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| author | Roger Frank <rfrank@pglaf.org> | 2025-10-15 04:53:20 -0700 |
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| committer | Roger Frank <rfrank@pglaf.org> | 2025-10-15 04:53:20 -0700 |
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diff --git a/18440-h/18440-h.htm b/18440-h/18440-h.htm new file mode 100644 index 0000000..23559ee --- /dev/null +++ b/18440-h/18440-h.htm @@ -0,0 +1,14939 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" + "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> + +<html xmlns="http://www.w3.org/1999/xhtml"> + <head> + <meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1" /> + <title> + The Project Gutenberg eBook of Logic, by Carveth Read, M.A. + </title> + <style type="text/css"> +/*<![CDATA[ XML blockout */ +<!-- + p { margin-top: .75em; + text-align: justify; + margin-bottom: .75em; + text-indent: 1em; + } + p.noindent { /* For paras continuing after quote, table, etc. (where no indent in original) MP */ + text-indent: 0; + } + h1,h2,h3,h4,h5,h6 { + text-align: center; /* all headings centered */ + clear: both; + } + hr { width: 33%; + margin-top: 2em; + margin-bottom: 2em; + margin-left: auto; + margin-right: auto; + clear: both; + } + + table {margin-left: auto; margin-right: auto;} + + body{margin-left: 10%; + margin-right: 10%; + } + + .linenum {position: absolute; top: auto; left: 4%;} /* poetry number */ + .blockquot{margin-left: 5%; margin-right: 10%;} + .pagenum {position: absolute; left: 92%; font-size: smaller; text-align: right; font-style: normal;} /* page numbers */ + .sidenote {width: 20%; padding-bottom: .5em; padding-top: .5em; + padding-left: .5em; padding-right: .5em; margin-left: 1em; + float: right; clear: right; margin-top: 1em; + font-size: smaller; background: #eeeeee; border: dashed 1px;} + + .bb {border-bottom: solid 2px;} + .bl {border-left: solid 2px;} + .bt {border-top: solid 2px;} + .br {border-right: solid 2px;} + .bbox {border: solid 2px;} + + .center {text-align: center;} + .smcap {font-variant: small-caps;} + .u {text-decoration: underline;} + + .caption {font-weight: bold;} + + .figcenter {margin: auto; text-align: center;} + + .figleft {float: left; clear: left; margin-left: 0; margin-bottom: 1em; margin-top: + 1em; margin-right: 1em; padding: 0; text-align: center;} + + .figright {float: right; clear: right; margin-left: 1em; margin-bottom: 1em; + margin-top: 1em; margin-right: 0; padding: 0; text-align: center;} + + .footnotes {border: dashed 1px;} + .footnote {margin-left: 10%; margin-right: 10%; font-size: 0.9em;} + .footnote .label {position: absolute; right: 84%; text-align: right;} + .fnanchor {vertical-align: super; font-size: .8em; text-decoration: none;} + + .example {margin-left:10%; margin-right:10%; text-align: left;} + .example br {display: none;} + .example .section {margin: 1em 0em 1em 0em;} + .example span.i0 {display: block; margin-left: 0em; padding-left: 3em; text-indent: -3em;} + .example span.i1 {display: block; margin-left: 1em; padding-left: 3em; text-indent: -3em;} + .example span.i2 {display: block; margin-left: 2em; padding-left: 3em; text-indent: -3em;} + .example span.i4 {display: block; margin-left: 4em; padding-left: 3em; text-indent: -3em;} + // --> + /* XML end ]]>*/ + </style> + </head> +<body> + + +<pre> + +The Project Gutenberg EBook of Logic, by Carveth Read + +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: Logic + Deductive and Inductive + +Author: Carveth Read + +Release Date: May 23, 2006 [EBook #18440] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK LOGIC *** + + + + +Produced by Susan Skinner and the Online Distributed +Proofreading Team at http://www.pgdp.net + + + + + + +</pre> + + + +<h1>LOGIC</h1> + +<h2>DEDUCTIVE AND INDUCTIVE</h2> + + +<hr style="width: 65%;" /> + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='left'><i>First Edition, June 1898.</i></td><td align='left'>(<i>Grant Richards.</i>)</td></tr> +<tr><td align='left'><i>Second Edition, November 1901.</i></td><td align='left'>(<i>Grant Richards.</i>)</td></tr> +<tr><td align='left'><i>Third Edition, January 1906.</i></td><td align='left'>(<i>A. Moring Ltd.</i>)</td></tr> +<tr><td align='left'><i>Reprinted, January 1908.</i></td><td align='left'>(<i>A. Moring Ltd.</i>)</td></tr> +<tr><td align='left'><i>Reprinted, May 1909.</i></td><td align='left'>(<i>A. Moring Ltd.</i>)</td></tr> +<tr><td align='left'><i>Reprinted, July 1910.</i></td><td align='left'>(<i>A. Moring Ltd.</i>)</td></tr> +<tr><td align='left'><i>Reprinted, September 1911.</i></td><td align='left'>(<i>A. Moring Ltd.</i>)</td></tr> +<tr><td align='left'><i>Reprinted, November 1912.</i></td><td align='left'>(<i>A. Moring Ltd.</i>)</td></tr> +<tr><td align='left'><i>Reprinted, April 1913.</i></td><td align='left'>(<i>A. Moring Ltd.</i>)</td></tr> +<tr><td align='left'><i>Reprinted, May 1920.</i></td><td align='left'>(<i>Simpkin.</i>)</td></tr> +</table></div> + +<hr style="width: 65%;" /> + +<h1>LOGIC</h1> + +<h2>DEDUCTIVE AND INDUCTIVE</h2> + + +<h3>BY</h3> + +<h2>CARVETH READ, M.A.</h2> + + +<p class="center">AUTHOR OF</p> + +<p class="center">"THE METAPHYSICS OF NATURE"</p> + +<p class="center">"NATURAL AND SOCIAL MORALS"</p> + +<p class="center">ETC.</p> + +<hr style="width: 45%;" /> + +<p class="center">FOURTH EDITION</p> + +<p class="center">ENLARGED, AND PARTLY REWRITTEN</p> + +<hr style="width: 45%;" /> + +<p class="center">SIMPKIN, MARSHALL, HAMILTON, KENT & CO. LTD., 4 STATIONERS' HALL COURT.<br /> +LONDON, E.C.4</p> + +<p><span class='pagenum'>[Pg v]<a name="Page_v" id="Page_v"></a></span></p> + + +<hr style="width: 65%;" /> +<h2><a name="PREFACE" id="PREFACE"></a>PREFACE</h2> + + +<p>In this edition of my <i>Logic</i>, the text has been revised throughout, +several passages have been rewritten, and some sections added. The chief +alterations and additions occur in cc. i., v., ix., xiii., xvi., xvii., +xx.</p> + +<p>The work may be considered, on the whole, as attached to the school of +Mill; to whose <i>System of Logic</i>, and to Bain's <i>Logic</i>, it is deeply +indebted. Amongst the works of living writers, the <i>Empirical Logic</i> of +Dr. Venn and the <i>Formal Logic</i> of Dr. Keynes have given me most +assistance. To some others acknowledgments have been made as occasion +arose.</p> + +<p>For the further study of contemporary opinion, accessible in English, +one may turn to such works as Mr. Bradley's <i>Principles of Logic</i>, Dr. +Bosanquet's <i>Logic; or the Morphology of Knowledge</i>, Prof. Hobhouse's +<i>Theory of Knowledge</i>, Jevon's <i>Principles of Science</i>, and Sigwart's +<i>Logic</i>. Ueberweg's <i>Logic, and History of Logical Doctrine</i> is +invaluable for the history of our subject. The attitude toward Logic of +the Pragmatists or Humanists may best be studied in Dr. Schiller's +<i>Formal Logic</i>, and in Mr. Alfred Sidgwick's <i>Process of Argument</i> and +recent <i>Elementary Logic</i>. The second part of this last work, on the +"Risks of Reasoning," gives an admirably succinct account of their +position. I agree with the Humanists that, in all argument, the +important thing to attend to is the meaning, and that the most serious +difficulties of reasoning occur in dealing with the matter reasoned +about; but I find <span class='pagenum'>[Pg vi]<a name="Page_vi" id="Page_vi"></a></span>that a pure science of relation has a necessary place +in the system of knowledge, and that the formulæ known as laws of +contradiction, syllogism and causation are useful guides in the framing +and testing of arguments and experiments concerning matters of fact. +Incisive criticism of traditionary doctrines, with some remarkable +reconstructions, may be read in Dr. Mercier's <i>New Logic</i>.</p> + +<p>In preparing successive editions of this book, I have profited by the +comments of my friends: Mr. Thomas Whittaker, Prof. Claude Thompson, Dr. +Armitage Smith, Mr. Alfred Sidgwick, Dr. Schiller, Prof. Spearman, and +Prof. Sully, have made important suggestions; and I might have profited +more by them, if the frame of my book, or my principles, had been more +elastic.</p> + +<p>As to the present edition, useful criticisms have been received from Mr. +S.C. Dutt, of Cotton College, Assam, and from Prof. M.A. Roy, of +Midnapore; and, especially, I must heartily thank my colleague, Dr. +Wolf, for communications that have left their impress upon nearly every +chapter.</p> + +<p style="text-align: right;"><span class="smcap">Carveth Read.</span></p> + +<p> +<span class="smcap">London,</span><br /> +<i>August</i>, 1914<br /> +</p> +<p><span class='pagenum'>[Pg vii]<a name="Page_vii" id="Page_vii"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CONTENTS" id="CONTENTS"></a>CONTENTS</h2> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td> </td><td> </td><td align='right'><span class="smcap">page</span></td></tr> +<tr><td> </td><td align='left'><span class="smcap"><a href="#PREFACE">Preface</a></span></td><td align='right'><a href="#Page_v">v</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_I">CHAPTER I</a></td></tr> +<tr><td align='center' colspan='3'>INTRODUCTORY</td></tr> +<tr><td align='right'><a href="#chap_1_sect_1">§1.</a></td><td align='left'>Definition of Logic</td><td align='right'><a href="#Page_1">1</a></td></tr> +<tr><td align='right'><a href="#chap_1_sect_2">§2.</a></td><td align='left'>General character of proof</td><td align='right'><a href="#Page_2">2</a></td></tr> +<tr><td align='right'><a href="#chap_1_sect_3">§3.</a></td><td align='left'>Division of the subject</td><td align='right'><a href="#Page_5">5</a></td></tr> +<tr><td align='right'><a href="#chap_1_sect_4">§4.</a></td><td align='left'>Uses of Logic</td><td align='right'><a href="#Page_6">6</a></td></tr> +<tr><td align='right'><a href="#chap_1_sect_5">§5.</a></td><td align='left'>Relation of Logic to other sciences</td><td align='right'><a href="#Page_8">8</a></td></tr> +<tr><td align='left'></td><td align='left'>to Mathematics (p. <a href="#Page_8">8</a>); to concrete Sciences (p. <a href="#Page_10">10</a>); +to Metaphysics (p. <a href="#Page_10">10</a>); to regulative sciences (p. <a href="#Page_11">11</a>)</td></tr> +<tr><td align='right'><a href="#chap_1_sect_6">§6.</a></td><td align='left'>Schools of Logicians</td><td align='right'><a href="#Page_11">11</a></td></tr> +<tr><td align='left'></td><td align='left'>Relation to Psychology (p. <a href="#Page_13">13</a>)</td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_II">CHAPTER II</a></td></tr> +<tr><td align='center' colspan='3'>GENERAL ANALYSIS OF PROPOSITIONS</td></tr> +<tr><td align='right'><a href="#chap_2_sect_1">§1.</a></td><td align='left'>Propositions and Sentences</td><td align='right'><a href="#Page_16">16</a></td></tr> +<tr><td align='right'><a href="#chap_2_sect_2">§2.</a></td><td align='left'>Subject, Predicate and Copula</td><td align='right'><a href="#Page_17">17</a></td></tr> +<tr><td align='right'><a href="#chap_2_sect_3">§3.</a></td><td align='left'>Compound Propositions</td><td align='right'><a href="#Page_17">17</a></td></tr> +<tr><td align='right'><a href="#chap_2_sect_4">§4.</a></td><td align='left'>Import of Propositions</td><td align='right'><a href="#Page_19">19</a></td></tr> +<tr><td align='right'><a href="#chap_2_sect_5">§5.</a></td><td align='left'>Form and Matter</td><td align='right'><a href="#Page_22">22</a></td></tr> +<tr><td align='right'><a href="#chap_2_sect_6">§6.</a></td><td align='left'>Formal and Material Logic</td><td align='right'><a href="#Page_23">23</a></td></tr> +<tr><td align='right'><a href="#chap_2_sect_7">§7.</a></td><td align='left'>Symbols used in Logic</td><td align='right'><a href="#Page_24">24</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_III">CHAPTER III</a></td></tr> +<tr><td align='center' colspan='3'>OF TERMS AND THEIR DENOTATION</td></tr> +<tr><td align='right'><a href="#chap_3_sect_1">§1.</a></td><td align='left'>Some Account of Language necessary</td><td align='right'><a href="#Page_27">27</a></td></tr> +<tr><td align='right'><a href="#chap_3_sect_2">§2.</a></td><td align='left'>Logic, Grammar and Rhetoric</td><td align='right'><a href="#Page_28">28</a></td></tr> +<tr><td align='right'><a href="#chap_3_sect_3">§3.</a></td><td align='left'>Words are Categorematic or Syncategorematic</td><td align='right'><a href="#Page_29">29</a></td></tr> +<tr><td align='right'><a href="#chap_3_sect_4">§4.</a></td><td align='left'>Terms Concrete or Abstract</td><td align='right'><a href="#Page_30">30</a></td></tr> +<tr><td align='right'><a href="#chap_3_sect_5">§5.</a></td><td align='left'>Concrete Terms, Singular, General or Collective</td><td align='right'><a href="#Page_33">33</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_IV">CHAPTER IV</a></td></tr> +<tr><td align='center' colspan='3'>THE CONNOTATION OF TERMS</td></tr> +<tr><td align='right'><a href="#chap_4_sect_1">§1.</a></td><td align='left'>Connotation of General Names</td><td align='right'><a href="#Page_37">37</a></td></tr> +<tr><td align='right'><a href="#chap_4_sect_2">§2.</a></td><td align='left'>Question of Proper Names</td><td align='right'><a href="#Page_38">38</a></td></tr> +<tr><td align='left'></td><td align='left'>other Singular Names (p. <a href="#Page_40">40</a>)</td></tr> +<tr><td align='right'><a href="#chap_4_sect_3">§3.</a></td><td align='left'>Question of Abstract Terms</td><td align='right'><a href="#Page_40">40</a></td></tr> +<tr><td align='right'><a href="#chap_4_sect_4">§4.</a></td><td align='left'>Univocal and Equivocal Terms</td><td align='right'><a href="#Page_41">41</a></td></tr> +<tr><td align='left'></td><td align='left'>Connotation determined by the <i>suppositio</i> (p. <a href="#Page_43">43</a>)</td></tr> +<tr><td align='right'><a href="#chap_4_sect_5">§5.</a></td><td align='left'>Absolute and Relative Terms</td><td align='right'><a href="#Page_43">43</a></td></tr> +<tr><td align='right'><a href="#chap_4_sect_6">§6.</a></td><td align='left'>Relation of Denotation to Connotation</td><td align='right'><a href="#Page_46">46</a></td></tr> +<tr><td align='right'><a href="#chap_4_sect_7">§7.</a></td><td align='left'>Contradictory Terms</td><td align='right'><a href="#Page_47">47</a></td></tr> +<tr><td align='right'><a href="#chap_4_sect_8">§8.</a></td><td align='left'>Positive and Negative Terms</td><td align='right'><a href="#Page_50">50</a></td></tr> +<tr><td align='left'></td><td align='left'>Infinites; Privitives; Contraries (pp. <a href="#Page_50">50</a>-<a href="#Page_51">51</a>)</td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_V">CHAPTER V</a></td></tr> +<tr><td align='center' colspan='3'>CLASSIFICATION OF PROPOSITIONS</td></tr> +<tr><td align='right'><a href="#chap_5_sect_1">§1.</a></td><td align='left'>As to Quantity</td><td align='right'><a href="#Page_53">53</a></td></tr> +<tr><td align='left'></td><td align='left'>Quantity of the Predicate (p. <a href="#Page_56">56</a>)</td></tr> +<tr><td align='right'><a href="#chap_5_sect_2">§2.</a></td><td align='left'>As to Quality</td><td align='right'><a href="#Page_57">57</a></td></tr> +<tr><td align='left'></td><td align='left'>Infinite Propositions (p. <a href="#Page_57">57</a>)</td></tr> +<tr><td align='right'><a href="#chap_5_sect_3">§3.</a></td><td align='left'>A. I. E. O.</td><td align='right'><a href="#Page_58">58</a></td></tr> +<tr><td align='right'><a href="#chap_5_sect_4">§4.</a></td><td align='left'>As to Relation</td><td align='right'><a href="#Page_59">59</a></td></tr> +<tr><td align='left'></td><td align='left'>Change of Relation (p. <a href="#Page_60">60</a>); Interpretation of 'either, or' (p. <a href="#Page_63">63</a>); +Function of the hypothetical form (p. <a href="#Page_64">64</a>)</td></tr> +<tr><td align='right'><a href="#chap_5_sect_5">§5.</a></td><td align='left'>As to Modality</td><td align='right'><a href="#Page_66">66</a></td></tr> +<tr><td align='right'><a href="#chap_5_sect_6">§6.</a></td><td align='left'>Verbal and Real Propositions</td><td align='right'><a href="#Page_67">67</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_VI">CHAPTER VI</a></td></tr> +<tr><td align='center' colspan='3'>CONDITIONS OF IMMEDIATE INFERENCE</td></tr> +<tr><td align='right'><a href="#chap_6_sect_1">§1.</a></td><td align='left'>Meaning of Inference</td><td align='right'><a href="#Page_69">69</a></td></tr> +<tr><td align='right'><a href="#chap_6_sect_2">§2.</a></td><td align='left'>Immediate and Mediate Inference</td><td align='right'><a href="#Page_70">70</a></td></tr> +<tr><td align='right'><a href="#chap_6_sect_3">§3.</a></td><td align='left'>The Laws of Thought</td><td align='right'><a href="#Page_72">72</a></td></tr> +<tr><td align='right'><a href="#chap_6_sect_4">§4.</a></td><td align='left'>Identity</td><td align='right'><a href="#Page_73">73</a></td></tr> +<tr><td align='right'><a href="#chap_6_sect_5">§5.</a></td><td align='left'>Contradiction and Excluded Middle</td><td align='right'><a href="#Page_74">74</a></td></tr> +<tr><td align='right'><a href="#chap_6_sect_6">§6.</a></td><td align='left'>The Scope of Formal Inference</td><td align='right'><a href="#Page_76">76</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_VII">CHAPTER VII</a></td></tr> +<tr><td align='center' colspan='3'>IMMEDIATE INFERENCES</td></tr> +<tr><td align='right'><a href="#chap_7_sect_1">§1.</a></td><td align='left'>Plan of the Chapter</td><td align='right'><a href="#Page_79">79</a></td></tr> +<tr><td align='right'><a href="#chap_7_sect_2">§2.</a></td><td align='left'>Subalternation</td><td align='right'><a href="#Page_79">79</a></td></tr> +<tr><td align='right'><a href="#chap_7_sect_3">§3.</a></td><td align='left'>Connotative Subalternation</td><td align='right'><a href="#Page_80">80</a></td></tr> +<tr><td align='right'><a href="#chap_7_sect_4">§4.</a></td><td align='left'>Conversion</td><td align='right'><a href="#Page_82">82</a></td></tr> +<tr><td align='left'></td><td align='left'>Reciprocality (p. <a href="#Page_84">84</a>)</td></tr> +<tr><td align='right'><a href="#chap_7_sect_5">§5.</a></td><td align='left'>Obversion</td><td align='right'><a href="#Page_85">85</a></td></tr> +<tr><td align='right'><a href="#chap_7_sect_6">§6.</a></td><td align='left'>Contrary Opposition</td><td align='right'><a href="#Page_87">87</a></td></tr> +<tr><td align='right'><a href="#chap_7_sect_7">§7.</a></td><td align='left'>Contradictory Opposition</td><td align='right'><a href="#Page_87">87</a></td></tr> +<tr><td align='right'><a href="#chap_7_sect_8">§8.</a></td><td align='left'>Sub-contrary Opposition</td><td align='right'><a href="#Page_88">88</a></td></tr> +<tr><td align='right'><a href="#chap_7_sect_9">§9.</a></td><td align='left'>The Square of Opposition</td><td align='right'><a href="#Page_89">89</a></td></tr> +<tr><td align='right'><a href="#chap_7_sect_10">§10.</a></td><td align='left'>Secondary modes of Immediate Inference</td><td align='right'><a href="#Page_90">90</a></td></tr> +<tr><td align='right'><a href="#chap_7_sect_11">§11.</a></td><td align='left'>Immediate Inferences from Conditionals</td><td align='right'><a href="#Page_93">93</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_VIII">CHAPTER VIII</a></td></tr> +<tr><td align='center' colspan='3'>ORDER OF TERMS, EULER'S DIAGRAMS, LOGICAL EQUATIONS, +EXISTENTIAL IMPORT OF PROPOSITIONS</td></tr> +<tr><td align='right'><a href="#chap_8_sect_1">§1.</a></td><td align='left'>Order of Terms in a proposition</td><td align='right'><a href="#Page_95">95</a></td></tr> +<tr><td align='right'><a href="#chap_8_sect_2">§2.</a></td><td align='left'>Euler's Diagrams</td><td align='right'><a href="#Page_97">97</a></td></tr> +<tr><td align='right'><a href="#chap_8_sect_3">§3.</a></td><td align='left'>Propositions considered as Equations</td><td align='right'><a href="#Page_101">101</a></td></tr> +<tr><td align='right'><a href="#chap_8_sect_4">§4.</a></td><td align='left'>Existential Import of Propositions</td><td align='right'><a href="#Page_104">104</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_IX">CHAPTER IX</a></td></tr> +<tr><td align='center' colspan='3'>FORMAL CONDITIONS OF MEDIATE INFERENCE</td></tr> +<tr><td align='right'><a href="#chap_9_sect_1">§1.</a></td><td align='left'>Nature of Mediate Inference and Syllogism</td><td align='right'><a href="#Page_107">107</a></td></tr> +<tr><td align='right'><a href="#chap_9_sect_2">§2.</a></td><td align='left'>General Canons of the Syllogism</td><td align='right'><a href="#Page_108">108</a></td></tr> +<tr><td align='left'></td><td align='left'>Definitions of Categorical Syllogism; Middle Term; +Minor Term; Major Term; Minor and Major Premise (p. <a href="#Page_109">109</a>); +Illicit Process (p. <a href="#Page_110">110</a>); Distribution of the Middle (p. <a href="#Page_110">110</a>); Negative Premises (p. <a href="#Page_112">112</a>); Particular Premises (p. <a href="#Page_113">113</a>)</td></tr> +<tr><td align='right'><a href="#chap_9_sect_3">§3.</a></td><td align='left'><i>Dictum de omni et nullo</i></td><td align='right'><a href="#Page_115">115</a></td></tr> +<tr><td align='right'><a href="#chap_9_sect_4">§4.</a></td><td align='left'>Syllogism in relation to the Laws of Thought</td><td align='right'><a href="#Page_116">116</a></td></tr> +<tr><td align='right'><a href="#chap_9_sect_5">§5.</a></td><td align='left'>Other Kinds of Mediate Inference</td><td align='right'><a href="#Page_118">118</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_X">CHAPTER X</a></td></tr> +<tr><td align='center' colspan='3'>CATEGORICAL SYLLOGISMS</td></tr> +<tr><td align='right'><a href="#chap_10_sect_1">§1.</a></td><td align='left'>Illustrations of the Syllogism</td><td align='right'><a href="#Page_121">121</a></td></tr> +<tr><td align='right'><a href="#chap_10_sect_2">§2.</a></td><td align='left'>Of Figures</td><td align='right'><a href="#Page_122">122</a></td></tr> +<tr><td align='right'><a href="#chap_10_sect_3">§3.</a></td><td align='left'>Of Moods</td><td align='right'><a href="#Page_123">123</a></td></tr> +<tr><td align='right'><a href="#chap_10_sect_4">§4.</a></td><td align='left'>How valid Moods are determined</td><td align='right'><a href="#Page_124">124</a></td></tr> +<tr><td align='right'><a href="#chap_10_sect_5">§5.</a></td><td align='left'>Special Canons of the Four Figures</td><td align='right'><a href="#Page_126">126</a></td></tr> +<tr><td align='right'><a href="#chap_10_sect_6">§6.</a></td><td align='left'>Ostensive Reduction and the Mnemonic Verses</td><td align='right'><a href="#Page_127">127</a></td></tr> +<tr><td align='right'><a href="#chap_10_sect_7">§7.</a></td><td align='left'>Another version of the Mnemonic Verses</td><td align='right'><a href="#Page_132">132</a></td></tr> +<tr><td align='right'><a href="#chap_10_sect_8">§8.</a></td><td align='left'>Indirect Reduction</td><td align='right'><a href="#Page_132">132</a></td></tr> +<tr><td align='right'><a href="#chap_10_sect_9">§9.</a></td><td align='left'>Uses of the several Figures</td><td align='right'><a href="#Page_134">134</a></td></tr> +<tr><td align='right'><a href="#chap_10_sect_10">§10.</a></td><td align='left'>Scientific Value of Reduction</td><td align='right'><a href="#Page_135">135</a></td></tr> +<tr><td align='right'><a href="#chap_10_sect_11">§11.</a></td><td align='left'>Euler's Diagrams for the Syllogism</td><td align='right'><a href="#Page_136">136</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_XI">CHAPTER XI</a></td></tr> +<tr><td align='center' colspan='3'>ABBREVIATED AND COMPOUND ARGUMENTS</td></tr> +<tr><td align='right'><a href="#chap_11_sect_1">§1.</a></td><td align='left'>Popular Arguments Informal</td><td align='right'><a href="#Page_138">138</a></td></tr> +<tr><td align='right'><a href="#chap_11_sect_2">§2.</a></td><td align='left'>The Enthymeme</td><td align='right'><a href="#Page_139">139</a></td></tr> +<tr><td align='right'><a href="#chap_11_sect_3">§3.</a></td><td align='left'>Monosyllogism, Polysyllogism, Prosyllogism, Episyllogism</td><td align='right'><a href="#Page_141">141</a></td></tr> +<tr><td align='right'><a href="#chap_11_sect_4">§4.</a></td><td align='left'>The Epicheirema</td><td align='right'><a href="#Page_142">142</a></td></tr> +<tr><td align='right'><a href="#chap_11_sect_5">§5.</a></td><td align='left'>The Sorites</td><td align='right'><a href="#Page_142">142</a></td></tr> +<tr><td align='right'><a href="#chap_11_sect_6">§6.</a></td><td align='left'>The Antinomy</td><td align='right'><a href="#Page_145">145</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_XII">CHAPTER XII</a></td></tr> +<tr><td align='center' colspan='3'>CONDITIONAL SYLLOGISMS</td></tr> +<tr><td align='right'><a href="#chap_12_sect_1">§1.</a></td><td align='left'>The Hypothetical Syllogism</td><td align='right'><a href="#Page_147">147</a></td></tr> +<tr><td align='right'><a href="#chap_12_sect_2">§2.</a></td><td align='left'>The Disjunctive Syllogism</td><td align='right'><a href="#Page_152">152</a></td></tr> +<tr><td align='right'><a href="#chap_12_sect_3">§3.</a></td><td align='left'>The Dilemma</td><td align='right'><a href="#Page_154">154</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_XIII">CHAPTER XIII</a></td></tr> +<tr><td align='center' colspan='3'>TRANSITION TO INDUCTION</td></tr> +<tr><td align='right'><a href="#chap_13_sect_1">§1.</a></td><td align='left'>Formal Consistency and Material Truth</td><td align='right'><a href="#Page_159">159</a></td></tr> +<tr><td align='right'><a href="#chap_13_sect_2">§2.</a></td><td align='left'>Real General Propositions assert more than has been +directly observed</td><td align='right'><a href="#Page_160">160</a></td></tr> +<tr><td align='right'><a href="#chap_13_sect_3">§3.</a></td><td align='left'>Hence, formally, a Syllogism's Premises seem to beg the +Conclusion</td><td align='right'><a href="#Page_162">162</a></td></tr> +<tr><td align='right'><a href="#chap_13_sect_4">§4.</a></td><td align='left'>Materially, a Syllogism turns upon the resemblance of the +Minor to the Middle Term and thus extends the +Major Premise to new cases</td><td align='right'><a href="#Page_163">163</a></td></tr> +<tr><td align='right'><a href="#chap_13_sect_5">§5.</a></td><td align='left'>Restatement of the <i>Dictum</i> for material reasoning</td><td align='right'><a href="#Page_165">165</a></td></tr> +<tr><td align='right'><a href="#chap_13_sect_6">§6.</a></td><td align='left'>Uses of the Syllogism</td><td align='right'><a href="#Page_167">167</a></td></tr> +<tr><td align='right'><a href="#chap_13_sect_7">§7.</a></td><td align='left'>Analysis of the Uniformity of Nature, considered as the +formal ground of all reasoning</td><td align='right'><a href="#Page_169">169</a></td></tr> +<tr><td align='right'><a href="#chap_13_sect_8">§8.</a></td><td align='left'>Grounds of our belief in Uniformity</td><td align='right'><a href="#Page_173">173</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_XIV">CHAPTER XIV</a></td></tr> +<tr><td align='center' colspan='3'>CAUSATION</td></tr> +<tr><td align='right'><a href="#chap_14_sect_1">§1.</a></td><td align='left'>The most important aspect of Uniformity in relation to +Induction is Causation</td><td align='right'><a href="#Page_174">174</a></td></tr> +<tr><td align='right'><a href="#chap_14_sect_2">§2.</a></td><td align='left'>Definition of "Cause" explained: five marks of Causation</td><td align='right'><a href="#Page_175">175</a></td></tr> +<tr><td align='right'><a href="#chap_14_sect_3">§3.</a></td><td align='left'>How strictly the conception of Cause can be applied +depends upon the subject under investigation</td><td align='right'><a href="#Page_183">183</a></td></tr> +<tr><td align='right'><a href="#chap_14_sect_4">§4.</a></td><td align='left'>Scientific conception of Effect. Plurality of Causes</td><td align='right'><a href="#Page_185">185</a></td></tr> +<tr><td align='right'><a href="#chap_14_sect_5">§5.</a></td><td align='left'>Some condition, but not the whole cause, may long precede +the Effect; and some co-effect, but not the whole effect, may long survive the Cause</td><td align='right'><a href="#Page_187">187</a></td></tr> +<tr><td align='right'><a href="#chap_14_sect_6">§6.</a></td><td align='left'>Mechanical Causes and the homogeneous Intermixture of Effects; +Chemical Causes and the heteropathic Intermixture of Effects</td><td align='right'><a href="#Page_188">188</a></td></tr> +<tr><td align='right'><a href="#chap_14_sect_7">§7.</a></td><td align='left'>Tendency, Resultant, Counteraction, Elimination, Resolution, +Analysis, Reciprocity</td><td align='right'><a href="#Page_189">189</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_XV">CHAPTER XV</a></td></tr> +<tr><td align='center' colspan='3'>INDUCTIVE METHOD</td></tr> +<tr><td align='right'><a href="#chap_15_sect_1">§1.</a></td><td align='left'>Outline of Inductive investigation</td><td align='right'><a href="#Page_192">192</a></td></tr> +<tr><td align='right'><a href="#chap_15_sect_2">§2.</a></td><td align='left'>Induction defined</td><td align='right'><a href="#Page_196">196</a></td></tr> +<tr><td align='right'><a href="#chap_15_sect_3">§3.</a></td><td align='left'>"Perfect Induction"</td><td align='right'><a href="#Page_196">196</a></td></tr> +<tr><td align='right'><a href="#chap_15_sect_4">§4.</a></td><td align='left'>Imperfect Induction methodical or immethodical</td><td align='right'><a href="#Page_197">197</a></td></tr> +<tr><td align='right'><a href="#chap_15_sect_5">§5.</a></td><td align='left'>Observation and Experiment, the material ground of +Induction, compared</td><td align='right'><a href="#Page_198">198</a></td></tr> +<tr><td align='right'><a href="#chap_15_sect_6">§6.</a></td><td align='left'>The principle of Causation is the formal ground of Induction</td><td align='right'><a href="#Page_201">201</a></td></tr> +<tr><td align='right'><a href="#chap_15_sect_7">§7.</a></td><td align='left'>The Inductive Canons are derived from the principle of +Causation, the more readily to detect it in facts observed</td><td align='right'><a href="#Page_202">202</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_XVI">CHAPTER XVI</a></td></tr> +<tr><td align='center' colspan='3'>THE CANONS OF DIRECT INDUCTION</td></tr> +<tr><td align='right'><a href="#chap_16_sect_1">§1.</a></td><td align='left'>The Canon of Agreement</td><td align='right'><a href="#Page_206">206</a></td></tr> +<tr><td align='left'></td><td align='left'>Negative Instances (p. <a href="#Page_208">208</a>); +Plurality of Causes (p. <a href="#Page_208">208</a>)</td></tr> +<tr><td align='left'></td><td align='left'>Agreement may show connection without direct Causation (p. <a href="#Page_209">209</a>)</td></tr> +<tr><td align='right'><a href="#chap_16_sect_2">§2.</a></td><td align='left'>The Canon of Agreement in Presence and in Absence</td><td align='right'><a href="#Page_212">212</a></td></tr> +<tr><td align='left'></td><td align='left'>It tends to disprove a Plurality of Causes (p. <a href="#Page_213">213</a>)</td></tr> +<tr><td align='right'><a href="#chap_16_sect_3">§3.</a></td><td align='left'>The Canon of Difference</td><td align='right'><a href="#Page_216">216</a></td></tr> +<tr><td align='left'></td><td align='left'>May be applied to observations (p. <a href="#Page_221">221</a>)</td></tr> +<tr><td align='right'><a href="#chap_16_sect_4">§4.</a></td><td align='left'>The Canon of Variations</td><td align='right'><a href="#Page_222">222</a></td></tr> +<tr><td align='left'></td><td align='left'>How related to Agreement and Difference (p. <a href="#Page_222">222</a>); +The Graphic Method (p. <a href="#Page_227">227</a>); Critical points (p. <a href="#Page_230">230</a>); Progressive effects (p. <a href="#Page_231">231</a>); +Gradations (p. <a href="#Page_231">231</a>)</td></tr> +<tr><td align='right'><a href="#chap_16_sect_5">§5.</a></td><td align='left'>The Canon of Residues</td><td align='right'><a href="#Page_232">232</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_XVII">CHAPTER XVII</a></td></tr> +<tr><td align='center' colspan='3'>COMBINATION OF INDUCTION WITH DEDUCTION</td></tr> +<tr><td align='right'><a href="#chap_17_sect_1">§1.</a></td><td align='left'>Deductive character of Formal Induction</td><td align='right'><a href="#Page_236">236</a></td></tr> +<tr><td align='right'><a href="#chap_17_sect_2">§2.</a></td><td align='left'>Further complication of Deduction with Induction</td><td align='right'><a href="#Page_238">238</a></td></tr> +<tr><td align='right'><a href="#chap_17_sect_3">§3.</a></td><td align='left'>The Direct Deductive (or Physical) Method</td><td align='right'><a href="#Page_240">240</a></td></tr> +<tr><td align='right'><a href="#chap_17_sect_4">§4.</a></td><td align='left'>Opportunities of Error in the Physical Method</td><td align='right'><a href="#Page_243">243</a></td></tr> +<tr><td align='right'><a href="#chap_17_sect_5">§5.</a></td><td align='left'>The Inverse Deductive (or Historical) Method</td><td align='right'><a href="#Page_246">246</a></td></tr> +<tr><td align='right'><a href="#chap_17_sect_6">§6.</a></td><td align='left'>Precautions in using the Historical Method</td><td align='right'><a href="#Page_251">251</a></td></tr> +<tr><td align='right'><a href="#chap_17_sect_7">§7.</a></td><td align='left'>The Comparative Method</td><td align='right'><a href="#Page_255">255</a></td></tr> +<tr><td align='right'><a href="#chap_17_sect_8">§8.</a></td><td align='left'>Historical Evidence</td><td align='right'><a href="#Page_261">261</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_XVIII">CHAPTER XVIII</a></td></tr> +<tr><td align='center' colspan='3'>HYPOTHESES</td></tr> +<tr><td align='right'><a href="#chap_18_sect_1">§1.</a></td><td align='left'>Hypothesis defined and distinguished from Theory</td><td align='right'><a href="#Page_266">266</a></td></tr> +<tr><td align='right'><a href="#chap_18_sect_2">§2.</a></td><td align='left'>An Hypothesis must be verifiable</td><td align='right'><a href="#Page_268">268</a></td></tr> +<tr><td align='right'><a href="#chap_18_sect_3">§3.</a></td><td align='left'>Proof of Hypotheses</td><td align='right'><a href="#Page_270">270</a></td></tr> +<tr><td align='left'></td><td align='left'>(1) Must an hypothetical agent be directly observable? (p. <a href="#Page_270">270</a>); +<i>Vera causa</i> (p. <a href="#Page_271">271</a>)</td></tr> +<tr><td align='left'></td><td align='left'>(2) An Hypothesis must be adequate to its pretensions (p. <a href="#Page_272">272</a>); +<i>Exceptio probat regulam</i> (p. <a href="#Page_274">274</a>)</td></tr> +<tr><td align='left'></td><td align='left'>(3) Every competing Hypothesis must be excluded (p. <a href="#Page_275">275</a>); +Crucial instance (p. <a href="#Page_277">277</a>)</td></tr> +<tr><td align='left'></td><td align='left'>(4) Hypotheses must agree with the laws of Nature (p. <a href="#Page_279">279</a>)</td></tr> +<tr><td align='right'><a href="#chap_18_sect_4">§4.</a></td><td align='left'>Hypotheses necessary in scientific investigation</td><td align='right'><a href="#Page_280">280</a></td></tr> +<tr><td align='right'><a href="#chap_18_sect_5">§5.</a></td><td align='left'>The Method of Abstractions</td><td align='right'><a href="#Page_283">283</a></td></tr> +<tr><td align='left'></td><td align='left'>Method of Limits (p. <a href="#Page_284">284</a>); +In what sense all knowledge is hypothetical (p. <a href="#Page_286">286</a>)</td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_XIX">CHAPTER XIX</a></td></tr> +<tr><td align='center' colspan='3'>LAWS CLASSIFIED; EXPLANATION; CO-EXISTENCE; ANALOGY</td></tr> +<tr><td align='right'><a href="#chap_19_sect_1">§1.</a></td><td align='left'>Axioms; Primary Laws; Secondary Laws, Derivative or Empirical; +Facts</td><td align='right'><a href="#Page_288">288</a></td></tr> +<tr><td align='right'><a href="#chap_19_sect_2">§2.</a></td><td align='left'>Secondary Laws either Invariable or Approximate Generalisations</td><td align='right'><a href="#Page_292">292</a></td></tr> +<tr><td align='right'><a href="#chap_19_sect_3">§3.</a></td><td align='left'>Secondary Laws trustworthy only in 'Adjacent Cases'</td><td align='right'><a href="#Page_293">293</a></td></tr> +<tr><td align='right'><a href="#chap_19_sect_4">§4.</a></td><td align='left'>Secondary Laws of Succession or of Co-existence</td><td align='right'><a href="#Page_295">295</a></td></tr> +<tr><td align='left'></td><td align='left'>Natural Kinds (p. <a href="#Page_296">296</a>); Co-existence of concrete things to be deduced from +Causation (p. <a href="#Page_297">297</a>)</td></tr> +<tr><td align='right'><a href="#chap_19_sect_5">§5.</a></td><td align='left'>Explanation consists in tracing resemblance, especially +of Causation</td><td align='right'><a href="#Page_299">299</a></td></tr> +<tr><td align='right'><a href="#chap_19_sect_6">§6.</a></td><td align='left'>Three modes of Explanation</td><td align='right'><a href="#Page_302">302</a></td></tr> +<tr><td align='left'></td><td align='left'>Analysis (p. <a href="#Page_302">302</a>); Concatenation (p. <a href="#Page_302">302</a>); Subsumption (p. <a href="#Page_303">303</a>)</td></tr> +<tr><td align='right'><a href="#chap_19_sect_7">§7.</a></td><td align='left'>Limits of Explanation</td><td align='right'><a href="#Page_305">305</a></td></tr> +<tr><td align='right'><a href="#chap_19_sect_8">§8.</a></td><td align='left'>Analogy</td><td align='right'><a href="#Page_307">307</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_XX">CHAPTER XX</a></td></tr> +<tr><td align='center' colspan='3'>PROBABILITY</td></tr> +<tr><td align='right'><a href="#chap_20_sect_1">§1.</a></td><td align='left'>Meaning of Chance and Probability</td><td align='right'><a href="#Page_310">310</a></td></tr> +<tr><td align='right'><a href="#chap_20_sect_2">§2.</a></td><td align='left'>Probability as a fraction or proportion</td><td align='right'><a href="#Page_312">312</a></td></tr> +<tr><td align='right'><a href="#chap_20_sect_3">§3.</a></td><td align='left'>Probability depends upon experience and statistics</td><td align='right'><a href="#Page_313">313</a></td></tr> +<tr><td align='right'><a href="#chap_20_sect_4">§4.</a></td><td align='left'>It is a kind of Induction, and pre-supposes Causation</td><td align='right'><a href="#Page_315">315</a></td></tr> +<tr><td align='right'><a href="#chap_20_sect_5">§5.</a></td><td align='left'>Of Averages and the Law of Error</td><td align='right'><a href="#Page_318">318</a></td></tr> +<tr><td align='right'><a href="#chap_20_sect_6">§6.</a></td><td align='left'>Interpretation of probabilities</td><td align='right'><a href="#Page_324">324</a></td></tr> +<tr><td align='left'></td><td align='left'>Personal Equation (p. <a href="#Page_325">325</a>); meaning of 'Expectation' (p. <a href="#Page_325">325</a>)</td></tr> +<tr><td align='right'><a href="#chap_20_sect_7">§7.</a></td><td align='left'>Rules of the combination of Probabilities</td><td align='right'><a href="#Page_325">325</a></td></tr> +<tr><td align='left'></td><td align='left'>Detection of a hidden Cause (p. <a href="#Page_326">326</a>); oral tradition (p. <a href="#Page_327">327</a>); +circumstantial and analogical evidence (p. <a href="#Page_328">328</a>)</td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_XXI">CHAPTER XXI</a></td></tr> +<tr><td align='center' colspan='3'>DIVISION AND CLASSIFICATION</td></tr> +<tr><td align='right'><a href="#chap_21_sect_1">§1.</a></td><td align='left'>Classification, scientific, special and popular</td><td align='right'><a href="#Page_330">330</a></td></tr> +<tr><td align='right'><a href="#chap_21_sect_2">§2.</a></td><td align='left'>Uses of classification</td><td align='right'><a href="#Page_332">332</a></td></tr> +<tr><td align='right'><a href="#chap_21_sect_3">§3.</a></td><td align='left'>Classification, Deductive and Inductive</td><td align='right'><a href="#Page_334">334</a></td></tr> +<tr><td align='right'><a href="#chap_21_sect_4">§4.</a></td><td align='left'>Division, or Deductive Classification: its Rules</td><td align='right'><a href="#Page_335">335</a></td></tr> +<tr><td align='right'><a href="#chap_21_sect_5">§5.</a></td><td align='left'>Rules for testing a Division</td><td align='right'><a href="#Page_337">337</a></td></tr> +<tr><td align='right'><a href="#chap_21_sect_6">§6.</a></td><td align='left'>Inductive Classification</td><td align='right'><a href="#Page_339">339</a></td></tr> +<tr><td align='right'><a href="#chap_21_sect_7">§7.</a></td><td align='left'>Difficulty of Natural Classification</td><td align='right'><a href="#Page_341">341</a></td></tr> +<tr><td align='right'><a href="#chap_21_sect_8">§8.</a></td><td align='left'>Darwin's influence on the theory of Classification</td><td align='right'><a href="#Page_342">342</a></td></tr> +<tr><td align='right'><a href="#chap_21_sect_9">§9.</a></td><td align='left'>Classification of Inorganic Bodies also dependent on Causation</td><td align='right'><a href="#Page_346">346</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_XXII">CHAPTER XXII</a></td></tr> +<tr><td align='center' colspan='3'>NOMENCLATURE, DEFINITION, PREDICABLES</td></tr> +<tr><td align='right'><a href="#chap_22_sect_1">§1.</a></td><td align='left'>Precise thinking needs precise language</td><td align='right'><a href="#Page_348">348</a></td></tr> +<tr><td align='right'><a href="#chap_22_sect_2">§2.</a></td><td align='left'>Nomenclature and Terminology</td><td align='right'><a href="#Page_349">349</a></td></tr> +<tr><td align='right'><a href="#chap_22_sect_3">§3.</a></td><td align='left'>Definition</td><td align='right'><a href="#Page_352">352</a></td></tr> +<tr><td align='right'><a href="#chap_22_sect_4">§4.</a></td><td align='left'>Rules for testing a Definition</td><td align='right'><a href="#Page_352">352</a></td></tr> +<tr><td align='right'><a href="#chap_22_sect_5">§5.</a></td><td align='left'>Every Definition is relative to a Classification</td><td align='right'><a href="#Page_353">353</a></td></tr> +<tr><td align='right'><a href="#chap_22_sect_6">§6.</a></td><td align='left'>Difficulties of Definition</td><td align='right'><a href="#Page_356">356</a></td></tr> +<tr><td align='left'></td><td align='left'>Proposals to substitute the Type (p. <a href="#Page_356">356</a>)</td></tr> +<tr><td align='right'><a href="#chap_22_sect_7">§7.</a></td><td align='left'>The Limits of Definition</td><td align='right'><a href="#Page_357">357</a></td></tr> +<tr><td align='right'><a href="#chap_22_sect_8">§8.</a></td><td align='left'>The five Predicables</td><td align='right'><a href="#Page_358">358</a></td></tr> +<tr><td align='left'></td><td align='left'>Porphyry's Tree (p. <a href="#Page_361">361</a>)</td></tr> +<tr><td align='right'><a href="#chap_22_sect_9">§9.</a></td><td align='left'>Realism and Nominalism</td><td align='right'><a href="#Page_364">364</a></td></tr> +<tr><td align='right'><a href="#chap_22_sect_10">§10.</a></td><td align='left'>The Predicaments</td><td align='right'><a href="#Page_366">366</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_XXIII">CHAPTER XXIII</a></td></tr> +<tr><td align='center' colspan='3'>DEFINITION OF COMMON TERMS</td></tr> +<tr><td align='right'><a href="#chap_23_sect_1">§1.</a></td><td align='left'>The rigour of scientific method must be qualified</td><td align='right'><a href="#Page_369">369</a></td></tr> +<tr><td align='right'><a href="#chap_23_sect_2">§2.</a></td><td align='left'>Still, Language comprises the Nomenclature of an imperfect +Classification, to which every Definition is relative;</td><td align='right'><a href="#Page_370">370</a></td></tr> +<tr><td align='right'><a href="#chap_23_sect_3">§3.</a></td><td align='left'>and an imperfect Terminology</td><td align='right'><a href="#Page_374">374</a></td></tr> +<tr><td align='right'><a href="#chap_23_sect_4">§4.</a></td><td align='left'>Maxims and precautions of Definition</td><td align='right'><a href="#Page_375">375</a></td></tr> +<tr><td align='right'><a href="#chap_23_sect_5">§5.</a></td><td align='left'>Words of common language in scientific use</td><td align='right'><a href="#Page_378">378</a></td></tr> +<tr><td align='right'><a href="#chap_23_sect_6">§6.</a></td><td align='left'>How Definitions affect the cogency of arguments</td><td align='right'><a href="#Page_380">380</a></td></tr> +<tr><td> </td></tr> +<tr><td align='center' colspan='3'><a href="#CHAPTER_XXIV">CHAPTER XXIV</a></td></tr> +<tr><td align='center' colspan='3'>FALLACIES</td></tr> +<tr><td align='right'><a href="#chap_24_sect_1">§1.</a></td><td align='left'>Fallacy defined and divided</td><td align='right'><a href="#Page_385">385</a></td></tr> +<tr><td align='right'><a href="#chap_24_sect_2">§2.</a></td><td align='left'>Formal Fallacies of Deduction</td><td align='right'><a href="#Page_385">385</a></td></tr> +<tr><td align='right'><a href="#chap_24_sect_3">§3.</a></td><td align='left'>Formal Fallacies of Induction</td><td align='right'><a href="#Page_388">388</a></td></tr> +<tr><td align='right'><a href="#chap_24_sect_4">§4.</a></td><td align='left'>Material Fallacies classified</td><td align='right'><a href="#Page_394">394</a></td></tr> +<tr><td align='right'><a href="#chap_24_sect_5">§5.</a></td><td align='left'>Fallacies of Observation</td><td align='right'><a href="#Page_394">394</a></td></tr> +<tr><td align='right'><a href="#chap_24_sect_6">§6.</a></td><td align='left'>Begging the Question</td><td align='right'><a href="#Page_396">396</a></td></tr> +<tr><td align='right'><a href="#chap_24_sect_7">§7.</a></td><td align='left'>Surreptitious Conclusion</td><td align='right'><a href="#Page_398">398</a></td></tr> +<tr><td align='right'><a href="#chap_24_sect_8">§8.</a></td><td align='left'>Ambiguity</td><td align='right'><a href="#Page_400">400</a></td></tr> +<tr><td align='right'><a href="#chap_24_sect_9">§9.</a></td><td align='left'>Fallacies, a natural rank growth of the Human mind, not +easy to classify, or exterminate</td><td align='right'><a href="#Page_403">403</a></td></tr> +<tr><td> </td></tr> +<tr><td> </td><td align='left'><span class="smcap"><a href="#QUESTIONS">Questions</a></span></td><td align='right'><a href="#Page_405">405</a></td></tr> +</table></div> + +<p><span class='pagenum'>[Pg 1]<a name="Page_1" id="Page_1"></a></span></p> + +<hr style="width: 65%;" /> +<h2>LOGIC</h2> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_I" id="CHAPTER_I"></a>CHAPTER I</h2> + +<h3>INTRODUCTORY</h3> + + +<p><a name="chap_1_sect_1" id="chap_1_sect_1"></a>§ 1. Logic is the science that explains what conditions must be +fulfilled in order that a proposition may be proved, if it admits of +proof. Not, indeed, every such proposition; for as to those that declare +the equality or inequality of numbers or other magnitudes, to explain +the conditions of their proof belongs to Mathematics: they are said to +be <i>quantitative</i>. But as to all other propositions, called +<i>qualitative</i>, like most of those that we meet with in conversation, in +literature, in politics, and even in sciences so far as they are not +treated mathematically (say, Botany and Psychology); propositions that +merely tell us that something happens (as that <i>salt dissolves in +water</i>), or that something has a certain property (as that <i>ice is +cold</i>): as to these, it belongs to Logic to show how we may judge +whether they are true, or false, or doubtful. When propositions are +expressed with the universality and definiteness that belong to +scientific statements, they are called laws; and laws, so far as they +are not laws of quantity, are tested by the principles of Logic, if they +at all admit of proof.</p> + +<p>But it is plain that the process of proving cannot go on for ever; +something must be taken for granted; and this is <span class='pagenum'>[Pg 2]<a name="Page_2" id="Page_2"></a></span>usually considered to +be the case (1) with particular facts that can only be perceived and +observed, and (2) with those highest laws that are called 'axioms' or +'first principles,' of which we can only say that we know of no +exceptions to them, that we cannot help believing them, and that they +are indispensable to science and to consistent thought. Logic, then, may +be briefly defined as the science of proof with respect to <i>qualitative</i> +laws and propositions, except those that are axiomatic.</p> + +<p><a name="chap_1_sect_2" id="chap_1_sect_2"></a>§ 2. Proof may be of different degrees or stages of completeness. +Absolute proof would require that a proposition should be shown to agree +with all experience and with the systematic explanation of experience, +to be a necessary part of an all-embracing and self-consistent +philosophy or theory of the universe; but as no one hitherto has been +able to frame such a philosophy, we must at present put up with +something less than absolute proof. Logic, assuming certain principles +to be true of experience, or at least to be conditions of consistent +discourse, distinguishes the kinds of propositions that can be shown to +agree with these principles, and explains by what means the agreement +can best be exhibited. Such principles are those of Contradiction (<a href="#CHAPTER_VI">chap. vi.</a>), the Syllogism (<a href="#CHAPTER_IX">chap. ix.</a>), Causation (<a href="#CHAPTER_XIV">chap. xiv.</a>), and +Probabilities (<a href="#CHAPTER_XX">chap. xx.</a>). To bring a proposition or an argument under +them, or to show that it agrees with them, is logical proof.</p> + +<p>The extent to which proof is requisite, again, depends upon the present +purpose: if our aim be general truth for its own sake, a systematic +investigation is necessary; but if our object be merely to remove some +occasional doubt that has occurred to ourselves or to others, it may be +enough to appeal to any evidence that is admitted or not questioned. +Thus, if a man doubts that <i>some acids are compounds of oxygen</i>, but +grants that <i>some compounds of oxygen are acids</i>, he may agree to the +former proposition when you point out that it has the same meaning as +the <span class='pagenum'>[Pg 3]<a name="Page_3" id="Page_3"></a></span>latter, differing from it only in the order of the words. This is +called proof by immediate inference.</p> + +<p>Again, suppose that a man holds in his hand a piece of yellow metal, +which he asserts to be copper, and that we doubt this, perhaps +suggesting that it is really gold. Then he may propose to dip it in +vinegar; whilst we agree that, if it then turns green, it is copper and +not gold. On trying this experiment the metal does turn green; so that +we may put his argument in this way:—</p> + + +<div class="example"><span class="i0"><i>Whatever yellow metal turns green in vinegar is copper;</i><br /></span> +<span class="i0"><i>This yellow metal turns green in vinegar;</i><br /></span> +<span class="i0"><i>Therefore, this yellow metal is copper.</i></span></div> + + +<p class="noindent">Such an argument is called proof by mediate inference; because one +cannot see directly that the yellow metal is copper; but it is admitted +that any yellow metal is copper that turns green in vinegar, and we are +shown that this yellow metal has that property.</p> + +<p>Now, however, it may occur to us, that the liquid in which the metal was +dipped was not vinegar, or not pure vinegar, and that the greenness was +due to the impurity. Our friend must thereupon show by some means that +the vinegar was pure; and then his argument will be that, since nothing +but the vinegar came in contact with the metal, the greenness was due to +the vinegar; or, in other words, that contact with that vinegar was the +cause of the metal turning green.</p> + +<p>Still, on second thoughts, we may suspect that we had formerly conceded +too much; we may reflect that, although it had often been shown that +copper turned green in vinegar, whilst gold did not, yet the same might +not always happen. May it not be, we might ask, that just at this +moment, and perhaps always for the future gold turns, and will turn +green in vinegar, whilst copper does not and never will again? He will +probably reply that this is to doubt the uniformity of causation: he may +hope that we are not serious: he <span class='pagenum'>[Pg 4]<a name="Page_4" id="Page_4"></a></span>may point out to us that in every +action of our life we take such uniformity for granted. But he will be +obliged to admit that, whatever he may say to induce us to assent to the +principle of Nature's uniformity, his arguments will not amount to +logical proof, because every argument in some way assumes that +principle. He has come, in fact, to the limits of Logic. Just as Euclid +does not try to prove that 'two magnitudes equal to the same third are +equal to one another,' so the Logician (as such) does not attempt to +prove the uniformity of causation and the other principles of his +science.</p> + +<p>Even when our purpose is to ascertain some general truth, the results of +systematic inquiry may have various degrees of certainty. If Logic were +confined to strict demonstration, it would cover a narrow field. The +greater part of our conclusions can only be more or less probable. It +may, indeed, be maintained, not unreasonably, that no judgments +concerning matters of fact can be more than probable. Some say that all +scientific results should be considered as giving the average of cases, +from which deviations are to be expected. Many matters can only be +treated statistically and by the methods of Probability. Our ordinary +beliefs are adopted without any methodical examination. But it is the +aim, and it is characteristic, of a rational mind to distinguish degrees +of certainty, and to hold each judgment with the degree of confidence +that it deserves, considering the evidence for and against it. It takes +a long time, and much self-discipline, to make some progress toward +rationality; for there are many causes of belief that are not good +grounds for it—have no value as evidence. Evidence consists of (1) +observation; (2) reasoning checked by observation and by logical +principles; (3) memory—often inaccurate; (4) testimony—often +untrustworthy, but indispensable, since all we learn from books or from +other men is taken on testimony; (5) the agreement of all our results. +On the other hand, belief is caused by many <span class='pagenum'>[Pg 5]<a name="Page_5" id="Page_5"></a></span>influences that are not +evidence at all: such are (1) desire, which makes us believe in whatever +serves our purpose; fear and suspicion, which (paradoxically) make us +believe in whatever seems dangerous; (2) habit, which resists whatever +disturbs our prejudices; (3) vanity, which delights to think oneself +always right and consistent and disowns fallibility; (4) imitativeness, +suggestibility, fashion, which carry us along with the crowd. All these, +and nobler things, such as love and fidelity, fix our attention upon +whatever seems to support our prejudices, and prevent our attending to +any facts or arguments that threaten to overthrow them.</p> + +<p><a name="chap_1_sect_3" id="chap_1_sect_3"></a>§ 3. Two departments of Logic are usually recognised, Deduction and +Induction; that is, to describe them briefly, proof from principles, and +proof from facts. Classification is sometimes made a third department; +sometimes its topics are distributed amongst those of the former two. In +the present work the order adopted is, Deduction in chaps. ii. to xiii.; +Induction in chaps. xiii. to xx.; and, lastly, Classification. But such +divisions do not represent fundamentally distinct and opposed aspects of +the science. For although, in discussing any question with an opponent +who makes admissions, it may be possible to combat his views with merely +deductive arguments based upon his admissions; yet in any question of +general truth, Induction and Deduction are mutually dependent and imply +one another.</p> + +<p>This may be seen in one of the above examples. It was argued that a +certain metal must be copper, because every metal is copper that turns +green when dipped in vinegar. So far the proof appealed to a general +proposition, and was deductive. But when we ask how the general +proposition is known to be true, experiments or facts must be alleged; +and this is inductive evidence. Deduction then depends on Induction. But +if we ask, again, how any number of past experiments can prove a general +proposition, which <span class='pagenum'>[Pg 6]<a name="Page_6" id="Page_6"></a></span>must be good for the future as well as for the past, +the uniformity of causation is invoked; that is, appeal is made to a +principle, and that again is deductive proof. Induction then depends +upon Deduction.</p> + +<p>We may put it in this way: Deduction depends on Induction, if general +propositions are only known to us through the facts: Induction depends +on Deduction, because one fact can never prove another, except so far as +what is true of the one is true of the other and of any other of the +same kind; and because, to exhibit this resemblance of the facts, it +must be stated in a general proposition.</p> + +<p><a name="chap_1_sect_4" id="chap_1_sect_4"></a>§ 4. The use of Logic is often disputed: those who have not studied it, +often feel confident of their ability to do without it; those who have +studied it, are sometimes disgusted with what they consider to be its +superficial analysis of the grounds of evidence, or needless +technicality in the discussion of details. As to those who, not having +studied Logic, yet despise it, there will be time enough to discuss its +utility with them, when they know something about it; and as for those +who, having studied it, turn away in disgust, whether they are justified +every man must judge for himself, when he has attained to equal +proficiency in the subject. Meanwhile, the following considerations may +be offered in its favour:</p> + +<p>Logic states, and partly explains and applies, certain abstract +principles which all other sciences take for granted; namely, the axioms +above mentioned—the principles of Contradiction, of the Syllogism and +of Causation. By exercising the student in the apprehension of these +truths, and in the application of them to particular propositions, it +educates the power of abstract thought. Every science is a model of +method, a discipline in close and consecutive thinking; and this merit +Logic ought to possess in a high degree.</p> + +<p>For ages Logic has served as an introduction to Philosophy that is, to +Metaphysics and speculative Ethics. It <span class='pagenum'>[Pg 7]<a name="Page_7" id="Page_7"></a></span>is of old and honourable +descent: a man studies Logic in very good company. It is the warp upon +which nearly the whole web of ancient, mediæval and modern Philosophy is +woven. The history of thought is hardly intelligible without it.</p> + +<p>As the science of proof, Logic gives an account of the <i>general</i> nature +of evidence deductive and inductive, as applied in the physical and +social sciences and in the affairs of life. The <i>general</i> nature of such +evidence: it would be absurd of the logician to pretend to instruct the +chemist, economist and merchant, as to the <i>special</i> character of the +evidence requisite in their several spheres of judgment. Still, by +investigating the general conditions of proof, he sets every man upon +his guard against the insufficiency of evidence.</p> + +<p>One application of the science of proof deserves special mention: +namely, to that department of Rhetoric which has been the most +developed, relating to persuasion by means of oratory, leader-writing, +or pamphleteering. It is usually said that Logic is useful to convince +the judgment, not to persuade the will: but one way of persuading the +will is to convince the judgment that a certain course is advantageous; +and although this is not always the readiest way, it is the most +honourable, and leads to the most enduring results. Logic is the +backbone of Rhetoric.</p> + +<p>It has been disputed whether Logic is a science or an art; and, in fact, +it may be considered in both ways. As a statement of general truths, of +their relations to one another, and especially to the first principles, +it is a science; but it is an art when, regarding truth as an end +desired, it points out some of the means of attaining it—namely, to +proceed by a regular method, to test every judgment by the principles of +Logic, and to distrust whatever cannot be made consistent with them. +Logic does not, in the first place, teach us to reason. We learn to +reason as we learn to walk and talk, by the natural growth of our powers +with <span class='pagenum'>[Pg 8]<a name="Page_8" id="Page_8"></a></span>some assistance from friends and neighbours. The way to develop +one's power of reasoning is, first, to set oneself problems and try to +solve them. Secondly, since the solving of a problem depends upon one's +ability to call to mind parallel cases, one must learn as many facts as +possible, and keep on learning all one's life; for nobody ever knew +enough. Thirdly one must check all results by the principles of Logic. +It is because of this checking, verifying, corrective function of Logic +that it is sometimes called a Regulative or Normative Science. It cannot +give any one originality or fertility of invention; but it enables us to +check our inferences, revise our conclusions, and chasten the vagaries +of ambitious speculation. It quickens our sense of bad reasoning both in +others and in ourselves. A man who reasons deliberately, manages it +better after studying Logic than he could before, if he is sincere about +it and has common sense.</p> + +<p><a name="chap_1_sect_5" id="chap_1_sect_5"></a>§ 5. The relation of Logic to other sciences:</p> + +<p>(<i>a</i>) Logic is regarded by Spencer as co-ordinate with Mathematics, both +being Abstract Sciences—that is, sciences of the <i>relations</i> in which +things stand to one another, whatever the particular things may be that +are so related; and this view seems to be, on the whole, just—subject, +however, to qualifications that will appear presently.</p> + +<p>Mathematics treats of the relations of all sorts of things considered as +quantities, namely, as equal to, or greater or less than, one another. +Things may be quantitatively equal or unequal in <i>degree</i>, as in +comparing the temperature of bodies; or in <i>duration</i>; or in <i>spatial +magnitude</i>, as with lines, superficies, solids; or in <i>number</i>. And it +is assumed that the equality or inequality of things that cannot be +directly compared, may be proved indirectly on the assumption that +'things equal to the same thing are equal,' etc.</p> + +<p>Logic also treats of the relations of all sorts of things, but not as to +their quantity. It considers (i) that one thing may be like or unlike +another in certain attributes, <span class='pagenum'>[Pg 9]<a name="Page_9" id="Page_9"></a></span>as that iron is in many ways like tin or +lead, and in many ways unlike carbon or sulphur: (ii) that attributes +co-exist or coinhere (or do not) in the same subject, as metallic +lustre, hardness, a certain atomic weight and a certain specific gravity +coinhere in iron: and (iii) that one event follows another (or is the +effect of it), as that the placing of iron in water causes it to rust. +The relations of likeness and of coinherence are the ground of +Classification; for it is by resemblance of coinhering attributes that +things form classes: coinherence is the ground of judgments concerning +Substance and Attribute, as that iron is metallic; and the relation of +succession, in the mode of Causation, is the chief subject of the +department of Induction. It is usual to group together these relations +of attributes and of order in time, and call them qualitative, in order +to contrast them with the quantitative relations which belong to +Mathematics. And it is assumed that qualitative relations of things, +when they cannot be directly perceived, may be proved indirectly by +assuming the axiom of the Syllogism (<a href="#CHAPTER_IX">chap. ix.</a>) and the law of Causation +(<a href="#CHAPTER_XIV">chap. xiv.</a>).</p> + +<p>So far, then, Logic and Mathematics appear to be co-ordinate and +distinct sciences. But we shall see hereafter that the satisfactory +treatment of that special order of events in time which constitutes +Causation, requires a combination of Logic with Mathematics; and so does +the treatment of Probability. And, again, Logic may be said to be, in a +certain sense, 'prior to' or 'above' Mathematics as usually treated. For +the Mathematics assume that one magnitude must be either equal or +unequal to another, and that it cannot be both equal and unequal to it, +and thus take for granted the principles of Contradiction and Excluded +Middle; but the statement and elucidation of these Principles are left +to Logic (<a href="#CHAPTER_VI">chap. vi.</a>). The Mathematics also classify and define +magnitudes, as (in Geometry) triangles, squares, cubes, spheres; but the +principles of classification and definition remain for Logic to +discuss.</p><p><span class='pagenum'>[Pg 10]<a name="Page_10" id="Page_10"></a></span></p> + +<p>(<i>b</i>) As to the concrete Sciences, such as Astronomy, Chemistry, +Zoology, Sociology—Logic (as well as Mathematics) is implied in them +all; for all the propositions of which they consist involve causation, +co-existence, and class-likeness. Logic is therefore said to be prior to +them or above them: meaning by 'prior' not that it should be studied +earlier, for that is not a good plan; meaning by 'above' not in dignity, +for distinctions of dignity amongst liberal studies are absurd. But it +is a philosophical idiom to call the abstract 'prior to,' or 'higher +than,' the concrete (see Porphyry's Tree, <a href="#chap_22_sect_8">chap. xxii. § 8</a>); and Logic is +more abstract than Astronomy or Sociology. Philosophy may thank that +idiom for many a foolish notion.</p> + +<p>(<i>c</i>) But, as we have seen, Logic does not investigate the truth, +trustworthiness, or validity of its own principles; nor does +Mathematics: this task belongs to Metaphysics, or Epistemology, the +criticism of knowledge and beliefs.</p> + +<p>Logic assumes, for example, that things are what to a careful scrutiny +they seem to be; that animals, trees, mountains, planets, are bodies +with various attributes, existing in space and changing in time; and +that certain principles, such as Contradiction and Causation, are true +of things and events. But Metaphysicians have raised many plausible +objections to these assumptions. It has been urged that natural objects +do not really exist on their own account, but only in dependence on some +mind that contemplates them, and that even space and time are only our +way of perceiving things; or, again, that although things do really +exist on their own account, it is in an entirely different way from that +in which we know them. As to the principle of Contradiction—that if an +object has an attribute, it cannot at the same time and in the same way +be without it (<i>e.g.</i>, if an animal is conscious, it is false that it is +not conscious)—it has been contended that the speciousness of this +principle is only due to the obtuseness of our minds, or even to the +poverty of language, which <span class='pagenum'>[Pg 11]<a name="Page_11" id="Page_11"></a></span>cannot make the fine distinctions that exist +in Nature. And as to Causation, it is sometimes doubted whether events +always have physical causes; and it is often suggested that, granting +they have physical causes, yet these are such as we can neither perceive +nor conceive; belonging not to the order of Nature as we know it, but to +the secret inwardness and reality of Nature, to the wells and reservoirs +of power, not to the spray of the fountain that glitters in our +eyes—'occult causes,' in short. Now these doubts and surmises are +metaphysical spectres which it remains for Metaphysics to lay. Logic has +no direct concern with them (although, of course, metaphysical +discussion is expected to be logical), but keeps the plain path of plain +beliefs, level with the comprehension of plain men. Metaphysics, as +examining the grounds of Logic itself, is sometimes regarded as 'the +higher Logic'; and, certainly, the study of Metaphysics is necessary to +every one who would comprehend the nature and functions of Logic, or the +place of his own mind and of Reason in the world.</p> + +<p>(<i>d</i>) The relation of Logic to Psychology will be discussed in the next +section.</p> + +<p>(<i>e</i>) As a Regulative Science, pointing out the conditions of true +inference (within its own sphere), Logic is co-ordinate with (i) Ethics, +considered as assigning the conditions of right conduct, and with (ii) +Æsthetics, considered as determining the principles of criticism and +good taste.</p> + +<p><a name="chap_1_sect_6" id="chap_1_sect_6"></a>§ 6. Three principal schools of Logicians are commonly recognised: +Nominalist, Conceptualist, and Materialist, who differ as to what it is +that Logic really treats of: the Nominalists say, 'of language'; the +Conceptualists, 'of thought'; the Materialists, 'of relations of fact.' +To illustrate these positions let us take authors who, if some of them +are now neglected, have the merit of stating their contrasted views with +a distinctness that later refinements tend to obscure.</p><p><span class='pagenum'>[Pg 12]<a name="Page_12" id="Page_12"></a></span></p> + +<p>(<i>a</i>) Whately, a well-known Nominalist, regarded Logic as the Science +and Art of Reasoning, but at the same time as "entirely conversant about +language"; that is to say, it is the business of Logic to discover those +modes of statement which shall ensure the cogency of an argument, no +matter what may be the subject under discussion. Thus, <i>All fish are +cold-blooded</i>, ∴ <i>some cold-blooded things are fish:</i> this is a sound +inference by the mere manner of expression; and equally sound is the +inference, <i>All fish are warm-blooded</i>, ∴ <i>some warm-blooded things are +fish</i>. The latter proposition may be false, but it follows; and +(according to this doctrine) Logic is only concerned with the consistent +use of words: the truth or falsity of the proposition itself is a +question for Zoology. The short-coming of extreme Nominalism lies in +speaking of language as if its meaning were unimportant. But Whately did +not intend this: he was a man of great penetration and common-sense.</p> + +<p>(<i>b</i>) Hamilton, our best-known Conceptualist, defined Logic as the +science of the "formal laws of thought," and "of thought as thought," +that is, without regard to the matter thought about. Just as Whately +regarded Logic as concerned merely with cogent forms of statement, so +Hamilton treated it as concerned merely with the necessary relations of +thought. This doctrine is called Conceptualism, because the simplest +element of thought is the Concept; that is, an abstract idea, such as is +signified by the word <i>man, planet, colour, virtue</i>; not a +representative or generic image, but the thought of all attributes +common to any class of things. Men, planets, colours, virtuous actions +or characters, have, severally, something in common on account of which +they bear these general names; and the thought of what they have in +common, as the ground of these names, is a Concept. To affirm or deny +one concept of another, as <i>Some men are virtuous</i>, or <i>No man is +perfectly virtuous</i>, is to form a Judgment, corresponding to the +Proposition of which the other schools of Logic discourse.<span class='pagenum'>[Pg 13]<a name="Page_13" id="Page_13"></a></span> +Conceptualism, then, investigates the conditions of consistent judgment.</p> + +<p>To distinguish Logic from Psychology is most important in connection +with Conceptualism. Concepts and Judgments being mental acts, or +products of mental activity, it is often thought that Logic must be a +department of Psychology. It is recognised of course, that Psychology +deals with much more than Logic does, with sensation, pleasure and pain, +emotion, volition; but in the region of the intellect, especially in its +most deliberate and elaborate processes, namely, conception, judgment, +and reasoning, Logic and Psychology seem to occupy common ground. In +fact, however, the two sciences have little in common except a few +general terms, and even these they employ in different senses. It is +usual to point out that Psychology tries to explain the subjective +<i>processes</i> of conception, judgment and reasoning, and to give their +natural history; but that Logic is wholly concerned with the <i>results</i> +of such processes, with concepts, judgments and reasonings, and merely +with the validity of the results, that is, with their truth or +consistency; whilst Psychology has nothing to do with their validity, +but only with their causes. Besides, the logical judgment (in Formal +Logic at least) is quite a different thing from the psychological: the +latter involves feeling and belief, whereas the former is merely a given +relation of concepts. <i>S is P</i>: that is a model logical judgment; there +can be no question of believing it; but it is logically valid if <i>M is +P</i> and <i>S is M</i>. When, again, in Logic, one deals with belief, it +depends upon evidence; whereas, in Psychology belief is shown to depend +upon causes which may have evidentiary value or may not; for Psychology +explains quite impartially the growth of scientific insight and the +growth of prejudice.</p> + +<p>(<i>c</i>) Mill, Bain, and Venn are the chief Materialist logicians; and to +guard against the error of confounding Materialism in Logic with the +ontological doctrine that nothing exists but<span class='pagenum'>[Pg 14]<a name="Page_14" id="Page_14"></a></span> Matter, it may suffice to +remember that in Metaphysics all these philosophers are Idealists. +Materialism in Logic consists in regarding propositions as affirming or +denying relations (<i>cf.</i> <a href="#chap_1_sect_5">§ 5</a>) between matters-of-fact in the widest +sense; not only physical facts, but ideas, social and moral relations; +it consists, in short, in attending to the meaning of propositions. It +treats the first principles of Contradiction and Causation as true of +things so far as they are known to us, and not merely as conditions or +tendencies of thought; and it takes these principles as conditions of +right thinking, because they seem to hold good of Nature and human life.</p> + +<p>To these differences of opinion it will be necessary to recur in the +next chapter (<a href="#chap_2_sect_4">§ 4</a>); but here I may observe that it is easy to exaggerate +their importance in Logic. There is really little at issue between +schools of logicians as such, and as far as their doctrines run +parallel; it is on the metaphysical grounds of their study, or as to its +scope and comprehension, that they find a battle-field. The present work +generally proceeds upon the third, or Materialist doctrine. If Deduction +and Induction are regarded as mutually dependent parts of one science, +uniting the discipline of consistent discourse with the method of +investigating laws of physical phenomena, the Materialist doctrine, that +the principles of Logic are founded on fact, seems to be the most +natural way of thinking. But if the unity of Deduction and Induction is +not disputed by the other schools, the Materialist may regard them as +allies exhibiting in their own way the same body of truths. The +Nominalist may certainly claim that his doctrine is indispensable: +consistently cogent forms of statement are necessary both to the +Conceptualist and to the Materialist; neither the relations of thought +nor those of fact can be arrested or presented without the aid of +language or some equivalent system of signs. The Conceptualist may urge +that the Nominalist's forms of statement and argument exist for the sake +of their meaning, namely, judgments <span class='pagenum'>[Pg 15]<a name="Page_15" id="Page_15"></a></span>and reasonings; and that the +Materialist's laws of Nature are only judgments founded upon our +conceptions of Nature; that the truth of observations and experiments +depends upon our powers of perception; that perception is inseparable +from understanding, and that a system of Induction may be constructed +upon the axiom of Causation, regarded as a principle of Reason, just as +well as by considering it as a law of Nature, and upon much the same +lines. The Materialist, admitting all this, may say that a judgment is +only the proximate meaning of a proposition, and that the ultimate +meaning, the meaning of the judgment itself, is always some +matter-of-fact; that the other schools have not hitherto been eager to +recognise the unity of Deduction and Induction or to investigate the +conditions of trustworthy experiments and observations within the limits +of human understanding; that thought is itself a sort of fact, as +complex in its structure, as profound in its relations, as subtle in its +changes as any other fact, and therefore at least as hard to know; that +to turn away from the full reality of thought in perception, and to +confine Logic to artificially limited concepts, is to abandon the effort +to push method to the utmost and to get as near truth as possible; and +that as to Causation being a principle of Reason rather than of Nature, +the distinction escapes his apprehension, since Nature seems to be that +to which our private minds turn upon questions of Causation for +correction and instruction; so that if he does not call Nature the +Universal Reason, it is because he loves severity of style.</p><p><span class='pagenum'>[Pg 16]<a name="Page_16" id="Page_16"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_II" id="CHAPTER_II"></a>CHAPTER II</h2> + +<h3>GENERAL ANALYSIS OF PROPOSITIONS</h3> + + +<p><a name="chap_2_sect_1" id="chap_2_sect_1"></a>§ 1. Since Logic discusses the proof or disproof, or (briefly) the +testing of propositions, we must begin by explaining their nature. A +proposition, then, may first be described in the language of grammar as +<i>a sentence indicative</i>; and it is usually expressed in the present +tense.</p> + +<p>It is true that other kinds of sentences, optative, imperative, +interrogative, exclamatory, if they express or imply an assertion, are +not beyond the view of Logic; but before treating such sentences, Logic, +for greater precision, reduces them to their equivalent sentences +indicative. Thus, <i>I wish it were summer</i> may be understood to mean, +<i>The coming of summer is an object of my desire</i>. <i>Thou shalt not kill</i> +may be interpreted as <i>Murderers are in danger of the judgment</i>. +Interrogatories, when used in argument, if their form is affirmative, +have negative force, and affirmative force if their form is negative. +Thus, <i>Do hypocrites love virtue?</i> anticipates the answer, <i>No</i>. <i>Are +not traitors the vilest of mankind?</i> anticipates the answer, <i>Yes</i>. So +that the logical form of these sentences is, <i>Hypocrites are not lovers +of virtue</i>; <i>Traitors are the vilest of mankind</i>. Impersonal +propositions, such as <i>It rains</i>, are easily rendered into logical forms +of equivalent meaning, thus: <i>Rain is falling</i>; or (if that be +tautology), <i>The clouds are raining</i>. Exclamations may seem capricious, +but are often part of the argument. <i>Shade of Chatham!</i> usually means +<i>Chatham, being aware of our present foreign policy, is much +disgusted</i>.<span class='pagenum'>[Pg 17]<a name="Page_17" id="Page_17"></a></span> It is in fact, an appeal to authority, without the +inconvenience of stating what exactly it is that the authority declares.</p> + +<p><a name="chap_2_sect_2" id="chap_2_sect_2"></a>§ 2. But even sentences indicative may not be expressed in the way most +convenient to logicians. <i>Salt dissolves in water</i> is a plain enough +statement; but the logician prefers to have it thus: <i>Salt is soluble in +water</i>. For he says that a proposition is analysable into three +elements: (1) a Subject (as <i>Salt</i>) about which something is asserted or +denied; (2) a Predicate (as <i>soluble in water</i>) which is asserted or +denied of the Subject, and (3) the Copula (<i>is</i> or <i>are</i>, or <i>is not</i> or +<i>are not</i>), the sign of relation between the Subject and Predicate. The +Subject and Predicate are called the Terms of the proposition: and the +Copula may be called the sign of predication, using the verb 'to +predicate' indefinitely for either 'to affirm' or 'to deny.' Thus <i>S is +P</i> means that the term <i>P</i> is given as related in some way to the term +<i>S</i>. We may, therefore, further define a Proposition as 'a sentence in +which one term is predicated of another.'</p> + +<p>In such a proposition as <i>Salt dissolves</i>, the copula (<i>is</i>) is +contained in the predicate, and, besides the subject, only one element +is exhibited: it is therefore said to be <i>secundi adjacentis</i>. When all +three parts are exhibited, as in <i>Salt is soluble</i>, the proposition is +said to be <i>tertii adjacentis</i>.</p> + +<p>For the ordinary purposes of Logic, in predicating attributes of a thing +or class of things, the copula <i>is</i>, or <i>is not</i>, sufficiently +represents the relation of subject and predicate; but when it is +desirable to realise fully the nature of the relation involved, it may +be better to use a more explicit form. Instead of saying +<i>Salt—is—soluble</i>, we may say <i>Solubility—coinheres with—the nature +of salt</i>, or <i>The putting of salt in water—is a cause of—its +dissolving</i>: thus expanding the copula into a full expression of the +relation we have in view, whether coinherence or causation.</p> + +<p><a name="chap_2_sect_3" id="chap_2_sect_3"></a>§ 3. The sentences of ordinary discourse are, indeed, for <span class='pagenum'>[Pg 18]<a name="Page_18" id="Page_18"></a></span>the most +part, longer and more complicated than the logical form of propositions; +it is in order to prove them, or to use them in the proof of other +propositions, that they are in Logic reduced as nearly as possible to +such simple but explicit expressions as the above (<i>tertii adjacentis</i>). +A Compound Proposition, reducible to two or more simple ones, is said to +be exponible.</p> + +<p>The modes of compounding sentences are explained in every grammar-book. +One of the commonest forms is the copulative, such as <i>Salt is both +savoury and wholesome</i>, equivalent to two simple propositions: <i>Salt is +savoury; Salt is wholesome. Pure water is neither sapid nor odorous</i>, +equivalent to <i>Water is not sapid; Water is not odorous</i>. Or, again, +<i>Tobacco is injurious, but not when used in moderation</i>, equivalent to +<i>Much tobacco is injurious; a little is not</i>.</p> + +<p>Another form of Exponible is the Exceptive, as <i>Kladderadatsch is +published daily, except on week-days</i>, equivalent to <i>Kladderadatsch is +published on Sunday; it is not published any other day</i>. Still another +Exponible is the Exclusive, as <i>Only men use fire</i>, equivalent to <i>Men +are users of fire; No other animals are</i>. Exceptive and exclusive +sentences are, however, equivalent forms; for we may say, +<i>Kladderadatsch is published only on Sunday</i>; and <i>No animals use fire, +except men</i>.</p> + +<p>There are other compound sentences that are not exponible, since, though +they contain two or more verbal clauses, the construction shows that +these are inseparable. Thus, <i>If cats are scarce, mice are plentiful</i>, +contains two verbal clauses; but <i>if cats are scarce</i> is conditional, +not indicative; and <i>mice are plentiful</i> is subject to the condition +that <i>cats are scarce</i>. Hence the whole sentence is called a Conditional +Proposition. For the various forms of Conditional Propositions see <a href="#chap_5_sect_4">chap. +v. § 4</a>.</p> + +<p>But, in fact, to find the logical force of recognised grammatical forms +is the least of a logician's difficulties in <span class='pagenum'>[Pg 19]<a name="Page_19" id="Page_19"></a></span>bringing the discourses of +men to a plain issue. Metaphors, epigrams, innuendoes and other figures +of speech present far greater obstacles to a lucid reduction whether for +approval or refutation. No rules can be given for finding everybody's +meaning. The poets have their own way of expressing themselves; +sophists, too, have their own way. And the point often lies in what is +unexpressed. Thus, "barbarous nations make, the civilised write +history," means that civilised nations do not make history, which none +is so brazen as openly to assert. Or, again, "Alcibiades is dead, but X +is still with us"; the whole meaning of this 'exponible' is that X would +be the lesser loss to society. Even an epithet or a suffix may imply a +proposition: <i>This personage</i> may mean <i>X is a pretentious nobody</i>.</p> + +<p>How shall we interpret such illusive predications except by cultivating +our literary perceptions, by reading the most significant authors until +we are at home with them? But, no doubt, to disentangle the compound +propositions, and to expand the abbreviations of literature and +conversation, is a useful logical exercise. And if it seem a laborious +task thus to reduce to its logical elements a long argument in a speech +or treatise, it should be observed that, as a rule, in a long discourse +only a few sentences are of principal importance to the reasoning, the +rest being explanatory or illustrative digression, and that a close +scrutiny of these cardinal sentences will frequently dispense us from +giving much attention to the rest.</p> + +<p><a name="chap_2_sect_4" id="chap_2_sect_4"></a>§ 4. But now, returning to the definition of a Proposition given in <a href="#chap_2_sect_2">§ 2</a>, +that it is 'a sentence in which one term is predicated of another,' we +must consider what is the import of such predication. For the +definition, as it stands, seems to be purely Nominalist. Is a +proposition nothing more than a certain synthesis of words; or, is it +meant to correspond with something further, a synthesis of ideas, or a +relation of facts?</p> + +<p>Conceptualist logicians, who speak of judgments instead <span class='pagenum'>[Pg 20]<a name="Page_20" id="Page_20"></a></span>of +propositions, of course define the judgment in their own language. +According to Hamilton, it is "a recognition of the relation of +congruence or confliction in which two concepts stand to each other." To +lighten the sentence, I have omitted one or two qualifications +(Hamilton's <i>Lectures on Logic</i>, xiii.). "Thus," he goes on "if we +compare the thoughts <i>water</i>, <i>iron</i>, and <i>rusting</i>, we find them +congruent, and connect them into a single thought, thus: <i>water rusts +iron</i>—in that case we form a judgment." When a judgment is expressed in +words, he says, it is called a proposition.</p> + +<p>But has a proposition no meaning beyond the judgment it expresses? Mill, +who defines it as "a portion of discourse in which a predicate is +affirmed or denied of a subject" (<i>Logic</i>, Book 1., chap. iv. § 1.), +proceeds to inquire into the import of propositions (Book 1., chap. v.), +and finds three classes of them: (<i>a</i>) those in which one proper name is +predicated of another; and of these Hobbes's Nominalist definition is +adequate, namely, that a proposition asserts or denies that the +predicate is a name for the same thing as the subject, as <i>Tully is +Cicero</i>.</p> + +<p>(<i>b</i>) Propositions in which the predicate means a part (or the whole) of +what the subject means, as <i>Horses are animals</i>, <i>Man is a rational +animal</i>. These are Verbal Propositions (see below: <a href="#chap_5_sect_6">chap. v. § 6</a>), and +their import consists in affirming or denying a coincidence between the +meanings of names, as <i>The meaning of 'animal' is part of the meaning of +'horse.'