
+refutation from the modifications likely to be introduced by
+subsequent discoveries. Unfortunately the use of scientific
+generalisations of a sweeping kind as the basis of philosophy is just
+that kind of use which an instinct of scientific caution would avoid,
+since, as a rule, it would only lead to true results if the
+generalisation upon which it is based stood in <i>no</i> need of
+correction.</p>
+
+<p>We may illustrate these general considerations by means of two
+examples, namely, the conservation of energy and the principle of
+evolution.</p>
+
+<p>(1) Let us begin with the conservation of energy, or, as Herbert
+Spencer used to call it, the persistence of force. He says:<a name="FNanchor_21_21" id="FNanchor_21_21"></a><a href="#Footnote_21_21" class="fnanchor">[21]</a></p>
+
+<div class="block"><p>"Before taking a first step in the rational interpretation of
+Evolution, it is needful to recognise, not only the facts that
+Matter is indestructible and Motion continuous, but also the fact
+that Force persists. An attempt to assign the <i>causes</i> of
+Evolution would manifestly be absurd if that agency to which the
+metamorphosis in general and in detail is due, could either come
+into existence or cease to exist. The succession of phenomena
+would in such case be altogether arbitrary, and deductive Science
+impossible."</p></div>
+
+<p><span class='pagenum'><a name="Page_104" id="Page_104">[104]</a></span>This paragraph illustrates the kind of way in which the philosopher is
+tempted to give an air of absoluteness and necessity to empirical
+generalisations, of which only the approximate truth in the regions
+hitherto investigated can be guaranteed by the unaided methods of
+science. It is very often said that the persistence of something or
+other is a necessary presupposition of all scientific investigation,
+and this presupposition is then thought to be exemplified in some
+quantity which physics declares to be constant. There are here, as it
+seems to me, three distinct errors. First, the detailed scientific
+investigation of nature does not <i>presuppose</i> any such general laws as
+its results are found to verify. Apart from particular observations,
+science need presuppose nothing except the general principles of
+logic, and these principles are not laws of nature, for they are
+merely hypothetical, and apply not only to the actual world but to
+whatever is <i>possible</i>. The second error consists in the
+identification of a constant quantity with a persistent entity. Energy
+is a certain function of a physical system, but is not a thing or
+substance persisting throughout the changes of the system. The same is
+true of mass, in spite of the fact that mass has often been defined as
+<i>quantity of matter</i>. The whole conception of quantity, involving, as
+it does, numerical measurement based largely upon conventions, is far
+more artificial, far more an embodiment of mathematical convenience,
+than is commonly believed by those who philosophise on physics. Thus
+even if (which I cannot for a moment admit) the persistence of some
+entity were among the necessary postulates of science, it would be a
+sheer error to infer from this the constancy of any physical quantity,
+or the <i>a priori</i> necessity of any such constancy which may be
+empirically discovered. In the third place, it <span class='pagenum'><a name="Page_105" id="Page_105">[105]</a></span>has become more and
+more evident with the progress of physics that large generalisations,
+such as the conservation of energy or mass, are far from certain and
+are very likely only approximate. Mass, which used to be regarded as
+the most indubitable of physical quantities, is now generally believed
+to vary according to velocity, and to be, in fact, a vector quantity
+which at a given moment is different in different directions. The
+detailed conclusions deduced from the supposed constancy of mass for
+such motions as used to be studied in physics will remain very nearly
+exact, and therefore over the field of the older investigations very
+little modification of the older results is required. But as soon as
+such a principle as the conservation of mass or of energy is erected
+into a universal <i>a priori</i> law, the slightest failure in absolute
+exactness is fatal, and the whole philosophic structure raised upon
+this foundation is necessarily ruined. The prudent philosopher,
+therefore, though he may with advantage study the methods of physics,
+will be very chary of basing anything upon what happen at the moment
+to be the most general results apparently obtained by those methods.</p>
+
+<p>(2) The philosophy of evolution, which was to be our second example,
+illustrates the same tendency to hasty generalisation, and also
+another sort, namely, the undue preoccupation with ethical notions.
+There are two kinds of evolutionist philosophy, of which both Hegel
+and Spencer represent the older and less radical kind, while
+Pragmatism and Bergson represent the more modern and revolutionary
+variety. But both these sorts of evolutionism have in common the
+emphasis on <i>progress</i>, that is, upon a continual change from the
+worse to the better, or from the simpler to the more complex. It
+<span class='pagenum'><a name="Page_106" id="Page_106">[106]</a></span>would be unfair to attribute to Hegel any scientific motive or
+foundation, but all the other evolutionists, including Hegel's modern
+disciples, have derived their impetus very largely from the history of
+biological development. To a philosophy which derives a law of
+universal progress from this history there are two objections. First,
+that this history itself is concerned with a very small selection of
+facts confined to an infinitesimal fragment of space and time, and
+even on scientific grounds probably not an average sample of events in
+the world at large. For we know that decay as well as growth is a
+normal occurrence in the world. An extra-terrestrial philosopher, who
+had watched a single youth up to the age of twenty-one and had never
+come across any other human being, might conclude that it is the
+nature of human beings to grow continually taller and wiser in an
+indefinite progress towards perfection; and this generalisation would
+be just as well founded as the generalisation which evolutionists base
+upon the previous history of this planet. Apart, however, from this
+scientific objection to evolutionism, there is another, derived from
+the undue admixture of ethical notions in the very idea of progress
+from which evolutionism derives its charm. Organic life, we are told,
+has developed gradually from the protozoon to the philosopher, and
+this development, we are assured, is indubitably an advance.
+Unfortunately it is the philosopher, not the protozoon, who gives us
+this assurance, and we can have no security that the impartial
+outsider would agree with the philosopher's self-complacent
+assumption. This point has been illustrated by the philosopher Chuang
+Tz&#365; in the following instructive anecdote:</p>
+
+<div class="block"><p>"The Grand Augur, in his ceremonial robes, approached the shambles<span class='pagenum'><a name="Page_107" id="Page_107">[107]</a></span>
+and thus addressed the pigs: 'How can you object to die? I shall
+fatten you for three months. I shall discipline myself for ten
+days and fast for three. I shall strew fine grass, and place you
+bodily upon a carved sacrificial dish. Does not this satisfy you?'</p>
+
+<p>Then, speaking from the pigs' point of view, he continued: 'It is
+better, perhaps, after all, to live on bran and escape the
+shambles....'</p>
+
+<p>'But then,' added he, speaking from his own point of view, 'to
+enjoy honour when alive one would readily die on a war-shield or
+in the headsman's basket.'</p>
+
+<p>So he rejected the pigs' point of view and adopted his own point
+of view. In what sense, then, was he different from the pigs?"</p></div>
+
+<p>I much fear that the evolutionists too often resemble the Grand Augur
+and the pigs.</p>
+
+<p>The ethical element which has been prominent in many of the most
+famous systems of philosophy is, in my opinion, one of the most
+serious obstacles to the victory of scientific method in the
+investigation of philosophical questions. Human ethical notions, as
+Chuang Tz&#365; perceived, are essentially anthropocentric, and involve,
+when used in metaphysics, an attempt, however veiled, to legislate for
+the universe on the basis of the present desires of men. In this way
+they interfere with that receptivity to fact which is the essence of
+the scientific attitude towards the world. To regard ethical notions
+as a key to the understanding of the world is essentially
+pre-Copernican. It is to make man, with the hopes and ideals which he
+happens to have at the present moment, the centre of the universe and
+the interpreter of its supposed aims and purposes. Ethical metaphysics
+is fundamentally an attempt, however disguised, to <span class='pagenum'><a name="Page_108" id="Page_108">[108]</a></span>give legislative
+force to our own wishes. This may, of course, be questioned, but I
+think that it is confirmed by a consideration of the way in which
+ethical notions arise. Ethics is essentially a product of the
+gregarious instinct, that is to say, of the instinct to co-operate
+with those who are to form our own group against those who belong to
+other groups. Those who belong to our own group are good; those who
+belong to hostile groups are wicked. The ends which are pursued by our
+own group are desirable ends, the ends pursued by hostile groups are
+nefarious. The subjectivity of this situation is not apparent to the
+gregarious animal, which feels that the general principles of justice
+are on the side of its own herd. When the animal has arrived at the
+dignity of the metaphysician, it invents ethics as the embodiment of
+its belief in the justice of its own herd. So the Grand Augur invokes
+ethics as the justification of Augurs in their conflicts with pigs.
+But, it may be said, this view of ethics takes no account of such
+truly ethical notions as that of self-sacrifice. This, however, would
+be a mistake. The success of gregarious animals in the struggle for
+existence depends upon co-operation within the herd, and co-operation
+requires sacrifice, to some extent, of what would otherwise be the
+interest of the individual. Hence arises a conflict of desires and
+instincts, since both self-preservation and the preservation of the
+herd are biological ends to the individual. Ethics is in origin the
+art of recommending to others the sacrifices required for co-operation
+with oneself. Hence, by reflexion, it comes, through the operation of
+social justice, to recommend sacrifices by oneself, but all ethics,
+however refined, remains more or less subjective. Even vegetarians do
+not hesitate, for example, to save the life of a man in a fever,
+although in doing so they destroy the lives of many millions of
+m<span class='pagenum'><a name="Page_109" id="Page_109">[109]</a></span>icrobes. The view of the world taken by the philosophy derived from
+ethical notions is thus never impartial and therefore never fully
+scientific. As compared with science, it fails to achieve the
+imaginative liberation from self which is necessary to such
+understanding of the world as man can hope to achieve, and the
+philosophy which it inspires is always more or less parochial, more or
+less infected with the prejudices of a time and a place.</p>
+
+<p>I do not deny the importance or value, within its own sphere, of the
+kind of philosophy which is inspired by ethical notions. The ethical
+work of Spinoza, for example, appears to me of the very highest
+significance, but what is valuable in such work is not any
+metaphysical theory as to the nature of the world to which it may give
+rise, nor indeed anything which can be proved or disproved by
+argument. What is valuable is the indication of some new way of
+feeling towards life and the world, some way of feeling by which our
+own existence can acquire more of the characteristics which we must
+deeply desire. The value of such work, however immeasurable it is,
+belongs with practice and not with theory. Such theoretic importance
+as it may possess is only in relation to human nature, not in relation
+to the world at large. The scientific philosophy, therefore, which
+aims only at understanding the world and not directly at any other
+improvement of human life, cannot take account of ethical notions
+without being turned aside from that submission to fact which is the
+essence of the scientific temper.</p>
+
+<span class='pagenum'><a name="Page_110" id="Page_110">[110]</a></span><br />
+
+<h4>II</h4>
+
+<p>If the notion of the universe and the notion of good and evil are
+extruded from scientific philosophy, it may be asked what specific
+problems remain for the philosopher as opposed to the man of science?
+It would be difficult to give a precise answer to this question, but
+certain characteristics may be noted as distinguishing the province of
+philosophy from that of the special sciences.</p>
+
+<p>In the first place a philosophical proposition must be general. It
+must not deal specially with things on the surface of the earth, or
+with the solar system, or with any other portion of space and time. It
+is this need of generality which has led to the belief that philosophy
+deals with the universe as a whole. I do not believe that this belief
+is justified, but I do believe that a philosophical proposition must
+be applicable to everything that exists or may exist. It might be
+supposed that this admission would be scarcely distinguishable from
+the view which I wish to reject. This, however, would be an error, and
+an important one. The traditional view would make the universe itself
+the subject of various predicates which could not be applied to any
+particular thing in the universe, and the ascription of such peculiar
+predicates to the universe would be the special business of
+philosophy. I maintain, on the contrary, that there are no
+propositions of which the "universe" is the subject; in other words,
+that there is no such thing as the "universe." What I do maintain is
+that there are general propositions which may be asserted of each
+individual thing, such as the propositions of logic. This does not
+involve that all the things there are form a whole which could be
+regarded as another thing and be made <span class='pagenum'><a name="Page_111" id="Page_111">[111]</a></span>the subject of predicates. It
+involves only the assertion that there are properties which belong to
+each separate thing, not that there are properties belonging to the
+whole of things collectively. The philosophy which I wish to advocate
+may be called logical atomism or absolute pluralism, because, while
+maintaining that there are many things, it denies that there is a
+whole composed of those things. We shall see, therefore, that
+philosophical propositions, instead of being concerned with the whole
+of things collectively, are concerned with all things distributively;
+and not only must they be concerned with all things, but they must be
+concerned with such properties of all things as do not depend upon the
+accidental nature of the things that there happen to be, but are true
+of any possible world, independently of such facts as can only be
+discovered by our senses.</p>
+
+<p>This brings us to a second characteristic of philosophical
+propositions, namely, that they must be <i>a priori</i>. A philosophical
+proposition must be such as can be neither proved nor disproved by
+empirical evidence. Too often we find in philosophical books arguments
+based upon the course of history, or the convolutions of the brain, or
+the eyes of shell-fish. Special and accidental facts of this kind are
+irrelevant to philosophy, which must make only such assertions as
+would be equally true however the actual world were constituted.</p>
+
+<p>We may sum up these two characteristics of philosophical propositions
+by saying that <i>philosophy is the science of the possible</i>. But this
+statement unexplained is liable to be misleading, since it may be
+thought that the possible is something other than the general, whereas
+in fact the two are indistinguishable.</p>
+
+<p>Philosophy, if what has been said is correct, becomes
+indistinguishable from logic as that word has now come <span class='pagenum'><a name="Page_112" id="Page_112">[112]</a></span>to be used.
+The study of logic consists, broadly speaking, of two not very sharply
+distinguished portions. On the one hand it is concerned with those
+general statements which can be made concerning everything without
+mentioning any one thing or predicate or relation, such for example as
+"if <i>x</i> is a member of the class &alpha; and every member of &alpha;
+is a member of &beta;, then <i>x</i> is a member of the class
+&beta;, whatever <i>x</i>, &alpha;, and &beta; may
+be." On the other hand, it is concerned with the analysis and
+enumeration of logical <i>forms</i>, i.e. with the kinds of propositions
+that may occur, with the various types of facts, and with the
+classification of the constituents of facts. In this way logic
+provides an inventory of possibilities, a repertory of abstractly
+tenable hypotheses.</p>
+
+<p>It might be thought that such a study would be too vague and too
+general to be of any very great importance, and that, if its problems
+became at any point sufficiently definite, they would be merged in the
+problems of some special science. It appears, however, that this is
+not the case. In some problems, for example, the analysis of space and
+time, the nature of perception, or the theory of judgment, the
+discovery of the logical form of the facts involved is the hardest
+part of the work and the part whose performance has been most lacking
+hitherto. It is chiefly for want of the right logical hypothesis that
+such problems have hitherto been treated in such an unsatisfactory
+manner, and have given rise to those contradictions or antinomies in
+which the enemies of reason among philosophers have at all times
+delighted.</p>
+
+<p>By concentrating attention upon the investigation of logical forms, it
+becomes possible at last for philosophy to deal with its problems
+piecemeal, and to obtain, as the sciences do, such partial and
+probably not wholly correct results as subsequent investigation can
+utilise <span class='pagenum'><a name="Page_113" id="Page_113">[113]</a></span>even while it supplements and improves them. Most
+philosophies hitherto have been constructed all in one block, in such
+a way that, if they were not wholly correct, they were wholly
+incorrect, and could not be used as a basis for further
+investigations. It is chiefly owing to this fact that philosophy,
+unlike science, has hitherto been unprogressive, because each original
+philosopher has had to begin the work again from the beginning,
+without being able to accept anything definite from the work of his
+predecessors. A scientific philosophy such as I wish to recommend will
+be piecemeal and tentative like other sciences; above all, it will be
+able to invent hypotheses which, even if they are not wholly true,
+will yet remain fruitful after the necessary corrections have been
+made. This possibility of successive approximations to the truth is,
+more than anything else, the source of the triumphs of science, and to
+transfer this possibility to philosophy is to ensure a progress in
+method whose importance it would be almost impossible to exaggerate.</p>
+
+<p>The essence of philosophy as thus conceived is analysis, not
+synthesis. To build up systems of the world, like Heine's German
+professor who knit together fragments of life and made an intelligible
+system out of them, is not, I believe, any more feasible than the
+discovery of the philosopher's stone. What is feasible is the
+understanding of general forms, and the division of traditional
+problems into a number of separate and less baffling questions.
+"Divide and conquer" is the maxim of success here as elsewhere.</p>
+
+<p>Let us illustrate these somewhat general maxims by examining their
+application to the philosophy of space, for it is only in application
+that the meaning or importance of a method can be understood. Suppose
+we are confronted with the problem of space as presented in <span class='pagenum'><a name="Page_114" id="Page_114">[114]</a></span>Kant's
+Transcendental &AElig;sthetic, and suppose we wish to discover what are the
+elements of the problem and what hope there is of obtaining a solution
+of them. It will soon appear that three entirely distinct problems,
+belonging to different studies, and requiring different methods for
+their solution, have been confusedly combined in the supposed single
+problem with which Kant is concerned. There is a problem of logic, a
+problem of physics, and a problem of theory of knowledge. Of these
+three, the problem of logic can be solved exactly and perfectly; the
+problem of physics can probably be solved with as great a degree of
+certainty and as great an approach to exactness as can be hoped in an
+empirical region; the problem of theory of knowledge, however, remains
+very obscure and very difficult to deal with. Let us see how these
+three problems arise.</p>
+
+<p>(1) The logical problem has arisen through the suggestions of
+non-Euclidean geometry. Given a body of geometrical propositions, it
+is not difficult to find a minimum statement of the axioms from which
+this body of propositions can be deduced. It is also not difficult, by
+dropping or altering some of these axioms, to obtain a more general or
+a different geometry, having, from the point of view of pure
+mathematics, the same logical coherence and the same title to respect
+as the more familiar Euclidean geometry. The Euclidean geometry itself
+is true perhaps of actual space (though this is doubtful), but
+certainly of an infinite number of purely arithmetical systems, each
+of which, from the point of view of abstract logic, has an equal and
+indefeasible right to be called a Euclidean space. Thus space as an
+object of logical or mathematical study loses its uniqueness; not only
+are there many kinds of spaces, but there are an infinity of examples
+of each kind, <span class='pagenum'><a name="Page_115" id="Page_115">[115]</a></span>though it is difficult to find any kind of which the
+space of physics may be an example, and it is impossible to find any
+kind of which the space of physics is certainly an example. As an
+illustration of one possible logical system of geometry we may
+consider all relations of three terms which are analogous in certain
+formal respects to the relation "between" as it appears to be in
+actual space. A space is then defined by means of one such three-term
+relation. The points of the space are all the terms which have this
+relation to something or other, and their order in the space in
+question is determined by this relation. The points of one space are
+necessarily also points of other spaces, since there are necessarily
+other three-term relations having those same points for their field.
+The space in fact is not determined by the class of its points, but by
+the ordering three-term relation. When enough abstract logical
+properties of such relations have been enumerated to determine the
+resulting kind of geometry, say, for example, Euclidean geometry, it
+becomes unnecessary for the pure geometer in his abstract capacity to
+distinguish between the various relations which have all these
+properties. He considers the whole class of such relations, not any
+single one among them. Thus in studying a given kind of geometry the
+pure mathematician is studying a certain class of relations defined by
+means of certain abstract logical properties which take the place of
+what used to be called axioms. The nature of geometrical <i>reasoning</i>
+therefore is purely deductive and purely logical; if any special
+epistemological peculiarities are to be found in geometry, it must not
+be in the reasoning, but in our knowledge concerning the axioms in
+some given space.</p>
+
+<p>(2) The physical problem of space is both more interesting and more
+difficult than the logical problem. <span class='pagenum'><a name="Page_116" id="Page_116">[116]</a></span>The physical problem may be
+stated as follows: to find in the physical world, or to construct from
+physical materials, a space of one of the kinds enumerated by the
+logical treatment of geometry. This problem derives its difficulty
+from the attempt to accommodate to the roughness and vagueness of the
+real world some system possessing the logical clearness and exactitude
+of pure mathematics. That this can be done with a certain degree of
+approximation is fairly evident If I see three people <i>A</i>, <i>B</i>, and
+<i>C</i> sitting in a row, I become aware of the fact which may be
+expressed by saying that <i>B</i> is between <i>A</i> and <i>C</i> rather than that
+<i>A</i> is between <i>B</i> and <i>C</i>, or <i>C</i> is between <i>A</i> and <i>B</i>. This
+relation of "between" which is thus perceived to hold has some of the
+abstract logical properties of those three-term relations which, we
+saw, give rise to a geometry, but its properties fail to be exact, and
+are not, as empirically given, amenable to the kind of treatment at
+which geometry aims. In abstract geometry we deal with points,
+straight lines, and planes; but the three people <i>A</i>, <i>B</i>, and <i>C</i>
+whom I see sitting in a row are not exactly points, nor is the row
+exactly a straight line. Nevertheless physics, which formally assumes
+a space containing points, straight lines, and planes, is found
+empirically to give results applicable to the sensible world. It must
+therefore be possible to find an interpretation of the points,
+straight lines, and planes of physics in terms of physical data, or at
+any rate in terms of data together with such hypothetical additions as
+seem least open to question. Since all data suffer from a lack of
+mathematical precision through being of a certain size and somewhat
+vague in outline, it is plain that if such a notion as that of a point
+is to find any application to empirical material, the point must be
+neither a datum nor a hypothetical addition to <span class='pagenum'><a name="Page_117" id="Page_117">[117]</a></span>data, but a
+<i>construction</i> by means of data with their hypothetical additions. It
+is obvious that any hypothetical filling out of data is less dubious
+and unsatisfactory when the additions are closely analogous to data
+than when they are of a radically different sort. To assume, for
+example, that objects which we see continue, after we have turned away
+our eyes, to be more or less analogous to what they were while we were
+looking, is a less violent assumption than to assume that such objects
+are composed of an infinite number of mathematical points. Hence in
+the physical study of the geometry of physical space, points must not
+be assumed <i>ab initio</i> as they are in the logical treatment of
+geometry, but must be constructed as systems composed of data and
+hypothetical analogues of data. We are thus led naturally to define a
+physical point as a certain class of those objects which are the
+ultimate constituents of the physical world. It will be the class of
+all those objects which, as one would naturally say, <i>contain</i> the
+point. To secure a definition giving this result, without previously
+assuming that physical objects are composed of points, is an agreeable
+problem in mathematical logic. The solution of this problem and the
+perception of its importance are due to my friend Dr. Whitehead. The
+oddity of regarding a point as a class of physical entities wears off
+with familiarity, and ought in any case not to be felt by those who
+maintain, as practically every one does, that points are mathematical
+fictions. The word "fiction" is used glibly in such connexions by many
+men who seem not to feel the necessity of explaining how it can come
+about that a fiction can be so useful in the study of the actual world
+as the points of mathematical physics have been found to be. By our
+definition, which regards a point as a class of physical objects, it
+is explained both how <span class='pagenum'><a name="Page_118" id="Page_118">[118]</a></span>the use of points can lead to important
+physical results, and how we can nevertheless avoid the assumption
+that points are themselves entities in the physical world.</p>
+
+<p>Many of the mathematically convenient properties of abstract logical
+spaces cannot be either known to belong or known not to belong to the
+space of physics. Such are all the properties connected with
+continuity. For to know that actual space has these properties would
+require an infinite exactness of sense-perception. If actual space is
+continuous, there are nevertheless many possible non-continuous spaces
+which will be empirically indistinguishable from it; and, conversely,
+actual space may be non-continuous and yet empirically
+indistinguishable from a possible continuous space. Continuity,
+therefore, though obtainable in the <i>a priori</i> region of arithmetic,
+is not with certainty obtainable in the space or time of the physical
+world: whether these are continuous or not would seem to be a question
+not only unanswered but for ever unanswerable. From the point of view
+of philosophy, however, the discovery that a question is unanswerable
+is as complete an answer as any that could possibly be obtained. And
+from the point of view of physics, where no empirical means of
+distinction can be found, there can be no empirical objection to the
+mathematically simplest assumption, which is that of continuity.</p>
+
+<p>The subject of the physical theory of space is a very large one,
+hitherto little explored. It is associated with a similar theory of
+time, and both have been forced upon the attention of philosophically
+minded physicists by the discussions which have raged concerning the
+theory of relativity.</p>
+
+<p>(3) The problem with which Kant is concerned in the Transcendental
+&AElig;sthetic is primarily the epistemological <span class='pagenum'><a name="Page_119" id="Page_119">[119]</a></span>problem: "How do we come to
+have knowledge of geometry <i>a priori</i>?" By the distinction between the
+logical and physical problems of geometry, the bearing and scope of
+this question are greatly altered. Our knowledge of pure geometry is
+<i>a priori</i> but is wholly logical. Our knowledge of physical geometry
+is synthetic, but is not <i>a priori</i>. Our knowledge of pure geometry is
+hypothetical, and does not enable us to assert, for example, that the
+axiom of parallels is true in the physical world. Our knowledge of
+physical geometry, while it does enable us to assert that this axiom
+is approximately verified, does not, owing to the inevitable
+inexactitude of observation, enable us to assert that it is verified
+<i>exactly</i>. Thus, with the separation which we have made between pure
+geometry and the geometry of physics, the Kantian problem collapses.
+To the question, "How is synthetic <i>a priori</i> knowledge possible?" we
+can now reply, at any rate so far as geometry is concerned, "It is not
+possible," if "synthetic" means "not deducible from logic alone." Our
+knowledge of geometry, like the rest of our knowledge, is derived
+partly from logic, partly from sense, and the peculiar position which
+in Kant's day geometry appeared to occupy is seen now to be a
+delusion. There are still some philosophers, it is true, who maintain
+that our knowledge that the axiom of parallels, for example, is true
+of actual space, is not to be accounted for empirically, but is as
+Kant maintained derived from an <i>a priori</i> intuition. This position is
+not logically refutable, but I think it loses all plausibility as soon
+as we realise how complicated and derivative is the notion of physical
+space. As we have seen, the application of geometry to the physical
+world in no way demands that there should really be points and
+straight lines among physical entities. The principle of economy,
+<span class='pagenum'><a name="Page_120" id="Page_120">[120]</a></span>therefore, demands that we should abstain from assuming the existence
+of points and straight lines. As soon, however, as we accept the view
+that points and straight lines are complicated constructions by means
+of classes of physical entities, the hypothesis that we have an <i>a
+priori</i> intuition enabling us to know what happens to straight lines
+when they are produced indefinitely becomes extremely strained and
+harsh; nor do I think that such an hypothesis would ever have arisen
+in the mind of a philosopher who had grasped the nature of physical
+space. Kant, under the influence of Newton, adopted, though with some
+vacillation, the hypothesis of absolute space, and this hypothesis,
+though logically unobjectionable, is removed by Occam's razor, since
+absolute space is an unnecessary entity in the explanation of the
+physical world. Although, therefore, we cannot refute the Kantian
+theory of an <i>a priori</i> intuition, we can remove its grounds one by
+one through an analysis of the problem. Thus, here as in many other
+philosophical questions, the analytic method, while not capable of
+arriving at a demonstrative result, is nevertheless capable of showing
+that all the positive grounds in favour of a certain theory are
+fallacious and that a less unnatural theory is capable of accounting
+for the facts.</p>
+
+<p>Another question by which the capacity of the analytic method can be
+shown is the question of realism. Both those who advocate and those
+who combat realism seem to me to be far from clear as to the nature of
+the problem which they are discussing. If we ask: "Are our objects of
+perception <i>real</i> and are they <i>independent</i> of the percipient?" it
+must be supposed that we attach some meaning to the words "real" and
+"independent," and yet, if either side in the controversy of realism
+is asked to define these two words, their answer is pretty <span class='pagenum'><a name="Page_121" id="Page_121">[121]</a></span>sure to
+embody confusions such as logical analysis will reveal.</p>
+
+<p>Let us begin with the word "real." There certainly are objects of
+perception, and therefore, if the question whether these objects are
+real is to be a substantial question, there must be in the world two
+sorts of objects, namely, the real and the unreal, and yet the unreal
+is supposed to be essentially what there is not. The question what
+properties must belong to an object in order to make it real is one to
+which an adequate answer is seldom if ever forthcoming. There is of
+course the Hegelian answer, that the real is the self-consistent and
+that nothing is self-consistent except the Whole; but this answer,
+true or false, is not relevant in our present discussion, which moves
+on a lower plane and is concerned with the status of objects of
+perception among other objects of equal fragmentariness. Objects of
+perception are contrasted, in the discussions concerning realism,
+rather with psychical states on the one hand and matter on the other
+hand than with the all-inclusive whole of things. The question we have
+therefore to consider is the question as to what can be meant by
+assigning "reality" to some but not all of the entities that make up
+the world. Two elements, I think, make up what is felt rather than
+thought when the word "reality" is used in this sense. A thing is real
+if it persists at times when it is not perceived; or again, a thing is
+real when it is correlated with other things in a way which experience
+has led us to expect. It will be seen that reality in either of these
+senses is by no means necessary to a thing, and that in fact there
+might be a whole world in which nothing was real in either of these
+senses. It might turn out that the objects of perception failed of
+reality in one or both of these respects, without its being in any way
+deducible that they are <span class='pagenum'><a name="Page_122" id="Page_122">[122]</a></span>not parts of the external world with which
+physics deals. Similar remarks will apply to the word "independent."