</i> They are partial or complete definitions.</p> + +<p>But (<i>c</i>) there are also Real Propositions, whose predicates do not mean +the same as their subjects, and whose import consists in affirming or +denying one of five different kinds of matter of fact: (1) That the +subject exists, or does not; as if we say <i>The bison exists</i>, <i>The great +auk is extinct</i>. (2) Co-existence, as <i>Man is mortal</i>; that is, <i>the +being subject to death coinheres with the qualities on account of which +we call certain objects men</i>. (3) Succession, as <i>Night follows day</i>.<span class='pagenum'>[Pg 21]<a name="Page_21" id="Page_21"></a></span> +(4) Causation (a particular kind of Succession), as <i>Water rusts iron</i>. +(5) Resemblance, as <i>The colour of this geranium is like that of a +soldier's coat</i>, or <i>A = B</i>.</p> + +<p>On comparing this list of real predications with the list of logical +relations given above (<a href="#chap_1_sect_5">chap. i. § 5</a> (<i>a</i>)), it will be seen that the two +differ only in this, that I have there omitted simple Existence. Nothing +simply exists, unrelated either in Nature or in knowledge. Such a +proposition as <i>The bison exists</i> may, no doubt, be used in Logic +(subject to interpretation) for the sake of custom or for the sake of +brevity; but it means that some specimens are still to be found in N. +America, or in Zoological gardens.</p> + +<p>Controversy as to the Import of Propositions really turns upon a +difference of opinion as to the scope of Logic and the foundations of +knowledge. Mill was dissatisfied with the "congruity" of concepts as the +basis of a judgment. Clearly, mere congruity does not justify belief. In +the proposition <i>Water rusts iron</i>, the concepts <i>water, rust</i> and +<i>iron</i> may be congruous, but does any one assert their connection on +that ground? In the proposition <i>Murderers are haunted by the ghosts of +their victims</i>, the concepts <i>victim, murderer, ghost</i> have a high +degree of congruity; yet, unfortunately, I cannot believe it: there +seems to be no such cheap defence of innocence. Now, Mill held that +Logic is concerned with the grounds of belief, and that the scope of +Logic includes Induction as well as Deduction; whereas, according to +Hamilton, Induction is only Modified Logic, a mere appendix to the +theory of the "forms of thought as thought." Indeed, Mill endeavoured in +his <i>Logic</i> to probe the grounds of belief deeper than usual, and +introduced a good deal of Metaphysics—either too much or not +enough—concerning the ground of axioms. But, at any rate, his great +point was that belief, and therefore (for the most part) the Real +Proposition, is concerned not merely with the relations of words, or +even of ideas, but with matters of fact; that is, both propositions and +judgments <span class='pagenum'>[Pg 22]<a name="Page_22" id="Page_22"></a></span>point to something further, to the relations of things which +we can examine, not merely by thinking about them (comparing them in +thought), but by observing them with the united powers of thought and +perception. This is what convinces us that <i>water rusts iron</i>: and the +difficulty of doing this is what prevents our feeling sure that +<i>murderers are haunted by the ghosts of their victims</i>. Hence, although +Mill's definition of a proposition, given above, is adequate for +propositions in general; yet that kind of proposition (the Real) with +regard to which Logic (in Mill's view) investigates the conditions of +proof, may be more explicitly and pertinently defined as 'a predication +concerning the relation of matters of fact.'</p> + +<p><a name="chap_2_sect_5" id="chap_2_sect_5"></a>§ 5. This leads to a very important distinction to which we shall often +have to refer in subsequent pages—namely, the distinction between the +Form and the Matter of a proposition or of an argument. The distinction +between Form and Matter, as it is ordinarily employed, is easily +understood. An apple growing in the orchard and a waxen apple on the +table may have the same shape or form, but they consist of different +materials; two real apples may have the same shape, but contain distinct +ounces of apple-stuff, so that after one is eaten the other remains to +be eaten. Similarly, tables may have the same shape, though one be made +of marble, another of oak, another of iron. The form is common to +several things, the matter is peculiar to each. Metaphysicians have +carried the distinction further: apples, they say, may have not only the +same outward shape, but the same inward constitution, which, therefore, +may be called the Form of apple-stuff itself—namely, a certain +pulpiness, juiciness, sweetness, <i>etc.</i>; qualities common to all dessert +apples: yet their Matter is different, one being here, another +there—differing in place or time, if in nothing else. The definition of +a species is the form of every specimen of it.</p> + +<p>To apply this distinction to the things of Logic: it is easy <span class='pagenum'>[Pg 23]<a name="Page_23" id="Page_23"></a></span>to see how +two propositions may have the same Form but different Matter: not using +'Form' in the sense of 'shape,' but for that which is common to many +things, in contrast with that which is peculiar to each. Thus, <i>All male +lions are tawny</i> and <i>All water is liquid at 50° Fahrenheit</i>, are two +propositions that have the same form, though their matter is entirely +different. They both predicate something of the whole of their subjects, +though their subjects are different, and so are the things predicated of +them. Again, <i>All male lions have tufted tails</i> and <i>All male lions have +manes</i>, are two propositions having the same form and, in their +subjects, the same matter, but different matter in their predicates. If, +however, we take two such propositions as these: <i>All male lions have +manes</i> and <i>Some male lions have manes</i>, here the matter is the same in +both, but the form is different—in the first, predication is made +concerning <i>every</i> male lion; in the second of only <i>some</i> male lions; +the first is <i>universal</i>, the second is <i>particular</i>. Or, again, if we +take <i>Some tigers are man-eaters</i> and <i>Some tigers are not man-eaters</i>, +here too the matter is the same, but the form is different; for the +first proposition is <i>affirmative</i>, whilst the second is <i>negative</i>.</p> + +<p><a name="chap_2_sect_6" id="chap_2_sect_6"></a>§ 6. Now, according to Hamilton and Whately, pure Logic has to do only +with the Form of propositions and arguments. As to their Matter, whether +they are really true in fact, that is a question, they said, not for +Logic, but for experience, or for the special sciences. But Mill desired +so to extend logical method as to test the material truth of +propositions: he thought that he could expound a method by which +experience itself and the conclusions of the special sciences may be +examined.</p> + +<p>To this method it may be objected, that the claim to determine Material +Truth takes for granted that the order of Nature will remain unchanged, +that (for example) water not only at present is a liquid at 50° +Fahrenheit, but will always be so; whereas (although we have no reason +to expect such a thing) the order of Nature may alter—it is at <span class='pagenum'>[Pg 24]<a name="Page_24" id="Page_24"></a></span>least +supposable—and in that event water may freeze at such a temperature. +Any matter of fact, again, must depend on observation, either directly, +or by inference—as when something is asserted about atoms or ether. But +observation and material inference are subject to the limitations of our +faculties; and however we may aid observation by microscopes and +micrometers, it is still observation; and however we may correct our +observations by repetition, comparison and refined mathematical methods +of making allowances, the correction of error is only an approximation +to accuracy. Outside of Formal Reasoning, suspense of judgment is your +only attitude.</p> + +<p>But such objections imply that nothing short of absolute truth has any +value; that all our discussions and investigations in science or social +affairs are without logical criteria; that Logic must be confined to +symbols, and considered entirely as mental gymnastics. In this book +prominence will be given to the character of Logic as a formal science, +and it will also be shown that Induction itself may be treated formally; +but it will be assumed that logical forms are valuable as representing +the actual relations of natural and social phenomena.</p> + +<p><a name="chap_2_sect_7" id="chap_2_sect_7"></a>§ 7. Symbols are often used in Logic instead of concrete terms, not only +in Symbolic Logic where the science is treated algebraically (as by Dr. +Venn in his <i>Symbolic Logic</i>), but in ordinary manuals; so that it may +be well to explain the use of them before going further.</p> + +<p>It is a common and convenient practice to illustrate logical doctrines +by examples: to show what is meant by a Proposition we may give <i>salt is +soluble</i>, or <i>water rusts iron:</i> the copulative exponible is exemplified +by <i>salt is savoury and wholesome</i>; and so on. But this procedure has +some disadvantages: it is often cumbrous; and it may distract the +reader's attention from the point to be explained by exciting his +interest in the special fact of the illustration. Clearly, too, so far +as Logic is formal, no particular matter <span class='pagenum'>[Pg 25]<a name="Page_25" id="Page_25"></a></span>of fact can adequately +illustrate any of its doctrines. Accordingly, writers on Logic employ +letters of the alphabet instead of concrete terms, (say) <i>X</i> instead of +<i>salt</i> or instead of <i>iron</i>, and (say) <i>Y</i> instead of <i>soluble</i> or +instead of <i>rusted by water</i>; and then a proposition may be represented +by <i>X is Y</i>. It is still more usual to represent a proposition by <i>S is +(or is not) P, S</i> being the initial of Subject and <i>P</i> of Predicate; +though this has the drawback that if we argue—<i>S is P</i>, therefore <i>P is +S</i>, the symbols in the latter proposition no longer have the same +significance, since the former subject is now the predicate.</p> + +<p>Again, negative terms frequently occur in Logic, such as <i>not-water</i>, or +<i>not-iron</i>, and then if <i>water</i> or <i>iron</i> be expressed by <i>X</i>, the +corresponding negative may be expressed by <i>x</i>; or, generally, if a +capital letter stand for a positive term, the corresponding small letter +represents the negative. The same device may be adopted to express +contradictory terms: either of them being <i>X</i>, the other is <i>x</i> (see +chap. iv., §§ <a href="#chap_4_sect_7">7</a>-<a href="#chap_4_sect_8">8</a>); or the contradictory terms may be expressed by <i>x</i> +and <i>x̄</i>, <i>y</i> and <i>ȳ</i>.</p> + +<p>And as terms are often compounded, it may be convenient to express them +by a combination of letters: instead of illustrating such a case by +<i>boiling water</i> or <i>water that is boiling</i>, we may write <i>XY</i>; or since +positive and negative terms may be compounded, instead of illustrating +this by <i>water that is not boiling</i>, we may write <i>Xy</i>.</p> + +<p>The convenience of this is obvious; but it is more than convenient; for, +if one of the uses of Logic be to discipline the power of abstract +thought, this can be done far more effectually by symbolic than by +concrete examples; and if such discipline were the only use of Logic it +might be best to discard concrete illustrations altogether, at least in +advanced text-books, though no doubt the practice would be too severe +for elementary manuals. On the other hand, to show the practical +applicability of Logic to the arguments and proofs of actual life, or +even of the concrete sciences, <span class='pagenum'>[Pg 26]<a name="Page_26" id="Page_26"></a></span>merely symbolic illustration may be not +only useless but even misleading. When we speak of politics, or poetry, +or species, or the weather, the terms that must be used can rarely have +the distinctness and isolation of X and Y; so that the perfunctory use +of symbolic illustration makes argument and proof appear to be much +simpler and easier matters than they really are. Our belief in any +proposition never rests on the proposition itself, nor merely upon one +or two others, but upon the immense background of our general knowledge +and beliefs, full of circumstances and analogies, in relation to which +alone any given proposition is intelligible. Indeed, for this reason, it +is impossible to illustrate Logic sufficiently: the reader who is in +earnest about the cogency of arguments and the limitation of proofs, and +is scrupulous as to the degrees of assent that they require, must +constantly look for illustrations in his own knowledge and experience +and rely at last upon his own sagacity.</p><p><span class='pagenum'>[Pg 27]<a name="Page_27" id="Page_27"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_III" id="CHAPTER_III"></a>CHAPTER III</h2> + +<h3>OF TERMS AND THEIR DENOTATION</h3> + + +<p><a name="chap_3_sect_1" id="chap_3_sect_1"></a>§ 1. In treating of Deductive Logic it is usual to recognise three +divisions of the subject: first, the doctrine of Terms, words, or other +signs used as subjects or predicates; secondly, the doctrine of +Propositions, analysed into terms related; and, thirdly, the doctrine of +the Syllogism in which propositions appear as the grounds of a +conclusion.</p> + +<p>The terms employed are either letters of the alphabet, or the words of +common language, or the technicalities of science; and since the words +of common language are most in use, it is necessary to give some account +of common language as subserving the purposes of Logic. It has been +urged that we cannot think or reason at all without words, or some +substitute for them, such as the signs of algebra; but this is an +exaggeration. Minds greatly differ, and some think by the aid of +definite and comprehensive picturings, especially in dealing with +problems concerning objects in space, as in playing chess blindfold, +inventing a machine, planning a tour on an imagined map. Most people +draw many simple inferences by means of perceptions, or of mental +imagery. On the other hand, some men think a good deal without any +continuum of words and without any imagery, or with none that seems +relevant to the purpose. Still the more elaborate sort of thinking, the +grouping and concatenation of inferences, which we call reasoning, +cannot be carried far without language or some equivalent system of +signs. It <span class='pagenum'>[Pg 28]<a name="Page_28" id="Page_28"></a></span>is not merely that we need language to express our reasonings +and communicate them to others: in solitary thought we often depend on +words—'talk to ourselves,' in fact; though the words or sentences that +then pass through our minds are not always fully formed or articulated. +In Logic, moreover, we have carefully to examine the grounds (at least +the proximate grounds) of our conclusions; and plainly this cannot be +done unless the conclusions in question are explicitly stated and +recorded.</p> + +<p>Conceptualists say that Logic deals not with the process of thinking +(which belongs to Psychology) but with its results; not with conceiving +but with concepts; not with judging but with judgments. Is the concept +self-consistent or adequate? Logic asks; is the judgment capable of +proof? Now, it is only by recording our thoughts in language that it +becomes possible to distinguish between the process and the result of +thought. Without language, the act and the product of thinking would be +identical and equally evanescent. But by carrying on the process in +language and remembering or otherwise recording it, we obtain a result +which may be examined according to the principles of Logic.</p> + +<p><a name="chap_3_sect_2" id="chap_3_sect_2"></a>§ 2. As Logic, then, must give some account of language, it seems +desirable to explain how its treatment of language differs from that of +Grammar and from that of Rhetoric.</p> + +<p>Grammar is the study of the words of some language, their classification +and derivation, and of the rules of combining them, according to the +usage at any time recognised and followed by those who are considered +correct writers or speakers. Composition may be faultless in its +grammar, though dull and absurd.</p> + +<p>Rhetoric is the study of language with a view to obtaining some special +effect in the communication of ideas or feelings, such as +picturesqueness in description, vivacity in narration, lucidity in +exposition, vehemence in persuasion, or literary charm. Some of these +ends are often gained in spite of faulty syntax or faulty logic; but +since the few whom bad <span class='pagenum'>[Pg 29]<a name="Page_29" id="Page_29"></a></span>grammar saddens or incoherent arguments divert +are not carried away, as they else might be, by an unsophisticated +orator, Grammar and Logic are necessary to the perfection of Rhetoric. +Not that Rhetoric is in bondage to those other sciences; for foreign +idioms and such figures as the ellipsis, the anacoluthon, the oxymoron, +the hyperbole, and violent inversions have their place in the +magnificent style; but authors unacquainted with Grammar and Logic are +not likely to place such figures well and wisely. Indeed, common idioms, +though both grammatically and rhetorically justifiable, both correct and +effective, often seem illogical. 'To fall asleep,' for example, is a +perfect English phrase; yet if we examine severally the words it +consists of, it may seem strange that their combination should mean +anything at all.</p> + +<p>But Logic only studies language so far as necessary in order to state, +understand, and check the evidence and reasonings that are usually +embodied in language. And as long as meanings are clear, good Logic is +compatible with false concords and inelegance of style.</p> + +<p><a name="chap_3_sect_3" id="chap_3_sect_3"></a>§ 3. Terms are either Simple or Composite: that is to say, they may +consist either of a single word, as 'Chaucer,' 'civilisation'; or of +more than one, as 'the father of English poetry,' or 'modern civilised +nations.' Logicians classify words according to their uses in forming +propositions; or, rather, they classify the uses of words as terms, not +the words themselves; for the same word may fall into different classes +of terms according to the way in which it is used. (<i>Cf.</i> Mr. Alfred +Sidgwick's <i>Distinction and the Criticism of Beliefs</i>, chap. xiv.)</p> + +<p>Thus words are classified as Categorematic or Syncategorematic. A word +is Categorematic if used singly as a term without the support of other +words: it is Syncategorematic when joined with other words in order to +constitute the subject or predicate of a proposition. If we say <i>Venus +is a planet whose orbit is inside the Earth's</i>, the subject, 'Venus,'<span class='pagenum'>[Pg 30]<a name="Page_30" id="Page_30"></a></span> +is a word used categorematically as a simple term; the predicate is a +composite term whose constituent words (whether substantive, relative, +verb, or preposition) are used syncategorematically.</p> + +<p>Prepositions, conjunctions, articles, adverbs, relative pronouns, in +their ordinary use, can only enter into terms along with other words +having a substantive, adjectival or participial force; but when they are +themselves the things spoken of and are used substantively (<i>suppositio +materialis</i>), they are categorematic. In the proposition, <i>'Of' was used +more indefinitely three hundred years ago than it is now</i>, 'of' is +categorematic. On the other hand, all substantives may be used +categorematically; and the same self-sufficiency is usually recognised +in adjectives and participles. Some, however, hold that the +categorematic use of adjectives and participles is due to an ellipsis +which the logician should fill up; that instead of <i>Gold is heavy</i>, he +should say <i>Gold is a heavy metal</i>; instead of <i>The sun is shining</i>, +<i>The sun is a body shining</i>. But in these cases the words 'metal' and +'body' are unmistakable tautology, since 'metal' is implied in gold and +'body' in sun. But, as we have seen, any of these kinds of word, +substantive, adjective, or participle, may occur syncategorematically in +connection with others to form a composite term.</p> + +<p><a name="chap_3_sect_4" id="chap_3_sect_4"></a>§ 4. Most terms (the exceptions and doubtful cases will be discussed +hereafter) have two functions, a denotative and a connotative. A term's +denotative function is, to be the name or sign of something or some +multitude of things, which are said to be called or denoted by the term. +Its connotative function is, to suggest certain qualities and +characteristics of the things denoted, so that it cannot be used +literally as the name of any other things; which qualities and +characteristics are said to be implied or connoted by the term. Thus +'sheep' is the name of certain animals, and its connotation prevents its +being used of any others. That which a term directly indicates, then, +<span class='pagenum'>[Pg 31]<a name="Page_31" id="Page_31"></a></span>is its <i>Denotation</i>; that sense or customary use of it which limits the +Denotation is its <i>Connotation</i> (ch. iv.). Hamilton and others use +'Extension' in the sense of Denotation, and 'Intension' or +'Comprehension' in the sense of Connotation. Now, terms may be +classified, first according to what they stand for or denote; that is, +according to their <i>Denotation</i>. In this respect, the use of a term is +said to be either Concrete or Abstract.</p> + +<p>A term is Concrete when it denotes a 'thing'; that is, any person, +object, fact, event, feeling or imagination, considered as capable of +having (or consisting of) qualities and a determinate existence. Thus +'cricket ball' denotes any object having a certain size, weight, shape, +colour, <i>etc.</i> (which are its qualities), and being at any given time in +some place and related to other objects—in the bowler's hands, on the +grass, in a shop window. Any 'feeling of heat' has a certain intensity, +is pleasurable or painful, occurs at a certain time, and affects some +part or the whole of some animal. An imagination, indeed (say, of a +fairy), cannot be said in the same sense to have locality; but it +depends on the thinking of some man who has locality, and is definitely +related to his other thoughts and feelings.</p> + +<p>A term is Abstract, on the other hand, when it denotes a quality (or +qualities), considered by itself and without determinate existence in +time, place, or relation to other things. 'Size,' 'shape,' 'weight,' +'colour,' 'intensity,' 'pleasurableness,' are terms used to denote such +qualities, and are then abstract in their denotation. 'Weight' is not +something with a determinate existence at a given time; it exists not +merely in some particular place, but wherever there is a heavy thing; +and, as to relation, at the same moment it combines in iron with +solidity and in mercury with liquidity. In fact, a quality is a point of +agreement in a multitude of different things; all heavy things agree in +weight, all round things in roundness, all red things in redness; and an +abstract term denotes such a point (or points) of agreement <span class='pagenum'>[Pg 32]<a name="Page_32" id="Page_32"></a></span>among the +things denoted by concrete terms. Abstract terms result from the +analysis of concrete things into their qualities; and conversely a +concrete term may be viewed as denoting the synthesis of qualities into +an individual thing. When several things agree in more than one quality, +there may be an abstract term denoting the union of qualities in which +they agree, and omitting their peculiarities; as 'human nature' denotes +the common qualities of men, 'civilisation' the common conditions of +civilised peoples.</p> + +<p>Every general name, if used as a concrete term, has, or may have, a +corresponding abstract term. Sometimes the concrete term is modified to +form the abstract, as 'greedy—greediness'; sometimes a word is adapted +from another language, as 'man—humanity'; sometimes a composite term is +used, as 'mercury—the nature of mercury,' <i>etc.</i> The same concrete may +have several abstract correlatives, as 'man—manhood, humanity, human +nature'; 'heavy—weight, gravity, ponderosity'; but in such cases the +abstract terms are not used quite synonymously; that is, they imply +different ways of considering the concrete.</p> + +<p>Whether a word is used as a concrete or abstract term is in most +instances plain from the word itself, the use of most words being pretty +regular one way or the other; but sometimes we must judge by the +context. 'Weight' may be used in the abstract for 'gravity,' or in the +concrete for a measure; but in the latter sense it is syncategorematic +(in the singular), needing at least the article 'a (or the) weight.' +'Government' may mean 'supreme political authority,' and is then +abstract; or, the men who happen to be ministers, and is then concrete; +but in this case, too, the article is usually prefixed. 'The life' of +any man may mean his vitality (abstract), as in "Thus following life in +creatures we dissect"; or, the series of events through which he passes +(concrete), as in 'the life of Nelson as narrated by Southey.'</p><p><span class='pagenum'>[Pg 33]<a name="Page_33" id="Page_33"></a></span></p> + +<p>It has been made a question whether the denotation of an abstract term +may itself be the subject of qualities. Apparently 'weight' may be +greater or less, 'government' good or bad, 'vitality' intense or dull. +But if every subject is modified by a quality, a quality is also +modified by making it the subject of another; and, if so, it seems then +to become a new quality. The compound terms 'great weight,' 'bad +government,' 'dull vitality,' have not the same denotation as the simple +terms 'weight, 'government,' 'vitality': they imply, and may be said to +connote, more special concrete experience, such as the effort felt in +lifting a trunk, disgust at the conduct of officials, sluggish movements +of an animal when irritated. It is to such concrete experiences that we +have always to refer in order fully to realise the meaning of abstract +terms, and therefore, of course, to understand any qualification of +them.</p> + +<p><a name="chap_3_sect_5" id="chap_3_sect_5"></a>§ 5. Concrete terms may be subdivided according to the number of things +they denote and the way in which they denote them. A term may denote one +thing or many: if one, it is called Singular; if many, it may do so +distributively, and then it is General; or, as taken all together, and +then it is Collective: one, then; any one of many; many in one.</p> + +<p>Among Singular Terms, each denoting a single thing, the most obvious are +Proper Names, such as Gibraltar or George Washington, which are merely +marks of individual things or persons, and may form no part of the +common language of a country. They are thus distinguished from other +Singular Terms, which consist of common words so combined as to restrict +their denotation to some individual, such as, 'the strongest man on +earth.'</p> + +<p>Proper Terms are often said to be arbitrary signs, because their use +does not depend upon any reason that may be given for them. Gibraltar +had a meaning among the Moors when originally conferred; but no one now +knows what it was, unless he happens to have learned it; yet the name +serves <span class='pagenum'>[Pg 34]<a name="Page_34" id="Page_34"></a></span>its purpose as well as if it were "Rooke's Nest." Every Newton +or Newport year by year grows old, but to alter the name would cause +only confusion. If such names were given by mere caprice it would make +no difference; and they could not be more cumbrous, ugly, or absurd than +many of those that are given 'for reasons.'</p> + +<p>The remaining kinds of Singular Terms are drawn from the common +resources of the language. Thus the pronouns 'he,' 'she,' 'it,' are +singular terms, whose present denotation is determined by the occasion +and context of discourse: so with demonstrative phrases—'the man,' +'that horse.' Descriptive names may be more complex, as 'the wisest man +of Gotham,' which is limited to some individual by the superlative +suffix; or 'the German Emperor,' which is limited by the definite +article—the general term 'German Emperor' being thereby restricted +either to the reigning monarch or to the one we happen to be discussing. +Instead of the definite, the indefinite article may be used to make +general terms singular, as 'a German Emperor was crowned at Versailles' +(<i>individua vaga</i>).</p> + +<p>Abstract Terms are ostensively singular: 'whiteness' (<i>e.g.</i>) is one +quality. But their full meaning is general: 'whiteness' stands for all +white things, so far as white. Abstract terms, in fact, are only +formally singular.</p> + +<p>General Terms are words, or combinations of words, used to denote any +one of many things that resemble one another in certain respects. +'George III.' is a Singular Term denoting one man; but 'King' is a +General Term denoting him and all other men of the same rank; whilst the +compound 'crowned head' is still more general, denoting kings and also +emperors. It is the nature of a general term, then, to be used in the +same sense of whatever it denotes; and its most characteristic form is +the Class-name, whether of objects, such as 'king,' 'sheep,' 'ghost'; or +of events, such as 'accession,' 'purchase,' 'manifestation.' Things and +events are known by their qualities and relations; and <span class='pagenum'>[Pg 35]<a name="Page_35" id="Page_35"></a></span>every such +aspect, being a point of resemblance to some other things, becomes a +ground of generalisation, and therefore a ground for the need and use of +general terms. Hence general terms are far the most important sort of +terms in Logic, since in them general propositions are expressed and, +moreover (with rare exceptions), all predicates are general. For, +besides these typical class-names, attributive words are general terms, +such as 'royal,' 'ruling,' 'woolly,' 'bleating,' 'impalpable,' +'vanishing.'</p> + +<p>Infinitives may also be used as general terms, as '<i>To err is human</i>'; +but for logical purposes they may have to be translated into equivalent +substantive forms, as <i>Foolish actions are characteristic of mankind</i>. +Abstract terms, too, are (as I observed) equivalent to general terms; +'folly' is abstract for 'foolish actions.' '<i>Honesty is the best +policy</i>' means <i>people who are honest may hope to find their account in +being so</i>; that is, in the effects of their honest actions, provided +they are wise in other ways, and no misfortunes attend them. The +abstract form is often much the more succinct and forcible, but for +logical treatment it needs to be interpreted in the general form.</p> + +<p>By antonomasia proper names may become general terms, as if we say <i>'A +Johnson' would not have written such a book</i>—<i>i.e.</i>, any man of his +genius for elaborate eloquence.</p> + +<p>A Collective Term denotes a multitude of similar things considered as +forming one whole, as 'regiment,' 'flock,' 'nation': not distributively, +that is, not the similar things severally; to denote them we must say +'soldiers of the regiment,' 'sheep of the flock,' and so on. If in a +multitude of things there is no resemblance, except the fact of being +considered as parts of one whole, as 'the world,' or 'the town of +Nottingham' (meaning its streets and houses, open spaces, people, and +civic organisation), the term denoting them as a whole is Singular; but +'the world' or 'town of Nottingham,' meaning the inhabitants only, is +Collective.</p><p><span class='pagenum'>[Pg 36]<a name="Page_36" id="Page_36"></a></span></p> + +<p>In their strictly collective use, all such expressions are equivalent to +singular terms; but many of them may also be used as general terms, as +when we speak of 'so many regiments of the line,' or discuss the +'plurality of worlds'; and in this general use they denote any of a +multitude of things of the same kind—regiments, or habitable worlds.</p> + +<p>Names of substances, such as 'gold,' 'air,' 'water,' may be employed as +singular, collective, or general terms; though, perhaps, as singular +terms only figuratively, as when we say <i>Gold is king</i>. If we say with +Thales, '<i>Water is the source of all things</i>,' 'water' seems to be used +collectively. But substantive names are frequently used as general +terms. For example, <i>Gold is heavy</i> means 'in comparison with other +things,' such as water. And, plainly, it does not mean that the +aggregate of gold is heavier than the aggregate of water, but only that +its specific gravity is greater; that is, bulk for bulk, any piece of +gold is heavier than water.</p> + +<p>Finally, any class-name may be used collectively if we wish to assert +something of the things denoted by it, not distributively but +altogether, as that <i>Sheep are more numerous than wolves</i>.</p><p><span class='pagenum'>[Pg 37]<a name="Page_37" id="Page_37"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_IV" id="CHAPTER_IV"></a>CHAPTER IV</h2> + +<h3>THE CONNOTATION OF TERMS</h3> + + +<p><a name="chap_4_sect_1" id="chap_4_sect_1"></a>§ 1. Terms are next to be classified according to their +Connotation—that is, according to what they imply as characteristic of +the things denoted. We have seen that general names are used to denote +many things in the same sense, because the things denoted resemble one +another in certain ways: it is this resemblance in certain points that +leads us to class the things together and call them by the same name; +and therefore the points of resemblance constitute the sense or meaning +of the name, or its Connotation, and limit its applicability to such +things as have these characteristic qualities. 'Sheep' for example, is +used in the same sense, to denote any of a multitude of animals that +resemble one another: their size, shape, woolly coats, cloven hoofs, +innocent ways and edibility are well known. When we apply to anything +the term 'sheep,' we imply that it has these qualities: 'sheep,' +denoting the animal, connotes its possessing these characteristics; and, +of course, it cannot, without a figure of speech or a blunder, be used +to denote anything that does not possess all these qualities. It is by a +figure of speech that the term 'sheep' is applied to some men; and to +apply it to goats would be a blunder.</p> + +<p>Most people are very imperfectly aware of the connotation of the words +they use, and are guided in using them merely by the custom of the +language. A man who employs a word quite correctly may be sadly posed by +a request to explain or define it. Moreover, so far as we are aware of +the connotation<span class='pagenum'>[Pg 38]<a name="Page_38" id="Page_38"></a></span> of terms, the number and the kind of attributes we +think of, in any given case, vary with the depth of our interest, and +with the nature of our interest in the things denoted. 'Sheep' has one +meaning to a touring townsman, a much fuller one to a farmer, and yet a +different one to a zoologist. But this does not prevent them agreeing in +the use of the word, as long as the qualities they severally include in +its meaning are not incompatible.</p> + +<p>All general names, and therefore not only class-names, like 'sheep,' but +all attributives, have some connotation. 'Woolly' denotes anything that +bears wool, and connotes the fact of bearing wool; 'innocent' denotes +anything that habitually and by its disposition does no harm (or has not +been guilty of a particular offence), and connotes a harmless character +(or freedom from particular guilt); 'edible' denotes whatever can be +eaten with good results, and connotes its suitability for mastication, +deglutition, digestion, and assimilation.</p> + +<p><a name="chap_4_sect_2" id="chap_4_sect_2"></a>§ 2. But whether all terms must connote as well as denote something, has +been much debated. Proper names, according to what seems the better +opinion, are, in their ordinary use, not connotative. To say that they +have no meaning may seem violent: if any one is called John Doe, this +name, no doubt, means a great deal to his friends and neighbours, +reminding them of his stature and physiognomy, his air and gait, his wit +and wisdom, some queer stories, and an indefinite number of other +things. But all this significance is local or accidental; it only exists +for those who know the individual or have heard him described: whereas a +general name gives information about any thing or person it denotes to +everybody who understands the language, without any particular knowledge +of the individual.</p> + +<p>We must distinguish, in fact, between the peculiar associations of the +proper name and the commonly recognised meaning of the general name. +This is why proper names <span class='pagenum'>[Pg 39]<a name="Page_39" id="Page_39"></a></span>are not in the dictionary. Such a name as +London, to be sure, or Napoleon Buonaparte, has a significance not +merely local; still, it is accidental. These names are borne by other +places and persons than those that have rendered them famous. There are +Londons in various latitudes, and, no doubt, many Napoleon Buonapartes +in Louisiana; and each name has in its several denotations an altogether +different suggestiveness. For its suggestiveness is in each application +determined by the peculiarities of the place or person denoted; it is +not given to the different places (or to the different persons) because +they have certain characteristics in common.</p> + +<p>However, the scientific grounds of the doctrine that proper names are +non-connotative, are these: The peculiarities that distinguish an +individual person or thing are admitted to be infinite, and anything +less than a complete enumeration of these peculiarities may fail to +distinguish and identify the individual. For, short of a complete +enumeration of them, the description may be satisfied by two or more +individuals; and in that case the term denoting them, if limited by such +a description, is not a proper but a general name, since it is +applicable to two or more in the same sense. The existence of other +individuals to whom it applies may be highly improbable; but, if it be +logically possible, that is enough. On the other hand, the enumeration +of infinite peculiarities is certainly impossible. Therefore proper +names have no assignable connotation. The only escape from this +reasoning lies in falling back upon time and place, the principles of +individuation, as constituting the connotation of proper names. Two +things cannot be at the same time in the same place: hence 'the man who +was at a certain spot on the bridge of Lodi at a certain instant in a +certain year' suffices to identify Napoleon Buonaparte for that instant. +Supposing no one else to have borne the name, then, is this its +connotation? No one has ever thought so. And, <span class='pagenum'>[Pg 40]<a name="Page_40" id="Page_40"></a></span>at any rate, time and +place are only extrinsic determinations (suitable indeed to events like +the battle of Lodi, or to places themselves like London); whereas the +connotation of a general term, such as 'sheep,' consists of intrinsic +qualities. Hence, then, the scholastic doctrine 'that individuals have +no essence' (see <a href="#chap_22_sect_9">chap. xxii. § 9</a>), and Hamilton's dictum 'that every +concept is inadequate to the individual,' are justified.</p> + +<p>General names, when used as proper names, lose their connotation, as +Euxine or Newfoundland.</p> + +<p>Singular terms, other than Proper, have connotation; either in +themselves, like the singular pronouns 'he,' 'she,' 'it,' which are +general in their applicability, though singular in application; or, +derivatively, from the general names that combine to form them, as in +'the first Emperor of the French' or the 'Capital of the British +Empire.'</p> + +<p><a name="chap_4_sect_3" id="chap_4_sect_3"></a>§ 3. Whether Abstract Terms have any connotation is another disputed +question. We have seen that they denote a quality or qualities of +something, and that is precisely what general terms connote: 'honesty' +denotes a quality of some men; 'honest' connotes the same quality, +whilst denoting the men who have it.</p> + +<p>The denotation of abstract terms thus seems to exhaust their force or +meaning. It has been proposed, however, to regard them as connoting the +qualities they directly stand for, and not denoting anything; but surely +this is too violent. To denote something is the same as to be the name +of something (whether real or unreal), which every term must be. It is a +better proposal to regard their denotation and connotation as +coinciding; though open to the objection that 'connote' means 'to mark +along with' something else, and this plan leaves nothing else. Mill +thought that abstract terms are connotative when, besides denoting a +quality, they suggest a quality of that quality (as 'fault' implies +'hurtfulness'); but against this it may be urged that one quality cannot +bear another, since every <span class='pagenum'>[Pg 41]<a name="Page_41" id="Page_41"></a></span>qualification of a quality constitutes a +distinct quality in the total ('milk-whiteness' is distinct from +'whiteness,' <i>cf.</i> <a href="#chap_3_sect_4">chap. iii. § 4</a>). After all, if it is the most +consistent plan, why not say that abstract, like proper, terms have no +connotation?</p> + +<p>But if abstract terms must be made to connote something, should it not +be those things, indefinitely suggested, to which the qualities belong? +Thus 'whiteness' may be considered to connote either snow or vapour, or +any white thing, apart from one or other of which the quality has no +existence; whose existence therefore it implies. By this course the +denotation and connotation of abstract and of general names would be +exactly reversed. Whilst the denotation of a general name is limited by +the qualities connoted, the connotation of an abstract name includes all +the things in which its denotation is realised. But the whole difficulty +may be avoided by making it a rule to translate, for logical purposes, +all abstract into the corresponding general terms.</p> + +<p><a name="chap_4_sect_4" id="chap_4_sect_4"></a>§ 4. If we ask how the connotation of a term is to be known, the answer +depends upon how it is used. If used scientifically, its connotation is +determined by, and is the same as, its definition; and the definition is +determined by examining the things to be denoted, as we shall see in +<a href="#CHAPTER_XXII">chap. xxii</a>. If the same word is used as a term in different sciences, as +'property' in Law and in Logic, it will be differently defined by them, +and will have, in each use, a correspondingly different connotation. But +terms used in popular discourse should, as far as possible, have their +connotations determined by classical usage, <i>i.e.</i>, by the sense in +which they are used by writers and speakers who are acknowledged masters +of the language, such as Dryden and Burke. In this case the classical +connotation determines the definition; so that to define terms thus used +is nothing else than to analyse their accepted meanings.</p> + +<p>It must not, however, be supposed that in popular use the <span class='pagenum'>[Pg 42]<a name="Page_42" id="Page_42"></a></span>connotation +of any word is invariable. Logicians have attempted to classify +terms into Univocal (having only one meaning) and Æquivocal (or +ambiguous); and no doubt some words (like 'civil,' 'natural,' 'proud,' +'liberal,' 'humorous') are more manifestly liable to ambiguous use than +some others. But in truth all general terms are popularly and +classically used in somewhat different senses.</p> + +<p>Figurative or tropical language chiefly consists in the transfer of +words to new senses, as by metaphor or metonymy. In the course of years, +too, words change their meanings; and before the time of Dryden our +whole vocabulary was much more fluid and adaptable than it has since +become. Such authors as Bacon, Milton, and Sir Thomas Browne often used +words derived from the Latin in some sense they originally had in Latin, +though in English they had acquired another meaning. Spenser and +Shakespeare, besides this practice, sometimes use words in a way that +can only be justified by their choosing to have it so; whilst their +contemporaries, Beaumont and Fletcher, write the perfect modern +language, as Dryden observed. Lapse of time, however, is not the chief +cause of variation in the sense of words. The matters which terms are +used to denote are often so complicated or so refined in the assemblage, +interfusion, or gradation of their qualities, that terms do not exist in +sufficient abundance and discriminativeness to denote the things and, at +the same time, to convey by connotation a determinate sense of their +agreements and differences. In discussing politics, religion, ethics, +æsthetics, this imperfection of language is continually felt; and the +only escape from it, short of coining new words, is to use such words as +we have, now in one sense, now in another somewhat different, and to +trust to the context, or to the resources of the literary art, in order +to convey the true meaning. Against this evil the having been born since +Dryden is no protection. It behoves us, then, to remember that terms are +not classifiable <span class='pagenum'>[Pg 43]<a name="Page_43" id="Page_43"></a></span>into Univocal and Æquivocal, but that all terms are +susceptible of being used æquivocally, and that honesty and lucidity +require us to try, as well as we can, to use each term univocally in the +same context.</p> + +<p>The context of any proposition always proceeds upon some assumption or +understanding as to the scope of the discussion, which controls the +interpretation of every statement and of every word. This was called by +De Morgan the "universe of discourse": an older name for it, revived by +Dr. Venn, and surely a better one, is <i>suppositio</i>. If we are talking of +children, and 'play' is mentioned, the <i>suppositio</i> limits the +suggestiveness of the word in one way; whilst if Monaco is the subject +of conversation, the same word 'play,' under the influence of a +different <i>suppositio</i>, excites altogether different ideas. Hence to +ignore the <i>suppositio</i> is a great source of fallacies of equivocation. +'Man' is generally defined as a kind of animal; but 'animal' is often +used as opposed to and excluding man. 'Liberal' has one meaning under +the <i>suppositio</i> of politics, another with regard to culture, and still +another as to the disposal of one's private means. Clearly, therefore, +the connotation of general terms is relative to the <i>suppositio</i>, or +"universe of discourse."</p> + +<p><a name="chap_4_sect_5" id="chap_4_sect_5"></a>§ 5. Relative and Absolute Terms.—Some words go in couples or groups: +like 'up-down,' 'former-latter,' 'father-mother-children,' +'hunter-prey,' 'cause-effect,' <i>etc.</i> These are called Relative Terms, +and their nature, as explained by Mill, is that the connotations of the +members of such a pair or group are derived from the same set of facts +(the <i>fundamentum relationis</i>). There cannot be an 'up' without a +'down,' a 'father' without a 'mother' and 'child'; there cannot be a +'hunter' without something hunted, nor 'prey' without a pursuer. What +makes a man a 'hunter' is his activities in pursuit; and what turns a +chamois into 'prey' is its interest in these activities. The meaning of +both terms, therefore, is derived from the <span class='pagenum'>[Pg 44]<a name="Page_44" id="Page_44"></a></span>same set of facts; neither +term can be explained without explaining the other, because the relation +between them is connoted by both; and neither can with propriety be used +without reference to the other, or to some equivalent, as 'game' for +'prey.'</p> + +<p>In contrast with such Relative Terms, others have been called Absolute +or Non-relative. Whilst 'hunter' and 'prey' are relative, 'man' and +'chamois' have been considered absolute, as we may use them without +thinking of any special connection between their meanings. However, if +we believe in the unity of Nature and in the relativity of knowledge +(that is, that all knowledge depends upon comparison, or a perception of +the resemblances and differences of things), it follows that nothing can +be completely understood except through its agreements or contrasts with +everything else, and that all terms derive their connotation from the +same set of facts, namely, from general experience. Thus both man and +chamois are animals; this fact is an important part of the meaning of +both terms, and to that extent they are relative terms. 'Five yards' and +'five minutes' are very different notions, yet they are profoundly +related; for their very difference helps to make both notions distinct; +and their intimate connection is shown in this, that five yards are +traversed in a certain time, and that five minutes are measured by the +motion of an index over some fraction of a yard upon the dial.</p> + +<p>The distinction, then, between relative and non-relative terms must +rest, not upon a fundamental difference between them (since, in fact, +all words are relative), but upon the way in which words are used. We +have seen that some words, such as 'up-down,' 'cause-effect,' can only +be used relatively; and these may, for distinction, be called +Correlatives. But other words, whose meanings are only partially +interdependent, may often be used without attending to their relativity, +and may then be considered as<span class='pagenum'>[Pg 45]<a name="Page_45" id="Page_45"></a></span> Absolute. We cannot say 'the hunter +returned empty handed,' without implying that 'the prey escaped'; but we +may say 'the man went supperless to bed,' without implying that 'the +chamois rejoiced upon the mountain.' Such words as 'man' and 'chamois' +may, then, in their use, be, as to one another, non-relative.</p> + +<p>To illustrate further the relativity of terms, we may mention some of +the chief classes of them.</p> + +<p>Numerical order: 1st, 2nd, 3rd, <i>etc</i>.; 1st implies 2nd, and 2nd 1st; +and 3rd implies 1st and 2nd, but these do not imply 3rd; and so on.</p> + +<p>Order in Time or Place: before-after; early-punctual-late; +right-middle-left; North-South, <i>etc</i>.</p> + +<p>As to Extent, Volume, and Degree: greater-equal-less; +large-medium-small; whole and part.</p> + +<p>Genus and Species are a peculiar case of whole and part (<i>cf.</i> chaps. +xxi.-ii.-iii.). Sometimes a term connotes all the attributes that +another does, and more besides, which, as distinguishing it, are called +differential. Thus 'man' connotes all that 'animal' does, and also (as +<i>differentiæ</i>) the erect gait, articulate speech, and other attributes. +In such a case as this, where there are well-marked classes, the term +whose connotation is included in the others' is called a Genus of that +Species. We have a Genus, triangle; and a Species, isosceles, marked off +from all other triangles by the differential quality of having two equal +sides: again—Genus, book; Species, quarto; Difference, having each +sheet folded into four leaves.</p> + +<p>There are other cases where these expressions 'genus' and 'species' +cannot be so applied without a departure from usage, as, <i>e.g</i>., if we +call snow a species of the genus 'white,' for 'white' is not a +recognised class. The connotation of white (<i>i.e</i>., whiteness) is, +however, part of the connotation of snow, just as the qualities of +'animal' are amongst those of 'man'; and for logical purposes it is +desirable to use 'genus and species' to express that <span class='pagenum'>[Pg 46]<a name="Page_46" id="Page_46"></a></span>relativity of +terms which consists in the connotation of one being part of the +connotation of the other.</p> + +<p>Two or more terms whose connotations severally include that of another +term, whilst at the same time exceeding it, are (in relation to that +other term) called Co-ordinate. Thus in relation to 'white,' snow and +silver are co-ordinate; in relation to colour, yellow and red and blue +are co-ordinate. And when all the terms thus related stand for +recognised natural classes, the co-ordinate terms are called co-ordinate +species; thus man and chamois are (in Logic) co-ordinate species of the +genus animal.</p> + +<p><a name="chap_4_sect_6" id="chap_4_sect_6"></a>§ 6. From such examples of terms whose connotations are related as whole +and part, it is easy to see the general truth of the doctrine that as +connotation decreases, denotation increases: for 'animal,' with less +connotation than man or chamois, denotes many more objects; 'white,' +with less connotation than snow or silver, denotes many more things, It +is not, however, certain that this doctrine is always true in the +concrete: since there may be a term connoting two or more qualities, all +of which qualities are peculiar to all the things it denotes; and, if +so, by subtracting one of the qualities from its connotation, we should +not increase its denotation. If 'man,' for example, has among mammals +the two peculiar attributes of erect gait and articulate speech, then, +by omitting 'articulate speech' from the connotation of man, we could +not apply the name to any more of the existing mammalia than we can at +present. Still we might have been able to do so; there might have been +an erect inarticulate ape, and perhaps there once was one; and, if so, +to omit 'articulate' from the connotation of man would make the term +'man' denote that animal (supposing that there was no other difference +to exclude it). Hence, potentially, an increase of the connotation of +any term implies a decrease of its denotation. And, on the other hand, +we can only increase the denotation of a term, or apply it to more +objects, by decreasing its connotation; <span class='pagenum'>[Pg 47]<a name="Page_47" id="Page_47"></a></span>for, if the new things denoted +by the term had already possessed its whole connotation, they must +already have been denoted by it. However, we may increase the <i>known</i> +denotation without decreasing the connotation, if we can discover the +full connotation in things not formerly supposed to have it, as when +dolphins were discovered to be mammals; or if we can impose the +requisite qualities upon new individuals, as when by annexing some +millions of Africans we extend the denotation of 'British subject' +without altering its connotation.</p> + +<p>Many of the things noticed in this chapter, especially in this section +and the preceding, will be discussed at greater length in the chapters +on Classification and Definition.</p> + +<p><a name="chap_4_sect_7" id="chap_4_sect_7"></a>§ 7. Contradictory Relative Terms.—Every term has, or may have, another +corresponding with it in such a way that, whatever differential +qualities (<a href="#chap_4_sect_5">§ 5</a>) it connotes, this other connotes merely their absence; +so that one or the other is always formally predicable of any Subject, +but both these terms are never predicable of the same Subject in the +same relation: such pairs of terms are called Contradictories. Whatever +Subject we take, it is either visible or invisible, but not both; either +human or non-human, but not both.</p> + +<p>This at least is true formally, though in practice we should think +ourselves trifled with if any one told us that 'A mountain is either +human or non-human, but not both.' It is symbolic terms, such as X and +x, that are properly said to be contradictories in relation to any +subject whatever, S or M. For, as we have seen, the ordinary use of +terms is limited by some <i>suppositio</i>, and this is true of +Contradictories. 'Human' and 'non-human' may refer to zoological +classification, or to the scope of physical, mental, or moral powers—as +if we ask whether to flourish a dumbbell of a ton weight, or to know the +future by intuition, or impeccability, be human or non-human. Similarly, +'visible' and 'invisible' refer either to the power of emitting or +reflecting light, so that the words have no hold <span class='pagenum'>[Pg 48]<a name="Page_48" id="Page_48"></a></span>upon a sound or a +scent, or else to power of vision and such qualifications as 'with the +naked eye' or 'with a microscope.'</p> + +<p>Again, the above definition of Contradictories tells us that they cannot +be predicated of the same Subject "in the same relation"; that is, at +the same time or place, or under the same conditions. The lamp is +visible to me now, but will be invisible if I turn it out; one side of +it is now visible, but the other is not: therefore without this +restriction, "in the same relation," few or no terms would be +contradictory.</p> + +<p>If a man is called wise, it may mean 'on the whole' or 'in a certain +action'; and clearly a man may for once be wise (or act wisely) who, on +the whole, is not-wise. So that here again, by this ambiguity, terms +that seem contradictory are predicable of the same subject, but not "in +the same relation." In order to avoid the ambiguity, however, we have +only to construct the term so as to express the relation, as 'wise on +the whole'; and this immediately generates the contradictory 'not-wise +on the whole.' Similarly, at one age a man may have black hair, at +another not-black hair; but the difficulty is practically removable by +stating the age referred to.</p> + +<p>Still, this case easily leads us to a real difficulty in the use of +contradictory terms, a difficulty arising from the continuous change or +'flux' of natural phenomena. If things are continually changing, it may +be urged that contradictory terms are always applicable to the same +subject, at least as fast as we can utter them: for if we have just said +that a man's hair is black, since (like everything else) his hair is +changing, it must now be not-black, though (to be sure) it may still +seem black. The difficulty, such as it is, lies in this, that the human +mind and its instrument language are not equal to the subtlety of +Nature. All things flow, but the terms of human discourse assume a +certain fixity of things; everything at every moment changes, but for +the <span class='pagenum'>[Pg 49]<a name="Page_49" id="Page_49"></a></span>most part we can neither perceive this change nor express it in +ordinary language.</p> + +<p>This paradox, however, may, I suppose, be easily over-stated. The change +that continually agitates Nature consists in the movements of masses or +molecules, and such movements of things are compatible with a +considerable persistence of their qualities. Not only are the molecular +changes always going on in a piece of gold compatible with its remaining +yellow, but its persistent yellowness depends on the continuance of some +of those changes. Similarly, a man's hair may remain black for some +years; though, no doubt, at a certain age its colour may begin to be +problematical, and the applicability to it of 'black' or 'not-black' may +become a matter of genuine anxiety. Whilst being on our guard, then, +against fallacies of contradiction arising from the imperfect +correspondence of fact with thought and language, we shall often have to +put up with it. Candour and humility having been satisfied by the above +acknowledgment of the subtlety of Nature, we may henceforward proceed +upon the postulate—that it is possible to use contradictory terms such +as cannot both be predicated of the same subject in the same relation, +though one of them may be; that, for example, it may be truly said of a +man for some years that his hair is black; and, if so, that during those +years to call it not-black is false or extremely misleading.</p> + +<p>The most opposed terms of the literary vocabulary, however, such as +'wise-foolish,' 'old-young,' 'sweet-bitter,' are rarely true +contradictories: wise and foolish, indeed, cannot be predicated of the +same man in the same relation; but there are many middling men, of whom +neither can be predicated on the whole. For the comparison of +quantities, again, we have three correlative terms, +'greater—equal—less,' and none of these is the contradictory of either +of the others. In fact, the contradictory of any term is one that +denotes the sum of its <span class='pagenum'>[Pg 50]<a name="Page_50" id="Page_50"></a></span>co-ordinates (<a href="#chap_4_sect_6">§ 6</a>); and to obtain a +contradictory, the surest way is to coin one by prefixing to the given +term the particle 'not' or (sometimes) 'non': as 'wise, not-wise,' +'human, non-human,' 'greater, not-greater.'</p> + +<p>The separate word 'not' is surer to constitute a contradictory than the +usual prefixes of negation, 'un-' or 'in-,' or even 'non'; since +compounds of these are generally warped by common use from a purely +negative meaning. Thus, 'Nonconformist' does not denote everybody who +fails to conform. 'Unwise' is not equivalent to 'not-wise,' but means +'rather foolish'; a very foolish action is not-wise, but can only be +called unwise by meiosis or irony. Still, negatives formed by 'in' or +'un' or 'non' are sometimes really contradictory of their positives; as +'visible, invisible,' 'equal, unequal.'</p> + +<p><a name="chap_4_sect_8" id="chap_4_sect_8"></a>§ 8. The distinction between Positive and Negative terms is not of much +value in Logic, what importance would else attach to it being absorbed +by the more definite distinction of contradictories. For contradictories +are positive and negative in essence and, when least ambiguously stated, +also in form. And, on the other hand, as we have seen, when positive and +negative terms are not contradictory, they are misleading. As with +'wise-unwise,' so with many others, such as 'happy-unhappy'; which are +not contradictories; since a man may be neither happy nor unhappy, but +indifferent, or (again) so miserable that he can only be called unhappy +by a figure of speech. In fact, in the common vocabulary a formal +negative often has a limited positive sense; and this is the case with +unhappy, signifying the state of feeling in the milder shades of +Purgatory.</p> + +<p>When a Negative term is fully contradictory of its Positive it is said +to be Infinite; because it denotes an unascertained multitude of things, +a multitude only limited by the positive term and the <i>suppositio</i>; thus +'not-wise' denotes all except the wise, within the <i>suppositio</i> of +'intelligent <span class='pagenum'>[Pg 51]<a name="Page_51" id="Page_51"></a></span>beings.' Formally (disregarding any <i>suppositio</i>), such a +negative term stands for all possible terms except its positive: x +denotes everything but X; and 'not-wise' may be taken to include stones, +triangles and hippogriffs. And even in this sense, a negative term has +some positive meaning, though a very indefinite one, not a specific +positive force like 'unwise' or 'unhappy': it denotes any and everything +that has not the attributes connoted by the corresponding positive term.</p> + +<p>Privative Terms connote the absence of a quality that normally belongs +to the kind of thing denoted, as 'blind' or 'deaf.' We may predicate +'blind' or 'deaf' of a man, dog or cow that happens not to be able to +see or hear, because the powers of seeing and hearing generally belong +to those species; but of a stone or idol these terms can only be used +figuratively. Indeed, since the contradictory of a privative carries +with it the privative limitation, a stone is strictly 'not-blind': that +is, it is 'not-something-that-normally-having-sight-wants-it.'</p> + +<p>Contrary Terms are those that (within a certain genus or <i>suppositio</i>) +severally connote differential qualities that are, in fact, mutually +incompatible in the same relation to the same thing, and therefore +cannot be predicated of the same subject in the same relation; and, so +far, they resemble Contradictory Terms: but they differ from +contradictory terms in this, that the differential quality connoted by +each of them is definitely positive; no Contrary Term is infinite, but +is limited to part of the <i>suppositio</i> excluded by the others; so that, +possibly, neither of two Contraries is truly predicable of a given +subject. Thus 'blue' and 'red' are Contraries, for they cannot both be +predicated of the same thing in the same relation; but are not +Contradictories, since, in a given case, neither may be predicable: if a +flower is blue in a certain part, it cannot in the same part be red; but +it may be neither blue nor red, but yellow; though it is certainly +either blue or not-blue. All co-<span class='pagenum'>[Pg 52]<a name="Page_52" id="Page_52"></a></span>ordinate terms are formal Contraries; +but if, in fact, a series of co-ordinates comprises only two (as +male-female), they are empirical Contradictories; since each includes +all that area of the <i>suppositio</i> which the other excludes.</p> + +<p>The extremes of a series of co-ordinate terms are Opposites; as, in a +list of colours, white and black, the most strongly contrasted, are said +to be opposites, or as among moods of feeling, rapture and misery are +opposites. But this distinction is of slight logical importance. +Imperfect Positive and Negative couples, like 'happy and unhappy,' which +(as we have seen) are not contradictories, are often called Opposites.</p> + +<p>The members of any series of Contraries are all included by any one of +them and its contradictory, as all colours come under 'red' and +'not-red,' all moods of feeling under 'happy' and 'not-happy.'</p><p><span class='pagenum'>[Pg 53]<a name="Page_53" id="Page_53"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_V" id="CHAPTER_V"></a>CHAPTER V</h2> + +<h3>THE CLASSIFICATION OF PROPOSITIONS</h3> + + +<p><a name="chap_5_sect_1" id="chap_5_sect_1"></a>§ 1. Logicians classify Propositions according to Quantity, Quality, +Relation and Modality.</p> + +<p>As to Quantity, propositions are either Universal or Particular; that is +to say, the predicate is affirmed or denied either of the whole subject +or of a part of it—of <i>All</i> or of <i>Some S</i>.</p> + +<div class="example"><div class="section"><span class="i0"><i>All S is P</i> (that is, <i>P</i> is predicated of <i>all S</i>).<br /></span> +<span class="i0"><i>Some S is P</i> (that is, <i>P</i> is predicated of <i>some S</i>).<br /></span></div></div> + +<p>An Universal Proposition may have for its subject a singular term, a +collective, a general term distributed, or an abstract term.</p> + +<p>(1) A proposition having a singular term for its subject, as <i>The Queen +has gone to France</i>, is called a Singular Proposition; and some +Logicians regard this as a third species of proposition with respect to +quantity, distinct from the Universal and Particular; but that is +needless.</p> + +<p>(2) A collective term may be the subject, as <i>The Black Watch is ordered +to India</i>. In this case, as well as in singular propositions, a +predication is made concerning the whole subject as a whole.</p> + +<p>(3) The subject may be a general term taken in its full denotation, as +<i>All apes are sagacious</i>; and in this case a Predication is made +concerning the whole subject distributively; that is, of each and +everything the subject stands for.</p> + +<p>(4) Propositions whose subjects are abstract terms, <span class='pagenum'>[Pg 54]<a name="Page_54" id="Page_54"></a></span>though they may +seem to be formally Singular, are really as to their meaning +distributive Universals; since whatever is true of a quality is true of +whatever thing has that quality so far as that quality is concerned. +<i>Truth will prevail</i> means that <i>All true propositions are accepted at +last</i> (by sheer force of being true, in spite of interests, prejudices, +ignorance and indifference). To bear this in mind may make one cautious +in the use of abstract terms.</p> + +<p>In the above paragraphs a distinction is implied between Singular and +Distributive Universals; but, technically, every term, whether subject +or predicate, when taken in its full denotation (or universally), is +said to be 'distributed,' although this word, in its ordinary sense, +would be directly applicable only to general terms. In the above +examples, then, 'Queen,' 'Black Watch,' 'apes,' and 'truth' are all +distributed terms. Indeed, a simple definition of the Universal +Proposition is 'one whose subject is distributed.'</p> + +<p>A Particular Proposition is one that has a general term for its subject, +whilst its predicate is not affirmed or denied of everything the subject +denotes; in other words, it is one whose subject is not distributed: as +<i>Some lions inhabit Africa</i>.</p> + +<p>In ordinary discourse it is not always explicitly stated whether +predication is universal or particular; it would be very natural to say +<i>Lions inhabit Africa</i>, leaving it, as far as the words go, uncertain +whether we mean <i>all</i> or <i>some</i> lions. Propositions whose quantity is +thus left indefinite are technically called 'preindesignate,' their +quantity not being stated or designated by any introductory expression; +whilst propositions whose quantity is expressed, as <i>All +foundling-hospitals have a high death-rate</i>, or <i>Some wine is made from +grapes</i>, are said to be 'predesignate.' Now, the rule is that +preindesignate propositions are, for logical purposes, to be treated as +particular; since it is an obvious precaution of the science of proof, +in any practical application, <i>not to go beyond the evidence</i>. Still, +the rule may be <span class='pagenum'>[Pg 55]<a name="Page_55" id="Page_55"></a></span>relaxed if the universal quantity of a preindesignate +proposition is well known or admitted, as in <i>Planets shine with +reflected light</i>—understood of the planets of our solar system at the +present time. Again, such a proposition as <i>Man is the paragon of +animals</i> is not a preindesignate, but an abstract proposition; the +subject being elliptical for <i>Man according to his proper nature</i>; and +the translation of it into a predesignate proposition is not <i>All men +are paragons</i>; nor can <i>Some men</i> be sufficient, since an abstract can +only be adequately rendered by a distributed term; but we must say, <i>All +men who approach the ideal</i>. Universal real propositions, true without +qualification, are very scarce; and we often substitute for them +<i>general</i> propositions, saying perhaps—<i>generally, though not +universally, S is P</i>. Such general propositions are, in strictness, +particular; and the logical rules concerning universals cannot be +applied to them without careful scrutiny of the facts.</p> + +<p>The marks or predesignations of Quantity commonly used in Logic are: for +Universals, <i>All</i>, <i>Any</i>, <i>Every</i>, <i>Whatever</i> (in the negative <i>No</i> or +<i>No one</i>, see next §); for Particulars, <i>Some</i>.</p> + +<p>Now <i>Some</i>, technically used, does not mean <i>Some only,</i> but <i>Some at +least</i> (it may be one, or more, or all). If it meant '<i>Some only</i>,' +every particular proposition would be an exclusive exponible (<a href="#chap_2_sect_3">chap. ii. +§ 3</a>); since <i>Only some men are wise</i> implies that <i>Some men are not +wise</i>. Besides, it may often happen in an investigation that all the +instances we have observed come under a certain rule, though we do not +yet feel justified in regarding the rule as universal; and this +situation is exactly met by the expression <i>Some</i> (<i>it may be all</i>).</p> + +<p>The words <i>Many</i>, <i>Most</i>, <i>Few</i> are generally interpreted to mean +<i>Some</i>; but as <i>Most</i> signifies that exceptions are known, and <i>Few</i> +that the exceptions are the more numerous, propositions thus +predesignate are in fact exponibles, mounting to <i>Some are</i> and <i>Some +are not</i>. If to work with <span class='pagenum'>[Pg 56]<a name="Page_56" id="Page_56"></a></span>both forms be too cumbrous, so that we must +choose one, apparently <i>Few are</i> should be treated as <i>Some are not</i>. +The scientific course to adopt with propositions predesignate by <i>Most</i> +or <i>Few</i>, is to collect statistics and determine the percentage; thus, +<i>Few men are wise</i>—say 2 per cent.</p> + +<p>The Quantity of a proposition, then, is usually determined entirely by +the quantity of the subject, whether <i>all</i> or <i>some</i>. Still, the +quantity of the predicate is often an important consideration; and +though in ordinary usage the predicate is seldom predesignate, Logicians +agree that in every Negative Proposition (see <a href="#chap_5_sect_2">§ 2</a>) the predicate is +'distributed,' that is to say, is denied altogether of the subject, and +that this is involved in the form of denial. To say <i>Some men are not +brave</i>, is to declare that the quality for which men may be called brave +is not found in any of the <i>Some men</i> referred to: and to say <i>No men +are proof against flattery</i>, cuts off the being 'proof against flattery' +entirely from the list of human attributes. On the other hand, every +Affirmative Proposition is regarded as having an undistributed +predicate; that is to say, its predicate is not affirmed exclusively of +the subject. <i>Some men are wise</i> does not mean that 'wise' cannot be +predicated of any other beings; it is equivalent to <i>Some men are wise</i> +(<i>whoever else may be</i>). And <i>All elephants are sagacious</i> does not +limit sagacity to elephants: regarding 'sagacious' as possibly denoting +many animals of many species that exhibit the quality, this proposition +is equivalent to '<i>All elephants are</i> some <i>sagacious animals</i>.' The +affirmative predication of a quality does not imply exclusive possession +of it as denial implies its complete absence; and, therefore, to regard +the predicate of an affirmative proposition as distributed would be to +go beyond the evidence and to take for granted what had never been +alleged.</p> + +<p>Some Logicians, seeing that the quantity of predicates, though not +distinctly expressed, is recognised, and holding that it is the part of +Logic "to make explicit in language <span class='pagenum'>[Pg 57]<a name="Page_57" id="Page_57"></a></span>whatever is implicit in thought," +have proposed to exhibit the quantity of predicates by predesignation, +thus: 'Some men are <i>some</i> wise (beings)'; 'some men are not <i>any</i> brave +(beings)'; <i>etc.</i> This is called the Quantification of the Predicate, +and leads to some modifications of Deductive Logic which will be +referred to hereafter. (See <a href="#chap_5_sect_1">§ 5</a>; <a href="#chap_7_sect_4">chap. vii. § 4</a>, and <a href="#chap_8_sect_3">chap. viii. § 3</a>.)</p> + +<p><a name="chap_5_sect_2" id="chap_5_sect_2"></a>§ 2. As to Quality, Propositions are either Affirmative or Negative. An +Affirmative Proposition is, formally, one whose copula is affirmative +(or, has no negative sign), as <i>S—is—P, All men—are—partial to +themselves</i>. A Negative Proposition is one whose copula is negative (or, +has a negative sign), as <i>S—is not—P, Some men—are not—proof against +flattery</i>. When, indeed, a Negative Proposition is of Universal +Quantity, it is stated thus: <i>No S is P, No men are proof against +flattery</i>; but, in this case, the detachment of the negative sign from +the copula and its association with the subject is merely an accident of +our idiom; the proposition is the same as <i>All men—are not—proof +against flattery</i>. It must be distinguished, therefore, from such an +expression as <i>Not every man is proof against flattery</i>; for here the +negative sign really restricts the subject; so that the meaning +is—<i>Some men at most</i> (it may be <i>none) are proof against flattery</i>; +and thus the proposition is Particular, and is rendered—<i>Some men—are +not—proof against flattery</i>.</p> + +<p>When the negative sign is associated with the predicate, so as to make +this an Infinite Term (<a href="#chap_4_sect_8">chap. iv. § 8</a>), the proposition is called an +Infinite Proposition, as <i>S is not-P</i> (or <i>p), All men are—incapable of +resisting flattery</i>, or <i>are—not-proof against flattery</i>.</p> + +<p>Infinite propositions, when the copula is affirmative, are formally, +themselves affirmative, although their force is chiefly negative; for, +as the last example shows, the difference between an infinite and a +negative proposition may depend upon a hyphen. It has been proposed, +indeed, <span class='pagenum'>[Pg 58]<a name="Page_58" id="Page_58"></a></span>with a view to superficial simplification, to turn all +Negatives into Infinites, and thus render all propositions Affirmative +in Quality. But although every proposition both affirms and denies +something according to the aspect in which you regard it (as <i>Snow is +white</i> denies that it is any other colour, and <i>Snow is not blue</i> +affirms that it is some other colour), yet there is a great difference +between the definite affirmation of a genuine affirmative and the vague +affirmation of a negative or infinite; so that materially an affirmative +infinite is the same as a negative.</p> + +<p>Generally Mill's remark is true, that affirmation and denial stand for +distinctions of fact that cannot be got rid of by manipulation of words. +Whether granite sinks in water, or not; whether the rook lives a hundred +years, or not; whether a man has a hundred dollars in his pocket, or +not; whether human bones have ever been found in Pliocene strata, or +not; such alternatives require distinct forms of expression. At the same +time, it may be granted that many facts admit of being stated with +nearly equal propriety in either Quality, as <i>No man is proof against +flattery</i>, or <i>All men are open to flattery</i>.</p> + +<p>But whatever advantage there is in occasionally changing the Quality of +a proposition may be gained by the process of Obversion (chap. vii. § +5); whilst to use only one Quality would impair the elasticity of +logical expression. It is a postulate of Logic that the negative sign +may be transferred from the copula to the predicate, or from the +predicate to the copula, without altering the sense of a proposition; +and this is justified by the experience that not to have an attribute +and to be without it are the same thing.</p> + +<p><a name="chap_5_sect_3" id="chap_5_sect_3"></a>§ 3. A. I. E. O.—Combining the two kinds of Quantity, Universal and +Particular, with the two kinds of Quality, Affirmative and Negative, we +get four simple types of proposition, which it is usual to symbolise by +the letters A. I. E. O., thus:</p><p><span class='pagenum'>[Pg 59]<a name="Page_59" id="Page_59"></a></span></p> + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='left'>A.</td><td align='left'>Universal Affirmative</td><td align='left'>— All S is P.</td></tr> +<tr><td align='left'>I.</td><td align='left'>Particular Affirmative</td><td align='left'>— Some S is P.</td></tr> +<tr><td align='left'>E.</td><td align='left'>Universal Negative</td><td align='left'>— No S is P.</td></tr> +<tr><td align='left'>O.</td><td align='left'>Particular Negative</td><td align='left'>— Some S is not P.</td></tr> +</table></div> + +<p>As an aid to the remembering of these symbols we may observe that A. and +I. are the first two vowels in <i>affirmo</i> and that E. and O. are the +vowels in <i>nego</i>.</p> + +<p>It must be acknowledged that these four kinds of proposition recognised +by Formal Logic constitute a very meagre selection from the list of +propositions actually used in judgment and reasoning.</p> + +<p>Those Logicians who explicitly quantify the predicate obtain, in all, +eight forms of proposition according to Quantity and Quality:</p> + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='left'>U.</td><td align='left'>Toto-total Affirmative</td><td align='left'>— All X is all Y.</td></tr> +<tr><td align='left'>A.</td><td align='left'>Toto-partial Affirmative</td><td align='left'>— All X is some Y.</td></tr> +<tr><td align='left'>Y.</td><td align='left'>Parti-total Affirmative</td><td align='left'>— Some X is all Y.</td></tr> +<tr><td align='left'>I.</td><td align='left'>Parti-partial Affirmative</td><td align='left'>— Some X is some Y.</td></tr> +<tr><td align='left'>E.</td><td align='left'>Toto-total Negative</td><td align='left'>— No X is any Y.</td></tr> +<tr><td align='left'>η.</td><td align='left'>Toto-partial Negative</td><td align='left'>— No X is some Y.</td></tr> +<tr><td align='left'>O.</td><td align='left'>Parti-total Negative</td><td align='left'>— Some X is not any Y.</td></tr> +<tr><td align='left'>ω.</td><td align='left'>Parti-partial Negative</td><td align='left'>— Some X is not some Y.</td></tr> +</table></div> + +<p class="noindent">Here A. I. E. O. correspond with those similarly symbolised in the usual +list, merely designating in the predicates the quantity which was +formerly treated as implicit.</p> + +<p><a name="chap_5_sect_4" id="chap_5_sect_4"></a>§ 4. As to Relation, propositions are either Categorical or Conditional. +A Categorical Proposition is one in which the predicate is directly +affirmed or denied of the subject without any limitation of time, place, +or circumstance, extraneous to the subject, as <i>All men in England are +secure of justice</i>; in which proposition, though there is a limitation +of place ('in England'), it is included in the subject. Of this kind are +nearly all the examples that have yet been given, according to the form +<i>S is P</i>.</p><p><span class='pagenum'>[Pg 60]<a name="Page_60" id="Page_60"></a></span></p> + +<p>A Conditional Proposition is so called because the predication is made +under some limitation or condition not included in the subject, as <i>If a +man live in England, he is secure of justice</i>. Here the limitation +'living in England' is put into a conditional sentence extraneous to the +subject, 'he,' representing any man.</p> + +<p>Conditional propositions, again, are of two kinds—Hypothetical and +Disjunctive. Hypothetical propositions are those that are limited by an +explicit conditional sentence, as above, or thus: <i>If Joe Smith was a +prophet, his followers have been unjustly persecuted</i>. Or in symbols +thus:</p> + + +<div class="example"><span class="i0">If A is, B is;<br /></span> +<span class="i0">If A is B, A is C;<br /></span> +<span class="i0">If A is B, C is D.</span></div> + + +<p>Disjunctive propositions are those in which the condition under which +predication is made is not explicit but only implied under the disguise +of an alternative proposition, as <i>Joe Smith was either a prophet or an +impostor</i>. Here there is no direct predication concerning Joe Smith, but +only a predication of one of the alternatives conditionally on the other +being denied, as, <i>If Joe Smith was not a prophet he was an impostor</i>; +or, <i>If he was not an impostor, he was a prophet</i>. Symbolically, +Disjunctives may be represented thus:</p> + + +<div class="example"><span class="i0">A is either B or C,<br /></span> +<span class="i0">Either A is B or C is D.</span></div> + + +<p>Formally, every Conditional may be expressed as a Categorical. For our +last example shows how a Disjunctive may be reduced to two Hypotheticals +(of which one is redundant, being the contrapositive of the other; see +<a href="#chap_7_sect_10">chap. vii. § 10</a>). And a Hypothetical is reducible to a Categorical thus: +<i>If the sky is clear, the night is cold</i> may be read—<i>The case of the +sky being clear is a case of the night being cold</i>; and this, though a +clumsy plan, is sometimes convenient. It would be better to say <i>The sky +being clear <span class='pagenum'>[Pg 61]<a name="Page_61" id="Page_61"></a></span>is a sign of the night being cold</i>, or a condition of it. +For, as Mill says, the essence of a Hypothetical is to state that one +clause of it (the indicative) may be inferred from the other (the +conditional). Similarly, we might write: <i>Proof of Joe Smith's not being +a prophet is a proof of his being an impostor</i>.</p> + +<p>This turning of Conditionals into Categoricals is called a Change of +Relation; and the process may be reversed: <i>All the wise are virtuous</i> +may be written, <i>If any man is wise he is virtuous</i>; or, again, <i>Either +a man is not-wise or he is virtuous</i>. But the categorical form is +usually the simplest.</p> + +<p>If, then, as substitutes for the corresponding conditionals, +categoricals are formally adequate, though sometimes inelegant, it may +be urged that Logic has nothing to do with elegance; or that, at any +rate, the chief elegance of science is economy, and that therefore, for +scientific purposes, whatever we may write further about conditionals +must be an ugly excrescence. The scientific purpose of Logic is to +assign the conditions of proof. Can we, then, in the conditional form +prove anything that cannot be proved in the categorical? Or does a +conditional require to be itself proved by any method not applicable to +the Categorical? If not, why go on with the discussion of Conditionals? +For all laws of Nature, however stated, are essentially categorical. 'If +a straight line falls on another straight line, the adjacent angles are +together equal to two right angles'; 'If a body is unsupported, it +falls'; 'If population increases, rents tend to rise': here 'if' means +'whenever' or 'all cases in which'; for to raise a doubt whether a +straight line is ever conceived to fall upon another, whether bodies are +ever unsupported, or population ever increases, is a superfluity of +scepticism; and plainly the hypothetical form has nothing to do with the +proof of such propositions, nor with inference from them.</p> + +<p>Still, the disjunctive form is necessary in setting out the <span class='pagenum'>[Pg 62]<a name="Page_62" id="Page_62"></a></span>relation of +contradictory terms, and in stating a Division (<a href="#CHAPTER_XXI">chap. xxi.</a>), whether +formal (<i>as A is B or not-B</i>) or material (as <i>Cats are white, or black, +or tortoiseshell, or tabby</i>). And in some cases the hypothetical form is +useful. One of these occurs where it is important to draw attention to +the condition, as something doubtful or especially requiring +examination. <i>If there is a resisting medium in space, the earth will +fall into the sun; If the Corn Laws are to be re-enacted, we had better +sell railways and buy land</i>: here the hypothetical form draws attention +to the questions whether there is a resisting medium in space, whether +the Corn Laws are likely to be re-enacted; but as to methods of +inference and proof, the hypothetical form has nothing to do with them. +The propositions predicate causation: <i>A resisting medium in space is a +condition of the earth's falling into the sun; A Corn Law is a condition +of the rise of rents, and of the fall of railway profits</i>.</p> + +<p>A second case in which the hypothetical is a specially appropriate form +of statement occurs where a proposition relates to a particular matter +and to future time, as <i>If there be a storm to-morrow, we shall miss our +picnic</i>. Such cases are of very slight logical interest. It is as +exercises in formal thinking that hypotheticals are of most value; +inasmuch as many people find them more difficult than categoricals to +manipulate.