+Most of the associations of this word are bound up with ideas as to
+causation which it is not now possible to maintain. <i>A</i> is independent
+of <i>B</i> when <i>B</i> is not an indispensable part of the <i>cause</i> of <i>A</i>.
+But when it is recognised that causation is nothing more than
+correlation, and that there are correlations of simultaneity as well
+as of succession, it becomes evident that there is no uniqueness in a
+series of casual antecedents of a given event, but that, at any point
+where there is a correlation of simultaneity, we can pass from one
+line of antecedents to another in order to obtain a new series of
+causal antecedents. It will be necessary to specify the causal law
+according to which the antecedents are to be considered. I received a
+letter the other day from a correspondent who had been puzzled by
+various philosophical questions. After enumerating them he says:
+"These questions led me from Bonn to Strassburg, where I found
+Professor Simmel." Now, it would be absurd to deny that these
+questions caused his body to move from Bonn to Strassburg, and yet it
+must be supposed that a set of purely mechanical antecedents could
+also be found which would account for this transfer of matter from one
+place to another. Owing to this plurality of causal series antecedent
+to a given event, the notion of <i>the</i> cause becomes indefinite, and
+the question of independence becomes correspondingly ambiguous. Thus,
+instead of asking simply whether <i>A</i> is independent of <i>B</i>, we ought
+to ask whether there is a series determined by such and such causal
+laws leading from <i>B</i> to <i>A</i>. This point is important in connexion
+with the particular question of objects of perception. It may be that
+no objects quite like those which we perceive ever exist unperceived;
+<span class='pagenum'><a name="Page_123" id="Page_123">[123]</a></span>in this case there will be a causal law according to which objects of
+perception are not independent of being perceived. But even if this be
+the case, it may nevertheless also happen that there are purely
+physical causal laws determining the occurrence of objects which are
+perceived by means of other objects which perhaps are not perceived.
+In that case, in regard to such causal laws objects of perception will
+be independent of being perceived. Thus the question whether objects
+of perception are independent of being perceived is, as it stands,
+indeterminate, and the answer will be yes or no according to the
+method adopted of making it determinate. I believe that this confusion
+has borne a very large part in prolonging the controversies on this
+subject, which might well have seemed capable of remaining for ever
+undecided. The view which I should wish to advocate is that objects of
+perception do not persist unchanged at times when they are not
+perceived, although probably objects more or less resembling them do
+exist at such times; that objects of perception are part, and the only
+empirically knowable part, of the actual subject-matter of physics,
+and are themselves properly to be called physical; that purely
+physical laws exist determining the character and duration of objects
+of perception without any reference to the fact that they are
+perceived; and that in the establishment of such laws the propositions
+of physics do not presuppose any propositions of psychology or even
+the existence of mind. I do not know whether realists would recognise
+such a view as realism. All that I should claim for it is, that it
+avoids difficulties which seem to me to beset both realism and
+idealism as hitherto advocated, and that it avoids the appeal which
+they have made to ideas which logical analysis shows to be ambiguous.
+A further defence and elaboration of <span class='pagenum'><a name="Page_124" id="Page_124">[124]</a></span>the positions which I advocate,
+but for which time is lacking now, will be found indicated in my book
+on <i>Our Knowledge of the External World</i>.<a name="FNanchor_22_22" id="FNanchor_22_22"></a><a href="#Footnote_22_22" class="fnanchor">[22]</a></p>
+
+<p>The adoption of scientific method in philosophy, if I am not mistaken,
+compels us to abandon the hope of solving many of the more ambitious
+and humanly interesting problems of traditional philosophy. Some of
+these it relegates, though with little expectation of a successful
+solution, to special sciences, others it shows to be such as our
+capacities are essentially incapable of solving. But there remain a
+large number of the recognised problems of philosophy in regard to
+which the method advocated gives all those advantages of division into
+distinct questions, of tentative, partial, and progressive advance,
+and of appeal to principles with which, independently of temperament,
+all competent students must agree. The failure of philosophy hitherto
+has been due in the main to haste and ambition: patience and modesty,
+here as in other sciences, will open the road to solid and durable
+progress.</p>
+
+<br />
+<hr style="width: 15%;" />
+<br />
+
+<h4>FOOTNOTES:</h4>
+
+<div class="footnote"><p class="noin"><a name="Footnote_19_19" id="Footnote_19_19"></a><a href="#FNanchor_19_19"><span class="label">[19]</span></a> Bosanquet, <i>Logic</i>, ii, p. 211.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_20_20" id="Footnote_20_20"></a><a href="#FNanchor_20_20"><span class="label">[20]</span></a> <i>Some Problems of Philosophy</i>, p 124.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_21_21" id="Footnote_21_21"></a><a href="#FNanchor_21_21"><span class="label">[21]</span></a> <i>First Principles</i> (1862), Part II, beginning of chap.
+viii.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_22_22" id="Footnote_22_22"></a><a href="#FNanchor_22_22"><span class="label">[22]</span></a> Open Court Company, 1914.</p></div>
+
+
+<br />
+<br />
+<br />
+<br />
+<a name="VII" id="VII"></a><hr />
+<span class='pagenum'><a name="Page_125" id="Page_125">[125]</a></span><br />
+
+<h3>VII<span class="totoc"><a href="#toc">ToC</a></span></h3>
+
+<h4>THE ULTIMATE CONSTITUENTS OF MATTER<a name="FNanchor_23_23" id="FNanchor_23_23"></a><a href="#Footnote_23_23" class="fnanchor">[23]</a></h4>
+<br />
+
+<p>I wish to discuss in this article no less a question than the ancient
+metaphysical query, "What is matter?" The question, "What is matter?"
+in so far as it concerns philosophy, is, I think, already capable of
+an answer which in principle will be as complete as an answer can hope
+to be; that is to say, we can separate the problem into an essentially
+soluble and an essentially insoluble portion, and we can now see how
+to solve the essentially soluble portion, at least as regards its main
+outlines. It is these outlines which I wish to suggest in the present
+article. My main position, which is realistic, is, I hope and believe,
+not remote from that of Professor Alexander, by whose writings on this
+subject I have profited greatly.<a name="FNanchor_24_24" id="FNanchor_24_24"></a><a href="#Footnote_24_24" class="fnanchor">[24]</a> It is also in close accord with
+that of Dr. Nunn.<a name="FNanchor_25_25" id="FNanchor_25_25"></a><a href="#Footnote_25_25" class="fnanchor">[25]</a></p>
+
+<p>Common sense is accustomed to the division of the world into mind and
+matter. It is supposed by all who have never studied philosophy that
+the distinction between mind and matter is perfectly clear and easy,
+that the two do not at any point overlap, and that only a fool or a
+philosopher could be in doubt as to whether any given entity is mental
+or material. This simple faith <span class='pagenum'><a name="Page_126" id="Page_126">[126]</a></span>survives in Descartes and in a
+somewhat modified form in Spinoza, but with Leibniz it begins to
+disappear, and from his day to our own almost every philosopher of
+note has criticised and rejected the dualism of common sense. It is my
+intention in this article to defend this dualism; but before defending
+it we must spend a few moments on the reasons which have prompted its
+rejection.</p>
+
+<p>Our knowledge of the material world is obtained by means of the
+senses, of sight and touch and so on. At first it is supposed that
+things are just as they seem, but two opposite sophistications soon
+destroy this na&iuml;ve belief. On the one hand the physicists cut up
+matter into molecules, atoms, corpuscles, and as many more such
+subdivisions as their future needs may make them postulate, and the
+units at which they arrive are uncommonly different from the visible,
+tangible objects of daily life. A unit of matter tends more and more
+to be something like an electromagnetic field filling all space,
+though having its greatest intensity in a small region. Matter
+consisting of such elements is as remote from daily life as any
+metaphysical theory. It differs from the theories of metaphysicians
+only in the fact that its practical efficacy proves that it contains
+some measure of truth and induces business men to invest money on the
+strength of it; but, in spite of its connection with the money market,
+it remains a metaphysical theory none the less.</p>
+
+<p>The second kind of sophistication to which the world of common sense
+has been subjected is derived from the psychologists and
+physiologists. The physiologists point out that what we see depends
+upon the eye, that what we hear depends upon the ear, and that all our
+senses are liable to be affected by anything which affects the brain,
+like alcohol or hasheesh. Psychologists point out how much of what we
+think we see is supplied by association <span class='pagenum'><a name="Page_127" id="Page_127">[127]</a></span>or unconscious inference, how
+much is mental interpretation, and how doubtful is the residuum which
+can be regarded as crude datum. From these facts it is argued by the
+psychologists that the notion of a datum passively received by the
+mind is a delusion, and it is argued by the physiologists that even if
+a pure datum of sense could be obtained by the analysis of experience,
+still this datum could not belong, as common sense supposes, to the
+outer world, since its whole nature is conditioned by our nerves and
+sense organs, changing as they change in ways which it is thought
+impossible to connect with any change in the matter supposed to be
+perceived. This physiologist's argument is exposed to the rejoinder,
+more specious than solid, that our knowledge of the existence of the
+sense organs and nerves is obtained by that very process which the
+physiologist has been engaged in discrediting, since the existence of
+the nerves and sense organs is only known through the evidence of the
+senses themselves. This argument may prove that some reinterpretation
+of the results of physiology is necessary before they can acquire
+metaphysical validity. But it does not upset the physiological
+argument in so far as this constitutes merely a <i>reductio ad absurdum</i>
+of na&iuml;ve realism.</p>
+
+<p>These various lines of argument prove, I think, that some part of the
+beliefs of common sense must be abandoned. They prove that, if we take
+these beliefs as a whole, we are forced into conclusions which are in
+part self-contradictory; but such arguments cannot of themselves
+decide what portion of our common-sense beliefs is in need of
+correction. Common sense believes that what we see is physical,
+outside the mind, and continuing to exist if we shut our eyes or turn
+them in another direction. I believe that common sense is right in
+<span class='pagenum'><a name="Page_128" id="Page_128">[128]</a></span>regarding what we see as physical and (in one of several possible
+senses) outside the mind, but is probably wrong in supposing that it
+continues to exist when we are no longer looking at it. It seems to me
+that the whole discussion of matter has been obscured by two errors
+which support each other. The first of these is the error that what we
+see, or perceive through any of our other senses, is subjective: the
+second is the belief that what is physical must be persistent.
+Whatever physics may regard as the ultimate constituents of matter, it
+always supposes these constituents to be indestructible. Since the
+immediate data of sense are not indestructible but in a state of
+perpetual flux, it is argued that these data themselves cannot be
+among the ultimate constituents of matter. I believe this to be a
+sheer mistake. The persistent particles of mathematical physics I
+regard as logical constructions, symbolic fictions enabling us to
+express compendiously very complicated assemblages of facts; and, on
+the other hand, I believe that the actual data in sensation, the
+immediate objects of sight or touch or hearing, are extra-mental,
+purely physical, and among the ultimate constituents of matter.</p>
+
+<p>My meaning in regard to the impermanence of physical entities may
+perhaps be made clearer by the use of Bergson's favourite illustration
+of the cinematograph. When I first read Bergson's statement that the
+mathematician conceives the world after the analogy of a
+cinematograph, I had never seen a cinematograph, and my first visit to
+one was determined by the desire to verify Bergson's statement, which
+I found to be completely true, at least so far as I am concerned.
+When, in a picture palace, we see a man rolling down hill, or running
+away from the police, or falling into a river, or doing any of those
+other things to which men in such places are addicted, we know <span class='pagenum'><a name="Page_129" id="Page_129">[129]</a></span>that
+there is not really only one man moving, but a succession of films,
+each with a different momentary man. The illusion of persistence
+arises only through the approach to continuity in the series of
+momentary men. Now what I wish to suggest is that in this respect the
+cinema is a better metaphysician than common sense, physics, or
+philosophy. The real man too, I believe, however the police may swear
+to his identity, is really a series of momentary men, each different
+one from the other, and bound together, not by a numerical identity,
+but by continuity and certain intrinsic causal laws. And what applies
+to men applies equally to tables and chairs, the sun, moon and stars.
+Each of these is to be regarded, not as one single persistent entity,
+but as a series of entities succeeding each other in time, each
+lasting for a very brief period, though probably not for a mere
+mathematical instant. In saying this I am only urging the same kind of
+division in time as we are accustomed to acknowledge in the case of
+space. A body which fills a cubic foot will be admitted to consist of
+many smaller bodies, each occupying only a very tiny volume; similarly
+a thing which persists for an hour is to be regarded as composed of
+many things of less duration. A true theory of matter requires a
+division of things into time-corpuscles as well as into
+space-corpuscles.</p>
+
+<p>The world may be conceived as consisting of a multitude of entities
+arranged in a certain pattern. The entities which are arranged I shall
+call "particulars." The arrangement or pattern results from relations
+among particulars. Classes or series of particulars, collected
+together on account of some property which makes it convenient to be
+able to speak of them as wholes, are what I call logical constructions
+or symbolic fictions. The particulars are to be conceived, not on the
+analogy of bricks <span class='pagenum'><a name="Page_130" id="Page_130">[130]</a></span>in a building, but rather on the analogy of notes
+in a symphony. The ultimate constituents of a symphony (apart from
+relations) are the notes, each of which lasts only for a very short
+time. We may collect together all the notes played by one instrument:
+these may be regarded as the analogues of the successive particulars
+which common sense would regard as successive states of one "thing."
+But the "thing" ought to be regarded as no more "real" or
+"substantial" than, for example, the r&ocirc;le of the trombone. As soon as
+"things" are conceived in this manner it will be found that the
+difficulties in the way of regarding immediate objects of sense as
+physical have largely disappeared.</p>
+
+<p>When people ask, "Is the object of sense mental or physical?" they
+seldom have any clear idea either what is meant by "mental" or
+"physical," or what criteria are to be applied for deciding whether a
+given entity belongs to one class or the other. I do not know how to
+give a sharp definition of the word "mental," but something may be
+done by enumerating occurrences which are indubitably mental:
+believing, doubting, wishing, willing, being pleased or pained, are
+certainly mental occurrences; so are what we may call experiences,
+seeing, hearing, smelling, perceiving generally. But it does not
+follow from this that what is seen, what is heard, what is smelt, what
+is perceived, must be mental. When I see a flash of lightning, my
+seeing of it is mental, but what I see, although it is not quite the
+same as what anybody else sees at the same moment, and although it
+seems very unlike what the physicist would describe as a flash of
+lightning, is not mental. I maintain, in fact, that if the physicist
+could describe truly and fully all that occurs in the physical world
+when there is a flash of lightning, it would contain as a constituent
+what I see, and also what <span class='pagenum'><a name="Page_131" id="Page_131">[131]</a></span>is seen by anybody else who would commonly
+be said to see the same flash. What I mean may perhaps be made plainer
+by saying that if my body could remain in exactly the same state in
+which it is, although my mind had ceased to exist, precisely that
+object which I now see when I see the flash would exist, although of
+course I should not see it, since my seeing is mental. The principal
+reasons which have led people to reject this view have, I think, been
+two: first, that they did not adequately distinguish between my seeing
+and what I see; secondly, that the causal dependence of what I see
+upon my body has made people suppose that what I see cannot be
+"outside" me. The first of these reasons need not detain us, since the
+confusion only needs to be pointed out in order to be obviated; but
+the second requires some discussion, since it can only be answered by
+removing current misconceptions, on the one hand as to the nature of
+space, and on the other, as to the meaning of causal dependence.</p>
+
+<p>When people ask whether colours, for example, or other secondary
+qualities are inside or outside the mind, they seem to suppose that
+their meaning must be clear, and that it ought to be possible to say
+yes or no without any further discussion of the terms involved. In
+fact, however, such terms as "inside" or "outside" are very ambiguous.
+What is meant by asking whether this or that is "in" the mind? The
+mind is not like a bag or a pie; it does not occupy a certain region
+in space, or, if (in a sense) it does, what is in that region is
+presumably part of the brain, which would not be said to be in the
+mind. When people say that sensible qualities are in the mind, they do
+not mean "spatially contained in" in the sense in which the blackbirds
+were in the pie. We might regard the mind as an assemblage of
+particulars, namely, what <span class='pagenum'><a name="Page_132" id="Page_132">[132]</a></span>would be called "states of mind," which
+would belong together in virtue of some specific common quality. The
+common quality of all states of mind would be the quality designated
+by the word "mental"; and besides this we should have to suppose that
+each separate person's states of mind have some common characteristic
+distinguishing them from the states of mind of other people. Ignoring
+this latter point, let us ask ourselves whether the quality designated
+by the word "mental" does, as a matter of observation, actually belong
+to objects of sense, such as colours or noises. I think any candid
+person must reply that, however difficult it may be to know what we
+mean by "mental," it is not difficult to see that colours and noises
+are not mental in the sense of having that intrinsic peculiarity which
+belongs to beliefs and wishes and volitions, but not to the physical
+world. Berkeley advances on this subject a plausible argument<a name="FNanchor_26_26" id="FNanchor_26_26"></a><a href="#Footnote_26_26" class="fnanchor">[26]</a>
+which seems to me to rest upon an ambiguity in the word "pain." He
+argues that the realist supposes the heat which he feels in
+approaching a fire to be something outside his mind, but that as he
+approaches nearer and nearer to the fire the sensation of heat passes
+imperceptibly into pain, and that no one could regard pain as
+something outside the mind. In reply to this argument, it should be
+observed in the first place that the heat of which we are immediately
+aware is not in the fire but in our own body. It is only by inference
+that the fire is judged to be the cause of the heat which we feel in
+our body. In the second place (and this is the more important point),
+when we speak of pain we may mean one of two things: we may mean the
+object of the sensation or other experience which has the quality of
+being painful, <span class='pagenum'><a name="Page_133" id="Page_133">[133]</a></span>or we may mean the quality of painfulness itself. When
+a man says he has a pain in his great toe, what he means is that he
+has a sensation associated with his great toe and having the quality
+of painfulness. The sensation itself, like every sensation, consists
+in experiencing a sensible object, and the experiencing has that
+quality of painfulness which only mental occurrences can have, but
+which may belong to thoughts or desires, as well as to sensations. But
+in common language we speak of the sensible object experienced in a
+painful sensation as a pain, and it is this way of speaking which
+causes the confusion upon which the plausibility of Berkeley's
+argument depends. It would be absurd to attribute the quality of
+painfulness to anything non-mental, and hence it comes to be thought
+that what we call a pain in the toe must be mental. In fact, however,
+it is not the sensible object in such a case which is painful, but the
+sensation, that is to say, the experience of the sensible object. As
+the heat which we experience from the fire grows greater, the
+experience passes gradually from being pleasant to being painful, but
+neither the pleasure nor the pain is a quality of the object
+experienced as opposed to the experience, and it is therefore a
+fallacy to argue that this object must be mental on the ground that
+painfulness can only be attributed to what is mental.</p>
+
+<p>If, then, when we say that something is in the mind we mean that it
+has a certain recognisable intrinsic characteristic such as belongs to
+thoughts and desires, it must be maintained on grounds of immediate
+inspection that objects of sense are not in any mind.</p>
+
+<p>A different meaning of "in the mind" is, however, to be inferred from
+the arguments advanced by those who regard sensible objects as being
+in the mind. The arguments used are, in the main, such as would prove
+the <span class='pagenum'><a name="Page_134" id="Page_134">[134]</a></span>causal dependence of objects of sense upon the percipient. Now
+the notion of causal dependence is very obscure and difficult, much
+more so in fact than is generally realised by philosophers. I shall
+return to this point in a moment. For the present, however, accepting
+the notion of causal dependence without criticism, I wish to urge that
+the dependence in question is rather upon our bodies than upon our
+minds. The visual appearance of an object is altered if we shut one
+eye, or squint, or look previously at something dazzling; but all
+these are bodily acts, and the alterations which they effect are to be
+explained by physiology and optics, not by psychology.<a name="FNanchor_27_27" id="FNanchor_27_27"></a><a href="#Footnote_27_27" class="fnanchor">[27]</a> They are in
+fact of exactly the same kind as the alterations effected by
+spectacles or a microscope. They belong therefore to the theory of the
+physical world, and can have no bearing upon the question whether what
+we see is causally dependent upon the mind. What they do tend to
+prove, and what I for my part have no wish to deny, is that what we
+see is causally dependent upon our body and is not, as crude common
+sense would suppose, something which would exist equally if our eyes
+and nerves and brain were absent, any more than the visual appearance
+presented by an object seen through a microscope would remain if the
+microscope were removed. So long as it is supposed that the physical
+world is composed of stable and more or less permanent constituents,
+the fact that what we see is changed by changes in our body appears to
+afford reason for regarding what we see as not an ultimate constituent
+of matter. But if it is recognised that the ultimate constituents of
+matter are as circumscribed in duration as in spatial extent, the
+whole of this difficulty vanishes.</p>
+
+<p>There remains, however, another difficulty, connected with space. When
+we look at the sun we wish to know <span class='pagenum'><a name="Page_135" id="Page_135">[135]</a></span>something about the sun itself,
+which is ninety-three million miles away; but what we see is dependent
+upon our eyes, and it is difficult to suppose that our eyes can affect
+what happens at a distance of ninety-three million miles. Physics
+tells us that certain electromagnetic waves start from the sun, and
+reach our eyes after about eight minutes. They there produce
+disturbances in the rods and cones, thence in the optic nerve, thence
+in the brain. At the end of this purely physical series, by some odd
+miracle, comes the experience which we call "seeing the sun," and it
+is such experiences which form the whole and sole reason for our
+belief in the optic nerve, the rods and cones, the ninety-three
+million miles, the electromagnetic waves, and the sun itself. It is
+this curious oppositeness of direction between the order of causation
+as affirmed by physics, and the order of evidence as revealed by
+theory of knowledge, that causes the most serious perplexities in
+regard to the nature of physical reality. Anything that invalidates
+our seeing, as a source of knowledge concerning physical reality,
+invalidates also the whole of physics and physiology. And yet,
+starting from a common-sense acceptance of our seeing, physics has
+been led step by step to the construction of the causal chain in which
+our seeing is the last link, and the immediate object which we see
+cannot be regarded as that initial cause which we believe to be
+ninety-three million miles away, and which we are inclined to regard
+as the "real" sun.</p>
+
+<p>I have stated this difficulty as forcibly as I can, because I believe
+that it can only be answered by a radical analysis and reconstruction
+of all the conceptions upon whose employment it depends.</p>
+
+<p>Space, time, matter and cause, are the chief of these conceptions. Let
+us begin with the conception of cause.</p>
+
+<p>Causal dependence, as I observed a moment ago, is a <span class='pagenum'><a name="Page_136" id="Page_136">[136]</a></span>conception which
+it is very dangerous to accept at its face value. There exists a
+notion that in regard to any event there is something which may be
+called <i>the</i> cause of that event&mdash;some one definite occurrence,
+without which the event would have been impossible and with which it
+becomes necessary. An event is supposed to be dependent upon its cause
+in some way which in it is not dependent upon other things. Thus men
+will urge that the mind is dependent upon the brain, or, with equal
+plausibility, that the brain is dependent upon the mind. It seems not
+improbable that if we had sufficient knowledge we could infer the
+state of a man's mind from the state of his brain, or the state of his
+brain from the state of his mind. So long as the usual conception of
+causal dependence is retained, this state of affairs can be used by
+the materialist to urge that the state of our brain causes our
+thoughts, and by the idealist to urge that our thoughts cause the
+state of our brain. Either contention is equally valid or equally
+invalid. The fact seems to be that there are many correlations of the
+sort which may be called causal, and that, for example, either a
+physical or a mental event can be predicted, theoretically, either
+from a sufficient number of physical antecedents or from a sufficient
+number of mental antecedents. To speak of <i>the</i> cause of an event is
+therefore misleading. Any set of antecedents from which the event can
+theoretically be inferred by means of correlations might be called a
+cause of the event. But to speak of <i>the</i> cause is to imply a
+uniqueness which does not exist.</p>
+
+<p>The relevance of this to the experience which we call "seeing the sun"
+is obvious. The fact that there exists a chain of antecedents which
+makes our seeing dependent upon the eyes and nerves and brain does not
+even tend to show that there is not another chain of antecedents in
+which the eyes and nerves and brain as physical things are ignored. If
+we are to escape from the dilemma which <span class='pagenum'><a name="Page_137" id="Page_137">[137]</a></span>seemed to arise out of the
+physiological causation of what we see when we say we see the sun, we
+must find, at least in theory, a way of stating causal laws for the
+physical world, in which the units are not material things, such as
+the eyes and nerves and brain, but momentary particulars of the same
+sort as our momentary visual object when we look at the sun. The sun
+itself and the eyes and nerves and brain must be regarded as
+assemblages of momentary particulars. Instead of supposing, as we
+naturally do when we start from an uncritical acceptance of the
+apparent dicta of physics, that <i>matter</i> is what is "really real" in
+the physical world, and that the immediate objects of sense are mere
+phantasms, we must regard matter as a logical construction, of which
+the constituents will be just such evanescent particulars as may, when
+an observer happens to be present, become data of sense to that
+observer. What physics regards as the sun of eight minutes ago will be
+a whole assemblage of particulars, existing at different times,
+spreading out from a centre with the velocity of light, and containing
+among their number all those visual data which are seen by people who
+are now looking at the sun. Thus the sun of eight minutes ago is a
+class of particulars, and what I see when I now look at the sun is one
+member of this class. The various particulars constituting this class
+will be correlated with each other by a certain continuity and certain
+intrinsic laws of variation as we pass outwards from the centre,
+together with certain modifications correlated extrinsically with
+other particulars which are not members of this class. It is these
+extrinsic modifications which represent the sort of facts that, in our
+former account, appeared as the influence of the eyes and nerves in
+modifying the appearance of the sun.<a name="FNanchor_28_28" id="FNanchor_28_28"></a><a href="#Footnote_28_28" class="fnanchor">[28]</a></p>
+
+<p><span class='pagenum'><a name="Page_138" id="Page_138">[138]</a></span>The <i>prima facie</i> difficulties in the way of this view are chiefly
+derived from an unduly conventional theory of space. It might seem at
+first sight as if we had packed the world much fuller than it could
+possibly hold. At every place between us and the sun, we said, there
+is to be a particular which is to be a member of the sun as it was a
+few minutes ago. There will also, of course, have to be a particular
+which is a member of any planet or fixed star that may happen to be
+visible from that place. At the place where I am, there will be
+particulars which will be members severally of all the "things" I am
+now said to be perceiving. Thus throughout the world, everywhere,
+there will be an enormous number of particulars coexisting in the same
+place. But these troubles result from contenting ourselves too readily
+with the merely three-dimensional space to which schoolmasters have
+accustomed us. The space of the real world is a space of six
+dimensions, and as soon as we realise this we see that there is plenty
+of room for all the particulars for which we want to find positions.