</p> + +<p>In discussing Conditional Propositions, the conditional sentence of a +Hypothetical, or the first alternative of a Disjunctive, is called the +Antecedent; the indicative sentence of a Hypothetical, or the second +alternative of a Disjunctive, is called the Consequent.</p> + +<p>Hypotheticals, like Categoricals, have been classed according to +Quantity and Quality. Premising that the quantity of a Hypothetical +depends on the quantity of its Antecedent (which determines its +limitation), whilst its quality depends on the quality of its consequent +(which makes the predication), we may exhibit four forms:</p><p><span class='pagenum'>[Pg 63]<a name="Page_63" id="Page_63"></a></span></p> + +<div class="example"><span class="i0">A. <i>If A is B, C is D;</i><br /></span> +<span class="i0">I. <i>Sometimes when A is B, C is D;</i><br /></span> +<span class="i0">E. <i>If A is B, C is not D;</i><br /></span> +<span class="i0">O. <i>Sometimes when A is B, C is not D.</i><br /></span></div> + +<p class="noindent">But I. and O. are rarely used.</p> + +<p>As for Disjunctives, it is easy to distinguish the two quantities thus:</p> + +<div class="example"><span class="i0">A. <i>Either A is B, or C is D;</i><br /></span> +<span class="i0">I. <i>Sometimes either A is B or C is D.</i><br /></span></div> + + +<p class="noindent">But I. is rarely used. The distinction of quality, however, cannot be +made: there are no true negative forms; for if we write—</p> + + +<div class="example"><span class="i0"><i>Neither is A B, nor C D,</i></span></div> + + +<p class="noindent">there is here no alternative predication, but only an Exponible +equivalent to <i>No A is B, and No C is D</i>. And if we write—</p> + + +<div class="example"><span class="i0"><i>Either A is not B, or C is not D,</i></span></div> + + +<p class="noindent">this is affirmative as to the alternation, and is for all methods of +treatment equivalent to A.</p> + +<p>Logicians are divided in opinion as to the interpretation of the +conjunction 'either, or'; some holding that it means 'not both,' others +that it means 'it may be both.' Grammatical usage, upon which the +question is sometimes argued, does not seem to be established in favour +of either view. If we say <i>A man so precise in his walk and conversation +is either a saint or a consummate hypocrite</i>; or, again, <i>One who is +happy in a solitary life is either more or less than man</i>; we cannot in +such cases mean that the subject may be both. On the other hand, if it +be said that <i>the author of 'A Tale of a Tub' is either a misanthrope or +a dyspeptic</i>, the alternatives are not incompatible. Or, again, given +that <i>X. is a lunatic, or a lover, or a poet</i>, the three predicates have +much congruity.</p> + +<p>It has been urged that in Logic, language should be made as exact and +definite as possible, and that this requires <span class='pagenum'>[Pg 64]<a name="Page_64" id="Page_64"></a></span>the exclusive +interpretation 'not both.' But it seems a better argument, that Logic +(1) should be able to express all meanings, and (2), as the science of +evidence, must not assume more than is given; to be on the safe side, it +must in doubtful cases assume the least, just as it generally assumes a +preindesignate term to be of particular quantity; and, therefore +'either, or' means 'one, or the other, or both.'</p> + +<p>However, when both the alternative propositions have the same subject, +as <i>Either A is B, or A is C</i>, if the two predicates are contrary or +contradictory terms (as 'saint' and 'hypocrite,' or 'saint' and +'not-saint'), they cannot in their nature be predicable in the same way +of the same subject; and, therefore, in such a case 'either, or' means +one or the other, but not both in the same relation. Hence it seems +necessary to admit that the conjunction 'either, or' may sometimes +require one interpretation, sometimes the other; and the rule is that it +implies the further possibility 'or both,' except when both alternatives +have the same subject whilst the predicates are contrary or +contradictory terms.</p> + +<p>If, then, the disjunctive <i>A is either B or C</i> (<i>B</i> and <i>C</i> being +contraries) implies that both alternatives cannot be true, it can only +be adequately rendered in hypotheticals by the two forms—(1) <i>If A is +B, it is not C</i>, and (2)<i>If A is not B, it is C</i>. But if the disjunctive +<i>A is either B or C</i> (<i>B</i> and <i>C</i> not being contraries) implies that +both may be true, it will be adequately translated into a hypothetical +by the single form, <i>If A is not B, it is C</i>. We cannot translate it +into—<i>If A is B, it is not C</i>, for, by our supposition, if '<i>A is B</i>' +is true, it does not follow that '<i>A is C</i>' must be false.</p> + +<p>Logicians are also divided in opinion as to the function of the +hypothetical form. Some think it expresses doubt; for the consequent +depends on the antecedent, and the antecedent, introduced by 'if,' may +or may not be realised, <span class='pagenum'>[Pg 65]<a name="Page_65" id="Page_65"></a></span>as in <i>If the sky is clear, the night is cold</i>: +whether the sky is, or is not, clear being supposed to be uncertain. And +we have seen that some hypothetical propositions seem designed to draw +attention to such uncertainty, as—<i>If there is a resisting medium in +space, etc</i>. But other Logicians lay stress upon the connection of the +clauses as the important matter: the statement is, they say, that the +consequent may be inferred from the antecedent. Some even declare that +it is given as a necessary inference; and on this ground Sigwart rejects +particular hypotheticals, such as <i>Sometimes when A is B, C is D</i>; for +if it happens only sometimes the connexion cannot be necessary. Indeed, +it cannot even be probably inferred without further grounds. But this is +also true whenever the antecedent and consequent are concerned with +different matter. For example, <i>If the soul is simple, it is +indestructible</i>. How do you know that? Because <i>Every simple substance +is indestructible</i>. Without this further ground there can be no +inference. The fact is that conditional forms often cover assertions +that are not true complex propositions but a sort of euthymemes (<a href="#chap_11_sect_2">chap. +xi. § 2</a>), arguments abbreviated and rhetorically disguised. Thus: <i>If +patience is a virtue there are painful virtues</i>—an example from Dr. +Keynes. Expanding this we have—</p> + +<div class="example"><span class="i1">Patience is painful;</span><br /> +<span class="i1">Patience is a virtue:</span><br /> +<span class="i0">∴ Some virtue is painful.<br /></span></div> + +<p class="noindent">And then we see the equivocation of the inference; for though patience +be painful <i>to learn</i>, it is not painful <i>as a virtue</i> to the patient +man.</p> + +<p>The hypothetical, '<i>If Plato was not mistaken poets are dangerous +citizens</i>,' may be considered as an argument against the laureateship, +and may be expanded (informally) thus: 'All Plato's opinions deserve +respect; one of them was that poets are bad citizens; therefore it +behoves us to <span class='pagenum'>[Pg 66]<a name="Page_66" id="Page_66"></a></span>be chary of encouraging poetry.' Or take this +disjunctive, '<i>Either Bacon wrote the works ascribed to Shakespeare, or +there were two men of the highest genius in the same age and country</i>.' +This means that it is not likely there should be two such men, that we +are sure of Bacon, and therefore ought to give him all the glory. Now, +if it is the part of Logic 'to make explicit in language all that is +implicit in thought,' or to put arguments into the form in which they +can best be examined, such propositions as the above ought to be +analysed in the way suggested, and confirmed or refuted according to +their real intention.</p> + +<p>We may conclude that no single function can be assigned to all +hypothetical propositions: each must be treated according to its own +meaning in its own context.</p> + +<p><a name="chap_5_sect_5" id="chap_5_sect_5"></a>§ 5. As to Modality, propositions are divided into Pure and Modal. A +Modal proposition is one in which the predicate is affirmed or denied, +not simply but <i>cum modo</i>, with a qualification. And some Logicians have +considered any adverb occurring in the predicate, or any sign of past or +future tense, enough to constitute a modal: as 'Petroleum is +<i>dangerously</i> inflammable'; 'English <i>will be</i> the universal language.' +But far the most important kind of modality, and the only one we need +consider, is that which is signified by some qualification of the +predicate as to the degree of certainty with which it is affirmed or +denied. Thus, 'The bite of the cobra is <i>probably</i> mortal,' is called a +Contingent or Problematic Modal: 'Water is <i>certainly</i> composed of +oxygen and hydrogen' is an Assertory or Certain Modal: 'Two straight +lines <i>cannot</i> enclose a space' is a Necessary or Apodeictic Modal (the +opposite being inconceivable). Propositions not thus qualified are +called Pure.</p> + +<p>Modal propositions have had a long and eventful history, but they have +not been found tractable by the resources of ordinary Logic, and are now +generally neglected by the authors of text-books. No doubt such +propositions are the commonest in ordinary discourse, and in some rough +way <span class='pagenum'>[Pg 67]<a name="Page_67" id="Page_67"></a></span>we combine them and draw inferences from them. It is understood +that a combination of assertory or of apodeictic premises may warrant an +assertory or an apodeictic conclusion; but that if we combine either of +these with a problematic premise our conclusion becomes problematic; +whilst the combination of two problematic premises gives a conclusion +less certain than either. But if we ask 'How much less certain?' there +is no answer. That the modality of a conclusion follows the less certain +of the premises combined, is inadequate for scientific guidance; so +that, as Deductive Logic can get no farther than this, it has abandoned +the discussion of Modals. To endeavour to determine the degree of +certainty attaching to a problematic judgment is not, however, beyond +the reach of Induction, by analysing circumstantial evidence, or by +collecting statistics with regard to it. Thus, instead of 'The cobra's +bite is <i>probably</i> fatal,' we might find that it is fatal 80 times in +100. Then, if we know that of those who go to India 3 in 1000 are +bitten, we can calculate what the chances are that any one going to +India will die of a cobra's bite (<a href="#CHAPTER_XX">chap. xx.</a>).</p> + +<p><a name="chap_5_sect_6" id="chap_5_sect_6"></a>§ 6. Verbal and Real Propositions.—Another important division of +propositions turns upon the relation of the predicate to the subject in +respect of their connotations. We saw, when discussing Relative Terms, +that the connotation of one term often implies that of another; +sometimes reciprocally, like 'master' and 'slave'; or by inclusion, like +species and genus; or by exclusion, like contraries and contradictories. +When terms so related appear as subject and predicate of the same +proposition, the result is often tautology—<i>e.g., The master has +authority over his slave; A horse is an animal; Red is not blue; British +is not foreign</i>. Whoever knows the meaning of 'master,' 'horse,' 'red,' +'British,' learns nothing from these propositions. Hence they are called +Verbal propositions, as only expounding the sense of words, or as if +they were propositions only by satisfying the forms of language, not by +<span class='pagenum'>[Pg 68]<a name="Page_68" id="Page_68"></a></span>fulfilling the function of propositions in conveying a knowledge of +facts. They are also called 'Analytic' and 'Explicative,' when they +separate and disengage the elements of the connotation of the subject. +Doubtless, such propositions may be useful to one who does not know the +language; and Definitions, which are verbal propositions whose +predicates analyse the whole connotations of their subjects, are +indispensable instruments of science (see <a href="#CHAPTER_XXII">chap. xxii.</a>).</p> + +<p>Of course, hypothetical propositions may also be verbal, as <i>If the soul +be material it is extended</i>; for 'extension' is connoted by 'matter'; +and, therefore, the corresponding disjunctive is verbal—<i>Either the +soul is not material, or it is extended</i>. But a true divisional +disjunctive can never be verbal (<a href="#chap_21_sect_4">chap. xxi. § 4</a>, rule 1).</p> + +<p>On the other hand, when there is no such direct relation between subject +and predicate that their connotations imply one another, but the +predicate connotes something that cannot be learnt from the connotation +of the subject, there is no longer tautology, but an enlargement of +meaning—<i>e.g., Masters are degraded by their slaves; The horse is the +noblest animal; Red is the favourite colour of the British army; If the +soul is simple, it is indestructible</i>. Such propositions are called +Real, Synthetic, or Ampliative, because they are propositions for which +a mere understanding of their subjects would be no substitute, since the +predicate adds a meaning of its own concerning matter of fact.</p> + +<p>To any one who understands the language, a verbal proposition can never +be an inference or conclusion from evidence; nor can a verbal +proposition ever furnish grounds for an inference, except as to the +meaning of words. The subject of real and verbal propositions will +inevitably recur in the chapters on Definition; but tautologies are such +common blemishes in composition, and such frequent pitfalls in argument, +that attention cannot be drawn to them too early or too often.</p><p><span class='pagenum'>[Pg 69]<a name="Page_69" id="Page_69"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_VI" id="CHAPTER_VI"></a>CHAPTER VI</h2> + +<h3>CONDITIONS OF IMMEDIATE INFERENCE</h3> + + +<p><a name="chap_6_sect_1" id="chap_6_sect_1"></a>§ 1. The word Inference is used in two different senses, which are often +confused but should be carefully distinguished. In the first sense, it +means a process of thought or reasoning by which the mind passes from +facts or statements presented, to some opinion or expectation. The data +may be very vague and slight, prompting no more than a guess or surmise; +as when we look up at the sky and form some expectation about the +weather, or from the trick of a man's face entertain some prejudice as +to his character. Or the data may be important and strongly significant, +like the footprint that frightened Crusoe into thinking of cannibals, or +as when news of war makes the city expect that Consols will fall. These +are examples of the act of inferring, or of inference as a process; and +with inference in this sense Logic has nothing to do; it belongs to +Psychology to explain how it is that our minds pass from one perception +or thought to another thought, and how we come to conjecture, conclude +and believe (<i>cf.</i> <a href="#chap_1_sect_6">chap. i. § 6</a>).</p> + +<p>In the second sense, 'inference' means not this process of guessing or +opining, but the result of it; the surmise, opinion, or belief when +formed; in a word, the conclusion: and it is in this sense that +Inference is treated of in Logic. The subject-matter of Logic is an +inference, judgment or conclusion concerning facts, embodied in a +proposition, which is to be examined in relation to the evidence that +may be adduced for it, in order to determine whether, or how <span class='pagenum'>[Pg 70]<a name="Page_70" id="Page_70"></a></span>far, the +evidence amounts to proof. Logic is the science of Reasoning in the +sense in which 'reasoning' means giving reasons, for it shows what sort +of reasons are good. Whilst Psychology explains how the mind goes +forward from data to conclusions, Logic takes a conclusion and goes back +to the data, inquiring whether those data, together with any other +evidence (facts or principles) that can be collected, are of a nature to +warrant the conclusion. If we think that the night will be stormy, that +John Doe is of an amiable disposition, that water expands in freezing, +or that one means to national prosperity is popular education, and wish +to know whether we have evidence sufficient to justify us in holding +these opinions, Logic can tell us what form the evidence should assume +in order to be conclusive. What <i>form</i> the evidence should assume: Logic +cannot tell us what kinds of fact are proper evidence in any of these +cases; that is a question for the man of special experience in life, or +in science, or in business. But whatever facts constitute the evidence, +they must, in order to prove the point, admit of being stated in +conformity with certain principles or conditions; and of these +principles or conditions Logic is the science. It deals, then, not with +the subjective process of inferring, but with the objective grounds that +justify or discredit the inference.</p> + +<p><a name="chap_6_sect_2" id="chap_6_sect_2"></a>§ 2. Inferences, in the Logical sense, are divided into two great +classes, the Immediate and the Mediate, according to the character of +the evidence offered in proof of them. Strictly, to speak of inferences, +in the sense of conclusions, as immediate or mediate, is an abuse of +language, derived from times before the distinction between inference as +process and inference as result was generally felt. No doubt we ought +rather to speak of Immediate and Mediate Evidence; but it is of little +use to attempt to alter the traditional expressions of the science.</p> + +<p>An Immediate Inference, then, is one that depends for its proof upon +only one other proposition, which has the same, <span class='pagenum'>[Pg 71]<a name="Page_71" id="Page_71"></a></span>or more extensive, +terms (or matter). Thus that <i>one means to national prosperity is +popular education</i> is an immediate inference, if the evidence for it is +no more than the admission that <i>popular education is a means to +national prosperity:</i> Similarly, it is an immediate inference that <i>Some +authors are vain</i>, if it be granted that <i>All authors are vain</i>.</p> + +<p>An Immediate Inference may seem to be little else than a verbal +transformation; some Logicians dispute its claims to be called an +inference at all, on the ground that it is identical with the pretended +evidence. If we attend to the meaning, say they, an immediate inference +does not really express any new judgment; the fact expressed by it is +either the same as its evidence, or is even less significant. If from +<i>No men are gods</i> we prove that <i>No gods are men</i>, this is nugatory; if +we prove from it that <i>Some men are not gods</i>, this is to emasculate the +sense, to waste valuable information, to lose the commanding sweep of +our universal proposition.</p> + +<p>Still, in Logic, it is often found that an immediate inference expresses +our knowledge in a more convenient form than that of the evidentiary +proposition, as will appear in the chapter on Syllogisms and elsewhere. +And by transforming an universal into a particular proposition, as <i>No +men are gods</i>, therefore, <i>Some men are not gods</i>,—we get a statement +which, though weaker, is far more easily proved; since a single instance +suffices. Moreover, by drawing all possible immediate inferences from a +given proposition, we see it in all its aspects, and learn all that is +implied in it.</p> + +<p>A Mediate Inference, on the other hand, depends for its evidence upon a +plurality of other propositions (two or more) which are connected +together on logical principles. If we argue—</p> + + <div class="example"><span class="i1">No men are gods;</span> + <span class="i1">Alexander the Great is a man;</span> +<span class="i0">∴ Alexander the Great is not a god:</span></div> + + +<p class="noindent"><span class='pagenum'>[Pg 72]<a name="Page_72" id="Page_72"></a></span>this is a Mediate Inference. The evidence consists of two propositions +connected by the term 'man,' which is common to both (a Middle Term), +mediating between 'gods' and 'Alexander.' Mediate Inferences comprise +Syllogisms with their developments, and Inductions; and to discuss them +further at present would be to anticipate future chapters. We must now +deal with the principles or conditions on which Immediate Inferences are +valid: commonly called the "Laws of Thought."</p> + +<p><a name="chap_6_sect_3" id="chap_6_sect_3"></a>§ 3. The Laws of Thought are conditions of the logical statement and +criticism of all sorts of evidence; but as to Immediate Inference, they +may be regarded as the only conditions it need satisfy. They are often +expressed thus: (1) The principle of Identity—'<i>Whatever is, is</i>'; (2) +The principle of Contradiction—'<i>It is impossible for the same thing to +be and not be</i>'; (3) The principle of Excluded Middle—'<i>Anything must +either be or not be</i>.' These principles are manifestly not 'laws' of +thought in the sense in which 'law' is used in Psychology; they do not +profess to describe the actual mental processes that take place in +judgment or reasoning, as the 'laws of association of ideas' account for +memory and recollection. They are not natural laws of thought; but, in +relation to thought, can only be regarded as laws when stated as +precepts, the observance of which (consciously or not) is necessary to +clear and consistent thinking: <i>e.g.</i>, Never assume that the same thing +can both be and not be.</p> + +<p>However, treating Logic as the science of thought only as embodied in +propositions, in respect of which evidence is to be adduced, or which +are to be used as evidence of other propositions, the above laws or +principles must be restated as the conditions of consistent argument in +such terms as to be directly applicable to propositions. It was shown in +the chapter on the connotation of terms, that terms are assumed by +Logicians to be capable of definite meaning, and of being used +univocally in the same context; <span class='pagenum'>[Pg 73]<a name="Page_73" id="Page_73"></a></span>if, or in so far as, this is not the +case, we cannot understand one another's reasons nor even pursue in +solitary meditation any coherent train of argument. We saw, too, that +the meanings of terms were related to one another: some being full +correlatives; others partially inclusive one of another, as species of +genus; others mutually incompatible, as contraries; or alternatively +predicable, as contradictories. We now assume that propositions are +capable of definite meaning according to the meaning of their component +terms and of the relation between them; that the meaning, the fact +asserted or denied, is what we are really concerned to prove or +disprove; that a mere change in the words that constitute our terms, or +of construction, does not affect the truth of a proposition as long as +the meaning is not altered, or (rather) as long as no fresh meaning is +introduced; and that if the meaning of any proposition is true, any +other proposition that denies it is false. This postulate is plainly +necessary to consistency of statement and discourse; and consistency is +necessary, if our thought or speech is to correspond with the unity and +coherence of Nature and experience; and the Laws of Thought or +Conditions of Immediate Inference are an analysis of this postulate.</p> + +<p><a name="chap_6_sect_4" id="chap_6_sect_4"></a>§ 4. The principle of Identity is usually written symbolically thus: <i>A +is A; not-A is not-A</i>. It assumes that there is something that may be +represented by a term; and it requires that, in any discussion, <i>every +relevant term, once used in a definite sense, shall keep that meaning +throughout</i>. Socrates in his father's workshop, at the battle of Delium, +and in prison, is assumed to be the same man denotable by the same name; +and similarly, 'elephant,' or 'justice,' or 'fairy,' in the same +context, is to be understood of the same thing under the same +<i>suppositio</i>.</p> + +<p>But, further, it is assumed that of a given term another term may be +predicated again and again in the same sense under the same conditions; +that is, we may speak of the identity of meaning in a proposition as +well as in a term.<span class='pagenum'>[Pg 74]<a name="Page_74" id="Page_74"></a></span> To symbolise this we ought to alter the usual +formula for Identity and write it thus: <i>If B is A, B is A; if B is +not-A, B is not-A</i>. If Socrates is wise, he is wise; if fairies frequent +the moonlight, they do; if Justice is not of this world, it is not. +<i>Whatever affirmation or denial we make concerning any subject, we are +bound to adhere to it for the purposes of the current argument or +investigation.</i> Of course, if our assertion turns out to be false, we +must not adhere to it; but then we must repudiate all that we formerly +deduced from it.</p> + +<p>Again, <i>whatever is true or false in one form of words is true or false +in any other</i>: this is undeniable, for the important thing is identity +of meaning; but in Formal Logic it is not very convenient. If Socrates +is wise, is it an identity to say 'Therefore the master of Plato is +wise'; or, further that he 'takes enlightened views of life'? If <i>Every +man is fallible</i>, is it an identical proposition that <i>Every man is +liable to error</i>? It seems pedantic to demand a separate proposition +that <i>Fallible is liable to error</i>. But, on the other hand, the +insidious substitution of one term for another speciously identical, is +a chief occasion of fallacy. How if we go on to argue: therefore, <i>Every +man is apt to blunder, prone to confusion of thought, inured to +self-contradiction</i>? Practically, the substitution of identities must be +left to candour and good-sense; and may they increase among us. Formal +Logic is, no doubt, safest with symbols; should, perhaps, content itself +with A and B; or, at least, hardly venture beyond Y and Z.</p> + +<p><a name="chap_6_sect_5" id="chap_6_sect_5"></a>§ 5. The principle of Contradiction is usually written symbolically, +thus: <i>A is not not-A</i>. But, since this formula seems to be adapted to a +single term, whereas we want one that is applicable to propositions, it +may be better to write it thus: <i>B is not both A and not-A</i>. That is to +say: <i>if any term may be affirmed of a subject, the contradictory term +may, in the same relation, be denied of it</i>. A leaf that is green on one +side of it may be not-green on the other; but it <span class='pagenum'>[Pg 75]<a name="Page_75" id="Page_75"></a></span>is not both green and +not-green on the same surface, at the same time, and in the same light. +If a stick is straight, it is false that it is at the same time +not-straight: having granted that two angles are equal, we must deny +that they are unequal.</p> + +<p>But is it necessarily false that the stick is 'crooked'; must we deny +that either angle is 'greater or less' than the other? How far is it +permissible to substitute any other term for the formal contradictory? +Clearly, the principle of Contradiction takes for granted the principle +of Identity, and is subject to the same difficulties in its practical +application. As a matter of fact and common sense, if we affirm any term +of a Subject, we are bound to deny of that Subject, in the same +relation, not only the contradictory but all synonyms for this, and also +all contraries and opposites; which, of course, are included in the +contradictory. But who shall determine what these are? Without an +authoritative Logical Dictionary to refer to, where all contradictories, +synonyms, and contraries may be found on record, Formal Logic will +hardly sanction the free play of common sense.</p> + +<p>The principle of Excluded Middle may be written: <i>B is either A or +not-A</i>; that is, <i>if any term be denied of a subject, the contradictory +term may, in the same relation, be affirmed</i>. Of course, we may deny +that a leaf is green on one side without being bound to affirm that it +is not-green on the other. But in the same relation a leaf is either +green or not-green; at the same time, a stick is either bent or +not-bent. If we deny that A is greater than B, we must affirm that it is +not-greater than B.</p> + +<p>Whilst, then, the principle of Contradiction (that 'of contradictory +predicates, one being affirmed, the other is denied ') might seem to +leave open a third or middle course, the denying of both +contradictories, the principle of Excluded Middle derives its name from +the excluding of this middle course, by declaring that the one or the +other must <span class='pagenum'>[Pg 76]<a name="Page_76" id="Page_76"></a></span>be affirmed. Hence the principle of Excluded Middle does not +hold good of mere contrary terms. If we deny that a leaf is green, we +are not bound to affirm it to be yellow; for it may be red; and then we +may deny both contraries, yellow and green. In fact, two contraries do +not between them cover the whole predicable area, but contradictories +do: the form of their expression is such that (within the <i>suppositio</i>) +each includes all that the other excludes; so that the subject (if +brought within the <i>suppositio</i>) must fall under the one or the other. +It may seem absurd to say that Mont Blanc is either wise or not-wise; +but how comes any mind so ill-organised as to introduce Mont Blanc into +this strange company? Being there, however, the principle is inexorable: +Mont Blanc is not-wise.</p> + +<p>In fact, the principles of Contradiction and Excluded Middle are +inseparable; they are implicit in all distinct experience, and may be +regarded as indicating the two aspects of Negation. The principle of +Contradiction says: <i>B is not both A and not-A</i>, as if <i>not-A</i> might be +nothing at all; this is abstract negation. But the principle of Excluded +Middle says: <i>Granting that B is not A, it is still something</i>—namely, +<i>not-A</i>; thus bringing us back to the concrete experience of a continuum +in which the absence of one thing implies the presence of something +else. Symbolically: to deny that B is A is to affirm that B is not A, +and this only differs by a hyphen from B is not-A.</p> + +<p>These principles, which were necessarily to some extent anticipated in +<a href="#chap_4_sect_7">chap. iv. § 7</a>, the next chapter will further illustrate.</p> + +<p><a name="chap_6_sect_6" id="chap_6_sect_6"></a>§ 6. But first we must draw attention to a maxim (also already +mentioned), which is strictly applicable to Immediate Inferences, though +(as we shall see) in other kinds of proof it may be only a formal +condition: this is the general caution <i>not to go beyond the evidence</i>. +An immediate inference ought to contain nothing that is not contained +(or formally implied) in the proposition by which it is proved.<span class='pagenum'>[Pg 77]<a name="Page_77" id="Page_77"></a></span> With +respect to quantity in denotation, this caution is embodied in the rule +'not to distribute any term that is not given distributed.' Thus, if +there is a predication concerning 'Some S,' or 'Some men,' as in the +forms I. and O., we cannot infer anything concerning 'All S.' or 'All +men'; and, as we have seen, if a term is given us preindesignate, we are +generally to take it as of particular quantity. Similarly, in the case +of affirmative propositions, we saw that this rule requires us to assume +that their predicates are undistributed.</p> + +<p>As to the grounds of this maxim, not to go beyond the evidence, not to +distribute a term that is given as undistributed, it is one of the +things so plain that to try to justify is only to obscure them. Still, +we must here state explicitly what Formal Logic assumes to be contained +or implied in the evidence afforded by any proposition, such as 'All S +is P.' If we remember that in <a href="#chap_4_sect_7">chap. iv. § 7</a>, it was assumed that every +term may have a contradictory; and if we bear in mind the principles of +Contradiction and Excluded Middle, it will appear that such a +proposition as 'All S is P' tells us something not only about the +relations of 'S' and 'P,' but also of their relations to 'not-S' and +'not-P'; as, for example, that 'S is not not-P,' and that 'not-P is +not-S.' It will be shown in the next chapter how Logicians have +developed these implications in series of Immediate Inferences.</p> + +<p>If it be asked whether it is true that every term, itself significant, +has a significant contradictory, and not merely a formal contradictory, +generated by force of the word 'not,' it is difficult to give any better +answer than was indicated in <a href="#chap_6_sect_3">§§ 3-5</a>, without venturing further into +Metaphysics. I shall merely say, therefore, that, granting that some +such term as 'Universe' or 'Being' may have no significant +contradictory, if it stand for 'whatever can be perceived or thought +of'; yet every term that stands for less than 'Universe' or 'Being' has, +of course, a contradictory <span class='pagenum'>[Pg 78]<a name="Page_78" id="Page_78"></a></span>which denotes the rest of the universe. And +since every argument or train of thought is carried on within a special +'universe of discourse,' or under a certain <i>suppositio</i>, we may say +that <i>within the given suppositio every term has a contradictory</i>, and +that every predication concerning a term implies some predication +concerning its contradictory. But the name of the <i>suppositio</i> itself +has no contradictory, except with reference to a wider and inclusive +<i>suppositio</i>.</p> + +<p>The difficulty of actual reasoning, not with symbols, but about matters +of fact, does not arise from the principles of Logic, but sometimes from +the obscurity or complexity of the facts, sometimes from the ambiguity +or clumsiness of language, sometimes from the deficiency of our own +minds in penetration, tenacity and lucidity. One must do one's best to +study the facts, and not be too easily discouraged.</p><p><span class='pagenum'>[Pg 79]<a name="Page_79" id="Page_79"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_VII" id="CHAPTER_VII"></a>CHAPTER VII</h2> + +<h3>IMMEDIATE INFERENCES</h3> + + +<p><a name="chap_7_sect_1" id="chap_7_sect_1"></a>§ 1. Under the general title of Immediate Inference Logicians discuss +three subjects, namely, Opposition, Conversion, and Obversion; to which +some writers add other forms, such as Whole and Part in Connotation, +Contraposition, Inversion, <i>etc.</i> Of Opposition, again, all recognise +four modes: Subalternation, Contradiction, Contrariety and +Sub-contrariety. The only peculiarities of the exposition upon which we +are now entering are, that it follows the lead of the three Laws of +Thought, taking first those modes of Immediate Inference in which +Identity is most important, then those which plainly involve +Contradiction and Excluded Middle; and that this method results in +separating the modes of Opposition, connecting Subalternation with +Conversion, and the other modes with Obversion. To make up for this +departure from usage, the four modes of Opposition will be brought +together again in <a href="#chap_7_sect_9">§ 9</a>.</p> + +<p><a name="chap_7_sect_2" id="chap_7_sect_2"></a>§ 2. Subalternation.—Opposition being the relation of propositions that +have the same matter and differ only in form (as A., E., I., O.), +propositions of the forms A. and I. are said to be Subalterns in +relation to one another, and so are E. and O.; the universal of each +quality being distinguished as 'subalternans,' and the particular as +'subalternate.'</p> + +<p>It follows from the principle of Identity that, the matter of the +propositions being the same, if A. is true I. is true, and that if E. is +true O. is true; for A. and E. predicate something of <i>All S</i> or <i>All +men</i>; and since I. and O. make <span class='pagenum'>[Pg 80]<a name="Page_80" id="Page_80"></a></span>the same predication of <i>Some S</i> or +<i>Some men</i>, the sense of these particular propositions has already been +predicated in A. or E. If <i>All S is P, Some S is P</i>; if <i>No S is P, Some +S is not P</i>; or, if <i>All men are fond of laughing, Some men are</i>; if <i>No +men are exempt from ridicule, Some men are not</i>.</p> + +<p>Similarly, if I. is false A. is false; if O. is false E. is false. If we +deny any predication about <i>Some S</i>, we must deny it of <i>All S</i>; since +in denying it of <i>Some</i>, we have denied it of at least part of <i>All</i>; +and whatever is false in one form of words is false in any other.</p> + +<p>On the other hand, if I. is true, we do not know that A. is; nor if O. +is true, that E. is; for to infer from <i>Some</i> to <i>All</i> would be going +beyond the evidence. We shall see in discussing Induction that the great +problem of that part of Logic is, to determine the conditions under +which we may in reality transcend this rule and infer from <i>Some</i> to +<i>All</i>; though even there it will appear that, formally, the rule is +observed. For the present it is enough that I. is an immediate inference +from A., and O. from E.; but that A. is not an immediate inference from +I., nor E. from O.</p> + +<p><a name="chap_7_sect_3" id="chap_7_sect_3"></a>§ 3. Connotative Subalternation.—We have seen (<a href="#chap_4_sect_6">chap. iv. § 6</a>) that if +the connotation of one term is only part of another's its denotation is +greater and includes that other's. Hence genus and species stand in +subaltern relation, and whatever is true of the genus is true of the +species: If <i>All animal life is dependent on vegetation, All human life +is dependent on vegetation</i>. On the other hand, whatever is not true of +the species or narrower term, cannot be true of the whole genus: If it +is false that '<i>All human life is happy</i>,' it is false that '<i>All animal +life is happy</i>.'</p> + +<p>Similar inferences may be drawn from the subaltern relation of +predicates; affirming the species we affirm the genus. To take Mill's +example, if <i>Socrates is a man, Socrates is a living creature</i>. On the +other hand, denying the genus we deny the species: if <i>Socrates is not +vicious, Socrates is not drunken</i>.</p><p><span class='pagenum'>[Pg 81]<a name="Page_81" id="Page_81"></a></span></p> + +<p>Such cases as these are recognised by Mill and Bain as immediate +inferences under the principle of Identity. But some Logicians might +treat them as imperfect syllogisms, requiring another premise to +legitimate the conclusion, thus:</p> + +<div class="example"><span class="i1"><i>All animal life is dependent on vegetation;</i></span> +<span class="i1"><i>All human life is animal life;</i></span> +<span class="i0">∴ <i>All human life is dependent on vegetation.</i></span></div> + +<p class="noindent">Or again:</p> + +<div class="example"><span class="i1"><i>All men are living creatures;</i></span> +<span class="i1"><i>Socrates is a man;</i></span> +<span class="i0">∴ <i>Socrates is a living creature.</i></span></div> + +<p>The decision of this issue turns upon the question (<i>cf.</i> <a href="#chap_6_sect_3">chap. vi. § 3</a>) +how far a Logician is entitled to assume that the terms he uses are +understood, and that the identities involved in their meanings will be +recognised. And to this question, for the sake of consistency, one of +two answers is required; failing which, there remains the rule of thumb. +First, it may be held that no terms are understood except those that are +defined in expounding the science, such as 'genus' and 'species,' +'connotation' and 'denotation.' But very few Logicians observe this +limitation; few would hesitate to substitute 'not wise' for 'foolish.' +Yet by what right? Malvolio being foolish, to prove that he is not-wise, +we may construct the following syllogism:</p> + + +<div class="example"><span class="i1"><i>Foolish is not-wise;</i><br /></span> +<span class="i1"><i>Malvolio is foolish;</i><br /></span> +<span class="i0">∴ <i>Malvolio is not-wise.</i></span></div> + + +<p class="noindent">Is this necessary? Why not?</p> + +<p>Secondly, it may be held that all terms may be assumed as understood +unless a definition is challenged. This principle will justify the +substitution of 'not-wise' for 'foolish'; but it will also legitimate +the above cases (concerning 'human life' and 'Socrates') as immediate +inferences, with innumerable others that might be based <span class='pagenum'>[Pg 82]<a name="Page_82" id="Page_82"></a></span>upon the +doctrine of relative terms: for example, <i>The hunter missed his aim</i>: +therefore, <i>The prey escaped</i>. And from this principle it will further +follow that all apparent syllogisms, having one premise a verbal +proposition, are immediate inferences (<i>cf.</i> <a href="#chap_9_sect_4">chap. ix. § 4</a>).</p> + +<p>Closely connected with such cases as the above are those mentioned by +Archbishop Thomson as "Immediate Inferences by added Determinants" +(<i>Laws of Thought</i>, § 87). He takes the case: '<i>A negro is a +fellow-creature</i>: therefore, <i>A negro in suffering is a fellow-creature +in suffering</i>.' This rests upon the principle that to increase the +connotations of two terms by the same attribute or determinant does not +affect the relationship of their denotations, since it must equally +diminish (if at all) the denotations of both classes, by excluding the +same individuals, if any want the given attribute. But this principle is +true only when the added attribute is not merely the same verbally, but +has the same significance in qualifying both terms. We cannot argue <i>A +mouse is an animal</i>; therefore, <i>A large mouse is a large animal</i>; for +'large' is an attribute relative to the normal magnitude of the thing +described.</p> + +<p><a name="chap_7_sect_4" id="chap_7_sect_4"></a>§ 4. Conversion is Immediate Inference by transposing the terms of a +given proposition without altering its quality. If the quantity is also +unaltered, the inference is called 'Simple Conversion'; but if the +quantity is changed from universal to particular, it is called +'Conversion by limitation' or '<i>per accidens.</i>' The given proposition is +called the 'convertend'; that which is derived from it, the 'converse.'</p> + +<p>Departing from the usual order of exposition, I have taken up Conversion +next to Subalternation, because it is generally thought to rest upon the +principle of Identity, and because it seems to be a good method to +exhaust the forms that come only under Identity before going on to those +that involve Contradiction and Excluded Middle. Some, indeed, dispute +the claims of Conversion to illustrate the principle of<span class='pagenum'>[Pg 83]<a name="Page_83" id="Page_83"></a></span> Identity; and +if the sufficient statement of that principle be 'A is A,' it may be a +question how Conversion or any other mode of inference can be referred +to it. But if we state it as above (<a href="#chap_6_sect_3">chap. vi. § 3</a>), that whatever is +true in one form of words is true in any other, there is no difficulty +in applying it to Conversion.</p> + +<p>Thus, to take the simple conversion of I.,</p> + + +<div class="example"><span class="i0"><i>Some S is P; ∴ Some P is S.</i><br /></span> +<span class="i0"><i>Some poets are business-like; ∴ Some business-like men are poets.</i></span></div> + + +<p class="noindent">Here the convertend and the converse say the same thing, and this is +true if that is.</p> + +<p>We have, then, two cases of simple conversion: of I. (as above) and of +E. For E.:</p> + + +<div class="example"><span class="i0"><i>No S is P; ∴ No P is S.</i></span> +<span class="i0"><i>No ruminants are carnivores; ∴ No carnivores are ruminants.</i></span></div> + + +<p class="noindent">In converting I., the predicate (P) when taken as the new subject, being +preindesignate, is treated as particular; and in converting E., the +predicate (P), when taken as the new subject, is treated as universal, +according to the rule in <a href="#chap_5_sect_1">chap. v. § 1</a>.</p> + +<p>A. is the one case of conversion by limitation:</p> + + +<div class="example"><span class="i0"><i>All S is P; ∴ Some P is S.</i></span> +<span class="i0"><i>All cats are grey in the dark; ∴ Some things grey in the dark are cats.</i></span></div> + + +<p class="noindent">The predicate is treated as particular, when taking it for the new +subject, according to the rule not to go beyond the evidence. To infer +that <i>All things grey in the dark are cats</i> would be palpably absurd; +yet no error of reasoning is commoner than the simple conversion of A. +The validity of conversion by limitation may be shown thus: if, <i>All S +is P</i>, then, by subalternation, <i>Some S is P</i>, and therefore, by simple +conversion, <i>Some P is S</i>.</p> + +<p>O. cannot be truly converted. If we take the proposition:<span class='pagenum'>[Pg 84]<a name="Page_84" id="Page_84"></a></span> <i>Some S is +not P</i>, to convert this into <i>No P is S</i>, or <i>Some P is not S</i>, would +break the rule in <a href="#chap_6_sect_6">chap. vi. § 6</a>; since <i>S,</i> undistributed in the +convertend, would be distributed in the converse. If we are told that +<i>Some men are not cooks</i>, we cannot infer that <i>Some cooks are not men</i>. +This would be to assume that '<i>Some men</i>' are identical with '<i>All +men</i>.'</p> + +<p>By quantifying the predicate, indeed, we may convert O. simply, thus:</p> + + +<div class="example"><span class="i0"><i>Some men are not cooks</i> ∴ <i>No cooks are some men.</i></span></div> + + +<p class="noindent">And the same plan has some advantage in converting A.; for by the usual +method <i>per accidens</i>, the converse of A. being I., if we convert this +again it is still I., and therefore means less than our original +convertend. Thus:</p> + + +<div class="example"><span class="i0"><i>All S is P ∴ Some P is S ∴ Some S is P.</i></span></div> + + +<p class="noindent">Such knowledge, as that <i>All S</i> (the whole of it) <i>is P</i>, is too +precious a thing to be squandered in pure Logic; and it may be preserved +by quantifying the predicate; for if we convert A. to Y., thus—</p> + + +<div class="example"><span class="i0"><i>All S is P ∴ Some P is all S—</i></span></div> + + +<p class="noindent">we may reconvert Y. to A. without any loss of meaning. It is the chief +use of quantifying the predicate that, thereby, every proposition is +capable of simple conversion.</p> + +<p>The conversion of propositions in which the relation of terms is +inadequately expressed (see <a href="#chap_2_sect_2">chap. ii., § 2</a>) by the ordinary copula (<i>is</i> +or <i>is not</i>) needs a special rule. To argue thus—</p> + + +<div class="example"><span class="i0"><i>A is followed by B</i> ∴ <i>Something followed by B is A</i>—</span></div> + +<p class="noindent">would be clumsy formalism. We usually say, and we ought to say—</p> + + +<div class="example"><span class="i0"><i>A is followed by B</i> ∴ <i>B follows A</i> (or <i>is preceded by A</i>).</span></div> + + +<p>Now, any relation between two terms may be viewed from either side—<i>A: +B</i> or <i>B: A</i>. It is in both cases the same fact; but, with the altered +point of view, it may present a different character. For example, in the +Immediate Inference—<i>A > B</i> ∴ <i>B < A</i>—a diminishing turns <span class='pagenum'>[Pg 85]<a name="Page_85" id="Page_85"></a></span>into an +increasing ratio, whilst the fact predicated remains the same. Given, +then, a relation between two terms as viewed from one to the other, the +same relation viewed from the other to the one may be called the +Reciprocal. In the cases of Equality, Co-existence and Simultaneity, the +given relation and its reciprocal are not only the same fact, but they +also have the same character: in the cases of Greater and Less and +Sequence, the character alters.</p> + +<p>We may, then, state the following rule for the conversion of +propositions in which the whole relation explicitly stated is taken as +the copula: Transpose the terms, and for the given relation substitute +its reciprocal. Thus—</p> + + +<div class="example"><span class="i0"><i>A is the cause of B ∴ B is the effect of A.</i></span></div> + + +<p>The rule assumes that the reciprocal of a given relation is definitely +known; and so far as this is true it may be extended to more concrete +relations—</p> + + +<div class="example"><span class="i0"><i>A is a genus of B ∴ B is a species of A</i></span> +<span class="i0"><i>A is the father of B ∴ B is a child of A.</i></span></div> + + +<p>But not every relational expression has only one definite reciprocal. If +we are told that <i>A is the brother of B</i>, we can only infer that <i>B is +either the brother or the sister of A</i>. A list of all reciprocal +relations is a desideratum of Logic.</p> + +<p><a name="chap_7_sect_5" id="chap_7_sect_5"></a>§ 5. Obversion (otherwise called Permutation or Æquipollence) is +Immediate Inference by changing the quality of the given proposition and +substituting for its predicate the contradictory term. The given +proposition is called the 'obvertend,' and the inference from it the +'obverse.' Thus the obvertend being—<i>Some philosophers are consistent +reasoners</i>, the obverse will be—<i>Some philosophers are not inconsistent +reasoners</i>.</p> + +<p>The legitimacy of this mode of reasoning follows, in the case of +affirmative propositions, from the principle of Contradiction, that if +any term be affirmed of a subject, the contradictory term may be denied +(<a href="#chap_6_sect_3">chap. vi. § 3</a>). To obvert affirmative propositions, then, the rule +is—Insert the <span class='pagenum'>[Pg 86]<a name="Page_86" id="Page_86"></a></span>negative sign, and for the predicate substitute its +contradictory term.</p> + + + +<div class='center'> +<table border="0" cellpadding="2" cellspacing="0" summary=""> +<tr><td align='left'>A.</td><td align='left'><i>All S is P ∴ No S is not-P</i></td></tr> +<tr><td align='left'></td><td align='left'><i>All men are fallible ∴ No men are infallible.</i></td></tr> +<tr><td align='left'>I.</td><td align='left'><i>Some S is P ∴ some S is not-P</i></td></tr> +<tr><td align='left'></td><td align='left'><i>Some philosophers are consistent ∴ Some philosophers are not inconsistent.</i></td></tr> +</table></div> + + +<p class="noindent">In agreement with this mode of inference, we have the rule of modern +English grammar, that 'two negatives make an affirmative.'</p> + +<p>Again, by the principle of Excluded Middle, if any term be denied of a +subject, its contradictory may be affirmed: to obvert negative +propositions, then, the rule is—Remove the negative sign, and for the +predicate substitute its contradictory term.</p> + + + +<div class='center'> +<table border="0" cellpadding="2" cellspacing="0" summary=""> +<tr><td align='left'>E.</td><td align='left'><i>No S is P ∴ All S is not-P</i></td></tr> +<tr><td align='left'></td><td align='left'><i> No matter is destructible ∴ All matter is indestructible.</i></td></tr> +<tr><td align='left'>O.</td><td align='left'><i>Some S is not P ∴ Some S is not-P</i></td></tr> +<tr><td align='left'></td><td align='left'><i>Some ideals are not attainable ∴ Some ideals are unattainable.</i></td></tr> +</table></div> + + +<p>Thus, by obversion, each of the four propositions retains its quantity +but changes its quality: A. to E., I. to O., E. to A., O. to I. And all +the obverses are infinite propositions, the affirmative infinites having +the sense of negatives, and the negative infinites having the sense of +affirmatives.</p> + +<p>Again, having obtained the obverse of a given proposition, it may be +desirable to recover the obvertend; or it may at any time be requisite +to change a given infinite proposition into the corresponding direct +affirmative or negative; and in such cases the process is still +obversion. Thus, if <i>No S is not-P</i> be given us to recover the obvertend +or to find the corresponding affirmative; the proposition being formally +negative, we apply the rule for obverting negatives: 'Remove the +negative sign, and for the predicate substitute its contradictory.' This +yields the affirmative <i>All S is P</i>.<span class='pagenum'>[Pg 87]<a name="Page_87" id="Page_87"></a></span> Similarly, to obtain the obvertend +of <i>All S is not-P</i>, apply the rule for obverting Affirmatives; and this +yields <i>No S is P</i>.</p> + +<p><a name="chap_7_sect_6" id="chap_7_sect_6"></a>§ 6. Contrariety.—We have seen in <a href="#chap_4_sect_8">chap. iv. § 8</a>, that contrary terms +are such that no two of them are predicable in the same way of the same +subject, whilst perhaps neither may be predicable of it. Similarly, +Contrary Propositions may be defined as those of which no two are ever +both true together, whilst perhaps neither may be true; or, in other +words, both may be false. This is the relation between A. and E. when +concerned with the same matter: as A.—<i>All men are wise</i>; E.—<i>No men +are wise</i>. Such propositions cannot both be true; but they may both be +false, for some men may be wise and some not. They cannot both be true; +for, by the principle of Contradiction, if <i>wise</i> may be affirmed of +<i>All men, not-wise</i> must be denied; but <i>All men are not-wise</i> is the +obverse of <i>No men are wise</i>, which therefore may also be denied.</p> + +<p>At the same time we cannot apply to A. and E. the principle of Excluded +Middle, so as to show that one of them must be true of the same matter. +For if we deny that <i>All men are wise</i>, we do not necessarily deny the +attribute 'wise' of each and every man: to say that <i>Not all are wise</i> +may mean no more than that <i>Some are not</i>. This gives a proposition in +the form of O.; which, as we have seen, does not imply its subalternans, +E.</p> + +<p>If, however, two Singular Propositions, having the same matter, but +differing in quality, are to be treated as universals, and therefore as +A. and E., they are, nevertheless, contradictory and not merely +contrary; for one of them must be false and the other true.</p> + +<p><a name="chap_7_sect_7" id="chap_7_sect_7"></a>§ 7. Contradiction is a relation between two propositions analogous to +that between contradictory terms (one of which being affirmed of a +subject the other is denied)—such, namely, that one of them is false +and the other true. This is the case with the forms A. and O., and E. +and I., in the same matter. If it be true that <i>All men are wise</i>, it is +false that<span class='pagenum'>[Pg 88]<a name="Page_88" id="Page_88"></a></span> <i>Some men are not wise</i> (equivalent by obversion to <i>Some +men are not-wise</i>); or else, since the 'Some men' are included in the +'All men,' we should be predicating of the same men that they are both +'wise' and 'not-wise'; which would violate the principle of +Contradiction. Similarly, <i>No men are wise</i>, being by obversion +equivalent to <i>All men are not-wise</i>, is incompatible with <i>Some men are +wise</i>, by the same principle of Contradiction.</p> + +<p>But, again, if it be false that <i>All men are wise</i>, it is always true +that <i>Some are not wise</i>; for though in denying that 'wise' is a +predicate of 'All men' we do not deny it of each and every man, yet we +deny it of 'Some men.' Of 'Some men,' therefore, by the principle of +Excluded Middle, 'not-wise' is to be affirmed; and <i>Some men are +not-wise</i>, is by obversion equivalent to <i>Some men are not wise</i>. +Similarly, if it be false that <i>No men are wise</i>, which by obversion is +equivalent to <i>All men are not-wise</i>, then it is true at least that +<i>Some men are wise</i>.</p> + +<p>By extending and enforcing the doctrine of relative terms, certain other +inferences are implied in the contrary and contradictory relations of +propositions. We have seen in <a href="#CHAPTER_IV">chap. iv.</a> that the contradictory of a +given term includes all its contraries: 'not-blue,' for example, +includes red and yellow. Hence, since <i>The sky is blue</i> becomes by +obversion, <i>The sky is not not-blue</i>, we may also infer <i>The sky is not +red, etc</i>. From the truth, then, of any proposition predicating a given +term, we may infer the falsity of all propositions predicating the +contrary terms in the same relation. But, on the other hand, from the +falsity of a proposition predicating a given term, we cannot infer the +truth of the predication of any particular contrary term. If it be false +that <i>The sky is red</i>, we cannot formally infer, that <i>The sky is blue</i> +(<i>cf.</i> <a href="#chap_4_sect_8">chap. iv. § 8</a>).</p> + +<p><a name="chap_7_sect_8" id="chap_7_sect_8"></a>§ 8. Sub-contrariety is the relation of two propositions, concerning the +same matter that may both be true but are never both false. This is the +case with I. and O. If it <span class='pagenum'>[Pg 89]<a name="Page_89" id="Page_89"></a></span>be true that <i>Some men are wise</i>, it may also +be true that <i>Some (other) men are not wise</i>. This follows from the +maxim in <a href="#chap_6_sect_6">chap. vi. § 6</a>, not to go beyond the evidence.</p> + +<p>For if it be true that <i>Some men are wise</i>, it may indeed be true that +<i>All are</i> (this being the subalternans): and if <i>All are</i>, it is (by +contradiction) false that <i>Some are not</i>; but as we are only told that +<i>Some men are</i>, it is illicit to infer the falsity of <i>Some are not</i>, +which could only be justified by evidence concerning <i>All men</i>.</p> + +<p>But if it be false that <i>Some men are wise</i>, it is true that <i>Some men +are not wise</i>; for, by contradiction, if <i>Some men are wise</i> is false, +<i>No men are wise</i> is true; and, therefore, by subalternation, <i>Some men +are not wise</i> is true.</p> + +<p><a name="chap_7_sect_9" id="chap_7_sect_9"></a>§ 9. The Square of Opposition.—By their relations of Subalternation, +Contrariety, Contradiction, and Sub-contrariety, the forms A. I. E. O. +(having the same matter) are said to stand in Opposition: and Logicians +represent these relations by a square having A. I. E. O. at its corners:</p> + +<div class="figcenter" style="width: 300px;"> +<img alt="" height="207" width="300" src="images/page089.png" /> +</div> + + +<p>As an aid to the memory, this diagram is useful; but as an attempt to +represent the logical relations of propositions, it is misleading. For, +standing at corners of the same square, A. and E., A. and I., E. and O., +and I. and O., seem to be couples bearing the same relation to one +another; whereas we have seen that their relations are entirely +different.<span class='pagenum'>[Pg 90]<a name="Page_90" id="Page_90"></a></span> The following traditional summary of their relations in +respect of truth and falsity is much more to the purpose:</p> + + +<div class='center'> +<table border="0" cellpadding="6" cellspacing="0" summary=""> +<tr><td align='left'>(1)</td><td align='left'>If A. is true,</td><td align='left'>I. is true,</td><td align='left'>E. is false,</td><td align='left'>O. is false.</td></tr> +<tr><td align='left'>(2)</td><td align='left'>If A. is false,</td><td align='left'>I. is unknown,</td><td align='left'>E. is unknown,</td><td align='left'>O. is true.</td></tr> +<tr><td align='left'>(3)</td><td align='left'>If I. is true,</td><td align='left'>A. is unknown,</td><td align='left'>E. is false,</td><td align='left'>O. is unknown.</td></tr> +<tr><td align='left'>(4)</td><td align='left'>If I. is false,</td><td align='left'>A. is false,</td><td align='left'>E. is true,</td><td align='left'>O. is true.</td></tr> +<tr><td align='left'>(5)</td><td align='left'>If E. is true,</td><td align='left'>A. is false,</td><td align='left'>I. is false,</td><td align='left'>O. is true.</td></tr> +<tr><td align='left'>(6)</td><td align='left'>If E. is false,</td><td align='left'>A. is unknown,</td><td align='left'>I. is true,</td><td align='left'>O. is unknown.</td></tr> +<tr><td align='left'>(7)</td><td align='left'>If O. is true,</td><td align='left'>A. is false,</td><td align='left'>I. is unknown,</td><td align='left'>E. is unknown.</td></tr> +<tr><td align='left'>(8)</td><td align='left'>If O. is false,</td><td align='left'>A. is true,</td><td align='left'>I. is true,</td><td align='left'>E. is false.</td></tr> +</table></div> + +<p>Where, however, as in cases 2, 3, 6, 7, alleging either the falsity +of universals or the truth of particulars, it follows that two of the +three Opposites are unknown, we may conclude further that one of them +must be true and the other false, because the two unknown are always +Contradictories.</p> + +<p><a name="chap_7_sect_10" id="chap_7_sect_10"></a>§ 10. Secondary modes of Immediate Inference are obtained by applying +the process of Conversion or Obversion to the results already obtained +by the other process. The best known secondary form of Immediate +Inference is the Contrapositive, and this is the converse of the obverse +of a given proposition. Thus:</p> + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'>DATUM.</td><td align='center'>OBVERSE.</td><td align='center'>CONTRAPOSITIVE.</td></tr> +<tr><td align='left'>A. <i>All S is P</i></td><td align='left'>∴ <i>No S is not-P</i></td><td align='left'>∴ <i>No not-P is S</i></td></tr> +<tr><td align='left'>I. <i>Some S is P</i></td><td align='left'>∴ <i>Some S is not not-P</i></td><td align='left'>∴ (none)</td></tr> +<tr><td align='left'>E. <i>No S is P</i></td><td align='left'>∴ <i>All S is not-P</i></td><td align='left'>∴ <i>Some not-P is S</i></td></tr> +<tr><td align='left'>O. <i>Some S is not P</i></td><td align='left'>∴ <i>Some S is not-P</i></td><td align='left'>∴ <i>Some not-P is S</i></td></tr> +</table></div> + +<p class="noindent">There is no contrapositive of I., because the obverse of I. is in the +form of O., and we have seen that O. cannot be converted. O., however, +has a contrapositive (<i>Some not-P is S</i>); and this is sometimes given +instead of the converse, and called the 'converse by negation.'</p> + +<p>Contraposition needs no justification by the Laws of Thought, as it is +nothing but a compounding of conversion with obversion, both of which +processes have already been justified. I give a table opposite of the +other ways of compounding these primary modes of Immediate Inference.</p><p><span class='pagenum'>[Pg 91]<a name="Page_91" id="Page_91"></a></span></p> + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'></td><td align='center'></td><td align='center'>A.</td><td align='center'>I.</td><td align='center'>E.</td><td align='center'>O.</td></tr> +<tr><td align='center'></td><td align='center'>1</td><td align='center'>All A is B.</td><td align='center'>Some A is B.</td><td align='center'>No A is B.</td><td align='center'>Some A is not B.</td></tr> +<tr><td align='right'>Obverse.</td><td align='center'>2</td><td align='center'>No A is b.</td><td align='center'>Some A is not b.</td><td align='center'>All A is b.</td><td align='center'>Some A is b.</td></tr> +<tr><td align='right'>Converse.</td><td align='center'>3</td><td align='center'>Some B is A.</td><td align='center'>Some B is A.</td><td align='center'>No B is A.</td><td align='center'>—</td></tr> +<tr><td align='right'>Obverse of Converse.</td><td align='center'>4</td><td align='center'>Some B is not a.</td><td align='center'>Some B is not a.</td><td align='center'>All B is a.</td><td align='center'>—</td></tr> +<tr><td align='right'>Contrapositive.</td><td align='center'>5</td><td align='center'>No b is A.</td><td align='center'>—</td><td align='center'>Some b is A.</td><td align='center'>Some b is A.</td></tr> +<tr><td align='right'>Obverse of Contrapositive.</td><td align='center'>6</td><td align='center'>All b is a.</td><td align='center'>—</td><td align='center'>Some b is not a.</td><td align='center'>Some b is not a.</td></tr> +<tr><td align='right'>Converse of Obverse of Converse.</td><td align='center'>7</td><td align='center'>—</td><td align='center'>—</td><td align='center'>Some a is B.</td><td align='center'>—</td></tr> +<tr><td align='right'>Obverse of Converse of Obverse of Converse.</td><td align='center'>8</td><td align='center'>—</td><td align='center'>—</td><td align='center'>Some a is not b.</td><td align='center'>—</td></tr> +<tr><td align='right'>Converse of Obverse of Contrapositive.</td><td align='center'>9</td><td align='center'>Some a is b.</td><td align='center'>—</td><td align='center'>—</td><td align='center'>—</td></tr> +<tr><td align='right'>Obverse of Converse of Obverse of Contrapositive.</td><td align='center'>10</td><td align='center'>Some a is not B.</td><td align='center'>—</td><td align='center'>—</td><td align='center'>—</td></tr> +</table></div> + + +<p><span class='pagenum'>[Pg 92]<a name="Page_92" id="Page_92"></a></span>In this table <i>a</i> and <i>b</i> stand for <i>not-A</i> and <i>not-B</i> and had better +be read thus: for <i>No A is b, No A is not-B</i>; for <i>All b is a</i> (col. 6), +<i>All not-B is not-A</i>; and so on.</p> + +<p>It may not, at first, be obvious why the process of alternately +obverting and converting any proposition should ever come to an end; +though it will, no doubt, be considered a very fortunate circumstance +that it always does end. On examining the results, it will be found that +the cause of its ending is the inconvertibility of O. For E., when +obverted, becomes A.; every A, when converted, degenerates into I.; +every I., when obverted, becomes O.; O cannot be converted, and to +obvert it again is merely to restore the former proposition: so that the +whole process moves on to inevitable dissolution. I. and O. are +exhausted by three transformations, whilst A. and E. will each endure +seven.</p> + +<p>Except Obversion, Conversion and Contraposition, it has not been usual +to bestow special names on these processes or their results. But the +form in columns 7 and 10 (<i>Some a is B—Some a is not B</i>), where the +original predicate is affirmed or denied of the contradictory of the +original subject, has been thought by Dr. Keynes to deserve a +distinctive title, and he has called it the 'Inverse.' Whilst the +Inverse is one form, however, Inversion is not one process, but is +obtained by different processes from E. and A. respectively. In this it +differs from Obversion, Conversion, and Contraposition, each of which +stands for one process.</p> + +<p>The Inverse form has been objected to on the ground that the inference +<i>All A is B ∴ Some not-A is not B</i>, distributes <i>B</i> (as predicate of a +negative proposition), though it was given as undistributed (as +predicate of an affirmative proposition). But Dr. Keynes defends it on +the ground that (1) it is obtained by obversions and conversions which +are all legitimate and (2) that although <i>All A is B</i> does not +distribute <i>B</i> in relation to <i>A</i>, it does distribute <i>B</i> in relation to +some <i>not-A</i> (namely, in relation to whatever <i>not-A</i> is <i>not-B</i>). This +is one reason why, in stating the rule in <a href="#chap_6_sect_6">chap. vi. § 6</a>, I <span class='pagenum'>[Pg 93]<a name="Page_93" id="Page_93"></a></span>have +written: "an immediate inference ought to contain nothing that is not +contained, <i>or formally implied</i>, in the proposition from which it is +inferred"; and have maintained that every term formally implies its +contradictory within the <i>suppositio</i>.</p> + +<p><a name="chap_7_sect_11" id="chap_7_sect_11"></a>§ 11. Immediate Inferences from Conditionals are those which +consist—(1) in changing a Disjunctive into a Hypothetical, or a +Hypothetical into a Disjunctive, or either into a Categorical; and (2) +in the relations of Opposition and the equivalences of Obversion, +Conversion, and secondary or compound processes, which we have already +examined in respect of Categoricals. As no new principles are involved, +it may suffice to exhibit some of the results.</p> + +<p>We have already seen (<a href="#chap_5_sect_4">chap. v. § 4</a>) how Disjunctives may be read as +Hypotheticals and Hypotheticals as Categoricals. And, as to Opposition, +if we recognise four forms of Hypothetical A. I. E. O., these plainly +stand to one another in a Square of Opposition, just as Categoricals do. +Thus A. and E. (<i>If A is B, C is D</i>, and <i>If A is B, C is not D</i>) are +contraries, but not contradictories; since both may be false (<i>C</i> may +sometimes be <i>D</i>, and sometimes not), though they cannot both be true. +And if they are both false, their subalternates are both true, being +respectively the contradictories of the universals of opposite quality, +namely, I. of E., and O. of A. But in the case of Disjunctives, we +cannot set out a satisfactory Square of Opposition; because, as we saw +(<a href="#chap_5_sect_4">chap. v. § 4</a>), the forms required for E. and O. are not true +Disjunctives, but Exponibles.</p> + +<p>The Obverse, Converse, and Contrapositive, of Hypotheticals (admitting +the distinction of quality) may be exhibited thus:</p> + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'><span class="smcap">Datum.</span></td><td align='center'><span class="smcap">Obverse.</span></td></tr> +<tr><td align='left'>A. <i>If A is B, C is D</i></td><td align='left'><i>If A is B, C is not d</i></td></tr> +<tr><td align='left'>I. Sometimes <i>when A is B, C is D</i></td><td align='left'>Sometimes <i>when A is B, C is not d</i></td></tr> +<tr><td align='left'>E. <i>If A is B, C is not D</i></td><td align='left'><i>If A is B, C is d</i></td></tr> +<tr><td align='left'>O. Sometimes <i>when A is B, C is not D</i></td><td align='left'>Sometimes <i>when A is B, C is d</i></td></tr> +<tr><td align='center'><span class="smcap">Converse.</span></td><td align='center'><span class="smcap">Contrapositive.</span></td></tr> +<tr><td align='left'>Sometimes <i>when C is D, A is B</i></td><td align='left'><i>If C is d, A is not B</i></td></tr> +<tr><td align='left'>Sometimes <i>when C is D, A is B</i></td><td align='center'>(none)</td></tr> +<tr><td align='left'><i>If C is D, A is not B</i></td><td align='left'>Sometimes <i>when C is d, A is B</i></td></tr> +<tr><td align='center'>(none)</td><td align='left'>Sometimes <i>when C is d, A is B</i></td></tr> +</table></div> +<p><span class='pagenum'>[Pg 94]<a name="Page_94" id="Page_94"></a></span></p> +<p>As to Disjunctives, the attempt to put them through these different +forms immediately destroys their disjunctive character. Still, given any +proposition in the form <i>A is either B or C</i>, we can state the +propositions that give the sense of obversion, conversion, <i>etc.</i>, thus:</p> + + +<div class="example"><span class="i0"><span class="smcap">Datum</span>.—<i>A is either B or C;</i><br /></span> +<span class="i0"><span class="smcap">Obverse</span>.—<i>A is not both b and c;</i><br /></span> +<span class="i0"><span class="smcap">Converse</span>.—<i>Something, either B or C, is A;</i><br /></span> +<span class="i0"><span class="smcap">Contrapositive</span>.—<i>Nothing that is both b and c is A</i>.<br /></span></div> + +<p>For a Disjunctive in I., of course, there is no Contrapositive. Given a +Disjunctive in the form <i>Either A is B or C is D</i>, we may write for its +Obverse—<i>In no case is A b, and C at the same time d</i>. But no Converse +or Contrapositive of such a Disjunctive can be obtained, except by first +casting it into the hypothetical or categorical form.</p> + +<p>The reader who wishes to pursue this subject further, will find it +elaborately treated in Dr. Keynes' <i>Formal Logic</i>, Part II.; to which +work the above chapter is indebted.</p><p><span class='pagenum'>[Pg 95]<a name="Page_95" id="Page_95"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_VIII" id="CHAPTER_VIII"></a>CHAPTER VIII</h2> + +<h3>ORDER OF TERMS, EULER'S DIAGRAMS, LOGICAL EQUATIONS, EXISTENTIAL IMPORT +OF PROPOSITIONS</h3> + + +<p><a name="chap_8_sect_1" id="chap_8_sect_1"></a>§ 1. Of the terms of a proposition which is the Subject and which the +Predicate? In most of the exemplary propositions cited by Logicians it +will be found that the subject is a substantive and the predicate an +adjective, as in <i>Men are mortal</i>. This is the relation of Substance and +Attribute which we saw (<a href="#chap_1_sect_5">chap. i. § 5</a>) to be the central type of +relations of coinherence; and on this model other predications may be +formed in which the subject is not a substance, but is treated as if it +were, and could therefore be the ground of attributes; as <i>Fame is +treacherous, The weather is changeable</i>. But, in literature, sentences +in which the adjective comes first are not uncommon, as <i>Loud was the +applause, Dark is the fate of man, Blessed are the peacemakers</i>, and so +on. Here, then, 'loud,' 'dark' and 'blessed' occupy the place of the +logical subject. Are they really the subject, or must we alter the order +of such sentences into <i>The applause was loud, etc</i>.? If we do, and then +proceed to convert, we get <i>Loud was the applause</i>, or (more +scrupulously) <i>Some loud noise was the applause</i>. The last form, it is +true, gives the subject a substantive word, but 'applause' has become +the predicate; and if the substantive 'noise' was not implied in the +first form, <i>Loud is the applause</i>, by what right is it now inserted? +The recognition of Conversion, in fact, requires us to admit that, +formally, in a logical <span class='pagenum'>[Pg 96]<a name="Page_96" id="Page_96"></a></span>proposition, the term preceding the copula is +subject and the one following is predicate. And, of course, materially +considered, the mere order of terms in a proposition can make no +difference in the method of proving it, nor in the inferences that can +be drawn from it.</p> + +<p>Still, if the question is, how we may best cast a literary sentence into +logical form, good grounds for a definite answer may perhaps be found. +We must not try to stand upon the naturalness of expression, for <i>Dark +is the fate of man</i> is quite as natural as <i>Man is mortal</i>. When the +purpose is not merely to state a fact, but also to express our feelings +about it, to place the grammatical predicate first may be perfectly +natural and most effective. But the grounds of a logical order of +statement must be found in its adaptation to the purposes of proof and +inference. Now general propositions are those from which most inferences +can be drawn, which, therefore, it is most important to establish, if +true; and they are also the easiest to disprove, if false; since a +single negative instance suffices to establish the contradictory. It +follows that, in re-casting a literary or colloquial sentence for +logical purposes, we should try to obtain a form in which the subject is +distributed—is either a singular term or a general term predesignate as +'All' or 'No.' Seeing, then, that most adjectives connote a single +attribute, whilst most substantives connote more than one attribute; and +that therefore the denotation of adjectives is usually wider than that +of substantives; in any proposition, one term of which is an adjective +and the other a substantive, if either can be distributed in relation to +the other, it is nearly sure to be the substantive; so that to take the +substantive term for subject is our best chance of obtaining an +universal proposition. These considerations seem to justify the practice +of Logicians in selecting their examples.</p> + +<p>For similar reasons, if both terms of a proposition are substantive, the +one with the lesser denotation is (at least <span class='pagenum'>[Pg 97]<a name="Page_97" id="Page_97"></a></span>in affirmative +propositions) the more suitable subject, as <i>Cats are carnivores</i>. And +if one term is abstract, that is the more suitable subject; for, as we +have seen, an abstract term may be interpreted by a corresponding +concrete one distributed, as <i>Kindness is infectious</i>; that is, <i>All +kind actions suggest imitation</i>.</p> + +<p>If, however, a controvertist has no other object in view than to refute +some general proposition laid down by an opponent, a particular +proposition is all that he need disentangle from any statement that +serves his purpose.</p> + +<p><a name="chap_8_sect_2" id="chap_8_sect_2"></a>§ 2. Toward understanding clearly the relations of the terms of a +proposition, it is often found useful to employ diagrams; and the +diagrams most in use are the circles of Euler.</p> + +<p>These circles represent the denotation of the terms. Suppose the +proposition to be <i>All hollow-horned animals ruminate</i>: then, if we +could collect all ruminants upon a prairie, and enclose them with a +circular palisade; and segregate from amongst them all the hollow-horned +beasts, and enclose them with another ring-fence inside the other; one +way of interpreting the proposition (namely, in denotation) would be +figured to us thus:</p> + +<div class="figcenter" style="width: 200px;"> +<img alt="Fig. 1." height="179" width="200" src="images/fig_1.png" /> +<span class="caption smcap">Fig. 1.</span> +</div> + +<p>An Universal Affirmative may also state a relation between two terms +whose denotation is co-extensive. A definition always does this, as <i>Man +is a rational animal</i>; and this, of course, we cannot represent by two +distinct <span class='pagenum'>[Pg 98]<a name="Page_98" id="Page_98"></a></span>circles, but at best by one with a thick circumference, to +suggest that two coincide, thus:</p> + +<div class="figcenter" style="width: 200px;"> +<img src="images/fig_2.png" width="200" height="196" alt="Fig. 2." title="" /> +<span class="caption smcap">Fig. 2.</span> +</div> + +<p>The Particular Affirmative Proposition may be represented in several +ways. In the first place, bearing in mind that 'Some' means 'some at +least, it may be all,' an I. proposition may be represented by Figs. 1 +and 2; for it is true that <i>Some horned animals ruminate</i>, and that +<i>Some men are rational</i>. Secondly, there is the case in which the 'Some +things' of which a predication is made are, in fact, not all; whilst the +predicate, though not given as distributed, yet might be so given if we +wished to state the whole truth; as if we say <i>Some men are Chinese</i>. +This case is also represented by Fig. 1, the outside circle representing +'Men,' and the inside one 'Chinese.' Thirdly, the predicate may +appertain to some only of the subject, but to a great many other things, +as in <i>Some horned beasts are domestic</i>; for it is true that some are +not, and that certain other kinds of animals are, domestic. This case, +therefore, must be illustrated by overlapping circles, thus:</p> + +<div class="figcenter" style="width: 250px;"> +<img src="images/fig_3.png" width="250" height="155" alt="Fig. 3." title="" /> +<span class="caption smcap">Fig. 3.</span> +</div><p><span class='pagenum'>[Pg 99]<a name="Page_99" id="Page_99"></a></span></p> + +<p>The Universal Negative is sufficiently represented by a single Fig. (4): +two circles mutually exclusive, thus:</p> + +<div class="figcenter" style="width: 300px;"> +<img src="images/fig_4.png" width="300" height="150" alt="Fig. 4." title="" /> +<span class="caption smcap">Fig. 4.</span> +</div> + +<p class="noindent">That is, <i>No horned beasts are carnivorous</i>.</p> + +<p>Lastly, the Particular Negative may be represented by any of the Figs. +1, 3, and 4; for it is true that <i>Some ruminants are not hollow-horned</i>, +that <i>Some horned animals are not domestic</i>, and that <i>Some horned +beasts are not carnivorous</i>.</p> + +<p>Besides their use in illustrating the denotative force of propositions, +these circles may be employed to verify the results of Obversion, +Conversion, and the secondary modes of Immediate Inference. Thus the +Obverse of A. is clear enough on glancing at Figs. 1 and 2; for if we +agree that whatever term's denotation is represented by a given circle, +the denotation of the contradictory term shall be represented by the +space outside that circle; then if it is true that <i>All hollow horned +animals are ruminants</i>, it is at the same time true that <i>No +hollow-horned animals are not-ruminants</i>; since none of the +hollow-horned are found outside the palisade that encloses the +ruminants. The Obverse of I., E. or O. may be verified in a similar +manner.</p> + +<p>As to the Converse, a Definition is of course susceptible of Simple +Conversion, and this is shown by Fig. 2: 'Men are rational animals' and +'Rational animals are men.' But any other A. proposition is presumably +convertible only by limitation, and this is shown by Fig. 1; where <i>All +hollow-horned animals are ruminants</i>, but we can only say that <i>Some +ruminants are hollow-horned</i>.</p><p><span class='pagenum'>[Pg 100]<a name="Page_100" id="Page_100"></a></span></p> + +<p>That I. may be simply converted may be seen in Fig. 3, which represents +the least that an I. proposition can mean; and that E. may be simply +converted is manifest in Fig. 4.</p> + +<p>As for O., we know that it cannot be converted, and this is made plain +enough by glancing at Fig. 1; for that represents the O., <i>Some +ruminants are not hollow-horned</i>, but also shows this to be compatible +with <i>All hollow-horned animals are ruminants</i> (A.). Now in conversion +there is (by definition) no change of quality. The Converse, then, of +<i>Some ruminants are not hollow-horned</i> must be a negative proposition, +having 'hollow-horned' for its subject, either in E. or O.; but these +would be respectively the contrary and contradictory of <i>All +hollow-horned animals are ruminants</i>; and, therefore, if this be true, +they must both be false.</p> + +<p>But (referring still to Fig. 1) the legitimacy of contrapositing O. is +equally clear; for if <i>Some ruminants are not hollow-horned</i>, <i>Some +animals that are not hollow-horned are ruminants</i>, namely, all the +animals between the two ring-fences. Similar inferences may be +illustrated from Figs. 3 and 4. And the Contraposition of A. may be +verified by Figs. 1 and 2, and the Contraposition of E. by Fig. 4.</p> + +<p>Lastly, the Inverse of A. is plain from Fig. 1—<i>Some things that are +not hollow-horned are not ruminants</i>, namely, things that lie outside +the outer circle and are neither 'ruminants' nor 'hollow-horned.' And +the Inverse of E may be studied in Fig. 4—<i>Some things that are +not-horned beasts are carnivorous</i>.</p> + +<p>Notwithstanding the facility and clearness of the demonstrations thus +obtained, it may be said that a diagrammatic method, representing +denotations, is not properly logical. Fundamentally, the relation +asserted (or denied) to exist between the terms of a proposition, is a +relation between the terms as determined by their attributes or +connotation; whether we take Mill's view, that a proposition asserts +that the connotation of the subject is a mark of the connota<span class='pagenum'>[Pg 101]<a name="Page_101" id="Page_101"></a></span>tion of the +predicate; or Dr. Venn's view, that things denoted by the subject (as +having its connotation) have (or have not) the attribute connoted by the +predicate; or, the Conceptualist view, that a judgment is a relation of +concepts (that is, of connotations). With a few exceptions artificially +framed (such as 'kings now reigning in Europe'), the denotation of a +term is never directly and exhaustively known, but consists merely in +'all things that have the connotation.' If the value of logical training +depends very much upon our habituating ourselves to construe +propositions, and to realise the force of inferences from them, +according to the connotation of their terms, we shall do well not to +turn too hastily to the circles, but rather to regard them as means of +verifying in denotation the conclusions that we have already learnt to +recognise as necessary in connotation.</p> + +<p><a name="chap_8_sect_3" id="chap_8_sect_3"></a>§ 3. The equational treatment of propositions is closely connected with +the diagrammatic. Hamilton thought it a great merit of his plan of +quantifying the predicate, that thereby every proposition is reduced to +its true form—an equation. According to this doctrine, the proposition +<i>All X is all Y</i> (U.) equates X and Y; the proposition <i>All X is some Y</i> +(A.) equates X with some part of Y; and similarly with the other +affirmatives (Y. and I.). And so far it is easy to follow his meaning: +the Xs are identical with some or all the Ys. But, coming to the +negatives, the equational interpretation is certainly less obvious. The +proposition <i>No X is Y</i> (E.) cannot be said in any sense to equate X and +Y; though, if we obvert it into <i>All X is some not-Y</i>, we have (in the +same sense, of course, as in the above affirmative forms) X equated with +part at least of 'not-Y.'</p> + +<p>But what is that sense? Clearly not the same as that in which +mathematical terms are equated, namely, in respect of some mode of +quantity. For if we may say <i>Some X is some Y</i>, these Xs that are also +Ys are not merely the same in number, or mass, or figure; they are the +same in every <span class='pagenum'>[Pg 102]<a name="Page_102" id="Page_102"></a></span>respect, both quantitative and qualitative, have the same +positions in time and place, are in fact identical. The proposition +2+2=4 means that any two things added to any other two are, <i>in respect +of number</i>, equal to any three things added to one other thing; and this +is true of all things that can be counted, however much they may differ +in other ways. But <i>All X is all Y</i> means that Xs and Ys are the same +things, although they have different names when viewed in different +aspects or relations. Thus all equilateral triangles are equiangular +triangles; but in one case they are named from the equality of their +angles, and in the other from the equality of their sides. Similarly, +'British subjects' and 'subjects of King George V' are the same people, +named in one case from the person of the Crown, and in the other from +the Imperial Government. These logical equations, then, are in truth +identities of denotation; and they are fully illustrated by the +relations of circles described in the previous section.</p> + +<p>When we are told that logical propositions are to be considered as +equations, we naturally expect to be shown some interesting developments +of method in analogy with the equations of Mathematics; but from +Hamilton's innovations no such thing results. This cannot be said, +however, of the equations of Symbolic Logic; which are the +starting-point of very remarkable processes of ratiocination. As the +subject of Symbolic Logic, as a whole, lies beyond the compass of this +work, it will be enough to give Dr. Venn's equations corresponding with +the four propositional forms of common Logic.</p> + +<p>According to this system, universal propositions are to be regarded as +not necessarily implying the existence of their terms; and therefore, +instead of giving them a positive form, they are translated into symbols +that express what they deny. For example, the proposition <i>All devils +are ugly</i> need not imply that any such things as 'devils' really exist; +but it certainly does imply that <i>Devils that are not ugly do </i><span class='pagenum'>[Pg 103]<a name="Page_103" id="Page_103"></a></span><i>not +exist</i>. Similarly, the proposition <i>No angels are ugly</i> implies that +<i>Angels that are ugly do not exist</i>. Therefore, writing <i>x</i> for +'devils,' <i>y</i> for 'ugly,' and <i>ȳ</i> for 'not-ugly,' we may express A., +the universal affirmative, thus:</p> + +<div class="example"><span class="i0">A. <i>xȳ</i> = 0.