+In order to realise this we have only to return for a moment from the
+polished space of physics to the rough and untidy space of our
+immediate sensible experience. The space of one man's sensible objects
+is a three-dimensional space. It does not appear probable that two men
+ever both perceive at the same time any one sensible object; when they
+are said to see the same thing or hear the same noise, there will
+always be some difference, however slight, between the actual shapes
+seen or the actual sounds heard. If this is so, and if, as is
+generally assumed, position in space is purely relative, it follows
+that the space of one man's objects and the space of another man's
+objects have no place in common, that they are in fact different
+spaces, and not merely different parts of one space. I mean by this
+that such immediate spatial relations as are perceived to hold
+<span class='pagenum'><a name="Page_139" id="Page_139">[139]</a></span>between the different parts of the sensible space perceived by one
+man, do not hold between parts of sensible spaces perceived by
+different men. There are therefore a multitude of three-dimensional
+spaces in the world: there are all those perceived by observers, and
+presumably also those which are not perceived, merely because no
+observer is suitably situated for perceiving them.</p>
+
+<p>But although these spaces do not have to one another the same kind of
+spatial relations as obtain between the parts of one of them, it is
+nevertheless possible to arrange these spaces themselves in a
+three-dimensional order. This is done by means of the correlated
+particulars which we regard as members (or aspects) of one physical
+thing. When a number of people are said to see the same object, those
+who would be said to be near to the object see a particular occupying
+a larger part of their field of vision than is occupied by the
+corresponding particular seen by people who would be said to be
+farther from the thing. By means of such considerations it is
+possible, in ways which need not now be further specified, to arrange
+all the different spaces in a three-dimensional series. Since each of
+the spaces is itself three-dimensional, the whole world of particulars
+is thus arranged in a six-dimensional space, that is to say, six
+co-ordinates will be required to assign completely the position of any
+given particular, namely, three to assign its position in its own
+space and three more to assign the position of its space among the
+other spaces.</p>
+
+<p>There are two ways of classifying particulars: we may take together
+all those that belong to a given "perspective," or all those that are,
+as common sense would say, different "aspects" of the same "thing."
+For example, if I am (as is said) seeing the sun, what I see belongs
+to two assemblages: (1) the assemblage of all my present objects of
+sense, which is what I call a "perspective"; <span class='pagenum'><a name="Page_140" id="Page_140">[140]</a></span>(2) the assemblage of
+all the different particulars which would be called aspects of the sun
+of eight minutes ago&mdash;this assemblage is what I define as <i>being</i> the
+sun of eight minutes ago. Thus "perspectives" and "things" are merely
+two different ways of classifying particulars. It is to be observed
+that there is no <i>a priori</i> necessity for particulars to be
+susceptible of this double classification. There may be what might be
+called "wild" particulars, not having the usual relations by which the
+classification is effected; perhaps dreams and hallucinations are
+composed of particulars which are "wild" in this sense.</p>
+
+<p>The exact definition of what is meant by a perspective is not quite
+easy. So long as we confine ourselves to visible objects or to objects
+of touch we might define the perspective of a given particular as "all
+particulars which have a simple (direct) spatial relation to the given
+particular." Between two patches of colour which I see now, there is a
+direct spatial relation which I equally see. But between patches of
+colour seen by different men there is only an indirect constructed
+spatial relation by means of the placing of "things" in physical space
+(which is the same as the space composed of perspectives). Those
+particulars which have direct spatial relations to a given particular
+will belong to the same perspective. But if, for example, the sounds
+which I hear are to belong to the same perspective with the patches of
+colour which I see, there must be particulars which have no direct
+spatial relation and yet belong to the same perspective. We cannot
+define a perspective as all the data of one percipient at one time,
+because we wish to allow the possibility of perspectives which are not
+perceived by any one. There will be need, therefore, in defining a
+perspective, of some principle derived neither from psychology nor
+from space.</p>
+
+<p>Such a principle may be obtained from the <span class='pagenum'><a name="Page_141" id="Page_141">[141]</a></span>consideration of <i>time</i>.
+The one all-embracing time, like the one all-embracing space, is a
+construction; there is no <i>direct</i> time-relation between particulars
+belonging to my perspective and particulars belonging to another
+man's. On the other hand, any two particulars of which I am aware are
+either simultaneous or successive, and their simultaneity or
+successiveness is sometimes itself a datum to me. We may therefore
+define the perspective to which a given particular belongs as "all
+particulars simultaneous with the given particular," where
+"simultaneous" is to be understood as a direct simple relation, not
+the derivative constructed relation of physics. It may be observed
+that the introduction of "local time" suggested by the principle of
+relativity has effected, for purely scientific reasons, much the same
+multiplication of times as we have just been advocating.</p>
+
+<p>The sum-total of all the particulars that are (directly) either
+simultaneous with or before or after a given particular may be defined
+as the "biography" to which that particular belongs. It will be
+observed that, just as a perspective need not be actually perceived by
+any one, so a biography need not be actually lived by any one. Those
+biographies that are lived by no one are called "official."</p>
+
+<p>The definition of a "thing" is effected by means of continuity and of
+correlations which have a certain differential independence of other
+"things." That is to say, given a particular in one perspective, there
+will usually in a neighbouring perspective be a very similar
+particular, differing from the given particular, to the first order of
+small quantities, according to a law involving only the difference of
+position of the two perspectives in perspective space, and not any of
+the other "things" in the universe. It is this continuity and
+differential independence in the law of change as we pass from one
+<span class='pagenum'><a name="Page_142" id="Page_142">[142]</a></span>perspective to another that defines the class of particulars which is
+to be called "one thing."</p>
+
+<p>Broadly speaking, we may say that the physicist finds it convenient to
+classify particulars into "things," while the psychologist finds it
+convenient to classify them into "perspectives" and "biographies,"
+since one perspective <i>may</i> constitute the momentary data of one
+percipient, and one biography <i>may</i> constitute the whole of the data
+of one percipient throughout his life.</p>
+
+<p>We may now sum up our discussion. Our object has been to discover as
+far as possible the nature of the ultimate constituents of the
+physical world. When I speak of the "physical world," I mean, to begin
+with, the world dealt with by physics. It is obvious that physics is
+an empirical science, giving us a certain amount of knowledge and
+based upon evidence obtained through the senses. But partly through
+the development of physics itself, partly through arguments derived
+from physiology, psychology or metaphysics, it has come to be thought
+that the immediate data of sense could not themselves form part of the
+ultimate constituents of the physical world, but were in some sense
+"mental," "in the mind," or "subjective." The grounds for this view,
+in so far as they depend upon physics, can only be adequately dealt
+with by rather elaborate constructions depending upon symbolic logic,
+showing that out of such materials as are provided by the senses it is
+possible to construct classes and series having the properties which
+physics assigns to matter. Since this argument is difficult and
+technical, I have not embarked upon it in this article. But in so far
+as the view that sense-data are "mental" rests upon physiology,
+psychology, or metaphysics, I have tried to show that it rests upon
+confusions and prejudices&mdash;prejudices in favour of permanence in the
+ultimate constituents of matter, and <span class='pagenum'><a name="Page_143" id="Page_143">[143]</a></span>confusions derived from unduly
+simple notions as to space, from the causal correlation of sense-data
+with sense-organs, and from failure to distinguish between sense-data
+and sensations. If what we have said on these subjects is valid, the
+existence of sense-data is logically independent of the existence of
+mind, and is causally dependent upon the <i>body</i> of the percipient
+rather than upon his mind. The causal dependence upon the body of the
+percipient, we found, is a more complicated matter than it appears to
+be, and, like all causal dependence, is apt to give rise to erroneous
+beliefs through misconceptions as to the nature of causal correlation.
+If we have been right in our contentions, sense-data are merely those
+among the ultimate constituents of the physical world, of which we
+happen to be immediately aware; they themselves are purely physical,
+and all that is mental in connection with them is our awareness of
+them, which is irrelevant to their nature and to their place in
+physics.</p>
+
+<p>Unduly simple notions as to space have been a great stumbling-block to
+realists. When two men look at the same table, it is supposed that
+what the one sees and what the other sees are in the same place. Since
+the shape and colour are not quite the same for the two men, this
+raises a difficulty, hastily solved, or rather covered up, by
+declaring what each sees to be purely "subjective"&mdash;though it would
+puzzle those who use this glib word to say what they mean by it. The
+truth seems to be that space&mdash;and time also&mdash;is much more complicated
+than it would appear to be from the finished structure of physics, and
+that the one all-embracing three-dimensional space is a logical
+construction, obtained by means of correlations from a crude space of
+six dimensions. The particulars occupying this six-dimensional space,
+classified in one way, form "things," from which with certain further
+manipulations we can obtain what physics can <span class='pagenum'><a name="Page_144" id="Page_144">[144]</a></span>regard as matter;
+classified in another way, they form "perspectives" and "biographies,"
+which may, if a suitable percipient happens to exist, form
+respectively the sense-data of a momentary or of a total experience.
+It is only when physical "things" have been dissected into series of
+classes of particulars, as we have done, that the conflict between the
+point of view of physics and the point of view of psychology can be
+overcome. This conflict, if what has been said is not mistaken, flows
+from different methods of classification, and vanishes as soon as its
+source is discovered.</p>
+
+<p>In favour of the theory which I have briefly outlined, I do not claim
+that it is <i>certainly</i> true. Apart from the likelihood of mistakes,
+much of it is avowedly hypothetical. What I do claim for the theory is
+that it <i>may</i> be true, and that this is more than can be said for any
+other theory except the closely analogous theory of Leibniz. The
+difficulties besetting realism, the confusions obstructing any
+philosophical account of physics, the dilemma resulting from
+discrediting sense-data, which yet remain the sole source of our
+knowledge of the outer world&mdash;all these are avoided by the theory
+which I advocate. This does not prove the theory to be true, since
+probably many other theories might be invented which would have the
+same merits. But it does prove that the theory has a better chance of
+being true than any of its present competitors, and it suggests that
+what can be known with certainty is likely to be discoverable by
+taking our theory as a starting-point, and gradually freeing it from
+all such assumptions as seem irrelevant, unnecessary, or unfounded. On
+these grounds, I recommend it to attention as a hypothesis and a basis
+for further work, though not as itself a finished or adequate solution
+of the problem with which it deals.</p>
+
+<br />
+<hr style="width: 15%;" />
+<br />
+
+<h4>FOOTNOTES:</h4>
+
+<div class="footnote"><p class="noin"><a name="Footnote_23_23" id="Footnote_23_23"></a><a href="#FNanchor_23_23"><span class="label">[23]</span></a> An address delivered to the Philosophical Society of
+Manchester in February, 1915. Reprinted from <i>The Monist</i>, July,
+1915.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_24_24" id="Footnote_24_24"></a><a href="#FNanchor_24_24"><span class="label">[24]</span></a> Cf. especially Samuel Alexander, "The Basis of Realism,"
+<i>British Academy</i>, Vol. VI.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_25_25" id="Footnote_25_25"></a><a href="#FNanchor_25_25"><span class="label">[25]</span></a> "Are Secondary Qualities Independent of Perception?"
+<i>Proc. Arist. Soc.</i>, 1909-10, pp. 191-218.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_26_26" id="Footnote_26_26"></a><a href="#FNanchor_26_26"><span class="label">[26]</span></a> First dialogue between Hylas and Philonous, <i>Works</i>
+(Fraser's edition 1901). I. p. 384.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_27_27" id="Footnote_27_27"></a><a href="#FNanchor_27_27"><span class="label">[27]</span></a> This point has been well urged by the American
+realists.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_28_28" id="Footnote_28_28"></a><a href="#FNanchor_28_28"><span class="label">[28]</span></a> Cf. T.P. Nunn, "Are Secondary Qualities Independent of
+Perception?" <i>Proc. Arist. Soc.</i>, 1909-1910.</p></div>
+
+
+<br />
+<br />
+<br />
+<br />
+<a name="VIII" id="VIII"></a><hr />
+<span class='pagenum'><a name="Page_145" id="Page_145">[145]</a></span><br />
+
+<h3>VIII<span class="totoc"><a href="#toc">ToC</a></span></h3>
+
+<h4>THE RELATION OF SENSE-DATA TO PHYSICS</h4>
+<br />
+
+<h4>I. THE PROBLEM STATED</h4>
+
+<p>Physics is said to be an empirical science, based upon observation and
+experiment.</p>
+
+<p>It is supposed to be verifiable, i.e. capable of calculating
+beforehand results subsequently confirmed by observation and
+experiment.</p>
+
+<p>What can we learn by observation and experiment?</p>
+
+<p>Nothing, so far as physics is concerned, except immediate data of
+sense: certain patches of colour, sounds, tastes, smells, etc., with
+certain spatio-temporal relations.</p>
+
+<p>The supposed contents of the physical world are <i>prima facie</i> very
+different from these: molecules have no colour, atoms make no noise,
+electrons have no taste, and corpuscles do not even smell.</p>
+
+<p>If such objects are to be verified, it must be solely through their
+relation to sense-data: they must have some kind of correlation with
+sense-data, and must be verifiable through their correlation <i>alone</i>.</p>
+
+<p>But how is the correlation itself ascertained? A correlation can only
+be ascertained empirically by the correlated objects being constantly
+<i>found</i> together. But in our case, only one term of the correlation,
+namely, the sensible term, is ever <i>found</i>: the other term seems
+<span class='pagenum'><a name="Page_146" id="Page_146">[146]</a></span>essentially incapable of being found. Therefore, it would seem, the
+correlation with objects of sense, by which physics was to be
+verified, is itself utterly and for ever unverifiable.</p>
+
+<p>There are two ways of avoiding this result.</p>
+
+<p>(1) We may say that we know some principle <i>a priori</i>, without the
+need of empirical verification, e.g. that our sense-data have <i>causes</i>
+other than themselves, and that something can be known about these
+causes by inference from their effects. This way has been often
+adopted by philosophers. It may be necessary to adopt this way to some
+extent, but in so far as it is adopted physics ceases to be empirical
+or based upon experiment and observation alone. Therefore this way is
+to be avoided as much as possible.</p>
+
+<p>(2) We may succeed in actually defining the objects of physics as
+functions of sense-data. Just in so far as physics leads to
+expectations, this <i>must</i> be possible, since we can only <i>expect</i> what
+can be experienced. And in so far as the physical state of affairs is
+inferred from sense-data, it must be capable of expression as a
+function of sense-data. The problem of accomplishing this expression
+leads to much interesting logico-mathematical work.</p>
+
+<p>In physics as commonly set forth, sense-data appear as functions of
+physical objects: when such-and-such waves impinge upon the eye, we
+see such-and-such colours, and so on. But the waves are in fact
+inferred from the colours, not vice versa. Physics cannot be regarded
+as validly based upon empirical data until the waves have been
+expressed as functions of the colours and other sense-data.</p>
+
+<p>Thus if physics is to be verifiable we are faced with the following
+problem: Physics exhibits sense-data as functions of physical objects,
+but verification is only possible if physical objects can be exhibited
+as functions of <span class='pagenum'><a name="Page_147" id="Page_147">[147]</a></span>sense-data. We have therefore to solve the equations
+giving sense-data in terms of physical objects, so as to make them
+instead give physical objects in terms of sense-data.</p>
+
+<br />
+
+<h4>II. CHARACTERISTICS OF SENSE-DATA</h4>
+
+<p>When I speak of a "sense-datum," I do not mean the whole of what is
+given in sense at one time. I mean rather such a part of the whole as
+might be singled out by attention: particular patches of colour,
+particular noises, and so on. There is some difficulty in deciding
+what is to be considered <i>one</i> sense-datum: often attention causes
+divisions to appear where, so far as can be discovered, there were no
+divisions before. An observed complex fact, such as that this patch of
+red is to the left of that patch of blue, is also to be regarded as a
+datum from our present point of view: epistemologically, it does not
+differ greatly from a simple sense-datum as regards its function in
+giving knowledge. Its <i>logical</i> structure is very different, however,
+from that of sense: <i>sense</i> gives acquaintance with particulars, and
+is thus a two-term relation in which the object can be <i>named</i> but not
+<i>asserted</i>, and is inherently incapable of truth or falsehood, whereas
+the observation of a complex fact, which may be suitably called
+perception, is not a two-term relation, but involves the propositional
+form on the object-side, and gives knowledge of a truth, not mere
+acquaintance with a particular. This logical difference, important as
+it is, is not very relevant to our present problem; and it will be
+convenient to regard data of perception as included among sense-data
+for the purposes of this paper. It is to be observed that the
+particulars which are constituents of a datum of perception are always
+sense-data in the strict sense.</p>
+
+<p><span class='pagenum'><a name="Page_148" id="Page_148">[148]</a></span>Concerning sense-data, we know that they are there while they are
+data, and this is the epistemological basis of all our knowledge of
+external particulars. (The meaning of the word "external" of course
+raises problems which will concern us later.) We do not know, except
+by means of more or less precarious inferences, whether the objects
+which are at one time sense-data continue to exist at times when they
+are not data. Sense-data at the times when they are data are all that
+we directly and primitively know of the external world; hence in
+epistemology the fact that they are <i>data</i> is all-important. But the
+fact that they are all that we directly know gives, of course, no
+presumption that they are all that there is. If we could construct an
+impersonal metaphysic, independent of the accidents of our knowledge
+and ignorance, the privileged position of the actual data would
+probably disappear, and they would probably appear as a rather
+haphazard selection from a mass of objects more or less like them. In
+saying this, I assume only that it is probable that there are
+particulars with which we are not acquainted. Thus the special
+importance of sense-data is in relation to epistemology, not to
+metaphysics. In this respect, physics is to be reckoned as
+metaphysics: it is impersonal, and nominally pays no special attention
+to sense-data. It is only when we ask how physics can be <i>known</i> that
+the importance of sense-data re-emerges.</p>
+
+<br />
+
+<h4>III. SENSIBILIA</h4>
+
+<p>I shall give the name <i>sensibilia</i> to those objects which have the
+same metaphysical and physical status as sense-data, without
+necessarily being data to any mind. Thus the relation of a <i>sensibile</i>
+to a sense-datum is like that of a man to a husband: a man becomes a
+husband by <span class='pagenum'><a name="Page_149" id="Page_149">[149]</a></span>entering into the relation of marriage, and similarly a
+<i>sensibile</i> becomes a sense-datum by entering into the relation of
+acquaintance. It is important to have both terms; for we wish to
+discuss whether an object which is at one time a sense-datum can still
+exist at a time when it is not a sense-datum. We cannot ask "Can
+sense-data exist without being given?" for that is like asking "Can
+husbands exist without being married?" We must ask "Can <i>sensibilia</i>
+exist without being given?" and also "Can a particular <i>sensibile</i> be
+at one time a sense-datum, and at another not?" Unless we have the
+word <i>sensibile</i> as well as the word "sense-datum," such questions are
+apt to entangle us in trivial logical puzzles.</p>
+
+<p>It will be seen that all sense-data are <i>sensibilia</i>. It is a
+metaphysical question whether all <i>sensibilia</i> are sense-data, and an
+epistemological question whether there exist means of inferring
+<i>sensibilia</i> which are not data from those that are.</p>
+
+<p>A few preliminary remarks, to be amplified as we proceed, will serve
+to elucidate the use which I propose to make of <i>sensibilia</i>.</p>
+
+<p>I regard sense-data as not mental, and as being, in fact, part of the
+actual subject-matter of physics. There are arguments, shortly to be
+examined, for their subjectivity, but these arguments seem to me only
+to prove <i>physiological</i> subjectivity, i.e. causal dependence on the
+sense-organs, nerves, and brain. The appearance which a thing presents
+to us is causally dependent upon these, in exactly the same way as it
+is dependent upon intervening fog or smoke or coloured glass. Both
+dependences are contained in the statement that the appearance which a
+piece of matter presents when viewed from a given place is a function
+not only of the piece of matter, but also of the intervening medium.
+(The terms used in <span class='pagenum'><a name="Page_150" id="Page_150">[150]</a></span>this statement&mdash;"matter," "view from a given
+place," "appearance," "intervening medium"&mdash;will all be defined in the
+course of the present paper.) We have not the means of ascertaining
+how things appear from places not surrounded by brain and nerves and
+sense-organs, because we cannot leave the body; but continuity makes
+it not unreasonable to suppose that they present <i>some</i> appearance at
+such places. Any such appearance would be included among <i>sensibilia</i>.
+If&mdash;<i>per impossibile</i>&mdash;there were a complete human body with no mind
+inside it, all those <i>sensibilia</i> would exist, in relation to that
+body, which would be sense-data if there were a mind in the body. What
+the mind adds to <i>sensibilia</i>, in fact, is <i>merely</i> awareness:
+everything else is physical or physiological.</p>
+
+<br />
+
+<h4>IV. SENSE-DATA ARE PHYSICAL</h4>
+
+<p>Before discussing this question it will be well to define the sense in
+which the terms "mental" and "physical" are to be used. The word
+"physical," in all preliminary discussions, is to be understood as
+meaning "what is dealt with by physics." Physics, it is plain, tells
+us something about some of the constituents of the actual world; what
+these constituents are may be doubtful, but it is they that are to be
+called physical, whatever their nature may prove to be.</p>
+
+<p>The definition of the term "mental" is more difficult, and can only be
+satisfactorily given after many difficult controversies have been
+discussed and decided. For present purposes therefore I must content
+myself with assuming a dogmatic answer to these controversies. I shall
+call a particular "mental" when it is aware of something, and I shall
+call a fact "mental" when it contains a mental particular as a
+constituent.</p>
+
+<p><span class='pagenum'><a name="Page_151" id="Page_151">[151]</a></span>It will be seen that the mental and the physical are not necessarily
+mutually exclusive, although I know of no reason to suppose that they
+overlap.</p>
+
+<p>The doubt as to the correctness of our definition of the "mental" is
+of little importance in our present discussion. For what I am
+concerned to maintain is that sense-data are physical, and this being
+granted it is a matter of indifference in our present inquiry whether
+or not they are also mental. Although I do not hold, with Mach and
+James and the "new realists," that the difference between the mental
+and the physical is <i>merely</i> one of arrangement, yet what I have to
+say in the present paper is compatible with their doctrine and might
+have been reached from their standpoint.</p>
+
+<p>In discussions on sense-data, two questions are commonly confused,
+namely:</p>
+
+<p>(1) Do sensible objects persist when we are not sensible of them? in
+other words, do <i>sensibilia</i> which are data at a certain time
+sometimes continue to exist at times when they are not data? And (2)
+are sense-data mental or physical?</p>
+
+<p>I propose to assert that sense-data are physical, while yet
+maintaining that they probably never persist unchanged after ceasing
+to be data. The view that they do not persist is often thought, quite
+erroneously in my opinion, to imply that they are mental; and this
+has, I believe, been a potent source of confusion in regard to our
+present problem. If there were, as some have held, a <i>logical
+impossibility</i> in sense-data persisting after ceasing to be data, that
+certainly would tend to show that they were mental; but if, as I
+contend, their non-persistence is merely a probable inference from
+empirically ascertained causal laws, then it carries no such
+implication with it, and we are quite free to treat them as part of
+the subject-matter of physics.</p>
+
+<p><span class='pagenum'><a name="Page_152" id="Page_152">[152]</a></span>Logically a sense-datum is an object, a particular of which the
+subject is aware. It does not contain the subject as a part, as for
+example beliefs and volitions do. The existence of the sense-datum is
+therefore not logically dependent upon that of the subject; for the
+only way, so far as I know, in which the existence of <i>A</i> can be
+<i>logically</i> dependent upon the existence of <i>B</i> is when <i>B</i> is part of
+<i>A</i>. There is therefore no <i>a priori</i> reason why a particular which is
+a sense-datum should not persist after it has ceased to be a datum,
+nor why other similar particulars should not exist without ever being
+data. The view that sense-data are mental is derived, no doubt, in
+part from their physiological subjectivity, but in part also from a
+failure to distinguish between sense-data and "sensations." By a
+sensation I mean the fact consisting in the subject's awareness of the
+sense-datum. Thus a sensation is a complex of which the subject is a
+constituent and which therefore is mental. The sense-datum, on the
+other hand, stands over against the subject as that external object of
+which in sensation the subject is aware. It is true that the
+sense-datum is in many cases in the subject's body, but the subject's
+body is as distinct from the subject as tables and chairs are, and is
+in fact merely a part of the material world. So soon, therefore, as
+sense-data are clearly distinguished from sensations, and as their
+subjectivity is recognised to be physiological not psychical, the
+chief obstacles in the way of regarding them as physical are removed.</p>
+
+<br />
+
+<h4>V. "SENSIBILIA" AND "THINGS"</h4>
+
+<p>But if "sensibilia" are to be recognised as the ultimate constituents
+of the physical world, a long and difficult journey is to be performed
+before we can arrive either at <span class='pagenum'><a name="Page_153" id="Page_153">[153]</a></span>the "thing" of common sense or at the
+"matter" of physics. The supposed impossibility of combining the
+different sense-data which are regarded as appearances of the same
+"thing" to different people has made it seem as though these
+"sensibilia" must be regarded as mere subjective phantasms. A given
+table will present to one man a rectangular appearance, while to
+another it appears to have two acute angles and two obtuse angles; to
+one man it appears brown, while to another, towards whom it reflects
+the light, it appears white and shiny. It is said, not wholly without
+plausibility, that these different shapes and different colours cannot
+co-exist simultaneously in the same place, and cannot therefore both
+be constituents of the physical world. This argument I must confess
+appeared to me until recently to be irrefutable. The contrary opinion
+has, however, been ably maintained by Dr. T.P. Nunn in an article
+entitled: "Are Secondary Qualities Independent of Perception?"<a name="FNanchor_29_29" id="FNanchor_29_29"></a><a href="#Footnote_29_29" class="fnanchor">[29]</a> The
+supposed impossibility derives its apparent force from the phrase:
+"<i>in the same place</i>," and it is precisely in this phrase that its
+weakness lies. The conception of space is too often treated in
+philosophy&mdash;even by those who on reflection would not defend such
+treatment&mdash;as though it were as given, simple, and unambiguous as
+Kant, in his psychological innocence, supposed. It is the unperceived
+ambiguity of the word "place" which, as we shall shortly see, has
+caused the difficulties to realists and given an undeserved advantage
+to their opponents. Two "places" of different kinds are involved in
+every sense-datum, namely the place <i>at</i> which it appears and the
+place <i>from</i> which it appears. These belong to different spaces,
+although, as we shall see, it is possible, with certain limitations,
+to establish a correlation between them. <span class='pagenum'><a name="Page_154" id="Page_154">[154]</a></span>What we call the different
+appearances of the same thing to different observers are each in a
+space private to the observer concerned. No place in the private world
+of one observer is identical with a place in the private world of
+another observer. There is therefore no question of combining the
+different appearances in the one place; and the fact that they cannot
+all exist in one place affords accordingly no ground whatever for
+questioning their physical reality. The "thing" of common sense may in
+fact be identified with the whole class of its appearances&mdash;where,
+however, we must include among appearances not only those which are
+actual sense-data, but also those "sensibilia," if any, which, on
+grounds of continuity and resemblance, are to be regarded as belonging
+to the same system of appearances, although there happen to be no
+observers to whom they are data.</p>
+
+<p>An example may make this clearer. Suppose there are a number of people
+in a room, all seeing, as they say, the same tables and chairs, walls
+and pictures. No two of these people have exactly the same sense-data,
+yet there is sufficient similarity among their data to enable them to
+group together certain of these data as appearances of one "thing" to
+the several spectators, and others as appearances of another "thing."
+Besides the appearances which a given thing in the room presents to
+the actual spectators, there are, we may suppose, other appearances
+which it would present to other possible spectators. If a man were to
+sit down between two others, the appearance which the room would
+present to him would be intermediate between the appearances which it
+presents to the two others: and although this appearance would not
+exist as it is without the sense organs, nerves and brain, of the
+newly arrived spectator, still it is not unnatural to suppose that,
+from the position <span class='pagenum'><a name="Page_155" id="Page_155">[155]</a></span>which he now occupies, <i>some</i> appearance of the
+room existed before his arrival. This supposition, however, need
+merely be noticed and not insisted upon.</p>
+
+<p>Since the "thing" cannot, without indefensible partiality, be
+identified with any single one of its appearances, it came to be
+thought of as something distinct from all of them and underlying them.
+But by the principle of Occam's razor, if the class of appearances
+will fulfil the purposes for the sake of which the thing was invented
+by the prehistoric metaphysicians to whom common sense is due, economy
+demands that we should identify the thing with the class of its
+appearances. It is not necessary to <i>deny</i> a substance or substratum
+underlying these appearances; it is merely expedient to abstain from
+asserting this unnecessary entity. Our procedure here is precisely
+analogous to that which has swept away from the philosophy of
+mathematics the useless menagerie of metaphysical monsters with which
+it used to be infested.</p>
+
+<br />
+
+<h4>VI. CONSTRUCTIONS VERSUS INFERENCES</h4>
+
+<p>Before proceeding to analyse and explain the ambiguities of the word
+"place," a few general remarks on method are desirable. The supreme
+maxim in scientific philosophising is this:</p>
+
+<div class="block"><p><i>Wherever possible, logical constructions are to be substituted
+for inferred entities.</i></p></div>
+
+<p>Some examples of the substitution of construction for inference in the
+realm of mathematical philosophy may serve to elucidate the uses of
+this maxim. Take first the case of irrationals. In old days,
+irrationals were inferred as the supposed limits of series of
+rationals which had no rational limit; but the objection to this
+procedure was <span class='pagenum'><a name="Page_156" id="Page_156">[156]</a></span>that it left the existence of irrationals merely
+optative, and for this reason the stricter methods of the present day
+no longer tolerate such a definition. We now define an irrational
+number as a certain class of ratios, thus constructing it logically by
+means of ratios, instead of arriving at it by a doubtful inference
+from them. Take again the case of cardinal numbers. Two equally
+numerous collections appear to have something in common: this
+something is supposed to be their cardinal number. But so long as the
+cardinal number is inferred from the collections, not constructed in
+terms of them, its existence must remain in doubt, unless in virtue of
+a metaphysical postulate <i>ad hoc</i>. By defining the cardinal number of
+a given collection as the class of all equally numerous collections,
+we avoid the necessity of this metaphysical postulate, and thereby
+remove a needless element of doubt from the philosophy of arithmetic.