</span></div> + + +<p class="noindent">That is, <i>x that is not y is nothing</i>; or, <i>Devils that are not-ugly do +not exist</i>. And, similarly, writing <i>x</i> for 'angels' and <i>y</i> for 'ugly,' +we may express E., the universal negative, thus:</p> + + +<div class="example"><span class="i0">E. <i>xy</i> = 0.</span></div> + + +<p class="noindent">That is, <i>x that is y is nothing</i>; or, <i>Angels that are ugly do not +exist</i>.</p> + +<p>On the other hand, particular propositions are regarded as implying the +existence of their terms, and the corresponding equations are so framed +as to express existence. With this end in view, the symbol v is adopted +to represent 'something,' or indeterminate reality, or more than +nothing. Then, taking any particular affirmative, such as <i>Some +metaphysicians are obscure</i>, and writing <i>x</i> for 'metaphysicians,' and +<i>y</i> for 'obscure,' we may express it thus:</p> + + +<div class="example"><span class="i0">I. <i>xy</i> = v.</span></div> + + +<p class="noindent">That is, <i>x that is y is something</i>; or, <i>Metaphysicians that are +obscure do occur in experience</i> (however few they may be, or whether +they all be obscure). And, similarly, taking any particular negative, +such as <i>Some giants are not cruel</i>, and writing <i>x</i> for 'giants' and +<i>y</i> for 'not-cruel,' we may express it thus:</p> + + +<div class="example"><span class="i0">O. <i>xȳ</i> = v.</span></div> + + +<p class="noindent">That is, <i>x that is not y is something</i>; or, <i>giants that are not-cruel +do occur</i>—in romances, if nowhere else.</p> + +<p>Clearly, these equations are, like Hamilton's, concerned with +denotation. A. and E. affirm that the compound terms xȳ and xy have no +denotation; and I. and O. declare that xȳ and xy have denotation, or +stand for something. Here, however, the resemblance to Hamilton's system +<span class='pagenum'>[Pg 104]<a name="Page_104" id="Page_104"></a></span>ceases; for the Symbolic Logic, by operating upon more than two terms +simultaneously, by adopting the algebraic signs of operations, +,-, ×, ÷ +(with a special signification), and manipulating the symbols by +quasi-algebraic processes, obtains results which the common Logic +reaches (if at all) with much greater difficulty. If, indeed, the value +of logical systems were to be judged of by the results obtainable, +formal deductive Logic would probably be superseded. And, as a mental +discipline, there is much to be said in favour of the symbolic method. +But, as an introduction to philosophy, the common Logic must hold its +ground. (Venn: <i>Symbolic Logic</i>, c. 7.)</p> + +<p><a name="chap_8_sect_4" id="chap_8_sect_4"></a>§ 4. Does Formal Logic involve any general assumption as to the real +existence of the terms of propositions?</p> + +<p>In the first place, Logic treats primarily of the <i>relations</i> implied in +propositions. This follows from its being the science of proof for all +sorts of (qualitative) propositions; since all sorts of propositions +have nothing in common except the relations they express.</p> + +<p>But, secondly, relations without terms of some sort are not to be +thought of; and, hence, even the most formal illustrations of logical +doctrines comprise such terms as S and P, X and Y, or x and y, in a +symbolic or representative character. Terms, therefore, of some sort are +assumed to exist (together with their negatives or contradictories) <i>for +the purposes of logical manipulation</i>.</p> + +<p>Thirdly, however, that Formal Logic cannot as such directly involve the +existence of any particular concrete terms, such as 'man' or 'mountain,' +used by way of illustration, is implied in the word 'formal,' that is, +'confined to what is common or abstract'; since the only thing common to +all terms is to be related in some way to other terms. The actual +existence of any concrete thing can only be known by experience, as with +'man' or 'mountain'; or by methodically justifiable inference from +experience, as with 'atom' or 'ether.' If 'man' or 'mountain,' or<span class='pagenum'>[Pg 105]<a name="Page_105" id="Page_105"></a></span> +'Cuzco' be used to illustrate logical forms, they bring with them an +existential import derived from experience; but this is the import of +language, not of the logical forms. 'Centaur' and 'El Dorado' signify to +us the non-existent; but they serve as well as 'man' and 'London' to +illustrate Formal Logic.</p> + +<p>Nevertheless, fourthly, the existence or non-existence of particular +terms may come to be implied: namely, wherever the very fact of +existence, or of some condition of existence, is an hypothesis or datum. +Thus, given the proposition <i>All S is P</i>, to be P is made a condition of +the existence of S: whence it follows that an S that is not P does not +exist (<i>xȳ</i> = 0). On the further hypothesis that S exists, it follows +that P exists. On the hypothesis that S does not exist, the existence of +P is problematic; but, then, if P does exist we cannot convert the +proposition; since <i>Some P is S</i> (P existing) would involve the +existence of S; which is contrary to the hypothesis.</p> + +<p>Assuming that Universals <i>do not</i>, whilst Particulars <i>do</i>, imply the +existence of their subjects, we cannot infer the subalternate (I. or O.) +from the subalternans (A. or E.), for that is to ground the actual on +the problematic; and for the same reason we cannot convert A. <i>per +accidens</i>.</p> + +<p>Assuming, again, a certain <i>suppositio</i> or universe, to which in a given +discussion every argument shall refer, then, any propositions whose +terms lie outside that <i>suppositio</i> are irrelevant, and for the purposes +of that discussion are sometimes called "false"; though it seems better +to call them irrelevant or meaningless, seeing that to call them false +implies that they might in the same case be true. Thus propositions +which, according to the doctrine of Opposition, appear to be +Contradictories, may then cease to be so; for of Contradictories one is +true and the other false; but, in the case supposed, both are +meaningless. If the subject of discussion be Zoology, all propositions +about centaurs or unicorns are absurd; and such specious<span class='pagenum'>[Pg 106]<a name="Page_106" id="Page_106"></a></span> +Contradictories as <i>No centaurs play the lyre—Some centaurs do play the +lyre</i>; or <i>All unicorns fight with lions—Some unicorns do not fight +with lions</i>, are both meaningless, because in Zoology there are no +centaurs nor unicorns; and, therefore, in this reference, the +propositions are not really contradictory. But if the subject of +discussion or <i>suppositio</i> be Mythology or Heraldry, such propositions +as the above are to the purpose, and form legitimate pairs of +Contradictories.</p> + +<p>In Formal Logic, in short, we may make at discretion any assumption +whatever as to the existence, or as to any condition of the existence of +any particular term or terms; and then certain implications and +conclusions follow in consistency with that hypothesis or datum. Still, +our conclusions will themselves be only hypothetical, depending on the +truth of the datum; and, of course, until this is empirically +ascertained, we are as far as ever from empirical reality. (Venn: +<i>Symbolic Logic</i>, c. 6; Keynes: <i>Formal Logic</i>, Part II. c. 7: <i>cf.</i> +Wolf: <i>Studies in Logic</i>.)</p><p><span class='pagenum'>[Pg 107]<a name="Page_107" id="Page_107"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_IX" id="CHAPTER_IX"></a>CHAPTER IX</h2> + +<h3>FORMAL CONDITIONS OF MEDIATE INFERENCE</h3> + + +<p><a name="chap_9_sect_1" id="chap_9_sect_1"></a>§ 1. A Mediate Inference is a proposition that depends for proof upon +two or more other propositions, so connected together by one or more +terms (which the evidentiary propositions, or each pair of them, have in +common) as to justify a certain conclusion, namely, the proposition in +question. The type or (more properly) the unit of all such modes of +proof, when of a strictly logical kind, is the Syllogism, to which we +shall see that all other modes are reducible. It may be exhibited +symbolically thus:</p> + + +<div class="example"> <span class="i1">M is P;<br /></span> + <span class="i1">S is M:<br /></span> +<span class="i0">∴ S is P.</span></div> + + +<p>Syllogisms may be classified, as to quantity, into Universal or +Particular, according to the quantity of the conclusion; as to quality, +into Affirmative or Negative, according to the quality of the +conclusion; and, as to relation, into Categorical, Hypothetical and +Disjunctive, according as all their propositions are categorical, or one +(at least) of their evidentiary propositions is a hypothetical or a +disjunctive.</p> + +<p>To begin with Categorical Syllogisms, of which the following is an +example:</p> + + + <div class="example"><span class="i1">All authors are vain;</span> + <span class="i1">Cicero is an author:</span> +<span class="i0">∴ Cicero is vain.</span></div> + + +<p class="noindent">Here we may suppose that there are no direct means of knowing that +Cicero is vain; but we happen to know that <span class='pagenum'>[Pg 108]<a name="Page_108" id="Page_108"></a></span>all authors are vain and +that he is an author; and these two propositions, put together, +unmistakably imply that he is vain. In other words, we do not at first +know any relation between 'Cicero' and 'vanity'; but we know that these +two terms are severally related to a third term, 'author,' hence called +a Middle Term; and thus we perceive, by mediate evidence, that they are +related to one another. This sort of proof bears an obvious resemblance +(though the relations involved are not the same) to the mathematical +proof of equality between two quantities, that cannot be directly +compared, by showing the equality of each of them to some third +quantity: A = B = C ∴ A = C. Here B is a middle term.</p> + +<p>We have to inquire, then, what conditions must be satisfied in order +that a Syllogism may be formally conclusive or valid. A specious +Syllogism that is not really valid is called a Parasyllogism.</p> + +<p><a name="chap_9_sect_2" id="chap_9_sect_2"></a>§ 2. General Canons of the Syllogism.</p> + +<p>(1) A Syllogism contains three, and no more, distinct propositions.</p> + +<p>(2) A Syllogism contains three, and no more, distinct univocal terms.</p> + +<p>These two Canons imply one another. Three propositions with less than +three terms can only be connected in some of the modes of Immediate +Inference. Three propositions with more than three terms do not show +that connection of two terms by means of a third, which is requisite for +proving a Mediate Inference. If we write—</p> + + +<div class="example"><span class="i0">All authors are vain;</span> +<span class="i0">Cicero is a statesman—</span></div> + + +<p class="noindent">there are four terms and no middle term, and therefore there is no +proof. Or if we write—</p> + + + <div class="example"><span class="i1">All authors are vain;<br /></span> + <span class="i1">Cicero is an author:<br /></span> +<span class="i0">∴ Cicero is a statesman—</span></div> + + +<p class="noindent"><span class='pagenum'>[Pg 109]<a name="Page_109" id="Page_109"></a></span>here the term 'statesman' occurs without any voucher; it appears in the +inference but not in the evidence, and therefore violates the maxim of +all formal proof, 'not to go beyond the evidence.' It is true that if +any one argued—</p> + + + <div class="example"><span class="i1">All authors are vain;<br /></span> + <span class="i1">Cicero wrote on philosophy:<br /></span> +<span class="i0">∴ Cicero is vain—</span></div> + + +<p class="noindent">this could not be called a bad argument or a material fallacy; but it +would be a needless departure from the form of expression in which the +connection between the evidence and the inference is most easily seen.</p> + +<p>Still, a mere adherence to the same form of words in the expression of +terms is not enough: we must also attend to their meaning. For if the +same word be used ambiguously (as 'author' now for 'father' and anon for +'man of letters'), it becomes as to its meaning two terms; so that we +have four in all. Then, if the ambiguous term be the Middle, no +connection is shown between the other two; if either of the others be +ambiguous, something seems to be inferred which has never been really +given in evidence.</p> + +<p>The above two Canons are, indeed, involved in the definition of a +categorical syllogism, which may be thus stated: A Categorical Syllogism +is a form of proof or reasoning (way of giving reasons) in which one +categorical proposition is established by comparing two others that +contain together only three terms, or that have one and only one term in +common.</p> + +<p>The proposition established, derived, or inferred, is called the +Conclusion: the evidentiary propositions by which it is proved are +called the Premises.</p> + +<p>The term common to the premises, by means of which the other terms are +compared, is called the Middle Term; the subject of the conclusion is +called the Minor Term; the predicate of the conclusion, the Major Term.</p> + +<p>The premise in which the minor term occurs is called the<span class='pagenum'>[Pg 110]<a name="Page_110" id="Page_110"></a></span> Minor Premise; +that in which the major term occurs is called the Major Premise. And a +Syllogism is usually written thus:</p> + +<div class="example"><span class="i0">Major Premise—All authors (Middle) are vain (Major);<br /></span> +<span class="i0">Minor Premise—Cicero (Minor) is an author (Middle):<br /></span> +<span class="i0">Conclusion—∴ Cicero (Minor) is vain (Major).</span></div> + +<p class="noindent">Here we have three propositions with three terms, each term occurring +twice. The minor and major terms are so called, because, when the +conclusion is an universal affirmative (which only occurs in Barbara; +see <a href="#chap_10_sect_6">chap. x. § 6</a>), its subject and predicate are respectively the less +and the greater in extent or denotation; and the premises are called +after the peculiar terms they contain: the expressions 'major premise' +and 'minor premise' have nothing to do with the order in which the +premises are presented; though it is usual to place the major premise +first.</p> + +<p>(3) No term must be distributed in the conclusion unless it is +distributed in the premises.</p> + +<p>It is usual to give this as one of the General Canons of the Syllogism; +but we have seen (<a href="#chap_6_sect_6">chap. vi. § 6</a>) that it is of wider application. +Indeed, 'not to go beyond the evidence' belongs to the definition of +formal proof. A breech of this rule in a syllogism is the fallacy of +Illicit Process of the Minor, or of the Major, according to which term +has been unwarrantably distributed. The following parasyllogism +illicitly distributes both terms of the conclusion:</p> + + + <div class="example"><span class="i1">All poets are pathetic;<br /></span> + <span class="i1">Some orators are not poets:<br /></span> +<span class="i0">∴ No orators are pathetic.</span></div> + + +<p>(4) The Middle Term must be distributed at least once in the premises +(in order to prove a conclusion in the given terms).</p> + +<p>For the use of mediate evidence is to show the relation of terms that +cannot be directly compared; this is only possible if the middle term +furnishes the ground of com<span class='pagenum'>[Pg 111]<a name="Page_111" id="Page_111"></a></span>parison; and this (in Logic) requires that +the whole denotation of the middle should be either included or excluded +by one of the other terms; since if we only know that the other terms +are related to <i>some</i> of the middle, their respective relations may not +be with the same part of it.</p> + +<p>It is true that in what has been called the "numerically definite +syllogism," an inference may be drawn, though our canon seems to be +violated. Thus:</p> + + +<div class="example"> <span class="i1">60 sheep in 100 are horned;<br /></span> + <span class="i1">60 sheep in 100 are blackfaced:<br /></span> +<span class="i0">∴ at least 20 blackfaced sheep in 100 are horned.</span></div> + + +<p class="noindent">But such an argument, though it may be correct Arithmetic, is not Logic +at all; and when such numerical evidence is obtainable the comparatively +indefinite arguments of Logic are needless. Another apparent exception +is the following:</p> + + +<div class="example"><span class="i1">Most men are 5 feet high;<br /></span> +<span class="i1">Most men are semi-rational:<br /></span> +<span class="i0">∴ Some semi-rational things are 5 feet high.</span></div> + + +<p class="noindent">Here the Middle Term (men) is distributed in neither premise, yet the +indisputable conclusion is a logical proposition. The premises, however, +are really arithmetical; for 'most' means 'more than half,' or more than +50 per cent.</p> + +<p>Still, another apparent exception is entirely logical. Suppose we are +given, the premises—<i>All P is M</i>, and <i>All S is M</i>—the middle term is +undistributed. But take the obverse of the contrapositive of both +premises:</p> + + +<div class="example"><span class="i1">All m is p;<br /></span> +<span class="i1">All m is s:<br /></span> +<span class="i0">∴ Some s is p.</span></div> + + +<p class="noindent">Here we have a conclusion legitimately obtained; but it is not in the +terms originally given.</p> + +<p>For Mediate Inference depending on truly logical pre<span class='pagenum'>[Pg 112]<a name="Page_112" id="Page_112"></a></span>mises, then, it is +necessary that one premise should distribute the middle term; and the +reason of this may be illustrated even by the above supposed numerical +exceptions. For in them the premises are such that, though neither of +the two premises by itself distributes the Middle, yet they always +overlap upon it. If each premise dealt with exactly half the Middle, +thus barely distributing it between them, there would be no logical +proposition inferrible. We require that the middle term, as used in one +premise, should necessarily overlap the same term as used in the other, +so as to furnish common ground for comparing the other terms. Hence I +have defined the middle term as 'that term common to both premises by +means of which the other terms are compared.'</p> + +<p>(5) One at least of the premises must be affirmative; or, from two +negative premises nothing can be inferred (in the given terms).</p> + +<p>The fourth Canon required that the middle term should be given +distributed, or in its whole extent, at least once, in order to afford +sure ground of comparison for the others. But that such comparison may +be effected, something more is requisite; the relation of the other +terms to the Middle must be of a certain character. One at least of them +must be, as to its extent or denotation, partially or wholly identified +with the Middle; so that to that extent it may be known to bear to the +other term, whatever relation we are told that so much of the Middle +bears to that other term. Now, identity of denotation can only be +predicated in an affirmative proposition: one premise, then, must be +affirmative.</p> + +<p>If both premises are negative, we only know that both the other terms +are partly or wholly excluded from the Middle, or are not identical with +it in denotation: where they lie, then, in relation to one another we +have no means of knowing. Similarly, in the mediate comparison of +quantities, if we are told that A and C are both of them <span class='pagenum'>[Pg 113]<a name="Page_113" id="Page_113"></a></span>unequal to B, +we can infer nothing as to the relation of C to A. Hence the premises—</p> + + +<div class="example"><span class="i0">No electors are sober;<br /></span> +<span class="i0">No electors are independent—</span></div> + + +<p class="noindent">however suggestive, do not formally justify us in inferring any +connection between sobriety and independence. Formally to draw a +conclusion, we must have affirmative grounds, such as in this case we +may obtain by obverting both premises:</p> + + +<div class="example"><span class="i1">All electors are not-sober;<br /></span> +<span class="i1">All electors are not-independent:<br /></span> +<span class="i0">∴ Some who are not-independent are not-sober.</span></div> + + +<p class="noindent">But this conclusion is not in the given terms.</p> + +<p>(6) (<i>a</i>) If one premise be negative, the conclusion must be negative: +and (<i>b</i>) to prove a negative conclusion, one premise must be negative.</p> + +<p>(<i>a</i>) For we have seen that one premise must be affirmative, and that +thus one term must be partly (at least) identified with the Middle. If, +then, the other premise, being negative, predicates the exclusion of the +remaining term from the Middle, this remaining term must be excluded +from the first term, so far as we know the first to be identical with +the Middle: and this exclusion will be expressed by a negative +conclusion. The analogy of the mediate comparison of quantities may here +again be noticed: if A is equal to B, and B is unequal to C, A is +unequal to C.</p> + +<p>(<i>b</i>) If both premises be affirmative, the relations to the Middle of +both the other terms are more or less inclusive, and therefore furnish +no ground for an exclusive inference. This also follows from the +function of the middle term.</p> + +<p>For the more convenient application of these canons to the testing of +syllogisms, it is usual to derive from them three Corollaries:</p> + +<p>(i) Two particular premises yield no conclusion.</p><p><span class='pagenum'>[Pg 114]<a name="Page_114" id="Page_114"></a></span></p> + +<p>For if both premises be affirmative, <i>all</i> their terms are +undistributed, the subjects by predesignation, the predicates by +position; and therefore the middle term must be undistributed, and there +can be no conclusion.</p> + +<p>If one premise be negative, its predicate is distributed by position: +the other terms remaining undistributed. But, by Canon 6, the conclusion +(if any be possible) must be negative; and therefore its predicate, the +major term, will be distributed. In the premises, therefore, both the +middle and the major terms should be distributed, which is impossible: +<i>e.g.</i>,</p> + + +<div class="example"><span class="i1">Some M is not P;<br /></span> +<span class="i1">Some S is M:<br /></span> +<span class="i0">∴ Some S is not P.</span></div> + + +<p class="noindent">Here, indeed, the major term is legitimately distributed (though the +negative premise might have been the minor); but M, the middle term, is +distributed in neither premise, and therefore there can be no +conclusion.</p> + +<p>Still, an exception may be made by admitting a bi-designate conclusion:</p> + + +<div class="example"><span class="i1">Some P is M;</span> +<span class="i1">Some S is not M:</span> +<span class="i0">∴ Some S is not some P.</span></div> + + +<p>(ii) If one premise be particular, so is the conclusion.</p> + +<p>For, again, if both premises be affirmative, they only distribute one +term, the subject of the universal premise, and this must be the middle +term. The minor term, therefore, is undistributed, and the conclusion +must be particular.</p> + +<p>If one premise be negative, the two premises together can distribute +only two terms, the subject of the universal and the predicate of the +negative (which may be the same premise). One of these terms must be the +middle; the other (since the conclusion is negative) must be the major. +The minor term, therefore, is undistributed, and the conclusion must be +particular.</p><p><span class='pagenum'>[Pg 115]<a name="Page_115" id="Page_115"></a></span></p> + +<p>(iii) From a particular major and a negative minor premise nothing can +be inferred.</p> + +<p>For the minor premise being negative, the major premise must be +affirmative (5th Canon); and therefore, being particular, distributes +the major term neither in its subject nor in its predicate. But since +the conclusion must be negative (6th Canon), a distributed major term is +demanded, <i>e.g.</i>,</p> + + +<div class="example"><span class="i1">Some M is P;<br /></span> +<span class="i1">No S is M:<br /></span> +<span class="i0">∴ ———</span></div> + + +<p class="noindent">Here the minor and the middle terms are both distributed, but not the +major (P); and, therefore, a negative conclusion is impossible.</p> + +<p><a name="chap_9_sect_3" id="chap_9_sect_3"></a>§ 3. First Principle or Axiom of the Syllogism.—Hitherto in this +chapter we have been analysing the conditions of valid mediate +inference. We have seen that a single step of such inference, a +Syllogism, contains, when fully expressed in language, three +propositions and three terms, and that these terms must stand to one +another in the relations required by the fourth, fifth, and sixth +Canons. We now come to a principle which conveniently sums up these +conditions; it is called the <i>Dictum de omni et nullo</i>, and may be +stated thus:</p> + +<div class="blockquot"><p>Whatever is predicated (affirmatively or negatively) of a +term distributed,</p> + +<p>With which term another term can be (partly or wholly) +identified,</p> + +<p>May be predicated in like manner (affirmatively or +negatively) of the latter term (or part of it).</p></div> + +<p>Thus stated (nearly as by Whately in the introduction to his <i>Logic</i>) +the <i>Dictum</i> follows line by line the course of a Syllogism in the First +Figure (see <a href="#chap_10_sect_2">chap. x. § 2</a>). To return to our former example: <i>All authors +are vain</i> is the same as—Vanity is predicated of all authors; <i>Cicero +is an author</i> is the same as—Cicero is identified as an author; +therefore<span class='pagenum'>[Pg 116]<a name="Page_116" id="Page_116"></a></span> <i>Cicero is vain</i>, or—Vanity may be predicated of Cicero. The +<i>Dictum</i> then requires: (1) three propositions; (2) three terms; (3) +that the middle term be distributed; (4) that one premise be +affirmative, since only by an affirmative proposition can one term be +identified with another; (5) that if one premise be negative the +conclusion shall be so too, since whatever is predicated of the middle +term is predicated <i>in like manner</i> of the minor.</p> + +<p>Thus far, then, the <i>Dictum</i> is wholly analytic or verbal, expressing no +more than is implied in the definitions of 'Syllogism' and 'Middle +Term'; since (as we have seen) all the General Canons (except the third, +which is a still more general condition of formal proof) are derivable +from those definitions. However, the <i>Dictum</i> makes a further statement +of a synthetic or real character, namely, that <i>when these conditions +are fulfilled an inference is justified</i>; that then the major and minor +terms are brought into comparison through the middle, and that the major +term may be predicated affirmatively or negatively of all or part of the +minor. It is this real assertion that justifies us in calling the +<i>Dictum</i> an Axiom.</p> + +<p><a name="chap_9_sect_4" id="chap_9_sect_4"></a>§ 4. Whether the Laws of Thought may not fully explain the Syllogism +without the need of any synthetic principle has, however, been made a +question. Take such a syllogism as the following:</p> + + +<div class="example"><span class="i1">All domestic animals are useful;<br /></span> +<span class="i1">All pugs are domestic animals:<br /></span> +<span class="i0">∴ All pugs are useful.</span></div> + + +<p class="noindent">Here (an ingenious man might urge), having once identified pugs with +domestic animals, that they are useful follows from the Law of Identity. +If we attend to the meaning, and remember that what is true in one form +of words is true in any other form, then, all domestic animals being +useful, of course pugs are. It is merely a case of subalternation: we +may put it in this way:</p><p><span class='pagenum'>[Pg 117]<a name="Page_117" id="Page_117"></a></span></p> + + +<div class="example"><span class="i1">All domestic animals are useful:<br /></span> +<span class="i0">∴ Some domestic animals (<i>e.g.</i>, pugs) are useful.</span></div> + + +<p class="noindent">The derivation of negative syllogisms from the Law of Contradiction (he +might add) may be shown in a similar manner.</p> + +<p>But the force of this ingenious argument depends on the participial +clause—'having once identified pugs with domestic animals.' If this is +a distinct step of the reasoning, the above syllogism cannot be reduced +to one step, cannot be exhibited as mere subalternation, nor be brought +directly under the law of Identity. If 'pug,' 'domestic,' and 'useful' +are distinct terms; and if 'pug' and 'useful' are only known to be +connected because of their relations to 'domestic': this is something +more than the Laws of Thought provide for: it is not Immediate +Inference, but Mediate; and to justify it, scientific method requires +that its conditions be generalised. The <i>Dictum</i>, then, as we have seen, +does generalise these conditions, and declares that when such conditions +are satisfied a Mediate Inference is valid.</p> + +<p>But, after all (to go back a little), consider again that proposition +<i>All pugs are domestic animals</i>: is it a distinct step of the reasoning; +that is to say, is it a Real Proposition? If, indeed, 'domestic' is no +part of the definition of 'pug,' the proposition is real, and is a +distinct part of the argument. But take such a case as this:</p> + + +<div class="example"><span class="i0">All dogs are useful;</span> +<span class="i0">All pugs are dogs.</span></div> + + +<p class="noindent">Here we clearly have, in the minor premise, only a verbal proposition; +to be a dog is certainly part of the definition of 'pug.' But, if so, +the inference 'All pugs are useful' involves no real mediation, and the +argument is no more than this:</p> + + +<div class="example"><span class="i1">All dogs are useful;<br /></span> +<span class="i0">∴ Some dogs (<i>e.g.</i>, pugs) are useful.</span></div> + + +<p class="noindent">Similarly, if the major premise be verbal, thus:</p> + + +<div class="example"><span class="i0">All men are rational;<br /></span> +<span class="i0">Socrates is a man—</span></div> + + +<p class="noindent"><span class='pagenum'>[Pg 118]<a name="Page_118" id="Page_118"></a></span>to conclude that 'Socrates is rational' is no Mediate Inference; for so +much was implied in the minor premise, 'Socrates is a man,' and the +major premise adds nothing to this.</p> + +<p>Hence we may conclude (as anticipated in <a href="#chap_7_sect_3">chap. vii. § 3</a>) that 'any +apparent syllogism, having one premise a verbal proposition, is really +an Immediate Inference'; but that, if both premises are real +propositions, the Inference is Mediate, and demands for its explanation +something more than the Laws of Thought.</p> + +<p>The fact is that to prove the minor to be a case of the middle term may +be an exceedingly difficult operation (<a href="#chap_13_sect_7">chap. xiii. § 7</a>). The difficulty +is disguised by ordinary examples, used for the sake of convenience.</p> + +<p><a name="chap_9_sect_5" id="chap_9_sect_5"></a>§ 5. Other kinds of Mediate Inference exist, yielding valid conclusions, +without being truly syllogistic. Such are mathematical inferences of +Equality, as—</p> + + +<div class="example"><span class="i0">A = B = C ∴ A = C.</span></div> + + +<p class="noindent">Here, according to the usual logical analysis, there are strictly four +terms—(1) A, (2) equal to B, (3) B, (4) equal to C.</p> + +<p>Similarly with the argument <i>a fortiori</i>,</p> + + +<div class="example"><span class="i0">A > B > C ∴ (much more) A > C.</span></div> + + +<p class="noindent">This also is said to contain four terms: (1) A, (2) greater than B, (3) +B, (4) greater than C. Such inferences are nevertheless intuitively +sound, may be verified by trial (within the limits of sense-perception), +and are generalised in appropriate axioms of their own, corresponding to +the <i>Dictum</i> of the syllogism; as 'Things equal to the same thing are +equal to one another,' <i>etc.</i></p> + +<p>Now, surely, this is an erroneous application of the usual logical +analysis of propositions. Both Logic and Mathematics treat of the +<i>relations</i> of terms; but whilst Mathematics employs the sign = for only +one kind of relation, and for that relation exclusive of the terms; +Logic employs <span class='pagenum'>[Pg 119]<a name="Page_119" id="Page_119"></a></span>the same signs (<i>is</i> or <i>is not</i>) for all relations, +recognising only a difference of quality in predication, and treating +every other difference of relation as belonging to one of the terms +related. Thus Logicians read <i>A—is—equal to B</i>: as if <i>equal to B</i> +could possibly be a term co-relative with A. Whence it follows that the +argument <i>A = B = C ∴ A = C</i> contains four terms; though everybody sees +that there are only three.</p> + +<p>In fact (as observed in <a href="#chap_2_sect_2">chap. ii. § 2</a>) the sign of logical relation +(<i>is</i> or <i>is not</i>), whilst usually adequate for class-reasoning +(coinherence) and sometimes extensible to causation (because a cause +implies a class of events), should never be stretched to include other +relations in such a way as to sacrifice intelligence to formalism. And, +besides mathematical or quantitative relations, there are others +(usually considered qualitative because indefinite) which cannot be +justly expressed by the logical copula. We ought to read propositions +expressing time-relations (and inferences drawn accordingly) thus:</p> + + +<div class="example"><span class="i1">B—is before—C;<br /></span> +<span class="i1">A—is before—B:<br /></span> +<span class="i0">∴ A—is before—C.</span></div> + + +<p class="noindent">And in like manner <i>A—is simultaneous with—B; etc.</i> Such arguments (as +well as the mathematical) are intuitively sound and verifiable, and +might be generalised in axioms if it were worth while: but it is not, +because no method could be founded on such axioms.</p> + +<p>The customary use of relative terms justifies some Mediate Inferences, +as, <i>The father of a father is a grand-father</i>.</p> + +<p>Some cases, however, that at first seem obvious, are really delusive +unless further data be supplied. Thus <i>A co-exists with B, B with C; ∴ A +with C</i>—is not sound unless <i>B</i> is an instantaneous event; for where B +is perdurable, <i>A</i> may co-exist with it at one time and <i>C</i> at another.</p> + +<p>Again: <i>A is to the left of B, B of C; ∴ A of C</i>. This may <span class='pagenum'>[Pg 120]<a name="Page_120" id="Page_120"></a></span>pass; but it +is not a parallel argument that if <i>A is north of B and B west of C</i>, +then <i>A is north-west of C</i>: for suppose that A is a mile to the north +of B, and B a yard to the west of C, then A is practically north of C; +at least, its westward position cannot be expressed in terms of the +mariner's compass. In such a case we require to know not only the +directions but the distances of A and C from B; and then the exact +direction of A from C is an affair of mathematical calculation.</p> + +<p>Qualitative reasoning concerning position is only applicable to things +in one dimension of space, or in time considered as having one +dimension. Under these conditions we may frame the following +generalisation concerning all Mediate Inferences: Two terms definitely +related to a third, and one of them positively, are related to one +another as the other term is related to the third (that is, positively +or negatively); provided that the relations given are of the same kind +(that is, of Time, or Coinherence, or Likeness, or Equality).</p> + +<p>Thus, to illustrate by relations of Time—</p> + + +<div class="example"><span class="i1">B is simultaneous with C;<br /></span> +<span class="i1">A is not simultaneous with B:<br /></span> +<span class="i0">∴ A is not simultaneous with C.</span></div> + + +<p class="noindent">Here the relations are of the same kind but of different logical +quality, and (as in the syllogism) a negative copula in the premises +leads to a negative conclusion.</p> + +<p>An examination in detail of particular cases would show that the above +generalisation concerning all Mediate Inferences is subject to too many +qualifications to be called an Axiom; it stands to the real Axioms (the +<i>Dictum</i>, <i>etc.</i>) as the notion of the Uniformity of Nature does to the +definite principles of natural order (<i>cf.</i> <a href="#chap_13_sect_8">chap. xiii. § 8</a>).</p><p><span class='pagenum'>[Pg 121]<a name="Page_121" id="Page_121"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_X" id="CHAPTER_X"></a>CHAPTER X</h2> + +<h3>CATEGORICAL SYLLOGISMS</h3> + + +<p><a name="chap_10_sect_1" id="chap_10_sect_1"></a>§ 1. The type of logical, deductive, mediate, categorical Inference is a +Syllogism directly conformable with the <i>Dictum</i>: as—</p> + + +<div class="example"><span class="i1">All carnivores (M) are excitable (P);<br /></span> +<span class="i1">Cats (S) are carnivores (M):<br /></span> +<span class="i0">∴ Cats (S) are excitable (P).</span></div> + + +<p class="noindent">In this example P is predicated of M, a term distributed; in which term, +M, S is given as included; so that P may be predicated of S.</p> + +<p>Many arguments, however, are of a type superficially different from the +above: as—</p> + + +<div class="example"><span class="i1">No wise man (P) fears death (M);<br /></span> +<span class="i1">Balbus (S) fears death (M):<br /></span> +<span class="i0">∴ Balbus (S) is not a wise man (P).</span></div> + + +<p class="noindent">In this example, instead of P being predicated of M, M is predicated of +P, and yet S is given as included not in P, but in M. The divergence of +such a syllogism from the <i>Dictum</i> may, however, be easily shown to be +superficial by writing, instead of <i>No wise man fears death</i>, the +simple, converse, <i>No man who fears death is wise</i>.</p> + +<p>Again:</p> + + +<div class="example"><span class="i1">Some dogs (M) are friendly to man (P);<br /></span> +<span class="i1">All dogs (M) are carnivores (S):<br /></span> +<span class="i0">∴ Some carnivores (S) are friendly to man (P).</span></div> + + +<p class="noindent">Here P is predicated of M undistributed; and instead of S being included +in M, M is included in S: so that the divergence from the type of +syllogism to which the <i>Dictum</i><span class='pagenum'>[Pg 122]<a name="Page_122" id="Page_122"></a></span> directly applies is still greater than +in the former case. But if we transpose the premises, taking first</p> + + +<div class="example"><span class="i0">All dogs (M) are carnivores (P),</span></div> + + +<p class="noindent">then P is predicated of M distributed; and, simply converting the other +premise, we get—</p> + + +<div class="example"><span class="i0">Some things friendly to man (S) are dogs (M):</span></div> + + +<p class="noindent">whence it follows that—</p> + + +<div class="example"><span class="i0">Some things friendly to man (S) are carnivores (P);</span></div> + + +<p class="noindent">and this is the simple converse of the original conclusion.</p> + +<p>Once more:</p> + + +<div class="example"><span class="i1">No pigs (P) are philosophers (M);<br /></span> +<span class="i1">Some philosophers (M) are hedonists (S):<br /></span> +<span class="i0">∴ Some hedonists (S) are not pigs (P).</span></div> + + +<p class="noindent">In this case, instead of P being predicated of M distributed, M is +predicated of P distributed; and instead of S (or part of it) being +included in M, we are told that some M is included in S. Still there is +no real difficulty. Simply convert both the premises, and we have:</p> + + +<div class="example"><span class="i0">No philosophers (M) are pigs (P);<br /></span> +<span class="i0">Some hedonists (S) are philosophers (M).</span></div> + + +<p>Whence the same conclusion follows; and the whole syllogism plainly +conforms directly to the <i>Dictum</i>.</p> + +<p>Such departures as these from the normal syllogistic form are said to +constitute differences of Figure (see <a href="#chap_10_sect_2">§ 2</a>); and the processes by which +they are shown to be unessential differences are called Reduction (see <a href="#chap_10_sect_6">§ 6</a>).</p> + +<p><a name="chap_10_sect_2" id="chap_10_sect_2"></a>§ 2. Figure is determined by the position of the Middle Term in the +premises; of which position there are four possible variations. The +middle term may be subject of the major premise, and predicate of the +minor, as in the first example above; and this position, being directly +conformable to the requirements of the <i>Dictum</i>, is called the First +Figure. Or the middle term may be predicate of both premises, as in the +second of the above examples; <span class='pagenum'>[Pg 123]<a name="Page_123" id="Page_123"></a></span>and this is called the Second Figure. Or +the middle term may be subject of both premises, as in the third of the +above examples; and this is called the Third Figure. Or, finally, the +middle term may be predicate of the major premise, and subject of the +minor, as in the fourth example given above; and this is the Fourth +Figure.</p> + +<p>It may facilitate the recollection of this most important point if we +schematise the figures thus:</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/page123.png" width="600" height="115" alt="" title="" /> +</div> + +<p>The horizontal lines represent the premises, and at the angles formed +with them by the slanting or by the perpendicular lines the middle term +occurs. The schema of Figure IV. resembles Z, the last letter of the +alphabet: this helps one to remember it in contrast with Figure I., +which is thereby also remembered. Figures II. and III. seem to stand +back to back.</p> + +<p><a name="chap_10_sect_3" id="chap_10_sect_3"></a>§ 3. The Moods of each Figure are the modifications of it which arise +from different combinations of propositions according to quantity and +quality. In Figure I., for example, four Moods are recognised: A.A.A., +E.A.E., A.I.I., E.I.O.</p> + + +<div class='center'> +<table border="0" cellpadding="2" cellspacing="0" summary=""> +<tr><td align='left'>A.</td><td align='left'>All M is P;</td></tr> +<tr><td align='left'>A.</td><td align='left'>All S is M:</td></tr> +<tr><td align='left'>A.</td><td align='left'>∴ All S is P.</td></tr> +<tr><td> </td></tr> +<tr><td align='left'>E.</td><td align='left'>No M is P;</td></tr> +<tr><td align='left'>A.</td><td align='left'>All S is M:</td></tr> +<tr><td align='left'>E.</td><td align='left'>∴ No S is P.</td></tr> +<tr><td> </td></tr> +<tr><td align='left'>A.</td><td align='left'>All M is P;</td></tr> +<tr><td align='left'>I.</td><td align='left'>Some S is M:</td></tr> +<tr><td align='left'>I.</td><td align='left'>∴ Some S is P.</td></tr> +<tr><td> </td></tr> +<tr><td align='left'>E.</td><td align='left'>No M is P;</td></tr> +<tr><td align='left'>I.</td><td align='left'>Some S is M:</td></tr> +<tr><td align='left'>O.</td><td align='left'>∴ Some S is not P.</td></tr> +</table></div> + +<p class="noindent"><span class='pagenum'>[Pg 124]<a name="Page_124" id="Page_124"></a></span>Now, remembering that there are four Figures, and four kinds of +propositions (A. I. E. O.), each of which propositions may be major +premise, minor premise, or conclusion of a syllogism, it appears that in +each Figure there may be 64 Moods, and therefore 256 in all. On +examining these 256 Moods, however, we find that only 24 of them are +valid (<i>i.e.</i>, of such a character that the conclusion strictly follows +from the premises), whilst 5 of these 24 are needless, because their +conclusions are 'weaker' or less extensive than the premises warrant; +that is to say, they are particular when they might be universal. Thus, +in Figure I., besides the above 4 Moods, A.A.I. and E.A.O. are valid in +the sense of being conclusive; but they are superfluous, because +included in A.A.A. and E.A.E. Omitting, then, these 5 needless Moods, +which are called 'Subalterns' because their conclusions are subaltern +(<a href="#chap_7_sect_2">chap. vii. § 2</a>) to those of other Moods, there remain 19 Moods that are +valid and generally recognised.</p> + +<p><a name="chap_10_sect_4" id="chap_10_sect_4"></a>§ 4. How these 19 Moods are determined must be our next inquiry. There +are several ways more or less ingenious and interesting; but all depend +on the application, directly or indirectly, of the Six Canons, which +were shown in the last chapter to be the conditions of Mediate +Inference.</p> + +<p>(1) One way is to begin by finding what Moods of Figure I. conform to +the <i>Dictum</i>. Now, the <i>Dictum</i> requires that, in the major premise, P +be predicated of a term distributed, from which it follows that no Mood +can be valid whose major premise is particular, as in I.A.I. or O.A.O. +Again, the <i>Dictum</i> requires that the minor premise be affirmative +("with which term another is identified"); so that no Mood can be valid +whose minor premise is negative, as in A.E.E. or A.O.O. By such +considerations we find that in Figure I., out of 64 Moods possible, only +six are valid, namely, those above-mentioned in <a href="#chap_10_sect_3">§ 3</a>, including the two +subalterns. The second step of this method is <span class='pagenum'>[Pg 125]<a name="Page_125" id="Page_125"></a></span>to test the Moods of the +Second, Third, and Fourth Figures, by trying whether they can be reduced +to one or other of the four Moods of the First (as briefly illustrated +in <a href="#chap_10_sect_1">§ 1</a>, and to be further explained in <a href="#chap_10_sect_6">§ 6</a>).</p> + +<p>(2) Another way is to take the above six General or Common Canons, and +to deduce from them Special Canons for testing each Figure: an +interesting method, which, on account of its length, will be treated of +separately in the next section.</p> + +<p>(3) Direct application of the Common Canons is, perhaps, the simplest +plan. First write out the 64 Moods that are possible without regard to +Figure, and then cross out those which violate any of the Canons or +Corollaries, thus:</p> + + +<div class="blockquot">AAA, <del>AAE</del> (6th Can. <i>b</i>). AAI, <del>AAO</del> (6th Can. <i>b</i>).<br /> +<del>AEA</del> (6th Can. <i>a</i>) AEE, <del>AEI</del> (6th Can. <i>a</i>) AEO,<br /> +<del>AIA</del> (Cor. ii.) <del>AIE</del> (6th Can. <i>b</i>) AII, <del>AIO</del> (6th Can. <i>b</i>)<br /> +<del>AOA</del> (6th Can. <i>a</i>) <del>AOE</del> (Cor. ii.) <del>AOI</del> (6th Can. <i>a</i>) AOO.</div> + + +<p>Whoever has the patience to go through the remaining 48 Moods will +discover that of the whole 64 only 11 are valid, namely:</p> + +<p class="blockquot noindent"> +A.A.A., A.A.I., A.E.E., A.E.O., A.I.I., A.O.O.,<br /> +E.A.E., E.A.O., E.I.O., I.A.I., O.A.O.<br /> +</p> + +<p>These 11 Moods have next to be examined in each Figure, and if valid in +every Figure there will still be 44 moods in all. We find, however, that +in the First Figure, A.E.E., A.E.O., A.O.O. involve illicit process of +the major term (3rd Can.); I.A.I., O.A.O. involve undistributed Middle +(4th Can.); and A.A.I., E.A.O. are subalterns. In the Second Figure all +the affirmative Moods, A.A.A., A.A.I., A.I.I., I.A.I., involve +undistributed Middle; O.A.O. gives illicit process of the major term; +and A.E.O., E.A.O. are subalterns. In the Third Figure, A.A.A., E.A.E., +involve illicit process of the minor term (3rd Can.); A.E.E., A.E.O., +A.O.O., illicit <span class='pagenum'>[Pg 126]<a name="Page_126" id="Page_126"></a></span>process of the major term. In the Fourth Figure, A.A.A. +and E.A.E. involve illicit process of the minor term; A.I.I., A.O.O., +undistributed Middle; O.A.O. involves illicit process of the major term; +and A.E.O. is subaltern.</p> + +<p>Those moods of each Figure which, when tried by these tests, are not +rejected, are valid, namely:</p> + +<div class="blockquot"><p>Fig. I.—A.A.A., E.A.E., A.I.I., E.I.O. (A.A.I., E.A.O., Subaltern);</p> + +<p>Fig. II.—E.A.E., A.E.E., E.I.O., A.O.O. (E.A.O., A.E.O., Subaltern);</p> + +<p>Fig. III.—A.A.I., I.A.I., A.I.I., E.A.O., O.A.O., E.I.O.;</p> + +<p>Fig. IV.—A.A.I., A.E.E., I.A.I., E.A.O., E.I.O. (A.E.O., Subaltern).</p></div> + +<p class="noindent">Thus, including subaltern Moods, there are six valid in each Figure. In +Fig. III. alone there is no subaltern Mood, because in that Figure there +can be no universal conclusion.</p> + +<p><a name="chap_10_sect_5" id="chap_10_sect_5"></a>§ 5. Special Canons of the several Figures, deduced from the Common +Canons, enable us to arrive at the same result by a somewhat different +course. They are not, perhaps, necessary to the Science, but afford a +very useful means of enabling one to thoroughly appreciate the character +of formal syllogistic reasoning. Accordingly, the proof of each rule +will be indicated, and its elaboration left to the reader. There is no +difficulty, if one bears in mind that Figure is determined by the +position of the middle term.</p> + +<p>Fig. I., Rule (<i>a</i>): <i>The minor premise must be affirmative</i>.</p> + +<p>For, if not, in negative Moods there will be illicit process of the +major term. Applying this rule to the eleven possible Moods given in § +4, as remaining after application of the Common Canons, it eliminates +A.E.E., A.E.O., A.O.O.</p> + +<p>(<i>b</i>) <i>The major premise must be universal</i>.</p> + +<p>For, if not, the minor premise being affirmative, the <span class='pagenum'>[Pg 127]<a name="Page_127" id="Page_127"></a></span>middle term will +be undistributed. This rule eliminates I.A.I., O.A.O.; leaving six +Moods, including two subalterns.</p> + +<p>Fig. II. (<i>a</i>) <i>One premise must be negative.</i></p> + +<p>For else neither premise will distribute the middle term. This rule +eliminates A.A.A., A.A.I., A.I.I., I.A.I.</p> + +<p>(<i>b</i>) <i>The major premise must be universal.</i></p> + +<p>For else, the conclusion being negative, there will be illicit process +of the major term. This eliminates I.A.I., O.A.O.; leaving six Moods, +including two subalterns.</p> + +<p>Fig. III. (<i>a</i>) <i>The minor premise must be affirmative.</i></p> + +<p>For else, in negative moods there will be illicit process of the major +term. This rule eliminates A.E.E., A.E.O., A.O.O.</p> + +<p>(<i>b</i>) <i>The conclusion must be particular.</i></p> + +<p>For, if not, the minor premise being affirmative, there will be illicit +process of the minor term. This eliminates A.A.A., A.E.E., E.A.E.; +leaving six Moods.</p> + +<p>Fig. IV. (<i>a</i>) <i>When the major premise is affirmative, the minor must be +universal.</i></p> + +<p>For else the middle term is undistributed. This eliminates A.I.I., +A.O.O.</p> + +<p>(<i>b</i>) <i>When the minor premise is affirmative the conclusion must be +particular.</i></p> + +<p>Otherwise there will be illicit process of the minor term. This +eliminates A.A.A., E.A.E.</p> + +<p>(<i>c</i>) <i>When either premise is negative, the major must be universal.</i></p> + +<p>For else, the conclusion being negative, there will be illicit process +of the major term. This eliminates O.A.O.; leaving six Moods, including +one subaltern.</p> + +<p><a name="chap_10_sect_6" id="chap_10_sect_6"></a>§ 6. Reduction is either—(1) Ostensive or (2) Indirect. Ostensive +Reduction consists in showing that an argument given in one Mood can +also be stated in another; the process is especially used to show that +the Moods of the second, third, and fourth Figures are equivalent to one +or <span class='pagenum'>[Pg 128]<a name="Page_128" id="Page_128"></a></span>another Mood of the first Figure. It thus proves the validity of the +former Moods by showing that they also essentially conform to the +<i>Dictum</i>, and that all Categorical Syllogisms are only superficial +varieties of one type of proof.</p> + +<p>To facilitate Reduction, the recognised Moods have all had names given +them; which names, again, have been strung together into mnemonic verses +of great force and pregnancy:</p> + + +<div class="example"><span class="i0">Barbara, Celarent, Darii, Ferioque prioris:<br /></span> +<span class="i0">Cesare, Camestres, Festino, Baroco, secundæ:<br /></span> +<span class="i0">Tertia, Darapti, Disamis, Datisi, Felapton,<br /></span> +<span class="i0">Bocardo, Ferison, habet: Quarta insuper addit<br /></span> +<span class="i0">Bramantip, Camenes, Dimaris, Fesapo, Fresison.</span></div> + + +<p>In the above verses the names of the Moods of Fig. I. begin with the +first four consonants B, C, D, F, in alphabetical order; and the names +of all other Moods likewise begin with these letters, thus signifying +(except in Baroco and Bocardo) the mood of Fig. I., to which each is +equivalent, and to which it is to be reduced: as Bramantip to Barbara, +Camestres to Celarent, and so forth.</p> + +<p>The vowels A, E, I, O, occurring in the several names, give the quantity +and quality of major premise, minor premise, and conclusion in the usual +order.</p> + +<p>The consonants s and p, occurring after a vowel, show that the +proposition which the vowel stands for is to be converted either (s) +simply or (p) <i>per accidens</i>; except where s or p occurs after the third +vowel of a name, the conclusion: then it refers not to the conclusion of +the given Mood (say Disamis), but to the conclusion of that Mood of the +first Figure to which the given Mood is reduced (Darii).</p> + +<p>M (<i>mutare</i>, metathesis) means 'transpose the premises' (as of +Ca<i>m</i>estres).</p> + +<p>C means 'substitute the contradictory of the conclusion for the +foregoing premise,' a process of the Indirect Reduction to be presently +explained (see Baroco, § 8).</p><p><span class='pagenum'>[Pg 129]<a name="Page_129" id="Page_129"></a></span></p> + +<p>The other consonants, r, n, t (with b and d, when not initial), +occurring here and there, have no mnemonic significance.</p> + +<p>What now is the problem of Reduction? The difference of Figures depends +upon the position of the Middle Term. To reduce a Mood of any other +Figure to the form of the First, then, we must so manipulate its +premises that the Middle Term shall be subject of the major premise and +predicate of the minor premise.</p> + +<p>Now in Fig. II. the Middle Term is predicate of both premises; so that +the minor premise may need no alteration, and to convert the major +premise may suffice. This is the case with Cesare, which reduces to +Celarent by simply converting the major premise; and with Festino, which +by the same process becomes Ferio. In Camestres, however, the minor +premise is negative; and, as this is impossible in Fig. I., the premises +must be transposed, and the new major premise must be simply converted: +then, since the transposition of the premises will have transposed the +terms of the conclusion (according to the usual reading of syllogisms), +the new conclusion must be simply converted in order to prove the +validity of the original conclusion. The process may be thus represented +(<i>s.c.</i> meaning 'simply convert')</p> + +<div class="figcenter" style="width: 400px;"> +<img src="images/page129.png" width="400" height="158" alt="" title="" /> +</div> + +<p>The Ostensive Reduction of Baroco also needs special explanation; for as +it used to be reduced indirectly, its name gives no indication of the +ostensive process. To reduce it ostensively let us call it Faksnoko, +where k means 'obvert the foregoing premise.' By thus obverting (k) and +simply <span class='pagenum'>[Pg 130]<a name="Page_130" id="Page_130"></a></span>converting (s) (in sum, contrapositing) the major premise, and +obverting the minor premise, we get a syllogism in Ferio, thus:</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/page130a.png" width="600" height="154" alt="" title="" /> +</div> + +<p>In Fig. III. the middle term is subject of both premises; so that, to +reduce its Moods to the First Figure, it may be enough to convert the +minor premise. This is the case with Darapti, Datisi, Felapton, and +Ferison. But, with Disamis, since the major premise must in the First +Figure be universal, we must transpose the premises, and then simply +convert the new minor premise; and, lastly, since the major and minor +terms have now changed places, we must simply convert the new conclusion +in order to verify the old one. Thus:</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/page130b.png" width="600" height="206" alt="" title="" /> +</div> + +<p>Bocardo, like Baroco, indicates by its name the indirect process. To +reduce it ostensively let its name be Doksamrosk, and proceed thus:</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/page130c.png" width="600" height="203" alt="" title="" /> +</div> +<p><span class='pagenum'>[Pg 131]<a name="Page_131" id="Page_131"></a></span></p> + +<p>In Fig. IV. the position of the middle term is, in both premises, the +reverse of what it is in the First Figure; we may therefore reduce its +Moods either by transposing the premises, as with Bramantip, Camenes, +and Dimaris; or by converting both premises, the course pursued with +Fesapo and Fresison. It may suffice to illustrate by the case of +Bramantip:</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/page131a.png" width="600" height="223" alt="" title="" /> +</div> + +<p>This case shows that a final significant consonant (s, p, or sk) in the +name of any Mood refers to the conclusion of the new syllogism in the +First Figure; since p in Bramantip cannot refer to that Mood's own +conclusion in I.; which, being already particular, cannot be converted +<i>per accidens</i>.</p> + +<p>Finally, in Fig. I., Darii and Ferio differ respectively from Barbara +and Celarent only in this, that their minor premises, and consequently +their conclusions, are subaltern to the corresponding propositions of +the universal Moods; a difference which seems insufficient to give them +rank as distinct forms of demonstration. And as for Barbara and +Celarent, they are easily reducible to one another by obverting their +major premises and the new conclusions, thus:</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/page131b.png" width="600" height="183" alt="" title="" /> +</div> + +<p class="noindent">There is, then, only one fundamental syllogism.</p><p><span class='pagenum'>[Pg 132]<a name="Page_132" id="Page_132"></a></span></p> + +<p><a name="chap_10_sect_7" id="chap_10_sect_7"></a>§ 7. A new version of the mnemonic lines was suggested in <i>Mind</i> No. 27, +with the object of (1) freeing them from all meaningless letters, (2) +showing by the name of each Mood the Figure to which it belongs, (3) +giving names to indicate the ostensive reduction of Baroco and Bocardo. +To obtain the first two objects, <i>l</i> is used as the mark of Fig. I., <i>n</i> +of Fig II., <i>r</i> of Fig. III., <i>t</i> of Fig. IV. The verses (to be scanned +discreetly) are as follows:</p> + + + + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='left'>Balala,</td><td align='left'>Celalel,</td><td align='left'>Dalii,</td><td align='left'>Felioque prioris:</td></tr> +<tr><td align='left'></td><td align='left'></td><td align='left'></td><td align='left'>{Faksnoko}</td></tr> +<tr><td align='left'>Cesane,</td><td align='left'>Camenes,</td><td align='left'>Fesinon,</td><td align='left'>{Banoco,} secundæ:</td></tr> +<tr><td align='left'>Tertia,</td><td align='left'>Darapri,</td><td align='left'>Drisamis,</td><td align='left'>Darisi, Ferapro,</td></tr> +<tr><td align='left'>Doksamrosk</td><td align='left'>}, Ferisor habet:</td><td align='left' colspan='2'>Quarta insuper addit.</td></tr> +<tr><td align='right'>Bocaro</td><td align='left'>}</td></tr> +<tr><td align='left'>Bamatip,</td><td align='left'>Cametes,</td><td align='left'>Dimatis,</td><td align='left'>Fesapto, Fesistot.</td></tr> +</table></div> + + + +<p>De Morgan praised the old verses as "more full of meaning than any +others that ever were made"; and in defence of the above alteration it +may be said that they now deserve that praise still more.</p> + +<p><a name="chap_10_sect_8" id="chap_10_sect_8"></a>§ 8. Indirect reduction is the process of proving a Mood to be valid by +showing that the supposition of its invalidity involves a contradiction. +Take Baroco, and (since the doubt as to its validity is concerned not +with the truth of the premises, but with their relation to the +conclusion) assume the premises to be true. Then, if the conclusion be +false, its contradictory is true. The conclusion being in O., its +contradictory will be in A. Substituting this A. for the minor premise +of Baroco, we have the premises of a syllogism in Barbara, which will be +found to give a conclusion in A., contradictory of the original minor +premise; thus:</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/page132.png" width="600" height="187" alt="" title="" /> +</div> + +<p class="noindent"><span class='pagenum'>[Pg 133]<a name="Page_133" id="Page_133"></a></span>But the original minor premise, <i>Some S is not M</i>, is true by +hypothesis; and therefore the conclusion of Barbara, <i>All S is M</i>, is +false. This falsity cannot, however, be due to the form of Barbara, +which we know to be valid; nor to the major premise, which, being taken +from Baroco, is true by hypothesis: it must, therefore, lie in the minor +premise of Barbara, <i>All S is P</i>; and since this is contradictory of the +conclusion of Baroco <i>Some S is not P</i>, that conclusion was true.</p> + +<p>Similarly, with Bocardo, the Indirect Reduction proceeds by substituting +for the major premise the contradictory of the conclusion; thus again +obtaining the premises of a syllogism in Barbara, whose conclusion is +contradictory of the original major premise. Hence the initial B in +Baroco and Bocardo: it points to a syllogism in Barbara as the means of +Indirect Reduction (<i>Reductio ad impossibile</i>).</p> + +<p>Any other Mood may be reduced indirectly: as, for example, Dimaris. If +this is supposed to be invalid and the conclusion false, substitute the +contradictory of the conclusion for the major premise, thus obtaining +the premises of Celarent:</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/page133.png" width="600" height="233" alt="" title="" /> +</div> + +<p class="noindent">The conclusion of Celarent, simply converted, contradicts the original +major premise of Dimaris, and is therefore false. Therefore the major +premise of Celarent is false, and the conclusion of Dimaris is true. We +might, of course, construct mnemonic names for the Indirect Reduction of +all the Moods: the name of Dimaris would then be Cicari.</p><p><span class='pagenum'>[Pg 134]<a name="Page_134" id="Page_134"></a></span></p> + +<p><a name="chap_10_sect_9" id="chap_10_sect_9"></a>§ 9. The need or use of any Figure but the First has been much discussed +by Logicians. Since, in actual debate, arguments are rarely stated in +syllogistic form, and, therefore, if reduced to that form for closer +scrutiny, generally have to be treated with some freedom; why not always +throw them at once into the First Figure? That Figure has manifest +advantages: it agrees directly with the <i>Dictum</i>; it gives conclusions +in all four propositional forms, and therefore serves every purpose of +full affirmation or denial, of showing agreement or difference (total or +partial), of establishing the contradictories of universal statements; +and it is the only Figure in which the subject and predicate of the +conclusion occupy the same positions in the premises, so that the course +of argument has in its mere expression an easy and natural flow.</p> + +<p>Still, the Second Figure also has a very natural air in some kinds of +negative arguments. The parallelism of the two premises, with the middle +term as predicate in both, brings out very forcibly the necessary +difference between the major and minor terms that is involved in their +opposite relations to the middle term. <i>P is not, whilst S is, M</i>, says +Cesare: that drives home the conviction that <i>S is not P</i>. Similarly in +Camestres: <i>Deer do, oxen do not, shed their horns</i>. What is the +conclusion?</p> + +<p>The Third Figure, again, furnishes in Darapti and Felapton, the most +natural forms of stating arguments in which the middle term is singular:</p> + + +<div class="example"><span class="i1">Socrates was truthful;</span> +<span class="i1">Socrates was a Greek:</span> +<span class="i0">∴ Some Greek was truthful.</span></div> + + +<p class="noindent">Reducing this to Fig I., we should get for the minor premise, <i>Some +Greek was Socrates</i>: which is certainly inelegant. Still, it might be +urged that, in relation to proof, elegance is an extraneous +consideration. And as for the other advantage claimed for Fig. +III.—that, as it yields only <span class='pagenum'>[Pg 135]<a name="Page_135" id="Page_135"></a></span>particular conclusions, it is useful in +establishing contradictories against universals—for that purpose none +of its Moods can be better than Darii or Ferio.</p> + +<p>As for Fig. IV., no particular advantage has been claimed for it. It is +of comparatively late recognition (sometimes called the 'Galenian,' +after Galen, its supposed discoverer); and its scientific claim to exist +at all is disputed. It is said to be a mere inversion of Fig. I.; which +is not true in any sense in which Figs. II. and III. may not be +condemned as partial inversions of Fig. I., and as having therefore +still less claim to recognition. It is also said to invert the order of +thought; as if thought had only one order, or as if the order of thought +had anything to do with Formal Logic. Surely, if distinction of Figure +be recognised at all, the Fourth Figure is scientifically necessary, +because it is inevitably generated by an analysis of the possible +positions of the middle term.</p> + +<p><a name="chap_10_sect_10" id="chap_10_sect_10"></a>§ 10. Is Reduction necessary, however; or have not all the Figures equal +and independent validity? In one sense not only every Figure but each +Mood has independent validity: for any one capable of abstract thinking +sees its validity by direct inspection; and this is true not only of the +abstract Moods, but very frequently of particular concrete arguments. +But science aims at unifying knowledge; and after reducing all possible +arguments that form categorical syllogisms to the nineteen Moods, it is +another step in the same direction to reduce these Moods to one form. +This is the very nature of science: and, accordingly, the efforts of +some Logicians to expound separate principles of each Figure seem to be +supererogatory. Grant that they succeed; and what can the next step be, +but either to reduce these principles to the <i>Dictum</i>, or the <i>Dictum</i> +and the rest to one of these principles? Unless this can be done there +is no science of Formal Logic. If it is done, what is gained by reducing +the principles of the other Figures to the <i>Dictum</i>, instead of the +Moods of the other Figures to <span class='pagenum'>[Pg 136]<a name="Page_136" id="Page_136"></a></span>those of the first Figure? It may, +perhaps, be said that to show (1) that the Moods of the second, third, +and fourth Figures flow from their own principles (though, in fact, +these principles are laboriously adapted to the Moods); and (2) that +these principles may be derived from the <i>Dictum</i>, is the more +uncompromisingly gradual and regular method: but is not Formal Logic +already sufficiently encumbered with formalities?</p> + +<p><a name="chap_10_sect_11" id="chap_10_sect_11"></a>§ 11. Euler's diagrams are used to illustrate the syllogism, though not +very satisfactorily, thus:</p> + +<div class="figcenter" style="width: 200px;"> +<img src="images/fig_5.png" width="200" height="138" alt="Fig. 5." title="" /> +<span class="caption smcap">Fig. 5.</span> +</div> + +<div class="figcenter" style="width: 400px;"> +<img src="images/fig_6.png" width="400" height="148" alt="Fig. 6." title="" /> +<span class="caption smcap">Fig. 6.</span> +</div> + +<div class="figcenter" style="width: 500px;"> +<img src="images/fig_7.png" width="500" height="160" alt="Fig. 7." title="" /> +<span class="caption smcap">Fig. 7.</span> +</div> + +<p class="noindent"><span class='pagenum'>[Pg 137]<a name="Page_137" id="Page_137"></a></span>Remembering that 'Some' means 'It may be all,' it is plain that any one +of these diagrams in Fig. 7, or the one given above for Barbara, may +represent the denotative relations of P, M and S in Darii; though no +doubt the diagram we generally think of as representing Darii is No. 1 +in Fig. 7.</p> + +<p>Remembering that A may be U, and that, therefore, wherever A occurs +there may be only one circle for S and P, these syllogisms may be +represented by only two circles, and Barbara by only one.</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/fig_8.png" width="600" height="278" alt="Fig. 8." title="" /> +<span class="caption smcap">Fig. 8.</span> +</div> + +<p>Here, again, probably, we generally think of No. 1 as the diagram +representing Ferio; but 2, or 3, or that given above for Celarent, is +compatible with the premises.</p> + +<p>If instead of dealing with M, P, and S, a concrete example be taken of +Darii or Ferio, a knowledge of the facts of the case will show what +diagram is suitable to it. But, then, surely it must be possible to do +without the diagram. These diagrams, of course, can be used to +illustrate Moods of the other Figures.</p><p><span class='pagenum'>[Pg 138]<a name="Page_138" id="Page_138"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_XI" id="CHAPTER_XI"></a>CHAPTER XI</h2> + +<h3>ABBREVIATED AND COMPOUND ARGUMENTS</h3> + + +<p><a name="chap_11_sect_1" id="chap_11_sect_1"></a>§ 1. In ordinary discussion, whether oral or written, it is but rarely +that the forms of Logic are closely adhered to. We often leave wide gaps +in the structure of our arguments, trusting the intelligence of those +addressed to bridge them over; or we invert the regular order of +propositions, beginning with the conclusion, and mentioning the +premises, perhaps, a good while after, confident that the sagacity of +our audience will make all smooth. Sometimes a full style, like +Macaulay's, may, by means of amplification and illustration, spread the +elements of a single syllogism over several pages—a pennyworth of logic +steeped in so much eloquence. These practices give a great advantage to +sophists; who would find it very inconvenient to state explicitly in +Mood and Figure the pretentious antilogies which they foist upon the +public; and, indeed, such licences of composition often prevent honest +men from detecting errors into which they themselves have unwittingly +fallen, and which, with the best intentions, they strive to communicate +to others: but we put up with these drawbacks to avoid the inelegance +and the tedium of a long discourse in accurate syllogisms.</p> + +<p>Many departures from the strictly logical statement of reasonings +consist in the use of vague or figurative language, or in the +substitution for one another of expressions supposed to be equivalent, +though, in fact, dangerously discrepant. Against such occasions of error +the logician can provide no safeguard, except the advice to be careful +and discriminating <span class='pagenum'>[Pg 139]<a name="Page_139" id="Page_139"></a></span>in what you say or hear. But as to any derangement +of the elements of an argument, or the omission of them, Logic +effectually aids the task of restoration; for it has shown what the +elements are that enter into the explicit statement of most +ratiocinations, namely, the four forms of propositions and what that +connected order of propositions is which most easily and surely exposes +the validity or invalidity of reasoning, namely, the premises and +conclusion of the Syllogism. Logic has even gone so far as to name +certain abbreviated forms of proof, which may be regarded as general +types of those that actually occur in debate, in leading articles, +pamphlets and other persuasive or polemic writings—namely, the +Enthymeme, Epicheirema and Sorites.</p> + +<p><a name="chap_11_sect_2" id="chap_11_sect_2"></a>§ 2. The Enthymeme, according to Aristotle, is the Syllogism of probable +reasoning about practical affairs and matters of opinion, in contrast +with the Syllogism of theoretical demonstration upon necessary grounds. +But, as now commonly treated, it is an argument with one of its elements +omitted; a Categorical Syllogism, having one or other of its premises, +or else its conclusion, suppressed. If the major premise be suppressed, +it is called an Enthymeme of the First Order; if the minor premise be +wanting, it is said to be of the Second Order; if the conclusion be left +to be understood, there is an Enthymeme of the Third Order.</p> + +<p>Let the following be a complete Syllogism:</p> + + +<div class="example"><span class="i1">All free nations are enterprising;<br /></span> +<span class="i1">The Dutch are a free nation:<br /></span> +<span class="i0">∴ The Dutch are enterprising.</span></div> + + +<p>Reduced to Enthymemes, this argument may be put thus:</p> + +<div class="blockquot"><p>In the First Order:</p> + +<div class="example"><span class="i1">The Dutch are a free nation:<br /></span> +<span class="i0">∴ The Dutch are enterprising.</span></div> + +<p><span class='pagenum'>[Pg 140]<a name="Page_140" id="Page_140"></a></span></p> + +<p>In the Second Order—</p> + + +<div class="example"><span class="i1">All free nations are enterprising;<br /></span> +<span class="i0">∴ The Dutch are enterprising.</span></div> + + +<p>In the Third Order—</p> + + +<div class="example"><span class="i0">All free nations are enterprising;<br /></span> +<span class="i0">And the Dutch are a free nation.</span></div></div> + + +<p>It is certainly very common to meet with arguments whose statement may +be represented by one or other of these three forms; indeed, the +Enthymeme is the natural substitute for a full syllogism in oratory: +whence the transition from Aristotle's to the modern meaning of the +term. The most unschooled of men readily apprehend its force; and a +student of Logic can easily supply the proposition that may be wanted in +any case to complete a syllogism, and thereby test the argument's formal +validity. In any Enthymeme of the Third Order, especially, to supply the +conclusion cannot present any difficulty at all; and hence it is a +favourite vehicle of innuendo, as in Hamilton's example:</p> + + +<div class="example"><span class="i0">Every liar is a coward;<br /></span> +<span class="i0">And Caius is a liar.</span></div> + + +<p class="noindent">The frankness of this statement and its reticence, together, make it a +biting sarcasm upon Caius.</p> + +<p>The process of finding the missing premise in an Enthymeme of either the +First or the Second Order, so as to constitute a syllogism, is sometimes +called Reduction; and for this a simple rule may be given: Take that +term of the given premise which does not occur in the conclusion (and +which must therefore be the Middle), and combine it with that term of +the conclusion which does not occur in the given premise; the +proposition thus formed is the premise which was requisite to complete +the Syllogism. If the premise thus constituted contain the predicate of +the conclusion, the Enthymeme was of the First Order; if it <span class='pagenum'>[Pg 141]<a name="Page_141" id="Page_141"></a></span>contain the +subject of the conclusion, the Enthymeme was of the Second Order.</p> + +<p>That a statement in the form of a Hypothetical Proposition may really be +an Enthymeme (as observed in <a href="#chap_5_sect_4">chap. v. § 4</a>) can easily be shown by +recasting one of the above Enthymemes thus: <i>If all free nations are +enterprising, the Dutch are enterprising</i>. Such statements should be +treated according to their true nature.</p> + +<p>To reduce the argument of any ordinary discourse to logical form, the +first care should be to make it clear to oneself what exactly the +conclusion is, and to state it adequately but as succinctly as possible. +Then look for the evidence. This may be of an inductive character, +consisting of instances, examples, analogies; and, if so, of course its +cogency must be evaluated by the principles of Induction, which we +shall presently investigate. But if the evidence be deductive, it will +probably consist of an Enthymeme, or of several Enthymemes one depending +on another. Each Enthymeme may be isolated and expanded into a +syllogism. And we may then inquire: (1) whether the syllogisms are +formally correct according to Barbara (or whatever the appropriate +Mood); (2) whether the premises, or the ultimate premises, are true in +fact.</p> + +<p><a name="chap_11_sect_3" id="chap_11_sect_3"></a>§ 3. A Monosyllogism is a syllogism considered as standing alone or +without relation to other arguments. But, of course, a disputant may be +asking to prove the premises of any syllogism; in which case other +syllogisms may be advanced for that purpose. When the conclusion of one +syllogism is used to prove another, we have a chain-argument which, +stated at full length, is a Polysyllogism. In any Polysyllogism, again, +a syllogism whose conclusion is used as the premise of another, is +called in relation to that other a Prosyllogism; whilst a syllogism one +of whose premises is the conclusion of another syllogism, is in relation +to that other an Episyllogism. Two modes of abbreviating a +Polysyllogism, are usually discussed, the Epicheirema and the Sorites.</p><p><span class='pagenum'>[Pg 142]<a name="Page_142" id="Page_142"></a></span></p> + +<p><a name="chap_11_sect_4" id="chap_11_sect_4"></a>§ 4. An Epicheirema is a syllogism for one or both of whose premises a +reason is added; as—</p> + + +<div class="example"><span class="i1">All men are mortal, for they are animals;<br /></span> +<span class="i1">Socrates is a man, for rational bipeds are men:<br /></span> +<span class="i0">∴ Socrates is mortal.</span></div> + + +<p class="noindent">The Epicheirema is called Single or Double, says Hamilton, according as +an "adscititious proposition" attaches to one or both of the premises. +The above example is of the double kind. The Single Epicheirema is said +to be of the First Order, if the adscititious proposition attach to the +major premise; if to the minor, of the Second Order. (Hamilton's +<i>Logic</i>: Lecture xix.)</p> + +<p>An Epicheirema, then, is an abbreviated chain of reasoning, or +Polysyllogism, comprising an Episyllogism with one or two enthymematic +Prosyllogisms. The major premise in the above case, <i>All men are mortal, +for they are animals,</i> is an Enthymeme of the First Order, suppressing +its own major premise, and may be restored thus:</p> + + +<div class="example"><span class="i1">All animals are mortal;<br /></span> +<span class="i1">All men are animals:<br /></span> +<span class="i0">∴ All men are mortal.</span></div> + + +<p class="noindent">The minor premise, <i>Socrates is a man, for rational bipeds are men</i>, is +an Enthymeme of the Second Order, suppressing its own minor premise, and +may be restored thus:</p> + + +<div class="example"><span class="i1">All rational bipeds are men;<br /></span> +<span class="i1">Socrates is a rational biped:<br /></span> +<span class="i0">∴ Socrates is a man.</span></div> + + +<p><a name="chap_11_sect_5" id="chap_11_sect_5"></a>§ 5. The Sorites is a Polysyllogism in which the Conclusions, and even +some of the Premises, are suppressed until the arguments end. If the +chain of arguments were freed of its enthymematic character, the +suppressed conclusions would appear as premises of Episyllogisms.</p> + +<p>Two varieties of Sorites are recognised, the Aristotelian (so called, +though not treated of by Aristotle), and the<span class='pagenum'>[Pg 143]<a name="Page_143" id="Page_143"></a></span> Goclenian (named after its +discoverer, Goclenius of Marburg, who flourished about 1600 A.D.). In +order to compare these two forms of argument, it will be convenient to +place side by side Hamilton's classical examples of them.</p> + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td> </td><td align='center'>Aristotelian.</td><td> </td><td align='center'>Goclenian.</td></tr> +<tr><td> </td><td align='left'>Bucephalus is a horse;</td><td> </td><td align='left'>An animal is a substance;</td></tr> +<tr><td> </td><td align='left'>A horse is a quadruped;</td><td> </td><td align='left'>A quadruped is an animal;</td></tr> +<tr><td> </td><td align='left'>A quadruped is an animal;</td><td> </td><td align='left'>A horse is a quadruped;</td></tr> +<tr><td> </td><td align='left'>An animal is a substance:</td><td> </td><td align='left'>Bucephalus is a horse:</td></tr> +<tr><td align='left'>∴</td><td align='left'>Bucephalus is a substance.</td><td align='left'>∴</td><td align='left'>Bucephalus is a substance.</td></tr> +</table></div> + +<p class="noindent">The reader wonders what is the difference between these two forms. In +the Aristotelian Sorites the minor term occurs in the first premise, and +the major term in the last; whilst in the Goclenian the major term +occurs in the first premise, and the minor in the last. But since the +character of premises is fixed by their terms, not by the order in which +they are written, there cannot be a better example of a distinction +without a difference. At a first glance, indeed, there may seem to be a +more important point involved; the premises of the Aristotelian Sorites +seem to proceed in the order of Fig. IV. But if that were really so the +conclusion would be, <i>Some Substance is Bucephalus</i>. That, on the +contrary, every one writes the conclusion, <i>Bucephalus is a substance</i>, +proves that the logical order of the premises is in Fig. I. Logically, +therefore, there is absolutely no difference between these two forms, +and pure reason requires either that the "Aristotelian Sorites" +disappear from the text-books, or that it be regarded as in Fig. IV., +and its conclusion converted. It is the shining merit of Goclenius to +have restored the premises of the Sorites to the usual order of Fig. I.: +whereby he has raised to himself a monument more durable than brass, and +secured indeed the very cheapest immortality.</p> + +<p>The common Sorites, then, being in Fig. I., its rules follow from those +of Fig. I:</p><p><span class='pagenum'>[Pg 144]<a name="Page_144" id="Page_144"></a></span></p> + +<p>(1) Only one premise can be particular; and, if any, only that in which +the minor term occurs.</p> + +<p>For, just as in Fig I., a particular premise anywhere else involves +undistributed Middle.</p> + +<p>(2) Only one premise can be negative; and, if any, only that in which +the major term occurs.</p> + +<p>For if there were two negative premises, at the point where the second +entered the chain of argument there must be a syllogism with two +negative premises, which is contrary to Rule 5; whilst if one premise be +negative it must be that which contains the major term, for the same +reason as in Fig. I., namely, that the conclusion will be negative, and +that therefore only a negative major premise can prevent illicit process +of the major term.</p> + +<p>If we expand a Sorites into its constituent syllogisms, the conclusions +successively suppressed will reappear as major premises; thus:</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='left'>(1)</td><td align='left'>An animal is a substance;</td></tr> +<tr><td align='left'></td><td align='left'>A quadruped is an animal:</td></tr> +<tr><td align='left'>∴</td><td align='left'>A quadruped is a substance.</td></tr> +<tr><td align='left'>(2)</td><td align='left'>A quadruped is a substance;</td></tr> +<tr><td align='left'></td><td align='left'>A horse is a quadruped:</td></tr> +<tr><td align='left'>∴</td><td align='left'>A horse is a substance.</td></tr> +<tr><td align='left'>(3)</td><td align='left'>A horse is a substance:</td></tr> +<tr><td align='left'></td><td align='left'>Bucephalus is a horse:</td></tr> +<tr><td align='left'>∴</td><td align='left'>Bucephalus is a substance.</td></tr> +</table></div> + + +<p>This suffices to show that the Protosyllogism of a Goclenian Sorites is +an Enthymeme of the Third Order; after which the argument is a chain of +Enthymemes of the First Order, or of the First and Third combined, since +the conclusions as well as the major premises are omitted, except in the +last one.</p> + +<p>Lest it should be thought that the Sorites is only good for arguments so +frivolous as the above, I subjoin an example collected from various +parts of Mill's <i>Political Economy</i>:—</p><p><span class='pagenum'>[Pg 145]<a name="Page_145" id="Page_145"></a></span></p> + + +<div class="example"><span class="i1">The cost of labour depends on the efficiency of labour;<br /></span> +<span class="i1">The rate of profits depends on the cost of labour;<br /></span> +<span class="i1">The investment of capital depends on the rate of profits;<br /></span> +<span class="i1">Wages depend on the investment of capital:<br /></span> +<span class="i0">∴ Wages depend on the efficiency of labour.</span></div> + + +<p class="noindent">Had it occurred to Mill to construct this Sorites, he would have +modified his doctrine of the wages-fund, and would have spared many +critics the malignant joy of refuting him.</p> + +<p><a name="chap_11_sect_6" id="chap_11_sect_6"></a>§ 6. The Antinomy is a combination of arguments by which contradictory +attributes are proved to be predicable of the same subject. In symbols, +thus:</p> + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='left'></td><td align='left'>All M is P;</td><td align='left'></td><td align='left'>All N is p;</td></tr> +<tr><td align='left'></td><td align='left'>All S is M:</td><td align='left'></td><td align='left'>All S is N:</td></tr> +<tr><td align='left'>∴</td><td align='left'>All S is P.</td><td align='left'>∴</td><td align='left'>All S is p.</td></tr> +</table></div> + +<p class="noindent">Now, by the principle of Contradiction, S cannot be P and p (not-P): +therefore, if both of the above syllogisms are sound, S, as the subject +of contradictory attributes, is logically an impossible thing. The +contradictory conclusions are called, respectively, Thesis and +Antithesis.</p> + +<p>To come to particulars, we may argue: (1) that a constitution which is +at once a monarchy, an aristocracy and a democracy, must comprise the +best elements of all three forms; and must, therefore, be the best of +all forms of government: the British Constitution is, therefore, the +best of all. But (2) such a constitution must also comprise the worst +elements of monarchy, aristocracy and democracy; and, therefore, must be +the worst of all forms. Are we, then, driven to conclude that the +British Constitution, thus proved to be both the best and worst, does +not really exist at all, being logically impossible? The proofs seem +equally cogent; but perhaps neither the best nor the worst elements of +the simpler constitutions need be present in our own in sufficient force +to make it either good or bad.</p><p><span class='pagenum'>[Pg 146]<a name="Page_146" id="Page_146"></a></span></p> + +<p>Again:</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='left'>(1)</td><td align='left'>Every being who is responsible for his actions is free;</td></tr> +<tr><td align='left'></td><td align='left'>Man is responsible for his actions:</td></tr> +<tr><td align='left'>∴</td><td align='left'>Man is free.</td></tr> +<tr><td align='left'>(2)</td><td align='left'>Every being whose actions enter into the course of nature is not free;</td></tr> +<tr><td align='left'></td><td align='left'>Man is such a being:</td></tr> +<tr><td align='left'>∴</td><td align='left'>Man is not free.</td></tr> +</table></div> + + +<p class="noindent">Does it, then, follow that 'Man,' as the subject of contradictory +attributes, is a nonentity? This doctrine, or something like it, has +been seriously entertained; but if to any reader it seem extravagant (as +it certainly does to me), he will no doubt find an error in the above +arguments. Perhaps the major term is ambiguous.</p> + +<p>For other examples it is enough to refer to the <i>Critique of Pure +Reason</i>, where Kant sets out the Antinomies of Rational Cosmology. But +even if we do not agree with Kant that the human understanding, in +attempting to deal with certain subjects beyond its reach, inevitably +falls into such contradictory reasonings; yet it can hardly be doubted +that we not unfrequently hold opinions which, if logically developed, +result in Antinomies. And, accordingly, the Antinomy, if it cannot be +imputed to Reason herself, may be a very fair, and a very wholesome +<i>argumentum ad hominem</i>. It was the favourite weapon of the Pyrrhonists +against the dogmatic philosophies that flourished after the death of +Aristotle.</p><p><span class='pagenum'>[Pg 147]<a name="Page_147" id="Page_147"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_XII" id="CHAPTER_XII"></a>CHAPTER XII</h2> + +<h3>CONDITIONAL SYLLOGISMS</h3> + + +<p><a name="chap_12_sect_1" id="chap_12_sect_1"></a>§ 1. Conditional Syllogisms may be generally described as those that +contain conditional propositions. They are usually divided into two +classes, Hypothetical and Disjunctive.</p> + +<p>A Hypothetical Syllogism is one that consists of a Hypothetical Major +Premise, a Categorical Minor Premise, and a Categorical Conclusion. Two +Moods are usually recognised the <i>Modus ponens</i>, in which the antecedent +of the hypothetical major premise is affirmed; and the <i>Modus tollens</i>, +in which its consequent is denied.</p> + +<p>(1) <i>Modus ponens</i>, or Constructive.</p> + + +<div class="example"><span class="i0">If A is B, C is D;<br /></span> +<span class="i1">A is B:<br /></span> +<span class="i0">∴ C is D.</span></div> + + +<p>If Aristotle's reasoning is conclusive, Plato's theory of Ideas is +erroneous;</p> + + +<div class="example"><span class="i1">Aristotle's reasoning is conclusive:<br /></span> +<span class="i0">∴ Plato's theory of Ideas is erroneous.</span></div> + + +<p>Rule of the <i>Modus ponens</i>: The antecedent of the major premise being +affirmed in the minor premise, the consequent is also affirmed in the +conclusion.</p> + +<p>(2) <i>Modus tollens</i>, or Destructive.</p> + + +<div class="example"><span class="i0">If A is B, C is D;<br /></span> +<span class="i1">C is not D:<br /></span> +<span class="i0">∴ A is not B.</span></div> +<p><span class='pagenum'>[Pg 148]<a name="Page_148" id="Page_148"></a></span></p> +<div class="example"><span class="i0">If Pythagoras is to be trusted, Justice is a number;<br /></span> +<span class="i1">Justice is not a number:<br /></span> +<span class="i0">∴ Pythagoras is not to be trusted.</span></div> + + +<p>Rule of the <i>Modus tollens</i>: The consequent of the major premise being +denied in the minor premise, the antecedent is denied in the conclusion.</p> + +<p>By using negative major premises two other forms are obtainable: then, +either by affirming the antecedent or by denying the consequent, we draw +a negative conclusion.</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'>Thus (<i>Modus ponens</i>):</td><td align='center'>(<i>Modus tollens</i>):</td></tr> +<tr><td align='left'>If A is B, C is not D;</td><td align='left'>If A is B, C is not D;</td></tr> +<tr><td align='left'><span style="margin-left: 1em;">A is B:</span></td><td align='left'><span style="margin-left: 1em;">C is D:</span></td></tr> +<tr><td align='left'>∴ C is not D.</td><td align='left'>∴ A is not B.</td></tr> +</table></div> + + +<p>Further, since the antecedent of the major premise, taken by itself, may +be negative, it seems possible to obtain four more forms, two in each +Mood, from the following major premises:</p> + + +<div class="example"><span class="i0">(1) If A is not B, C is D;<br /></span> +<span class="i0">(2) If A is not B, C is not D.</span></div> + + +<p class="noindent">But since the quality of a Hypothetical Proposition is determined by the +quality of its consequent, not at all by the quality of its antecedent, +we cannot get from these two major premises any really new Moods, that +is to say, Moods exhibiting any formal difference from the four +previously expounded.</p> + +<p>It is obvious that, given the hypothetical major premise—</p> + + +<div class="example"><span class="i0">If A is B, C is D—</span></div> + + +<p class="noindent">we cannot, by denying the antecedent, infer a denial of the consequent. +That A is B, is a mark of C being D; but we are not told that it is the +sole and indispensable condition of it. If men read good books, they +acquire knowledge; but they may acquire knowledge by other means, as by +<span class='pagenum'>[Pg 149]<a name="Page_149" id="Page_149"></a></span>observation. For the same reason, we cannot by affirming the consequent +infer the affirmation of the antecedent: Caius may have acquired +knowledge; but we cannot thence conclude that he has read good books.</p> + +<p>To see this in another light, let us recall <a href="#chap_5_sect_4">chap. v. § 4</a>, where it was +shown that a hypothetical proposition may be translated into a +categorical one; whence it follows that a Hypothetical Syllogism may be +translated into a Categorical Syllogism. Treating the above examples +thus, we find that the <i>Modus ponens</i> (with affirmative major premise) +takes the form of Barbara, and the <i>Modus tollens</i> the form of +Camestres:</p> + + + +<div class='center'> +<table border="0" cellpadding="6" cellspacing="0" summary=""> +<tr><td align='center'><i>Modus ponens.</i></td><td align='center'>Barbara.</td></tr> +<tr><td align='left'>If A is B, C is D;</td><td align='left'>The case of A being B is a case of C being D;</td></tr> +<tr><td align='left'><span style="margin-left: 1em;">A is B:</span></td><td align='left'><span style="margin-left: 1em;">This is a case of A being B:</span></td></tr> +<tr><td align='left'> ∴ C is D.</td><td align='left'>∴ This is a case of C being D.</td></tr> +</table></div> + + +<p>Now if, instead of this, we affirm the consequent, to form the new minor +premise,</p> + + +<div class="example"><span class="i0">This is a case of C being D,</span></div> + + +<p class="noindent">there will be a Syllogism in the Second Figure with two affirmative +premises, and therefore the fallacy of undistributed Middle. Again:</p> + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'><i>Modus tollens.</i></td><td align='center'>Camestres.</td></tr> +<tr><td align='left'>If A is B, C is D;</td><td align='left'>The case of A being B is a case of C being D:</td></tr> +<tr><td align='left'><span style="margin-left: 1em;">C is not D:</span></td><td align='left'><span style="margin-left: 1em;">This is not a case of C being D:</span></td></tr> +<tr><td align='left'> ∴ A is not B.</td><td align='left'>∴ This is not a case of A being B.</td></tr> +</table></div> + +<p class="noindent">But if, instead of this, we deny the antecedent, to form the new minor +premise,</p> + + +<div class="example"><span class="i0">This is not a case of A being B,</span></div> + + +<p class="noindent"><span class='pagenum'>[Pg 150]<a name="Page_150" id="Page_150"></a></span>there arises a syllogism in the First Figure with a negative minor +premise, and therefore the fallacy of illicit process of the major term.</p> + +<p>By thus reducing the Hypothetical Syllogism to the Categorical form, +what is lost in elegance is gained in intelligibility. For, first, we +may justify ourselves in speaking of the hypothetical premise as the +major, and of the categorical premise as the minor; since in the +categorical form they contain respectively the major and minor terms. +And, secondly, we may justify ourselves in treating the Hypothetical +Syllogism as a kind of Mediate Inference, in spite of the fact that it +does not exhibit two terms compared by means of a third; since in the +Categorical form such terms distinctly appear: a new term ('This') +emerges in the position of the minor; the place of the Middle is filled +by the antecedent of the major premise in the <i>Modus ponens</i>, and by the +consequent in the <i>Modus tollens</i>.</p> + +<p>The mediate element of the inference in a Hypothetical Syllogism +consists in asserting, or denying, the fulfilment of a given condition; +just as in a Categorical syllogism to identify the minor term with the +Middle is a condition of the major term's being predicated of it. In the +hypothetical proposition—</p> + + +<div class="example"><span class="i0">If A is B, C is D—</span></div> + + +<p class="noindent">the Antecedent, <i>A is B</i>, is the <i>conditio sufficiens</i>, or mark, of the +Consequent, <i>C is D</i>; and therefore the Consequent, <i>C is D</i>, is a +<i>conditio sine qua non</i> of the antecedent, <i>A is B</i>; and it is by means +of affirming the former condition, or else denying the latter, that a +conclusion is rendered possible.</p> + +<p>Indeed, we need not say that the element of mediation consists in +affirming, <i>or denying</i>, the fulfilment of a given condition: it is +enough to say 'in affirming.' For thus to explain the <i>Modus tollens</i>, +reduce it to the <i>Modus ponens</i> (contrapositing the major premise and +obverting the minor):</p><p><span class='pagenum'>[Pg 151]<a name="Page_151" id="Page_151"></a></span></p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='left'></td><td align='center'>Celarent.</td></tr> +<tr><td align='left'><span style="margin-left: 1em;">If A is B, C is D:</span></td><td align='left'>The case of C being not-D is</td></tr> +<tr><td align='left'>∴ If C is not-D, A is not B;</td><td align='left'><span style="margin-left: 2em;">not a case of A being B;</span></td></tr> +<tr><td align='left'><span style="margin-left: 1em;">C is not-D:</span></td><td align='left'>This is a case of C being not-D:</td></tr> +<tr><td align='left'>∴ A is not B.</td><td align='left'>∴ This is not a case of A being B.</td></tr> +</table></div> + + +<p>The above four forms commonly treated of as Hypothetical Syllogisms, are +called by Ueberweg and Dr. Keynes 'Hypothetico-Categorical.' Ueberweg +restricts the name 'Hypothetical' simply (and Dr. Keynes the name +'Conditional') to such Syllogisms as the following, having two +Hypothetical Premises:</p> + + +<div class="example"><span class="i1">If C is D, E is F;<br /></span> +<span class="i1">If A is B, C is D:<br /></span> +<span class="i0">∴ If A is B, E is F.</span></div> + + +<p class="noindent">If we recognise particular hypothetical propositions (see <a href="#chap_5_sect_4">chap. v. § 4</a>), +it is obvious that such Syllogisms may be constructed in all the Moods +and Figures of the Categorical Syllogism; and of course they may be +translated into Categoricals. We often reason in this hypothetical way. +For example:</p> + + +<div class="example"><span class="i1">If the margin of cultivation be extended, rents will rise;<br /></span> +<span class="i1">If prices of produce rise, the margin of cultivation will be extended:<br /></span> +<span class="i0">∴ If prices of produce rise, rents will rise.</span></div> + + +<p>But the function of the Hypothetical Syllogism (commonly so called), as +also of the Disjunctive Syllogism (to be discussed in the next section) +is to get rid of the conditional element of the premises, to pass from +suspense to certainty, and obtain a decisive categorical conclusion; +whereas these Syllogisms with two hypothetical premises leave us still +with a hypothetical conclusion. This circumstance seems to ally them +more closely with Categorical<span class='pagenum'>[Pg 152]<a name="Page_152" id="Page_152"></a></span> Syllogisms than with those that are +discussed in the present chapter. That they are Categoricals in disguise +may be seen by considering that the above syllogism is not materially +significant, unless in each proposition the word 'If' is equivalent to +'Whenever.' Accordingly, the name 'Hypothetical Syllogism,' is here +employed in the older usage.</p> + +<p><a name="chap_12_sect_2" id="chap_12_sect_2"></a>§ 2. A Disjunctive Syllogism consists of a Disjunctive Major Premise, a +Categorical Minor Premise, and a Categorical Conclusion.</p> + +<p>How many Moods are to be recognised in this kind of argument depends on +whether the alternatives of the Disjunctive Premise are regarded as +mutually exclusive or possibly coincident. In saying '<i>Either</i> A is B, +<i>or</i> C is D,' do we mean 'either, but not both,' or 'either, it may be +both'? (See <a href="#chap_5_sect_4">chap. v. § 4</a>.)</p> + +<p>When the alternatives of the Disjunctive are not exclusive, we have only +the</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center' colspan="4"><i>Modus tollendo ponens.</i></td></tr> +<tr><td align='left'>Either</td><td align='left'>A is B, or</td><td align='left'>C is D;</td></tr> +<tr><td align='left'></td><td align='left'>A is not B</td><td align='left'>(or C is not D):</td></tr> +<tr><td align='right'>∴</td><td align='left'> C is D</td><td align='left'>(or A is B).</td></tr> +</table></div> + +<div class="blockquot"><p>Either wages fall, or the weaker hands are dismissed;</p> + +<div class="example"><span class="i1">Wages do not fall:<br /></span> +<span class="i0">∴ The weaker hands are dismissed.</span></div></div> + + +<p class="noindent">But we cannot argue—</p> + + +<div class="example"><span class="i1">Wages fall:<br /></span> +<span class="i0">∴ The weaker hands are not dismissed;</span></div> + + +<p class="noindent">since in 'hard times' both events may happen together.</p> + +<p>Rule of the <i>Modus tollendo ponens</i>: If one alternative be denied, the +other is affirmed.</p> + +<p>When, however, the alternatives of the Disjunctive are mutually +exclusive, we have also the</p> + +<p><span class='pagenum'>[Pg 153]<a name="Page_153" id="Page_153"></a></span></p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center' colspan="3"><i>Modus ponendo tollens.</i></td></tr> +<tr><td align='right'>Either</td><td align='left'>A is B, or C is D;</td></tr> +<tr><td align='left'></td><td align='left'>A is B (or C is D):</td></tr> +<tr><td align='right'>∴</td><td align='left'>C is not D (or A is not B).</td></tr> +</table></div> + +<div class="blockquot"><p>Either the Tories or the Whigs win the election;</p> + +<div class="example"><span class="i1">The Tories win:<br /></span> +<span class="i0">∴ The Whigs do not win.</span></div></div> + + +<p>We may also, of course, argue as above in the <i>Modus tollendo ponens</i>—</p> + + +<div class="example"><span class="i1">The Tories do not win:<br /></span> +<span class="i0">∴ The Whigs do.</span></div> + + +<p class="noindent">But in this example, to make the <i>Modus tollendo ponens</i> materially +valid, it must be impossible that the election should result in a tie. +The danger of the Disjunctive Proposition is that the alternatives may +not, between them, exhaust the possible cases. Only contradictory +alternatives are sure to cover the whole ground.</p> + +<p>Rule of the <i>Modus ponendo tollens:</i> If one alternative be affirmed, the +other is denied.</p> + +<p>Since a disjunctive proposition may be turned into a hypothetical +proposition (<a href="#chap_5_sect_4">chap. v. § 4</a>,) a Disjunctive Syllogism may be turned into a +Hypothetical Syllogism:</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'><i>Modus tollendo ponens.</i></td><td align='center'><i>Modus ponens</i>.</td></tr> +<tr><td align='left'>Either A is B, or C is D;</td><td align='left'>If A is not B, C is D;</td></tr> +<tr><td align='left'><span style="margin-left: 3em;">A is not B:</span></td><td align='left'><span style="margin-left: 1em;">A is not B:</span></td></tr> +<tr><td align='left'><span style="margin-left: 2em;">∴ C is D.</span></td><td align='left'>∴ C is D.</td></tr> +</table></div> + + +<p class="noindent">Similarly the <i>Modus ponendo tollens</i> is equivalent to that kind of +<i>Modus ponens</i> which may be formed with a negative major premise; for if +the alternatives of a disjunctive proposition be exclusive, the +corresponding hypothetical be affirmative or negative:</p><p><span class='pagenum'>[Pg 154]<a name="Page_154" id="Page_154"></a></span></p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'><i>Modus ponendo tollens.</i></td><td align='center'><i>Modus ponens.</i></td></tr> +<tr><td align='left'>Either A is B, or C is D;</td><td align='left'>If A is B, C is not D;</td></tr> +<tr><td align='left'><span style="margin-left: 3em;">A is B:</span></td><td align='left'><span style="margin-left: 1em;">A is B:</span></td></tr> +<tr><td align='left'><span style="margin-left: 2em;">∴ C is not D.</span></td><td align='left'>∴ C is not D.</td></tr> +</table></div> + + +<p class="noindent">Hence, finally, a Disjunctive Syllogism being equivalent to a +Hypothetical, and a Hypothetical to a Categorical; a Disjunctive +Syllogism is equivalent and reducible to a Categorical. It is a form of +Mediate Inference in the same sense as the Hypothetical Syllogism is; +that is to say, the conclusion depends upon an affirmation, or denial, +of the fulfilment of a condition implied in the disjunctive major +premise.</p> + +<p><a name="chap_12_sect_3" id="chap_12_sect_3"></a>§ 3. The Dilemma is perhaps the most popularly interesting of all forms +of proof. It is a favourite weapon of orators and wits; and "impaled +upon the horns of a dilemma" is a painful situation in which every one +delights to see his adversary. It seems to have been described by +Rhetoricians before finding its way into works on Logic; and Logicians, +to judge from their diverse ways of defining it, have found some +difficulty in making up their minds as to its exact character.</p> + +<p>There is a famous Dilemma employed by Demosthenes, from which the +general nature of the argument may be gathered:</p> + +<div class="example"><span class="i0">If Æschines joined in the public rejoicings, he is +inconsistent; if he did not, he is unpatriotic;<br /></span> +<span class="i0">But either he joined, or he did not join:<br /></span> +<span class="i0">Therefore he is either inconsistent or unpatriotic.</span></div> + +<p class="noindent">That is, reduced to symbols:</p> + + +<div class="example"><span class="i0">If A is B, C is D; and if E is F, G is H:<br /></span> +<span class="i1">But either A is B, or E is F;<br /></span> +<span class="i0">∴ Either C is D or G is H (<i>Complex Constructive</i>).</span></div> + + +<p class="noindent">This is a compound Conditional Syllogism, which may be analysed as +follows:</p><p><span class='pagenum'>[Pg 155]<a name="Page_155" id="Page_155"></a></span></p> + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center' colspan="2">Either A is B or E is F.</td></tr> +<tr><td align='left'>Suppose that E is not F:</td><td align='left'>Suppose that A is not B:</td></tr> +<tr><td align='left'>Then A is B.</td><td align='left'>Then E is F.</td></tr> +<tr><td align='left'>But if A is B, C is D;</td><td align='left'>But if E is F, G is H;</td></tr> +<tr><td align='left'><span style="margin-left: 2em;">(A is B):</span></td><td align='left'><span style="margin-left: 2em;">(E is F):</span></td></tr> +<tr><td align='left'><span style="margin-left: 1em;">∴ C is D.</span></td><td align='left'><span style="margin-left: 1em;">∴ G is H.</span></td></tr> +<tr><td align='center' colspan='2'>∴ Either C is D or G is H.</td></tr> +</table></div> + +<p>A Dilemma, then, is a compound Conditional Syllogism, having for its +Major Premise two Hypothetical Propositions, and for its Minor Premise a +Disjunctive Proposition, whose alternative terms either affirm the +Antecedents or deny the Consequents of the two Hypothetical Propositions +forming the Major Premise.</p> + +<p>The hypothetical propositions in the major premise, may have all four +terms distinct (as in the above example); and then the conclusion is a +disjunctive proposition, and the Dilemma is said to be Complex. Or the +two hypothetical propositions may have a common antecedent or a common +consequent; and then the conclusion is a categorical proposition, and +the Dilemma is said to be Simple.</p> + +<p>Again, the alternatives of the disjunctive minor premise may be +affirmative or negative: if affirmative, the Dilemma is called +Constructive; and if negative, Destructive.</p> + +<p>Using, then, only affirmative hypothetical propositions in the major +premise, there are four Moods:</p> + +<p>1. The Simple Constructive—</p> + + +<div class="example"><span class="i0">If A is B, C is D; and if E is F, C is D:<br /></span> +<span class="i1">But either A is B, or E is F:<br /></span> +<span class="i0">∴ C is D.<br /></span></div> + +<div class="example"><span class="i1">If the Tories win the election, the Government will avoid +innovation; and if the Whigs win, the House of Lords will +prevent them innovating:<br /></span> +<span class="i1">But either the Tories or the Whigs will win:<br /></span> +<span class="i0">∴ There will be no innovation.</span></div> + +<p><span class='pagenum'>[Pg 156]<a name="Page_156" id="Page_156"></a></span>2. The Complex Constructive—</p> + + +<div class="example"><span class="i0">If A is B, C is D; and if E is F, G is H:<br /></span> +<span class="i1">But either A is B, or E is F:<br /></span> +<span class="i0">∴ Either C is D or G is H.</span></div> + + +<div class="example"><span class="i1">If appearance is all that exists, reality is a delusion; and +if there is a substance beyond consciousness, knowledge of +reality is impossible:<br /></span> + +<span class="i1">But either appearance is all, or there is a substance beyond +consciousness:<br /></span> + +<span class="i0">∴ Either reality is a delusion, or a knowledge of it is +impossible.</span></div> + +<p>3. Simple Destructive—</p> + + +<div class="example"><span class="i0">If A is B, C is D; and if A is B, E is F:<br /></span> +<span class="i1">But either C is not D, or E is not F:<br /></span> +<span class="i0">∴ A is not B.</span></div> + + +<div class="example"><span class="i1">If table-rappers are to be trusted, the departed are spirits; +and they also exert mechanical energy<br />:</span> + +<span class="i1">But either the departed are not spirits, or they do not exert +mechanical energy:<br /></span> + +<span class="i0">∴ Table-rappers are not to be trusted.</span></div> + +<p>4. Complex Destructive—</p> + + +<div class="example"><span class="i0">If A is B, C is D; and if E is F, G is H:<br /></span> +<span class="i1">But either C is not D, or G is not H:<br /></span> +<span class="i0">∴ Either A is not B, or E is not F.</span></div> + + +<div class="example"><span class="i1">If poetic justice is observed, virtue is rewarded; and if the +mirror is held up to Nature, the villain triumphs:<br /></span> + +<span class="i1">But either virtue is not rewarded, or the villain does not +triumph:<br /></span> + +<span class="i0">∴ Either poetic justice is not observed, or the mirror is not +held up to Nature.</span></div> + +<p>Such are the four Moods of the Dilemma that emerge if we only use +affirmative hypotheticals for the major premise; but, certainly, it is +often quite as natural to <span class='pagenum'>[Pg 157]<a name="Page_157" id="Page_157"></a></span>employ two negative hypotheticals (indeed, +one might be affirmative and the other negative; but waive that); and +then four more moods emerge, all having negative conclusions. It is +needless to intimidate the reader by drawing up these four moods in +battle array: they always admit of reduction to the foregoing moods by +obverting the hypotheticals. Still, by the same process we may greatly +decrease the number of moods of the Categorical Syllogism; and just as +some Syllogisms are most simply expressed in Celarent or Cesare, so some +Dilemmas are most simply stated with negative major premises—<i>e.g.</i>, +The example of a Simple Constructive Dilemma above given would run more +naturally thus: <i>If the Tories win, the Government will not innovate; +and if the Whigs, the Lords will not let them</i>: and similarly +Demosthenes' Dilemma—<i>If Æschines joined, he is not consistent; and if +he did not, he is not patriotic</i>. Moreover, the propriety of recognising +Dilemmas with negative major premises, follows from the above analysis +of the Dilemma into a combination of Conditional Syllogisms, even if (as +in <a href="#chap_12_sect_1">§ 1</a> of this chapter) we take account of only four Moods of the +Hypothetical Syllogism.</p> + +<p>In the rhetorical use of the Dilemma, it may be observed that the +disjunction in the minor premise ought to be obvious, or (at any rate) +easily acceptable to the audience. Thus, <i>Either the Tories or the Whigs +will win; Either Æschines joined in the rejoicings, or he did not</i>; such +propositions are not likely to be disputed. But if the orator must stop +to prove his minor premise, the smacking effect of this figure (if the +expression be allowed) will be lost. Hence the minor premises of other +examples given above are only fit for a select audience. That <i>Either +ghosts are not spirits, or they do not exert mechanical energy</i>, +supposes a knowledge of the principle, generally taught by physical +philosophers, that only matter is the vehicle of energy; and that +<i>Either appearance is all, or there is substance beyond consciousness</i>, +is a doctrine which only metaphysical <span class='pagenum'>[Pg 158]<a name="Page_158" id="Page_158"></a></span>philosophers could be expected to +understand, and upon which they could not be expected to agree. However, +the chief danger is that a plausible disjunction may not be really such +as to exclude any middle ground: <i>Either the Tories or the Whigs win</i>, +is bad, if a tie be possible; though in the above argument this is +negligible, seeing that a tie cannot directly cause innovations. <i>Either +Æschines joined in the rejoicings, or he did not</i>, does not allow for a +decent conformity with the public movement where resistance would be +vain; yet such conformity as need not be inconsistent with subsequent +condemnation of the proceedings, nor incompatible with patriotic reserve +founded on a belief that the rejoicings are premature and ominous.</p> + +<p>Another rhetorical consideration is, that the alternatives of the +disjunctive conclusion of a Complex Dilemma should both point the same +way, should be equally distasteful or paradoxical. 'Either inconsistent +or unpatriotic': horrid words to a politician! 'Either no reality or no +possible knowledge of it': very disappointing to an anxious inquirer! +Thus the disjunctive conclusion is as bad for an opponent as the +categorical one in a Simple Dilemma.</p> + +<p>Logicians further speak of the Trilemma, with three Hypotheticals and a +corresponding triple Disjunction; and of a Polylemma, with any further +number of perplexities. But anyone who has a taste for logical forms may +have it amply gratified in numerous text-books.</p><p><span class='pagenum'>[Pg 159]<a name="Page_159" id="Page_159"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_XIII" id="CHAPTER_XIII"></a>CHAPTER XIII</h2> + +<h3>TRANSITION TO INDUCTION</h3> + + +<p><a name="chap_13_sect_1" id="chap_13_sect_1"></a>§ 1. Having now discussed Terms, Propositions, Immediate and Mediate +Inferences, and investigated the conditions of formal truth or +consistency, we have next to consider the conditions of material truth: +whether (or how far) it is possible to arrive at propositions that +accurately represent the course of nature or of human life. Hitherto we +have dealt with no sort of proof that gives any such assurance. A valid +syllogism guarantees the truth of its conclusion, provided the premises +be true: but what of the premises? The relation between the premises of +a valid syllogism and its conclusion is the same as the relation between +the antecedent and consequent of a hypothetical proposition. If A is B, +C is D: grant that A is B, and it follows that C is D; and, similarly, +grant the premises of a syllogism, and the conclusion follows. Again, +grant that C is not D, and it follows that A is not B; and, similarly, +if the conclusion of a valid syllogism be false, it follows that one, or +other, or both of the premises must be false. But, once more, grant that +C is D, and it does not follow that A is B; so neither, if the +conclusion of a syllogism be true, does it follow that the premises are. +For example:—</p> + + +<div class="example"><span class="i1">Sociology is an exact science;<br /></span> +<span class="i1">Mathematics is a branch of Sociology:<br /></span> +<span class="i0">∴ Mathematics is an exact science.</span></div> + + +<p class="noindent"><span class='pagenum'>[Pg 160]<a name="Page_160" id="Page_160"></a></span>Here the conclusion is true although the premises are absurd. Or +again:—</p> + + +<div class="example"><span class="i1">Mathematics is an exact science;<br /></span> +<span class="i1">Sociology is a branch of Mathematics:<br /></span> +<span class="i0">∴ Sociology is an exact science.</span></div> + + +<p class="noindent">Here the major premise is true, but the minor is false, and the +conclusion is false. In both cases, however, whether the conclusion be +true or false, it equally follows from the premises, if there is any +cogency in Barbara. The explanation of this is, that Barbara has only +formal cogency; and that whether the conclusion of that, or any other +valid mood, shall be true according to fact and experience, depends upon +how the form is filled up. How to establish the premises, then, is a +most important problem; and it still remains to be solved.</p> + +<p><a name="chap_13_sect_2" id="chap_13_sect_2"></a>§ 2. We may begin by recalling the distinction between the denotation +and connotation of a general term: the denotation comprising the things +or events which the term is a name for; the connotation comprising the +common qualities on account of which these things are called by the same +name. Obviously, there are very few general terms whose denotation is +exhaustively known; since the denotation of a general term comprises all +the things that have its connotation, or that ever have had, or that +ever will have it, whether they exist here, or in Australia, or in the +Moon, or in the utmost stars. No one has examined all men, all mammoths, +all crystals, all falling bodies, all cases of fever, all revolutions, +all stars—nor even all planets, since from time to time new ones are +discerned. We have names for animals that existed long before there were +men to observe them, and of which we know only a few bones, the remains +of multitudinous species; and for others that may continue to exist when +men have disappeared from the earth.</p> + +<p>If, indeed, we definitely limit the time, or place, or <span class='pagenum'>[Pg 161]<a name="Page_161" id="Page_161"></a></span>quantity of +matter to be explored, we may sometimes learn, within the given limits, +all that there is to know: as all the bones of a particular animal, or +the list of English monarchs hitherto, or the names of all the members +of the House of Commons at the present time. Such cases, however, do not +invalidate the above logical truth that few general terms are +exhaustively known in their denotation; for the very fact of assigning +limits of time and place impairs the generality of a term. The bones of +a certain animal may be all examined, but not the bones of all animals, +nor even of one species. The English monarchs that have reigned hitherto +may be known, but there may be many still to reign.</p> + +<p>The general terms, then, with which Logic is chiefly concerned, the +names of Causes and Kinds, such as gravitation, diseases, social events, +minerals, plants and animals, stand for some facts that are, or have +been, known, and for a great many other similar ones that have not been, +and never will be, known. The use of a general term depends not upon our +direct knowledge of everything comprised in its denotation, but upon our +readiness to apply it to anything that has its connotation, whether we +have seen the thing or not, and even though we never can perceive it; as +when a man talks freely of the ichthyosaurus, or of the central heat of +planets, or of atoms and ether.</p> + +<p>Hence Universal Propositions, which consist of general terms, deceive +us, if we suppose that their predicates are directly known to be related +to all the facts denoted by their subjects. In exceptional cases, in +which the denotation of a subject is intentionally limited, such +exhaustive direct knowledge may be possible; as that "all the bones of a +certain animal consist of phosphate of lime," or that every member of +the present Parliament wears a silk hat. But what predication is +possible concerning the hats of all members of Parliament from the +beginning? Ordinarily, then, whilst the relation of predicate to subject +has been <span class='pagenum'>[Pg 162]<a name="Page_162" id="Page_162"></a></span>observed in some cases, in much the greater number of cases +our belief about it depends upon something besides observation, or may +be said (in a certain sense) to be taken on trust.</p> + +<p>'All rabbits are herbivorous': why do we believe that? We may have seen +a few wild rabbits feeding: or have kept tame ones, and tried +experiments with their diet; or have read of their habits in a book of +Natural History; or have studied the anatomy and physiology of the +digestive system in many sorts of animals: but with whatever care we add +testimony and scientific method to our own observation, it still remains +true that the rabbits observed by ourselves and others are few in +comparison with those that live, have lived and will live. Similarly of +any other universal proposition; that it 'goes beyond the evidence' of +direct observation plainly follows from the fact that the general terms, +of which such propositions consist, are never exhaustively known in +their denotation. What right have we then to state Universal +Propositions? That is the problem of Inductive Logic.</p> + +<p><a name="chap_13_sect_3" id="chap_13_sect_3"></a>§ 3. Universal Propositions, of course, cannot always be proved by +syllogisms; because to prove a universal proposition by a syllogism, its +premises must be universal propositions; and, then, these must be proved +by others. This process may sometimes go a little way, thus: <i>All men +are mortal</i>, because <i>All animals are</i>; and <i>All animals are mortal</i>, +because <i>All composite bodies are subject to dissolution.</i> Were there no +limit to such sorites, proof would always involve a <i>regressus ad +infinitum</i>, for which life is too short; but, in fact, prosyllogisms +soon fail us.</p> + +<p>Clearly, the form of the Syllogism must itself be misleading if the +universal proposition is so: if we think that premises prove the +conclusion because they themselves have been established by detailed +observation, we are mistaken. The consideration of any example will show +this. Suppose any one to argue:</p><p><span class='pagenum'>[Pg 163]<a name="Page_163" id="Page_163"></a></span></p> + + +<div class="example"><span class="i1">All ruminants are herbivorous;<br /></span> +<span class="i1">Camels are ruminants:<br /></span> +<span class="i0">∴ Camels are herbivorous.</span></div> + + +<p class="noindent">Have we, then, examined all ruminants? If so, we must have examined all +camels, and cannot need a syllogism to prove their herbivorous nature: +instead of the major premise proving the conclusion, the proof of the +conclusion must then be part of the proof of the major premise. But if +we have not examined all ruminants, having omitted most giraffes, most +deer, most oxen, etc., how do we know that the unexamined (say, some +camels) are not exceptional? Camels are vicious enough to be +carnivorous; and indeed it is said that Bactrian camels will eat flesh +rather than starve, though of course their habit is herbivorous.</p> + +<p>Or, again, it is sometimes urged that—</p> + + +<div class="example"><span class="i1">All empires decay:</span> +<span class="i0">∴ Britain will decay.</span></div> + + +<p class="noindent">This is manifestly a prediction: at present Britain flourishes, and +shows no signs of decay. Yet a knowledge of its decay seems necessary, +to justify any one in asserting the given premise. If it is a question +whether Britain will decay, to attempt (while several empires still +flourish) to settle the matter by asserting that <i>all</i> empires decay, +seems to be 'a begging of the question.' But although this latter case +is a manifest prediction, it does not really differ from the former one; +for the proof that camels are herbivorous has no limits in time. If +valid, it shows not only that they are, but also that they will be, +herbivorous.</p> + +<p>Hence, to resort to a dilemma, it may be urged: If <i>all</i> the facts of +the major premise of any syllogism have been examined, the syllogism is +needless; and if <i>some</i> of them have not been examined, it is a <i>petitio +principii</i>. But either all have been examined, or some have not. +Therefore; the syllogism is either useless or fallacious.</p> + +<p><a name="chap_13_sect_4" id="chap_13_sect_4"></a>§ 4. A way of escape from this dilemma is provided <span class='pagenum'>[Pg 164]<a name="Page_164" id="Page_164"></a></span>by distinguishing +between the formal and material aspects of the syllogism considered as a +means of proof. It begs the question formally, but not materially; that +is to say, if it be a question whether camels are herbivorous, and to +decide it we are told that '<i>all</i> ruminants are,' laying stress upon the +'all,' as if all had been examined, though in fact camels have not been, +then the question as to camels is begged. The form of a universal +proposition is then offered as evidence, when in fact the evidence has +not been universally ascertained. But if in urging that 'all ruminants +are herbivorous' no more is meant than that so many other ruminants of +different species are known to be herbivorous, and that the ruminant +stomach is so well adapted to a coarse vegetable diet, that the same +habit may be expected in other ruminants, such as camels, the argument +then rests upon material evidence without unfairly implying the case in +question. Now the nature of the material evidence is plainly this, that +the resemblance of camels to deer, oxen, <i>etc.</i>, in chewing the cud, +justifies us in believing that they have a further resemblance in +feeding on herbs; in other words, we assume that <i>resemblance is a +ground of inference</i>.</p> + +<p>Another way of putting this difficulty which we have just been +discussing, with regard to syllogistic evidence, is to urge that by the +Laws of Syllogism a conclusion must never go beyond the premises, and +that therefore no progress in knowledge can ever be established, except +by direct observation. Now, taking the syllogism formally, this is true: +if the conclusion go beyond the premises, there must be either four +terms, or illicit process of the major or minor term. But, taking it +materially, the conclusion may cover facts which were not in view when +the major premise was laid down; facts of which we predicate something +not as the result of direct observation, but because they resemble in a +certain way those facts which had been shown to carry the predicate when +the major premise was formed.</p><p><span class='pagenum'>[Pg 165]<a name="Page_165" id="Page_165"></a></span></p> + +<p>'What sort of resemblance is a sufficient ground of inference?' is, +therefore, the important question alike in material Deduction and in +Induction; and in endeavouring to answer it we shall find that the +surest ground of inference is resemblance of causation. For example, it +is due to causation that ruminants are herbivorous. Their instincts make +them crop the herb, and their stomachs enable them easily to digest it; +and in these characters camels are like the other ruminants.</p> + +<p><a name="chap_13_sect_5" id="chap_13_sect_5"></a>§ 5. In <a href="#chap_9_sect_3">ch. ix, § 3</a>, the <i>Dictum de omni et nullo</i> was stated: 'Whatever +may be predicated of a term distributed may be predicated of anything +that can be identified with that term.' Nothing was there said (as +nothing was needed) of the relations that might be implied in the +predication. But now that it comes to the ultimate validity of +predication, we must be clear as to what these relations are; and it +will also be convenient to speak no longer of terms, as in Formal Logic, +but of the things denoted. What relations, then, can be determined +between concrete facts or phenomena (physical or mental) with the +greatest certainty of general truth; and what axioms are there that +sanction mediate inferences concerning those relations?</p> + +<p>In his <i>Logic</i> (B. II. c. 2, § 3) Mill gives as the axiom of syllogistic +reasoning, instead of the <i>Dictum</i>: "A thing which co-exists with +another thing, which other co-exists with a third thing, also co-exists +with that third thing." Thus the peculiar properties of Socrates +co-exist with the attributes of man, which co-exist with mortality: +therefore, Socrates is mortal. But, again, he says that the ground of +the syllogism is Induction; that man is mortal is an induction. And, +further, the ground of Induction is causation; the law of causation is +the ultimate major premise of every sound induction. Now causation is +the principle of the succession of phenomena: how, then, can the +syllogism rest on an axiom concerning co-existence? On reflection, too, +it must appear that 'Man is mortal'<span class='pagenum'>[Pg 166]<a name="Page_166" id="Page_166"></a></span> predicates causation: the human +constitution issues in death.</p> + +<p>The explanation of this inconsistency may perhaps be found in the +history of Mill's work. Books I. and II. were written in 1831; but being +unable at that time to explain Induction, he did not write Book III. +until 1837-8. Then, no doubt, he revised the earlier Books, but not +enough to bring his theory of the syllogism into complete agreement with +the theory of Induction; so that the axiom of co-existence was allowed +to stand.</p> + +<p>Mill also introduced the doctrine of Natural Kinds as a ground of +Induction supplementary, at least provisionally, to causation; and to +reasoning about Kinds, or Substance and Attribute, his axiom of +co-existence is really adapted. Kinds are groups of things that agree +amongst themselves and differ from all others in a multitude of +qualities: these qualities co-exist, or co-inhere, with a high degree of +constancy; so that where some are found others may be inferred. Their +co-inherence is not to be considered an ultimate fact; for, "since +everything which occurs is determined by laws of causation and +collocations of the original causes, it follows that the co-existences +observable amongst effects cannot themselves be the subject of any +similar set of laws distinct from laws of causation" (B. III. c. 5, § +9). According to the theory of evolution (worked out since Mill wrote), +Kinds—that is, species of plants, animals and minerals—with their +qualities are all due to causation. Still, as we can rarely, or never, +trace the causes with any fullness or precision, a great deal of our +reasoning, as, <i>e.g.</i>, about men and camels, does in fact trust to the +relative permanence of natural Kinds as defined by co-inhering +attributes.</p> + +<p>To see this more clearly, we should consider that causation and natural +Kinds are not at present separable; propositions about causation in +concrete phenomena (as distinct from abstract 'forces') always involve +the assumption of<span class='pagenum'>[Pg 167]<a name="Page_167" id="Page_167"></a></span> Kinds. For example—'Water rusts iron,' or the oxygen +of water combines with iron immersed in it to form rust: this statement +of causation assumes that water, oxygen, iron, and iron-rust are known +Kinds. On the other hand, the constitution of every concrete thing, and +manifestly of every organised body, is always undergoing change, that +is, causation, upon which fact its properties depend.</p> + +<p>How, then, can we frame principles of mediate reasoning, about such +things? So far as we consider them as Kinds, it is enough to say: +<i>Whatever can be identified as a specimen of a known substance or Kind +has the properties of that Kind</i>. So far as we consider them as in the +relation of causation, we may say: <i>Whatever relation of events can be +identified with the relation of cause and effect is constant</i>. And these +principles may be generalised thus: <i>Whatever is constantly related to a +phenomenon (cause or Kind), determined by certain characters, is related +in the same way to any phenomenon, that has the same characters</i>. Taking +this as axiom of the syllogism materially treated, we see that +herbivorousness, being constantly related to ruminants, is constantly +related to camels; mortality to man and, therefore, to Socrates; rusting +to the immersion of iron in water generally and, therefore, to this +piece of iron. <i>Nota notæ, nota rei ipsius</i> is another statement of the +same principle; still another is Mill's axiom, "Whatever has a mark has +what it is a mark of." A mark is anything (A) that is never found +without something else (B)—a phenomenon constantly related to another +phenomenon—so that wherever A is found, B may be expected: human nature +is a mark of mortality.</p> + +<p><a name="chap_13_sect_6" id="chap_13_sect_6"></a>§ 6. The Syllogism has sometimes been discarded by those who have only +seen that, as formally stated, it is either useless or fallacious: but +those who also perceive its material grounds retain and defend it. In +fact, great advantages are gained by stating an argument as a formal +syllogism. For, in the first place, we can then examine <span class='pagenum'>[Pg 168]<a name="Page_168" id="Page_168"></a></span>separately the +three conditions on which the validity of the argument depends:</p> + +<p>(1) Are the Premises so connected that, <i>if they are true</i>, the +Conclusion follows? This depends upon the formal principles of <a href="#CHAPTER_X">chap. x.</a></p> + +<p>(2) Is the Minor Premise true? This question can only arise when the +minor premise is a real proposition; and then it may be very difficult +to answer. Water rusts iron; but is the metal we are now dealing with a +fair specimen of iron? Few people, comparatively, know how to determine +whether diamonds, or even gold or silver coins, are genuine. That +<i>Camels are ruminants</i> is now a verbal proposition to a Zoologist, but +not to the rest of us; and to the Zoologist the ascertaining of the +relation in which camels stand to such ruminants as oxen and deer, was +not a matter of analysing words but of dissecting specimens. What a long +controversy as to whether the human race constitutes a Family of the +Primates! That 'the British Empire is an empire' affords no matter for +doubt or inquiry; but how difficult to judge whether the British Empire +resembles Assyria, Egypt, Rome, Spain in those characters and +circumstances that caused their downfall!</p> + +<p>(3) Is the Major Premise true? Are all ruminants herbivorous? If there +be any exceptions to the rule, camels are likely enough to be among the +exceptions. And here the need of Inductive Logic is most conspicuous: +how can we prove our premises when they are universal propositions? +Universal propositions, however, are also involved in proving the minor +premise: to prove a thing to be iron, we must know the constant +reactions of iron.</p> + +<p>A second advantage of the syllogism is, that it makes us fully aware of +what an inference implies. An inference must have some grounds, or else +it is a mere prejudice; but whatever the grounds, if sufficient in a +particular case, they must be sufficient for all similar cases, they +must <span class='pagenum'>[Pg 169]<a name="Page_169" id="Page_169"></a></span>admit of being generalised; and to generalise the grounds of the +inference, is nothing else than to state the major premise. If the +evidence is sufficient to justify the argument that camels are +herbivorous <i>because</i> they are ruminants, it must also justify the major +premise, <i>All ruminants are herbivorous</i>; for else the inference cannot +really depend merely upon the fact of ruminating. To state our evidence +syllogistically, then, must be possible, if the evidence is mediate and +of a logical kind; and to state it in this formal way, as depending on +the truth of a general principle (the major premise), increases our +sense of responsibility for the inference that is thus seen to imply so +much; and if any negative instances lie within our knowledge, we are the +more likely to remember them. The use of syllogisms therefore tends to +strengthen our reasonings.</p> + +<p>A third advantage is, that to formulate an accurate generalisation may +be useful to others: it is indeed part of the systematic procedure of +science. The memoranda of our major premises, or reasons for believing +anything, may be referred to by others, and either confirmed or refuted. +When such a memorandum is used for further inferences, these inferences +are said, in the language of Formal Logic, to be drawn <i>from</i> it, as if +the conclusion were contained in our knowledge of the major premise; +but, considering the limited extent of the material evidence, it is +better to say that the inference is drawn <i>according to</i> the memorandum +or major premise, since the grounds of the major premise and of the +conclusion are in fact the same (Mill: <i>Logic</i>, B. II. c. 3). Inductive +proofs may be stated in Syllogisms, and inductive inferences are drawn +<i>according to</i> the Law of Causation.</p> + +<p><a name="chap_13_sect_7" id="chap_13_sect_7"></a>§ 7. To assume that resemblance is a ground of inference, and that +substance and attribute, or cause and effect, are phenomena constantly +related, implies belief in the Uniformity of Nature. The Uniformity of +Nature cannot be defined, and is therefore liable to be misunder<span class='pagenum'>[Pg 170]<a name="Page_170" id="Page_170"></a></span>stood. +In many ways Nature seems not to be uniform: there is great variety in +the sizes, shapes, colours and all other properties of things: bodies +falling in the open air—pebbles, slates, feathers—descend in different +lines and at different rates; the wind and weather are proverbially +uncertain; the course of trade or of politics, is full of surprises. Yet +common maxims, even when absurd, testify to a popular belief that the +relations of things are constant: the doctrine of St. Swithin and the +rhyme beginning 'Evening red and morning grey,' show that the weather is +held to be not wholly unpredictable; as to human affairs, it is +said that 'a green Yule makes a fat churchyard,' that 'trade follows the +flag,' and that 'history repeats itself'; and Superstition knows that +witches cannot enter a stable-door if a horse-shoe is nailed over it, +and that the devil cannot cross a threshold inscribed with a perfect +pentagram. But the surest proof of a belief in the uniformity of nature +is given by the conduct of men and animals; by that adherence to habit, +custom and tradition, to which in quiet times they chiefly owe their +safety, but which would daily disappoint and destroy them, if it were +not generally true that things may be found where they have been left +and that in similar circumstances there are similar events.</p> + +<p>Now this general belief, seldom distinctly conceived, for the most part +quite unconscious (as a principle), merely implied in what men do, is +also the foundation of all the Sciences; which are entirely occupied in +seeking the Laws (that is, the Uniformities) of Nature. As the +uniformity of nature cannot be defined, it cannot be proved; the most +convincing evidence in its favour is the steady progress made by Science +whilst trusting in it. Nevertheless, what is important is not the +comprehensive but indeterminate notion of Uniformity so much as a number +of First Principles, which may be distinguished in it as follows:</p> + +<p>(1) The Principles of Contradiction and Excluded Middle (<a href="#chap_6_sect_3">ch. vi. § 3</a>) +declare that in a given relation to a given <span class='pagenum'>[Pg 171]<a name="Page_171" id="Page_171"></a></span>phenomenon any two or more +other phenomena are incompatible (<i>B is not A and a</i>); whilst the given +phenomenon either stands related to another phenomenon or not (<i>B is +either A or a</i>). It is not only a matter of Logic but of fact that, if a +leaf is green, it is not under the same conditions red or blue, and that +if it is not green it is some other colour.</p> + +<p>(2) Certain Axioms of Mediate Evidence: as, in Mathematics, 'that +magnitudes equal to the same magnitude are equal to one another'; and, +in Logic, the <i>Dictum</i> or its material equivalent.</p> + +<p>(3) That all Times and all Spaces are commensurable; although in certain +relations of space (as π) the unit of measurement must be infinitely +small.—If Time really trotted with one man and galloped with another, +as it seems to; if space really swelled in places, as De Quincey dreamed +that it did; life could not be regulated, experience could not be +compared and science would be impossible. The Mathematical Axioms would +then never be applicable to space or time, or to the objects or +processes that fill them.</p> + +<p>(4) The Persistence of Matter and Energy: the physical principle that, +in all changes of the universe, the quantities of Matter and Energy +(actual and potential, so-called) remain the same.—For example, as to +matter, although dew is found on the grass at morning without any +apparent cause, and although a candle seems to burn away to a scrap of +blackened wick, yet every one knows that the dew has been condensed from +vapour in the air, and that the candle has only turned into gas and +smoke. As to energy, although a stone thrown up to the housetop and +resting there has lost actual energy, it has gained such a position that +the slightest touch may bring it to the earth again in the same time as +it took to travel upwards; so on the house-top it is said to have +potential energy. When a boiler works an engine, every time the piston +is thrust forward (mechanical energy), an equivalent in heat (molecular +<span class='pagenum'>[Pg 172]<a name="Page_172" id="Page_172"></a></span>energy) is lost. But for the elucidation of these principles, readers +must refer to treatises of Chemistry and Physics.</p> + +<p>(5) Causation, a special form of the foregoing principles of the +persistence of matter and energy, we shall discuss in the next chapter. +It is not to be conceived of as anything occult or noumenal, but merely +as a special mode of the uniformity of Nature or experience.</p> + +<p>(6) Certain Uniformities of Co-existence; but for want of a general +principle of Co-existence, corresponding to Causation (the principle of +Succession), we can only classify these uniformities as follows:</p> + +<p>(<i>a</i>) The Geometrical; as that, in a four-sided figure, if the opposite +angles are equal, the opposite sides are equal and parallel.—Countless +similar uniformities of co-existence are disclosed by Geometry. The +co-existent facts do not cause one another, nor are they jointly caused +by something else; they are mutually involved: such is the nature of +space.</p> + +<p>(<i>b</i>) Universal co-inherences among the properties of concrete +things.—The chief example is the co-inherence of gravity with inertia +in all material bodies. There is, I believe, no other entirely +satisfactory case; but some good approximations to such uniformity are +known to physical science.</p> + +<p>(<i>c</i>) Co-existence due to Causation; such as the positions of objects in +space at any time.—The houses of a town are where they are, because +they were put there; and they remain in their place as long as no other +causes arise strong enough to remove or destroy them. Similarly, the +relative positions of rocks in geological strata, and of trees in a +forest, are due to causes.</p> + +<p>(<i>d</i>) The co-inherence of properties in Natural Kinds; which we call the +constitution, defining characters, or specific nature of such +things.—Oxygen, platinum, sulphur and the other elements; water, common +salt, alcohol and other compounds; the various species of plants and +animals: all these are known to us as different groups of <span class='pagenum'>[Pg 173]<a name="Page_173" id="Page_173"></a></span>co-inherent +properties. It may be conjectured that these groupings of properties are +also due to causation, and sometimes the causes can be traced: but very +often the causes are still unknown; and, until resolved into their +causes, they must be taken as necessary data in the investigation of +nature. Laws of the co-inherence of the properties of Kinds do not, like +laws of causation, admit of methodical proof upon their own principles, +but only by constancy in experience and statistical probability (<a href="#chap_19_sect_4">c. xix, +§ 4</a>).</p> + +<p>(<i>e</i>) There are also a few cases in which properties co-exist in an +unaccountable way, without being co-extensive with any one species, +genus, or order: as most metals are whitish, and scarlet flowers are +wanting in fragrance. (On this § 7, see Venn's <i>Empirical Logic</i>, c. 4.)</p> + +<p><a name="chap_13_sect_8" id="chap_13_sect_8"></a>§ 8. Inasmuch as Axioms of Uniformity are ultimate truths, they cannot +be deduced; and inasmuch as they are universal, no proof by experience +can ever be adequate. The grounds of our belief in them seem to be +these:</p> + +<p>(1) Every inference takes for granted an order of Nature corresponding +with it; and every attempt to explain the origin of anything assumes +that it is the transformation of something else: so that uniformity of +order and conservation of matter and energy are necessary +presuppositions of reasoning.</p> + +<p>(2) On the rise of philosophic reflection, these tacit presuppositions +are first taken as dogmas, and later as postulates of scientific +generalisation, and of the architectonic unification of science. Here +they are indispensable.</p> + +<p>(3) The presuppositions or postulates are, in some measure, verifiable +in practical life and in scientific demonstration, and the better +verifiable as our methods become more exact.</p> + +<p>(4) There is a cause of this belief that cannot be said to contain any +evidence for it, namely, the desire to find in Nature a foundation for +confidence in our own power to foresee and to control events.</p><p><span class='pagenum'>[Pg 174]<a name="Page_174" id="Page_174"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_XIV" id="CHAPTER_XIV"></a>CHAPTER XIV</h2> + +<h3>CAUSATION</h3> + + +<p><a name="chap_14_sect_1" id="chap_14_sect_1"></a>§ 1. For the theory of Induction, the specially important aspect of the +Uniformity of Nature is Causation.</p> + +<p>For (1) the Principles of Contradiction and Excluded Middle are implied +in all logical operations, and need no further explication.</p> + +<p>(2) That one thing is a mark of another or constantly related to it, +must be established by Induction; and the surest of all marks is a +Cause. So that the application of the axiom of the Syllogism in +particular cases requires, when most valid, a previous appeal to +Causation.</p> + +<p>(3) The uniformity of Space and of Time is involved in Causation, so far +as we conceive Causation as essentially matter in motion—for motion is +only known as a traversing of space in time; and so far as forces vary +in any way according to the distance between bodies; so that if space +and time were not uniform, causation would be irregular. Not that time +and space are agents, but they are conditions of every agent's +operation.</p> + +<p>(4) The persistence of Matter and Energy, being nothing else than +Causation in the general movement of the world, is applied under the +name of that principle in explaining any particular limited phenomenon, +such as a soap-bubble, or a thunderstorm, or the tide.</p> + +<p>(5) As to co-existences, the Geometrical do not belong to Logic: those +involved in the existence of plants, animals, and inorganic bodies, +must, as far as possible, be traced to causes; and so, of course, must +the relative positions <span class='pagenum'>[Pg 175]<a name="Page_175" id="Page_175"></a></span>of objects in space at any time: and what +Co-existences remain do not admit of methodical inductive treatment; +they will be briefly discussed in <a href="#CHAPTER_XIX">chap. xix.</a></p> + +<p>Causation, then, is that mode or aspect of the Uniformity of Nature +which especially concerns us in Induction; and we must make it as +definite as possible. It is nothing occult, but merely a convenient name +for phenomena in a particular relation to other phenomena, called their +effect. Similarly, if the word 'force' is sometimes used for convenience +in analysing causation, it means nothing more than something in time and +space, itself moving, or tending to move, or hindering or accelerating +other things. If any one does not find these words convenient for the +purpose, he can use others.</p> + +<p><a name="chap_14_sect_2" id="chap_14_sect_2"></a>§ 2. A Cause, according to Mill, is "the invariable unconditional +antecedent" of a given phenomenon. To enlarge upon this:</p> + +<p>(1) A Cause is <i>relative to a given phenomenon</i>, called the Effect. +Logic has no method for investigating the cause of the universe as a +whole, but only of a part or epoch of it: we select from the infinite +continuum of Nature any portion that is neither too large nor too small +for a trained mind to comprehend. The magnitude of the phenomenon may be +a matter of convenience. If the cause of disease in general be too wide +a problem, can fevers be dealt with; or, if that be too much, is typhus +within the reach of inquiry? In short, how much can we deal with +accurately?</p> + +<p>(2) The given phenomenon is always <i>an event</i>; that is to say, not a new +thing (nothing is wholly new), but a change in something, or in the +relative position of things. We may ask the cause of the phases of the +moon, of the freezing of water, of the kindling of a match, of a deposit +of chalk, of the differentiation of species. To inquire the cause of +France being a republic, or Russia an autocracy, implies that these +countries were once otherwise governed, or had no government: to inquire +the cause of the earth being <span class='pagenum'>[Pg 176]<a name="Page_176" id="Page_176"></a></span>shaped like an orange, implies that the +matter of the earth had once another shape.</p> + +<p>(3) The Cause is <i>antecedent</i> to the Effect, which accordingly is often +called its <i>consequent</i>. This is often misunderstood and sometimes +disputed. It has been said that the meaning of 'cause' implies an +'effect,' so that until an effect occurs there can be no cause. But this +is a blunder; for whilst the word 'cause' implies 'effect,' it also +implies the relative futurity of the effect; and effect implies the +relative priority of the cause. The connotation of the words, therefore, +agrees well enough with Mill's doctrine. In fact, the danger is that any +pair of contrasted words may suggest too strongly that the phenomena +denoted are separate in Nature; whereas every natural process is +continuous. If water, dripping from the roof wears away a stone, it fell +on the roof as rain; the rain came from a condensing cloud; the cloud +was driven by the wind from the sea, whence it exhaled; and so on. There +is no known beginning to this, and no break in it. We may take any one +of these changes, call it an effect, and ask for its cause; or call it a +cause, and ask for its effect. There is not in Nature one set of things +called causes and another called effects; but every change is both cause +(or a condition) of the future and effect of the past; and whether we +consider an event as the one or the other, depends upon the direction of +our curiosity or interest.</p> + +<p>Still, taking the event as effect, its cause is the antecedent process; +or, taking it as a cause, its effect is the consequent process. This +follows from the conception of causation as essentially motion; for that +<i>motion takes time</i> is (from the way our perceptive powers grow) an +ultimate intuition. But, for the same reason, there is no interval of +time between cause and effect; since all the time is filled up with +motion.</p> + +<p>Nor must it be supposed that the whole cause is ante<span class='pagenum'>[Pg 177]<a name="Page_177" id="Page_177"></a></span>cedent to the +effect as a whole: for we often take the phenomenon on such a scale that +minutes, days, years, ages, may elapse before we consider the cause as +exhausted (<i>e.g.</i>, an earthquake, a battle, an expansion of credit, +natural selection operating on a given variety); and all that time the +effect has been accumulating. But we may further consider such a cause +as made up of moments or minute factors, and the effect as made up of +corresponding moments; and then the cause, taken in its moments, is +antecedent throughout to the effect, taken in its corresponding moments.</p> + +<p>(4) The Cause is the <i>invariable</i> antecedent of the effect; that is to +say, whenever a given cause occurs it always has the same effect: in +this, in fact, consists the Uniformity of Causation. Accordingly, not +every antecedent of an event is its Cause: to assume that it is so, is +the familiar fallacy of arguing '<i>post hoc ergo propter hoc</i>.' Every +event has an infinite number of antecedents that have no ascertainable +connection with it: if a picture falls from the wall in this room, there +may have occurred, just previously, an earthquake in New Zealand, an +explosion in a Japanese arsenal, a religious riot in India, a political +assassination in Russia and a vote of censure in the House of Commons, +besides millions of other less noticeable events, between none of which +and the falling of the picture can any direct causation be detected; +though, no doubt, they are all necessary occurrences in the general +world-process, and remotely connected. The cause, however, was that a +door slammed violently in the room above and shook the wall, and that +the picture was heavy and the cord old and rotten. Even if two events +invariably occur one after the other, as day follows night, or as the +report follows the flash of a gun, they may not be cause and effect, +though it is highly probable that they are closely connected by +causation; and in each of these two examples the events are co-effects +of a common cause, and may be regarded as elements of <span class='pagenum'>[Pg 178]<a name="Page_178" id="Page_178"></a></span>its total effect. +Still, whilst it is not true that every antecedent, or that every +invariable antecedent, of an event is its cause, the cause is conceived +of as some change in certain conditions, or some state and process of +things, such that should it exactly recur the same event would +invariably follow. If we consider the antecedent state and process of +things very widely or very minutely, it never does exactly recur; nor +does the consequent. But the purpose of induction is to get as near the +truth as possible within the limits set by our faculties of observation +and calculation. Complex causal instances that are most unlikely to +recur as a whole, may be analysed into the laws of their constituent +conditions.</p> + +<p>(5) The Cause is the Unconditional Antecedent. A cause is never simple, +but may be analysed into several conditions; and 'Condition' means any +necessary factor of a Cause: any thing or agent that exerts, absorbs, +transforms, or deflects energy; or any relation of time or space in +which agents stand to one another. A positive condition is one that +cannot be omitted without frustrating the effect; a negative condition +is one that cannot be introduced without frustrating the effect. In the +falling of the picture, <i>e.g.</i>, the positive conditions were the picture +(as being heavy), the slamming of the door, and the weakness of the +cord: a negative condition was that the picture should have no support +but the cord. When Mill, then, defines the Cause of any event as its +"unconditional" antecedent, he means that it is that group of conditions +(state and process of things) which, without any further condition, is +followed by the event in question: it is the least antecedent that +suffices, positive conditions being present and negative absent.</p> + +<p>Whatever item of the antecedent can be left out, then, without affecting +the event, is no part of the cause. Earthquakes have happened in New +Zealand and votes of censure in the House of Commons without a picture's +falling in <span class='pagenum'>[Pg 179]<a name="Page_179" id="Page_179"></a></span>this room: they were not unconditional antecedents; +something else was needed to bring down a picture. Unconditionality also +distinguishes a true cause from an invariable antecedent that is only a +co-effect: for when day follows night something else happens; the Earth +rotates upon her axis: a flash of gunpowder is not an unconditional +antecedent of a report; the powder must be ignited in a closed chamber.</p> + +<p>By common experience, and more precisely by experiment, it is found +possible to select from among the antecedents of an event a certain +number upon which, so far as can be perceived, it is dependent, and to +neglect the rest: to purge the cause of all irrelevant antecedents is +the great art of inductive method. Remote or minute conditions may +indeed modify the event in ways so refined as to escape our notice. +Subject to the limitations of our human faculties, however, we are able +in many cases to secure an unconditional antecedent upon which a certain +event invariably follows. Everybody takes this for granted: if the gas +will not burn, or a gun will not go off, we wonder 'what can be wrong +with it,' that is, what positive condition is wanting, or what negative +one is present. No one now supposes that gunnery depends upon those +"remotest of all causes," the stars, or upon the sun being in +Sagittarius rather than in Aquarius, or that one shoots straightest with +a silver bullet, or after saying the alphabet backwards.</p> + +<p>(6) That the Cause of any event is an Immediate Antecedent follows from +its being an unconditional one. For if there are three events, A B C, +causally connected, it is plain that A is not the unconditional +antecedent of C, but requires the further condition of first giving rise +to B. But that is not all; for the B that gives rise to C is never +merely the effect of A; it involves something further. Take such a +simple case as the motion of the earth round the sun (neglecting all +other conditions, the other planets,<span class='pagenum'>[Pg 180]<a name="Page_180" id="Page_180"></a></span> <i>etc.</i>); and let the earth's +motion at three successive moments be A B C: A is not the whole cause of +B in velocity and direction; we must add relation to the sun, say x. But +then, again, the cause of C will not be merely Bx, for the relation to +the sun will have altered; so that we must represent it as Bx'. The +series, therefore, is Ax Bx' C. What is called a "remote cause" is, +therefore, doubly conditional; first, because it supposes an intervening +cause; and secondly, because it only in part determines the conditions +that constitute this intervening cause.</p> + +<p>The immediacy of a cause being implied in its unconditionalness, is an +important clue to it; but as far as the detection of causes depends upon +sense-perception, our powers (however aided by instruments) are unequal +to the subtlety of Nature. Between the event and what seems to us the +immediate antecedent many things (molecular or etherial changes) may +happen in Chemistry or Physics. The progress of science would be +impossible were not observation supplemented by hypothesis and +calculation. And where phenomena are treated upon a large scale, as in +the biological and social sciences, immediacy, as a mark of causation, +must be liberally interpreted. So far, then, as to the qualitative +character of Causation.</p> + +<p>(7) But to complete our account of it, we must briefly consider its +quantitative character. As to the Matter contained, and as to the Energy +embodied, Cause and Effect are conceived to be <i>equal</i>. As to matter, +indeed, they may be more properly called identical; since the effect is +nothing but the cause redistributed. When oxygen combines with hydrogen +to form water, or with mercury to form red precipitate, the weight of +the compound is exactly equal to the weight of the elements combined in +it; when a shell explodes and knocks down a wall, the materials of the +shell and wall are scattered about. As to energy, we see that in the +heavenly bodies, which meet with no sensible impediment, it remains the +same from age to age: with <span class='pagenum'>[Pg 181]<a name="Page_181" id="Page_181"></a></span>things 'below the moon' we have to allow for +the more or less rapid conversion of the visible motion of a mass into +other forms of energy, such as sound and heat. But the right +understanding of this point involves physical considerations of some +difficulty, as to which the reader must refer to appropriate books, such +as Balfour Stewart's on <i>The Conservation of Energy</i>.</p> + +<p>The comprehension of the quantitative aspect of causation is greatly +aided by Bain's analysis of any cause into a 'Moving or an Inciting +Power' and a 'Collocation' of circumstances. When a demagogue by making +a speech stirs up a mob to a riot, the speech is the moving or inciting +power; the mob already in a state of smouldering passion, and a street +convenient to be wrecked, are the collocation. When a small quantity of +strychnine kills a man, the strychnine is the inciting power; the nature +of his nervo-muscular system, apt to be thrown into spasms by that drug, +and all the organs of his body dependent on that system, are the +collocation. Now any one who thinks only of the speech, or the drug, in +these cases, may express astonishment at the disproportion of cause and +effect:</p> + + +<div class="example"><span class="i0">"What great events from trivial causes spring!"</span></div> + + +<p class="noindent">But, remembering that the whole cause of the riot included the excited +mob, every one sees that its muscular power is enough to wreck a street; +and remembering that breathing depends upon the normal action of the +intercostal muscles, it is plain that if this action is stopped by +strychnine, a man must die. Again, a slight rise of temperature may be a +sufficient inciting power to occasion extensive chemical changes in a +collocation of elements otherwise stable; a spark is enough to explode a +powder magazine. Hence, when sufficient energy to account for any effect +cannot be found in the inciting power, or manifestly active condition, +we must look for it in the collocation which is often supposed to be +passive.</p><p><span class='pagenum'>[Pg 182]<a name="Page_182" id="Page_182"></a></span></p> + +<p>And that reminds us of another common misapprehension, namely, that in +Nature some things are passive and others active: the distinction +between 'agent' and 'patient.' This is a merely relative distinction: in +Nature all things are active. To the eye some things seem at rest and +others in motion; but we know that nothing is really at rest, that +everything palpitates with molecular change, and whirls with the planet +through space. Everything that is acted upon reacts according to its own +nature: the quietest-looking object (say, a moss-covered stone), if we +try to push or lift it, pushes or pulls us back, assuring us that +'action and reaction are equal and opposite.' 'Inertia' does not mean +want of vigour, but may be metaphorically described as the inexpugnable +resolve of everything to have its own way.</p> + +<p>The equality of cause and effect defines and interprets the +unconditionality of causation. The cause, we have seen, is that group of +conditions which, without any further condition, is followed by a given +event. But how is such a group to be conceived? Unquantified, it admits +only of a general description: quantified, it must mean a group of +conditions equal to the effect in mass and energy, the essence of the +physical world. Apparently, a necessary conception of the human mind: +for if a cause seem greater than its effect, we ask what has become of +the surplus matter and energy; or if an effect seem greater than its +cause, we ask whence the surplus matter and energy has arisen. So +convinced of this truth is every experimenter, that if his results +present any deviation from it, he always assumes that it is he who has +made some mistake or oversight, never that there is indeterminism or +discontinuity in Nature.</p> + +<p>The transformation of matter and energy, then, is the essence of +causation: because it is continuous, causation is immediate; and because +in the same circumstances the transformation always follows the same +course, a cause <span class='pagenum'>[Pg 183]<a name="Page_183" id="Page_183"></a></span>has invariably the same effect. If a fire be lit +morning after morning in the same grate, with coal, wood, and paper of +the same quality and similarly arranged, there will be each day the same +flaming of paper, crackling of wood and glowing of coal, followed in +about the same time by the same reduction of the whole mass partly to +ashes and partly to gases and smoke that have gone up the chimney. The +flaming, crackling and glowing are, physically, modes of energy; and the +change of materials into gas and ashes is a chemical and physical +redistribution: and, if some one be present, he will be aware of all +this; and then, besides the physical changes, there will be sensations +of light, sound and heat; and these again will be always the same in the +same circumstances.</p> + +<p>The Cause of any event, then, when exactly ascertainable, has five +marks: it is (quantitatively) <i>equal</i> to the effect, and (qualitatively) +<i>the immediate, unconditional, invariable antecedent of the effect</i>.</p> + +<p><a name="chap_14_sect_3" id="chap_14_sect_3"></a>§ 3. This scientific conception of causation has been developed and +rendered definite by the investigations of those physical sciences that +can avail themselves of exact experiments and mathematical calculation; +and it is there, in Chemistry and Physics, that it is most at home. The +conception can indeed be carried into the Biological and Social +Sciences, even in its quantitative form, by making the proper +allowances. For the limbs of animals are levers, and act upon mechanical +principles; and digestion and the aeration of the blood by breathing are +partly chemical processes. There is a quantitative relation between the +food a man eats and the amount of work he can do. The numbers of any +species of plant or animal depend upon the food supply. The value of a +country's imports is equal to the value of its exports and of the +services it renders to foreigners. But, generally, the less experiment +and exact calculation are practicable in any branch of inquiry, the less +rigorously can the conception of causation <span class='pagenum'>[Pg 184]<a name="Page_184" id="Page_184"></a></span>be applied there, the more +will its application depend upon the qualitative marks, and the more +need there will be to use it judiciously. In every inquiry the greatest +possible precision must be aimed at; but it is unreasonable to expect in +any case more precise proof than the subject admits of in the existing +state of culture.</p> + +<p>Wherever mental action is involved, there is a special difficulty in +applying the physical notion of causation. For if a Cause be conceived +of as matter in motion, a thought, or feeling, or volition can be +neither cause nor effect. And since mental action is involved in all +social affairs, and in the life of all men and animals, it may seem +impossible to interpret social or vital changes according to laws of +causation. Still, animals and men are moving bodies; and it is +recognised that their thoughts and feelings are so connected with their +movements and with the movements of other things acting upon them, that +we can judge of one case by another; although the connection is by no +means well understood, and the best words (such as all can agree to use) +have not yet been found to express even what we know about it. Hence, a +regular connection being granted, I have not hesitated, to use +biological and social events and the laws of them, to illustrate +causation and induction; because, though less exact than chemical or +mechanical examples, they are to most people more familiar and +interesting.</p> + +<p>In practical affairs, it is felt that everything depends upon causation; +how to play the fiddle, or sail a yacht, or get one's living, or defeat +the enemy. The price of pig-iron six months hence, the prospects of the +harvest, the issue in a Coroner's Court, Home Rule and Socialism, are +all questions of causation. But, in such cases, the conception of a +cause is rarely applied in its full scientific acceptation, as the +unconditional antecedent, or 'all the conditions' (neither more nor +less) upon which the event depends. This is not because men of affairs +are bad logicians, or <span class='pagenum'>[Pg 185]<a name="Page_185" id="Page_185"></a></span>incapable of scientific comprehension; for very +often the reverse is conspicuously true; but because practical affairs +call for promptitude and a decisive seizing upon what is predominantly +important. How learn to play the fiddle? "Go to a good teacher." (Then, +beginning young enough, with natural aptitude and great diligence, all +may be well.) How defeat the enemy? "Be two to one at the critical +juncture." (Then, if the men are brave, disciplined, well armed and well +fed, there is a good chance of victory.) Will the price of iron improve? +"Yes: for the market is oversold": (that is, many have sold iron who +have none to deliver, and must at some time buy it back; and that will +put up the price—if the stock is not too great, if the demand does not +fall off, and if those who have bought what they cannot pay for are not +in the meanwhile obliged to sell.) These prompt and decisive judgments +(with the parenthetic considerations unexpressed) as to what is the +Cause, or predominantly important condition, of any event, are not as +good as a scientific estimate of all the conditions, when this can be +obtained; but, when time is short, the insight of trained sagacity may +be much better than an imperfect theoretical treatment of such problems.</p> + +<p><a name="chap_14_sect_4" id="chap_14_sect_4"></a>§ 4. To regard the Effect of certain antecedents in a narrow selective +way, is another common mistake. In the full scientific conception of an +Effect it is the sum of the unconditional consequences of a given state +and process of things: the consequences immediately flowing from that +situation without further conditions. Always to take account of all the +consequences of any cause would no doubt be impracticable; still the +practical, as well as the scientific interest, often requires that we +should enlarge our views of them; and there is no commoner error in +private effort or in legislation than to aim at some obvious good, +whilst overlooking other consequences of our action, the evil of which +may far outweigh that good. An important consequence of eating is to +satisfy hunger, and this is the ordinary <span class='pagenum'>[Pg 186]<a name="Page_186" id="Page_186"></a></span>motive to eat; but it is a +poor account of the physiological consequences. An important consequence +of firing a gun is the propulsion of the bullet or shell; but there are +many other consequences in the whole effect, and one of them is the +heating of the barrel, which, accumulating with rapid firing, may at +last put the gun out of action. The tides have consequences to shipping +and in the wear and tear of the coast that draw every one's attention; +but we are told that they also retard the rotation of the earth, and at +last may cause it to present always the same face to the sun, and, +therefore, to be uninhabitable. Such concurrent consequences of any +cause may be called its Co-effects: the Effect being the sum of them.</p> + +<p>The neglect to take account of the whole effect (that is, of all the +co-effects) in any case of causation is perhaps the reason why many +philosophers have maintained the doctrine of a "Plurality of Causes": +meaning not that more than one condition is operative in the antecedent +of every event (which is true), but that the same event may be due at +different times to different antecedents, that in fact there may be +<i>vicarious</i> causes. If, however, we take any effect as a whole, this +does not seem to be true. A fire may certainly be lit in many ways: with +a match or a flint and steel, or by rubbing sticks together, or by a +flash of lightning: have we not here a plurality of causes? Not if we +take account of the whole effect; for then we shall find it modified in +each case according to the difference of the cause. In one case there +will be a burnt match, in another a warm flint, in the last a changed +state of electrical tension. And similar differences are found in cases +of death under different conditions, as stabbing, hanging, cholera; or +of shipwreck from explosion, scuttling, tempest. Hence a Coroner's Court +expects to find, by examining a corpse, the precise cause of death. In +short, if we knew the facts minutely enough, it would be found that +there is only one Cause (sum of conditions) for each Effect (sum of +co-effects), <span class='pagenum'>[Pg 187]<a name="Page_187" id="Page_187"></a></span>and that the order of events is as uniform backwards as +forwards.</p> + +<p>Still, as we are far from knowing events minutely, it is necessary in +practical affairs, and even in the more complex and unmanageable +scientific investigations, especially those that deal with human life, +to acknowledge a possible plurality of causes for any effect. Indeed, +forgetfulness of this leads to many rash generalisations; as that +'revolutions always begin in hunger'; or that 'myths are a disease of +language.' Then there is great waste of ingenuity in reconciling such +propositions with the recalcitrant facts. A scientific method recognises +that there may be other causes of effects thus vaguely conceived, and +then proceeds to distinguish in each class of effects the peculiarities +due to different causes.</p> + +<p><a name="chap_14_sect_5" id="chap_14_sect_5"></a>§ 5. The understanding of the complex nature of Causes and Effects helps +us to overcome some other difficulties that perplex the use of these +words. We have seen that the true cause is an <i>immediate</i> antecedent; +but if the cause is confounded with <i>one</i> of its constituent conditions, +it may seem to have long preceded the event which is regarded as its +effect. Thus, if one man's death is ascribed to another's desire of +revenge, this desire may have been entertained for years before the +assassination occurred: similarly, if a shipwreck is ascribed to a +sunken reef, the rock was waiting for ages before the ship sailed that +way. But, of course, neither the desire of revenge nor the sunken rock +was 'the sum of the conditions' on which the one or the other event +depended: as soon as this is complete the effect appears.