+A similar method, as I have shown elsewhere, can be applied to classes
+themselves, which need not be supposed to have any metaphysical
+reality, but can be regarded as symbolically constructed fictions.</p>
+
+<p>The method by which the construction proceeds is closely analogous in
+these and all similar cases. Given a set of propositions nominally
+dealing with the supposed inferred entities, we observe the properties
+which are required of the supposed entities in order to make these
+propositions true. By dint of a little logical ingenuity, we then
+construct some logical function of less hypothetical entities which
+has the requisite properties. This constructed function we substitute
+for the supposed inferred entities, and thereby obtain a new and less
+doubtful interpretation of the body of propositions in question. This
+method, so fruitful in the philosophy of mathematics, will be found
+equally applicable in the philosophy of <span class='pagenum'><a name="Page_157" id="Page_157">[157]</a></span>physics, where, I do not
+doubt, it would have been applied long ago but for the fact that all
+who have studied this subject hitherto have been completely ignorant
+of mathematical logic. I myself cannot claim originality in the
+application of this method to physics, since I owe the suggestion and
+the stimulus for its application entirely to my friend and
+collaborator Dr. Whitehead, who is engaged in applying it to the more
+mathematical portions of the region intermediate between sense-data
+and the points, instants and particles of physics.</p>
+
+<p>A complete application of the method which substitutes constructions
+for inferences would exhibit matter wholly in terms of sense-data, and
+even, we may add, of the sense-data of a single person, since the
+sense-data of others cannot be known without some element of
+inference. This, however, must remain for the present an ideal, to be
+approached as nearly as possible, but to be reached, if at all, only
+after a long preliminary labour of which as yet we can only see the
+very beginning. The inferences which are unavoidable can, however, be
+subjected to certain guiding principles. In the first place they
+should always be made perfectly explicit, and should be formulated in
+the most general manner possible. In the second place the inferred
+entities should, whenever this can be done, be similar to those whose
+existence is given, rather than, like the Kantian <i>Ding an sich</i>,
+something wholly remote from the data which nominally support the
+inference. The inferred entities which I shall allow myself are of two
+kinds: (<i>a</i>) the sense-data of other people, in favour of which there
+is the evidence of testimony, resting ultimately upon the analogical
+argument in favour of minds other than my own; (<i>b</i>) the "sensibilia"
+which would appear from places where there happen to be no minds, and
+which I suppose to be real although they are no one's <span class='pagenum'><a name="Page_158" id="Page_158">[158]</a></span>data. Of these
+two classes of inferred entities, the first will probably be allowed
+to pass unchallenged. It would give me the greatest satisfaction to be
+able to dispense with it, and thus establish physics upon a
+solipsistic basis; but those&mdash;and I fear they are the majority&mdash;in
+whom the human affections are stronger than the desire for logical
+economy, will, no doubt, not share my desire to render solipsism
+scientifically satisfactory. The second class of inferred entities
+raises much more serious questions. It may be thought monstrous to
+maintain that a thing can present any appearance at all in a place
+where no sense organs and nervous structure exist through which it
+could appear. I do not myself feel the monstrosity; nevertheless I
+should regard these supposed appearances only in the light of a
+hypothetical scaffolding, to be used while the edifice of physics is
+being raised, though possibly capable of being removed as soon as the
+edifice is completed. These "sensibilia" which are not data to anyone
+are therefore to be taken rather as an illustrative hypothesis and as
+an aid in preliminary statement than as a dogmatic part of the
+philosophy of physics in its final form.</p>
+
+<br />
+
+<h4>VII. PRIVATE SPACE AND THE SPACE OF PERSPECTIVES</h4>
+
+<p>We have now to explain the ambiguity in the word "place," and how it
+comes that two places of different sorts are associated with every
+sense-datum, namely the place <i>at</i> which it is and the place <i>from</i>
+which it is perceived. The theory to be advocated is closely analogous
+to Leibniz's monadology, from which it differs chiefly in being less
+smooth and tidy.</p>
+
+<p>The first fact to notice is that, so far as can be discovered, no
+sensibile is ever a datum to two people at <span class='pagenum'><a name="Page_159" id="Page_159">[159]</a></span>once. The things seen by
+two different people are often closely similar, so similar that the
+same <i>words</i> can be used to denote them, without which communication
+with others concerning sensible objects would be impossible. But, in
+spite of this similarity, it would seem that some difference always
+arises from difference in the point of view. Thus each person, so far
+as his sense-data are concerned, lives in a private world. This
+private world contains its own space, or rather spaces, for it would
+seem that only experience teaches us to correlate the space of sight
+with the space of touch and with the various other spaces of other
+senses. This multiplicity of private spaces, however, though
+interesting to the psychologist, is of no great importance in regard
+to our present problem, since a merely solipsistic experience enables
+us to correlate them into the one private space which embraces all our
+own sense-data. The place <i>at</i> which a sense-datum is, is a place in
+private space. This place therefore is different from any place in the
+private space of another percipient. For if we assume, as logical
+economy demands, that all position is relative, a place is only
+definable by the things in or around it, and therefore the same place
+cannot occur in two private worlds which have no common constituent.
+The question, therefore, of combining what we call different
+appearances of the same thing in the same place does not arise, and
+the fact that a given object appears to different spectators to have
+different shapes and colours affords no argument against the physical
+reality of all these shapes and colours.</p>
+
+<p>In addition to the private spaces belonging to the private worlds of
+different percipients, there is, however, another space, in which one
+whole private world counts as a point, or at least as a spatial unit.
+This might be <span class='pagenum'><a name="Page_160" id="Page_160">[160]</a></span>described as the space of points of view, since each
+private world may be regarded as the appearance which the universe
+presents from a certain point of view. I prefer, however, to speak of
+it as the space of <i>perspectives</i>, in order to obviate the suggestion
+that a private world is only real when someone views it. And for the
+same reason, when I wish to speak of a private world without assuming
+a percipient, I shall call it a "perspective."</p>
+
+<p>We have now to explain how the different perspectives are ordered in
+one space. This is effected by means of the correlated "sensibilia"
+which are regarded as the appearances, in different perspectives, of
+one and the same thing. By moving, and by testimony, we discover that
+two different perspectives, though they cannot both contain the same
+"sensibilia," may nevertheless contain very similar ones; and the
+spatial order of a certain group of "sensibilia" in a private space of
+one perspective is found to be identical with, or very similar to, the
+spatial order of the correlated "sensibilia" in the private space of
+another perspective. In this way one "sensibile" in one perspective is
+correlated with one "sensibile" in another. Such correlated
+"sensibilia" will be called "appearances of one thing." In Leibniz's
+monadology, since each monad mirrored the whole universe, there was in
+each perspective a "sensibile" which was an appearance of each thing.
+In our system of perspectives, we make no such assumption of
+completeness. A given thing will have appearances in some
+perspectives, but presumably not in certain others. The "thing" being
+defined as the class of its appearances, if &kappa; is the
+class of perspectives in which a certain thing &theta; appears,
+then &theta; is a member of the multiplicative class of &kappa;, &kappa;
+being a class of mutually exclusive classes of
+"sensibilia." And <span class='pagenum'><a name="Page_161" id="Page_161">[161]</a></span>similarly a perspective is a member of the
+multiplicative class of the things which appear in it.</p>
+
+<p>The arrangement of perspectives in a space is effected by means of the
+differences between the appearances of a given thing in the various
+perspectives. Suppose, say, that a certain penny appears in a number
+of different perspectives; in some it looks larger and in some
+smaller, in some it looks circular, in others it presents the
+appearance of an ellipse of varying eccentricity. We may collect
+together all those perspectives in which the appearance of the penny
+is circular. These we will place on one straight line, ordering them
+in a series by the variations in the apparent size of the penny. Those
+perspectives in which the penny appears as a straight line of a
+certain thickness will similarly be placed upon a plane (though in
+this case there will be many different perspectives in which the penny
+is of the same size; when one arrangement is completed these will form
+a circle concentric with the penny), and ordered as before by the
+apparent size of the penny. By such means, all those perspectives in
+which the penny presents a visual appearance can be arranged in a
+three-dimensional spatial order. Experience shows that the same
+spatial order of perspectives would have resulted if, instead of the
+penny, we had chosen any other thing which appeared in all the
+perspectives in question, or any other method of utilising the
+differences between the appearances of the same things in different
+perspectives. It is this empirical fact which has made it possible to
+construct the one all-embracing space of physics.</p>
+
+<p>The space whose construction has just been explained, and whose
+elements are whole perspectives, will be called "perspective-space."</p>
+
+<span class='pagenum'><a name="Page_162" id="Page_162">[162]</a></span><br />
+
+<h4>VIII. THE PLACING OF "THINGS" AND "SENSIBILIA" IN PERSPECTIVE SPACE</h4>
+
+<p>The world which we have so far constructed is a world of six
+dimensions, since it is a three-dimensional series of perspectives,
+each of which is itself three-dimensional. We have now to explain the
+correlation between the perspective space and the various private
+spaces contained within the various perspectives severally. It is by
+means of this correlation that the one three-dimensional space of
+physics is constructed; and it is because of the unconscious
+performance of this correlation that the distinction between
+perspective space and the percipient's private space has been blurred,
+with disastrous results for the philosophy of physics. Let us revert
+to our penny: the perspectives in which the penny appears larger are
+regarded as being nearer to the penny than those in which it appears
+smaller, but as far as experience goes the apparent size of the penny
+will not grow beyond a certain limit, namely, that where (as we say)
+the penny is so near the eye that if it were any nearer it could not
+be seen. By touch we may prolong the series until the penny touches
+the eye, but no further. If we have been travelling along a line of
+perspectives in the previously defined sense, we may, however, by
+imagining the penny removed, prolong the line of perspectives by
+means, say, of another penny; and the same may be done with any other
+line of perspectives defined by means of the penny. All these lines
+meet in a certain place, that is, in a certain perspective. This
+perspective will be defined as "the place where the penny is."</p>
+
+<p>It is now evident in what sense two places in constructed physical
+space are associated with a given "sensibile." There is first the
+place which is the <span class='pagenum'><a name="Page_163" id="Page_163">[163]</a></span>perspective of which the "sensibile" is a member.
+This is the place <i>from</i> which the "sensibile" appears. Secondly there
+is the place where the thing is of which the "sensibile" is a member,
+in other words an appearance; this is the place <i>at</i> which the
+"sensibile" appears. The "sensibile" which is a member of one
+perspective is correlated with another perspective, namely, that which
+is the place where the thing is of which the "sensibile" is an
+appearance. To the psychologist the "place from which" is the more
+interesting, and the "sensibile" accordingly appears to him subjective
+and where the percipient is. To the physicist the "place at which" is
+the more interesting, and the "sensibile" accordingly appears to him
+physical and external. The causes, limits and partial justification of
+each of these two apparently incompatible views are evident from the
+above duplicity of places associated with a given "sensibile."</p>
+
+<p>We have seen that we can assign to a physical thing a place in the
+perspective space. In this way different parts of our body acquire
+positions in perspective space, and therefore there is a meaning
+(whether true or false need not much concern us) in saying that the
+perspective to which our sense-data belong is inside our head. Since
+our mind is correlated with the perspective to which our sense-data
+belong, we may regard this perspective as being the position of our
+mind in perspective space. If, therefore, this perspective is, in the
+above defined sense, inside our head, there is a good meaning for the
+statement that the mind is in the head. We can now say of the various
+appearances of a given thing that some of them are nearer to the thing
+than others; those are nearer which belong to perspectives that are
+nearer to "the place where the thing is." We can thus find a meaning,
+true or false, for the statement that more is to <span class='pagenum'><a name="Page_164" id="Page_164">[164]</a></span>be learnt about a
+thing by examining it close to than by viewing it from a distance. We
+can also find a meaning for the phrase "the things which intervene
+between the subject and a thing of which an appearance is a datum to
+him." One reason often alleged for the subjectivity of sense-data is
+that the appearance of a thing may change when we find it hard to
+suppose that the thing itself has changed&mdash;for example, when the
+change is due to our shutting our eyes, or to our screwing them up so
+as to make the thing look double. If the thing is defined as the class
+of its appearances (which is the definition adopted above), there is
+of course necessarily <i>some</i> change in the thing whenever any one of
+its appearances changes. Nevertheless there is a very important
+distinction between two different ways in which the appearances may
+change. If after looking at a thing I shut my eyes, the appearance of
+my eyes changes in every perspective in which there is such an
+appearance, whereas most of the appearances of the thing will remain
+unchanged. We may say, as a matter of definition, that a thing changes
+when, however near to the thing an appearance of it may be, there are
+changes in appearances as near as, or still nearer to, the thing. On
+the other hand we shall say that the change is in some other thing if
+all appearances of the thing which are at not more than a certain
+distance from the thing remain unchanged, while only comparatively
+distant appearances of the thing are altered. From this consideration
+we are naturally led to the consideration of <i>matter</i>, which must be
+our next topic.</p>
+
+<br />
+
+<h4>IX. THE DEFINITION OF MATTER</h4>
+
+<p>We defined the "physical thing" as the class of its appearances, but
+this can hardly be taken as a definition of matter. We want to be able
+to express the fact that <span class='pagenum'><a name="Page_165" id="Page_165">[165]</a></span>the appearance of a thing in a given
+perspective is causally affected by the matter between the thing and
+the perspective. We have found a meaning for "between a thing and a
+perspective." But we want matter to be something other than the whole
+class of appearances of a thing, in order to state the influence of
+matter on appearances.</p>
+
+<p>We commonly assume that the information we get about a thing is more
+accurate when the thing is nearer. Far off, we see it is a man; then
+we see it is Jones; then we see he is smiling. Complete accuracy would
+only be attainable as a limit: if the appearances of Jones as we
+approach him tend towards a limit, that limit may be taken to be what
+Jones really is. It is obvious that from the point of view of physics
+the appearances of a thing close to "count" more than the appearances
+far off. We may therefore set up the following tentative definition:</p>
+
+<p>The <i>matter</i> of a given thing is the limit of its appearances as their
+distance from the thing diminishes.</p>
+
+<p>It seems probable that there is something in this definition, but it
+is not quite satisfactory, because empirically there is no such limit
+to be obtained from sense-data. The definition will have to be eked
+out by constructions and definitions. But probably it suggests the
+right direction in which to look.</p>
+
+<p>We are now in a position to understand in outline the reverse journey
+from matter to sense-data which is performed by physics. The
+appearance of a thing in a given perspective is a function of the
+matter composing the thing and of the intervening matter. The
+appearance of a thing is altered by intervening smoke or mist, by blue
+spectacles or by alterations in the sense-organs or nerves of the
+percipient (which also must be reckoned as part of the intervening
+medium). The nearer we approach to <span class='pagenum'><a name="Page_166" id="Page_166">[166]</a></span>the thing, the less its appearance
+is affected by the intervening matter. As we travel further and
+further from the thing, its appearances diverge more and more from
+their initial character; and the causal laws of their divergence are
+to be stated in terms of the matter which lies between them and the
+thing. Since the appearances at very small distances are less affected
+by causes other than the thing itself, we come to think that the limit
+towards which these appearances tend as the distance diminishes is
+what the thing "really is," as opposed to what it merely seems to be.
+This, together with its necessity for the statement of causal laws,
+seems to be the source of the entirely erroneous feeling that matter
+is more "real" than sense-data.</p>
+
+<p>Consider for example the infinite divisibility of matter. In looking
+at a given thing and approaching it, one sense-datum will become
+several, and each of these will again divide. Thus <i>one</i> appearance
+may represent <i>many</i> things, and to this process there seems no end.
+Hence in the limit, when we approach indefinitely near to the thing
+there will be an indefinite number of units of matter corresponding to
+what, at a finite distance, is only one appearance. This is how
+infinite divisibility arises.</p>
+
+<p>The whole causal efficacy of a thing resides in its matter. This is in
+some sense an empirical fact, but it would be hard to state it
+precisely, because "causal efficacy" is difficult to define.</p>
+
+<p>What can be known empirically about the matter of a thing is only
+approximate, because we cannot get to know the appearances of the
+thing from very small distances, and cannot accurately infer the limit
+of these appearances. But it <i>is</i> inferred <i>approximately</i> by means of
+the appearances we can observe. It then turns out that these
+appearances can be exhibited by physics as a function of <span class='pagenum'><a name="Page_167" id="Page_167">[167]</a></span>the matter
+in our immediate neighbourhood; e.g. the visual appearance of a
+distant object is a function of the light-waves that reach the eyes.
+This leads to confusions of thought, but offers no real difficulty.</p>
+
+<p>One appearance, of a visible object for example, is not sufficient to
+determine its other simultaneous appearances, although it goes a
+certain distance towards determining them. The determination of the
+hidden structure of a thing, so far as it is possible at all, can only
+be effected by means of elaborate dynamical inferences.</p>
+
+<br />
+
+<h4>X. TIME<a name="FNanchor_30_30" id="FNanchor_30_30"></a><a href="#Footnote_30_30" class="fnanchor">[30]</a></h4>
+
+<p>It seems that the one all-embracing time is a construction, like the
+one all-embracing space. Physics itself has become conscious of this
+fact through the discussions connected with relativity.</p>
+
+<p>Between two perspectives which both belong to one person's experience,
+there will be a direct time-relation of before and after. This
+suggests a way of dividing history in the same sort of way as it is
+divided by different experiences, but without introducing experience
+or anything mental: we may define a "biography" as everything that is
+(directly) earlier or later than, or simultaneous with, a given
+"sensibile." This will give a series of perspectives, which <i>might</i>
+all form parts of one person's experience, though it is not necessary
+that all or any of them should actually do so. By this means, the
+history of the world is divided into a number of mutually exclusive
+biographies.</p>
+
+<p><span class='pagenum'><a name="Page_168" id="Page_168">[168]</a></span>We have now to correlate the times in the different biographies. The
+natural thing would be to say that the appearances of a given
+(momentary) thing in two different perspectives belonging to different
+biographies are to be taken as simultaneous; but this is not
+convenient. Suppose <i>A</i> shouts to <i>B</i>, and <i>B</i> replies as soon as he
+hears <i>A's</i> shout. Then between <i>A's</i> hearing of his own shout and his
+hearing of <i>B's</i> there is an interval; thus if we made <i>A's</i> and <i>B's</i>
+hearing of the same shout exactly simultaneous with each other, we
+should have events exactly simultaneous with a given event but not
+with each other. To obviate this, we assume a "velocity of sound."
+That is, we assume that the time when <i>B</i> hears <i>A's</i> shout is
+half-way between the time when <i>A</i> hears his own shout and the time
+when he hears <i>B's</i>. In this way the correlation is effected.</p>
+
+<p>What has been said about sound applies of course equally to light. The
+general principle is that the appearances, in different perspectives,
+which are to be grouped together as constituting what a certain thing
+is at a certain moment, are not to be all regarded as being at that
+moment. On the contrary they spread outward from the thing with
+various velocities according to the nature of the appearances. Since
+no <i>direct</i> means exist of correlating the time in one biography with
+the time in another, this temporal grouping of the appearances
+belonging to a given thing at a given moment is in part conventional.
+Its motive is partly to secure the verification of such maxims as that
+events which are exactly simultaneous with the same event are exactly
+simultaneous with one another, partly to secure convenience in the
+formulation of causal laws.</p>
+
+<span class='pagenum'><a name="Page_169" id="Page_169">[169]</a></span><br />
+
+<h4>XI. THE PERSISTENCE OF THINGS AND MATTER</h4>
+
+<p>Apart from any of the fluctuating hypotheses of physics, three main
+problems arise in connecting the world of physics with the world of
+sense, namely:</p>
+
+<div class="block">
+<p class="noin">1. the construction of a single space;<br />
+2. the construction of a single time;<br />
+3. the construction of permanent things or matter.</p>
+</div>
+
+<p>We have already considered the first and second of these problems; it
+remains to consider the third.</p>
+
+<p>We have seen how correlated appearances in different perspectives are
+combined to form one "thing" at one moment in the all-embracing time
+of physics. We have now to consider how appearances at different times
+are combined as belonging to one "thing," and how we arrive at the
+persistent "matter" of physics. The assumption of permanent substance,
+which technically underlies the procedure of physics, cannot of course
+be regarded as metaphysically legitimate: just as the one thing
+simultaneously seen by many people is a construction, so the one thing
+seen at different times by the same or different people must be a
+construction, being in fact nothing but a certain grouping of certain
+"sensibilia."</p>
+
+<p>We have seen that the momentary state of a "thing" is an assemblage of
+"sensibilia," in different perspectives, not all simultaneous in the
+one constructed time, but spreading out from "the place where the
+thing is" with velocities depending upon the nature of the
+"sensibilia." The time <i>at</i> which the "thing" is in this state is the
+lower limit of the times at which these appearances occur. We have now
+to consider what leads us to speak of another set of appearances as
+belonging to the same "thing" at a different time.</p>
+
+<p><span class='pagenum'><a name="Page_170" id="Page_170">[170]</a></span>For this purpose, we may, at least to begin with, confine ourselves
+within a single biography. If we can always say when two "sensibilia"
+in a given biography are appearances of one thing, then, since we have
+seen how to connect "sensibilia" in different biographies as
+appearances of the same momentary state of a thing, we shall have all
+that is necessary for the complete construction of the history of a
+thing.</p>
+
+<p>It is to be observed, to begin with, that the identity of a thing for
+common sense is not always correlated with the identity of matter for
+physics. A human body is one persisting thing for common sense, but
+for physics its matter is constantly changing. We may say, broadly,
+that the common-sense conception is based upon continuity in
+appearances at the ordinary distances of sense-data, while the
+physical conception is based upon the continuity of appearances at
+very small distances from the thing. It is probable that the
+common-sense conception is not capable of complete precision. Let us
+therefore concentrate our attention upon the conception of the
+persistence of matter in physics.</p>
+
+<p>The first characteristic of two appearances of the same piece of
+matter at different times is <i>continuity</i>. The two appearances must be
+connected by a series of intermediaries, which, if time and space form
+compact series, must themselves form a compact series. The colour of
+the leaves is different in autumn from what it is in summer; but we
+believe that the change occurs gradually, and that, if the colours are
+different at two given times, there are intermediate times at which
+the colours are intermediate between those at the given times.</p>
+
+<p>But there are two considerations that are important as regards
+continuity.</p>
+
+<p>First, it is largely hypothetical. We do not observe <span class='pagenum'><a name="Page_171" id="Page_171">[171]</a></span>any one thing
+continuously, and it is merely a hypothesis to assume that, while we
+are not observing it, it passes through conditions intermediate
+between those in which it is perceived. During uninterrupted
+observation, it is true, continuity is nearly verified; but even here,
+when motions are very rapid, as in the case of explosions, the
+continuity is not actually capable of direct verification. Thus we can
+only say that the sense-data are found to <i>permit</i> a hypothetical
+complement of "sensibilia" such as will preserve continuity, and that
+therefore there <i>may</i> be such a complement. Since, however, we have
+already made such use of hypothetical "sensibilia," we will let this
+point pass, and admit such "sensibilia" as are required to preserve
+continuity.</p>
+
+<p>Secondly, continuity is not a sufficient criterion of material
+identity. It is true that in many cases, such as rocks, mountains,
+tables, chairs, etc., where the appearances change slowly, continuity
+is sufficient, but in other cases, such as the parts of an
+approximately homogeneous fluid, it fails us utterly. We can travel by
+sensibly continuous gradations from any one drop of the sea at any one
+time to any other drop at any other time. We infer the motions of
+sea-water from the effects of the current, but they cannot be inferred
+from direct sensible observation together with the assumption of
+continuity.</p>
+
+<p>The characteristic required in addition to continuity is conformity
+with the laws of dynamics. Starting from what common sense regards as
+persistent things, and making only such modifications as from time to
+time seem reasonable, we arrive at assemblages of "sensibilia" which
+are found to obey certain simple laws, namely those of dynamics. By
+regarding "sensibilia" at different times as belonging to the same
+piece of matter, we are able to define <i>motion</i>, which presupposes the
+assumption <span class='pagenum'><a name="Page_172" id="Page_172">[172]</a></span>or construction of something persisting throughout the
+time of the motion. The motions which are regarded as occurring,
+during a period in which all the "sensibilia" and the times of their
+appearance are given, will be different according to the manner in
+which we combine "sensibilia" at different times as belonging to the
+same piece of matter. Thus even when the whole history of the world is
+given in every particular, the question what motions take place is
+still to a certain extent arbitrary even after the assumption of
+continuity. Experience shows that it is possible to determine motions
+in such a way as to satisfy the laws of dynamics, and that this
+determination, roughly and on the whole, is fairly in agreement with
+the common-sense opinions about persistent things. This determination,
+therefore, is adopted, and leads to a criterion by which we can
+determine, sometimes practically, sometimes only theoretically,
+whether two appearances at different times are to be regarded as
+belonging to the same piece of matter. The persistence of all matter
+throughout all time can, I imagine, be secured by definition.</p>
+
+<p>To recommend this conclusion, we must consider what it is that is
+proved by the empirical success of physics. What is proved is that its
+hypotheses, though unverifiable where they go beyond sense-data, are
+at no point in contradiction with sense-data, but, on the contrary,
+are ideally such as to render all sense-data calculable when a
+sufficient collection of "sensibilia" is given. Now physics has found
+it empirically possible to collect sense-data into series, each series
+being regarded as belonging to one "thing," and behaving, with regard
+to the laws of physics, in a way in which series not belonging to one
+thing would in general not behave. If it is to be unambiguous whether
+two appearances belong to the same <span class='pagenum'><a name="Page_173" id="Page_173">[173]</a></span>thing or not, there must be only
+one way of grouping appearances so that the resulting things obey the
+laws of physics. It would be very difficult to prove that this is the
+case, but for our present purposes we may let this point pass, and
+assume that there is only one way. Thus we may lay down the following
+definition: <i>Physical things are those series of appearances whose
+matter obeys the laws of physics</i>. That such series exist is an
+empirical fact, which constitutes the verifiability of physics.</p>
+
+<br />
+
+<h4>XII. ILLUSIONS, HALLUCINATIONS, AND DREAMS</h4>
+
+<p>It remains to ask how, in our system, we are to find a place for
+sense-data which apparently fail to have the usual connection with the
+world of physics. Such sense-data are of various kinds, requiring
+somewhat different treatment. But all are of the sort that would be
+called "unreal," and therefore, before embarking upon the discussion,
+certain logical remarks must be made upon the conceptions of reality
+and unreality.</p>
+
+<p>Mr. A. Wolf<a name="FNanchor_31_31" id="FNanchor_31_31"></a><a href="#Footnote_31_31" class="fnanchor">[31]</a> says:</p>
+
+<div class="block"><p>"The conception of mind as a system of transparent activities is,
+I think, also untenable because of its failure to account for the
+very possibility of dreams and hallucinations. It seems impossible
+to realise how a bare, transparent activity can be directed to
+what is not there, to apprehend what is not given."</p></div>
+
+<p>This statement is one which, probably, most people would endorse. But
+it is open to two objections. First it is difficult to see how an
+activity, however un-"transparent," can be directed towards a nothing:
+a term of a relation cannot be a mere nonentity. Secondly, no reason
+<span class='pagenum'><a name="Page_174" id="Page_174">[174]</a></span>is given, and I am convinced that none can be given, for the assertion
+that dream-objects are not "there" and not "given." Let us take the
+second point first.</p>
+
+<p>(1) The belief that dream-objects are not given comes, I think, from
+failure to distinguish, as regards waking life, between the
+sense-datum and the corresponding "thing." In dreams, there is no such
+corresponding "thing" as the dreamer supposes; if, therefore, the
+"thing" were given in waking life, as e.g. Meinong maintains,<a name="FNanchor_32_32" id="FNanchor_32_32"></a><a href="#Footnote_32_32" class="fnanchor">[32]</a> then
+there would be a difference in respect of givenness between dreams and
+waking life. But if, as we have maintained, what is given is never the
+thing, but merely one of the "sensibilia" which compose the thing,
+then what we apprehend in a dream is just as much given as what we
+apprehend in waking life.</p>
+
+<p>Exactly the same argument applies as to the dream-objects being
+"there." They have their position in the private space of the
+perspective of the dreamer; where they fail is in their correlation
+with other private spaces and therefore with perspective space. But in
+the only sense in which "there" can be a datum, they are "there" just
+as truly as any of the sense-data of waking life.</p>
+
+<p>(2) The conception of "illusion" or "unreality," and the correlative
+conception of "reality," are generally used in a way which embodies
+profound logical confusions. Words that go in pairs, such as "real"
+and "unreal," "existent" and "non-existent," "valid" and "invalid,"
+etc., are all derived from the one fundamental pair, "true" and
+"false." Now "true" and "false" are applicable only&mdash;except in
+derivative significations&mdash;to <i>propositions</i>. Thus wherever the above
+pairs can be significantly applied, we must be dealing either with
+propositions or with such incomplete phrases as <span class='pagenum'><a name="Page_175" id="Page_175">[175]</a></span>only acquire meaning
+when put into a context which, with them, forms a proposition. Thus
+such pairs of words can be applied to <i>descriptions</i>,<a name="FNanchor_33_33" id="FNanchor_33_33"></a><a href="#Footnote_33_33" class="fnanchor">[33]</a> but not to
+proper names: in other words, they have no application whatever to
+data, but only to entities or non-entities described in terms of data.</p>
+
+<p>Let us illustrate by the terms "existence" and "non-existence." Given
+any datum <i>x</i>, it is meaningless either to assert or to deny that <i>x</i>
+"exists." We might be tempted to say: "Of course <i>x</i> exists, for
+otherwise it could not be a datum." But such a statement is really
+meaningless, although it is significant and true to say "My present
+sense-datum exists," and it may also be true that "<i>x</i> is my present
+sense-datum." The inference from these two propositions to "<i>x</i>
+exists" is one which seems irresistible to people unaccustomed to
+logic; yet the apparent proposition inferred is not merely false, but
+strictly meaningless. To say "My present sense-datum exists" is to say
+(roughly): "There is an object of which 'my present sense-datum' is a
+description." But we cannot say: "There is an object of which '<i>x</i>' is
+a description," because '<i>x</i>' is (in the case we are supposing) a
+name, not a description. Dr. Whitehead and I have explained this point
+fully elsewhere (<i>loc. cit.</i>) with the help of symbols, without which
+it is hard to understand; I shall not therefore here repeat the
+demonstration of the above propositions, but shall proceed with their
+application to our present problem.</p>
+
+<p>The fact that "existence" is only applicable to descriptions is
+concealed by the use of what are grammatically proper names in a way
+which really transforms them into descriptions. It is, for example, a
+legitimate <span class='pagenum'><a name="Page_176" id="Page_176">[176]</a></span>question whether Homer existed; but here "Homer" means
+"the author of the Homeric poems," and is a description. Similarly we
+may ask whether God exists; but then "God" means "the Supreme Being"
+or "the <i>ens realissimum</i>" or whatever other description we may
+prefer. If "God" were a proper name, God would have to be a datum; and
+then no question could arise as to His existence. The distinction
+between existence and other predicates, which Kant obscurely felt, is
+brought to light by the theory of descriptions, and is seen to remove
+"existence" altogether from the fundamental notions of metaphysics.</p>
+
+<p>What has been said about "existence" applies equally to "reality,"
+which may, in fact, be taken as synonymous with "existence."
+Concerning the immediate objects in illusions, hallucinations, and
+dreams, it is meaningless to ask whether they "exist" or are "real."
+There they are, and that ends the matter. But we may legitimately
+inquire as to the existence or reality of "things" or other
+"sensibilia" inferred from such objects. It is the unreality of these
+"things" and other "sensibilia," together with a failure to notice
+that they are not data, which has led to the view that the objects of
+dreams are unreal.</p>
+
+<p>We may now apply these considerations in detail to the stock arguments
+against realism, though what is to be said will be mainly a repetition
+of what others have said before.</p>
+
+<p>(1) We have first the variety of normal appearances, supposed to be
+incompatible. This is the case of the different shapes and colours
+which a given thing presents to different spectators. Locke's water
+which seems both hot and cold belongs to this class of cases. Our
+system of different perspectives fully accounts for these cases, and
+shows that they afford no argument against realism.</p>
+
+<p>(2) We have cases where the correlation between <span class='pagenum'><a name="Page_177" id="Page_177">[177]</a></span>different senses is
+unusual. The bent stick in water belongs here. People say it looks
+bent but is straight: this only means that it is straight to the
+touch, though bent to sight. There is no "illusion," but only a false
+inference, if we think that the stick would feel bent to the touch.
+The stick would look just as bent in a photograph, and, as Mr.
+Gladstone used to say, "the photograph cannot lie."<a name="FNanchor_34_34" id="FNanchor_34_34"></a><a href="#Footnote_34_34" class="fnanchor">[34]</a> The case of
+seeing double also belongs here, though in this case the cause of the
+unusual correlation is physiological, and would therefore not operate
+in a photograph. It is a mistake to ask whether the "thing" is
+duplicated when we see it double. The "thing" is a whole system of
+"sensibilia," and it is only those visual "sensibilia" which are data
+to the percipient that are duplicated. The phenomenon has a purely
+physiological explanation; indeed, in view of our having two eyes, it
+is in less need of explanation than the single visual sense-datum
+which we normally obtain from the things on which we focus.</p>
+
+<p>(3) We come now to cases like dreams, which may, at the moment of
+dreaming, contain nothing to arouse suspicion, but are condemned on
+the ground of their supposed incompatibility with earlier and later
+data. Of course it often happens that dream-objects fail to behave in
+the accustomed manner: heavy objects fly, solid objects melt, babies
+turn into pigs or undergo even greater changes. But none of these
+unusual occurrences <i>need</i> happen in a dream, and it is not on account
+of such occurrences that dream-objects are called "unreal." It is
+their lack of continuity with the dreamer's past and future that makes
+him, when he wakes, condemn them; and it is their lack <span class='pagenum'><a name="Page_178" id="Page_178">[178]</a></span>of correlation
+with other private worlds that makes others condemn them. Omitting the
+latter ground, our reason for condemning them is that the "things"
+which we infer from them cannot be combined according to the laws of
+physics with the "things" inferred from waking sense-data. This might
+be used to condemn the "things" inferred from the data of dreams.
+Dream-data are no doubt appearances of "things," but not of such
+"things" as the dreamer supposes. I have no wish to combat
+psychological theories of dreams, such as those of the
+psycho-analysts. But there certainly are cases where (whatever
+psychological causes may contribute) the presence of physical causes
+also is very evident. For instance, a door banging may produce a dream
+of a naval engagement, with images of battleships and sea and smoke.
+The whole dream will be an appearance of the door banging, but owing
+to the peculiar condition of the body (especially the brain) during
+sleep, this appearance is not that expected to be produced by a door
+banging, and thus the dreamer is led to entertain false beliefs. But
+his sense-data are still physical, and are such as a completed physics
+would include and calculate.</p>
+
+<p>(4) The last class of illusions are those which cannot be discovered
+within one person's experience, except through the discovery of
+discrepancies with the experiences of others. Dreams might conceivably
+belong to this class, if they were jointed sufficiently neatly into
+waking life; but the chief instances are recurrent sensory
+hallucinations of the kind that lead to insanity. What makes the
+patient, in such cases, become what others call insane is the fact
+that, within his own experience, there is nothing to show that the
+hallucinatory sense-data do not have the usual kind of connection with
+"sensibilia" in other perspectives. Of course he may learn this
+through testimony, but he <span class='pagenum'><a name="Page_179" id="Page_179">[179]</a></span>probably finds it simpler to suppose that
+the testimony is untrue and that he is being wilfully deceived. There
+is, so far as I can see, no theoretical criterion by which the patient
+can decide, in such a case, between the two equally satisfactory
+hypotheses of his madness and of his friends' mendacity.</p>
+
+<p>From the above instances it would appear that abnormal sense-data, of
+the kind which we regard as deceptive, have intrinsically just the
+same status as any others, but differ as regards their correlations or
+causal connections with other "sensibilia" and with "things." Since
+the usual correlations and connections become part of our unreflective
+expectations, and even seem, except to the psychologist, to form part
+of our data, it comes to be thought, mistakenly, that in such cases
+the data are unreal, whereas they are merely the causes of false
+inferences. The fact that correlations and connections of unusual
+kinds occur adds to the difficulty of inferring things from sense and
+of expressing physics in terms of sense-data. But the unusualness
+would seem to be always physically or physiologically explicable, and
+therefore raises only a complication, not a philosophical objection.</p>
+
+<p>I conclude, therefore, that no valid objection exists to the view
+which regards sense-data as part of the actual substance of the
+physical world, and that, on the other hand, this view is the only one
+which accounts for the empirical verifiability of physics. In the
+present paper, I have given only a rough preliminary sketch. In
+particular, the part played by <i>time</i> in the construction of the
+physical world is, I think, more fundamental than would appear from
+the above account. I should hope that, with further elaboration, the
+part played by unperceived "sensibilia" could be indefinitely
+diminished, probably by invoking the history of a "thing" to eke out
+the inferences derivable from its momentary appearance.</p>
+
+<br />
+<hr style="width: 15%;" />
+<br />
+
+<h4>FOOTNOTES:</h4>
+
+<div class="footnote"><p class="noin"><a name="Footnote_29_29" id="Footnote_29_29"></a><a href="#FNanchor_29_29"><span class="label">[29]</span></a> <i>Proc. Arist. Soc.</i>, 1909-1910, pp. 191-218.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_30_30" id="Footnote_30_30"></a><a href="#FNanchor_30_30"><span class="label">[30]</span></a> On this subject, compare <i>A Theory of Time and Space</i>,
+by Mr. A.A. Robb (Camb. Univ. Press), which first suggested to me the
+views advocated here, though I have, for present purposes, omitted
+what is most interesting and novel in his theory. Mr. Robb has given a
+sketch of his theory in a pamphlet with the same title (Heffer and
+Sons, Cambridge, 1913).</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_31_31" id="Footnote_31_31"></a><a href="#FNanchor_31_31"><span class="label">[31]</span></a> "Natural Realism and Present Tendencies in Philosophy,"
+<i>Proc. Arist. Soc.</i>, 1908-1909, p. 165.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_32_32" id="Footnote_32_32"></a><a href="#FNanchor_32_32"><span class="label">[32]</span></a> <i>Die Erfahrungsgrundlagen unseres Wissens</i>, p. 28.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_33_33" id="Footnote_33_33"></a><a href="#FNanchor_33_33"><span class="label">[33]</span></a> Cf. <i>Principia Mathematica</i>, Vol. I, * 14, and
+Introduction, Chap. III. For the definition of <i>existence</i>, cf. * 14.
+02.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_34_34" id="Footnote_34_34"></a><a href="#FNanchor_34_34"><span class="label">[34]</span></a> Cf. Edwin B. Holt, <i>The Place of Illusory Experience in
+a Realistic World.</i> "The New Realism," p. 303, both on this point and
+as regards <i>seeing double</i>.</p></div>
+
+
+<br />
+<br />
+<br />
+<br />
+<a name="IX" id="IX"></a><hr />
+<span class='pagenum'><a name="Page_180" id="Page_180">[180]</a></span><br />
+
+<h3>IX<span class="totoc"><a href="#toc">ToC</a></span></h3>
+
+<h4>ON THE NOTION OF CAUSE</h4>
+<br />
+
+<p>In the following paper I wish, first, to maintain that the word
+"cause" is so inextricably bound up with misleading associations as to
+make its complete extrusion from the philosophical vocabulary
+desirable; secondly, to inquire what principle, if any, is employed in
+science in place of the supposed "law of causality" which philosophers
+imagine to be employed; thirdly, to exhibit certain confusions,
+especially in regard to teleology and determinism, which appear to me
+to be connected with erroneous notions as to causality.</p>
+
+<p>All philosophers, of every school, imagine that causation is one of
+the fundamental axioms or postulates of science, yet, oddly enough, in
+advanced sciences such as gravitational astronomy, the word "cause"
+never occurs. Dr. James Ward, in his <i>Naturalism and Agnosticism</i>,
+makes this a ground of complaint against physics: the business of
+those who wish to ascertain the ultimate truth about the world, he
+apparently thinks, should be the discovery of causes, yet physics
+never even seeks them. To me it seems that philosophy ought not to
+assume such legislative functions, and that the reason why physics has
+ceased to look for causes is that, in fact, there are no such things.
+The law of causality, I believe, like much that passes muster among
+philosophers, is a relic of a bygone age, surviving, like the
+monarchy, only because it is erroneously supposed to do no harm. <span class='pagenum'><a name="Page_181" id="Page_181">[181]</a></span>In
+order to find out what philosophers commonly understand by "cause," I
+consulted Baldwin's <i>Dictionary</i>, and was rewarded beyond my
+expectations, for I found the following three mutually incompatible
+definitions:&mdash;</p>
+
+<div class="block3"><p class="hang">"<span class="sc">Causality.</span> (1) The necessary connection of events in
+the time-series....</p>
+
+<p class="hang">"<span class="sc">Cause</span> (notion of). Whatever may be included in the
+thought or perception of a process as taking place in
+consequence of another process....</p>
+
+<p class="hang">"<span class="sc">Cause and Effect.</span> (1) Cause and effect ... are
+correlative terms denoting any two distinguishable things,
+phases, or aspects of reality, which are so related to each
+other that whenever the first ceases to exist the second comes
+into existence immediately after, and whenever the second comes
+into existence the first has ceased to exist immediately
+before."</p></div>
+
+<p>Let us consider these three definitions in turn. The first, obviously,
+is unintelligible without a definition of "necessary." Under this
+head, Baldwin's <i>Dictionary</i> gives the following:&mdash;</p>
+
+<div class="block3"><p class="hang">"<span class="sc">Necessary.</span> That is necessary which not only is true,
+but would be true under all circumstances. Something more than
+brute compulsion is, therefore, involved in the conception;
+there is a general law under which the thing takes place."</p></div>
+
+<p>The notion of cause is so intimately connected with that of necessity
+that it will be no digression to linger over the above definition,
+with a view to discovering, if possible, <i>some</i> meaning of which it is
+capable; for, as it stands, it is very far from having any definite
+signification.</p>
+
+<p>The first point to notice is that, if any meaning is to be given to
+the phrase "would be true under all circumstances," the subject of it
+must be a propositional <span class='pagenum'><a name="Page_182" id="Page_182">[182]</a></span>function, not a proposition.<a name="FNanchor_35_35" id="FNanchor_35_35"></a><a href="#Footnote_35_35" class="fnanchor">[35]</a> A
+proposition is simply true or false, and that ends the matter: there
+can be no question of "circumstances." "Charles I's head was cut off"
+is just as true in summer as in winter, on Sundays as on Mondays. Thus
+when it is worth saying that something "would be true under all
+circumstances," the something in question must be a propositional
+function, i.e. an expression containing a variable, and becoming a
+proposition when a value is assigned to the variable; the varying
+"circumstances" alluded to are then the different values of which the
+variable is capable. Thus if "necessary" means "what is true under all
+circumstances," then "if <i>x</i> is a man, <i>x</i> is mortal" is necessary,
+because it is true for any possible value of <i>x</i>. Thus we should be
+led to the following definition:&mdash;</p>
+
+<div class="block3"><p class="hang">"<span class="sc">Necessary</span> is a predicate of a propositional function,
+meaning that it is true for all possible values of its
+argument or arguments."</p></div>
+
+<p>Unfortunately, however, the definition in Baldwin's <i>Dictionary</i> says
+that what is necessary is not only "true under all circumstances" but
+is also "true." Now these two are incompatible. Only propositions can
+be "true," and only propositional functions can be "true under all
+circumstances." Hence the definition as it stands is nonsense. What is
+meant seems to be this: "A proposition is necessary when it is a value
+of a propositional function which is true under all circumstances,
+i.e. for all values of its argument or arguments." But if we adopt
+this definition, the same proposition will be necessary or contingent
+according as we choose one or other of its <span class='pagenum'><a name="Page_183" id="Page_183">[183]</a></span>terms as the argument to
+our propositional function. For example, "if Socrates is a man,
+Socrates is mortal," is necessary if Socrates is chosen as argument,
+but not if <i>man</i> or <i>mortal</i> is chosen. Again, "if Socrates is a man,
+Plato is mortal," will be necessary if either Socrates or <i>man</i> is
+chosen as argument, but not if Plato or <i>mortal</i> is chosen. However,
+this difficulty can be overcome by specifying the constituent which is
+to be regarded as argument, and we thus arrive at the following
+definition:</p>
+
+<p>"A proposition is <i>necessary</i> with respect to a given constituent if
+it remains true when that constituent is altered in any way compatible
+with the proposition remaining significant."</p>
+
+<p>We may now apply this definition to the definition of causality quoted
+above. It is obvious that the argument must be the time at which the
+earlier event occurs. Thus an instance of causality will be such as:
+"If the event <i>e</i><sub>1</sub> occurs at the time <i>t</i><sub>1</sub>, it will be followed by
+the event <i>e</i><sub>2</sub>." This proposition is intended to be necessary with
+respect to <i>t</i><sub>1</sub>, i.e. to remain true however <i>t</i><sub>1</sub> may be varied.
+Causality, as a universal law, will then be the following: "Given any
+event <i>e</i><sub>1</sub>, there is an event <i>e</i><sub>2</sub> such that, whenever <i>e</i><sub>1</sub> occurs,
+<i>e</i><sub>2</sub> occurs later." But before this can be considered precise, we
+must specify how much later <i>e</i><sub>2</sub> is to occur. Thus the principle
+becomes:&mdash;</p>
+
+<p>"Given any event <i>e</i><sub>1</sub>, there is an event <i>e</i><sub>2</sub> and a time-interval
+&tau; such that, whenever <i>e</i><sub>1</sub> occurs, <i>e</i><sub>2</sub> follows after an
+interval &tau;."</p>
+
+<p>I am not concerned as yet to consider whether this law is true or
+false. For the present, I am merely concerned to discover what the law
+of causality is supposed to be. I pass, therefore, to the other
+definitions quoted above.</p>
+
+<p><span class='pagenum'><a name="Page_184" id="Page_184">[184]</a></span>The second definition need not detain us long, for two reasons. First,
+because it is psychological: not the "thought or perception" of a
+process, but the process itself, must be what concerns us in
+considering causality. Secondly, because it is circular: in speaking
+of a process as "taking place in consequence of" another process, it
+introduces the very notion of cause which was to be defined.</p>
+
+<p>The third definition is by far the most precise; indeed as regards
+clearness it leaves nothing to be desired. But a great difficulty is
+caused by the temporal contiguity of cause and effect which the
+definition asserts. No two instants are contiguous, since the
+time-series is compact; hence either the cause or the effect or both
+must, if the definition is correct, endure for a finite time; indeed,
+by the wording of the definition it is plain that both are assumed to
+endure for a finite time. But then we are faced with a dilemma: if the
+cause is a process involving change within itself, we shall require
+(if causality is universal) causal relations between its earlier and
+later parts; moreover, it would seem that only the later parts can be
+relevant to the effect, since the earlier parts are not contiguous to
+the effect, and therefore (by the definition) cannot influence the
+effect. Thus we shall be led to diminish the duration of the cause
+without limit, and however much we may diminish it, there will still
+remain an earlier part which might be altered without altering the
+effect, so that the true cause, as defined, will not have been
+reached, for it will be observed that the definition excludes
+plurality of causes. If, on the other hand, the cause is purely
+static, involving no change within itself, then, in the first place,
+no such cause is to be found in nature, and in the second place, it
+seems strange&mdash;too strange to be accepted, in spite of bare <span class='pagenum'><a name="Page_185" id="Page_185">[185]</a></span>logical
+possibility&mdash;that the cause, after existing placidly for some time,
+should suddenly explode into the effect, when it might just as well
+have done so at any earlier time, or have gone on unchanged without
+producing its effect. This dilemma, therefore, is fatal to the view
+that cause and effect can be contiguous in time; if there are causes
+and effects, they must be separated by a finite time-interval &tau;,
+as was assumed in the above interpretation of the first
+definition.</p>
+
+<p>What is essentially the same statement of the law of causality as the
+one elicited above from the first of Baldwin's definitions is given by
+other philosophers. Thus John Stuart Mill says:&mdash;</p>
+
+<p>"The Law of Causation, the recognition of which is the main pillar of
+inductive science, is but the familiar truth, that invariability of
+succession is found by observation to obtain between every fact in
+nature and some other fact which has preceded it."<a name="FNanchor_36_36" id="FNanchor_36_36"></a><a href="#Footnote_36_36" class="fnanchor">[36]</a></p>
+
+<p>And Bergson, who has rightly perceived that the law as stated by
+philosophers is worthless, nevertheless continues to suppose that it
+is used in science. Thus he says:&mdash;</p>
+
+<p>"Now, it is argued, this law [the law of causality] means that every
+phenomenon is determined by its conditions, or, in other words, that
+the same causes produce the same effects."<a name="FNanchor_37_37" id="FNanchor_37_37"></a><a href="#Footnote_37_37" class="fnanchor">[37]</a></p>
+
+<p>And again:&mdash;</p>
+
+<p>"We perceive physical phenomena, and these phenomena obey laws. This
+means: (1) That phenomena <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i>, previously perceived,
+can occur again in the same shape; (2) that a certain phenomenon P,
+which <span class='pagenum'><a name="Page_186" id="Page_186">[186]</a></span>appeared after the conditions <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i>, and after
+these conditions only, will not fail to recur as soon as the same
+conditions are again present."<a name="FNanchor_38_38" id="FNanchor_38_38"></a><a href="#Footnote_38_38" class="fnanchor">[38]</a></p>
+
+<p>A great part of Bergson's attack on science rests on the assumption
+that it employs this principle. In fact, it employs no such principle,
+but philosophers&mdash;even Bergson&mdash;are too apt to take their views on
+science from each other, not from science. As to what the principle
+is, there is a fair consensus among philosophers of different schools.
+There are, however, a number of difficulties which at once arise. I
+omit the question of plurality of causes for the present, since other
+graver questions have to be considered. Two of these, which are forced
+on our attention by the above statement of the law, are the
+following:&mdash;</p>
+
+<div class="block"><p>(1) What is meant by an "event"?</p>
+
+<p>(2) How long may the time-interval be between cause and effect?</p></div>
+
+<p>(1) An "event," in the statement of the law, is obviously intended to
+be something that is likely to recur since otherwise the law becomes
+trivial. It follows that an "event" is not a particular, but some
+universal of which there may be many instances. It follows also that
+an "event" must be something short of the whole state of the universe,
+since it is highly improbable that this will recur. What is meant by
+an "event" is something like striking a match, or dropping a penny
+into the slot of an automatic machine. If such an event is to recur,
+it must not be defined too narrowly: we must not state with what
+degree of force the match is to be struck, nor what is to be the
+temperature of the penny. For if such considerations were relevant,
+our "event" would occur at <span class='pagenum'><a name="Page_187" id="Page_187">[187]</a></span>most once, and the law would cease to give
+information. An "event," then, is a universal defined sufficiently
+widely to admit of many particular occurrences in time being instances
+of it.</p>
+
+<p>(2) The next question concerns the time-interval. Philosophers, no
+doubt, think of cause and effect as contiguous in time, but this, for
+reasons already given, is impossible. Hence, since there are no
+infinitesimal time-intervals, there must be some finite lapse of time
+&tau; between cause and effect. This, however, at once raises
+insuperable difficulties. However short we make the interval &tau;,
+something may happen during this interval which prevents the
+expected result. I put my penny in the slot, but before I can draw out
+my ticket there is an earthquake which upsets the machine and my
+calculations. In order to be sure of the expected effect, we must know
+that there is nothing in the environment to interfere with it. But
+this means that the supposed cause is not, by itself, adequate to
+insure the effect. And as soon as we include the environment, the
+probability of repetition is diminished, until at last, when the whole
+environment is included, the probability of repetition becomes almost
+<i>nil</i>.</p>
+
+<p>In spite of these difficulties, it must, of course, be admitted that
+many fairly dependable regularities of sequence occur in daily life.
+It is these regularities that have suggested the supposed law of
+causality; where they are found to fail, it is thought that a better
+formulation could have been found which would have never failed. I am
+far from denying that there may be such sequences which in fact never
+do fail. It may be that there will never be an exception to the rule
+that when a stone of more than a certain mass, moving with more than a
+certain velocity, comes in contact with a pane of glass of <span class='pagenum'><a name="Page_188" id="Page_188">[188]</a></span>less than
+a certain thickness, the glass breaks. I also do not deny that the
+observation of such regularities, even when they are not without
+exceptions, is useful in the infancy of a science: the observation
+that unsupported bodies in air usually fall was a stage on the way to
+the law of gravitation. What I deny is that science assumes the
+existence of invariable uniformities of sequence of this kind, or that
+it aims at discovering them. All such uniformities, as we saw, depend
+upon a certain vagueness in the definition of the "events." That
+bodies fall is a vague qualitative statement; science wishes to know
+how fast they fall. This depends upon the shape of the bodies and the
+density of the air. It is true that there is more nearly uniformity
+when they fall in a vacuum; so far as Galileo could observe, the
+uniformity is then complete. But later it appeared that even there the
+latitude made a difference, and the altitude. Theoretically, the
+position of the sun and moon must make a difference. In short, every
+advance in a science takes us farther away from the crude uniformities
+which are first observed, into greater differentiation of antecedent
+and consequent, and into a continually wider circle of antecedents
+recognised as relevant.</p>
+
+<p>The principle "same cause, same effect," which philosophers imagine to
+be vital to science, is therefore utterly otiose. As soon as the
+antecedents have been given sufficiently fully to enable the
+consequent to be calculated with some exactitude, the antecedents have
+become so complicated that it is very unlikely they will ever recur.
+Hence, if this were the principle involved, science would remain
+utterly sterile.</p>
+
+<p>The importance of these considerations lies partly in the fact that
+they lead to a more correct account of scientific procedure, partly in
+the fact that they remove <span class='pagenum'><a name="Page_189" id="Page_189">[189]</a></span>the analogy with human volition which makes
+the conception of cause such a fruitful source of fallacies. The
+latter point will become clearer by the help of some illustrations.
+For this purpose I shall consider a few maxims which have played a
+great part in the history of philosophy.</p>
+
+<p>(1) "Cause and effect must more or less resemble each other." This
+principle was prominent in the philosophy of occasionalism, and is
+still by no means extinct. It is still often thought, for example,
+that mind could not have grown up in a universe which previously
+contained nothing mental, and one ground for this belief is that
+matter is too dissimilar from mind to have been able to cause it. Or,
+more particularly, what are termed the nobler parts of our nature are
+supposed to be inexplicable, unless the universe always contained
+something at least equally noble which could cause them. All such
+views seem to depend upon assuming some unduly simplified law of
+causality; for, in any legitimate sense of "cause" and "effect,"
+science seems to show that they are usually very widely dissimilar,
+the "cause" being, in fact, two states of the whole universe, and the
+"effect" some particular event.</p>
+
+<p>(2) "Cause is analogous to volition, since there must be an
+intelligible <i>nexus</i> between cause and effect." This maxim is, I
+think, often unconsciously in the imaginations of philosophers who
+would reject it when explicitly stated. It is probably operative in
+the view we have just been considering, that mind could not have
+resulted from a purely material world. I do not profess to know what
+is meant by "intelligible"; it seems to mean "familiar to
+imagination." Nothing is less "intelligible," in any other sense, than
+the connection between <span class='pagenum'><a name="Page_190" id="Page_190">[190]</a></span>an act of will and its fulfilment. But
+obviously the sort of nexus desired between cause and effect is such
+as could only hold between the "events" which the supposed law of
+causality contemplates; the laws which replace causality in such a
+science as physics leave no room for any two events between which a
+nexus could be sought.</p>
+
+<p>(3) "The cause <i>compels</i> the effect in some sense in which the effect
+does not compel the cause." This belief seems largely operative in the
+dislike of determinism; but, as a matter of fact, it is connected with
+our second maxim, and falls as soon as that is abandoned. We may
+define "compulsion" as follows: "Any set of circumstances is said to
+compel A when A desires to do something which the circumstances
+prevent, or to abstain from something which the circumstances cause."