</p> + +<p>We have also seen the true effect of any state and process of things is +the immediate consequence; but if the effect be confounded with <i>one</i> of +its constituent factors, it may seem to long outlive the cessation of +the cause. Thus, in nearly every process of human industry and art, one +factor of the effect—a road, a house, a tool, a picture—may, and +<span class='pagenum'>[Pg 188]<a name="Page_188" id="Page_188"></a></span>generally does, remain long after the work has ceased: but such a +result is not the whole effect of the operations that produce it. The +other factors may be, and some always are, evanescent. In most of such +works some heat is produced by hammering or friction, and the labourers +are fatigued; but these consequences soon pass off. Hence the effect as +a whole only momentarily survives the cause. Consider a pendulum which, +having been once set agoing, swings to and fro in an arc, under the +joint control of the shaft, gravitation and its own inertia: at every +moment its speed and direction change; and each change may be considered +as an effect, of which the antecedent change was one condition. In such +a case as this, which, though a very simple, is a perfectly fair example +of all causation, the duration of either cause or effect is quite +insensible: so that, as Dr. Venn says, an Effect, rigorously conceived, +is only "the initial tendency" of its Cause.</p> + +<p><a name="chap_14_sect_6" id="chap_14_sect_6"></a>§ 6. Mill contrasted two forms under which causation appears to us: that +is to say, the conditions constituting a cause may be modified, or +'intermixed' in the effect, in two ways, which are typified respectively +by Mechanical and Chemical action. In mechanical causation, which is +found in Astronomy and all branches of Physics, the effects are all +reducible to modes of energy, and are therefore commensurable with their +causes. They are either directly commensurable, as in the cases treated +of in the consideration of the mechanical powers; or, if different forms +of energy enter into cause and effect, such as mechanical energy, +electrical energy, heat, these different forms are severally reducible +to units, between which equivalents have been established. Hence Mill +calls this the "homogeneous intermixture of effects," because the +antecedents and consequents are fundamentally of the same kind.</p> + +<p>In chemical causation, on the other hand, cause and effect (at least, as +they present themselves to us) differ in almost every way: in the act of +combination the properties <span class='pagenum'>[Pg 189]<a name="Page_189" id="Page_189"></a></span>of elements (except weight) disappear, and +are superseded by others in the compound. If, for example, mercury (a +heavy, silvery liquid) be heated in contact with oxygen (a colourless +gas), oxide of mercury is formed (red precipitate, which is a powder). +This compound presents very different phenomena from those of its +elements; and hence Mill called this class of cases "the heteropathic +intermixture of effects." Still, in chemical action, the effect is not +(in Nature) heterogeneous with the cause: for the weight of a compound +is equal to the sum of the weights of the elements that are merged in +it; and an equivalence has been ascertained between the energy of +chemical combination and the heat, light, <i>etc.,</i> produced in the act of +combination.</p> + +<p>The heteropathic intermixture of effects is also found in organic +processes (which, indeed, are partly chemical): as when a man eats bread +and milk, and by digestion and assimilation converts them into nerve, +muscle and bone. Such phenomena may make us wonder that people should +ever have believed that 'effects resemble their causes,' or that 'like +produces like.' A dim recognition of the equivalence of cause and effect +in respect of matter and motion may have aided the belief; and the +resemblance of offspring to parents may have helped: but it is probably +a residuum of magical rites; in which to whistle may be regarded as a +means of raising the wind, because the wind whistles; and rain-wizards +may make a victim shed tears that the clouds also may weep.</p> + +<p><a name="chap_14_sect_7" id="chap_14_sect_7"></a>§ 7. Another consideration arises out of the complex character of causes +and effects. When a cause consists of two or more conditions or forces, +we may consider what effect any one of them would have if it operated +alone, that is to say, its <i>Tendency</i>. This is best illustrated by the +Parallelogram of Forces: if two forces acting upon a point, but not in +the same direction, be represented by straight lines drawn in the +direction of the forces, and in length <span class='pagenum'>[Pg 190]<a name="Page_190" id="Page_190"></a></span>proportional to their +magnitudes, these lines, meeting in an angle, represent severally the +tendencies of the forces; whilst if the parallelogram be completed on +these lines, the diagonal drawn from the point in which they meet +represents their <i>Resultant</i> or effect.</p> + +<p>Again, considering the tendency of any force if it operated alone, we +may say that, when combined with another force (not in the same +direction) in any resultant, its tendency is <i>counteracted</i>: either +partially, when the direction of the resultant is different; or wholly +when, the other force being equal and opposite, the resultant is +equilibrium. If the two forces be in the same direction, they are merely +added together. Counteraction is only one mode of combination; in no +case is any force destroyed.</p> + +<p>Sometimes the separate tendencies of combined forces can only be +theoretically distinguished: as when the motion of a projectile is +analysed into a tendency to travel in the straight line of its +discharge, and a tendency to fall straight to the ground. But sometimes +a tendency can be isolated: as when,—after dropping a feather in some +place sheltered from the wind, and watching it drift to and fro, as the +air, offering unequal resistances to its uneven surface, counteracts its +weight with varying success, until it slowly settles upon the +ground,—we take it up and drop it again in a vacuum, when it falls like +lead. Here we have the tendency of a certain cause (namely, the relation +between the feather and the earth) free from counteraction: and this is +called the <i>Elimination</i> of the counteracting circumstances. In this +case indeed there is physical elimination; whereas, in the case of a +projectile, when we say that its actual motion is resolvable (neglecting +the resistance of the air) into two tendencies, one in the line of +discharge, the other earthwards, there is only theoretical elimination +of either tendency, considered as counteracting the other; and this is +more specifically called the <i>Resolution</i> or Analysis of the total +effect into its component conditions. Now, Elimina<span class='pagenum'>[Pg 191]<a name="Page_191" id="Page_191"></a></span>tion and Resolution +may be said to be the essential process of Induction in the widest sense +of the term, as including the combination of Induction with Deduction.</p> + +<p>The several conditions constituting any cause, then, by aiding or +counteracting one another's tendencies, jointly determine the total +effect. Hence, viewed in relation one to another, they may be said to +stand in <i>Reciprocity</i> or mutual influence. This relation at any moment +is itself one of co-existence, though it is conceived with reference to +a possible effect. As Kant says, all substances, as perceived in space +at the same time, are in reciprocal activity. And what is true of the +world of things at any moment (as connected, say, by gravity), is true +of any selected group of circumstances which we regard as the particular +cause of any event to come. The use of the concept of reciprocity, then, +lies in the analysis of a cause: we must not think of reciprocity as +obtaining in the succession of cause and effect, as if the effect could +turn back upon its cause; for as the effect arises its cause disappears, +and is irrecoverable by Nature or Magic. There are many cases of +rhythmic change and of moving equilibria, in which one movement or +process produces another, and this produces something closely resembling +the former, and so on in long series; as with the swing of a pendulum or +the orbit of a planet: but these are series of cause and effect, not of +reciprocity.</p><p><span class='pagenum'>[Pg 192]<a name="Page_192" id="Page_192"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_XV" id="CHAPTER_XV"></a>CHAPTER XV</h2> + +<h3>INDUCTIVE METHOD</h3> + + +<p><a name="chap_15_sect_1" id="chap_15_sect_1"></a>§ 1. It is necessary to describe briefly the process of investigating +laws of causation, not with the notion of teaching any one the Art of +Discovery, which each man pursues for himself according to his natural +gifts and his experience in the methods of his own science, but merely +to cast some light upon the contents of the next few chapters. Logic is +here treated as a process of proof; proof supposes that some general +proposition or hypothesis has been suggested as requiring proof; and the +search for such propositions may spring from scientific curiosity or +from practical interests.</p> + +<p>We may, as Bain observes (<i>Logic</i>: B. iii. ch. 5), desire to detect a +process of causation either (1) amidst circumstances that have no +influence upon the process but only obscure it; as when, being pleased +with a certain scent in a garden, we wish to know from what flower it +rises; or, being attracted by the sound of some instrument in an +orchestra, we desire to know which it is: or (2) amidst circumstances +that alter the effect from what it would have been by the sole operation +of some cause; as when the air deflects a falling feather; or in some +more complex case, such as a rise or fall of prices that may extend over +many years.</p> + +<p>To begin with, we must form definite ideas as to what the phenomenon is +that we are about to investigate; and in a case of any complexity this +is best done by writing a detailed description of it: <i>e.g.</i>, to +investigate the cause <span class='pagenum'>[Pg 193]<a name="Page_193" id="Page_193"></a></span>of a recent fall of prices, we must describe +exactly the course of the phenomenon, dating the period over which it +extends, recording the successive fluctuations of prices, with their +maxima and minima, and noting the classes of goods or securities that +were more or less affected, <i>etc</i>.</p> + +<p>Then the first step of elimination (as Bain further observes) is "to +analyse the situation mentally," in the light of analogies suggested by +our experience or previous knowledge. Dew, for example, is moisture +formed upon the surface of bodies from no apparent source. But two +possible sources are easily suggested by common experience: is it +deposited from the air, like the moisture upon a mirror when we breathe +upon it; or does it exude from the bodies themselves, like gum or +turpentine? Or, again, as to a fall of prices, a little experience in +business, or knowledge of Economics, readily suggests two possible +explanations: either cheaper production in making goods or carrying +them; or a scarcity of that in which the purchasing power of the chief +commercial nations is directly expressed, namely, gold.</p> + +<p>Having thus analysed the situation and considered the possibility of +one, two, three, or more possible causes, we fix upon one of them for +further investigation; that is to say, we frame an hypothesis that this +is the cause. When an effect is given to find its cause, an inquirer +nearly always begins his investigations by thus framing an hypothesis as +to the cause.</p> + +<p>The next step is to try to <i>verify</i> this Hypothesis. This we may +sometimes do by <i>varying the circumstances</i> of the phenomenon, according +to the Canons of direct Inductive Proof to be discussed in the next +chapter; that is to say, by <i>observing</i> or <i>experimenting</i> in such a way +as to get rid of or eliminate the obscuring or disturbing conditions. +Thus, to find out which flower in a garden gives a certain scent, it is +usually enough to rely on observation, going up to the likely flowers +one after the other and smelling them: at close quarters, the greater +relative intensity of the scent <span class='pagenum'>[Pg 194]<a name="Page_194" id="Page_194"></a></span>is sufficiently decisive. Or we may +resort to a sort of experiment, plucking a likely flower, as to which we +frame the hypothesis (this is the cause), and carrying it to some place +where the air is free from conflicting odours. Should observation or +experiment disprove our first hypothesis we try a second; and so on +until we succeed, or exhaust the known possibilities.</p> + +<p>But if the phenomenon is so complex and extensive as a continuous fall +of prices, direct observation or experiment is a useless or impossible +method; and we must then resort to Deduction; that is, to indirect +Induction. If, for example, we take the hypothesis that the fall is due +to a scarcity of gold, we must show that there is a scarcity; what +effect such a scarcity may be expected to have upon prices from the +acknowledged laws of prices, and from the analogy of other cases of an +expanded or restricted currency; that this expectation agrees with the +statistics of recent commerce: and finally, that the alternative +hypothesis that the fall is due to cheaper production is not true; +either because there has not been a sufficient cheapening of general +production; or because, if there has been, the results to be rationally +expected from it are not such as to agree with the statistics of recent +commerce. (<a href="#CHAPTER_XVIII">Ch. xviii.</a>)</p> + +<p>But now suppose that, a phenomenon having been suggested for +explanation, we are unable at the time to think of any cause—to frame +any hypothesis about it; we must then wait for the phenomenon to occur +again, and, once more observing its course and accompaniments and trying +to recall its antecedents, do our best to conceive an hypothesis, and +proceed as before. Thus, in the first great epidemic of influenza, some +doctors traced it to a deluge in China, others to a volcanic eruption +near Java; some thought it a mild form of Asiatic plague, and others +caught a specific microbe. As the disease often recurred, there were +fresh opportunities of framing hypotheses; and the microbe was +identified.</p><p><span class='pagenum'>[Pg 195]<a name="Page_195" id="Page_195"></a></span></p> + +<p>Again, the investigation may take a different form: given a supposed +Cause to find its Effect; <i>e.g.</i>, a new chemical element, to find what +compounds it forms with other elements; or, the spots on the sun—have +they any influence upon our weather?</p> + +<p>Here, if the given cause be under control, as a new element may be, it +is possible to try experiments with it according to the Canons of +Inductive Proof. The inquirer may form some hypothesis or expectation as +to the effects, to guide his observation of them, but will be careful +not to hold his expectation so confidently as to falsify his observation +of what actually happens.</p> + +<p>But if the cause be, like the sun-spots, not under control, the inquirer +will watch on all sides what events follow their appearance and +development; he must watch for consequences of the new cause he is +studying in many different circumstances, that his observations may +satisfy the canons of proof. But he will also resort for guidance to +deduction; arguing from the nature of the cause, if anything is known of +its nature, what consequences may be expected, and comparing the results +of this deduction with any consequent which he suspects to be connected +with the cause. And if the results of deduction and observation agree, +he will still consider whether the facts observed may not be due to some +other cause.</p> + +<p>A cause, however, may be under control and yet be too dangerous to +experiment with; such as the effects of a poison—though, if too +dangerous to experiment with upon man, it may be tried upon animals; or +such as a proposed change of the constitution by legislation; or even +some minor Act of Parliament, for altering the Poor Law, or regulating +the hours of labour. Here the first step must be deductive. We must ask +what consequences are to be expected from the nature of the change +(comparing it with similar changes), and from the laws of the special +circumstances in which it is to operate? And sometimes we <span class='pagenum'>[Pg 196]<a name="Page_196" id="Page_196"></a></span>may partially +verify our deduction by trying experiments upon a small scale or in a +mild form. There are conflicting deductions as to the probable effect of +giving Home Rule to Ireland; and experiments have been made in more or +less similar cases, as in the Colonies and in some foreign countries. As +to the proposal to make eight hours the legal limit of a day's labour in +all trades, we have all tried to forecast the consequences of this; and +by way of verification we might begin with nine hours; or we might +induce some other country to try the experiment first. Still, no +verification by experiments on a small scale, or in a mild form, or in +somewhat similar yet different circumstances, can be considered +logically conclusive. What proofs are conclusive we shall see in the +following chapters.</p> + +<p><a name="chap_15_sect_2" id="chap_15_sect_2"></a>§ 2. To begin with the conditions of direct Induction.—An Induction is +an universal real proposition, based on observation, in reliance on the +uniformity of Nature: when well ascertained, it is called a Law. Thus, +that all life depends on the presence of oxygen is (1) an universal +proposition; (2) a real one, since the 'presence of oxygen' is not +connoted by 'life'; (3) it is based on observation; (4) it relies on the +uniformity of Nature, since all cases of life have not been examined.</p> + +<p>Such a proposition is here called 'an induction,' when it is inductively +proved; that is, proved by facts, not merely deduced from more general +premises (except the premise of Nature's uniformity): and by the +'process of induction' is meant the method of inductive proof. The +phrase 'process of induction' is often used in another sense, namely for +the inference or judgment by which such propositions are arrived at. But +it is better to call this 'the process of hypothesis,' and to regard it +as a preliminary to the process of induction (that is, proof), as +furnishing the hypothesis which, if it can stand the proper tests, +becomes an induction or law.</p> + +<p><a name="chap_15_sect_3" id="chap_15_sect_3"></a>§ 3. Inductive proofs are usually classed as Perfect and<span class='pagenum'>[Pg 197]<a name="Page_197" id="Page_197"></a></span> Imperfect. +They are said to be perfect when all the instances within the scope of +the given proposition have been severally examined, and the proposition +has been found true in each case. But we have seen (<a href="#chap_13_sect_2">chap. xiii. § 2</a>) +that the instances included in universal propositions concerning Causes +and Kinds cannot be exhaustively examined: we do not know all planets, +all heat, all liquids, all life, <i>etc.</i>; and we never can, since a man's +life is never long enough. It is only where the conditions of time, +place, etc., are arbitrarily limited that examination can be exhaustive. +Perfect induction might show (say) that every member of the present +House of Commons has two Christian names. Such an argument is sometimes +exhibited as a Syllogism in Darapti with a Minor premise in U., which +legitimates a Conclusion in A., thus:</p> + + +<div class="example"><span class="i1">A.B. to Z have two Christian names;<br /></span> +<span class="i1">A.B. to Z are all the present M.P.'s:<br /></span> +<span class="i0">∴ All the present M.P.'s have two Christian names.</span></div> + + +<p class="noindent">But in such an investigation there is no need of logical method to find +the major premise; it is mere counting: and to carry out the syllogism +is a hollow formality. Accordingly, our definition of Induction excludes +the kind unfortunately called Perfect, by including in the notion of +Induction a reliance on the uniformity of Nature; for this would be +superfluous if every instance in question had been severally examined. +Imperfect Induction, then, is what we have to deal with: the method of +showing the credibility of an universal real proposition by an +examination of <i>some</i> of the instances it includes, generally a small +fraction of them.</p> + +<p><a name="chap_15_sect_4" id="chap_15_sect_4"></a>§ 4. Imperfect Induction is either Methodical or Immethodical. Now, +Method is procedure upon a principle; and if the method is to be precise +and conclusive, the principle must be clear and definite.</p> + +<p>There is a Geometrical Method, because the axioms of<span class='pagenum'>[Pg 198]<a name="Page_198" id="Page_198"></a></span> Geometry are clear +and definite, and by their means, with the aid of definitions, laws are +deduced of the equality of lines and angles and other relations of +position and magnitude in space. The process of proof is purely +Deductive (the axioms and definitions being granted). Diagrams are used +not as facts for observation, but merely to fix our attention in +following the general argument; so that it matters little how badly they +are drawn, as long as their divergence from the conditions of the +proposition to be proved is not distracting. Even the appeal to +"superposition" to prove the equality of magnitudes (as in Euclid I. 4), +is not an appeal to observation, but to our judgment of what is implied +in the foregoing conditions. Hence no inference is required from the +special case to all similar ones; for they are all proved at once.</p> + +<p>There is also, as we have seen, a method of Deductive Logic resting on +the Principles of Consistency and the <i>Dictum de omni et nullo</i>. And we +shall find that there is a method of Inductive Logic, resting on the +principle of Causation.</p> + +<p>But there are a good many general propositions, more or less trustworthy +within a certain range of conditions, which cannot be methodically +proved for want of a precise principle by which they may be tested; and +they, therefore, depend upon Immethodical Induction, that is, upon the +examination of as many instances as can be found, relying for the rest +upon the undefinable principle of the Uniformity of Nature, since we are +not able to connect them with any of its definite modes enumerated in +<a href="#chap_13_sect_7">chap. xiii. § 7</a>. To this subject we shall return in <a href="#CHAPTER_XIX">chap. xix.</a>, after +treating of Methodical Induction, or the means of determining that a +relation of events is of the nature of cause and effect, because the +relation can be shown to have the marks of causation, or some of them.</p> + +<p><a name="chap_15_sect_5" id="chap_15_sect_5"></a>§ 5. Observations and Experiments are the <i>material</i> grounds of +Induction. An experiment is an observation <span class='pagenum'>[Pg 199]<a name="Page_199" id="Page_199"></a></span>made under prepared, and +therefore known, conditions; and, when obtainable, it is much to be +preferred. Simple observation shows that the burning of the fire +depends, for one thing, on the supply of air; but it cannot show us that +it depends on oxygen. To prove this we must make experiments as by +obtaining pure oxygen and pure nitrogen (which, mixed in the proportion +of one to four, form the air) in separate vessels, and then plunging a +burning taper into the oxygen—when it will blaze fiercely; and again +plunging it into the nitrogen—when it will be extinguished. This shows +that the greater part of the air does nothing to keep the fire alight, +except by diminishing its intensity and so making it last longer. +Experiments are more perfect the more carefully they are prepared, and +the more completely the conditions are known under which the given +phenomenon is to be observed. Therefore, they become possible only when +some knowledge has already been gained by observation; for else the +preparation which they require could not be made.</p> + +<p>Observation, then, was the first material ground of Induction, and in +some sciences it remains the chief ground. The heavenly bodies, the +winds and tides, the strata of the earth, and the movements of history, +are beyond our power to experiment with. Experiments upon the living +body or mind are indeed resorted to when practicable, even in the case +of man, as now in all departments of Psychology; but, if of a grave +nature, they are usually thought unjustifiable. And in political affairs +experiments are hindered by the reflection, that those whose interests +are affected must bear the consequences and may resent them. Hence, it +is in physical and chemical inquiries and in the physiology of plants +and animals (under certain conditions) that direct experiment is most +constantly practised.</p> + +<p>Where direct experiment is possible, however, it has many advantages +over unaided observation. If one <span class='pagenum'>[Pg 200]<a name="Page_200" id="Page_200"></a></span>experiment does not enable us to +observe the phenomenon satisfactorily, we may try again and again; +whereas the mere observer, who wishes to study the bright spots on Mars, +or a commercial crisis, must wait for a favourable opportunity. Again, +in making experiments we can vary the conditions of the phenomenon, so +as to observe its different behaviour in each case; whereas he who +depends solely on observation must trust the bounty of nature to supply +him with a suitable diversity of instances. It is a particular advantage +of experiment that a phenomenon may sometimes be 'isolated,' that is, +removed from the influence of all agents except that whose operation we +desire to observe, or except those whose operation is already known: +whereas a simple observer, who has no control over the conditions of the +subject he studies, can never be quite sure that its movements or +changes are not due to causes that have never been conspicuous enough to +draw his attention. Finally, experiment enables us to observe coolly and +circumspectly and to be precise as to what happens, the time of its +occurrence, the order of successive events, their duration, intensity +and extent.</p> + +<p>But whether we proceed by observation or experiment, the utmost +attainable exactness of measurements and calculation is requisite; and +these presuppose some Unit, in multiples or divisions of which the +result may be expressed. This unit cannot be an abstract number as in +Arithmetic, but must be one something—an hour, or a yard, or a +pound—according to the nature of the phenomenon to be measured. But +what is an hour, or a yard or a pound? There must in each case be some +constant Standard of reference to give assurance that the unit may +always have the same value. "The English pound is defined by a certain +lump of platinum preserved at Westminster." The unit may be identical +with the standard or some division or multiple of it; and, in measuring +the same kind of phenomena, different units may be used for <span class='pagenum'>[Pg 201]<a name="Page_201" id="Page_201"></a></span>different +purposes as long as each bears a constant relation to the standard. +Thus, taking the rotation of the earth as the standard of Time, the +convenient unit for long periods is a year (which is a multiple); for +shorter periods, a day (which is identical); for shorter still, an hour +(which is a division), or a second, or a thousandth of a second. (See +Jevons' <i>Principles of Science</i>, ch. 14.)</p> + +<p><a name="chap_15_sect_6" id="chap_15_sect_6"></a>§ 6. The principle of Causation is the <i>formal</i> ground of Induction; and +the Inductive Canons derived from it are means of testing the formal +sufficiency of observations to justify the statement of a Law. If we can +observe the process of cause and effect in nature we may generalise our +observation into a law, because that process is invariable. First, then, +can we observe the course of cause and effect? Our power to do so is +limited by the refinement of our senses aided by instruments, such as +lenses, thermometers, balances, <i>etc.</i> If the causal process is +essentially molecular change, as in the maintenance of combustion by +oxygen, we cannot directly observe it; if the process is partly cerebral +or mental, as in social movements which depend on feeling and opinion, +it can but remotely be inferred; even if the process is a collision of +moving masses (billiard-balls), we cannot really observe what happens, +the elastic yielding, and recoil and the internal changes that result; +though no doubt photography will throw some light upon this, as it has +done upon the galloping of horses and the impact of projectiles. Direct +observation is limited to the effect which any change in a phenomenon +(or its index) produces upon our senses; and what we believe to be the +causal process is a matter of inference and calculation. The meagre and +abstract outlines of Inductive Logic are apt to foster the notion, that +the evidence on which Science rests is simple; but it is amazingly +intricate and cumulative.</p> + +<p>Secondly, so far as we can observe the process of nature, how shall we +judge whether a true causal instance, a re<span class='pagenum'>[Pg 202]<a name="Page_202" id="Page_202"></a></span>lation of cause and effect, +is before us? By looking for the five marks of Causation. Thus, in the +experiment above described, showing that oxygen supports combustion, we +find—(1) that the taper which only glowed before being plunged into the +oxygen, bursts into flame when there—Sequence; (2) that this begins to +happen at once without perceptible interval—Immediacy; (3) that no +other agent or disturbing circumstance was present (the preparation of +the experiment having excluded any such thing)—Unconditionalness; (4) +the experiment may be repeated as often as we like with the same +result—Invariableness. Invariableness, indeed, I do not regard as +formally necessary to be shown, supposing the other marks to be clear; +for it can only be proved within our experience; and the very object of +Induction is to find grounds of belief beyond actual experience. +However, for material assurance, to guard against his own liability to +error, the inquirer will of course repeat his experiments.</p> + +<p>The above four are the qualitative marks of Causation: the fifth and +quantitative mark is the Equality of Cause and Effect; and this, in the +above example, the Chemist determines by showing that, instead of the +oxygen and wax that have disappeared during combustion, an equivalent +weight of carbon dioxide, water, <i>etc.</i>, has been formed.</p> + +<p>Here, then, we have all the marks of causation; but in the ordinary +judgments of life, in history, politics, criticism, business, we must +not expect such clear and direct proofs; in subsequent chapters it will +appear how different kinds of evidence are combined in different +departments of investigation.</p> + +<p><a name="chap_15_sect_7" id="chap_15_sect_7"></a>§ 7. The Inductive Canons, to be explained in the next chapter, describe +the character of observations and experiments that justify us in drawing +conclusions about causation; and, as we have mentioned, they are derived +from the principle of Causation itself. According to that principle, +cause and effect are invariably, immediately and uncon<span class='pagenum'>[Pg 203]<a name="Page_203" id="Page_203"></a></span>ditionally +antecedent and consequent, and are equal as to the matter and energy +embodied.</p> + +<p>Invariability can only be observed, in any of the methods of induction, +by collecting more and more instances, or repeating experiments. Of +course it can never be exhaustively observed.</p> + +<p>Immediacy, too, in direct Induction, is a matter for observation the +most exact that is possible.</p> + +<p>Succession, or the relation itself of antecedent and consequent, must +either be directly observed (or some index of it); or else ascertained +by showing that energy gained by one phenomenon has been lost by +another, for this implies succession.</p> + +<p>But to determine the unconditionality of causation, or the +indispensability of some condition, is the great object of the methods, +and for that purpose the meaning of unconditionality may be further +explicated by the following rules for the determination of a Cause.</p> + + +<h3><span class="smcap">A. Qualitative Determination</span></h3> + +<h4><i>I.—For Positive Instances.</i></h4> + +<p>To prove a supposed Cause: (<i>a</i>) Any agent whose introduction among +certain conditions (without further change) is followed by a given +phenomenon; or, (<i>b</i>) whose removal is followed by the cessation (or +modification) of that phenomenon, is (so far) the cause or an +indispensable condition of it.</p> + +<p>To find the Effect: (<i>c</i>) Any event that follows a given phenomenon, +when there is no further change; or, (<i>d</i>) that does not occur when the +conditions of a former occurrence are exactly the same, except for the +absence of that phenomenon, is the effect of it (or is dependent on +it).</p><p><span class='pagenum'>[Pg 204]<a name="Page_204" id="Page_204"></a></span></p> + + +<h4><i>II.—For Negative Instances</i>.</h4> + +<p>To exclude a supposed Cause: (<i>a</i>) Any agent that can be introduced +among certain conditions without being followed by a given phenomenon +(or that is found without that phenomenon); or (<i>b</i>) that can be removed +when that phenomenon is present without impairing it (or that is absent +when that phenomenon is present), is not the cause, or does not complete +the cause, of that phenomenon in those circumstances.</p> + +<p>To exclude a supposed Effect: (<i>c</i>) Any event that occurs without the +introduction (or presence) of a given phenomenon; or (<i>d</i>) that does not +occur when that phenomenon is introduced (or is present), is not the +effect of that phenomenon.</p> + +<hr style='width: 15%;' /> + +<p>Subject to the conditions thus stated, the rules may be briefly put as +follows:</p> + +<p>I. (<i>a</i>) That which (without further change) is followed by a given +event is its cause.</p> + +<p>II. (<i>a</i>) That which is not so followed is not the cause.</p> + +<p>I. (<i>b</i>) That which cannot be left out without impairing a phenomenon is +a condition of it.</p> + +<p>II. (<i>b</i>) That which can be left out is not a condition of it.</p> + + +<h3><span class="smcap">B. Quantitative Determination</span></h3> + +<p>The Equality of Cause and Effect may be further explained by these +rules:</p> + +<p>III. (<i>a</i>) When a cause (or effect) increases or decreases, so does its +effect (or cause).</p> + +<p>III. (<i>b</i>) If two phenomena, having the other marks of cause and effect, +seem unequal, the less contains an unexplored factor.</p> + +<p>III. (<i>c</i>) If an antecedent and consequent do not increase <span class='pagenum'>[Pg 205]<a name="Page_205" id="Page_205"></a></span>or decrease +correspondingly, they are not cause and effect, so far as they vary.</p> + +<p>It will next be shown that these propositions are variously combined in +Mill's five Canons of Induction: Agreement, the Joint Method, +Difference, Variations, Residues. The first three are sometimes called +Qualitative Methods, and the two last Quantitative; and although this +grouping is not quite accurate, seeing that Difference is often used +quantitatively, yet it draws attention to an important distinction +between a mere description of conditions and determination by exact +measurement.</p> + +<p>To avoid certain misunderstandings, some slight alterations have been +made in the wording of the Canons. It may seem questionable whether the +Canons add anything to the above propositions: I think they do. They are +not discussed in the ensuing chapter merely out of reverence for Mill, +or regard for a nascent tradition; but because, as describing the +character of observations and experiments that justify us in drawing +conclusions about causation, they are guides to the analysis of +observations and to the preparation of experiments. To many eminent +investigators the Canons (as such) have been unknown; but they prepared +their work effectively so far only as they had definite ideas to the +same purport. A definite conception of the conditions of proof is the +necessary antecedent of whatever preparations may be made for proving +anything.</p><p><span class='pagenum'>[Pg 206]<a name="Page_206" id="Page_206"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_XVI" id="CHAPTER_XVI"></a>CHAPTER XVI</h2> + +<h3>THE CANONS OF DIRECT INDUCTION</h3> + + +<p><a name="chap_16_sect_1" id="chap_16_sect_1"></a>§ 1. Let me begin by borrowing an example from Bain (<i>Logic</i>: B. III. c. +6). The North-East wind is generally detested in this country: as long +as it blows few people feel at their best. Occasional well-known causes +of a wind being injurious are violence, excessive heat or cold, +excessive dryness or moisture, electrical condition, the being laden +with dust or exhalations. Let the hypothesis be that the last is the +cause of the North-East wind's unwholesome quality; since we know it is +a ground current setting from the pole toward the equator and bent +westward by the rotation of the earth; so that, reaching us over +thousands of miles of land, it may well be fraught with dust, effluvia, +and microbes. Now, examining many cases of North-East wind, we find that +this is the only circumstance in which all the instances agree: for it +is sometimes cold, sometimes hot; generally dry, but sometimes wet; +sometimes light, sometimes violent, and of all electrical conditions. +Each of the other circumstances, then, can be omitted without the N.E. +wind ceasing to be noxious; but one circumstance is never absent, +namely, that it is a ground current. That circumstance, therefore, is +probably the cause of its injuriousness. This case illustrates:—</p> + + +<h3><span class="smcap">(I) The Canon of Agreement.</span></h3> + +<p><i>If two or more instances of a phenomenon under investigation have only +one other circumstance (antecedent or consequent) in common, that +circumstance is probably the cause</i><span class='pagenum'>[Pg 207]<a name="Page_207" id="Page_207"></a></span> <i>(or an indispensable condition) or +the effect of the phenomenon, or is connected with it by causation.</i></p> + +<p>This rule of proof (so far as it is used to establish direct causation) +depends, first, upon observation of an invariable connection between the +given phenomenon and one other circumstance; and, secondly, upon I. +(<i>a</i>) and II. (<i>b</i>) among the propositions obtained from the +unconditionality of causation at the close of the last chapter.</p> + +<p>To prove that A is causally related to <i>p</i>, suppose two instances of the +occurrence of A, an antecedent, and <i>p</i>, a consequent, with concomitant +facts or events—and let us represent them thus:</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='left'>Antecedents:</td><td align='left'>A</td><td align='left'>B</td><td align='left'>C</td><td></td><td align='left'>A</td><td align='left'>D</td><td align='left'>E</td></tr> +<tr><td align='left'>Consequents:</td><td align='left'><i>p</i></td><td align='left'><i>q</i></td><td align='left'><i>r</i></td><td></td><td align='left'><i>p</i></td><td align='left'><i>s</i></td><td align='left'><i>t</i>;</td></tr> +</table></div> + + +<p class="noindent">and suppose further that, in this case, the immediate succession of +events can be observed. Then A is probably the cause, or an +indispensable condition, of <i>p</i>. For, as far as our instances go, A is +the invariable antecedent of <i>p</i>; and <i>p</i> is the invariable consequent +of A. But the two instances of A or <i>p</i> agree in no other circumstance. +Therefore A is (or completes) the unconditional antecedent of <i>p</i>. For B +and C are not indispensable conditions of <i>p</i>, being absent in the +second instance (Rule II. (<i>b</i>)); nor are D and E, being absent in the +first instance. Moreover, <i>q</i> and <i>r</i> are not effects of A, being absent +in the second instance (Rule II. (<i>d</i>)); nor are <i>s</i> and <i>t</i>, being +absent in the first instance.</p> + +<p>It should be observed that the cogency of the proof depends entirely +upon its tending to show the unconditionality of the sequence A-<i>p</i>, or +the indispensability of A as a condition of <i>p</i>. That <i>p</i> follows A, +even immediately, is nothing by itself: if a man sits down to study and, +on the instant, a hand-organ begins under his window, he must not infer +malice in the musician: thousands of things follow one another every +moment without traceable connection; and this we call 'accidental.' Even +invariable sequence is <span class='pagenum'>[Pg 208]<a name="Page_208" id="Page_208"></a></span>not enough to prove direct causation; for, in +our experience does not night invariable follow day? The proof requires +that the instances be such as to show not merely what events <i>are</i> in +invariable sequence, but also what <i>are not</i>. From among the occasional +antecedents of <i>p</i> (or consequents of A) we have to eliminate the +accidental ones. And this is done by finding or making 'negative +instances' in respect of each of them. Thus the instance</p> + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='left'>A</td><td align='left'>D</td><td align='left'>E</td></tr> +<tr><td align='left'><i>p</i></td><td align='left'><i>s</i></td><td align='left'><i>t</i></td></tr> +</table></div> + +<p class="noindent">is a negative instance of B and C considered as supposable causes of <i>p</i> +(and of <i>q</i> and <i>r</i> as supposable effects of A); for it shows that they +are absent when <i>p</i> (or A) is present.</p> + +<p>To insist upon the cogency of 'negative instances' was Bacon's great +contribution to Inductive Logic. If we neglect them, and merely collect +examples of the sequence A-<i>p</i>, this is 'simple enumeration'; and +although simple enumeration, when the instances of agreement are +numerous enough, may give rise to a strong belief in the connection of +phenomena, yet it can never be a methodical or logical proof of +causation, since it does not indicate the unconditionalness of the +sequence. For simple enumeration of the sequence A-<i>p</i> leaves open the +possibility that, besides A, there is always some other antecedent of +<i>p</i>, say X; and then X may be the cause of <i>p</i>. To disprove it, we must +find, or make, a negative instance of X—where <i>p</i> occurs, but X is +absent.</p> + +<p>So far as we recognise the possibility of a plurality of causes, this +method of Agreement cannot be quite satisfactory. For then, in such +instances as the above, although D is absent in the first, and B in the +second, it does not follow that they are not the causes of <i>p</i>; for they +may be alternative causes: B may have produced <i>p</i> in the first +instance, and D in the second; A being in both cases an accidental +circumstance in relation to <i>p</i>. To remedy this shortcoming by the +method of Agreement itself, the only course is to find more instances of +<i>p</i>. We may never find <span class='pagenum'>[Pg 209]<a name="Page_209" id="Page_209"></a></span>a negative instance of A; and, if not, the +probability that A is the cause of <i>p</i> increases with the number of +instances. But if there be no antecedent that we cannot sometimes +exclude, yet the collection of instances will probably give at last all +the causes of <i>p</i>; and by finding the proportion of instances in which +A, B, or X precedes <i>p</i>, we may estimate the probability of any one of +them being the cause of <i>p</i> in any given case of its occurrence.</p> + +<p>But this is not enough. Since there cannot really be vicarious causes, +we must define the effect (<i>p</i>) more strictly, and examine the cases to +find whether there may not be varieties of <i>p</i>, with each of which one +of the apparent causes is correlated: A with <i>p</i><sup>1</sup> B with <i>p</i><sup>11</sup>, X +with <i>p</i><sup>111</sup>. Or, again, it may be that none of the recognised +antecedents is effective: as we here depend solely on observation, the +true conditions may be so recondite and disguised by other phenomena as +to have escaped our scrutiny. This may happen even when we suppose that +the chief condition has been isolated: the drinking of foul water was +long believed to cause dysentery, because it was a frequent antecedent; +whilst observation had overlooked the bacillus, which was the +indispensable condition.</p> + +<p>Again, though we have assumed that, in the instances supposed above, +immediate sequence is observable, yet in many cases it may not be so, if +we rely only on the canon of Agreement; if instances cannot be obtained +by experiment, and we have to depend on observation. The phenomena may +then be so mixed together that A and <i>p</i> seem to be merely concomitant; +so that, though connection of some sort may be rendered highly probable, +we may not be able to say which is cause and which is effect. We must +then try (as Bain says) to trace the expenditure of energy: if <i>p</i> gains +when A loses, the course of events if from A to <i>p</i>.</p> + +<p>Moreover, where succession cannot be traced, the method of Agreement may +point to a connection between two or more facts (perhaps as co-effects +of a remote cause) where <span class='pagenum'>[Pg 210]<a name="Page_210" id="Page_210"></a></span>direct causation seems to be out of the +question: <i>e.g.</i>, that Negroes, though of different tribes, different +localities, customs, <i>etc.</i>, are prognathous, woolly-haired and +dolichocephalic.</p> + +<p>The Method of Agreement, then, cannot by itself prove causation. Its +chief use (as Mill says) is to suggest hypotheses as to the cause; which +must then be used (if possible) experimentally to try if it produces the +given effect. A bacillus, for example, being always found with a certain +disease, is probably the chief condition of it: give it to a guinea-pig, +and observe whether the disease appears in that animal.</p> + +<p>Men often use arguments which, if they knew it, might be shown to +conform more or less to this canon; for they collect many instances to +show that two events are connected; but usually neglect to bring out the +negative side of the proof; so that their arguments only amount to +simple enumeration. Thus Ascham in his <i>Toxophilus</i>, insisting on the +national importance of archery, argues that victory has always depended +on superiority in shooting; and, to prove it, he shows how the Parthians +checked the Romans, Sesostris conquered a great part of the known world, +Tiberius overcame Arminius, the Turks established their empire, and the +English defeated the French (with many like examples)—all by superior +archery. But having cited these cases to his purpose, he is content; +whereas he might have greatly strengthened his proof by showing how one +or the other instance excludes other possible causes of success. Thus: +the cause was not discipline, for the Romans were better disciplined +than the Parthians; nor yet the boasted superiority of a northern +habitat, for Sesostris issued from the south; nor better manhood, for +here the Germans probably had the advantage of the Romans; nor superior +civilisation, for the Turks were less civilised than most of those they +conquered; nor numbers, nor even a good cause, for the French were more +<span class='pagenum'>[Pg 211]<a name="Page_211" id="Page_211"></a></span>numerous than the English, and were shamefully attacked by Henry V. on +their own soil. Many an argument from simple enumeration may thus be +turned into an induction of greater plausibility according to the Canon +of Agreement.</p> + +<p>Still, in the above case, the effect (victory) is so vaguely conceived, +that a plurality of causes must be allowed for: although, <i>e.g.</i>, +discipline did not enable the Romans to conquer the Parthians, it may +have been their chief advantage over the Germans; and it was certainly +important to the English under Henry V. in their war with the French.</p> + +<p>Here is another argument, somewhat similar to the above, put forward by +H. Spencer with a full consciousness of its logical character. States +that make war their chief object, he says, assume a certain type of +organisation, involving the growth of the warrior class and the +treatment of labourers as existing solely to sustain the warriors; the +complete subordination of individuals to the will of the despotic +soldier-king, their property, liberty and life being at the service of +the State; the regimentation of society not only for military but also +for civil purposes; the suppression of all private associations, <i>etc.</i> +This is the case in Dahomey and in Russia, and it was so at Sparta, in +Egypt, and in the empire of the Yncas. But the similarity of +organisation in these States cannot have been due to race, for they are +all of different races; nor to size, for some are small, some large; nor +to climate or other circumstances of habitat, for here again they differ +widely: the one thing they have in common is the military purpose; and +this, therefore, must be the cause of their similar organisation. +(<i>Political Institutions.</i>)</p> + +<p>By this method, then, to prove that one thing is causally connected with +another, say A with <i>p</i>, we show, first, that in all instances of <i>p</i>, A +is present; and, secondly, that any other supposable cause of <i>p</i> may be +absent without disturbing <i>p</i>. We next come to a method the use of which +greatly strengthens the foregoing, by showing that <span class='pagenum'>[Pg 212]<a name="Page_212" id="Page_212"></a></span>where <i>p</i> is absent +A is also absent, and (if possible) that A is the only supposable cause +that is always absent along with <i>p</i>.</p> + + +<h3><span class="smcap"><a name="chap_16_sect_2" id="chap_16_sect_2"></a>§ 2. The Canon of the Joint Method of Agreement in Presence and in +Absence.</span></h3> + +<p><i>If</i> (1) <i>two or more instances in which a phenomenon occurs have only +one other circumstance (antecedent or consequent) in common, while</i> (2) +<i>two or more instances in which it does not occur (though in important +points they resemble the former set of instances) have nothing else in +common save the absence of that circumstance—the circumstance in which +alone the two sets of instances differ throughout (being present in the +first set and absent in the second) is probably the effect, or the +cause, or an indispensable condition of the phenomenon.</i></p> + +<p>The first clause of this Canon is the same as that of the method of +Agreement, and its significance depends upon the same propositions +concerning causation. The second clause, relating to instances in which +the phenomenon is absent, depends for its probative force upon Prop. II. +(<i>a</i>), and I. (<i>b</i>): its function is to exclude certain circumstances +(whose nature or manner of occurrence gives them some claim to +consideration) from the list of possible causes (or effects) of the +phenomenon investigated. It might have been better to state this second +clause separately as the Canon of the Method of Exclusions.</p> + +<p>To prove that A is causally related to <i>p</i>, let the two sets of +instances be represented as follows:</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center' colspan='3'>Instances of Presence.</td><td align='center' colspan='3'>Instances of Absence.</td></tr> +<tr><td align='right'>A</td><td align='center'>B</td><td align='left'>C</td><td align='right'>C</td><td align='center'>H</td><td align='left'>F</td></tr> +<tr><td align='right'><i>p</i></td><td align='center'><i>q</i></td><td align='left'><i>r</i></td><td align='right'><i>r</i></td><td align='center'><i>x</i></td><td align='left'><i>v</i></td></tr> +<tr><td align='right'>A</td><td align='center'>D</td><td align='left'>E</td><td align='right'>B</td><td align='center'>D</td><td align='left'>K</td></tr> +<tr><td align='right'><i>p</i></td><td align='center'><i>s</i></td><td align='left'><i>t</i></td><td align='right'><i>q</i></td><td align='center'><i>y</i></td><td align='left'><i>s</i></td></tr> +<tr><td align='right'>A</td><td align='center'>F</td><td align='left'>G</td><td align='right'>E</td><td align='center'>G</td><td align='left'>M</td></tr> +<tr><td align='right'><i>p</i></td><td align='center'><i>u</i></td><td align='left'><i>v</i></td><td align='right'><i>t</i></td><td align='center'><i>f</i></td><td align='left'><i>u</i></td></tr> +</table></div> + + +<p class="noindent"><span class='pagenum'>[Pg 213]<a name="Page_213" id="Page_213"></a></span>Then A is probably the cause or a condition of <i>p</i>, or <i>p</i> is dependent +upon A: first, by the Canon of Agreement in Presence, as represented by +the first set of instances; and, secondly, by Agreement in Absence in +the second set of instances. For there we see that C, H, F, B, D, K, E, +G, M occur without the phenomenon <i>p</i>, and therefore (by Prop. II. +(<i>a</i>)) are not its cause, or not the whole cause, unless they have been +counteracted (which is a point for further investigation). We also see +that <i>r, v, q, s, t, u</i> occur without A, and therefore are not the +effects of A. And, further, if the negative instances represent all +possible cases, we see that (according to Prop. I. (<i>b</i>)) A is the cause +of <i>p</i>, because it cannot be omitted without the cessation of <i>p</i>. The +inference that A and <i>p</i> are cause and effect, suggested by their being +present throughout the first set of instances, is therefore strengthened +by their being both absent throughout the second set.</p> + +<p>So far as this Double Method, like the Single Method of Agreement, +relies on observation, sequence may not be perceptible in the instances +observed, and then, direct causation cannot be proved by it, but only +the probability of causal connection; and, again, the real cause, though +present, may be so obscure as to evade observation. It has, however, one +peculiar advantage, namely, that if the second list of instances (in +which the phenomenon and its supposed antecedent are both absent) can be +made exhaustive, it precludes any hypothesis of a plurality of causes; +since all possible antecedents will have been included in this list +without producing the phenomenon. Thus, in the above symbolic example, +taking the first set of instances, the supposition is left open that B, +C, D, E, F, G may, at one time or another, have been a condition of <i>p</i>; +but, in the second list, these antecedents all occur, here or there, +without producing <i>p</i>, and therefore (unless counteracted somehow) +cannot be a condition of <i>p</i>. A, <span class='pagenum'>[Pg 214]<a name="Page_214" id="Page_214"></a></span>then, stands out as the one thing that +is present whenever <i>p</i> is present, and absent whenever <i>p</i> is absent.</p> + +<p>Stated in this abstract way, the Double Method may seem very elaborate +and difficult; yet, in fact, its use may be very simple. Tyndall, to +prove that dispersed light in the air is due to motes, showed by a +number of cases (1) that any gas containing motes is luminous; (2) that +air in which the motes had been destroyed by heat, and any gas so +prepared as to exclude motes, are not luminous. All the instances are of +gases, and the result is: motes—luminosity; no motes—no luminosity. +Darwin, to show that cross-fertilisation is favourable to flowers, +placed a net about 100 flower-heads, and left 100 others of the same +varieties exposed to the bees: the former bore no seed, the latter +nearly 3,000. We must assume that, in Darwin's judgment, the net did not +screen the flowers from light and heat sufficiently to affect the +result.</p> + +<p>There are instructive applications of this Double Method in Wallace's +<i>Darwinism</i>. In chap. viii., on <i>Colour in Animals</i>, he observes, that +the usefulness of their coloration to animals is shown by the fact that, +"as a rule, colour and marking are constant in each species of wild +animal, while, in almost every domesticated animal, there arises great +variability. We see this in our horses and cattle, our dogs and cats, +our pigeons and poultry. Now the essential difference between the +conditions of life of domesticated and wild animals is, that the former +are protected by man, while the latter have to protect themselves." Wild +animals protect themselves by acquiring qualities adapted to their mode +of life; and coloration is a very important one, its chief, though not +its only use, being concealment. Hence a useful coloration having been +established in any species, individuals that occasionally may vary from +it, will generally, perish; whilst, among domestic animals, variation of +colour or marking is sub<span class='pagenum'>[Pg 215]<a name="Page_215" id="Page_215"></a></span>ject to no check except the taste of owners. We +have, then, two lists of instances; first, innumerable species of wild +animals in which the coloration is constant and which depend upon their +own qualities for existence; secondly, several species of domestic +animals in which the coloration is <i>not</i> constant, and which do <i>not</i> +depend upon their own qualities for existence. In the former list two +circumstances are present together (under all sorts of conditions); in +the latter they are absent together. The argument may be further +strengthened by adding a third list, parallel to the first, comprising +domestic animals in which coloration is approximately constant, but +where (as we know) it is made a condition of existence by owners, who +only breed from those specimens that come up to a certain standard of +coloration.</p> + +<p>Wallace goes on to discuss the colouring of arctic animals. In the +arctic regions, he says, some animals are wholly white all the year +round, such as the polar bear, the American polar hare, the snowy owl +and the Greenland falcon: these live amidst almost perpetual snow. +Others, that live where the snow melts in summer, only turn white in +winter, such as the arctic hare, the arctic fox, the ermine and the +ptarmigan. In all these cases the white colouring is useful, concealing +the herbivores from their enemies, and also the carnivores in +approaching their prey; this usefulness, therefore, is a condition of +the white colouring. Two other explanations have, however, been +suggested: first, that the prevalent white of the arctic regions +directly colours the animals, either by some photographic or chemical +action on the skin, or by a reflex action through vision (as in the +chameleon); secondly, that a white skin checks radiation and keeps the +animals warm. But there are some exceptions to the rule of white +colouring in arctic animals which refute these hypotheses, and confirm +the author's. The sable remains brown throughout the winter; but it +frequents trees, with <span class='pagenum'>[Pg 216]<a name="Page_216" id="Page_216"></a></span>whose bark its colour assimilates. The musk-sheep +is brown and conspicuous; but it is gregarious, and its safety depends +upon its ability to recognise its kind and keep with the herd. The raven +is always black; but it fears no enemy and feeds on carrion, and +therefore does not need concealment for either defence or attack. The +colour of the sable, then, though not white, serves for concealment; the +colour of the musk-sheep serves a purpose more important than +concealment; the raven needs no concealment. There are thus two sets of +instances:—in one set the animals are white (<i>a</i>) all the year, (<i>b</i>) +in winter; and white conceals them (<i>a</i>) all the year, (<i>b</i>) in winter; +in the other set, the animals are <i>not</i> white, and to them either +whiteness would <i>not</i> give concealment, or concealment would <i>not</i> be +advantageous. And this second list refutes the rival hypotheses: for the +sable, the musk-sheep and the raven are as much exposed to the glare of +the snow, and to the cold, as the other animals are.</p> + + +<h3><span class="smcap"><a name="chap_16_sect_3" id="chap_16_sect_3"></a>§ 3. The Canon of Difference</span>.</h3> + +<p><i>If an instance in which a phenomenon occurs, and an instance in which +it does not occur, have every other circumstance in common save one, +that one (whether consequent or antecedent) occurring only in the +former; the circumstance in which alone the two instances differ is the +effect, or the cause, or an indispensable condition of the phenomenon.</i></p> + +<p>This follows from Props. I (<i>a</i>) and (<i>b</i>), in <a href="#chap_15_sect_7">chapter xv. § 7</a>. To prove +that A is a condition of <i>p</i>, let two instances, such as the Canon +requires, be represented thus:</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'>A</td><td align='center'>B</td><td align='center'>C</td><td> </td><td align='center'>B</td><td align='center'>C</td></tr> +<tr><td align='center'><i>p</i></td><td align='center'><i>q</i></td><td align='center'><i>r</i></td><td> </td><td align='center'><i>q</i></td><td align='center'><i>r</i></td></tr> +</table></div> + + +<p class="noindent">Then A is the cause or a condition of <i>p</i>. For, in the first instance, A +being introduced (without further change), <i>p</i> arises (Prop. I. (<i>a</i>)); +and, in the second instance, A having been removed (without other +change), <i>p</i> disappears<span class='pagenum'>[Pg 217]<a name="Page_217" id="Page_217"></a></span> (Prop. I. (<i>b</i>)). Similarly we may prove, by +the same instances, that <i>p</i> is the effect of A.</p> + +<p>The order of the phenomena and the immediacy of their connection is a +matter for observation, aided by whatever instruments and methods of +inspection and measurement may be available.</p> + +<p>As to the invariability of the connection, it may of course be tested by +collecting more instances or making more experiments; but it has been +maintained, that a single perfect experiment according to this method is +sufficient to prove causation, and therefore implies invariability +(since causation is uniform), though no other instances should ever be +obtainable; because it establishes once for all the unconditionality of +the connection</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'>A</td><td align='center'>B</td><td align='center'>C</td></tr> +<tr><td align='center'><i>p</i></td><td align='center'><i>q</i></td><td align='center'><i>r</i>.</td></tr> +</table></div> + + +<p class="noindent">Now, formally this is true; but in any actual investigation how shall we +decide what is a satisfactory or perfect experiment? Such an experiment +requires that in the negative instance</p> + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'>B</td><td align='center'>C</td></tr> +<tr><td align='center'><i>q</i></td><td align='center'><i>r</i>,</td></tr> +</table></div> + +<p class="noindent">BC shall be the least assemblage of conditions necessary to co-operate +with A in producing <i>p</i>; and that it is so cannot be ascertained without +either general prior knowledge of the nature of the case or special +experiments for the purpose. So that invariability will not really be +inferred from a single experiment; besides that every prudent inquirer +repeats his experiments, if only to guard against his own liability to +error.</p> + +<p>The supposed plurality of causes does not affect the method of +Difference. In the above symbolic case, A is clearly <i>one</i> cause (or +condition) of <i>p</i>, whatever other causes may be possible; whereas with +the Single Method of Agreement, it remained doubtful (admitting a +plurality of causes) whether A, in spite of being always present with +<i>p</i>, was ever a cause or condition of it.</p> + +<p>This method of Difference without our being distinctly aware of it, is +oftener than any other the basis of <span class='pagenum'>[Pg 218]<a name="Page_218" id="Page_218"></a></span>ordinary judgments. That the sun +gives light and heat, that food nourishes and fire burns, that a stone +breaks a window or kills a bird, that the turning of a tap permits or +checks the flow of water or of gas, and thousands of other propositions +are known to be true by rough but often emphatic applications of this +method in common experience.</p> + +<p>The method of Difference may be applied either (1) by observation, on +finding two instances (distinct assemblages of conditions) differing +only in one phenomenon together with its antecedent or consequent; or +(2) by experiment, and then, either (<i>a</i>) by preparing two instances +that may be compared side by side, or (<i>b</i>) by taking certain +conditions, and then introducing (or subtracting) some agent, supposed +to be the cause, to see what happens: in the latter case the "two +instances" are the same assemblage of conditions considered before and, +again, after, the introduction of the agent. As an example of (<i>a</i>) +there is an experiment to show that radium gives off heat: take two +glass tubes, in one put some chloride of radium, in both thermometers, +and close them with cotton-wool. Soon the thermometer in the tube along +with radium reads 54° F. higher than the other one. The tube without the +radium, whose temperature remains unaltered, is called the "control" +experiment. Most experiments are of the type (<i>b</i>); and since the Canon, +which describes two co-existing instances, does not readily apply to +this type, an alternative version may be offered: <i>Any agent whose +introduction into known circumstances (without further change) is +immediately followed by a definite phenomenon is a condition of the +occurrence of that phenomenon.</i></p> + +<p>The words <i>into known circumstances</i> are necessary to emphasise what is +required by this Method, namely, that the two instances differ in only +one thing; for this cannot be ascertained unless all the other +conditions are known; and this further implies that they have been +prepared.<span class='pagenum'>[Pg 219]<a name="Page_219" id="Page_219"></a></span> It is, therefore, not true (as Sigwart asserts) that this +method determines only one condition of a phenomenon, and that it is +then necessary to inquire into the other conditions. If they were not +known they must be investigated; but then the experiment would not have +been made upon this method. Practically, experiments have to be made in +all degrees of imperfection, and the less perfect they are, that is, the +less the circumstances are known beforehand, the more remains to be +done. A common imperfection is delay, or the occurrence of a latent +period between the introduction of an agent and the manifestation of its +effects; it cannot then be the unconditional cause; though it may be an +indispensable remote condition of whatever change occurs. If, feeling +out of sorts, you take a drug and some time afterwards feel better, it +is not clear on this ground alone that the drug was the cause of +recovery, for other curative processes may have been active +meanwhile—food, or sleep, or exercise.</p> + +<p>Any book of Physics or of Chemistry will furnish scores of examples of +the method of Difference: such as Galileo's experiment to show that air +has weight, by first weighing a vessel filled with ordinary air, and +then filling it with condensed air and weighing it again; when the +increased weight can only be due to the greater quantity of air +contained. The melting-point of solids is determined by heating them +until they do melt (as silver at 1000° C., gold at 1250°, platinum at +2000°); for the only difference between bodies at the time of melting +and just before is the addition of so much heat. Similarly with the +boiling point of liquids. That the transmission of sound depends upon +the continuity of an elastic ponderable medium, is proved by letting a +clock strike in a vacuum (under a glass from which the air has been +withdrawn by an air pump), and standing upon a non-elastic pedestal: +when the clock be seen to strike, but makes only such a faint sound <span class='pagenum'>[Pg 220]<a name="Page_220" id="Page_220"></a></span>as +may be due to the imperfections of the vacuum and the pedestal.</p> + +<p>The experiments by which the chemical analysis or synthesis of various +forms of matter is demonstrated are simple or compound applications of +this method of Difference, together with the quantitative mark of +causation (that cause and effect are equal); since the bodies resulting +from an analysis are equal in weight to the body analysed, and the body +resulting from a synthesis is equal in weight to the bodies synthesised. +That an electric current resolves water into oxygen and hydrogen may be +proved by inserting the poles of a galvanic battery in a vessel of +water; when this one change is followed by another, the rise of bubbles +from each pole and the very gradual decrease of the water. If the +bubbles are caught in receivers placed over them, it can be shown that +the joint weight of the two bodies of gas thus formed is equal to the +weight of the water that has disappeared; and that the gases are +respectively oxygen and hydrogen may then be shown by proving that they +have the properties of those gases according to further experiments by +the method of Difference; as (<i>e.g.</i>) that one of them is oxygen because +it supports combustion, <i>etc.</i></p> + +<p>When water was first decomposed by the electric current, there appeared +not only oxygen and hydrogen, but also an acid and an alkali. These +products were afterwards traced to impurities of the water and of the +operator's hands. Mill observes that in any experiment the effect, or +part of it, may be due, not to the supposed agent, but to the means +employed in introducing it. We should know not only the other conditions +of an experiment, but that the agent or change introduced is nothing +else than what it is supposed to be.</p> + +<p>In the more complex sciences the method of Difference is less easily +applicable, because of the greater difficulty of being sure that only +one circumstance at a time has altered; <span class='pagenum'>[Pg 221]<a name="Page_221" id="Page_221"></a></span>still, it is frequently used. +Thus, if by dividing a certain nerve certain muscles are paralysed, it +is shown that normally that nerve controls those muscles. That the sense +of smell in flies and cockroaches is connected with the antennae has +been shown by cutting them off: whereupon the insects can no longer find +carrion. In his work on <i>Earthworms</i>, Darwin shows that, though +sensitive to mechanical tremors, they are deaf (or, at least, not +sensitive to sonorous vibrations transmitted through the air), by the +following experiment. He placed a pot containing a worm that had come to +the surface, as usual at night, upon a table, whilst close by a piano +was violently played; but the worm took no notice of the noise. He then +placed the pot upon the piano, whilst it was being played, when the +worm, probably feeling mechanical vibrations, hastily slid back into its +burrow.</p> + +<p>When, instead of altering one circumstance in an instance (which we have +done our best not otherwise to disturb) and then watching what follows, +we try to find two ready-made instances of a phenomenon, which only +differ in one other circumstance, it is, of course, still more difficult +to be sure that there is only one other circumstance in which they +differ. It may be worth while, however, to look for such instances. +Thus, that the temperature of ocean currents influences the climate of +the shores they wash, seems to be shown by the fact that the average +temperature of Newfoundland is lower than that of the Norwegian coast +some 15° farther north. Both regions have great continents at their +back; and as the mountains of Norway are higher and capped with +perennial snow, we might expect a colder climate there: but the shore of +Norway is visited by the Gulf Stream, whilst the shore of Newfoundland +is traversed by a cold current from Greenland. Again, when in 1841 the +railway from Rouen to Paris was being built, gangs of English and gangs +of French workmen were employed upon it, and the English <span class='pagenum'>[Pg 222]<a name="Page_222" id="Page_222"></a></span>got through +about one-third more work per man than the French. It was suspected that +this difference was due to one other difference, namely, that the +English fed better, preferring beef to thin soup. Now, logically, it +might have been objected that the evidence was unsatisfactory, seeing +that the men differed in other things besides diet—in 'race' (say), +which explains so much and so easily. But the Frenchmen, having been +induced to try the same diet as the English, were, in a few days, able +to do as much work: so that the "two instances" were better than they +looked. It often happens that evidence, though logically questionable, +is good when used by experts, whose familiarity with the subject makes +it good.</p> + + +<h3><span class="smcap"><a name="chap_16_sect_4" id="chap_16_sect_4"></a>§ 4. The Canon Of Concomitant Variations.</span></h3> + +<p><i>Whatever phenomenon varies in any manner whenever another phenomenon +(consequent or antecedent) varies in some particular manner [no other +change having concurred] is either the cause or effect of that +phenomenon [or is connected with it through some fact of causation].</i></p> + +<p>This is not an entirely fresh method, but may be regarded as a special +case either of Agreement or of Difference, to prove the cause or effect, +not of a phenomenon as a whole, but of some increment of it (positive or +negative). There are certain forces, such as gravitation, heat, +friction, that can never be eliminated altogether, and therefore can +only be studied in their degrees. To such phenomena the method of +Difference cannot be applied, because there are no negative instances. +But we may obtain negative instances of a given quantity of such a +phenomenon (say, heat), and may apply the method of Difference to that +quantity. Thus, if the heat of a body increases 10 degrees, from 60 to +70, the former temperature of 60 was a negative instance in respect of +those 10 <span class='pagenum'>[Pg 223]<a name="Page_223" id="Page_223"></a></span>degrees; and if only one other circumstance (say, friction) +has altered at the same time, that circumstance (if an antecedent) is +the cause. Accordingly, if in the above Canon we insert, after +'particular manner,' "[no other change having concurred,]" it is a +statement of the method of Difference as applicable to the increment of +a phenomenon, instead of to the phenomenon as a whole; and we may then +omit the last clause—"[or is connected, <i>etc.</i>]." For these words are +inserted to provide for the case of co-effects of a common cause (such +as the flash and report of a gun); but if no other change (such as the +discharge of a gun) has concurred with the variations of two phenomena, +there cannot have been a common cause, and they are therefore cause and +effect.</p> + +<p>If, on the other hand, we omit the clause "[no other change having +concurred,]" the Canon is a statement of the method of Agreement as +applicable to the increment of a phenomenon instead of to the phenomenon +as a whole; and it is then subject to the imperfections of that method: +that is to say, it leaves open the possibilities, that an inquirer may +overlook a plurality of causes; or may mistake a connection of two +phenomena, which (like the flash and report of a gun) are co-effects of +a common cause, for a direct relation of cause and effect.</p> + +<p>It may occur to the reader that we ought also to distinguish Qualitative +and Quantitative Variations as two orders of phenomena to which the +present method is applicable. But, in fact, Qualitative Variations may +be adequately dealt with by the foregoing methods of Agreement, Double +Agreement, and Difference; because a change of quality or property +entirely gets rid of the former phase of that quality, or substitutes +one for another; as when the ptarmigan changes from brown to white in +winter, or as when a stag grows and sheds its antlers with the course of +the seasons. The peculiar use of the method of Variations, however, is +to formulate the <span class='pagenum'>[Pg 224]<a name="Page_224" id="Page_224"></a></span>conditions of proof in respect of those causes or +effects which cannot be entirely got rid of, but can be obtained only in +greater or less amount; and such phenomena are or course, quantitative.</p> + +<p>Even when there are two parallel series of phenomena the one +quantitative and the other qualitative—like the rate of air-vibration +and the pitch of sound, or the rate of ether-vibration and the +colour-series of the spectrum—the method of Variations is not +applicable. For (1) two such series cannot be said to vary together, +since the qualitative variations are heterogeneous: 512: 576 is a +definite ratio; but the corresponding notes, C, D, in the treble clef, +present only a difference. Hence (2) the correspondence of each note +with each number is a distinct fact. Each octave even is a distinct +fact; there is a difference between C 64 and C 128 that could never have +been anticipated without the appropriate experience. There is, +therefore, no such law of these parallel series as there is for +temperature and change of volume (say) in mercury. Similar remarks apply +to the physical and sensitive light-series.</p> + +<p>We may illustrate the two cases of the method thus (putting a dash +against any letter, A' or <i>p</i>', to signify an increase or decrease of +the phenomenon the letter stands for): Agreement in Variations (other +changes being admissible)—</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'>A</td><td align='center'>B</td><td align='center'>C</td><td> </td><td align='center'>A'</td><td align='center'>D</td><td align='center'>E</td><td> </td><td align='center'>A''</td><td align='center'>F</td><td align='center'>G</td></tr> +<tr><td align='center'><i>p</i></td><td align='center'><i>q</i></td><td align='center'><i>r</i></td><td> </td><td align='center'><i>p'</i></td><td align='center'><i>s</i></td><td align='center'><i>t</i></td><td> </td><td align='center'><i>p''</i></td><td align='center'><i>u</i></td><td align='center'><i>v</i></td></tr> +</table></div> + + +<p class="noindent">Here the accompanying phenomena (<i>B C q r, D E s t, F G u v</i>) change +from time to time, and the one thing in which the instances agree +throughout is that any increase of A (A' or A'') is followed or +accompanied by an increase of <i>p (p' or p'')</i>: whence it is argued that +A is the cause of <i>p</i>, according to Prop. III. (<i>a</i>) (<a href="#chap_15_sect_7">ch. xv. § 7</a>). +Still, it is supposable that, in the second instance, D or E may be the +<span class='pagenum'>[Pg 225]<a name="Page_225" id="Page_225"></a></span>cause of the increment of <i>p</i>; and that, in the third instance, F or G +may be its cause: though the probability of such vicarious causation +decreases rapidly with the increase of instances in which A and <i>p</i> vary +together. And, since an actual investigation of this type must rely on +observation, it is further possible that some undiscovered cause, X, is +the real determinant of both A and <i>p</i> and of their concomitant +variations.</p> + +<p>Professor Ferri, in his <i>Criminal Sociology</i>, observes: "I have shown +that in France there is a manifest correspondence of increase and +decrease between the number of homicides, assaults and malicious +wounding, and the more or less abundant vintage, especially in the years +of extraordinary variations, whether of failure of the vintage (1853-5, +1859, 1867, 1873, 1878-80), attended by a remarkable diminution of crime +(assaults and wounding), or of abundant vintages (1850, 1856-8, 1862-3, +1865, 1868, 1874-5), attended by an increase of crime" (p. 117, Eng. +trans.). And earlier he had remarked that such crimes also "in their +oscillations from month to month display a characteristic increase +during the vintage periods, from June to December, notwithstanding the +constant diminution of other offences" (p. 77). This is necessarily an +appeal to the canon of Concomitant Variations, because France is never +without her annual vintage, nor yet without her annual statistics of +crime. Still, it is an argument whose cogency is only that of Agreement, +showing that probably the abuse of the vintage is a cause of crimes of +violence, but leaving open the supposition, that some other circumstance +or circumstances, arising or varying from year to year, may determine +the increase or decrease of crime; or that there is some unconsidered +agent which affects both the vintage and crimes of violence. French +sunshine, it might be urged, whilst it matures the generous grape, also +excites a morbid fermentation in the human mind.</p> +<p><span class='pagenum'>[Pg 226]<a name="Page_226" id="Page_226"></a></span></p> +<p>Difference in Variations may be symbolically represented thus (no other +change having concurred):</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'>A</td><td align='center'>B</td><td> </td><td align='center'>A'</td><td align='center'>B</td><td> </td><td align='center'>A''</td><td align='center'>B</td></tr> +<tr><td align='center'><i>p</i></td><td align='center'><i>q</i>,</td><td> </td><td align='center'><i>p'</i></td><td align='center'><i>q</i>,</td><td> </td><td align='center'><i>p''</i></td><td align='center'><i>q</i>.</td></tr> +</table></div> + + +<p>Here the accompanying phenomena are always the same B/q; and the only +point in which the successive instances differ is in the increments of A +(A', A'') followed by corresponding increments of <i>p</i> (<i>p', p''</i>): hence +the increment of A is the cause of the increment of <i>p</i>.</p> + +<p>For examples of the application of this method, the reader should refer +to some work of exact science. He will find in Deschanel's <i>Natural +Philosophy</i>, c. 32, an account of some experiments by which the +connection between heat and mechanical work has been established. It is +there shown that "whenever work is performed by the agency of heat" [as +in driving an engine], "an amount of heat disappears equivalent to the +work performed; and whenever mechanical work is spent in generating +heat" [as in rubbing two sticks together], "the heat generated is +equivalent to the work thus spent." And an experiment of Joule's is +described, which consisted in fixing a rod with paddles in a vessel of +water, and making it revolve and agitate the water by means of a string +wound round the rod, passed over a pulley and attached to a weight that +was allowed to fall. The descent of the weight was measured by a +graduated rule, and the rise of the water's temperature by a +thermometer. "It was found that the heat communicated to the water by +the agitation amounted to one pound-degree Fahrenheit for every 772 +foot-pounds of work" expended by the falling weight. As no other +material change seems to take place during such an experiment, it shows +that the progressive expenditure of mechanical energy is the cause of +the progressive heating of the water.</p> +<p><span class='pagenum'>[Pg 227]<a name="Page_227" id="Page_227"></a></span></p> +<p>The thermometer itself illustrates this method. It has been found that +the application of heat to mercury expands it according to a law; and +hence the volume of the mercury, measured by a graduated index, is used +to indicate the temperature of the air, water, animal body, <i>etc.</i>, in +which the thermometer is immersed, or with which it is brought into +contact. In such cases, if no other change has taken place, the heat of +the air, water, or body is the cause of the rise of the mercury in its +tube. If some other substance (say spirit) be substituted for mercury in +constructing a thermometer, it serves the same purpose, provided the +index be graduated according to the law of the expansion of that +substance by heat, as experimentally determined.</p> + +<p>Instances of phenomena that do not vary together indicate the exclusion +of a supposed cause (by Prop. III (<i>c</i>)). The stature of the human race +has been supposed to depend on temperature; but there is no +correspondence. The "not varying together," however, must not be +confused with "varying inversely," which when regular indicates a true +concomitance. It is often a matter of convenience whether we regard +concomitant phenomena as varying directly or inversely. It is usual to +say—'the greater the friction the less the speed'; but it is really +more intelligible to say—'the greater the friction the more rapidly +molar is converted into molecular motion.'</p> + +<p>The Graphic Method exhibits Concomitant Variations to the eye, and is +extensively used in physical and statistical inquiries. Along a +horizontal line (the abscissa) is measured one of the conditions (or +agents) with which the inquiry is concerned, called the Variable; and +along perpendiculars (ordinates) is measured some phenomenon to be +compared with it, called the Variant.</p> + +<p>Thus, the expansion of a liquid by heat may be represented by measuring +degrees of temperature along the <span class='pagenum'>[Pg 228]<a name="Page_228" id="Page_228"></a></span>horizontal, and the expansion of a +column of the liquids in units of length along the perpendicular.</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/page228.png" width="600" height="248" alt="Fig. 9." title="" /> +<span class="caption">Fig. 9.</span> +</div> + +<p>In the next diagram (Fig. 10), reduced from one given by Mr. C.H. Denyer +in an article on the Price of Tea (<i>Economic Journal</i>, No. 9), the +condition measured horizontally is Time; and, vertically, three variants +are measured simultaneously, so that their relations to one another from +time to time may be seen at a glance. From this it is evident that, as +the duty on tea falls, the price of tea falls, whilst the consumption of +tea rises; and, in spite of some irregularity of correspondence in the +courses of the three phenomena, their general causal connection can +hardly be mistaken. However, the causal connection may also be inferred +by general reasoning; the statistical Induction can be confirmed by a +Deduction; thus illustrating the combined method of proof to be +discussed in the next chapter. Without such confirmation the proof by +Concomitant Variations would not be complete; because, from the +complexity of the circumstances, social statistics can only yield +evidence according to the method of Agreement in Variations. For, +besides the agents that are measured, there may always be some other +important influence at work. During the last fifty years, for example, +crime has decreased whilst education has increased: true, but at the +same time wages have risen and many other things have happened.</p><p><span class='pagenum'>[Pg 229]<a name="Page_229" id="Page_229"></a></span></p> + +<p class="center"> Diagram showing (1)<b>— · — ·</b> the average Price of Tea (in bond), but with duty added per lb.; +(2)<b>· · · · · ·</b> the rate of Duty; (3)---------- the consumption per head, from 1809 to 1889.