+This presupposes that some meaning has been found for the word
+"cause"&mdash;a point to which I shall return later. What I want to make
+clear at present is that compulsion is a very complex notion,
+involving thwarted desire. So long as a person does what he wishes to
+do, there is no compulsion, however much his wishes may be calculable
+by the help of earlier events. And where desire does not come in,
+there can be no question of compulsion. Hence it is, in general,
+misleading to regard the cause as compelling the effect.</p>
+
+<p>A vaguer form of the same maxim substitutes the word "determine" for
+the word "compel"; we are told that the cause <i>determines</i> the effect
+in a sense in which the effect does not <i>determine</i> the cause. It is
+not quite clear what is meant by "determining"; the only precise
+sense, so far as I know, is that of a function or one-many relation.
+If we admit plurality of causes, but not of effects, that is, if we
+suppose that, given the cause, the effect must be such and such, but,
+given the effect, the <span class='pagenum'><a name="Page_191" id="Page_191">[191]</a></span>cause may have been one of many alternatives,
+then we may say that the cause determines the effect, but not the
+effect the cause. Plurality of causes, however, results only from
+conceiving the effect vaguely and narrowly and the cause precisely and
+widely. Many antecedents may "cause" a man's death, because his death
+is vague and narrow. But if we adopt the opposite course, taking as
+the "cause" the drinking of a dose of arsenic, and as the "effect" the
+whole state of the world five minutes later, we shall have plurality
+of effects instead of plurality of causes. Thus the supposed lack of
+symmetry between "cause" and "effect" is illusory.</p>
+
+<p>(4) "A cause cannot operate when it has ceased to exist, because what
+has ceased to exist is nothing." This is a common maxim, and a still
+more common unexpressed prejudice. It has, I fancy, a good deal to do
+with the attractiveness of Bergson's "<i>dur&eacute;e</i>": since the past has
+effects now, it must still exist in some sense. The mistake in this
+maxim consists in the supposition that causes "operate" at all. A
+volition "operates" when what it wills takes place; but nothing can
+operate except a volition. The belief that causes "operate" results
+from assimilating them, consciously or unconsciously, to volitions. We
+have already seen that, if there are causes at all, they must be
+separated by a finite interval of time from their effects, and thus
+cause their effects after they have ceased to exist.</p>
+
+<p>It may be objected to the above definition of a volition "operating"
+that it only operates when it "causes" what it wills, not when it
+merely happens to be followed by what it wills. This certainly
+represents the usual view of what is meant by a volition "operating,"
+but as it involves the very view of causation which we are engaged in
+combating, it is not open to us as a definition. We <span class='pagenum'><a name="Page_192" id="Page_192">[192]</a></span>may say that a
+volition "operates" when there is some law in virtue of which a
+similar volition in rather similar circumstances will usually be
+followed by what it wills. But this is a vague conception, and
+introduces ideas which we have not yet considered. What is chiefly
+important to notice is that the usual notion of "operating" is not
+open to us if we reject, as I contend that we should, the usual notion
+of causation.</p>
+
+<p>(5) "A cause cannot operate except where it is." This maxim is very
+widespread; it was urged against Newton, and has remained a source of
+prejudice against "action at a distance." In philosophy it has led to
+a denial of transient action, and thence to monism or Leibnizian
+monadism. Like the analogous maxim concerning temporal contiguity, it
+rests upon the assumption that causes "operate," i.e. that they are in
+some obscure way analogous to volitions. And, as in the case of
+temporal contiguity, the inferences drawn from this maxim are wholly
+groundless.</p>
+
+<p>I return now to the question, What law or laws can be found to take
+the place of the supposed law of causality?</p>
+
+<p>First, without passing beyond such uniformities of sequence as are
+contemplated by the traditional law, we may admit that, if any such
+sequence has been observed in a great many cases, and has never been
+found to fail, there is an inductive probability that it will be found
+to hold in future cases. If stones have hitherto been found to break
+windows, it is probable that they will continue to do so. This, of
+course, assumes the inductive principle, of which the truth may
+reasonably be questioned; but as this principle is not our present
+concern, I shall in this discussion treat it as indubitable. We may
+then say, in the case of any such frequently observed sequence, that
+<span class='pagenum'><a name="Page_193" id="Page_193">[193]</a></span>the earlier event is the <i>cause</i> and the later event the <i>effect</i>.</p>
+
+<p>Several considerations, however, make such special sequences very
+different from the traditional relation of cause and effect. In the
+first place, the sequence, in any hitherto unobserved instance, is no
+more than probable, whereas the relation of cause and effect was
+supposed to be necessary. I do not mean by this merely that we are not
+sure of having discovered a true case of cause and effect; I mean
+that, even when we have a case of cause and effect in our present
+sense, all that is meant is that on grounds of observation, it is
+probable that when one occurs the other will also occur. Thus in our
+present sense, A may be the cause of B even if there actually are
+cases where B does not follow A. Striking a match will be the cause of
+its igniting, in spite of the fact that some matches are damp and fail
+to ignite.</p>
+
+<p>In the second place, it will not be assumed that <i>every</i> event has
+some antecedent which is its cause in this sense; we shall only
+believe in causal sequences where we find them, without any
+presumption that they always are to be found.</p>
+
+<p>In the third place, <i>any</i> case of sufficiently frequent sequence will
+be causal in our present sense; for example, we shall not refuse to
+say that night is the cause of day. Our repugnance to saying this
+arises from the ease with which we can imagine the sequence to fail,
+but owing to the fact that cause and effect must be separated by a
+finite interval of time, <i>any</i> such sequence <i>might</i> fail through the
+interposition of other circumstances in the interval. Mill, discussing
+this instance of night and day, says:&mdash;</p>
+
+<p>"It is necessary to our using the word cause, that we should believe
+not only that the antecedent always <i>has</i> <span class='pagenum'><a name="Page_194" id="Page_194">[194]</a></span>been followed by the
+consequent, but that as long as the present constitution of things
+endures, it always <i>will</i> be so."<a name="FNanchor_39_39" id="FNanchor_39_39"></a><a href="#Footnote_39_39" class="fnanchor">[39]</a></p>
+
+<p>In this sense, we shall have to give up the hope of finding causal
+laws such as Mill contemplated; any causal sequence which we have
+observed may at any moment be falsified without a falsification of any
+laws of the kind that the more advanced sciences aim at establishing.</p>
+
+<p>In the fourth place, such laws of probable sequence, though useful in
+daily life and in the infancy of a science, tend to be displaced by
+quite different laws as soon as a science is successful. The law of
+gravitation will illustrate what occurs in any advanced science. In
+the motions of mutually gravitating bodies, there is nothing that can
+be called a cause, and nothing that can be called an effect; there is
+merely a formula. Certain differential equations can be found, which
+hold at every instant for every particle of the system, and which,
+given the configuration and velocities at one instant, or the
+configurations at two instants, render the configuration at any other
+earlier or later instant theoretically calculable. That is to say, the
+configuration at any instant is a function of that instant and the
+configurations at two given instants. This statement holds throughout
+physics, and not only in the special case of gravitation. But there is
+nothing that could be properly called "cause" and nothing that could
+be properly called "effect" in such a system.</p>
+
+<p>No doubt the reason why the old "law of causality" has so long
+continued to pervade the books of philosophers is simply that the idea
+of a function is unfamiliar to most of them, and therefore they seek
+an unduly simplified statement. There is no question of repetitions of
+the "same" cause producing the "same" effect; it <span class='pagenum'><a name="Page_195" id="Page_195">[195]</a></span>is not in any
+sameness of causes and effects that the constancy of scientific law
+consists, but in sameness of relations. And even "sameness of
+relations" is too simple a phrase; "sameness of differential
+equations" is the only correct phrase. It is impossible to state this
+accurately in non-mathematical language; the nearest approach would be
+as follows: "There is a constant relation between the state of the
+universe at any instant and the rate of change in the rate at which
+any part of the universe is changing at that instant, and this
+relation is many-one, i.e. such that the rate of change in the rate of
+change is determinate when the state of the universe is given." If the
+"law of causality" is to be something actually discoverable in the
+practice of science, the above proposition has a better right to the
+name than any "law of causality" to be found in the books of
+philosophers.</p>
+
+<p>In regard to the above principle, several observations must be made&mdash;</p>
+
+<p>(1) No one can pretend that the above principle is <i>a priori</i> or
+self-evident or a "necessity of thought." Nor is it, in any sense, a
+premiss of science: it is an empirical generalisation from a number of
+laws which are themselves empirical generalisations.</p>
+
+<p>(2) The law makes no difference between past and future: the future
+"determines" the past in exactly the same sense in which the past
+"determines" the future. The word "determine," here, has a purely
+logical significance: a certain number of variables "determine"
+another variable if that other variable is a function of them.</p>
+
+<p>(3) The law will not be empirically verifiable unless the course of
+events within some sufficiently small volume <span class='pagenum'><a name="Page_196" id="Page_196">[196]</a></span>will be approximately
+the same in any two states of the universe which only differ in regard
+to what is at a considerable distance from the small volume in
+question. For example, motions of planets in the solar system must be
+approximately the same however the fixed stars may be distributed,
+provided that all the fixed stars are very much farther from the sun
+than the planets are. If gravitation varied directly as the distance,
+so that the most remote stars made the most difference to the motions
+of the planets, the world might be just as regular and just as much
+subject to mathematical laws as it is at present, but we could never
+discover the fact.</p>
+
+<p>(4) Although the old "law of causality" is not assumed by science,
+something which we may call the "uniformity of nature" is assumed, or
+rather is accepted on inductive grounds. The uniformity of nature does
+not assert the trivial principle "same cause, same effect," but the
+principle of the permanence of laws. That is to say, when a law
+exhibiting, e.g. an acceleration as a function of the configuration
+has been found to hold throughout the observable past, it is expected
+that it will continue to hold in the future, or that, if it does not
+itself hold, there is some other law, agreeing with the supposed law
+as regards the past, which will hold for the future. The ground of
+this principle is simply the inductive ground that it has been found
+to be true in very many instances; hence the principle cannot be
+considered certain, but only probable to a degree which cannot be
+accurately estimated.</p>
+
+<p>The uniformity of nature, in the above sense, although it is assumed
+in the practice of science, must not, in its generality, be regarded
+as a kind of major premiss, without which all scientific reasoning
+would be in error. The assumption that <i>all</i> laws of nature are
+permanent has, of <span class='pagenum'><a name="Page_197" id="Page_197">[197]</a></span>course, less probability than the assumption that
+this or that particular law is permanent; and the assumption that a
+particular law is permanent for all time has less probability than the
+assumption that it will be valid up to such and such a date. Science,
+in any given case, will assume what the case requires, but no more. In
+constructing the <i>Nautical Almanac</i> for 1915 it will assume that the
+law of gravitation will remain true up to the end of that year; but it
+will make no assumption as to 1916 until it comes to the next volume
+of the almanac. This procedure is, of course, dictated by the fact
+that the uniformity of nature is not known <i>a priori</i>, but is an
+empirical generalisation, like "all men are mortal." In all such
+cases, it is better to argue immediately from the given particular
+instances to the new instance, than to argue by way of a major
+premiss; the conclusion is only probable in either case, but acquires
+a higher probability by the former method than by the latter.</p>
+
+<p>In all science we have to distinguish two sorts of laws: first, those
+that are empirically verifiable but probably only approximate;
+secondly, those that are not verifiable, but may be exact. The law of
+gravitation, for example, in its applications to the solar system, is
+only empirically verifiable when it is assumed that matter outside the
+solar system may be ignored for such purposes; we believe this to be
+only approximately true, but we cannot empirically verify the law of
+universal gravitation which we believe to be exact. This point is very
+important in connection with what we may call "relatively isolated
+systems." These may be defined as follows:&mdash;</p>
+
+<p>A system relatively isolated during a given period is one which,
+within some assignable margin of error, will behave in the same way
+throughout that period, however the rest of the universe may be
+constituted.</p>
+
+<p><span class='pagenum'><a name="Page_198" id="Page_198">[198]</a></span>A system may be called "practically isolated" during a given period
+if, although there <i>might</i> be states of the rest of the universe which
+would produce more than the assigned margin of error, there is reason
+to believe that such states do not in fact occur.</p>
+
+<p>Strictly speaking, we ought to specify the respect in which the system
+is relatively isolated. For example, the earth is relatively isolated
+as regards falling bodies, but not as regards tides; it is
+<i>practically</i> isolated as regards economic phenomena, although, if
+Jevons' sunspot theory of commercial crises had been true, it would
+not have been even practically isolated in this respect.</p>
+
+<p>It will be observed that we cannot prove in advance that a system is
+isolated. This will be inferred from the observed fact that
+approximate uniformities can be stated for this system alone. If the
+complete laws for the whole universe were known, the isolation of a
+system could be deduced from them; assuming, for example, the law of
+universal gravitation, the practical isolation of the solar system in
+this respect can be deduced by the help of the fact that there is very
+little matter in its neighbourhood. But it should be observed that
+isolated systems are only important as providing a possibility of
+<i>discovering</i> scientific laws; they have no theoretical importance in
+the finished structure of a science.</p>
+
+<p>The case where one event A is said to "cause" another event B, which
+philosophers take as fundamental, is really only the most simplified
+instance of a practically isolated system. It may happen that, as a
+result of general scientific laws, whenever A occurs throughout a
+certain period, it is followed by B; in that case, A and B form a
+system which is practically isolated throughout that period. It is,
+however, to be regarded as a piece of good fortune if this occurs; it
+will always be due to special <span class='pagenum'><a name="Page_199" id="Page_199">[199]</a></span>circumstances, and would not have been
+true if the rest of the universe had been different though subject to
+the same laws.</p>
+
+<p>The essential function which causality has been supposed to perform is
+the possibility of inferring the future from the past, or, more
+generally, events at any time from events at certain assigned times.
+Any system in which such inference is possible may be called a
+"deterministic" system. We may define a deterministic system as
+follows:&mdash;</p>
+
+<div class="block"><p>A system is said to be "deterministic" when, given certain data,
+<i>e</i><sub>1</sub>, <i>e</i><sub>2</sub>, ..., <i>e</i><sub>n</sub>, at times <i>t</i><sub>1</sub>, <i>t</i><sub>2</sub>, ..., <i>t</i><sub>n</sub>
+respectively, concerning this system, if E<sub><i>t</i></sub> is the state of the
+system at any time <i>t</i>, there is a functional relation of the form</p>
+
+<div class="block">
+<p>E<sub>t</sub> = <i>f</i> (<i>e</i><sub>1</sub>, <i>t</i><sub>1</sub>, <i>e</i><sub>2</sub>, <i>t</i><sub>2</sub>, ..., <i>e</i><sub>n</sub>, <i>t</i><sub>n</sub>, <i>t</i>). &nbsp;&nbsp;&nbsp; (A)</p>
+</div>
+
+<p>The system will be "deterministic throughout a given period" if
+<i>t</i>, in the above formula, may be any time within that period,
+though outside that period the formula may be no longer true. If
+the universe, as a whole, is such a system, determinism is true of
+the universe; if not, not. A system which is part of a
+deterministic system I shall call "determined"; one which is not
+part of any such system I shall call "capricious."</p></div>
+
+<p>The events <i>e</i><sub>1</sub>, <i>e</i><sub>2</sub>, ..., <i>e</i><sub>n</sub> I shall call "determinants" of the
+system. It is to be observed that a system which has one set of
+determinants will in general have many. In the case of the motions of
+the planets, for example, the configurations of the solar system at
+any two given times will be determinants.</p>
+
+<p>We may take another illustration from the hypothesis of
+psycho-physical parallelism. Let us assume, for the purposes of this
+illustration, that to a given state of brain <span class='pagenum'><a name="Page_200" id="Page_200">[200]</a></span>a given state of mind
+always corresponds, and vice versa, i.e. that there is a one-one
+relation between them, so that each is a function of the other. We may
+also assume, what is practically certain, that to a given state of a
+certain brain a given state of the whole material universe
+corresponds, since it is highly improbable that a given brain is ever
+twice in exactly the same state. Hence there will be a one-one
+relation between the state of a given person's mind and the state of
+the whole material universe. It follows that, if <i>n</i> states of the
+material universe are determinants of the material universe, then <i>n</i>
+states of a given man's mind are determinants of the whole material
+and mental universe&mdash;assuming, that is to say, that psycho-physical
+parallelism is true.</p>
+
+<p>The above illustration is important in connection with a certain
+confusion which seems to have beset those who have philosophised on
+the relation of mind and matter. It is often thought that, if the
+state of the mind is determinate when the state of the brain is given,
+and if the material world forms a deterministic system, then mind is
+"subject" to matter in some sense in which matter is not "subject" to
+mind. But if the state of the brain is also determinate when the state
+of the mind is given, it must be exactly as true to regard matter as
+subject to mind as it would be to regard mind as subject to matter. We
+could, theoretically, work out the history of mind without ever
+mentioning matter, and then, at the end, deduce that matter must
+meanwhile have gone through the corresponding history. It is true that
+if the relation of brain to mind were many-one, not one-one, there
+would be a one-sided dependence of mind on brain, while conversely, if
+the relation were one-many, as Bergson supposes, there would be a
+one-aided dependence of brain on mind. But the dependence involved is,
+in any case, only <span class='pagenum'><a name="Page_201" id="Page_201">[201]</a></span>logical; it does not mean that we shall be
+compelled to do things we desire not to do, which is what people
+instinctively imagine it to mean.</p>
+
+<p>As another illustration we may take the case of mechanism and
+teleology. A system may be defined as "mechanical" when it has a set
+of determinants that are purely material, such as the positions of
+certain pieces of matter at certain times. It is an open question
+whether the world of mind and matter, as we know it, is a mechanical
+system or not; let us suppose, for the sake of argument, that it is a
+mechanical system. This supposition&mdash;so I contend&mdash;throws no light
+whatever on the question whether the universe is or is not a
+"teleological" system. It is difficult to define accurately what is
+meant by a "teleological" system, but the argument is not much
+affected by the particular definition we adopt. Broadly, a
+teleological system is one in which purposes are realised, i.e. in
+which certain desires&mdash;those that are deeper or nobler or more
+fundamental or more universal or what not&mdash;are followed by their
+realisation. Now the fact&mdash;if it be a fact&mdash;that the universe is
+mechanical has no bearing whatever on the question whether it is
+teleological in the above sense. There might be a mechanical system in
+which all wishes were realised, and there might be one in which all
+wishes were thwarted. The question whether, or how far, our actual
+world is teleological, cannot, therefore, be settled by proving that
+it is mechanical, and the desire that it should be teleological is no
+ground for wishing it to be not mechanical.</p>
+
+<p>There is, in all these questions, a very great difficulty in avoiding
+confusion between what we can infer and what is in fact determined.
+Let us consider, for a moment, the various senses in which the future
+may be "determined." There is one sense&mdash;and a very important <span class='pagenum'><a name="Page_202" id="Page_202">[202]</a></span>one&mdash;in
+which it is determined quite independently of scientific laws, namely,
+the sense that it will be what it will be. We all regard the past as
+determined simply by the fact that it has happened; but for the
+accident that memory works backward and not forward, we should regard
+the future as equally determined by the fact that it will happen.
+"But," we are told, "you cannot alter the past, while you can to some
+extent alter the future." This view seems to me to rest upon just
+those errors in regard to causation which it has been my object to
+remove. You cannot make the past other than it was&mdash;true, but this is
+a mere application of the law of contradiction. If you already know
+what the past was, obviously it is useless to wish it different. But
+also you cannot make the future other than it will be; this again is
+an application of the law of contradiction. And if you happen to know
+the future&mdash;e.g. in the case of a forthcoming eclipse&mdash;it is just as
+useless to wish it different as to wish the past different. "But," it
+will be rejoined, "our wishes can <i>cause</i> the future, sometimes, to be
+different from what it would be if they did not exist, and they can
+have no such effect upon the past." This, again, is a mere tautology.
+An effect being <i>defined</i> as something subsequent to its cause,
+obviously we can have no <i>effect</i> upon the past. But that does not
+mean that the past would not have been different if our present wishes
+had been different. Obviously, our present wishes are conditioned by
+the past, and therefore could not have been different unless the past
+had been different; therefore, if our present wishes were different,
+the past would be different. Of course, the past cannot be different
+from what it was, but no more can our present wishes be different from
+what they are; this again is merely the law of contradiction. The
+facts seem to be merely (1) that wishing generally <span class='pagenum'><a name="Page_203" id="Page_203">[203]</a></span>depends upon
+ignorance, and is therefore commoner in regard to the future than in
+regard to the past; (2) that where a wish concerns the future, it and
+its realisation very often form a "practically independent system,"
+i.e. many wishes regarding the future are realised. But there seems no
+doubt that the main difference in our feelings arises from the
+accidental fact that the past but not the future can be known by
+memory.</p>
+
+<p>Although the sense of "determined" in which the future is determined
+by the mere fact that it will be what it will be is sufficient (at
+least so it seems to me) to refute some opponents of determinism,
+notably M. Bergson and the pragmatists, yet it is not what most people
+have in mind when they speak of the future as determined. What they
+have in mind is a formula by means of which the future can be
+exhibited, and at least theoretically calculated, as a function of the
+past. But at this point we meet with a great difficulty, which besets
+what has been said above about deterministic systems, as well as what
+is said by others.</p>
+
+<p>If formul&aelig; of any degree of complexity, however great, are admitted,
+it would seem that any system, whose state at a given moment is a
+function of certain measurable quantities, must be a deterministic
+system. Let us consider, in illustration, a single material particle,
+whose co-ordinates at time <i>t</i> are <i>x</i><sub>t</sub>, <i>y</i><sub>t</sub>, <i>z</i><sub>t</sub>. Then,
+however, the particle moves, there must be, theoretically, functions
+<i>f</i><sub>1</sub>, <i>f</i><sub>2</sub>, <i>f</i><sub>3</sub>, such that</p>
+
+<div class="block">
+<p><i>x</i><sub>t</sub> = <i>f</i><sub>t</sub>&nbsp;(<i>t</i>), &nbsp;&nbsp;&nbsp; <i>y</i><sub>t</sub> = <i>f</i><sub>2</sub>&nbsp;(<i>t</i>), &nbsp;&nbsp;&nbsp; <i>z</i><sub>t</sub> = <i>f</i><sub>3</sub>&nbsp;(<i>t</i>).</p>
+</div>
+
+<p>It follows that, theoretically, the whole state of the material
+universe at time <i>t</i> must be capable of being exhibited as a function
+of <i>t</i>. Hence our universe will be deterministic in the sense defined
+above. But if this be <span class='pagenum'><a name="Page_204" id="Page_204">[204]</a></span>true, no information is conveyed about the
+universe in stating that it is deterministic. It is true that the
+formul&aelig; involved may be of strictly infinite complexity, and therefore
+not practically capable of being written down or apprehended. But
+except from the point of view of our knowledge, this might seem to be
+a detail: in itself, if the above considerations are sound, the
+material universe <i>must</i> be deterministic, <i>must</i> be subject to laws.</p>
+
+<p>This, however, is plainly not what was intended. The difference
+between this view and the view intended may be seen as follows. Given
+some formula which fits the facts hitherto&mdash;say the law of
+gravitation&mdash;there will be an infinite number of other formul&aelig;, not
+empirically distinguishable from it in the past, but diverging from it
+more and more in the future. Hence, even assuming that there are
+persistent laws, we shall have no reason for assuming that the law of
+the inverse square will hold in future; it may be some other hitherto
+indistinguishable law that will hold. We cannot say that <i>every</i> law
+which has held hitherto must hold in the future, because past facts
+which obey one law will also obey others, hitherto indistinguishable
+but diverging in future. Hence there must, at every moment, be laws
+hitherto unbroken which are now broken for the first time. What
+science does, in fact, is to select the <i>simplest</i> formula that will
+fit the facts. But this, quite obviously, is merely a methodological
+precept, not a law of Nature. If the simplest formula ceases, after a
+time, to be applicable, the simplest formula that remains applicable
+is selected, and science has no sense that an axiom has been
+falsified. We are thus left with the brute fact that, in many
+departments of science, quite simple laws have hitherto been found to
+hold. This fact cannot be regarded as having any <i>a priori</i> ground,
+nor can it be used to support inductively the opinion that <span class='pagenum'><a name="Page_205" id="Page_205">[205]</a></span>the same
+laws will continue; for at every moment laws hitherto true are being
+falsified, though in the advanced sciences these laws are less simple
+than those that have remained true. Moreover it would be fallacious to
+argue inductively from the state of the advanced sciences to the
+future state of the others, for it may well be that the advanced
+sciences are advanced simply because, hitherto, their subject-matter
+has obeyed simple and easily ascertainable laws, while the
+subject-matter of other sciences has not done so.</p>
+
+<p>The difficulty we have been considering seems to be met partly, if not
+wholly, by the principle that the <i>time</i> must not enter explicitly
+into our formul&aelig;. All mechanical laws exhibit acceleration as a
+function of configuration, not of configuration and time jointly; and
+this principle of the irrelevance of the time may be extended to all
+scientific laws. In fact we might interpret the "uniformity of nature"
+as meaning just this, that no scientific law involves the time as an
+argument, unless, of course, it is given in an integrated form, in
+which case <i>lapse</i> of time, though not absolute time, may appear in
+our formul&aelig;. Whether this consideration suffices to overcome our
+difficulty completely, I do not know; but in any case it does much to
+diminish it.</p>
+
+<p>It will serve to illustrate what has been said if we apply it to the
+question of free will.</p>
+
+<p>(1) Determinism in regard to the will is the doctrine that our
+volitions belong to some deterministic system, i.e. are "determined"
+in the sense defined above. Whether this doctrine is true or false, is
+a mere question of fact; no <i>a priori</i> considerations (if our previous
+discussions have been correct) can exist on either side. On the one
+hand, there is no <i>a priori</i> category of causality, but merely certain
+observed uniformities. As a matter <span class='pagenum'><a name="Page_206" id="Page_206">[206]</a></span>of fact, there are observed
+uniformities in regard to volitions; thus there is some empirical
+evidence that volitions are determined. But it would be very rash to
+maintain that the evidence is overwhelming, and it is quite possible
+that some volitions, as well as some other things, are not determined,
+except in the sense in which we found that everything must be
+determined.</p>
+
+<p>(2) But, on the other hand, the subjective sense of freedom, sometimes
+alleged against determinism, has no bearing on the question whatever.