</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/page229.png" width="600" height="287" alt="Fig. 10." title="" /> +<span class="caption smcap">Fig. 10.</span> +</div> +<p class="center">One horizontal space = 5 years. One vertical space = 6 pence, or 6 ounces.</p> + +<p><span class='pagenum'>[Pg 230]<a name="Page_230" id="Page_230"></a></span></p> + +<p>It will be noticed that in the diagram the three lines, especially those +of Price and Consumption (which may be considered <i>natural</i> resultants, +in contrast with the arbitrary fixation of a Tax), do not depart widely +from regular curves; and accordingly, assuming the causes at work to +vary continuously during the intervals between points of measurement, +curves may be substituted. In fact, a curve often represents the course +of a phenomenon more truthfully than can be done by a line that zigzags +along the exact measurements; because it is less influenced by temporary +and extraordinary causes that may obscure the operation of those that +are being investigated. On the other hand, the abrupt deviations of a +punctilious zigzag may have their own logical value, as will appear in +the next section.</p> + +<p>In working with the Method of Variations one must allow for the +occurrence in a series of 'critical points,' at which sudden and +sometimes heterogeneous changes may take place. Every substance exists +at different temperatures in three states, gaseous, liquid, solid; and +when the change takes place, from one state to another, the series of +variations is broken. Water, <i>e.g.</i>, follows the general law that +cooling is accompanied by decrease of volume between 212° and 39° F.: +but above 212°, undergoes a sudden expansion in becoming a gas; and +below 39° begins to expand, until at 32° the expansion is considerable +on its becoming solid. This illustrates a common experience that +concomitant variations are most regular in the 'median range,' and are +apt to become irregular at the extremities of the series, where new +conditions begin to operate.</p> + +<p>The Canon of Variations, again, deals not with sudden irruptions of a +cause, force or agent, but with some increase or decrease of an agent +already present, and a corresponding increase or decrease of some other +phenomenon—say an increase of tax and a rise of price. But there are +cases <span class='pagenum'>[Pg 231]<a name="Page_231" id="Page_231"></a></span>in which the energy of a cause is not immediately discharged and +dissipated. Whilst a tax of 6<i>d.</i> per lb. on tea raises the price per +lb. by about 6<i>d.</i>, however long it lasts, the continuous application of +friction to a body may gradually raise its temperature to the point of +combustion; because heat is received faster than it is radiated, and +therefore accumulates. Such cases are treated by Mill under the title of +'progressive effects' (<i>Logic</i>: B. III., c. 15): he gives as an example +of it the acceleration of falling bodies. The storage of effects is a +fact of the utmost importance in all departments of nature, and is +especially interesting in Biology and Sociology, where it is met with as +heredity, experience, tradition. Evolution of species of plants and +animals would (so far as we know) be impossible, if the changes (however +caused) that adapt some individuals better than others to the conditions +of life were not inherited by, and accumulated in, their posterity. The +eyes in the peacock's tail are supposed to have reached their present +perfection gradually, through various stages that may be illustrated by +the ocelli in the wings of the Argus pheasant and other genera of +<i>Phasianidæ</i>. Similarly the progress of societies would be impossible +without tradition, whereby the improvements made in any generation may +be passed on to the next, and the experience of mankind may be gradually +accumulated in various forms of culture. The earliest remains of culture +are flint implements and weapons; in which we can trace the effect of +tradition in the lives of our remote forefathers, as they slowly through +thousands of years learnt to improve the chipping of flints, until the +first rudely shaped lumps gave place to works of unmistakable design, +and these to the beautiful weapons contemporary with the Bronze Age.</p> + +<p>The Method of Gradations, the arranging of any phenomena to be studied +in series, according to the degree in which some character is exhibited, +is, perhaps, the most <span class='pagenum'>[Pg 232]<a name="Page_232" id="Page_232"></a></span>definite device in the Art of Discovery. (Bain: +<i>Induction</i>, c. 6, and App. II.) If the causes are unknown it is likely +to suggest hypotheses: and if the causes are partly known, variation in +the character of the series is likely to indicate a corresponding +variation of the conditions.</p> + + +<h3><span class="smcap"><a name="chap_16_sect_5" id="chap_16_sect_5"></a>§ 5. The Canon Of Residues.</span></h3> + +<p><i>Subduct from any phenomenon such part as previous inductions have shown +to be the effect of certain antecedents, and the residue of the +phenomenon is the effect of the remaining antecedents</i>.</p> + +<p>The phenomenon is here assumed to be an effect: a similar Canon may be +framed for residuary causes.</p> + +<p>This also is not a fresh method, but a special case of the method of +Difference. For if we suppose the phenomenon to be <i>p q r</i>, and the +antecedent to be A B C, and that we already know B and C to have (either +severally or together) the consequents <i>q r</i>, in which their efficacy is +exhausted; we may regard</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'>B</td><td align='center'>C</td></tr> +<tr><td align='center'><i>q</i></td><td align='center'><i>r</i></td></tr> +</table></div> + + +<p class="noindent">as an instance of the absence of <i>p</i> obtained deductively from the whole +phenomenon</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'>A</td><td align='center'>B</td><td align='center'>C</td></tr> +<tr><td align='center'><i>p</i></td><td align='center'><i>q</i></td><td align='center'><i>r</i></td></tr> +</table></div> + + +<p class="noindent">by our knowledge of the laws of B and C; so that</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'>A</td><td align='center'>B</td><td align='center'>C</td></tr> +<tr><td align='center'><i>p</i></td><td align='center'><i>q</i></td><td align='center'><i>r</i></td></tr> +</table></div> + + +<p class="noindent">is an instance of the presence of <i>p</i>, differing otherwise from</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'>B</td><td align='center'>C</td></tr> +<tr><td align='center'><i>q</i></td><td align='center'><i>r</i></td></tr> +</table></div> + + +<p class="noindent">in nothing except that A is also present. By the Canon of Difference, +therefore A is the cause of <i>p</i>. Or, again, when phenomena thus treated +are strictly quantitative, the method may be based on Prop. III. (<i>b</i>), +<a href="#chap_15_sect_7">ch. xv. § 7</a>.</p> + +<p>Of course, if A can be obtained apart from B C and directly experimented +with so as to produce <i>p</i>, so much the better; and this may often be +done; but the special value of the method of Residues appears, when some +complex phenomenon has been for the most part accounted <span class='pagenum'>[Pg 233]<a name="Page_233" id="Page_233"></a></span>for by known +causes, whilst there remains some excess, or shortcoming, or deviation +from the result which those causes alone would lead us to expect, and +this residuary fact has to be explained in relation to the whole. Here +the negative instance is constituted by deduction, showing what would +happen but for the interference of some unknown cause which is to be +investigated; and this prominence of the deductive process has led some +writers to class the method as deductive. But we have seen that all the +Canons involve deduction; and, considering how much in every experiment +is assumed as already known (what circumstances are 'material,' and when +conditions may be called 'the same'), the wonder is that no one has +insisted upon regarding every method as concerned with residues. In +fact, as scientific explanation progresses, the phenomena that may be +considered as residuary become more numerous and the importance of this +method increases.</p> + +<p>Examples: The recorded dates of ancient eclipses having been found to +differ from those assigned by calculation, it appears that the average +length of a day has in the meanwhile increased. This is a residuary +phenomenon not accounted for by the causes formerly recognised as +determining the rotation of the earth on its axis; and it may be +explained by the consideration that the friction of the tides reduces +the rate of the earth's rotation, and thereby lengthens the day. +Astronomy abounds in examples of the method of Residues, of which the +discovery of Neptune is the most famous.</p> + +<p>Capillarity seems to be a striking exception to the principle that water +(or any liquid) 'finds its level,' that being the condition of +equilibrium; yet capillarity proves to be only a refined case of +equilibrium when account is taken of the forces of adhesion exerted by +different kinds of bodies in contact.</p> + +<p>"Many of the new elements of Chemistry," says Herschel,<span class='pagenum'>[Pg 234]<a name="Page_234" id="Page_234"></a></span> "have been +detected in the investigation of residual phenomena." Thus, Lord +Rayleigh and Sir W. Ramsay found that nitrogen from the atmosphere was +slightly heavier than nitrogen got from chemical sources; and, seeking +the cause of this difference, discovered argon.</p> + +<p>The Economist shows that when a country imports goods the chief means of +paying for them is to export other goods. If this were all, imports and +exports would be of equal value: yet the United Kingdom imports about +£400,000,000 annually, and exports about £300,000,000. Here, then, is a +residuary phenomenon of £100,000,000 to be accounted for. But foreign +countries owe us about £50,000,000 for the use of shipping, and +£70,000,000 as interest on the capital we have lent them, and +£15,000,000 in commissions upon business transacted for them. These sums +added together amount to £135,000,000; and that is £35,000,000 too much. +Thus another residuary phenomenon emerges; for whilst foreigners seem to +owe us £435,000,000 they only send us £400,000,000 of imports. These +£35,000,000 are accounted for by the annual investment of our capital +abroad, in return for which no immediate payment is due; and, these +being omitted, exports and imports balance. Since this was written the +figures of our foreign trade have greatly risen; but the character of +the explanation remains the same.</p> + +<p>When, in pursuing the method of Variations, the phenomena compared do +not always correspond in their fluctuations, the irregular movements of +that phenomenon which we regard as the effect may often be explained by +treating them as residuary phenomena, and then seeking for exceptional +causes, whose temporary interference has obscured the influence of the +general cause. Thus, returning to the diagram of the Price of Tea in § +4, it is clear that generally the price falls as the duty falls; but in +Mr. Denyer's more minutely wrought diagram, from which this is reduced, +it may be seen that in 1840 the price of <span class='pagenum'>[Pg 235]<a name="Page_235" id="Page_235"></a></span>tea rose from 3<i>s.</i> 9<i>d.</i> to +4<i>s.</i> 9<i>d.</i> without any increase of duty. This, however, is readily +explained by the Chinese War of that year, which checked the supply. +Again, from 1869 to 1889 the duty was constant, whilst the price of tea +fell as much as 8<i>d.</i> per lb.; but this residuary phenomenon is +explained by the prodigiously increased production of tea during that +period in India and Ceylon.</p> + +<p>The above examples of the method of Residues are all quantitative; but +the method is often employed where exact estimates are unobtainable. +Thus Darwin, having found certain modifications of animals in form, +coloration and habits, that were not clearly derivable from their +struggle for existence in relation to other species or to external +conditions, suggested that they were due to Sexual Selection.</p> + +<p>The 'vestiges' and 'survivals' so common in Biology and Sociology are +residuary phenomena. It is a general inference from the doctrine of +Natural Selection that every organ of a plant, animal, or society is in +some way useful to it. There occur, however, organs that have at present +no assignable utility, are at least wasteful, and sometimes even +injurious. And the explanation is that formerly they were useful; but +that, their uses having lapsed, they are now retained by the force of +heredity or tradition. Either they are not injurious enough to be +eliminated by natural selection; or they are correlated with other +organs, whose utility outweighs their disutility.</p><p><span class='pagenum'>[Pg 236]<a name="Page_236" id="Page_236"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_XVII" id="CHAPTER_XVII"></a>CHAPTER XVII</h2> + +<h3>COMBINATION OF INDUCTION WITH DEDUCTION</h3> + + +<p><a name="chap_17_sect_1" id="chap_17_sect_1"></a>§ 1. We have now reviewed Mill's five Canons of Inductive Proof. At +bottom, as he observes, there are only two, namely, Agreement and +Difference: since the Double Method, Variations and Residues are only +special forms of the other two. Indeed, in their function of <i>proof</i>, +they are all reducible to one, namely, Difference; for the cogency of +the method of Agreement (as distinguished from a simple enumeration of +instances agreeing in the coincidence of a supposed cause and its +effect), depends upon the omission, in one instance after another, of +all other circumstances; which omission is a point of difference.</p> + +<p>The Canons are an analysis of the conditions of proving directly (where +possible), by means of observation or experiment, any proposition that +predicates causation. But if we say 'by means of observation or +experiment,' it is not to be understood that these are the only means +and that nothing else is involved; for it has been shown that the Law of +Causation is itself an indispensable foundation of the evidence. In fact +Inductive Logic may be considered as having a purely formal character. +It consists (1) in a statement of the Law of Cause and Effect; (2) in +certain immediate inferences from this Law, expanded into the Canons; +(3) in the syllogistic application of the Canons to special predications +of causation by means of minor premises, showing that certain instances +satisfy the Canons.</p><p><span class='pagenum'>[Pg 237]<a name="Page_237" id="Page_237"></a></span></p> + +<p>At the risk of some pedantry, we may exhibit the process as follows +(<i>cf.</i> Prof. Ray's <i>Logic</i>: Appendix D):</p> + +<p>Whatever relation of events has certain marks is a case of causation;</p> + +<div class="blockquot"><p class="noindent">The relation A: <i>p</i> has some or all of these marks (as shown +by observation and by the conformity of instances to such or +such a Canon):</p></div> + +<p>Therefore, the relation A: <i>p</i> is a case of causation. Now, the +parenthesis, "as shown by the conformity, <i>etc.</i>," is an adscititious +member of an Epicheirema, which may be stated, as a Prosyllogism, thus:</p> + +<div class="blockquot"><p>If an instance, etc. (Canon of Difference);</p> + +<p>The instances</p> + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='center'>A</td><td align='center'>B</td><td align='center'>C</td><td> </td><td align='center'>B</td><td align='center'>C</td></tr> +<tr><td align='center'><i>p</i></td><td align='center'><i>q</i></td><td align='center'><i>r'</i></td><td> </td><td align='center'><i>q</i></td><td align='center'><i>r</i></td></tr> +</table></div> + +<p>are of the kind required:</p> + +<p>Therefore, A, present where <i>p</i> occurs and absent where it +does not occur, is an indispensable antecedent of <i>p</i>.</p></div> + +<p>Such is the bare Logic of Induction: so that, strictly speaking, +observation or experiment is no part of the logic, but a means of +applying the logic to actual, that is, not merely symbolical, +propositions. The Formal Logic of Induction is essentially deductive; +and it has been much questioned whether any transition from the formal +to the material conditions of proof is possible. As long as we are +content to illustrate the Canons with symbols, such as A and <i>p</i>, all +goes well; but can we in any actual investigation show that the relevant +facts or 'instances' correspond with those symbols?</p> + +<p>In the first place, as Dr. Venn shows, natural phenomena want the +distinctness and capability of isolation that belong to symbols. +Secondly, the observing whether instances conform to a Canon, must +always be subject at last to the limits of our faculties. How can we +ascertain exact equality, immediate sequence? The Canon of Difference, +in its experimental application, is usually considered the most cogent +sort of proof: yet when can the two <span class='pagenum'>[Pg 238]<a name="Page_238" id="Page_238"></a></span>sequent instances, before and after +the introduction of a certain agent, be said to differ in nothing else? +Are not earth and stars always changing position; is not every molecule +in the room and apparatus always oscillating? It is true that our senses +are now aided by elaborate instruments; but the construction of these +depends on scientific theories, which again depend on experiments.</p> + +<p>It is right to touch upon this well-known sceptical topic; but to insist +much upon it is not a sign of good sense. The works of Herschel, +Whewell, and Jevons should be consulted for the various methods of +correcting observations, by repeating them, averaging them, verifying +one experimental process by another, always refining the methods of +exact measurement, multiplying the opportunities of error (that if any +exist it may at last show itself), and by other devices of what may be +called Material Logic or Methodology. But only direct experience and +personal manipulation of scientific processes, can give a just sense of +their effectiveness; and to stand by, suggesting academic doubts, is +easier and more amusing.</p> + +<p><a name="chap_17_sect_2" id="chap_17_sect_2"></a>§ 2. Still, it is not so much in laws based upon direct observation or +experiment, that the material validity of scientific reasoning appears, +as in the cumulative evidence that arises from the co-ordination of laws +within each science, and the growing harmony and coherence of all +sciences. This requires a more elaborate combination of deduction with +observation and experiment. During the last three hundred years many +departments of science have been reduced under principles of the +greatest generality, such as the Conservation of Energy, the Law of +Gravitation, the Undulatory theory of Light, the Law of combining +Equivalents, and the Theory of Natural Selection; connecting and +explaining the less general laws, which, again, are said to connect and +explain the facts. Meanwhile, those sciences that were the first to make +progress have helped to develop others which, like Biology and<span class='pagenum'>[Pg 239]<a name="Page_239" id="Page_239"></a></span> +Sociology, present greater difficulties; and it becomes more and more +apparent that the distinctions drawn among sciences are entirely for the +convenience of study, and that all sciences tend to merge in one +universal Science of Nature. Now, this process of the 'unification of +knowledge' is almost another name for deduction; but at the same time it +depends for its reality and solidity upon a constant reference to +observation and experiment. Only a very inadequate notion of it can be +given in the ensuing chapters.</p> + +<p>We saw in <a href="#chap_14_sect_6">chap. xiv. § 6</a>, that when two or more agents or forces combine +to produce a phenomenon, their effects are intermixed in it, and this in +one of two ways according to their nature. In chemical action and in +vegetable and animal life, the causal agents concerned are blended in +their results in such a way that most of the qualities which they +exhibited severally are lost, whilst new qualities appear instead. Thus +chlorine (a greenish-yellow gas) and sodium (a metal) unite to form +common salt NaCl; which is quite unlike either of them: a man eats +bread, and it becomes muscle, nerve and bone. In such cases we cannot +trace the qualities of the causal agents in the qualities of the +effects; given such causes, we can prove experimentally, according to +the canons of induction, that they have such effects; but we may not be +able in any new case to calculate what the effects will be.</p> + +<p>On the other hand, in Astronomy and Physics, the causes treated of are +mechanical; at least, it is the aim of Physics to attain to a mechanical +conception of phenomena; so that, in every new combination of forces, +the intermixed effect, or resultant, may be calculated beforehand; +provided that the forces concerned admit of being quantitatively +estimated, and that the conditions of their combination are not so +complex as to baffle the powers of mathematicians. In such cases, when +direct observation or experiment is insufficient to resolve an effect +into the <span class='pagenum'>[Pg 240]<a name="Page_240" id="Page_240"></a></span>laws of its conditions, the general method is to calculate +what may be expected from a combination of its conditions, as either +known or hypothetically assumed, and to compare this anticipation with +the actual phenomenon.</p> + +<p><a name="chap_17_sect_3" id="chap_17_sect_3"></a>§ 3. This is what Mill calls the Direct Deductive Method; or, the +Physical Method, because it is so much relied on in treating of Light, +Heat, Sound, <i>etc.</i>; it is also the method of Astronomy and much used in +Economics: Deduction leads the way, and its results are tested +inductively by experiments or observations. Given any complex mechanical +phenomenon, the inquirer considers—(1) what laws already ascertained +seem likely to apply to it (in default of known laws, hypotheses are +substituted: <i>cf.</i> <a href="#CHAPTER_VIII">chap. xviii.</a>); he then—(2) computes the effect that +will follow from these laws in circumstances similar to the case before +him; and (3) he verifies his conclusion by comparing it with the actual +phenomenon.</p> + +<p>A simple example of this method is the explanation of the rise of water +in the 'common pump.' We know three laws applicable to this case: (<i>a</i>) +that the atmosphere weighs upon the water outside the pump with a +pressure of 15 lb. to the square inch; (<i>b</i>) that a liquid (and +therefore the water) transmits pressure equally in all directions +(upwards as well as downwards and sideways); and (<i>c</i>) that pressure +upon a body in any direction, if not counteracted by an opposite +pressure, produces motion. Hence, when the rise of the piston of the +pump removes the pressure upon the water within the cylinder, tending to +produce a vacuum there, this water is pushed up by the pressure of the +air upon the water outside the cylinder, and follows the rising piston, +until the column of water inside the cylinder exerts a pressure equal to +that of the atmosphere upon an equal area. So much for the computation; +does it correspond with the fact? It is found that at the sea level +water can be pumped to the height of 33 ft; and that such a column of +water has a pressure of 15 lb.<span class='pagenum'>[Pg 241]<a name="Page_241" id="Page_241"></a></span> to the square inch. We may show further +that, at the sea level, spirits of wine may be pumped higher according +to its less specific gravity; and that if we attempt to pump water at +successive altitudes above the sea level, we can only raise it to less +and less heights, corresponding with the lessened atmospheric pressure +at those altitudes, where the column of air producing the pressure is +shorter. Finally, if we try to work a pump, having first produced a +vacuum over the water outside the cylinder, we shall find that the water +inside will not rise at all; the piston can be raised, but the water +does not follow it. The verification thus shows that the computed effect +corresponds with the phenomenon to be explained; that the result does +not depend upon the nature of water only, but is true (allowing for +differences of specific gravity) of other liquids; that if the pressure +of the outside air is diminished, the height of pumping is so too (canon +of Variations); and that if that pressure is entirely removed, pumping +becomes impossible (canon of Difference).</p> + +<p>Any text-book of Astronomy or Physics furnishes numerous illustrations +of the deductive method. Take, for example, the first chapter of +Deschanel's <i>Optics</i>, where are given three methods of determining the +velocity of Light. This was first deduced from observation of Jupiter's +satellites. The one nearest the planet passes behind it, or into its +shadow, and is eclipsed, at intervals of about 42½ hours. But it can +be shown that, when Jupiter and the Earth are nearest together on the +same side of the Sun, an eclipse of this satellite is visible from the +earth 16 min. 26.6 sec. earlier than when Jupiter and the earth are +furthest apart on opposite sides of the Sun: 16 min. 26.6 sec, then, is +the time in which light traverses the diameter of the Earth's orbit. +Therefore, supposing the Earth's distance from the Sun to be 92 millions +of miles, light travels about 186,000 miles a second. Another deduction, +agreeing with this, starts from the fact <span class='pagenum'>[Pg 242]<a name="Page_242" id="Page_242"></a></span>of aberration, or the +displacement of the apparent from the actual position of the stars in +the direction of the earth's motion. Aberration depends partly on the +velocity of light, partly on the velocity of the Earth; and the latter +being known, the former can be computed. Now, these two deductive +arguments, verifying each other, have also been verified experimentally. +Foucault's experiment to measure the velocity of light is too elaborate +to be described here: a full account of it will be found in the treatise +above cited, § 687.</p> + +<p>When the phenomena to be explained are of such a character, so vast in +extent, power or duration, that it is impossible, in the actual +circumstances of the case, to frame experiments in order to verify a +deductive explanation, it may still be possible to reproduce a similar +phenomenon upon a smaller scale. Thus Monge's explanation of mirage by +the great heat of the desert sand, which makes the lowest stratum of air +less dense than those above it, so that rays of light from distant +objects are refracted in descending, until they are actually turned +upwards again to the eye of the beholders, giving him inverted images of +the objects as if they were reflected in water, is manifestly incapable +of being verified by experiment in the natural conditions of the +phenomenon. But by heating the bottom of "a sheet-iron box, with its +ends cut away," the rarefied air at the bottom of the box may sometimes +be made to yield reflections; and this shows at least that the supposed +cause is a possible one (Deschanel, <i>Optics,</i> § 726). Similarly as to +the vastest of all phenomena, the evolution of the stellar system, and +of the solar system as part of it, from an immense cloudlike volume of +matter: H. Spencer, in his Essay on <i>The Nebular Hypothesis</i>, says, +amidst a great array of deductive arguments from mechanical principles, +that "this <i>a priori</i> reasoning harmonises with the results of +experiment. Dr. Plateau has shown that when a mass of fluid is, as far +as may be, <span class='pagenum'>[Pg 243]<a name="Page_243" id="Page_243"></a></span>protected from the action of external forces, it will, if +made to rotate with adequate velocity, form detached rings; and that +these rings will break up into spheroids, which turn on their axes in +the same direction with the central mass." The theory of the evolution +of species of plants and animals by Natural Selection, again, though, of +course, it cannot be verified by direct experiment (since experiment +implies artificial arrangement), and the process is too slow for +observation, is, nevertheless, to some extent confirmed by the practice +of gardeners and breeders of animals: since, by taking advantage of +accidental variations of form and colour in the plants or animals under +their care, and relying on the inheritability of these variations they +obtain extensive modifications of the original stocks, and adapt them to +the various purposes for which flowers and cereals, poultry, dogs and +cattle are domesticated. This shows, at least, that living forms are +plastic, and extensively modifiable in a comparatively short time.</p> + +<p><a name="chap_17_sect_4" id="chap_17_sect_4"></a>§ 4. Suppose, however, that, in verifying a deductive argument, the +effect as computed from the laws of the causes assigned, does not +correspond with the facts observed: there must then be an error +somewhere. If the fact has been accurately observed, the error must lie +either in the process of deduction and computation, or else in the +premises. As to the process of deduction, it may be very simple and +easily revised, as in the above explanation of the common pump; or it +may be very involved and comprise long trains of mathematical +calculation. If, however, on re-examining the computations, we find them +correct, it remains to look for some mistake in the premises.</p> + +<p>(1) We may not have accurately ascertained the laws, or the modes of +operation, or the amounts of the forces present. Thus, the rate at which +bodies fall was formerly believed to vary in proportion to their +relative weights; and any estimate based upon this belief cannot agree +with <span class='pagenum'>[Pg 244]<a name="Page_244" id="Page_244"></a></span>the facts. Again, the corpuscular theory of light, namely, that +the physical cause of light is a stream of fine particles projected in +straight lines from the luminous object, though it seemed adequate to +the explanation of many optical phenomena, could not be made to agree +with the facts of interference and double refraction.</p> + +<p>(2) The circumstances in which the agents are combined may not have been +correctly conceived. When Newton began to inquire whether the attraction +of the earth determined the orbit of the moon, he was at first +disappointed. "According to Newton's calculations, made at this time," +says Whewell, "the moon, by her motion in her orbit, was deflected from +the tangent every minute through a space of thirteen feet. But by +noticing the space which bodies would fall in one minute at the earth's +surface, and supposing this to be diminished in the ratio of the inverse +square, it appeared that gravity would, at the moon's orbit, draw a body +through more than fifteen feet." In view of this discrepancy he gave up +the inquiry for sixteen years, until in 1682, having obtained better +data, he successfully renewed it. "He had been mistaken in the magnitude +of the earth, and consequently in the distance of the moon, which is +determined by measurements of which the earth's radius is the base." It +was not, therefore, a mistake as to the law or as to the nature of the +forces concerned (namely, the law of the inverse square and the identity +of celestial with terrestrial gravity), but as to the circumstances in +which the agents (earth and moon) were combined, that prevented his +calculations being verified. (<i>Hist. Ind. Sc.</i>: VII. ii. 3.)</p> + +<p>(3) One or more of the agents affecting the result may have been +overlooked and omitted from the estimate. Thus, an attempt to explain +the tides by taking account only of the earth and the moon, will not +entirely agree with the facts, since the sun also influences the tides. +This illustration, however, shows that when the conclusion of <span class='pagenum'>[Pg 245]<a name="Page_245" id="Page_245"></a></span>a +deductive explanation does not entirely agree with the facts, it is not +always to be inferred that the reasoning is, properly speaking, wrong; +it may be right as far as it goes, and merely inadequate. Hence (<i>a</i>) in +such cases an opportunity occurs of applying the Method of Residues, by +discovering the agent that must be allowed for in order to complete the +explanation. And (<i>b</i>) the investigation of a phenomenon is often +designedly begun upon an imperfect basis for the sake of simplicity; the +result being regarded as a first approximation, to be afterwards +corrected by including, one by one, the remaining agents or +circumstances affecting the phenomenon, until the theory is complete; +that is, until its agreement with the facts is satisfactory.</p> + +<p>(4) We may have included among the data of our reasonings agents or +circumstances that do not exist or do not affect the phenomenon in +question. In the early days of science purely fanciful powers were much +relied upon: such as the solid spheres that carried the planets and +stars; the influence of the planets upon human destiny; the tendency of +everything to seek "its own place," so that fire rises to heaven, and +solids fall to the earth; the "plastic virtue" of the soil, which was +once thought to have produced fossils. When, however, such conceptions +hindered the progress of explanation, it was not so much by vitiating +the deductive method as by putting men off from exact inquiries. More to +our present purpose were the supposed cataclysms, or extraordinary +convulsions of the earth, a belief in which long hindered the progress +of Geology. Again, in Biology, Psychology, and Sociology many +explanations have depended upon the doctrine that any improvement of +structure or faculty acquired by an individual may be inherited by his +descendants: as that, if an animal learns to climb trees, his offspring +have a greater aptitude for that mode of life; that if a man tries to be +good, his children find it easier <span class='pagenum'>[Pg 246]<a name="Page_246" id="Page_246"></a></span>to be virtuous; that if the +inhabitants of a district carry on cloth-work, it becomes easier for +each successive generation to acquire dexterity in that art. But now the +inheritability of powers acquired by the individual through his own +efforts, is disputed; and, if the denial be made good, all such +explanations as the above must be revised.</p> + +<p>If, then, the premises of a deductive argument be vitiated in any of +these four ways, its conclusion will fail to agree with the results of +observation and experiment, unless, of course, one kind of error happen +to be cancelled by another that is 'equal and opposite.' We now come to +a variation of the method of combining Induction with Deduction, so +important as to require separate treatment.</p> + +<p><a name="chap_17_sect_5" id="chap_17_sect_5"></a>§ 5. The Inverse or Historical Method has of late years become +remarkably fruitful. When the forces determining a phenomenon are too +numerous, or too indefinite, to be combined in a direct deduction, we +may begin by collecting an empirical law of the phenomenon (as that 'the +democracies of City-States are arbitrary and fickle'), and then +endeavour to show by deductions from "the nature of the case," that is, +from a consideration of the circumstances and forces known to be +operative (of which, in the above instance, the most important is +sympathetic contagion), that such a law was to be expected. Deduction is +thus called in to verify a previous induction; whereas in the 'Physical +Method' a deduction was verified by comparing it with an induction or an +experiment; hence the method now to be discussed has been named the +Inverse Deductive Method.</p> + +<p>But although it is true that, in such inquiries as we are now dealing +with, induction generally takes the lead; yet I cannot think that the +mere order in which the two logical processes occur is the essential +distinction between the two ways of combining them. For, in the first +place, in investigations of any complexity both induction and deduction +recur again and again in whatever order may <span class='pagenum'>[Pg 247]<a name="Page_247" id="Page_247"></a></span>be most convenient; and, in +the second place, the so-called 'inverse order' is sometimes resorted to +in Astronomy and Physics. For example, Kepler's Laws were first +collected empirically from observations of the planetary motions, and +afterwards deduced by Newton from the Law of Gravitation; this, then, +was the Inverse Method; but the result is something very different from +any that can be obtained by the Historical Method. The essential +difference between the Physical and Historical Methods is that, in the +former, whether Direct or Inverse, the deductive process, when complete, +amounts to exact demonstration; whereas, in the latter, the deductions +may consist of qualitative reasonings, and the results are indefinite. +They establish—(1) a merely probable connection between the phenomena +according to an empirical law (say, between City-democracy and fickle +politics); (2) connect this with other historical or social +generalisations, by showing that they all alike flow from the same +causes, namely, from the nature of races of men under certain social and +geographical conditions; and (3) explain why such empirical laws may +fail, according to the differences that prevail among races of men and +among the conditions under which they live. Thus, seeing how rapidly +excitement is propagated by the chatter, grimacing, and gesticulation of +townsmen, it is probable enough that the democracy of a City-state +should be fickle (and arbitrary, because irresponsible). A similar +phenomenon of panic, sympathetic hope and despair, is exhibited by every +stock-exchange, and is not peculiar to political life. And when +political opinion is not manufactured solely in the reverberating +furnace of a city, fickleness ceases to characterise democracy; and, in +fact, is not found in Switzerland, or the United States, nor in France +so far as politics, depend upon the peasantry.</p> + +<p>This is called the Historical Method, then, because it is especially +useful in explaining the movements of history, <span class='pagenum'>[Pg 248]<a name="Page_248" id="Page_248"></a></span>and in verifying the +generalisations of political and social science. We must not, however, +suppose that its use is confined to such studies. Only a ridiculous +pedantry would allot to each subject its own method and forbid the use +of any other; as if it were not our capital object to establish truth by +any means. Wherever the forces determining a phenomenon are too numerous +or too indefinite to be combined in a deductive demonstration, there the +Historical Method is likely to be useful; and this seems often to be the +case in Geology and Biology, as well as in the Science of History, or +Sociology, and its various subsidiary studies.</p> + +<p>Consider upon what causes historical events depend: the customs, +character, and opinions of all the people concerned; the organisation of +their government, and the character of their religious institutions; the +development of industry among them, of the military art, of fine art, +literature and science; their relations, commercial, political and +social, with other nations; the physical conditions of climate and +geographical position amidst which they live. Hardly an event of +importance occurs in any nation that is not, directly or indirectly, +influenced by every one of these circumstances, and that does not react +upon them. Now, from the nature of the Canons of direct Induction, a +satisfactory employment of them in such a complex and tangled situation +as history presents, is rarely possible; for they all require the actual +or virtual isolation of the phenomenon under investigation. They also +require the greatest attainable immediacy of connection between cause +and effect; whereas the causes of social events may accumulate during +hundreds of years. In collecting empirical laws from history, therefore, +only very rough inductions can be hoped for, and we may have to be +content with simple enumeration. Hence the importance of supporting such +laws by deduction from the nature of the case, however faint a +probability of the <span class='pagenum'>[Pg 249]<a name="Page_249" id="Page_249"></a></span>asserted connection is thereby raised; and this even +if each law is valued merely for its own sake. Still more, if anything +worth the name of Historical Science is to be constructed, must a mere +collection of such empiricisms fail to content us; and the only way to +give them a scientific character is to show deductively their common +dependence upon various combinations of the same causes. Yet even those +who profess to employ the Historical Method often omit the deductive +half of it; and of course 'practical politicians' boast of their entire +contentment with what they call 'the facts.'</p> + +<p>Sometimes, however, politicians, venturing upon deductive reasoning, +have fallen into the opposite error of omitting to test their results by +any comparison with the facts: arguing from certain 'Rights of Man,' or +'Interests of Classes,' or 'Laws of Supply and Demand,' that this or +that event will happen, or ought to happen, without troubling themselves +to observe whether it does happen or ever has happened. This method of +Deduction without any empirical verification, is called by Mill the +Geometrical; and, plainly, it can be trustworthy only where there is no +actual conflict of forces to be considered. In pure mathematical +reasoning about space, time, and number, provided the premises and the +reasoning be correct, verification by a comparison with the facts may be +needless, because there is no possibility of counteraction. But when we +deal with actual causes, no computation of their effects can be relied +upon without comparing our conclusions with the facts: not even in +Astronomy and Physics, least of all in Politics.</p> + +<p>Burke, then, has well said that "without the guide and light of sound, +well-understood principles all our reasoning in politics, as in +everything else, would be only a confused jumble of particular facts and +details without the means of drawing any sort of theoretical or +practical conclusion"; but that, on the other hand, the statesman, who +<span class='pagenum'>[Pg 250]<a name="Page_250" id="Page_250"></a></span>does not take account of circumstances, infinite and infinitely +combined, "is not erroneous, but stark mad—he is metaphysically mad" +(<i>On the Petition of the Unitarians</i>). There is, or ought to be, no +logical difference between the evidence required by a statesman and that +appealed to by a philosopher; and since, as we have seen, the +combination of principles with circumstances cannot, in solving problems +of social science, be made with the demonstrative precision that belongs +to astronomical and physical investigations, there remains the +Historical Method as above described.</p> + +<p>Examples of the empirical laws from which this method begins abound in +histories, newspapers, and political discussions, and are of all shades +of truth or half-truth: as that 'History consists in the biographies of +great men'; in other words, that the movements of society are due to +exceptional personal powers, not to general causes; That at certain +epochs great men occur in groups; That every Fine Art passes through +periods of development, culmination and decline; That Democracies tend +to change into Despotisms; That the possession of power, whether by +classes or despots, corrupts the possessor: That 'the governments most +distinguished for sustained vigour and abilities have generally been +aristocracies'; That 'revolutions always begin in hunger'; That +civilisation is inimical to individuality; That the civilisation of the +country proceeds from the town; That 'the movement of progressive +societies has hitherto been a movement from <i>Status</i> to <i>Contract</i> +(<i>i.e.</i>, from a condition in which the individual's rights and duties +depend on his caste, or position in his family as slave, child, or +patriarch, to a condition in which his rights and duties are largely +determined by the voluntary agreements he enters into)'; and this last +is treated by H. Spencer as one aspect of the law first stated by Comte, +that the progress of societies is from the military to the industrial +state.</p><p><span class='pagenum'>[Pg 251]<a name="Page_251" id="Page_251"></a></span></p> + +<p>The deductive process we may illustrate by Spencer's explanation of the +co-existence in the military state of those specific characters, the +inductive proof of which furnished an illustration of the method of +Agreement (<a href="#chap_16_sect_1">ch. xvi. § 1</a>). The type of the military State involves the +growth of the warrior class, and the treatment of labourers as existing +solely to support the warriors; the complete subordination of all +individuals to the will of the despotic soldier-king, their property, +liberty and life being at the service of the State; the regimentation of +society, not only for military, but also for civil purposes; the +suppression of all private associations, <i>etc.</i> Now all these +characteristics arise from their utility for the purpose of war, a +utility amounting to necessity if war is the State's chief purpose. For +every purpose is best served when the whole available force co-operates +toward it: other things equal, the bigger the army the better; and to +increase it, men must be taken from industry, until only just enough +remain to feed and equip the soldiers. As this arrangement is not to +everybody's taste, there must be despotic control; and this control is +most effective through regimentation by grades of command. Private +associations, of course, cannot live openly in such a State, because +they may have wills of their own and are convenient for conspiracy. Thus +the induction of characteristics is verified by a deduction of them from +the nature of the case.</p> + +<p><a name="chap_17_sect_6" id="chap_17_sect_6"></a>§ 6. The greater indefiniteness of the Historical compared with the +Physical Method, both in its inductions and in its deductions, makes it +even more difficult to work with. It wants much sagacity and more +impartiality; for the demon of Party is too much with us. Our first care +should be to make the empirical law as nearly true as possible, +collecting as many as we can of the facts which the law is supposed to +generalise, and examining them according to the canons of Induction, +with due allowance <span class='pagenum'>[Pg 252]<a name="Page_252" id="Page_252"></a></span>for the imperfect applicability of those canons to +such complex, unwieldy, and indefinite instances. In the examples of +such laws given above, it is clear that in some cases no pains have been +taken to examine the facts. What is the inductive evidence that +Democracies change into Despotisms; that revolutions always begin in +hunger; or that civilisation is inimical to individuality? Even Mill's +often quoted saying, "that the governments remarkable in history for +sustained vigour and ability have generally been aristocracies," is +oddly over-stated. For if you turn to the passage (<i>Rep. Gov.</i> chap. +vi.), the next sentence tells you that such governments have always been +aristocracies of public functionaries; and the next sentence but one +restricts, apparently, the list of such remarkable governments to +two—Rome and Venice. Whence, then, comes the word "generally" into +Mill's law?</p> + +<p>As to deducing our empirical law from a consideration of the nature of +the case, it is obvious that we ought—(<i>a</i>) to take account of all the +important conditions; (<i>b</i>) to allow weight to them severally in +proportion to their importance; and (<i>c</i>) not to include in our +estimates any condition which we cannot show to be probably present and +operative. Thus the Great-Man-Theory of history must surely be admitted +to assign a real condition of national success. The great man organises, +directs, inspires: is that nothing? On the other hand, to recognise no +other condition of national success is the manifest frenzy of a mind in +the mythopœic age. We must allow the great man his due weight, and then +inquire into the general conditions that (<i>a</i>) bring him to birth in one +nation rather than another, and (<i>b</i>) give him his opportunity.</p> + +<p>Mill's explanation of the success of the aristocratic governments of +Rome and Venice is, that they were, in fact, bureaucracies; that is to +say, their members were <span class='pagenum'>[Pg 253]<a name="Page_253" id="Page_253"></a></span>trained in the science and art of +administration and command. Here, again, we have, no doubt, a real +condition; but is it the only one? The popular mind, which little +relishes the scaling down of Mill's original law to those two remote +cases, is persuaded that an aristocracy is the depository of hereditary +virtue, especially with reference to government, and would at once +ascribe to this circumstance the greater part of the success of any +aristocratic constitution. Now, if the effects of training are +inherited, they must, in an hereditary aristocracy, increase the energy +of the cause assigned by Mill; but, if not, such heredity is a condition +"not present or not operative." Still, if families are ennobled for +their extraordinary natural powers of administration or command (as +sometimes happens), it is agreed on all hands that innate qualities are +inheritable; at least, if care be taken to intermarry with families +similarly distinguished, and if by natural or artificial selection all +the failures among the offspring be eliminated. The Spartans had some +crude notion of both these precautions; and if such measures had been +widely adopted, we might deduce from the doctrine of heredity a +probability in favour of Mill's original proposition, and thereby verify +it in its generality, if it could be collected from the facts.</p> + +<p>The Historical Method may be further illustrated by the course adopted +in that branch of Social Science which has been found susceptible of the +most extensive independent development, namely, Economics. First, by way +of contrast, I should say that the abstract, or theoretical treatment of +Economics follows the Physical Method; because, as Mill explains, +although the phenomena of industry are no doubt influenced, like other +social affairs, by all the other circumstances of Society, government, +religion, war, art, <i>etc.</i>; yet, where industry is most developed, as in +England and the United States, certain special conditions affecting it +are so much the most important that, for the <span class='pagenum'>[Pg 254]<a name="Page_254" id="Page_254"></a></span>purpose at least of a +first outline of the science, they may conveniently be considered as the +only ones. These conditions are: (1) the general disposition of men to +obtain wealth with as little trouble as possible, and (2) to spend it so +as to obtain the greatest satisfaction of their various desires; (3) the +facts that determine population; and (4) the tendency of extractive +industry, when pushed beyond a certain limit without any improvement in +the industrial arts, to yield "diminishing returns." From these premises +it is easy to infer the general laws of prices, of wages and interest +(which are the prices of labour and of the use of capital), and of rent; +and it remains to verify these laws by comparing them with the facts in +each case; and (if they fail to agree with the facts) to amend them, +according to the Method of Residues, by taking account of those +influential conditions which were omitted from the first draft of the +theory.</p> + +<p>Whilst, however, this is usually the procedure of those inquirers who +have done most to give Economics its scientific character, to insist +that no other plan shall be adopted would be sheer pedantry; and Dr. +Keynes has shown, in his <i>Scope and Method of Political Economy</i>, that +Mill has himself sometimes solved economic problems by the Historical +Method. With an analysis of his treatment of Peasant Proprietorship +(<i>Political Economy</i>, B. II., cc. 7 and 8) we may close this section. +Mill first shows inductively, by collecting evidence from Switzerland, +Germany, Norway, Belgium, and France (countries differing in race, +government, climate and situation), that peasant proprietors are +superhumanly industrious; intelligent cultivators, and generally +intelligent men; prudent, temperate, and independent, and that they +exercise self-control in avoiding improvident marriages. This group of +empirical generalisations as to the character of peasant proprietors he +then deduces from the nature of the case: their industry, he says, is a +natural consequence of the fact that, <span class='pagenum'>[Pg 255]<a name="Page_255" id="Page_255"></a></span>however much they produce, it is +all their own; they cultivate intelligently, because for generations +they have given their whole mind to it; they are generally intelligent +men, because the variety of work involved in small farming, requiring +foresight and calculation, necessarily promotes intelligence; they are +prudent, because they have something to save, and by saving can improve +their station and perhaps buy more land; they are temperate, because +intemperance is incompatible with industry and prudence; they are +independent, because secure of the necessaries of life, and from having +property to fall back upon; and they avoid improvidence in marriage, +because the extent and fertility of their fields is always plainly +before them, and therefore how many children they can maintain is easily +calculated. The worst of them is that they work too hard and deny +themselves too much: but, over the greater part of the world, other +peasantry work too hard; though they can scarcely be said to deny +themselves too much; since all their labour for others brings them no +surplus to squander upon self-indulgence.</p> + +<p><a name="chap_17_sect_7" id="chap_17_sect_7"></a>§ 7. The foregoing account of the Historical Method is based upon Mill's +discussions in B. VI. of his <i>Logic</i>, especially cc. 6 to 11. Mill +ascribes to Comte the first clear statement of the method; and it is +highly scientific, and important in generalising the connections of +historical events. But perhaps the expression, 'Historical Method,' is +more frequently applied to the Comparative Method, as used in +investigating the history of institutions or the true sense of legends.</p> + +<p>(1) Suppose we are trying to explain the institution of capital +punishment as it now exists in England. (1) We must try to trace the +history of it back to the earliest times; for <i>social custom and +tradition is one line of causation</i>. At present the punishment of death +is legally incident only to murder and high treason. But early in the +last century malefactors were hung for forgery, sheep-<span class='pagenum'>[Pg 256]<a name="Page_256" id="Page_256"></a></span>stealing, arson +and a long list of other offences down to pocket-picking: earlier still +the list included witchcraft and heresy. At present hanging is the only +mode of putting a malefactor to death; but formerly the ways of putting +to death included also burning, boiling, pressing, beheading, and mixed +modes. Before the Restoration, however, the offences punishable with +death were far fewer than they afterwards became; and until the twelfth +century, the penalty of death might be avoided by paying compensation, +the wer-geld.</p> + +<p>(2) Every change in the history of an institution must be explained by +pointing to <i>the special causes</i> in operation during the time when the +change was in progress. Thus the restriction of the death penalty, in +the nineteenth century, to so few offences was due partly to the growth +of humane feelings, partly to the belief that the infliction, or threat, +of the extreme penalty had failed to enforce the law and had demoralised +the administration of Justice. The continual extension of the death +penalty throughout the eighteenth century may be attributed to a belief +that it was the most effectual means of deterring evil-doers when the +means of detecting and apprehending criminals were feeble and +ill-organised. The various old brutal ways of execution were adopted +sometimes to strike terror, sometimes for vengeance, sometimes from +horror of the crime, or even from 'conscientious scruples';—which last +were the excuse for preferring the burning of heretics to any sort of +bloodshed.</p> + +<p>(3) The causes of any change in the history of an institution in any +country may not be directly discoverable: they must then be investigated +by the Comparative Method. Again, the recorded history of a nation, and +of all its institutions, followed backwards, comes at last to an end: +then the antecedent history must also be supplied by the Comparative +Method; whose special use is to indicate the existence of facts for +which there is no direct evidence.</p><p><span class='pagenum'>[Pg 257]<a name="Page_257" id="Page_257"></a></span></p> + +<p>This method rests upon the principle that where the causes are alike the +effects will be alike, and that similar effects are traceable to similar +causes. Every department of study—Astronomy, Chemistry, Zoology, +Sociology—is determined by the fact that the phenomena it investigates +have certain common characteristics; and we are apt to infer that any +process observed in some of these phenomena, if depending on those +common characteristics, will be found in others. For example, the +decomposition, or radio-activity, of certain elements prepares one to +believe that all elements may exhibit it. Where the properties of an +object are known to be closely interdependent, as in the organisation of +plants, animals and societies, we are especially justified in inferring +from one case to another. The whole animal Kingdom has certain common +characters—the metabolic process, dependence upon oxygen, upon +vegetable food (ultimately), heredity, etc., and, upon this ground, any +process (say, the differentiation of species by Natural Selection) that +has been established for some kinds of animal is readily extended to +others. If instead of the whole animal Kingdom we take some district of +it—Class, Order, Family—our confidence in such inferences increases; +because the common characters are more numerous and the conditions of +life are more alike; or, in other words, the common causes are more +numerous that initiate and control the development of nearly allied +animals. For such reasons a few fragmentary remains of an extinct animal +enable the palæontologist to reconstruct with some probability an +outline of its appearance, organisation, food, habitat and habits.</p> + +<p>Applied to History, the Comparative Method rests upon an assumption +(which the known facts of (say) 6,000 years amply justify) that human +nature, after attaining a recognisable type as <i>homo sapiens</i>, is +approximately uniform in all countries and in all ages, though more +especially where states of culture are similar. Men living in society +<span class='pagenum'>[Pg 258]<a name="Page_258" id="Page_258"></a></span>are actuated by similar motives and reasons in similar ways; they are +all dependent upon the supply of food and therefore on the sun and the +seasons and the weather and upon means of making fire, and so on. +Accordingly, they entertain similar beliefs, and develop similar +institutions through similar series of changes. Hence, if in one nation +some institution has been altered for reasons that we cannot directly +discover, whereas we know the reasons why a similar change was adopted +elsewhere, we may conjecture with more or less probability, after making +allowance for differences in other circumstances, that the motives or +causes in the former case were similar to those in the latter, or in any +cases that are better known. Or, again, if in one nation we cannot trace +an institution beyond a certain point, but can show that elsewhere a +similar institution has had such or such an antecedent history, we may +venture to reconstruct with more or less probability the earlier history +of that institution in the nation we are studying.</p> + +<p>Amongst the English and Saxon tribes that settled in Britain, death was +the penalty for murder, and the criminal was delivered to the +next-of-kin of his victim for execution; he might, however, compound for +his crime by paying a certain compensation. Studying the history of +other tribes in various parts of the world, we are able, with much +probability, to reconstruct the antecedents of this death-penalty in our +own prehistoric ages, and to trace it to the blood-feud; that is, to a +tribal condition in which the next-of-kin of a murdered man was socially +and religiously bound to avenge him by slaying the murderer or one of +his kindred. This duty of revenge is sometimes (and perhaps was at first +everywhere) regarded as necessary to appease the ghost of the victim; +sometimes as necessary to compensate the surviving members of his +family. In the latter case, it is open to them to accept compensation in +money or cattle, <i>etc.</i> Whether <span class='pagenum'>[Pg 259]<a name="Page_259" id="Page_259"></a></span>the kin will be ready to accept +compensation must depend upon the value they set upon wealth in +comparison with revenge; but for the sake of order and tribal strength, +it is the interest of the tribe, or its elders, or chieftain, to +encourage or even to enforce such acceptance. It is also their interest +to take the questions—whether a crime has been committed, by whom, and +what compensation is due—out of the hands of the injured party, and to +submit them to some sort of court or judicial authority. At first, +following ancient custom as much as possible, the act of requital, or +the choice of accepting compensation, is left to the next-of-kin; but +with the growth of central power these things are entrusted to ministers +of the Government. Then revenge has undergone its full transformation +into punishment. Very likely the wrong itself will come to be treated as +having been done not to the kindred of the murdered man, but to the +State or the King, as in fact a "breach of the King's peace." This +happened in our own history.</p> + +<p>(4) The Comparative Method assumes that human nature is approximately +the same in different countries and ages; but, of course, +'approximately' is an important word. Although there is often a striking +and significant resemblance between the beliefs and institutions of +widely separated peoples, we expect to draw the most instructive +parallels between those who are nearly related by descent, or +neighbourhood, or culture. To shed light upon our own manners, we turn +first to other Teutons, then to Slavonians and Kelts, or other Aryans, +and so on; and we prefer evidence from Europe to examples from Africa.</p> + +<p>(5) As to national culture, that it exhibits certain 'stages' of +development is popularly recognised in the distinction drawn between +savages, barbarians and civilised folk. But the idea remains rather +vague; and there is not space here to define it. I refer, therefore, to +the<span class='pagenum'>[Pg 260]<a name="Page_260" id="Page_260"></a></span> classifications of stages of culture given by A. Sutherland, +(<i>Origin and Growth of Moral Instinct</i>, Vol. I, p. 103), and L.T. +Hobhouse (<i>Morals in Evolution</i>, c. 2). That in any 'state of Society,' +its factors—religion, government, science, <i>etc.</i>—are mutually +dependent, was a leading doctrine with Comte, adopted by Mill. There +must be some truth in it; but in some cases we do not understand social +influences sufficiently well to trace the connection of factors; and +whilst preferring to look for historical parallels between nations of +similar culture, we find many cases in which barbarous or savage customs +linger in a civilised country.</p> + +<p>(6) It was another favourite doctrine with Comte, also adopted by +Mill—that the general state of culture is chiefly determined by the +prevailing intellectual condition of a people, especially by the +accepted ground of explanation—whether the will of supernatural beings, +or occult powers, or physical antecedents: the "law of three stages," +Fetichism, Metaphysics, Positivism. And this also is, at least, so far +true, that it is useless to try to interpret the manners and +institutions of any nation until we know its predominant beliefs. Magic +and animism are beliefs everywhere held by mankind in early stages of +culture, and they influence every action of life. But that is not all: +these beliefs retain their hold upon great multitudes of civilised men +and affect the thoughts of the most enlightened. Whilst the saying 'that +human nature is the same in all ages' seems to make no allowance for the +fact that, in some nations, a considerable number of individuals has +attained to powers of deliberation, self-control, and exact reasoning, +far above the barbarous level, it is yet so far true that, even in +civilised countries, masses of people, were it not for the example and +instruction of those individuals, would fall back upon magic and animism +and the manners that go with those beliefs. The different degrees of +enlightenment enjoyed by different classes of<span class='pagenum'>[Pg 261]<a name="Page_261" id="Page_261"></a></span> the population often +enable the less educated to preserve a barbarous custom amidst many +civilised characteristics of the national life.</p> + +<p><a name="chap_17_sect_8" id="chap_17_sect_8"></a>§ 8. Historical reasoning must start from, or be verified by, +observations. If we are writing the history of ourselves: if of another +time or country, we can observe some of the present conditions of the +country, its inhabitants, language, manners, institutions, which are +effects of the past and must be traceable to it; we may also be able to +observe ancient buildings or their ruins, funerary remains, coins, +dating from the very times we are to treat of. Our own observations, of +course, are by no means free from error.</p> + +<p>But even in treating of our own age and country, most of our information +must be derived from the testimony of others, who may have made mistakes +of observation and further mistakes in reporting their observations, or +may have intentionally falsified them. Testimony is of two kinds: Oral; +and Written, inscribed or printed. In investigating the events of a +remote age, nearly all our direct evidence must be some sort of +testimony.</p> + +<p>(1) Oral testimony depends upon the character of the witness; and the +best witness is not perfectly trustworthy; for he may not have observed +accurately, or he may not have reported correctly; especially if some +time elapsed between the event and his account of it; for no man's +memory is perfect. Since witnesses vary widely in capacity and +integrity, we must ask concerning any one of them—was he a good judge +of what he saw, and of what was really important in the event? Had he +good opportunities of knowing the circumstances? Had he any interest in +the event—personal, or partisan, or patriotic? Such interests would +colour his report; and so would the love of telling a dramatic story, if +that was a weakness of his. Nay, a love of truth might lead him to +<span class='pagenum'>[Pg 262]<a name="Page_262" id="Page_262"></a></span>modify the report of what he remembered if—as he remembered it—the +matter seemed not quite credible. We must also bear in mind that, for +want of training, precision in speaking the truth is not understood or +appreciated by many honest people even now, still less in unscientific +ages.</p> + +<p>Oral tradition is formed by passing a report from one to another, +generation by generation; and it is generally true that such a tradition +loses credit at every step, because every narrator has some weakness. +However, the value of tradition depends upon the motives people have to +report correctly, and on the form of the communication, and on whether +monuments survive in connection with the story. Amongst the things best +remembered are religious and magic formulæ, heroic poems, lists of +ancestors, popular legends about deeply impressive events, such as +migrations, conquests, famines, plagues. We are apt now to underrate the +value of tradition, because the use of writing has made tradition less +important, and therefore less pains are taken to preserve it. In the +middle of last century, it was usual (and then quite justifiable) to +depreciate oral tradition as nearly worthless; but the spread of +archæological and anthropological research, and the growth of the +Comparative Method, have given new significance to legends and +traditions which, merely by themselves, could not deserve the slightest +confidence.</p> + +<p>(2) As to written evidence, contemporary inscriptions—such as are found +on rocks and stones and bricks in various parts of the world, and most +abundantly in Egypt and Western Asia—are of the highest value, because +least liable to fraudulent abuse; but must be considered with reference +to the motives of those who set them forth. Manuscripts and books give +rise to many difficulties. We have to consider whether they were +originally written by some one contemporary with the events recorded: if +<span class='pagenum'>[Pg 263]<a name="Page_263" id="Page_263"></a></span>so they have the same value as immediate oral testimony, provided they +have not been tampered with since. But if not contemporary records, they +may have been derived from other records that were contemporary, or only +from oral tradition. In the latter case they are vitiated by the +weakness of oral tradition. In the former case, we have to ask what was +the trustworthiness of the original records, and how far do the extant +writings fairly represent those records?</p> + +<p>Our answers to these questions will partly depend upon what we know or +can discover of the authors of the MSS. or books. Who was the author? If +a work bears some man's name, did he really write it? The evidence +bearing upon this question is usually divided into internal, external +and mixed; but perhaps no evidence is purely internal, if we define it +as that which is derived entirely from the work itself. Under the name +of internal evidence it is usual to put the language, the style, +consistency of ideas; but if we had no grounds of judgment but the book +itself, we could not possibly say whether the style was the author's: +this requires us to know his other works. Nor could we say whether the +language was that of his age, unless we knew other literature of the +same age; nor even that different passages seem to be written in the +manner of different ages, but for our knowledge of change in other +literatures. There must in every case be some external reference. Thus +we judge that a work is not by the alleged author, nor contemporary with +him, if words are used that only became current at a later date, or are +used in a sense that they only later acquired, or if later writers are +imitated, or if events are mentioned that happened later +('anachronism'). Books are sometimes forged outright, that is, are +written by one man and deliberately fathered upon another; but sometimes +books come to be ascribed to a well-known name, which were written by +some one else <span class='pagenum'>[Pg 264]<a name="Page_264" id="Page_264"></a></span>without fraudulent intent, dramatically or as a +rhetorical exercise.</p> + +<p>As to external evidence, if from other sources we have some knowledge of +the facts described in a given book, and if it presents no serious +discrepancies with those facts, this is some confirmation of a claim to +contemporaneity. But the chief source of external evidence is other +literature, where we may find the book in question referred to or +quoted. Such other literature may be by another author, as when +Aristotle refers to a dialogue of Plato's, or Shakespeare quotes +Marlowe; or may be other work of the author himself, as when Aristotle +in the <i>Ethics</i> refers to his own <i>Physics</i>, or Chaucer in <i>The +Canterbury Tales</i> mentions as his own <i>The Legend of Good Women</i>, and in +<i>The Legend</i> gives a list of other works of his. This kind of argument +assumes that the authorship of the work we start from is undisputed; +which is practically the case with the <i>Ethics</i> and <i>The Canterbury +Tales</i>.</p> + +<p>But, now, granting that a work is by a good author, or contemporary with +the events recorded, or healthily related to others that were +contemporary, it remains to consider whether it has been well preserved +and is likely to retain its original sense. It is, therefore, desirable +to know the history of a book or MS., and through whose hands it has +passed. Have there been opportunities of tampering with it; and have +there been motives to do so? In reprinting books, but still more in +copying MSS., there are opportunities of omitting or interpolating +passages, or of otherwise altering the sense. In fact, slight changes +are almost sure to be made even without meaning to make them, especially +in copying MSS., through the carelessness or ignorance of transcribers. +Hence the oldest MS. is reckoned the best.</p> + +<p>If a work contains stories that are physically impossible, it shows a +defect of judgment in the author, and decreases our confidence in his +other statements; but it does not <span class='pagenum'>[Pg 265]<a name="Page_265" id="Page_265"></a></span>follow that these others are to be +rejected. We must try to compare them with other evidence. Even +incredible stories are significant: they show what people were capable +of believing, and, therefore, under what conditions they reasoned and +acted. One cause of the incredibility of popular stories is the fusion +of legend with myth. A legend is a traditionary story about something +that really happened: it may have been greatly distorted by stupidity, +or exaggeration, or dramatisation, or rationalisation, but may still +retain a good deal of the original fact. A myth, however, has not +necessarily any basis of fact: it may be a sort of primitive philosophy, +an hypothesis freely invented to explain some fact in nature, such as +eclipses, or to explain some social custom whose origin is forgotten, +such as the sacrificing of a ram.</p> + +<p>All historical conclusions, then, depend on a sum of convergent and +conflicting probabilities in the nature of circumstantial evidence. The +best testimony is only highly probable, and it is always incomplete. To +complete the picture of any past age there is no resource but the +Comparative Method. We use this method without being aware of it, +whenever we make the records of the last generation intelligible to +ourselves by our own experience. Without it nothing would be +intelligible: an ancient coin or weapon would have no meaning, were we +not acquainted with the origins and uses of other coins and weapons. +Generally, the further we go back in history, the more the evidence +needs interpretation and reconstruction, and the more prominent becomes +the appeal to the Comparative Method. Our aim is to construct a history +of the world, and of the planet as part of the world, and of mankind as +part of the life of the planet, in such a way that every event shall be +consistent with, and even required by, the rest according to the +principle of Causation.</p><p><span class='pagenum'>[Pg 266]<a name="Page_266" id="Page_266"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_XVIII" id="CHAPTER_XVIII"></a>CHAPTER XVIII</h2> + +<h3>HYPOTHESES</h3> + + +<p><a name="chap_18_sect_1" id="chap_18_sect_1"></a>§ 1. An Hypothesis, sometimes employed instead of a known law, as a +premise in the deductive investigation of nature, is defined by Mill as +"any supposition which we make (either without actual evidence, or on +evidence avowedly insufficient) in order to endeavour to deduce from it +conclusions in accordance with facts which are known to be real; under +the idea that if the conclusions to which the hypothesis leads are known +truths, the hypothesis itself either must be, or at least is likely to +be, true." The deduction of known truths from an hypothesis is its +Verification; and when this has been accomplished in a good many cases, +and there are no manifest failures, the hypothesis is often called a +Theory; though this term is also used for the whole system of laws of a +certain class of phenomena, as when Astronomy is called the 'theory of +the heavens.' Between hypothesis and theory in the former sense no +distinct line can be drawn; for the complete proof of any speculation +may take a long time, and meanwhile the gradually accumulating evidence +produces in different minds very different degrees of satisfaction; so +that the sanguine begin to talk of 'the theory,' whilst the circumspect +continue to call it 'the hypothesis.'</p> + +<p>An Hypothesis may be made concerning (1) an Agent, such as the ether; or +(2) a Collocation, such as the plan of our solar system—whether +geocentric or heliocentric; or (3) a Law of an agent's operation, as +that light is trans<span class='pagenum'>[Pg 267]<a name="Page_267" id="Page_267"></a></span>mitted by a wave motion of such lengths or of such +rates of vibration.</p> + +<p>The received explanation of light involves both an agent, the ether, as +an all-pervading elastic fluid, and also the law of its operation, as +transmitting light in waves of definite form and length, with definite +velocity. The agreement between the calculated results of this complex +hypothesis and the observed phenomena of light is the chief part of the +verification; which has now been so successfully accomplished that we +generally hear of the 'Undulatory Theory.' Sometimes a new agent only is +proposed; as the planet Neptune was at first assumed to exist in order +to account for perturbations in the movements of Uranus, influencing it +according to the already established law of gravitation. Sometimes the +agents are known, and only the law of their operation is hypothetical, +as was at first the case with the law of gravitation itself. For the +agents, namely, Earth, falling bodies on the Earth, Moon, Sun, and +planets were manifest; and the hypothesis was that their motions might +be due to their attracting one another with a force inversely +proportional to the squares of the distances between them. In the +Ptolemaic Astronomy, again, there was an hypothesis as to the +collocation of the heavenly bodies (namely, that our Earth was the +centre of the universe, and that Moon, Sun, planets and stars revolved +around her): in the early form of the system there was also an +hypothesis concerning agents upon which this arrangement depended +(namely, the crystalline spheres in which the heavenly bodies were +fixed, though these were afterwards declared to be imaginary); and an +hypothesis concerning the law of operation (namely, that circular motion +is the most perfect and eternal, and therefore proper to celestial +things).</p> + +<p>Hypotheses are by no means confined to the physical sciences: we all +make them freely in private life. In searching for anything, we guess +where it may be before <span class='pagenum'>[Pg 268]<a name="Page_268" id="Page_268"></a></span>going to look for it: the search for the North +Pole was likewise guided by hypotheses how best to get there. In +estimating the characters or explaining the conduct of acquaintances or +of public men, we frame hypotheses as to their dispositions and +principles. 'That we should not impute motives' is a peculiarly absurd +maxim, as there is no other way of understanding human life. To impute +bad motives, indeed, when good are just as probable, is to be wanting in +the scientific spirit, which views every subject in 'a dry light.' Nor +can we help 'judging others by ourselves'; for self-knowledge is the +only possible starting-point when we set out to interpret the lives of +others. But to understand the manifold combinations of which the +elements of character are susceptible, and how these are determined by +the breeding of race or family under various conditions, and again by +the circumstances of each man's life, demands an extraordinary union of +sympathetic imagination with scientific habits of thought. Such should +be the equipment of the historian, who pursues the same method of +hypothesis when he attempts to explain (say) the state of parties upon +the Exclusion Bill, or the policy of Louis XI. Problems such as the +former of these are the easier; because, amidst the compromises of a +party, personal peculiarities obliterate one another, and expose a +simpler scheme of human nature with fewer fig-leaves. Much more +hazardous hypotheses are necessary in interpreting the customs of +savages, and the feelings of all sorts of animals. Literary criticisms, +again, abound with hypotheses: <i>e.g.</i>, as to the composition of the +Homeric poems, the order of the Platonic dialogues, the authorship of +the Cædmonic poems, or the Ossianic, or of the letters of Junius. Thus +the method of our everyday thoughts is identical with that of our most +refined speculations; and in every case we have to find whether the +hypothesis accounts for the facts.</p> + +<p><a name="chap_18_sect_2" id="chap_18_sect_2"></a>§ 2. It follows from the definition of an hypothesis that <span class='pagenum'>[Pg 269]<a name="Page_269" id="Page_269"></a></span>none is of +any use that does not admit of verification (proof or disproof), by +comparing the results that may be deduced from it with facts or laws. If +so framed as to elude every attempt to test it by facts, it can never be +proved by them nor add anything to our understanding of them.</p> + +<p>Suppose that a conjurer asserts that his table is controlled by the +spirit of your deceased relative, and makes it rap out an account of +some adventure that could not easily have been within a stranger's +knowledge. So far good. Then, trying again, the table raps out some +blunder about your family which the deceased relative could not have +committed; but the conjurer explains that 'a lying spirit' sometimes +possesses the table. This amendment of the hypothesis makes it equally +compatible with success and with failure. To pass from small things to +great, not dissimilar was the case of the Ptolemaic Astronomy: by +successive modifications, its hypothesis was made to correspond with +accumulating observations of the celestial motions so ingeniously that, +until the telescope was invented, it may be said to have been +unverifiable. Consider, again, the sociological hypothesis, that civil +order was at first founded on a Contract which remains binding upon all +mankind: this is reconcilable with the most opposite institutions. For +we have no record of such an event: and if the institutions of one State +(say the British) include ceremonies, such as the coronation oath and +oath of allegiance, which may be remnants of an original contract, they +may nevertheless be of comparatively recent origin; whereas if the +institutions of another State (say the Russian) contain nothing that +admits of similar interpretation, yet traces of the contract once +existing may long since have been obliterated. Moreover, the actual +contents of the contract not having been preserved, every adherent of +this hypothesis supplies them at his own discretion, 'according to the +dictates of<span class='pagenum'>[Pg 270]<a name="Page_270" id="Page_270"></a></span> Reason'; and so one derives from it the duty of passive +obedience, and another with equal cogency establishes the right of +rebellion.</p> + +<p>To be verifiable, then, an hypothesis must be definite; if somewhat +vague in its first conception (which is reasonably to be expected), it +must be made definite in order to be put to the proof. But, except this +condition of verifiability, and definiteness for the sake of +verifiability, without which a proposition does not deserve the name of +an hypothesis, it seems inadvisable to lay down rules for a 'legitimate' +hypothesis. The epithet is misleading. It suggests that the Logician +makes rules for scientific inquirers; whereas his business is to +discover the principles which they, in fact, employ in what are +acknowledged to be their most successful investigations. If he did make +rules for them, and they treated him seriously, they might be +discouraged in the exercise of that liberty of hypothesising which is +the condition of all originality; whilst if they paid no attention to +him, he must suffer some loss of dignity. Again, to say that a +'legitimate hypothesis' must explain all the facts, at least in the +department for which it is invented, is decidedly discouraging. No doubt +it may be expected to do this in the long run when (if ever) it is +completely established; but this may take a long time: is it meanwhile +illegitimate? Or can this adjective be applied to Newton's corpuscular +theory of light, even though it has failed to explain all the facts?</p> + +<p><a name="chap_18_sect_3" id="chap_18_sect_3"></a>§ 3. Given a verifiable hypothesis, however, what constitutes proof or +disproof?</p> + +<p>(1) <i>If a new agent be proposed, it is desirable that we should be able +directly to observe it, or at least to obtain some evidence of its +existence of a different kind from the very facts which it has been +invented to explain.</i> Thus, in the discovery of Neptune, after the +existence of such a planet outside the orbit of Uranus had been +conjectured (to <span class='pagenum'>[Pg 271]<a name="Page_271" id="Page_271"></a></span>account for the movements of the latter), the place in +the heavens which such a body should occupy at a certain time was +calculated, and there by means of the telescope it was actually seen.</p> + +<p>Agents, however, are assumed and reasoned upon very successfully which, +by their nature, never can be objects of perception: such are the atoms +of Chemistry and the ether of Optics. But the severer methodologists +regard them with suspicion: Mill was never completely convinced about +the ether; the defining of which has been found very difficult. He was +willing, however, to make the most of the evidence that has been adduced +as indicating a certain property of it distinct from those by which it +transmits radiation, namely, mechanical inertia, whereby it has been +supposed to retard the career of the heavenly bodies, as shown +especially by the history of Encke's comet. This comet returned sooner +than it should, as calculated from the usual data; the difference was +ascribed to the influence of a resisting medium in reducing the extent +of its orbit; and such a medium may be the ether. If this conjecture +(now of less credit) should gain acceptance, the ether might be regarded +as a <i>vera causa</i> (that is, a condition whose existence may be proved +independently of the phenomena it was intended to explain), in spite of +its being excluded by its nature from the sphere of direct perception. +However, science is not a way of perceiving things, but essentially a +way of thinking about them. It starts, indeed, from perception and +returns to it, and its thinking is controlled by the analogies of +perception. Atoms and ether are thought about as if they could be seen +or felt, not as noumena; and if still successful in connecting and +explaining perceptions, and free from contradiction, they will stand as +hypotheses on that ground.