+The view that it has a bearing rests upon the belief that causes
+compel their effects, or that nature enforces obedience to its laws as
+governments do. These are mere anthropomorphic superstitions, due to
+assimilation of causes with volitions and of natural laws with human
+edicts. We feel that our will is not compelled, but that only means
+that it is not other than we choose it to be. It is one of the
+demerits of the traditional theory of causality that it has created an
+artificial opposition between determinism and the freedom of which we
+are introspectively conscious.</p>
+
+<p>(3) Besides the general question whether volitions are determined,
+there is the further question whether they are <i>mechanically</i>
+determined, i.e. whether they are part of what was above defined as a
+mechanical system. This is the question whether they form part of a
+system with purely material determinants, i.e. whether there are laws
+which, given certain material data, make all volitions functions of
+those data. Here again, there is empirical evidence up to a point, but
+it is not conclusive in regard to all volitions. It is important to
+observe, however that even if volitions are part of a mechanical
+system, this by no means implies any supremacy of matter over mind. It
+may well be that the same system which is <span class='pagenum'><a name="Page_207" id="Page_207">[207]</a></span>susceptible of material
+determinants is also susceptible of mental determinants; thus a
+mechanical system may be determined by sets of volitions, as well as
+by sets of material facts. It would seem, therefore, that the reasons
+which make people dislike the view that volitions are mechanically
+determined are fallacious.</p>
+
+<p>(4) The notion of <i>necessity</i>, which is often associated with
+determinism, is a confused notion not legitimately deducible from
+determinism. Three meanings are commonly confounded when necessity is
+spoken of:&mdash;</p>
+
+<p>(&alpha;) An <i>action</i> is necessary when it will be performed
+however much the agent may wish to do otherwise. Determinism does not
+imply that actions are necessary in this sense.</p>
+
+<p>(&beta;) A <i>propositional function</i> is necessary when all its
+values are true. This sense is not relevant to our present discussion.</p>
+
+<p>(&gamma;) A <i>proposition</i> is necessary with respect to a given
+constituent when it is the value, with that constituent as argument,
+of a necessary propositional function, in other words, when it remains
+true however that constituent may be varied. In this sense, in a
+deterministic system, the connection of a volition with its
+determinants is necessary, if the time at which the determinants occur
+be taken as the constituent to be varied, the time-interval between
+the determinants and the volition being kept constant. But this sense
+of necessity is purely logical, and has no emotional importance.</p>
+
+<p>We may now sum up our discussion of causality. We found first that the
+law of causality, as usually stated by philosophers, is false, and is
+not employed in science. We then considered the nature of scientific
+laws, and found that, instead of stating that one event A is always
+followed <span class='pagenum'><a name="Page_208" id="Page_208">[208]</a></span>by another event B, they stated functional relations between
+certain events at certain times, which we called determinants, and
+other events at earlier or later times or at the same time. We were
+unable to find any <i>a priori</i> category involved: the existence of
+scientific laws appeared as a purely empirical fact, not necessarily
+universal, except in a trivial and scientifically useless form. We
+found that a system with one set of determinants may very likely have
+other sets of a quite different kind, that, for example, a
+mechanically determined system may also be teleologically or
+volitionally determined. Finally we considered the problem of free
+will: here we found that the reasons for supposing volitions to be
+determined are strong but not conclusive, and we decided that even if
+volitions are mechanically determined, that is no reason for denying
+freedom in the sense revealed by introspection, or for supposing that
+mechanical events are not determined by volitions. The problem of free
+will <i>versus</i> determinism is therefore, if we were right, mainly
+illusory, but in part not yet capable of being decisively solved.</p>
+
+<br />
+<hr style="width: 15%;" />
+<br />
+
+<h4>FOOTNOTES:</h4>
+
+<div class="footnote"><p class="noin"><a name="Footnote_35_35" id="Footnote_35_35"></a><a href="#FNanchor_35_35"><span class="label">[35]</span></a> A propositional function is an expression containing a
+variable, or undetermined constituent, and becoming a proposition as
+soon as a definite value is assigned to the variable. Examples are: "A
+is A," "<i>x</i> is a number." The variable is called the <i>argument</i> of the
+function.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_36_36" id="Footnote_36_36"></a><a href="#FNanchor_36_36"><span class="label">[36]</span></a> <i>Logic</i>, Bk. III, Chap. V, &sect; 2.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_37_37" id="Footnote_37_37"></a><a href="#FNanchor_37_37"><span class="label">[37]</span></a> <i>Time and Free Will</i>, p. 199.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_38_38" id="Footnote_38_38"></a><a href="#FNanchor_38_38"><span class="label">[38]</span></a> <i>Time and Free Will.</i> p. 202.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_39_39" id="Footnote_39_39"></a><a href="#FNanchor_39_39"><span class="label">[39]</span></a> <i>Loc. cit.</i>, &sect; 6</p></div>
+
+
+<br />
+<br />
+<br />
+<br />
+<a name="X" id="X"></a><hr />
+<span class='pagenum'><a name="Page_209" id="Page_209">[209]</a></span><br />
+
+<h3>X<span class="totoc"><a href="#toc">ToC</a></span></h3>
+
+<h4>KNOWLEDGE BY ACQUAINTANCE AND KNOWLEDGE BY DESCRIPTION</h4>
+<br />
+
+<p>The object of the following paper is to consider what it is that we
+know in cases where we know propositions about "the so-and-so" without
+knowing who or what the so-and-so is. For example, I know that the
+candidate who gets most votes will be elected, though I do not know
+who is the candidate who will get most votes. The problem I wish to
+consider is: What do we know in these cases, where the subject is
+merely described? I have considered this problem elsewhere<a name="FNanchor_40_40" id="FNanchor_40_40"></a><a href="#Footnote_40_40" class="fnanchor">[40]</a> from a
+purely logical point of view; but in what follows I wish to consider
+the question in relation to theory of knowledge as well as in relation
+to logic, and in view of the above-mentioned logical discussions, I
+shall in this paper make the logical portion as brief as possible.</p>
+
+<p>In order to make clear the antithesis between "acquaintance" and
+"description," I shall first of all try to explain what I mean by
+"acquaintance." I say that I am <i>acquainted</i> with an object when I
+have a direct cognitive relation to that object, i.e. when I am
+directly aware of the object itself. When I speak of a cognitive
+relation here, I do not mean the sort of relation which constitutes
+judgment, but the sort which constitutes presentation. In fact, I
+think the relation of subject and <span class='pagenum'><a name="Page_210" id="Page_210">[210]</a></span>object which I call acquaintance is
+simply the converse of the relation of object and subject which
+constitutes presentation. That is, to say that S has acquaintance with
+O is essentially the same thing as to say that O is presented to S.
+But the associations and natural extensions of the word <i>acquaintance</i>
+are different from those of the word <i>presentation</i>. To begin with, as
+in most cognitive words, it is natural to say that I am acquainted
+with an object even at moments when it is not actually before my mind,
+provided it has been before my mind, and will be again whenever
+occasion arises. This is the same sense in which I am said to know
+that 2+2=4 even when I am thinking of something else. In the second
+place, the word <i>acquaintance</i> is designed to emphasise, more than the
+word <i>presentation</i>, the relational character of the fact with which
+we are concerned. There is, to my mind, a danger that, in speaking of
+presentation, we may so emphasise the object as to lose sight of the
+subject. The result of this is either to lead to the view that there
+is no subject, whence we arrive at materialism; or to lead to the view
+that what is presented is part of the subject, whence we arrive at
+idealism, and should arrive at solipsism but for the most desperate
+contortions. Now I wish to preserve the dualism of subject and object
+in my terminology, because this dualism seems to me a fundamental fact
+concerning cognition. Hence I prefer the word <i>acquaintance</i> because
+it emphasises the need of a subject which is acquainted.</p>
+
+<p>When we ask what are the kinds of objects with which we are
+acquainted, the first and most obvious example is <i>sense-data</i>. When I
+see a colour or hear a noise, I have direct acquaintance with the
+colour or the noise. The sense-datum with which I am acquainted in
+these cases is generally, if not always, complex. This is
+particularly <span class='pagenum'><a name="Page_211" id="Page_211">[211]</a></span>obvious in the case of sight. I do not mean, of course,
+merely that the supposed physical object is complex, but that the
+direct sensible object is complex and contains parts with spatial
+relations. Whether it is possible to be aware of a complex without
+being aware of its constituents is not an easy question, but on the
+whole it would seem that there is no reason why it should not be
+possible. This question arises in an acute form in connection with
+self-consciousness, which we must now briefly consider.</p>
+
+<p>In introspection, we seem to be immediately aware of varying
+complexes, consisting of objects in various cognitive and conative
+relations to ourselves. When I see the sun, it often happens that I am
+aware of my seeing the sun, in addition to being aware of the sun; and
+when I desire food, it often happens that I am aware of my desire for
+food. But it is hard to discover any state of mind in which I am aware
+of myself alone, as opposed to a complex of which I am a constituent.
+The question of the nature of self-consciousness is too large and too
+slightly connected with our subject, to be argued at length here. It
+is difficult, but probably not impossible, to account for plain facts
+if we assume that we do not have acquaintance with ourselves. It is
+plain that we are not only <i>acquainted</i> with the complex
+"Self-acquainted-with-A," but we also <i>know</i> the proposition "I am
+acquainted with A." Now here the complex has been analysed, and if "I"
+does not stand for something which is a direct object of acquaintance,
+we shall have to suppose that "I" is something known by description.
+If we wished to maintain the view that there is no acquaintance with
+Self, we might argue as follows: We are acquainted with
+<i>acquaintance</i>, and we know that it is a relation. Also we are
+acquainted with a complex in which we perceive that acquaintance <span class='pagenum'><a name="Page_212" id="Page_212">[212]</a></span>is
+the relating relation. Hence we know that this complex must have a
+constituent which is that which is acquainted, i.e. must have a
+subject-term as well as an object-term. This subject-term we define as
+"I." Thus "I" means "the subject-term in awarenesses of which <i>I</i> am
+aware." But as a definition this cannot be regarded as a happy effort.
+It would seem necessary, therefore, either to suppose that I am
+acquainted with myself, and that "I," therefore, requires no
+definition, being merely the proper name of a certain object, or to
+find some other analysis of self-consciousness. Thus
+self-consciousness cannot be regarded as throwing light on the
+question whether we can know a complex without knowing its
+constituents. This question, however, is not important for our present
+purposes, and I shall therefore not discuss it further.</p>
+
+<p>The awarenesses we have considered so far have all been awarenesses of
+particular existents, and might all in a large sense be called
+sense-data. For, from the point of view of theory of knowledge,
+introspective knowledge is exactly on a level with knowledge derived
+from sight or hearing. But, in addition to awareness of the above kind
+of objects, which may be called awareness of <i>particulars</i>; we have
+also (though not quite in the same sense) what may be called awareness
+of <i>universals</i>. Awareness of universals is called <i>conceiving</i>, and a
+universal of which we are aware is called a <i>concept</i>. Not only are we
+aware of particular yellows, but if we have seen a sufficient number
+of yellows and have sufficient intelligence, we are aware of the
+universal <i>yellow</i>; this universal is the subject in such judgments as
+"yellow differs from blue" or "yellow resembles blue less than green
+does." And the universal yellow is the predicate in such judgments as
+"this is yellow," where "this" is a particular sense-datum. And
+universal relations, too, <span class='pagenum'><a name="Page_213" id="Page_213">[213]</a></span>are objects of awarenesses; up and down,
+before and after, resemblance, desire, awareness itself, and so on,
+would seem to be all of them objects of which we can be aware.</p>
+
+<p>In regard to relations, it might be urged that we are never aware of
+the universal relation itself, but only of complexes in which it is a
+constituent. For example, it may be said that we do not know directly
+such a relation as <i>before</i>, though we understand such a proposition
+as "this is before that," and may be directly aware of such a complex
+as "this being before that." This view, however, is difficult to
+reconcile with the fact that we often know propositions in which the
+relation is the subject, or in which the relata are not definite given
+objects, but "anything." For example, we know that if one thing is
+before another, and the other before a third, then the first is before
+the third; and here the things concerned are not definite things, but
+"anything." It is hard to see how we could know such a fact about
+"before" unless we were acquainted with "before," and not merely with
+actual particular cases of one given object being before another given
+object. And more directly: A judgment such as "this is before that,"
+where this judgment is derived from awareness of a complex,
+constitutes an analysis, and we should not understand the analysis if
+we were not acquainted with the meaning of the terms employed. Thus we
+must suppose that we are acquainted with the meaning of "before," and
+not merely with instances of it.</p>
+
+<p>There are thus at least two sorts of objects of which we are aware,
+namely, particulars and universals. Among particulars I include all
+existents, and all complexes of which one or more constituents are
+existents, such as this-before-that, this-above-that,
+the-yellowness-of-this. <span class='pagenum'><a name="Page_214" id="Page_214">[214]</a></span>Among universals I include all objects of
+which no particular is a constituent. Thus the disjunction
+"universal-particular" includes all objects. We might also call it the
+disjunction "abstract-concrete." It is not quite parallel with the
+opposition "concept-percept," because things remembered or imagined
+belong with particulars, but can hardly be called percepts. (On the
+other hand, universals with which we are acquainted may be identified
+with concepts.)</p>
+
+<p>It will be seen that among the objects with which we are acquainted
+are not included physical objects (as opposed to sense-data), nor
+other people's minds. These things are known to us by what I call
+"knowledge by description," which we must now consider.</p>
+
+<p>By a "description" I mean any phrase of the form "a so-and-so" or "the
+so-and-so." A phrase of the form "a so-and-so" I shall call an
+"ambiguous" description; a phrase of the form "the so-and-so" (in the
+singular) I shall call a "definite" description. Thus "a man" is an
+ambiguous description, and "the man with the iron mask" is a definite
+description. There are various problems connected with ambiguous
+descriptions, but I pass them by, since they do not directly concern
+the matter I wish to discuss. What I wish to discuss is the nature of
+our knowledge concerning objects in cases where we know that there is
+an object answering to a definite description, though we are not
+<i>acquainted</i> with any such object. This is a matter which is concerned
+exclusively with <i>definite</i> descriptions. I shall, therefore, in the
+sequel, speak simply of "descriptions" when I mean "definite
+descriptions." Thus a description will mean any phrase of the form
+"the so-and-so" in the singular.</p>
+
+<p>I shall say that an object is "known by description" when we know that
+it is "<i>the</i> so-and-so," i.e. when we <span class='pagenum'><a name="Page_215" id="Page_215">[215]</a></span>know that there is one object,
+and no more, having a certain property; and it will generally be
+implied that we do not have knowledge of the same object by
+acquaintance. We know that the man with the iron mask existed, and
+many propositions are known about him; but we do not know who he was.
+We know that the candidate who gets most votes will be elected, and in
+this case we are very likely also acquainted (in the only sense in
+which one can be acquainted with some one else) with the man who is,
+in fact, the candidate who will get most votes, but we do not know
+which of the candidates he is, i.e. we do not know any proposition of
+the form "A is the candidate who will get most votes" where A is one
+of the candidates by name. We shall say that we have "<i>merely</i>
+descriptive knowledge" of the so-and-so when, although we know that
+the so-and-so exists, and although we may possibly be acquainted with
+the object which is, in fact, the so-and-so, yet we do not know any
+proposition "<i>a</i> is the so-and-so," where <i>a</i> is something with which
+we are acquainted.</p>
+
+<p>When we say "the so-and-so exists," we mean that there is just one
+object which is the so-and-so. The proposition "<i>a</i> is the so-and-so"
+means that <i>a</i> has the property so-and-so, and nothing else has. "Sir
+Joseph Larmor is the Unionist candidate" means "Sir Joseph Larmor is a
+Unionist candidate, and no one else is." "The Unionist candidate
+exists" means "some one is a Unionist candidate, and no one else is."
+Thus, when we are acquainted with an object which we know to be the
+so-and-so, we know that the so-and-so exists but we may know that the
+so-and-so exists when we are not acquainted with any object which we
+know to be the so-and-so, and even when we are not acquainted with any
+object which, in fact, is the so-and-so.</p>
+
+<p><span class='pagenum'><a name="Page_216" id="Page_216">[216]</a></span>Common words, even proper names, are usually really descriptions. That
+is to say, the thought in the mind of a person using a proper name
+correctly can generally only be expressed explicitly if we replace the
+proper name by a description. Moreover, the description required to
+express the thought will vary for different people, or for the same
+person at different times. The only thing constant (so long as the
+name is rightly used) is the object to which the name applies. But so
+long as this remains constant, the particular description involved
+usually makes no difference to the truth or falsehood of the
+proposition in which the name appears.</p>
+
+<p>Let us take some illustrations. Suppose some statement made about
+Bismarck. Assuming that there is such a thing as direct acquaintance
+with oneself, Bismarck himself might have used his name directly to
+designate the particular person with whom he was acquainted. In this
+case, if he made a judgment about himself, he himself might be a
+constituent of the judgment. Here the proper name has the direct use
+which it always wishes to have, as simply standing for a certain
+object, and not for a description of the object. But if a person who
+knew Bismarck made a judgment about him, the case is different. What
+this person was acquainted with were certain sense-data which he
+connected (rightly, we will suppose) with Bismarck's body. His body as
+a physical object, and still more his mind, were only known as the
+body and the mind connected with these sense-data. That is, they were
+known by description. It is, of course, very much a matter of chance
+which characteristics of a man's appearance will come into a friend's
+mind when he thinks of him; thus the description actually in the
+friend's mind is accidental. The essential point is that he knows that
+the various descriptions all apply to the <span class='pagenum'><a name="Page_217" id="Page_217">[217]</a></span>same entity, in spite of
+not being acquainted with the entity in question.</p>
+
+<p>When we, who did not know Bismarck, make a judgment about him, the
+description in our minds will probably be some more or less vague mass
+of historical knowledge&mdash;far more, in most cases, than is required to
+identify him. But, for the sake of illustration, let us assume that we
+think of him as "the first Chancellor of the German Empire." Here all
+the words are abstract except "German." The word "German" will again
+have different meanings for different people. To some it will recall
+travels in Germany, to some the look of Germany on the map, and so on.
+But if we are to obtain a description which we know to be applicable,
+we shall be compelled, at some point, to bring in a reference to a
+particular with which we are acquainted. Such reference is involved in
+any mention of past, present, and future (as opposed to definite
+dates), or of here and there, or of what others have told us. Thus it
+would seem that, in some way or other, a description known to be
+applicable to a particular must involve some reference to a particular
+with which we are acquainted, if our knowledge about the thing
+described is not to be merely what follows logically from the
+description. For example, "the most long-lived of men" is a
+description which must apply to some man, but we can make no judgments
+concerning this man which involve knowledge about him beyond what the
+description gives. If, however, we say, "the first Chancellor of the
+German Empire was an astute diplomatist," we can only be assured of
+the truth of our judgment in virtue of something with which we are
+acquainted&mdash;usually a testimony heard or read. Considered
+psychologically, apart from the information we convey to others, apart
+from the fact about the actual <span class='pagenum'><a name="Page_218" id="Page_218">[218]</a></span>Bismarck, which gives importance to
+our judgment, the thought we really have contains the one or more
+particulars involved, and otherwise consists wholly of concepts. All
+names of places&mdash;London, England, Europe, the earth, the Solar
+System&mdash;similarly involve, when used, descriptions which start from
+some one or more particulars with which we are acquainted. I suspect
+that even the Universe, as considered by metaphysics, involves such a
+connection with particulars. In logic, on the contrary, where we are
+concerned not merely with what does exist, but with whatever might or
+could exist or be, no reference to actual particulars is involved.</p>
+
+<p>It would seem that, when we make a statement about something only
+known by description, we often <i>intend</i> to make our statement, not in
+the form involving the description, but about the actual thing
+described. That is to say, when we say anything about Bismarck, we
+should like, if we could, to make the judgment which Bismarck alone
+can make, namely, the judgment of which he himself is a constituent.
+In this we are necessarily defeated, since the actual Bismarck is
+unknown to us. But we know that there is an object B called Bismarck,
+and that B was an astute diplomatist. We can thus <i>describe</i> the
+proposition we should like to affirm, namely, "B was an astute
+diplomatist," where B is the object which was Bismarck. What enables
+us to communicate in spite of the varying descriptions we employ is
+that we know there is a true proposition concerning the actual
+Bismarck, and that, however we may vary the description (so long as
+the description is correct), the proposition described is still the
+same. This proposition, which is described and is known to be true, is
+what interests us; but we are not acquainted with the proposition
+itself, and do not know <i>it</i>, though we know it is true.</p>
+
+<p><span class='pagenum'><a name="Page_219" id="Page_219">[219]</a></span>It will be seen that there are various stages in the removal from
+acquaintance with particulars: there is Bismarck to people who knew
+him, Bismarck to those who only know of him through history, the man
+with the iron mask, the longest-lived of men. These are progressively
+further removed from acquaintance with particulars, and there is a
+similar hierarchy in the region of universals. Many universals, like
+many particulars, are only known to us by description. But here, as in
+the case of particulars, knowledge concerning what is known by
+description is ultimately reducible to knowledge concerning what is
+known by acquaintance.</p>
+
+<p>The fundamental epistemological principle in the analysis of
+propositions containing descriptions is this: <i>Every proposition which
+we can understand must be composed wholly of constituents with which
+we are acquainted.</i> From what has been said already, it will be plain
+why I advocate this principle, and how I propose to meet the case of
+propositions which at first sight contravene it. Let us begin with the
+reasons for supposing the principle true.</p>
+
+<p>The chief reason for supposing the principle true is that it seems
+scarcely possible to believe that we can make a judgment or entertain
+a supposition without knowing what it is that we are judging or
+supposing about. If we make a judgment about (say) Julius C&aelig;sar, it is
+plain that the actual person who was Julius C&aelig;sar is not a constituent
+of the judgment. But before going further, it may be well to explain
+what I mean when I say that this or that is a constituent of a
+judgment, or of a proposition which we understand. To begin with
+judgments: a judgment, as an occurrence, I take to be a relation of a
+mind to several entities, namely, the entities which compose what is
+judged. If, e.g. I judge <span class='pagenum'><a name="Page_220" id="Page_220">[220]</a></span>that A loves B, the judgment as an event
+consists in the existence, at a certain moment, of a specific
+four-term relation, called <i>judging</i>, between me and A and love and B.
+That is to say, at the time when I judge, there is a certain complex
+whose terms are myself and A and love and B, and whose relating
+relation is <i>judging</i>. My reasons for this view have been set forth
+elsewhere,<a name="FNanchor_41_41" id="FNanchor_41_41"></a><a href="#Footnote_41_41" class="fnanchor">[41]</a> and I shall not repeat them here. Assuming this view of
+judgment, the constituents of the judgment are simply the constituents
+of the complex which is the judgment. Thus, in the above case, the
+constituents are myself and A and love and B and judging. But myself
+and judging are constituents shared by all my judgments; thus the
+<i>distinctive</i> constituents of the particular judgment in question are
+A and love and B. Coming now to what is meant by "understanding a
+proposition," I should say that there is another relation possible
+between me and A and love and B, which is called my <i>supposing</i> that A
+loves B.<a name="FNanchor_42_42" id="FNanchor_42_42"></a><a href="#Footnote_42_42" class="fnanchor">[42]</a> When we can <i>suppose</i> that A loves B, we "understand the
+proposition" <i>A loves B</i>. Thus we often understand a proposition in
+cases where we have not enough knowledge to make a judgment.
+Supposing, like judging, is a many-term relation, of which a mind is
+one term. The other terms of the relation are called the constituents
+of the proposition supposed. Thus the principle which I enunciated may
+be re-stated as follows: <i>Whenever a <span class='pagenum'><a name="Page_221" id="Page_221">[221]</a></span>relation of supposing or judging
+occurs, the terms to which the supposing or judging mind is related by
+the relation of supposing or judging must be terms with which the mind
+in question is acquainted.</i> This is merely to say that we cannot make
+a judgment or a supposition without knowing what it is that we are
+making our judgment or supposition about. It seems to me that the
+truth of this principle is evident as soon as the principle is
+understood; I shall, therefore, in what follows, assume the principle,
+and use it as a guide in analysing judgments that contain
+descriptions.</p>
+
+<p>Returning now to Julius C&aelig;sar, I assume that it will be admitted that
+he himself is not a constituent of any judgment which I can make. But
+at this point it is necessary to examine the view that judgments are
+composed of something called "ideas," and that it is the "idea" of
+Julius C&aelig;sar that is a constituent of my judgment. I believe the
+plausibility of this view rests upon a failure to form a right theory
+of descriptions. We may mean by my "idea" of Julius C&aelig;sar the things
+that I know about him, e.g. that he conquered Gaul, was assassinated
+on the Ides of March, and is a plague to schoolboys. Now I am
+admitting, and indeed contending, that in order to discover what is
+actually in my mind when I judge about Julius C&aelig;sar, we must
+substitute for the proper name a description made up of some of the
+things I know about him. (A description which will often serve to
+express my thought is "the man whose name was <i>Julius C&aelig;sar</i>." For
+whatever else I may have forgotten about him, it is plain that when I
+mention him I have not forgotten that that was his name.) But although
+I think the theory that judgments consist of ideas may have been
+suggested in some such way, yet I think the theory itself is
+fundamentally mistaken. The <span class='pagenum'><a name="Page_222" id="Page_222">[222]</a></span>view seems to be that there is some
+mental existent which may be called the "idea" of something outside
+the mind of the person who has the idea, and that, since judgment is a
+mental event, its constituents must be constituents of the mind of the
+person judging. But in this view ideas become a veil between us and
+outside things&mdash;we never really, in knowledge, attain to the things we
+are supposed to be knowing about, but only to the ideas of those
+things. The relation of mind, idea, and object, on this view, is
+utterly obscure, and, so far as I can see, nothing discoverable by
+inspection warrants the intrusion of the idea between the mind and the
+object. I suspect that the view is fostered by the dislike of
+relations, and that it is felt the mind could not know objects unless
+there were something "in" the mind which could be called the state of
+knowing the object. Such a view, however, leads at once to a vicious
+endless regress, since the relation of idea to object will have to be
+explained by supposing that the idea itself has an idea of the object,
+and so on <i>ad infinitum</i>. I therefore see no reason to believe that,
+when we are acquainted with an object, there is in us something which
+can be called the "idea" of the object. On the contrary, I hold that
+acquaintance is wholly a relation, not demanding any such constituent
+of the mind as is supposed by advocates of "ideas." This is, of
+course, a large question, and one which would take us far from our
+subject if it were adequately discussed. I therefore content myself
+with the above indications, and with the corollary that, in judging,
+the actual objects concerning which we judge, rather than any supposed
+purely mental entities, are constituents of the complex which is the
+judgment.</p>
+
+<p>When, therefore, I say that we must substitute for "Julius C&aelig;sar" some
+description of Julius C&aelig;sar, in order <span class='pagenum'><a name="Page_223" id="Page_223">[223]</a></span>to discover the meaning of a
+judgment nominally about him, I am not saying that we must substitute
+an idea. Suppose our description is "the man whose name was <i>Julius
+C&aelig;sar</i>." Let our judgment be "Julius C&aelig;sar was assassinated." Then it
+becomes "the man whose name was <i>Julius C&aelig;sar</i> was assassinated." Here
+<i>Julius C&aelig;sar</i> is a noise or shape with which we are acquainted, and
+all the other constituents of the judgment (neglecting the tense in
+"was") are <i>concepts</i> with which we are acquainted. Thus our judgment
+is wholly reduced to constituents with which we are acquainted, but
+Julius C&aelig;sar himself has ceased to be a constituent of our judgment.
+This, however, requires a proviso, to be further explained shortly,
+namely that "the man whose name was <i>Julius C&aelig;sar</i>" must not, as a
+whole, be a constituent of our judgment, that is to say, this phrase
+must not, as a whole, have a meaning which enters into the judgment.
+Any right analysis of the judgment, therefore, must break up this
+phrase, and not treat it as a subordinate complex which is part of the
+judgment. The judgment "the man whose name was <i>Julius C&aelig;sar</i> was
+assassinated" may be interpreted as meaning "one and only one man was
+called <i>Julius C&aelig;sar</i>, and that one was assassinated." Here it is
+plain that there is no constituent corresponding to the phrase "the
+man whose name was <i>Julius C&aelig;sar</i>." Thus there is no reason to regard
+this phrase as expressing a constituent of the judgment, and we have
+seen that this phrase must be broken up if we are to be acquainted
+with all the constituents of the judgment. This conclusion, which we
+have reached from considerations concerned with the theory of
+knowledge, is also forced upon us by logical considerations, which
+must now be briefly reviewed.</p>
+
+<p>It is common to distinguish two aspects, <i>meaning</i> and <span class='pagenum'><a name="Page_224" id="Page_224">[224]</a></span><i>denotation</i>,
+such phrases as "the author of Waverley." The meaning will be a
+certain complex, consisting (at least) of authorship and Waverley with
+some relation; the denotation will be Scott. Similarly "featherless
+bipeds" will have a complex meaning, containing as constituents the
+presence of two feet and the absence of feathers, while its denotation
+will be the class of men. Thus when we say "Scott is the author of
+Waverley" or "men are the same as featherless bipeds," we are
+asserting an identity of denotation, and this assertion is worth
+making because of the diversity of meaning.<a name="FNanchor_43_43" id="FNanchor_43_43"></a><a href="#Footnote_43_43" class="fnanchor">[43]</a> I believe that the
+duality of meaning and denotation, though capable of a true
+interpretation, is misleading if taken as fundamental. The denotation,
+I believe, is not a constituent of the proposition, except in the case
+of proper names, i.e. of words which do not assign a property to an
+object, but merely and solely name it. And I should hold further that,
+in this sense, there are only two words which are strictly proper
+names of particulars, namely, "I" and "this."<a name="FNanchor_44_44" id="FNanchor_44_44"></a><a href="#Footnote_44_44" class="fnanchor">[44]</a></p>
+
+<p>One reason for not believing the denotation to be a constituent of the
+proposition is that we may know the proposition even when we are not
+acquainted with the denotation. The proposition "the author of
+Waverley is a novelist" was known to people who did not know that "the
+author of Waverley" denoted Scott. This reason has been already
+sufficiently emphasised.</p>
+
+<p>A second reason is that propositions concerning "the so-and-so" are
+possible even when "the so-and-so" has no denotation. Take, e.g. "the
+golden mountain does not exist" or "the round square is
+self-contradictory." <span class='pagenum'><a name="Page_225" id="Page_225">[225]</a></span>If we are to preserve the duality of meaning and
+denotation, we have to say, with Meinong, that there are such objects
+as the golden mountain and the round square, although these objects do
+not have being. We even have to admit that the existent round square
+is existent, but does not exist.<a name="FNanchor_45_45" id="FNanchor_45_45"></a><a href="#Footnote_45_45" class="fnanchor">[45]</a> Meinong does not regard this as a
+contradiction, but I fail to see that it is not one. Indeed, it seems
+to me evident that the judgment "there is no such object as the round
+square" does not presuppose that there is such an object. If this is
+admitted, however, we are led to the conclusion that, by parity of
+form, no judgment concerning "the so-and-so" actually involves the
+so-and-so as a constituent.</p>
+
+<p>Miss Jones<a name="FNanchor_46_46" id="FNanchor_46_46"></a><a href="#Footnote_46_46" class="fnanchor">[46]</a> contends that there is no difficulty in admitting
+contradictory predicates concerning such an object as "the present
+King of France," on the ground that this object is in itself
+contradictory. Now it might, of course, be argued that this object,
+unlike the round square, is not self-contradictory, but merely
+non-existent. This, however, would not go to the root of the matter.
+The real objection to such an argument is that the law of
+contradiction ought not to be stated in the traditional form "A is not
+both B and not B," but in the form "no proposition is both true and
+false." The traditional form only applies to certain propositions,
+namely, to those which attribute a predicate to a subject. When the
+law is stated of propositions, instead of being stated concerning
+subjects and predicates, it is at once evident that propositions about
+the present King of France or the round square can form no exception,
+but are just as incapable of being both true and false as other
+propositions. Miss Jones<a name="FNanchor_47_47" id="FNanchor_47_47"></a><a href="#Footnote_47_47" class="fnanchor">[47]</a> argues that "Scott is the author of
+<span class='pagenum'><a name="Page_226" id="Page_226">[226]</a></span>Waverley" asserts identity of denotation between <i>Scott</i> and <i>the
+author of Waverley</i>. But there is some difficulty in choosing among
+alternative meanings of this contention. In the first place, it should
+be observed that <i>the author of Waverley</i> is not a <i>mere</i> name, like
+<i>Scott</i>. <i>Scott</i> is merely a noise or shape conventionally used to
+designate a certain person; it gives us no information about that
+person, and has nothing that can be called meaning as opposed to
+denotation. (I neglect the fact, considered above, that even proper
+names, as a rule, really stand for descriptions.) But <i>the author of
+Waverley</i> is not merely conventionally a name for Scott; the element
+of mere convention belongs here to the separate words, <i>the</i> and
+<i>author</i> and <i>of</i> and <i>Waverley</i>. Given what these words stand for,
+<i>the author of Waverley</i> is no longer arbitrary. When it is said that
+Scott is the author of Waverley, we are not stating that these are two
+<i>names</i> for one man, as we should be if we said "Scott is Sir Walter."
+A man's name is what he is called, but however much Scott had been
+called the author of Waverley, that would not have made him be the
+author; it was necessary for him actually to write Waverley, which was
+a fact having nothing to do with names.</p>
+
+<p>If, then, we are asserting identity of denotation, we must not mean by
+<i>denotation</i> the mere relation of a name to the thing named. In fact,
+it would be nearer to the truth to say that the <i>meaning</i> of "Scott"
+is the <i>denotation</i> of "the author of Waverley." The relation of
+"Scott" to Scott is that "Scott" means Scott, just as the relation of
+"author" to the concept which is so called is that "author" means this
+concept. Thus if we distinguish meaning and denotation in "the author
+of Waverley," we shall have to say that "Scott" has meaning but not
+denotation. Also when we say "Scott is the <span class='pagenum'><a name="Page_227" id="Page_227">[227]</a></span>author of Waverley," the
+<i>meaning</i> of "the author of Waverley" is relevant to our assertion.
+For if the denotation alone were relevant, any other phrase with the
+same denotation would give the same proposition. Thus "Scott is the
+author of Marmion" would be the same proposition as "Scott is the
+author of Waverley." But this is plainly not the case, since from the
+first we learn that Scott wrote Marmion and from the second we learn
+that he wrote Waverley, but the first tells us nothing about Waverley
+and the second nothing about Marmion. Hence the meaning of "the author
+of Waverley," as opposed to the denotation, is certainly relevant to
+"Scott is the author of Waverley."</p>
+
+<p>We have thus agreed that "the author of Waverley" is not a mere name,
+and that its meaning is relevant in propositions in which it occurs.
+Thus if we are to say, as Miss Jones does, that "Scott is the author
+of Waverley" asserts an identity of denotation, we must regard the
+denotation of "the author of Waverley" as the denotation of what is
+<i>meant</i> by "the author of Waverley." Let us call the meaning of "the
+author of Waverley" M. Thus M is what "the author of Waverley" means.
+Then we are to suppose that "Scott is the author of Waverley" means
+"Scott is the denotation of M." But here we are explaining our
+proposition by another of the same form, and thus we have made no
+progress towards a real explanation. "The denotation of M," like "the
+author of Waverley," has both meaning and denotation, on the theory we
+are examining. If we call its meaning M', our proposition becomes
+"Scott is the denotation of M'." But this leads at once to an endless
+regress. Thus the attempt to regard our proposition as asserting
+identity of denotation breaks down, and it becomes imperative to find
+some other analysis. When this analysis has been <span class='pagenum'><a name="Page_228" id="Page_228">[228]</a></span>completed, we shall
+be able to reinterpret the phrase "identity of denotation," which
+remains obscure so long as it is taken as fundamental.</p>
+
+<p>The first point to observe is that, in any proposition about "the
+author of Waverley," provided Scott is not explicitly mentioned, the
+denotation itself, i.e. Scott, does not occur, but only the concept of
+denotation, which will be represented by a variable. Suppose we say
+"the author of Waverley was the author of Marmion," we are certainly
+not saying that both were Scott&mdash;we may have forgotten that there was
+such a person as Scott. We are saying that there is some man who was
+the author of Waverley and the author of Marmion. That is to say,
+there is some one who wrote Waverley and Marmion, and no one else
+wrote them. Thus the identity is that of a variable, i.e. of an
+indefinite subject, "some one." This is why we can understand
+propositions about "the author of Waverley," without knowing who he
+was. When we say "the author of Waverley was a poet," we mean "one and
+only one man wrote Waverley, and he was a poet"; when we say "the
+author of Waverley was Scott" we mean "one and only one man wrote
+Waverley, and he was Scott." Here the identity is between a variable,
+i.e. an indeterminate subject ("he"), and Scott; "the author of
+Waverley" has been analysed away, and no longer appears as a
+constituent of the proposition.<a name="FNanchor_48_48" id="FNanchor_48_48"></a><a href="#Footnote_48_48" class="fnanchor">[48]</a></p>
+
+<p>The reason why it is imperative to analyse away the phrase "the author
+of Waverley" may be stated as follows. It is plain that when we say
+"the author of Waverley is the author of Marmion," the <i>is</i> expresses
+<span class='pagenum'><a name="Page_229" id="Page_229">[229]</a></span>identity. We have seen also that the common <i>denotation</i>, namely
+Scott, is not a constituent of this proposition, while the <i>meanings</i>
+(if any) of "the author of Waverley" and "the author of Marmion" are
+not identical. We have seen also that, in any sense in which the
+meaning of a word is a constituent of a proposition in whose verbal
+expression the word occurs, "Scott" means the actual man Scott, in the
+same sense (so far as concerns our present discussion) in which
+"author" means a certain universal. Thus, if "the author of Waverley"
+were a subordinate complex in the above proposition, its <i>meaning</i>
+would have to be what was said to be identical with the <i>meaning</i> of
+"the author of Marmion." This is plainly not the case; and the only
+escape is to say that "the author of Waverley" does not, by itself,
+have a meaning, though phrases of which it is part do have a meaning.
+That is, in a right analysis of the above proposition, "the author of
+Waverley" must disappear. This is effected when the above proposition
+is analysed as meaning: "Some one wrote Waverley and no one else did,
+and that some one also wrote Marmion and no one else did." This may be
+more simply expressed by saying that the propositional function "<i>x</i>
+wrote Waverley and Marmion, and no one else did" is capable of truth,
+i.e. some value of <i>x</i> makes it true, but no other value does. Thus
+the true subject of our judgment is a propositional function, i.e. a
+complex containing an undetermined constituent, and becoming a
+proposition as soon as this constituent is determined.</p>
+
+<p>We may now define the denotation of a phrase. If we know that the
+proposition "<i>a</i> is the so-and-so" is true, i.e. that <i>a</i> is so-and-so
+and nothing else is, we call <i>a</i> the denotation of the phrase "the
+so-and-so." A very great many of the propositions we naturally make
+about "the <span class='pagenum'><a name="Page_230" id="Page_230">[230]</a></span>so-and-so" will remain true or remain false if we
+substitute <i>a</i> for "the so-and-so," where <i>a</i> is the denotation of
+"the so-and-so." Such propositions will also remain true or remain
+false if we substitute for "the so-and-so" any other phrase having the
+same denotation. Hence, as practical men, we become interested in the
+denotation more than in the description, since the denotation decides
+as to the truth or falsehood of so many statements in which the
+description occurs. Moreover, as we saw earlier in considering the
+relations of description and acquaintance, we often wish to reach the
+denotation, and are only hindered by lack of acquaintance: in such
+cases the description is merely the means we employ to get as near as
+possible to the denotation. Hence it naturally comes to be supposed
+that the denotation is part of the proposition in which the
+description occurs. But we have seen, both on logical and on
+epistemological grounds, that this is an error. The actual object (if
+any) which is the denotation is not (unless it is explicitly
+mentioned) a constituent of propositions in which descriptions occur;
+and this is the reason why, in order to understand such propositions,
+we need acquaintance with the constituents of the description, but do
+not need acquaintance with its denotation. The first result of
+analysis, when applied to propositions whose grammatical subject is
+"the so-and-so," is to substitute a variable as subject; i.e. we
+obtain a proposition of the form: "There is <i>something</i> which alone is
+so-and-so, and that <i>something</i> is such-and-such." The further
+analysis of propositions concerning "the so-and-so" is thus merged in
+the problem of the nature of the variable, i.e. of the meanings of
+<i>some</i>, <i>any</i>, and <i>all</i>. This is a difficult problem, concerning
+which I do not intend to say anything at present.</p>
+
+<p>To sum up our whole discussion. We began by <span class='pagenum'><a name="Page_231" id="Page_231">[231]</a></span>distinguishing two sorts
+of knowledge of objects, namely, knowledge by <i>acquaintance</i> and
+knowledge by <i>description</i>. Of these it is only the former that brings
+the object itself before the mind. We have acquaintance with
+sense-data, with many universals, and possibly with ourselves, but not
+with physical objects or other minds. We have <i>descriptive</i> knowledge
+of an object when we know that it is <i>the</i> object having some property
+or properties with which we are acquainted; that is to say, when we
+know that the property or properties in question belong to one object
+and no more, we are said to have knowledge of that one object by
+description, whether or not we are acquainted with the object. Our
+knowledge of physical objects and of other minds is only knowledge by
+description, the descriptions involved being usually such as involve
+sense-data. All propositions intelligible to us, whether or not they
+primarily concern things only known to us by description, are composed
+wholly of constituents with which we are acquainted, for a constituent
+with which we are not acquainted is unintelligible to us. A judgment,
+we found, is not composed of mental constituents called "ideas," but
+consists of an occurrence whose constituents are a mind<a name="FNanchor_49_49" id="FNanchor_49_49"></a><a href="#Footnote_49_49" class="fnanchor">[49]</a> and
+certain objects, particulars or universals. (One at least must be a
+universal.) When a judgment is rightly analysed, the objects which are
+constituents of it must all be objects with which the mind which is a
+constituent of it is acquainted. This conclusion forces us to analyse
+descriptive phrases occurring in propositions, and to say that the
+objects denoted by such phrases are not constituents of judgments in
+which such phrases occur (unless these objects are explicitly
+<span class='pagenum'><a name="Page_232" id="Page_232">[232]</a></span>mentioned). This leads us to the view (recommended also on purely
+logical grounds) that when we say "the author of Marmion was the
+author of Waverley," Scott himself is not a constituent of our
+judgment, and that the judgment cannot be explained by saying that it
+affirms identity of denotation with diversity of meaning. It also,
+plainly, does not assert identity of meaning. Such judgments,
+therefore, can only be analysed by breaking up the descriptive
+phrases, introducing a variable, and making propositional functions
+the ultimate subjects. In fact, "the so-and-so is such-and-such" will
+mean that "<i>x</i> is so-and-so and nothing else is, and <i>x</i> is
+such-and-such" is capable of truth. The analysis of such judgments
+involves many fresh problems, but the discussion of these problems is
+not undertaken in the present paper.</p>
+
+<br />
+<hr style="width: 15%;" />
+<br />
+
+<h4>FOOTNOTES:</h4>
+
+<div class="footnote"><p class="noin"><a name="Footnote_40_40" id="Footnote_40_40"></a><a href="#FNanchor_40_40"><span class="label">[40]</span></a> See references later.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_41_41" id="Footnote_41_41"></a><a href="#FNanchor_41_41"><span class="label">[41]</span></a> <i>Philosophical Essays</i>, "The Nature of Truth." I have
+been persuaded by Mr. Wittgenstein that this theory is somewhat unduly
+simple, but the modification which I believe it to require does not
+affect the above argument [1917].</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_42_42" id="Footnote_42_42"></a><a href="#FNanchor_42_42"><span class="label">[42]</span></a> Cf. Meinong, <i>Ueber Annahmen</i>, <i>passim</i>. I formerly
+supposed, contrary to Meinong's view, that the relationship of
+supposing might be merely that of presentation. In this view I now
+think I was mistaken, and Meinong is right. But my present view
+depends upon the theory that both in judgment and in assumption there
+is no single Objective, but the several constituents of the judgment
+or assumption are in a many-term relation to the mind.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_43_43" id="Footnote_43_43"></a><a href="#FNanchor_43_43"><span class="label">[43]</span></a> This view has been recently advocated by Miss E.E.C.
+Jones. "A New Law of Thought and its Implications," <i>Mind</i>, January,
+1911.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_44_44" id="Footnote_44_44"></a><a href="#FNanchor_44_44"><span class="label">[44]</span></a> I should now exclude "I" from proper names in the strict
+sense, and retain only "this" [1917].</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_45_45" id="Footnote_45_45"></a><a href="#FNanchor_45_45"><span class="label">[45]</span></a> Meinong, <i>Ueber Annahmen</i>, 2nd ed., Leipzig, 1910, p.
+141.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_46_46" id="Footnote_46_46"></a><a href="#FNanchor_46_46"><span class="label">[46]</span></a> <i>Mind</i>, July, 1910, p. 380.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_47_47" id="Footnote_47_47"></a><a href="#FNanchor_47_47"><span class="label">[47]</span></a> <i>Mind</i>, July, 1910, p. 379.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_48_48" id="Footnote_48_48"></a><a href="#FNanchor_48_48"><span class="label">[48]</span></a> The theory which I am advocating is set forth fully,
+with the logical grounds in its favour, in <i>Principia Mathematica</i>,
+Vol. I. Introduction, Chap. III; also, less fully, in <i>Mind</i>, October,
+1905.</p></div>
+
+<div class="footnote"><p class="noin"><a name="Footnote_49_49" id="Footnote_49_49"></a><a href="#FNanchor_49_49"><span class="label">[49]</span></a> I use this phrase merely to denote the something
+psychological which enters into judgment, without intending to
+prejudge the question as to what this something is.</p></div>
+
+<br />
+<br />
+<br />
+<br />
+<a name="INDEX" id="INDEX"></a><hr />
+<span class='pagenum'><a name="Page_233" id="Page_233">[233]</a></span><br />
+
+<h3>INDEX<span class="totoc"><a href="#toc">ToC</a></span></h3>
+<br />
+
+<ul><li>Achilles and the tortoise, <a href="#Page_80">80 ff</a>, <a href="#Page_89">89 ff</a></li>
+
+<li>Acquaintance, the relation of, <a href="#Page_209">209 ff</a></li>
+
+<li>Alexander, <a href="#Page_125">125</a></li>
+
+<li>American Realists, the, <a href="#Page_134">134</a></li>
+
+<li>Aristotle, <a href="#Page_42">42</a>, <a href="#Page_76">76</a>, <a href="#Page_97">97</a><br /><br /></li>
+
+
+<li>Bacon, <a href="#Page_41">41</a></li>
+
+<li>Bergson, <a href="#Page_14">14 ff</a>, <a href="#Page_22">22</a>, <a href="#Page_105">105</a>, <a href="#Page_128">128</a>, <a href="#Page_185">185 ff</a>, <a href="#Page_203">203</a></li>
+
+<li>Berkeley, <a href="#Page_97">97</a>, <a href="#Page_132">132</a></li>
+
+<li>Blake, <a href="#Page_1">1</a></li>
+
+<li>Bosanquet, <a href="#Page_99">99</a></li>
+
+<li>Broad, <a href="#Page_89">89 <i>n</i></a><br /><br /></li>
+
+
+<li>Calculus, the, <a href="#Page_82">82</a></li>
+
+<li>Cantor, Georg, <a href="#Page_64">64</a>, <a href="#Page_81">81 ff</a>, <a href="#Page_85">85</a>, <a href="#Page_91">91</a></li>
+
+<li>Carlyle, <a href="#Page_50">50</a>, <a href="#Page_82">82</a></li>
+
+<li>Cause, the conception of, <a href="#Page_135">135 <i>n</i></a>, <a href="#Page_180">180 ff</a></li>
+
+<li>Christianity and renunciation, <a href="#Page_51">51</a></li>
+
+<li>Chuang Tz&#365;, <a href="#Page_106">106</a></li>
+
+<li>Construction of permanent things and matter, <a href="#Page_169">169 ff</a></li>
+
+<li>Constructions, logical, <a href="#Page_155">155 ff</a><br /><br /></li>
+
+
+<li>Darwin, <a href="#Page_15">15</a>, <a href="#Page_23">23</a>, <a href="#Page_43">43</a></li>
+
+<li>Dedekind, <a href="#Page_64">64</a>, <a href="#Page_81">81 ff</a>, <a href="#Page_85">85</a></li>
+
+<li>Descartes, <a href="#Page_97">97</a>, <a href="#Page_126">126</a></li>
+
+<li>Descriptions, <a href="#Page_175">175</a>, <a href="#Page_214">214 ff</a><br /><br /></li>
+
+
+<li>Education, <a href="#Page_37">37 ff</a></li>
+
+<li>Euclid, <a href="#Page_62">62</a>, <a href="#Page_92">92</a>, <a href="#Page_94">94</a></li>
+
+<li>Evolutionism, <a href="#Page_23">23 ff</a>, <a href="#Page_28">28</a><br /><br /></li>
+
+
+<li>Fano, <a href="#Page_93">93</a></li>
+
+<li>Faraday, <a href="#Page_34">34</a></li>
+
+<li>Free will, <a href="#Page_205">205 ff</a></li>
+
+<li>Frege, <a href="#Page_78">78 <i>n</i></a><br /><br /></li>
+
+
+<li>Galileo, <a href="#Page_42">42</a></li>
+
+<li>Gladstone, <a href="#Page_177">177</a></li>
+
+<li>Good and evil, <a href="#Page_26">26 ff</a><br /><br /></li>
+
+
+<li>Hegel, <a href="#Page_8">8</a>, <a href="#Page_10">10</a>, <a href="#Page_18">18</a>, <a href="#Page_85">85</a>, <a href="#Page_97">97</a>, <a href="#Page_105">105 ff</a></li>
+
+<li>Heine, <a href="#Page_113">113</a></li>
+
+<li>Heraclitus, <a href="#Page_1">1 ff</a>, <a href="#Page_10">10</a></li>
+
+<li>Hertz, <a href="#Page_34">34</a></li>
+
+<li>Holt, <a href="#Page_177">177 <i>n</i></a></li>
+
+<li>Hume, <a href="#Page_1">1</a>, <a href="#Page_97">97</a><br /><br /></li>
+
+
+<li>Infinite, the mathematical, <a href="#Page_84">84 ff</a><br /><br /></li>
+
+
+<li>James, William, <a href="#Page_100">100</a></li>
+
+<li>Jones, Miss E.E.C., <a href="#Page_224">224 <i>n</i></a>, <a href="#Page_225">225</a></li>
+
+<li>Judgment, <a href="#Page_219">219 ff</a><br /><br /></li>
+
+
+<li>Kant, <a href="#Page_85">85</a>, <a href="#Page_96">96</a>, <a href="#Page_97">97</a>, <a href="#Page_99">99</a>, <a href="#Page_118">118 ff</a></li>
+
+<li>Knowledge by acquaintance, <a href="#Page_209">209 ff</a>;
+  <ul class="nest">
+  <li>by description, <a href="#Page_214">214 ff</a></li>
+  </ul>
+<br /></li>
+
+
+<li>Laplace, <a href="#Page_23">23</a></li>
+
+<li>Leibniz, <a href="#Page_76">76</a>, <a href="#Page_79">79</a>, <a href="#Page_82">82 ff</a>, <a href="#Page_97">97</a>, <a href="#Page_126">126</a>, <a href="#Page_144">144</a>, <a href="#Page_160">160</a></li>
+
+<li>Locke, <a href="#Page_97">97</a></li>
+
+<li>Logic, the laws of, <a href="#Page_68">68 ff</a><br /><br /></li>
+
+
+<li>Macaulay and Taylor's theorem, <a href="#Page_95">95</a></li>
+
+<li>Malthus, <a href="#Page_43">43</a></li>
+
+<li>Mathematics, <a href="#Page_58">58 ff</a>;
+  <ul class="nest">
+  <li>and the Metaphysicians, <a href="#Page_74">74 ff</a>;</li>
+  <li>and logic, <a href="#Page_75">75 ff</a>;</li>
+  <li>and the infinitesimal, <a href="#Page_82">82 ff</a></li>
+  </ul>
+</li>
+
+<li>Matter, the nature of, <a href="#Page_125">125 ff</a>;
+  <ul class="nest">
+  <li>definition of, <a href="#Page_164">164 ff</a></li>
+  </ul>
+</li>
+
+<li>Maxwell, <a href="#Page_34">34</a></li>
+
+<li>Meaning and denotation, <a href="#Page_223">223 ff</a></li>
+
+<li>Meinong, <a href="#Page_174">174</a>, <a href="#Page_220">220 <i>n</i></a>, <a href="#Page_225">225</a></li>
+
+<li>Militarism, <a href="#Page_50">50</a></li>
+
+<li>Mill, <a href="#Page_185">185</a>, <a href="#Page_193">193 ff</a></li>
+
+<li>Mysticism and logic, <a href="#Page_1">1 ff</a><br /><br /></li>
+
+
+<li>Necessity, the notion of, <a href="#Page_207">207 ff</a><span class='pagenum'><a name="Page_234" id="Page_234">[234]</a></span></li>
+
+<li>Nietzsche, <a href="#Page_22">22</a>, <a href="#Page_50">50</a></li>
+
+<li>Nunn, <a href="#Page_125">125</a>, <a href="#Page_137">137 <i>n</i></a>, <a href="#Page_153">153</a><br /><br /></li>
+
+
+<li>Parmenides, <a href="#Page_7">7 ff</a>, <a href="#Page_18">18</a>, <a href="#Page_21">21</a></li>
+
+<li>Particulars, awareness of, <a href="#Page_210">210 ff</a></li>
+
+<li>Peano, <a href="#Page_78">78 ff</a>, <a href="#Page_93">93 ff</a></li>
+
+<li>Perspectives, <a href="#Page_139">139 ff</a>;
+  <ul class="nest">
+  <li>the space of, <a href="#Page_158">158 ff</a></li>
+  </ul>
+</li>
+
+<li>Philosophy and logic, <a href="#Page_111">111</a></li>
+
+<li>Physics, sense-data and, <a href="#Page_145">145 ff</a></li>
+
+<li>Pierce, <a href="#Page_76">76 <i>n</i></a></li>
+
+<li>Plato, <a href="#Page_1">1 ff</a>, <a href="#Page_10">10</a>, <a href="#Page_30">30</a>, <a href="#Page_60">60</a>, <a href="#Page_97">97</a></li>
+
+<li>Pragmatism, <a href="#Page_22">22</a>, <a href="#Page_105">105</a><br /><br /></li>
+
+
+<li>Realism and the analytic method, <a href="#Page_120">120 ff</a></li>
+
+<li>Reason and intuition, <a href="#Page_12">12 ff</a></li>
+
+<li>Relatives, the logic of, <a href="#Page_76">76</a></li>
+
+<li>Robb, <a href="#Page_167">167 <i>n</i></a><br /><br /></li>
+
+
+<li>Santayana, <a href="#Page_20">20</a></li>
+
+<li>Sense-data, <a href="#Page_147">147</a>, <a href="#Page_210">210 ff</a>;
+  <ul class="nest">
+  <li>and physics, <a href="#Page_145">145 ff</a></li>
+  </ul>
+</li>
+
+<li>Sensibilia, <a href="#Page_148">148 ff</a></li>
+
+<li>Space, <a href="#Page_138">138 ff</a>;
+  <ul class="nest">
+  <li>private, <a href="#Page_158">158 ff</a>;</li>
+  <li>the logical problem, <a href="#Page_114">114 ff</a>;</li>
+  <li>the problem in physics, <a href="#Page_115">115 ff</a>;</li>
+  <li>the epistemological problem, <a href="#Page_118">118 ff</a></li>
+  </ul>
+</li>
+
+<li>Systems, deterministic, <a href="#Page_199">199</a>;
+  <ul class="nest">
+  <li>practically isolated, <a href="#Page_198">198</a>;</li>
+  <li>relatively isolated, <a href="#Page_197">197</a>;</li>
+  <li>mechanical, <a href="#Page_201">201</a></li>
+  </ul>
+<br /></li>
+
+
+<li>Time, <a href="#Page_10">10</a>, <a href="#Page_21">21 ff</a>, <a href="#Page_141">141 ff</a>, <a href="#Page_167">167 ff</a></li>
+
+<li>Tristram Shandy, the paradox of, <a href="#Page_90">90 ff</a><br /><br /></li>
+
+
+<li>Unity and Plurality, <a href="#Page_18">18 ff</a></li>
+
+<li>Universals, awareness of, <a href="#Page_212">212 ff</a><br /><br /></li>
+
+
+<li>Ward, <a href="#Page_180">180</a></li>
+
+<li>Weierstrass, <a href="#Page_80">80</a>, <a href="#Page_82">82</a>, <a href="#Page_95">95</a></li>
+
+<li>Whitehead, <a href="#Page_117">117</a>, <a href="#Page_157">157</a>, <a href="#Page_175">175</a></li>
+
+<li>Wolf, <a href="#Page_173">173</a><br /><br /></li>
+
+
+<li>Zeno the Eleatic, <a href="#Page_64">64</a>, <a href="#Page_80">80</a>, <a href="#Page_84">84</a>, <a href="#Page_89">89 ff</a></li>
+</ul>
+
+<br />
+<hr />
+<br />
+<br />
+<br />
+<br />
+
+<div class="img">
+<img border="0" src="images/deco.png" width="15%" alt="Publisher's mark" />
+</div>
+
+<h4>GEORGE ALLEN &amp; UNWIN LTD</h4>
+
+<h4><i>London: 40 Museum Street, W.C. 1</i></h4>
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+<hr />
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+<div class="tr">
+<p class="cen"><a name="TN" id="TN"></a>Typographical errors corrected in text:</p>
+<br />
+Page 111: &nbsp;charateristic replaced with characteristic<br />
+Page &nbsp;&nbsp;71: &nbsp;inexpugnable replaced with inexpungable<br />
+</div>
+
+<br />
+<hr />
+<br />
+
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
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diff --git a/LICENSE.txt b/LICENSE.txt
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+This eBook, including all associated images, markup, improvements,
+metadata, and any other content or labor, has been confirmed to be
+in the PUBLIC DOMAIN IN THE UNITED STATES.
+
+Procedures for determining public domain status are described in
+the "Copyright How-To" at https://www.gutenberg.org.
+
+No investigation has been made concerning possible copyrights in
+jurisdictions other than the United States. Anyone seeking to utilize
+this eBook outside of the United States should confirm copyright
+status under the laws that apply to them.
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+Project Gutenberg (https://www.gutenberg.org) public repository for
+eBook #25447 (https://www.gutenberg.org/ebooks/25447)