</p> + +<p>On the other hand, a great many agents, once assumed in order to explain +phenomena, have since been explained away. Of course, a <i>fact</i> can never +be 'explained away':<span class='pagenum'>[Pg 272]<a name="Page_272" id="Page_272"></a></span> the phrase is properly applicable to the fate of +erroneous hypotheses, when, not only are they disproved, but others are +established in their places. Of the Aristotelian spheres, which were +supposed to support and translate sun, moon and planets, no trace has +ever been found: they would have been very much in the way of the +comets. Phlogiston, again, an agent much in favour with the earlier +Chemists, was found, Whewell tells us, when their theories were tested +by exact weighing, to be not merely non-existent but a minus quantity; +that is to say, it required the assumption of its absolute lightness "so +that it diminished the weight of the compounds into which it entered." +These agents, then, the spheres and phlogiston, have been explained +away, and instead of them we have the laws of motion and oxygen.</p> + +<p>(2) <i>Whether the hypothetical agent be perceptible or not, it cannot be +established as a cause, nor can a supposed law of such an agent be +accepted as sufficient to the given inquiry, unless it is adequate to +account for the effects which it is called upon to explain, at least so +far as it pretends to explain them.</i> The general truth of this is +sufficiently obvious, since to explain the facts is the purpose of an +hypothesis; and we have seen that Newton gave up his hypothesis that the +moon was a falling body, as long as he was unable to show that the +amount of its deflection from a tangent (or fall) in a given time, was +exactly what it should be, if the Moon was controlled by the same force +as falling bodies on the Earth.</p> + +<p>It is important to observe the limitations to this canon. In the first +place, it says that, unless adequate to explain the facts in question, +an hypothesis cannot be '<i>established</i>'; but, for all that, such an +hypothesis may be a very promising one, not to be hastily rejected, +since it may take a very long time fully to verify an hypothesis. Some +facts may not be obtainable that are necessary to show the connection of +others: as, for example, the <span class='pagenum'>[Pg 273]<a name="Page_273" id="Page_273"></a></span>hypothesis that all species of animals +have arisen from earlier ones by some process of gradual change, can be +only imperfectly verified by collecting the fossil remains of extinct +species, because immense depths and expanses of fossiliferous strata +have been destroyed. Or, again, the general state of culture may be such +as to prevent men from tracing the consequences of an hypothesis; for +which reason, apparently, the doctrine that the Sun is the centre of our +planetary system remained a discredited hypothesis for 2000 years. This +should instruct us not to regard an hypothesis as necessarily erroneous +or illegitimate merely because we cannot yet see how it works out: but +neither can we in such a case regard it as established, unless we take +somebody's word for it.</p> + +<p>Secondly, the canon says that an hypothesis is not established, unless +it accounts for the phenomena <i>so far as it professes to</i>. But it +implies a complete misunderstanding to assail a doctrine for not +explaining what lies beyond its scope. Thus, it is no objection to a +theory of the origin of species, that it does not explain the origin of +life: it does not profess to. For the same reason, it is no objection to +the theory of Natural Selection, that it does not account for the +variations which selection presupposes. But such objections might be +perfectly fair against a general doctrine of Evolution.</p> + +<p>An interesting case in Wallace's <i>Darwinism</i> (chap. x.) will illustrate +the importance of attending to the exact conditions of an hypothesis. He +says that in those groups of "birds that need protection from enemies," +"when the male is brightly coloured and the female sits exposed on the +nest, she is always less brilliant and generally of quite sober and +protective hues"; and his hypothesis is, that these sober hues have been +acquired or preserved by Natural Selection, because it is important to +the family that the sitting bird should be inconspicuous. Now to this it +might be objected that in some birds both sexes <span class='pagenum'>[Pg 274]<a name="Page_274" id="Page_274"></a></span>are brilliant or +conspicuous; but the answer is that the female of such species <i>does not +sit exposed on the nest</i>; for the nests are either domed over, or made +in a hole; so that the sitting bird does not need protective colouring. +If it be objected, again, that some sober-coloured birds build domed +nests, it may be replied that the proposition 'All conspicuously +coloured birds are concealed in the nest,' is not to be converted simply +into 'All birds that sit concealed in the nest are conspicuously +coloured.' In the cases alleged the domed nests are a protection against +the weather, and the sober colouring is a general protection to the +bird, which inhabits an open country. It may be urged, however, that +jays, crows, and magpies are conspicuous birds, and yet build open +nests: but these are aggressive birds, <i>not needing protection from +enemies</i>. Finally, there are cases, it must be confessed, in which the +female is more brilliant than the male, and which yet have open nests. +Yes: but <i>then the male sits upon the eggs</i>, and the female is stronger +and more pugnacious!</p> + +<p>Thus every objection is shown to imply some inattention to the +conditions of the hypothesis; and in each case it may be said, <i>exceptio +probat regulam</i>—the exception <i>tests</i> the rule. (Of course, the usual +translation "proves the rule," in the restricted modern sense of +"prove," is absurd.) That is to say, it appears on examination: (1) that +the alleged exception is not really one, and (2) that it stands in such +relation to the rule as to confirm it. For to all the above objections +it is replied that, granting the phenomenon in question (special +protective colouring for the female) to be absent, the alleged cause +(need of protection) is also absent; so that the proof is, by means of +the objections, extended, from being one by the method of Agreement, +into one by the Double Method.</p> + +<p>Thirdly, an hypothesis originally intended to account for the whole of a +phenomenon and failing to do so, though it cannot be established in that +sense, may nevertheless <span class='pagenum'>[Pg 275]<a name="Page_275" id="Page_275"></a></span>contain an essential part of the explanation. +The Neptunian Hypothesis in Geology, was an attempt to explain the +formation of the Earth's outer crust, as having been deposited from an +universal ocean of mud. In the progress of the science other causes, +seismic, fluvial and atmospheric, have been found necessary in order to +complete the theory of the history of the Earth's crust; but it remains +true that the stratified rocks, and some that have lost their stratified +character, were originally deposited under water. Inadequacy, therefore, +is not a reason for entirely rejecting an hypothesis or treating it as +illegitimate.</p> + +<p>(3) Granting that the hypothetical cause is real and adequate, the +investigation is not complete. Agreement with the facts is a very +persuasive circumstance, the more so the more extensive the agreement, +especially if no exceptions are known. Still, if this is all that can be +said in favour of an hypothesis, it amounts to proof at most by the +method of Agreement; it does not exclude the possibility of vicarious +causes; and if the hypothesis proposes a new agent that cannot be +directly observed, an equally plausible hypothesis about another +imagined agent may perhaps be invented.</p> + +<p>According to Whewell, it is a strong mark of the truth of an hypothesis +when it agrees with distinct inductions concerning different classes of +facts, and he calls this the 'Consilience of Inductions,' because they +jump together in the unity of the hypothesis. It is particularly +convincing when this consilience takes place easily and naturally +without necessitating the mending and tinkering of the hypothesis; and +he cites the Theory of Gravitation and the Undulatory Theory of Light as +the most conspicuous examples of such ever-victorious hypotheses. Thus, +gravitation explains the fall of bodies on the Earth, and the orbits of +the planets and their satellites; it applies to the tides, the comets, +the double stars, and gives con<span class='pagenum'>[Pg 276]<a name="Page_276" id="Page_276"></a></span>sistency to the Nebular Hypothesis, +whence flow important geological inferences; and all this without any +need of amendment. Nevertheless, Mill, with his rigorous sense of duty, +points out, that an induction is merely a proposition concerning many +facts, and that a consilience of inductions is merely a multiplication +of the facts explained; and that, therefore, if the proof is merely +Agreement in each case, there can be no more in the totality; the +possibility of vicarious causes is not precluded; and the hypothesis +may, after all, describe an accidental circumstance.</p> + +<p>Whewell also laid great stress upon prediction as a mark of a true +hypothesis. Thus, Astronomers predict eclipses, occultations, transits, +long beforehand with the greatest precision; and the prediction of the +place of Neptune by sheer force of deduction is one of the most +astonishing things in the history of science. Yet Mill persisted in +showing that a predicted fact is only another fact, and that it is +really not very extraordinary that an hypothesis, that happens to agree +with many known facts, should also agree with some still undiscovered. +Certainly, there seems to be some illusion in the common belief in the +probative force of prediction. Prediction surprises us, puts us off our +guard, and renders persuasion easy; in this it resembles the force of an +epigram in rhetoric. But cases can be produced in which erroneous +hypotheses have led to prediction; and Whewell himself produces them. +Thus, he says that the Ptolemaic theory was confirmed by its predicting +eclipses and other celestial phenomena, and by leading to the +construction of Tables in which the places of the heavenly bodies were +given at every moment of time. Similarly, both Newton's theory of light +and the chemical doctrine of phlogiston led to predictions which came +true.</p> + +<p>What sound method demands in the proof of an hypothesis, then, is <i>not +merely that it be shown to agree with the <span class='pagenum'>[Pg 277]<a name="Page_277" id="Page_277"></a></span>facts, but that every other +hypothesis be excluded.</i> This, to be sure, may be beyond our power; +there may in some cases be no such negative proof except the exhaustion +of human ingenuity in the course of time. The present theory of colour +has in its favour the failure of Newton's corpuscular hypothesis and of +Goethe's anti-mathematical hypothesis; but the field of conjecture +remains open. On the other hand, Newton's proof that the solar system is +controlled by a central force, was supported by the demonstration that a +force having any other direction could not have results agreeing with +Kepler's second law of the planetary motions, namely, that, as a planet +moves in its orbit, the areas described by a line drawn from the sun to +the planet are proportional to the times occupied in the planet's +motion. When a planet is nearest to the sun, the area described by such +a line is least for any given distance traversed by the planet; and then +the planet moves fastest: when the planet is furthest from the sun, the +area described by such a line is greatest for an equal distance +traversed; and then the planet moves slowest. This law may be deduced +from the hypothesis of a central force, but not from any other; the +proof, therefore, as Mill says, satisfies the method of Difference.</p> + +<p>Apparently, to such completeness of demonstration certain conditions are +necessary: the possibilities must lie between alternatives, such as A or +not-A, or amongst some definite list of cases that may be exhausted, +such as equal, greater or less. He whose hypothesis cannot be brought to +such a definite issue, must try to refute whatever other hypotheses are +offered, and naturally he will attack first the strongest rivals. With +this object in view he looks about for a "crucial instance," that is, an +observation or experiment that stands like a cross (sign-post) at the +parting of the ways to guide us into the right way, or, in plain words, +an instance that can be explained by one hypothesis but not by another. +Thus the phases of Venus, <span class='pagenum'>[Pg 278]<a name="Page_278" id="Page_278"></a></span>similar to those of the Moon, but concurring +with great changes of apparent size, presented, when discovered by +Galileo, a crucial instance in favour of the Copernican hypothesis, as +against the Ptolemaic, so far at least as to prove that Venus revolved +around the Sun inside the orbit of the Earth. Foucault's experiment +determining the velocity of Light (cited in the last chapter) was at +first intended as an <i>experimentum crucis</i> to decide between the +corpuscular and undulatory theories; and answered this purpose, by +showing that the velocity of a beam passed through water was less than +it should be by the former, but in agreement with the latter doctrine +(Deschanel: § 813).</p> + +<p>Perhaps experiments of this decisive character are commonest in +Chemistry: chemical tests, says Herschel, "are almost universally +crucial experiments." The following is abridged from Playfair (<i>Encycl. +Met., Diss.</i> III.): The Chemists of the eighteenth century observed that +metals were rendered heavier by calcination; and there were two ways of +accounting for this: either something had been added in the process, +though what, they could not imagine; or, something had been driven off +that was in its nature light, namely, phlogiston. To decide between +these hypotheses, Lavoisier hermetically sealed some tin in a glass +retort, and weighed the whole. He then heated it; and, when the tin was +calcined, weighed the whole again, and found it the same as before. No +substance, therefore, either light or heavy, had escaped. Further, when +the retort was cooled and opened, the air rushed in, showing that some +of the air formerly within had disappeared or lost its elasticity. On +weighing the whole again, its weight was now found to have increased by +ten grains; so that ten grains of air had entered when it was opened. +The calcined tin was then weighed separately, and proved to be exactly +ten grains heavier than when it was placed in the retort; showing that +the ten grains of air that had disappeared had combined with the metal +during calcina<span class='pagenum'>[Pg 279]<a name="Page_279" id="Page_279"></a></span>tion. This experiment, then, decided against phlogiston, +and led to an analysis of common air confirming Priestley's discovery of +oxygen.</p> + +<p>(4) <i>An hypothesis must agree with the rest of the laws of Nature; and, +if not itself of the highest generality, must be derivable from primary +laws</i> (<a href="#chap_19_sect_1">chap. xix. § 1</a>). Gravitation and the diffusion of heat, light and +sound from a centre, all follow the 'law of the inverse square,' and +agree with the relation of the radius of a sphere to its surface. Any +one who should think that he had discovered a new central force would +naturally begin to investigate it on the hypothesis that it conformed to +the same law as gravitation or light. A Chemist again, who should +believe himself to have discovered a new element, would expect it to +fill one of the vacant places in the Periodic Table. Conformity, in such +cases, is strong confirmation, and disagreement is an occasion of +misgivings.</p> + +<p>A narrower hypothesis, as 'that the toad's ugliness is protective', +would be supported by the general theory of protective colouring and +figure, and by the still more general theory of Natural Selection, if +facts could be adduced to show that the toad's appearance does really +deter its enemies. Such an hypothesis resembles an Empirical Law in its +need of derivation (chap. xix. §§ <a href="#chap_19_sect_1">1</a>, <a href="#chap_19_sect_2">2</a>). If underivable from, or +irreconcilable with, known laws, it is a mere conjecture or prejudice. +The absolute leviation of phlogiston, in contrast with the gravitation +of all other forms of matter, discredited that supposed agent. That +Macpherson should have found the Ossianic poems extant in the Gaelic +memory, was contrary to the nature of oral tradition; except where +tradition is organised, as it was for ages among the Brahmins. The +suggestion that xanthochroid Aryans were "bleached" by exposure during +the glacial period, does not agree with Wallace's doctrine concerning +the coloration of Arctic animals. That our forefathers being predatory, +like bears, white <span class='pagenum'>[Pg 280]<a name="Page_280" id="Page_280"></a></span>variations amongst them were then selected by the +advantage of concealment, is a more plausible hypothesis.</p> + +<p>Although, then, the consilience of Inductions or Hypotheses is not a +sufficient proof of their truth, it is still a condition of it; +nonconsilience is a suspicious circumstance, and resilience (so to +speak), or mutual repugnance, is fatal to one or all.</p> + +<p><a name="chap_18_sect_4" id="chap_18_sect_4"></a>§ 4. We have now seen that a scientific hypothesis, to deserve the name, +must be verifiable and therefore definite; and that to establish itself +as a true theory, it must present some symptom of reality, and be +adequate and exclusive and in harmony with the system of experience. +Thus guarded, hypotheses seem harmless enough; but some people have a +strong prejudice against them, as against a tribe of savages without +government, or laws, or any decent regard for vested interests. It is +well known, too, that Bacon and Newton disparaged them. But Bacon, in +his examples of an investigation according to his own method, is +obliged, after a preliminary classification of facts, to resort to an +hypothesis, calling it <i>permissio intellectus</i>, <i>interpretatio inchoata</i> +or <i>vindemiatio prima</i>. And Newton when he said <i>hypotheses non fingo</i>, +meant that he did not deal in fictions, or lay stress upon supposed +forces (such as 'attraction'), that add nothing to the law of the facts. +Hypotheses are essential aids to discovery: speaking generally, +deliberate investigation depends wholly upon the use of them.</p> + +<p>It is true that we may sometimes observe a train of events that chances +to pass before us, when either we are idle or engaged with some other +inquiry, and so obtain a new glimpse of the course of nature; or we may +try experiments haphazard, and watch the results. But, even in these +cases, before our new notions can be considered knowledge, they must be +definitely framed in hypotheses and reobserved or experimented upon, +with whatever calculations or precautions may be necessary to ensure +<span class='pagenum'>[Pg 281]<a name="Page_281" id="Page_281"></a></span>accuracy or isolation. As a rule, when inquiring deliberately into the +cause of an event, whether in nature or in history, we first reflect +upon the circumstances of the case and compare it with similar ones +previously investigated, and so are guided by a preconception more or +less definite of 'what to look for,' what the cause is likely to be, +that is, by an hypothesis. Then, if our preconception is justified, or +something which we observe leads to a new hypothesis, either we look for +other instances to satisfy the canons of Agreement; or (if the matter +admits of experiment) we endeavour, under known conditions according to +the canon of Difference, to reproduce the event by means of that which +our hypothesis assigns as the cause; or we draw remote inferences from +our hypothesis, and try to test these by the Inductive Canons.</p> + +<p>If we argue from an hypothesis and express ourselves formally, it will +usually appear as the major premise; but this is not always the case. In +extending ascertained laws to fresh cases, the minor premise may be an +hypothesis, as in testing the chemical constitution of any doubtful +substance, such as a piece of ore. Some solution or preparation, A, is +generally made which (it is known) will, on the introduction of a +certain agent, B, give a reaction, C, if the preparation contains a +given substance, X. The major premise is the law of reaction—</p> + + +<div class="example"><span class="i0">Whenever A is X, if treated with B it is C.</span></div> + + +<p>The minor premise is an hypothesis that the preparation contains X. An +experiment then treats A with B. If C result, a probability is raised in +favour of the hypothesis that A is X; or a certainty, if we know that C +results on that condition only.</p> + +<p>So important are hypotheses to science, that Whewell insists that they +have often been extremely valuable even though erroneous. Of the +Ptolemaic system he says, "We can hardly imagine that Astronomy could, +in its <span class='pagenum'>[Pg 282]<a name="Page_282" id="Page_282"></a></span>outset, have made so great a progress under any other form." It +served to connect men's thoughts on the subject and to sustain their +interest in working it out; by successive corrections "to save +appearances," it attained at last to a descriptive sort of truth, which +was of great practical utility; it also occasioned the invention of +technical terms, and, in general digested the whole body of observations +and prepared them for assimilation by a better hypothesis in the fulness +of time. Whewell even defends the maxim that "Nature abhors a vacuum," +as having formerly served to connect many facts that differ widely in +their first aspect. "And in reality is it not true," he asks, "that +nature <i>does</i> abhor a vacuum, and does all she can to avoid it?" Let no +forlorn cause despair of a champion! Yet no one has accused Whewell of +Quixotry; and the sense of his position is that the human mind is a +rather feeble affair, that can hardly begin to think except with +blunders.</p> + +<p>The progress of science may be plausibly attributed to a process of +Natural Selection; hypotheses are produced in abundance and variety, and +those unfit to bear verification are destroyed, until only the fittest +survive. Wallace, a practical naturalist, if there ever was one, as well +as an eminent theorist, takes the same view as Whewell of such +inadequate conjectures. Of 'Lemuria,' an hypothetical continent in the +Indian Ocean, once supposed to be traceable in the islands of +Madagascar, Seychelles, and Mauritius, its surviving fragments, and +named from the Lemurs, its characteristic denizens, he says (<i>Island +Life</i>, chap. xix.) that it was "essentially a provisional hypothesis, +very useful in calling attention to a remarkable series of problems in +geographical distribution [of plants and animals], but not affording the +true solution of those problems." We see, then, that 'provisional +hypotheses,' or working hypotheses,' though erroneous, may be very +useful or (as Whewell says) necessary.</p><p><span class='pagenum'>[Pg 283]<a name="Page_283" id="Page_283"></a></span></p> + +<p>Hence, to be prolific of hypotheses is the first attribute of scientific +genius; the first, because without it no progress whatever can be made. +And some men seem to have a marked felicity, a sort of instinctive +judgment even in their guesses, as if their heads were made according to +Nature. But others among the greatest, like Kepler, guess often and are +often wrong before they hit upon the truth, and themselves, like Nature, +destroy many vain shoots and seedlings of science for one that they find +fit to live. If this is how the mind works in scientific inquiry (as it +certainly is, with most men, in poetry, in fine art, and in the scheming +of business), it is useless to complain. We should rather recognise a +place for fools' hypotheses, as Darwin did for "fools' experiments." But +to complete the scientific character, there must be great patience, +accuracy, and impartiality in examining and testing these conjectures, +as well as great ingenuity in devising experiments to that end. The want +of these qualities leads to crude work and public failure and brings +hypotheses into derision. Not partially and hastily to believe in one's +own guesses, nor petulantly or timidly to reject them, but to consider +the matter, to suspend judgment, is the moral lesson of science: +difficult, distasteful, and rarely mastered.</p> + +<p><a name="chap_18_sect_5" id="chap_18_sect_5"></a>§ 5. The word 'hypothesis' is often used also for the scientific device +of treating an Abstraction as, for the purposes of argument, equivalent +to the concrete facts. Thus, in Geometry, a line is treated as having no +breadth; in Mechanics, a bar may be supposed absolutely rigid, or a +machine to work without friction; in Economics, man is sometimes +regarded as actuated solely by love of gain and dislike of exertion. The +results reached by such reasoning may be made applicable to the concrete +facts, if allowance be made for the omitted circumstances or properties, +in the several cases of lines, bars, and men; but otherwise all +conclusions from abstract terms are limited by their definitions. +Abstract reasoning, then (that is, <span class='pagenum'>[Pg 284]<a name="Page_284" id="Page_284"></a></span>reasoning limited by definitions), +is often said to imply 'the hypothesis' that things exist as their names +are defined, having no properties but those enumerated in their +definitions. This seems, however, a needless and confusing extension of +the term; for an hypothesis proposes an agent, collocation, or law +hitherto unknown; whereas abstract reasoning proposes to exclude from +consideration a good deal that is well known. There seems no reason why +the latter device should not be plainly called an Abstraction.</p> + +<p>Such abstractions are necessary to science; for no object is +comprehensible by us in all its properties at once. But if we forget the +limitations of our abstract data, we are liable to make strange blunders +by mistaking the character of the results: treating the results as +simply true of actual things, instead of as true of actual things only +so far as they are represented by the abstractions. In addressing +abstract reasoning, therefore, to those who are unfamiliar with +scientific methods, pains should be taken to make it clear what the +abstractions are, what are the consequent limitations upon the argument +and its conclusions, and what corrections and allowances are necessary +in order to turn the conclusions into an adequate account of the +concrete facts. The greater the number, variety, and subtlety of the +properties possessed by any object (such as human nature), the greater +are the qualifications required in the conclusions of abstract +reasoning, before they can hold true of such an object in practical +affairs.</p> + +<p>Closely allied to this method of Abstraction is the Mathematical Method +of Limits. In his <i>History of Scientific Ideas</i> (B. II. c. 12), Whewell +says: "The <i>Idea of a Limit</i> supplies a new mode of establishing +mathematical truths. Thus with regard to the length of any portion of a +curve, a problem which we have just mentioned; a curve is not made up of +straight lines, and therefore we <span class='pagenum'>[Pg 285]<a name="Page_285" id="Page_285"></a></span>cannot by means of any of the +doctrines of elementary geometry measure the length of any curve. But we +may make up a figure nearly resembling any curve by putting together +many short straight lines, just as a polygonal building of very many +sides may nearly resemble a circular room. And in order to approach +nearer and nearer to a curve, we may make the sides more and more small, +more and more numerous. We may then possibly find some mode of +measurement, some relation of these small lines to other lines, which is +not disturbed by the multiplication of the sides, however far it be +carried. And thus we may do what is equivalent to measuring the curve +itself; for by multiplying the sides we may approach more and more +closely to the curve till no appreciable difference remains. The curve +line is the <i>Limit</i> of the polygon; and in this process we proceed on +the <i>Axiom</i> that 'What is true up to the Limit is true at the Limit.'"</p> + +<p>What Whewell calls the Axiom here, others might call an Hypothesis; but +perhaps it is properly a Postulate. And it is just the obverse of the +Postulate implied in the Method of Abstractions, namely, that 'What is +true of the Abstraction is true of concrete cases the more nearly they +approach the Abstraction.' What is true of the 'Economic Man' is truer +of a broker than of a farmer, of a farmer than of a labourer, of a +labourer than of the artist of romance. Hence the Abstraction may be +called a Limit or limiting case, in the sense that it stands to concrete +individuals, as a curve does to the figures made up "by putting together +many short straight lines." Correspondingly, the Proper Name may be +called the Limit of the class-name; since its attributes are infinite, +whereas any name whose attributes are less than infinite stands for a +possible class. In short, for logical purposes, a Limit may be defined +as any extreme case to which actual examples may approach without ever +reaching it. And in this sense 'Method of Limits' might be used as a +term <span class='pagenum'>[Pg 286]<a name="Page_286" id="Page_286"></a></span>including the Method of Abstractions; though it would be better to +speak of them generically as 'Methods of Approximation.'</p> + +<p>We may also notice the Assumptions (as they may be called) that are +sometimes employed to facilitate an investigation, because some definite +ground must be taken and nothing better can be thought of: as in +estimating national wealth, that furniture is half the value of the +houses.</p> + +<p>It is easy to conceive of an objector urging that such devices as the +above are merely ways of avoiding the actual problems, and that they +display more cunning than skill. But science, like good sense, puts up +with the best that can be had; and, like prudence, does not reject the +half-loaf. The position, that a conceivable case that can be dealt with +may, under certain conditions, be substituted for one that is +unworkable, is a touchstone of intelligence. To stand out for ideals +that are known to be impossible, is only an excuse for doing nothing at +all.</p> + +<p>In another sense, again, the whole of science is sometimes said to be +hypothetical, because it takes for granted the Uniformity of Nature; for +this, in its various aspects, can only be directly ascertained by us as +far as our experience extends; whereas the whole value of the principle +of Uniformity consists in its furnishing a formula for the extension of +our other beliefs beyond our actual experience. Transcendentalists, +indeed, call it a form of Reason, just because it is presupposed in all +knowledge; and they and the Empiricists agree that to adduce material +evidence for it, in its full extent, is impossible. If, then, material +evidence is demanded by any one, he cannot regard the conclusions of +Mathematics and Physical Science as depending on what is itself +unproved; he must, with Mill, regard these conclusions as drawn "not +from but according to" the axioms of Equality and Causation. That is to +say, if the axioms are true, the conclusions are; the <span class='pagenum'>[Pg 287]<a name="Page_287" id="Page_287"></a></span>material evidence +for both the axioms and the conclusions being the same, namely, +uncontradicted experience. Now when we say, 'If Nature is uniform, +science is true,' the hypothetical character of science appears in the +form of the statement. Nevertheless, it seems undesirable to call our +confidence in Nature's uniformity an 'hypothesis': it is incongruous to +use the same term for our tentative conjectures and for our most +indispensable beliefs. 'The Universal Postulate' is a better term for +the principle which, in some form or other, every generalisation takes +for granted.</p> + +<p>We are now sometimes told that, instead of the determinism and +continuity of phenomena hitherto assumed by science, we should recognise +indeterminism and discontinuity. But it will be time enough to fall in +with this doctrine when its advocates produce a new Logic of Induction, +and explain the use of the method of Difference and of control +experiments according to the new postulates.</p><p><span class='pagenum'>[Pg 288]<a name="Page_288" id="Page_288"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_XIX" id="CHAPTER_XIX"></a>CHAPTER XIX</h2> + +<h3>LAWS CLASSIFIED; EXPLANATION; CO-EXISTENCE; ANALOGY</h3> + + +<p><a name="chap_19_sect_1" id="chap_19_sect_1"></a>§ 1. Laws are classified, according to their degrees of generality, as +higher and lower, though the grades may not be decisively +distinguishable.</p> + +<p>First, there are Axioms or Principles, that is real, universal, +self-evident propositions. They are—(1) real propositions; not, like +'The whole is greater than any of its parts,' merely definitions, or +implied in definitions. (2) They are regarded as universally true of +phenomena, as far as the form of their expression extends; that is, for +example, Axioms concerning quantity are true of everything that is +considered in its quantitative aspect, though not (of course) in its +qualitative aspect. (3) They are self-evident; that is, each rests upon +its own evidence (whatever that may be); they cannot be derived from one +another, nor from any more general law. Some, indeed, are more general +than others: the Logical Principle of Contradiction, 'if A is B, it is +not not-B', is true of qualities as well as of quantities; whereas the +Axioms of Mathematics apply only to quantities. The Mathematical Axioms, +again, apply to time, space, mental phenomena, and matter and energy; +whereas the Law of Causation is only true of concrete events in the +redistribution of matter and energy: such, at least, is the strict limit +of Causation, if we identify it with the Conservation of Energy; +although our imperfect knowledge of life and <span class='pagenum'>[Pg 289]<a name="Page_289" id="Page_289"></a></span>mind often drives us to +speak of feelings, ideas, volitions, as causes. Still, the Law of +Causation cannot be derived from the Mathematical Axioms, nor these from +the Logical. The kind of evidence upon which Axioms rest, or whether any +evidence can be given for them, is (as before observed) a question for +Metaphysics, not for Logic. Axioms are the upward limit of Logic, which, +like all the special sciences, necessarily takes them for granted, as +the starting point of all deduction and the goal of all generalisation.</p> + +<p>Next to Axioms, come Primary Laws of Nature: these are of less +generality than the Axioms, and are subject to the conditions of +methodical proof; being universally true only of certain forces or +properties of matter, or of nature under certain conditions; so that +proof of them by logical or mathematical reasoning is expected, because +they depend upon the Axioms for their formal evidence. Such are the law +of gravitation, in Astronomy; the law of definite proportions, in +Chemistry; the law of heredity, in Biology; and in Psychology, the law +of relativity.</p> + +<p>Then, there are Secondary Laws, of still less generality, resulting from +a combination of conditions or forces in given circumstances, and +therefore conceivably derivable from the laws of those conditions or +forces, if we can discover them and compute their united effects. +Accordingly, Secondary Laws are either—(1) Derivative, having been +analysed into, and deduced from, Primary Laws; or (2) Empirical, those +that have not yet been deduced (though from their comparatively special +and complex character, it seems probable they may be, given sufficient +time and ingenuity), and that meanwhile rest upon some unsatisfactory +sort of induction by Agreement or Simple Enumeration.</p> + +<p>Whether laws proved only by the canon of Difference are to be considered +Empirical, is perhaps a question: their proof derives them from the +principle of Causation; but, being of narrow scope, some more special +account of <span class='pagenum'>[Pg 290]<a name="Page_290" id="Page_290"></a></span>them seems requisite in relation to the Primary Laws before +we can call them Derivative in the technical sense.</p> + +<p>Many Secondary Laws, again, are partially or imperfectly Derivative; we +can give general reasons for them, without being able to determine +theoretically the precise relations of the phenomena they describe. +Meteorologists can explain the general conditions of all sorts of +weather, but have made little progress toward predicting the actual +course of it (at least, for our island): Geologists know the general +causes of mountain ranges, but not why they rise just where we find +them: Economists explain the general course of a commercial crisis, but +not why the great crises recurred at intervals of about ten years.</p> + +<p>Derivative Laws make up the body of the exact sciences, having been +assimilated and organised; whilst Empirical Laws are the undigested +materials of science. The theorems of Euclid are good examples of +derivative laws in Mathematics; in Astronomy, Kepler's laws and the laws +of the tides; in Physics, the laws of shadows, of perspective, of +harmony; in Biology, the law of protective coloration; in Economics, the +laws of prices, wages, interest, and rent.</p> + +<p>Empirical Laws are such as Bode's law of the planetary distances; the +laws of the expansion of different bodies by heat, and formulæ +expressing the electrical conductivity of each substance as a function +of the temperature. Strictly speaking, I suppose, all the laws of +chemical combination are empirical: the law of definite proportions is +verifiable in all cases that have been examined, except for variations +that may be ascribed to errors of experiment. Much the same is true in +Biology; most of the secondary laws are empirical, except so far as +structures or functions may be regarded as specialised cases in Physics +or Chemistry and deducible from these sciences. The theory of Natural +Selection, however, has been the means of rendering many laws, that were +once wholly empirical, at least <span class='pagenum'>[Pg 291]<a name="Page_291" id="Page_291"></a></span>partially derivative; namely, the laws +of the geographical distribution of plants and animals, and of their +adaptation in organisation, form and colour, habits and instincts, to +their various conditions of life. The laws that remain empirical in +Biology are of all degrees of generality from that of the tendency to +variation in size and in every other character shown by every species +(though as to the reason of this there are promising hypotheses), down +to such curious cases as that the colour of roses and carnations never +varies into blue, that scarlet flowers are never sweet-scented, that +bullfinches fed on hemp-seed turn black, that the young of white, yellow +and dun pigeons are born almost naked (whilst others have plenty of +down); and so on. The derivation of empirical laws is the greater part +of the explanation of Nature (§§ <a href="#chap_19_sect_5">5</a>, <a href="#chap_19_sect_6">6</a>).</p> + +<p>A 'Fact,' in the common use of the word, is a particular observation: it +is the material of science in its rawest state. As perceived by a mind, +it is, of course, never absolutely particular: for we cannot perceive +anything without classing it, more or less definitely, with things +already known to us; nor describe it without using connotative terms +which imply a classification of the things denoted. Still, we may +consider an observation as particular, in comparison with a law that +includes it with numerous others in one general proposition. To turn an +observation into an experiment, or (where experiment is impracticable) +to repeat it with all possible precautions and exactness, and to +describe it as to the duration, quantity, quality and order of +occurrence of its phenomena, is the first stage of scientific +manufacture. Then comes the formulation of an empirical law; and lastly, +if possible, deduction or derivation, either from higher laws previously +ascertained, or from an hypothesis. However, as a word is used in +various senses, we often speak of laws as 'facts': we say the law of +gravitation is a fact, meaning that it is real, or verifiable by +observations or experiments.</p><p><span class='pagenum'>[Pg 292]<a name="Page_292" id="Page_292"></a></span></p> + +<p><a name="chap_19_sect_2" id="chap_19_sect_2"></a>§ 2. Secondary Laws may also be classified according to their constancy +into—(1) the Invariable (as far as experience reaches), and (2) +Approximate Generalisations in the form—Most X's are Y. Of the +invariable we have given examples above. The following are approximate +generalisations: Most comets go round the Sun from East to West; Most +metals are solid at ordinary temperatures; Most marsupials are +Australasian; Most arctic animals are white in winter; Most cases of +plague are fatal; Most men think first of their own interests. Some of +these laws are empirical, as that 'Most metals are solid at ordinary +temperatures': at present no reason can be given for this; nor do we +know why most cases of plague are fatal. Others, however, are at least +partially derivative, as that 'Most arctic animals are white'; for this +seems to be due to the advantage of concealment in the snow; whether, as +with the bear, the better to surprise its prey, or, with the hare, to +escape the notice of its enemies.</p> + +<p>But the scientific treatment of such a proposition requires that we +should also explain the exceptions: if 'Most are,' this implies that +'Some are not'; why not, then? Now, if we can give reasons for all the +exceptions, the approximate generalisation may be converted into an +universal one, thus: 'All arctic animals are white, unless (like the +raven) they need no concealment either to prey or to escape; or unless +mutual recognition is more important to them than concealment (as with +the musk-sheep)'. The same end of universal statement may be gained by +including the conditions on which the phenomenon depends, thus: 'All +arctic animals to whom concealment is of the utmost utility are white.'</p> + +<p>When statistics are obtainable, it is proper to convert an approximate +generalisation into a proportional statement of the fact, thus: instead +of 'Most attacks of plague are fatal', we might find that in a certain +country 70 per <span class='pagenum'>[Pg 293]<a name="Page_293" id="Page_293"></a></span>cent. were so. Then, if we found that in another country +the percentage of deaths was 60, in another 40, we might discover, in +the different conditions of these countries, a clue to the high rate of +mortality from this disease. Even if the proportion of cases in which +two facts are connected does not amount to 'Most,' yet, if any definite +percentage is obtainable, the proposition has a higher scientific value +than a vague 'Some': as if we know that 2 per cent. of the deaths in +England are due to suicide, this may be compared with the rates of +suicide in other countries; from which perhaps inferences may be drawn +as to the causes of suicide.</p> + +<p>In one department of life, namely, Politics, there is a special +advantage in true approximate generalisations amounting to 'Most cases.' +The citizens of any State are so various in character, enlightenment, +and conditions of life, that we can expect to find few propositions +universally true of them: so that propositions true of the majority must +be trusted as the bases of legislation. If most men are deterred from +crime by fear of punishment; if most men will idle if they can obtain +support without industry; if most jurymen will refuse to convict of a +crime for which the prescribed penalties seem to them too severe; these +are most useful truths, though there should be numerous exceptions to +them all.</p> + +<p><a name="chap_19_sect_3" id="chap_19_sect_3"></a>§ 3. Secondary Laws can only be trusted in 'Adjacent Cases'; that is, +where the circumstances are similar to those in which the laws are known +to be true.</p> + +<p>A Derivative Law will be true wherever the forces concerned exist in the +combinations upon which the law depends, if there are no counteracting +conditions. That water can be pumped to about 33 feet at the sea-level, +is a derivative law on this planet: is it true in Mars? That depends on +whether there are in Mars bodies of a liquid similar to our water; +whether there is an atmosphere there, and how great its pressure is; +which will vary <span class='pagenum'>[Pg 294]<a name="Page_294" id="Page_294"></a></span>with its height and density. If there is no atmosphere +there can be no pumping; or if there is an atmosphere of less pressure +than ours, water such as ours can only be pumped to a less height than +33 feet. Again, we know that there are arctic regions in Mars; if there +are also arctic animals, are they white? That may depend upon whether +there are any beasts of prey. If not, concealment seems to be of no use.</p> + +<p>An Empirical Law, being one whose conditions we do not know, the extent +of its prevalence is still less ascertainable. Where it has not been +actually observed to be true, we cannot trust it unless the +circumstances, on the whole, resemble so closely those amongst which it +has been observed, that the unknown causes, whatever they may be, are +likely to prevail there. And, even then, we cannot have much confidence +in it; for there may be unknown circumstances which entirely frustrate +the effect. The first naturalist who travelled (say) from Singapore +eastward by Sumatra and Java, or Borneo, and found the mammalia there +similar to those of Asia, may naturally have expected the same thing in +Celebes and Papua; but, if so, he was entirely disappointed; for in +Papua the mammalia are marsupials like those of Australia. Thus his +empirical law, 'The mammalia of the Eastern Archipelago are Asiatic,' +would have failed for no apparent reason. According to Mr. Wallace, +there is a reason for it, though such as could only be discovered by +extensive researches; namely, that the sea is deep between Borneo and +Celebes, so that they must have been separated for many ages; whereas it +is shallow from Borneo westward to Asia, and also southward from Celebes +to Australia; so that these regions, respectively, may have been +recently united: and the true law is that similar mammalia belong to +those tracts which at comparatively recent dates have formed parts of +the same continents (unless they are the remains of a former much wider +distribution).</p><p><span class='pagenum'>[Pg 295]<a name="Page_295" id="Page_295"></a></span></p> + +<p>A considerable lapse of time may make an empirical law no longer +trustworthy; for the forces from whose combination it resulted may have +ceased to operate, or to operate in the same combination; and since we +do not know what those forces were, even the knowledge that great +changes have taken place in the meantime cannot enable us, after an +interval, to judge whether or not the law still holds true. New stars +shine in the sky and go out; species of plants and animals become +extinct; diseases die out and fresh ones afflict mankind: all these +things doubtless have their causes, but if we do not know what they are, +we have no measure of the effects, and cannot tell when or where they +will happen.</p> + +<p>Laws of Concomitant Variations may hold good only within certain limits. +That bodies contract as the temperature falls, is not true of water +below 39° F. In Psychology, Weber's Law is only true within the median +range of sensation-intensities, not for very faint, nor for very strong, +stimuli. In such cases the failure of the laws may depend upon something +imperfectly understood in the collocation: as to water, on its molecular +constitution; as to sensation, upon the structure of the nervous system.</p> + +<p><a name="chap_19_sect_4" id="chap_19_sect_4"></a>§ 4. Secondary Laws, again, are either of Succession or of Co-existence.</p> + +<p>Those of Succession are either—(1) of direct causation, as that 'Water +quenches fire,' or (more strictly) that 'Evaporation reduces +temperature'; or (2) of the effect of a remote cause, as 'Bad harvests +tend to raise the price of bread'; or (3) of the joint effects of the +same cause, as that 'Night follows day' (from the revolution of the +earth), or the course of the seasons (from the inclination of the +earth's axis).</p> + +<p>Laws of Co-existence are of several classes. (1) One has the generality +of a primary law, though it is proved only by Agreement, namely, 'All +gravitating bodies are inert'. Others, though less general than this, +are of very exten<span class='pagenum'>[Pg 296]<a name="Page_296" id="Page_296"></a></span>sive range, as that 'All gases that are not decomposed +by rise of temperature have the same rate of expansion'; and, in Botany +that 'All monocotyledonous plants are endogenous'. These laws of +Co-existence are concerned with fundamental properties of bodies.</p> + +<p>(2) Next come laws of the Co-existence of those properties which are +comprised in the definitions of Natural Kinds. Mill distinguished +between (α) classes of things that agree among themselves and differ +from others only in one or a few attributes (such as 'red things,' +'musical notes', 'carnivorous animals', 'soldiers'), and (β) classes of +things that agree among themselves and differ from others in a multitude +of characters: and the latter he calls Natural Kinds. These comprise the +chemical elements and their pure compounds (such as water, alcohol, +rock-salt), and the species of plants and animals. Clearly, each of +these is constituted by the co-existence or co-inherence of a multitude +of properties, some of which are selected as the basis of their +definitions. Thus, Gold is a metal of high specific gravity, atomic +weight 197.2, high melting point, low chemical affinities, great +ductility, yellow colour, <i>etc.</i>: a Horse has 'a vertebral column, +mammæ, a placental embryo, four legs, a single well-developed toe in +each foot provided with a hoof, a bushy tail, and callosities on the +inner sides of both the fore and the hind legs' (Huxley).</p> + +<p>Since Darwinism has obtained general acceptance, some Logicians have +doubted the propriety of calling the organic species 'Kinds,' on the +ground that they are not, as to definiteness and permanence, on a par +with the chemical elements or such compounds as water and rock-salt; +that they vary extensively, and that it is only by the loss of former +generations of animals that we are able to distinguish species at all. +But to this it may be replied that species are often approximately +constant for immense periods of time, and may be called permanent in +com<span class='pagenum'>[Pg 297]<a name="Page_297" id="Page_297"></a></span>parison with human generations; and that, although the leading +principles of Logic are perhaps eternal truths, yet upon a detail such +as this, the science may condescend to recognise a distinction if it is +good for (say) only 100,000 years. That if former generations of plants +and animals were not lost, all distinctions of species would disappear, +may be true; but they are lost—for the most part beyond hope of +recovery; and accordingly the distinction of species is still +recognised; although there are cases, chiefly at the lower stages of +organisation, in which so many varieties occur as to make adjacent +species almost or quite indistinguishable. So far as species are +recognised, then, they present a complex co-inherence of qualities, +which is, in one aspect, a logical problem; and, in another, a logical +datum; and, coming more naturally under the head of Natural Kinds than +any other, they must be mentioned in this place.</p> + +<p>(3) There are, again, certain coincidences of qualities not essential to +any kind, and sometimes prevailing amongst many different kinds: such as +'Insects of nauseous taste have vivid (warning) colours'; 'White +tom-cats with blue eyes are deaf'; 'White spots and patches, when they +appear in domestic animals, are most frequent on the left side.'</p> + +<p>(4) Finally, there may be constancy of relative position, as of sides +and angles in Geometry; and also among concrete things (at least for +long periods of time), as of the planetary orbits, the apparent +positions of fixed stars in the sky, the distribution of land and water +on the globe, opposite seasons in opposite hemispheres.</p> + +<p>All these cases of Co-existence (except the geometrical) present the +problem of deriving them from Causation; for there is no general Law of +Co-existence from which they can be derived; and, indeed, if we conceive +of the external world as a perpetual redistribution of matter and +energy, it follows that the whole state of Nature at any instant, <span class='pagenum'>[Pg 298]<a name="Page_298" id="Page_298"></a></span>and +therefore every co-existence included in it, is due to causation issuing +from some earlier distribution of matter and energy. Hence, indeed, it +is not likely that the problems of co-existence as a whole will ever be +solved, since the original distribution of matter is, of course, +unknown. Still, starting with any given state of Nature, we may hope to +explain some of the co-existences in any subsequent state. We do not, +indeed, know why heavy bodies are always inert, nor why the chemical +elements are what they are; but it is known that "the properties of the +elements are functions of their atomic weight," which (though, at +present, only an empirical law) may be a clue to some deeper +explanation. As to plants and animals, we know the conditions of their +generation, and can trace a connection between most of their +characteristics and the conditions of their life: as that the teeth and +stomach of animals vary with their food, and that their colour generally +varies with their habitat.</p> + +<p>Geometrical Co-existence, when it is not a matter of definition (as 'a +square is a rectangle with four equal sides'), is deduced from the +definitions and axioms: as when it is shown that in triangles the +greater side is opposite the greater angle. The deductions of theorems +or secondary laws, in Geometry is a type of what is desirable in the +Physical Sciences: the demonstration, namely, that all the connections +of phenomena, whether successive or co-existent, are consequences of the +redistribution of matter and energy according to the principle of +Causation.</p> + +<p>Coincidences of Co-existence (Group (3)) may sometimes be deduced and +sometimes not. That 'nauseous insects have vivid coloration' comes under +the general law of 'protective coloration'; as they are easily +recognised and therefore avoided by insectivorous birds and other +animals. But why white tom-cats with blue-eyes should be deaf, is (I +believe) unknown. When co-existences cannot be derived from causation, +they can only <span class='pagenum'>[Pg 299]<a name="Page_299" id="Page_299"></a></span>be proved by collecting examples and trusting vaguely to +the Uniformity of Nature. If no exceptions are found, we have an +empirical law of considerable probability within the range of our +exploration. If exceptions occur, we have at most an approximate +generalisation, as that 'Most metals are whitish,' or 'Most domestic +cats are tabbies' (but this probably is the ancestral colouring). We may +then resort to statistics for greater definiteness, and find that in +Hampshire (say) 90 <i>per cent.</i> of the domestic cats are tabby.</p> + +<p><a name="chap_19_sect_5" id="chap_19_sect_5"></a>§ 5. Scientific Explanation consists in discovering, deducing, and +assimilating the laws of phenomena; it is the analysis of that +Heracleitan 'flux' which so many philosophers have regarded as +intractable to human inquiry. In the ordinary use of the word, +'explanation' means the satisfying a man's understanding; and what may +serve this purpose depends partly upon the natural soundness of his +understanding, and partly on his education; but it is always at last an +appeal to the primary functions of cognition, discrimination and +assimilation.</p> + +<p>Generally, what we are accustomed to seems to need no explanation, +unless our curiosity is particularly directed to it. That boys climb +trees and throw stones, and that men go fox-hunting, may easily pass for +matters of course. If any one is so exacting as to ask the reason, there +is a ready answer in the 'need of exercise.' But this will not explain +the peculiar zest of those exercises, which is something quite different +from our feelings whilst swinging dumb-bells or tramping the highway. +Others, more sophisticated, tell us that the civilised individual +retains in his nature the instincts of his remote ancestors, and that +these assert themselves at stages of his growth corresponding with +ancestral periods of culture or savagery: so that if we delight to climb +trees, throw stones, and hunt, it is because our forefathers once lived +in trees, had no missiles but stones, and depended for a livelihood +<span class='pagenum'>[Pg 300]<a name="Page_300" id="Page_300"></a></span>upon killing something. To some of us, again, this seems an +explanation; to others it merely gives annoyance, as a superfluous +hypothesis, the fruit of a wanton imagination and too much leisure.</p> + +<p>However, what we are not accustomed to immediately excites curiosity. If +it were exceptional to climb trees, throw stones, ride after foxes, +whoever did such things would be viewed with suspicion. An eclipse, a +shooting star, a solitary boulder on the heath, a strange animal, or a +Chinaman in the street, calls for explanation; and among some nations, +eclipses have been explained by supposing a dragon to devour the sun or +moon; solitary boulders, as the missiles of a giant; and so on. Such +explanations, plainly, are attempts to regard rare phenomena as similar +to others that are better known; a snake having been seen to swallow a +rabbit, a bigger one may swallow the sun: a giant is supposed to bear +much the same relation to a boulder as a boy does to half a brick. When +any very common thing seems to need no explanation, it is because the +several instances of its occurrence are a sufficient basis of +assimilation to satisfy most of us. Still, if a reason for such a thing +be demanded, the commonest answer has the same implication, namely, that +assimilation or classification is a sufficient reason for it. Thus, if +climbing trees is referred to the need of exercise, it is assimilated to +running, rowing, <i>etc.</i>; if the customs of a savage tribe are referred +to the command of its gods, they are assimilated to those things that +are done at the command of chieftains.</p> + +<p>Explanation, then, is a kind of classification; it is the finding of +resemblance between the phenomenon in question and other phenomena. In +Mathematics, the explanation of a theorem is the same as its proof, and +consists in showing that it repeats, under different conditions, the +definitions and axioms already assumed and the theorems already +demonstrated. In Logic, the major <span class='pagenum'>[Pg 301]<a name="Page_301" id="Page_301"></a></span>premise of every syllogism is an +explanation of the conclusion; for the minor premise asserts that the +conclusion is an example of the major premise.</p> + +<p>In Concrete Sciences, to discover the cause of a phenomenon, or to +derive an empirical law from laws of causation, is to explain it; +because a cause is an invariable antecedent, and therefore reminds us +of, or enables us to conceive, an indefinite number of cases similar to +the present one wherever the cause exists. It classifies the present +case with other instances of causation, or brings it under the universal +law; and, as we have seen that the discovery of the laws of nature is +essentially the discovery of causes, the discovery and derivation of +laws is scientific explanation.</p> + +<p>The discovery of quantitative laws is especially satisfactory, because +it not only explains why an event happens at all, but why it happens +just in this direction, degree, or amount; and not only is the given +relation of cause and effect definitely assimilated to other causal +instances, but the effect is identified with the cause as the same +matter and energy redistributed; wherefore, whether the conservation of +matter and energy be universally true or not, it must still be an +universal postulate of scientific explanation.</p> + +<p>The mere discovery of an empirical law of co-existence, as that 'white +tom-cats with blue eyes are deaf', is indeed something better than an +isolated fact: every general proposition relieves the mind of a load of +facts; and, for many people, to be able to say—'It is always so'—may +be enough; but for scientific explanation we require to know the reason +of it, that is, the cause. Still, if asked to explain an axiom, we can +only say, 'It is always so:' though it is some relief to point out +particular instances of its realisation, or to exhibit the similarity of +its form to that of other axioms—as of the <i>Dictum</i> to the axiom of +equality.</p><p><span class='pagenum'>[Pg 302]<a name="Page_302" id="Page_302"></a></span></p> + +<p><a name="chap_19_sect_6" id="chap_19_sect_6"></a>§ 6. There are three modes of scientific Explanation; First, the +analysis of a phenomenon into the laws of its causes and the concurrence +of those causes.</p> + +<p>The pumping of water implies (1) pressure of the air, (2) distribution +of pressure in a liquid, (3) that motion takes the direction of least +resistance. Similarly, that thunder follows forked lightning, and that +the report of a gun follows the flash, are resolvable into (1) the +discharge of electricity, or the explosion of gunpowder; (2) distance of +the observer from the event; (3) that light travels faster than sound. +The planetary orbits are analysable into the tendency of planets to fall +into the sun, and their tendency to travel in a straight line. When this +conception is helped out by swinging a ball round by a string, and then +letting it go, to show what would happen to the earth if gravitation +ceased, we see how the recognition of resemblance lies at the bottom of +explanation.</p> + +<p>Secondly, the discovery of steps of causation between a cause and its +remote effects; the interpolation and concatenation of causes.</p> + +<p>The maxim 'No cats no clover' is explained by assigning the intermediate +steps in the following series; that the fructification of red clover +depends on the visits of humble-bees, who distribute the pollen in +seeking honey; that if field-mice are numerous they destroy the +humble-bees' nests; and that (owls and weasels being exterminated by +gamekeepers) the destruction of field-mice depends upon the supply of +cats; which, therefore, are a remote condition of the clover crop. +Again, the communication of thought by speech is an example of something +so common that it seems to need no explanation; yet to explain it is a +long story. A thought in one man's mind is the remote cause of a similar +thought in another's: here we have (1) a thought associated with mental +words; (2) a connection between these thoughts and some tracts of the +brain; (3) a connection between these tracts of <span class='pagenum'>[Pg 303]<a name="Page_303" id="Page_303"></a></span>the brain and the +muscles of the larynx, the tongue and the lips; (4) movements of the +chest, larynx and mouth, propelling and modifying waves of air; (5) the +impinging of these air-waves upon another man's ear, and by a complex +mechanism exciting the aural nerve; (6) the transfer of this excitation +to certain tracts of his brain; (7) a connection there with sounds of +words and their associated thoughts. If one of these links fail, there +is no communication.</p> + +<p>Thirdly, the subsumption of several laws under one more general +expression.</p> + +<p>The tendency of bodies to fall to the earth and the tendency of the +earth itself (with the other planets) to fall into the sun, are subsumed +under the general law that 'All matter gravitates.' The same law +subsumes the movements of the tide. By means of the notion of specific +gravity, it includes 'levitation,' or the actual rising of some bodies, +as of corks in water, of balloons, or flames in the air: the fact being +that these things do not tend to rise, but to fall like everything else; +only as the water or air weighs more in proportion to its volume than +corks or balloons, the latter are pushed up.</p> + +<p>This process of subsumption bears the same relation to secondary laws, +that these do to particular facts. The generalisation of many particular +facts (that is, a statement of that in which they agree) is a law; and +the generalisation of these laws (that is, again, a statement of that in +which they agree) is a higher law; and this process, upwards or +downwards, is characteristic of scientific progress. The perfecting of +any science consists in comprehending more and more of the facts within +its province, and in showing that they all exemplify a smaller and +smaller number of principles, which express their most profound +resemblances.</p> + +<p>These three modes of explanation (analysis, interpolation, subsumption) +all consist in generalising or assimilating the <span class='pagenum'>[Pg 304]<a name="Page_304" id="Page_304"></a></span>phenomena. The pressure +of the air, of a liquid, and motion in the direction of least +resistance, are all commoner facts than pumping; that light travels +faster than sound is a commoner fact than a thunderstorm or gun-firing. +Each of the laws—'Cats kill mice,' 'Mice destroy humble-bees' nests,' +'Humble-bees fructify red clover'—is wider and expresses the +resemblance of more numerous cases than the law that 'Clover depends on +cats'; because each of them is less subject to further conditions. +Similarly, every step in the communication of thought by language is +less conditional, and therefore more general, than the completion of the +process.</p> + +<p>In all the above cases, again, each law into which the phenomenon +(whether pumping or conversation) is resolved, suggests a host of +parallel cases: as the modifying of air-waves by the larynx and lips +suggests the various devices by which the strings and orifices of +musical instruments modify the character of notes.</p> + +<p>Subsumption consists entirely in proving the existence of an essential +similarity between things where it was formerly not observed: as that +the gyrations of the moon, the fall of apples, and the flotation of +bubbles are all examples of gravitation: or that the purifying of the +blood by breathing, the burning of a candle, and the rusting of iron are +all cases of oxidation: or that the colouring of the underside of a +red-admiral's wings, the spots of the giraffe, the shape and attitude of +a stick-caterpillar, the immobility of a bird on its nest, and countless +other cases, though superficially so different, agree in this, that they +conceal and thereby protect the organism.</p> + +<p>Not any sort of likeness, however, suffices for scientific explanation: +the only satisfactory explanation of concrete things or events, is to +discover their likeness to others in respect of Causation. Hence +attempts to help the understanding by familiar comparisons are often +worse than useless. Any of the above examples will show that the <span class='pagenum'>[Pg 305]<a name="Page_305" id="Page_305"></a></span>first +result of explanation is not to make a phenomenon seem familiar, but to +put (as the saying is) 'quite a new face upon it.' When, indeed, we have +thought it over in all its newly discovered relations, we feel more at +home with it than ever; and this is one source of our satisfaction in +explaining things; and hence to substitute immediate familiarisation for +radical explanation, is the easily besetting sin of human understanding: +the most plausible of fallacies, the most attractive, the most difficult +to avoid even when we are on our guard against it.</p> + +<p><a name="chap_19_sect_7" id="chap_19_sect_7"></a>§ 7. The explanation of Nature (if it be admitted to consist in +generalisation, or the discovery of resemblance amidst differences) can +never be completed. For—(1) there are (as Mill says) facts, namely, +fundamental states or processes of consciousness, which are distinct; in +other words, they do not resemble one another, and therefore cannot be +generalised or subsumed under one explanation. Colour, heat, smell, +sound, touch, pleasure and pain, are so different that there is one +group of conditions to be sought for each; and the laws of these +conditions cannot be subsumed under a more general one without leaving +out the very facts to be explained. A general condition of sensation, +such as the stimulating of the sensory organs of a living animal, gives +no account of the <i>special</i> characters of colour, smell, <i>etc.</i>; which +are, however, the phenomena in question; and each of them has its own +law. Nay, each distinct sensation-quality, or degree, must have its own +law; for in each ultimate difference there is something that cannot be +assimilated. Such differences amount, according to experimental +Psychologists, to more than 50,000. Moreover, a neural process can never +explain a conscious process in the way of cause and effect; for there is +no equivalence between them, and one can never absorb the other.</p> + +<p>(2) When physical science is treated objectively (that is, with as +little reference as possible to the fact that all <span class='pagenum'>[Pg 306]<a name="Page_306" id="Page_306"></a></span>phenomena are only +known in relation to the human mind), colour, heat, smell, sound +(considered as sensations) are neglected, and attention is fixed upon +certain of their conditions: extension, figure, resistance, weight, +motion, with their derivatives, density, elasticity, <i>etc.</i> These are +called the Primary Qualities of Matter; and it is assumed that they +belong to matter by itself, whether we look on or not: whilst colour, +heat, sound, <i>etc.</i>, are called Secondary Qualities, as depending +entirely upon the reaction of some conscious animal. By physical science +the world is considered in the abstract, as a perpetual redistribution +of matter and energy, and the distracting multiplicity of sensations +seems to be got rid of.</p> + +<p>But, not to dwell upon the difficulty of reducing the activities of life +and chemistry to mechanical principles—even if this were done, complete +explanation could not be attained. For—(<i>a</i>) as explanation is the +discovery of causes, we no sooner succeed in assigning the causes of the +present state of the world than we have to inquire into the causes of +those causes, and again the still earlier causes, and so on to infinity. +But, this being impossible, we must be content, wherever we stop, to +contemplate the uncaused, that is, the unexplained; and then all that +follows is only relatively explained.</p> + +<p>Besides this difficulty, however, there is another that prevents the +perfecting of any theory of the abstract material world, namely (<i>b</i>), +that it involves more than one first principle. For we have seen that +the Uniformity of Nature is not really a principle, but a merely nominal +generalisation, since it cannot be definitely stated; and, therefore, +the principles of Contradiction, Mediate Equality, and Causation remain +incapable of subsumption; nor can any one of them be reduced to another: +so that they remain unexplained.</p> + +<p>(3) Another limit to explanation lies in the infinite character of every +particular fact; so that we may know <span class='pagenum'>[Pg 307]<a name="Page_307" id="Page_307"></a></span>the laws of many of its properties +and yet come far short of understanding it as a whole. A lump of +sandstone in the road: we may know a good deal about its specific +gravity, temperature, chemical composition, geological conditions; but +if we inquire the causes of the particular modifications it exhibits of +these properties, and further why it is just so big, containing so many +molecules, neither more nor less, disposed in just such relations to one +another as to give it this particular figure, why it lies exactly there +rather than a yard off, and so forth, we shall get no explanation of all +this. The causes determining each particular phenomenon are infinite, +and can never be computed; and, therefore, it can never be fully +explained.</p> + +<p><a name="chap_19_sect_8" id="chap_19_sect_8"></a>§ 8. Analogy is used in two senses: (1) for the resemblance of relations +between terms that have little or no resemblance—as <i>The wind drives +the clouds as a shepherd drives his sheep</i>—where wind and shepherd, +clouds and sheep are totally unlike. Such analogies are a favourite +figure in poetry and rhetoric, but cannot prove anything. For valid +reasoning there must be parallel cases, according to substance and +attribute, or cause and effect, or proportion: <i>e.g. As cattle and deer +are to herbivorousness, so are camels; As bodies near the earth fall +toward it, so does the moon; As 2 is to 3 so is 4 to 6.</i></p> + +<p>(2) Analogy is discussed in Logic as a kind of probable proof based upon +imperfect similarity (as the best that can be discovered) between the +<i>data</i> of comparison and the subject of our inference. Like Deduction +and Induction, it assumes that things which are alike in some respects +are also alike in others; but it differs from them in not appealing to a +definite general law assigning the essential points of resemblance upon +which the argument relies. In Deductive proof, this is done by the major +premise of every syllogism: if the major says that 'All fat men are +humorists,' and we can establish the minor, 'X is a fat man,' we have +secured the essential <span class='pagenum'>[Pg 308]<a name="Page_308" id="Page_308"></a></span>resemblance that carries the conclusion. In +induction, the Law of Causation and its representatives, the Canons, +serve the same purpose, specifying the essential marks of a cause. But, +in Analogy, the resemblance relied on cannot be stated categorically.</p> + +<p>If we argue that Mars is inhabited because it resembles the datum, our +Earth, (1) in being a planet, (2) neither too hot nor too cold for life, +(3) having an atmosphere, (4) land and water, <i>etc.</i>, we are not +prepared to say that 'All planets having these characteristics are +inhabited.' It is, therefore, not a deduction; and since we do not know +the original causes of life on the Earth, we certainly cannot show by +induction that adequate causes exist in Mars. We rely, then, upon some +such vague notion of Uniformity as that 'Things alike in some points are +alike in others'; which, plainly, is either false or nugatory. But if +the linear markings upon the surface of Mars indicate a system of +canals, the inference that he has intelligent inhabitants is no longer +analogical, since canals can have no other cause.</p> + +<p>The cogency of any proof depends upon the <i>character</i> and <i>definiteness</i> +of the likeness which one phenomenon bears to another; but Analogy +trusts to the general <i>quantity</i> of likeness between them, in ignorance +of what may be the really important likeness. If, having tried with a +stone, an apple, a bullet, <i>etc.</i>, we find that they all break an +ordinary window, and thence infer that a cricket ball will do so, we do +not reason by analogy, but make instinctively a deductive extension of +an induction, merely omitting the explicit generalisation, 'All missiles +of a certain weight, size and solidity break windows.' But if, knowing +nothing of snakes except that the viper is venomous, a child runs away +from a grass-snake, he argues by analogy; and, though his conduct is +prudentially justifiable, his inference is wrong: for there is no law +that 'All snakes are venomous,' but only that those are <span class='pagenum'>[Pg 309]<a name="Page_309" id="Page_309"></a></span>venomous that +have a certain structure of fang; a point which he did not stay to +examine.</p> + +<p>The discovery of an analogy, then, may suggest hypotheses; it states a +problem—to find the causes of the analogy; and thus it may lead to +scientific proof; but merely analogical argument is only probable in +various degrees. (1) The greater the number and importance of the points +of agreement, the more probable is the inference. (2) The greater the +number and importance of the points of difference, the less probable is +the inference. (3) The greater the number of unknown properties in the +subject of our argument, the less the value of any inference from those +that we do know. Of course the number of unknown properties can itself +be estimated only by analogy. In the case of Mars, they are probably +very numerous; and, apart from the evidence of canals, the prevalent +assumption that there are intelligent beings in that planet, seems to +rest less upon probability than on a curiously imaginative extension of +the gregarious sentiment, the chilly discomfort of mankind at the +thought of being alone in the universe, and a hope that there may be +conversable and 'clubable' souls nearer than the Dog-star.</p><p><span class='pagenum'>[Pg 310]<a name="Page_310" id="Page_310"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_XX" id="CHAPTER_XX"></a>CHAPTER XX</h2> + +<h3>PROBABILITY</h3> + + +<p><a name="chap_20_sect_1" id="chap_20_sect_1"></a>§ 1. Chance was once believed to be a distinct power in the world, +disturbing the regularity of Nature; though, according to Aristotle, it +was only operative in occurrences below the sphere of the moon. As, +however, it is now admitted that every event in the world is due to some +cause, if we can only trace the connection, whilst nevertheless the +notion of Chance is still useful when rightly conceived, we have to find +some other ground for it than that of a spontaneous capricious force +inherent in things. For such a conception can have no place in any +logical interpretation of Nature: it can never be inferred from a +principle, seeing that every principle expresses an uniformity; nor, +again, if the existence of a capricious power be granted, can any +inference be drawn from it. Impossible alike as premise and as +conclusion, for Reason it is nothing at all.</p> + +<p>Every event is a result of causes: but the multitude of forces and the +variety of collocations being immeasurably great, the overwhelming +majority of events occurring about the same time are only related by +Causation so remotely that the connection cannot be followed. Whilst my +pen moves along the paper, a cab rattles down the street, bells in the +neighbouring steeple chime the quarter, a girl in the next house is +practising her scales, and throughout the world innumerable events are +happening which may never happen together again; so that should one of +<span class='pagenum'>[Pg 311]<a name="Page_311" id="Page_311"></a></span>them recur, we have no reason to expect any of the others. This is +Chance, or chance coincidence. The word Coincidence is vulgarly used +only for the inexplicable concurrence of <i>interesting</i> events—"quite a +coincidence!"</p> + +<p>On the other hand, many things are now happening together or coinciding, +that will do so, for assignable reasons, again and again; thousands of +men are leaving the City, who leave at the same hour five days a week. +But this is not chance; it is causal coincidence due to the custom of +business in this country, as determined by our latitude and longitude +and other circumstances. No doubt the above chance +coincidences—writing, cab-rattling, chimes, scales, <i>etc.</i>—are +causally connected at some point of past time. They were predetermined +by the condition of the world ten minutes ago; and that was due to +earlier conditions, one behind the other, even to the formation of the +planet. But whatever connection there may have been, we have no such +knowledge of it as to be able to deduce the coincidence, or calculate +its recurrence. Hence Chance is defined by Mill to be: Coincidence +giving no ground to infer uniformity.</p> + +<p>Still, some chance coincidences do recur according to laws of their own: +I say <i>some</i>, but it may be all. If the world is finite, the possible +combinations of its elements are exhaustible; and, in time, whatever +conditions of the world have concurred will concur again, and in the +same relation to former conditions. This writing, that cab, those +chimes, those scales will coincide again; the Argonautic expedition, and +the Trojan war, and all our other troubles will be renewed. But let us +consider some more manageable instance, such as the throwing of dice. +Every one who has played much with dice knows that double sixes are +sometimes thrown, and sometimes double aces. Such coincidences do not +happen once and only once; they occur again and again, and a great +number of trials will show that, though their recurrence has not the +regu<span class='pagenum'>[Pg 312]<a name="Page_312" id="Page_312"></a></span>larity of cause and effect, it yet has a law of its own, namely—a +tendency to average regularity. In 10,000 throws there will be some +number of double sixes; and the greater the number of throws the more +closely will the average recurrence of double sixes, or double aces, +approximate to one in thirty-six. Such a law of average recurrence is +the basis of Probability. Chance being the fact of coincidence without +assignable cause, Probability is expectation based on the average +frequency of its happening.</p> + +<p><a name="chap_20_sect_2" id="chap_20_sect_2"></a>§ 2. Probability is an ambiguous term. Usually, when we say that an +event is 'probable,' we mean that it is more likely than not to happen. +But, scientifically, an event is probable if our expectation of its +occurrence is less than certainty, as long as the event is not +impossible. Probability, thus conceived, is represented by a fraction. +Taking 1 to stand for certainty, and 0 for impossibility, probability +may be 999/1000, or 1/1000, or (generally) 1/<i>m</i>. The denominator +represents the number of times that an event happens, and the numerator +the number of times that it coincides with another event. In throwing a +die, the probability of ace turning up is expressed by putting the +number of throws for the denominator and the number of times that ace is +thrown for the numerator; and we may assume that the more trials we make +the nearer will the resulting fraction approximate to 1/6.</p> + +<p>Instead of speaking of the 'throwing of the die' and its 'turning up +ace' as two events, the former is called 'the event' and the latter 'the +way of its happening.' And these expressions may easily be extended to +cover relations of distinct events; as when two men shoot at a mark and +we desire to represent the probability of both hitting the bull's eye +together, each shot may count as an event (denominator) and the +coincidence of 'bull's-eyes' as the way of its happening (numerator).</p> + +<p>It is also common to speak of probability as a propor<span class='pagenum'>[Pg 313]<a name="Page_313" id="Page_313"></a></span>tion. If the +fraction expressing the probability of ace being cast is 1/6, the +proportion of cases in which it happens is 1 to 5; or (as it is, +perhaps, still more commonly put) 'the chances are 5 to 1 against it.'</p> + +<p><a name="chap_20_sect_3" id="chap_20_sect_3"></a>§ 3. As to the grounds of probability opinions differ. According to one +view the ground is subjective: probability depends, it is said, upon the +quantity of our Belief in the happening of a certain event, or in its +happening in a particular way. According to the other view the ground is +objective, and, in fact, is nothing else than experience, which is most +trustworthy when carefully expressed in statistics.</p> + +<p>To the subjective view it may be objected, (<i>a</i>) that belief cannot by +itself be satisfactorily measured. No one will maintain that belief, +merely as a state of mind, always has a definite numerical value of +which one is conscious, as 1/100 or 1/10. Let anybody mix a number of +letters in a bag, knowing nothing of them except that one of them is X, +and then draw them one by one, endeavouring each time to estimate the +value of his belief that the next will be X; can he say that his belief +in the drawing of X next time regularly increases as the number of +letters left decreases?</p> + +<p>If not, we see that (<i>b</i>) belief does not uniformly correspond with the +state of the facts. If in such a trial as proposed above, we really wish +to draw X, as when looking for something in a number of boxes, how +common it is, after a few failures, to feel quite hopeless and to say: +"Oh, of course it will be in the last." For belief is subject to hope +and fear, temperament, passion, and prejudice, and not merely to +rational considerations. And it is useless to appeal to 'the Wise Man,' +the purely rational judge of probability, unless he is producible. Or, +if it be said that belief is a short cut to the evaluation of +experience, because it is the resultant of all past experience, we may +reply that this is not true. For one striking experience, <span class='pagenum'>[Pg 314]<a name="Page_314" id="Page_314"></a></span>or two or +three recent ones, will immensely outweigh a great number of faint or +remote experiences. Moreover, the experience of two men may be +practically equal, whilst their beliefs upon any question greatly +differ. Any two Englishmen have about the same experience, personal and +ancestral, of the weather; yet their beliefs in the saw that 'if it rain +on St. Swithin's Day it will rain for forty days after,' may differ as +confident expectation and sheer scepticism. Upon which of these beliefs +shall we ground the probability of forty days' rain?</p> + +<p>But (<i>c</i>) at any rate, if Probability is to be connected with Inductive +Logic, it must rest upon the same ground, namely—observation. +Induction, in any particular case, is not content with beliefs or +opinions, but aims at testing, verifying or correcting them by appealing +to the facts; and Probability has the same object and the same basis.</p> + +<p>In some cases, indeed, the conditions of an event are supposed to be +mathematically predetermined, as in tossing a penny, throwing dice, +dealing cards. In throwing a die, the ways of happening are six; in +tossing a penny only two, head and tail: and we usually assume that the +odds with a die are fairly 5 to 1 against ace, whilst with a penny 'the +betting is even' on head or tail. Still, this assumption rests upon +another, that the die is perfectly fair, or that the head and tail of a +penny are exactly alike; and this is not true. With an ordinary die or +penny, a very great number of trials would, no doubt, give an average +approximating to 1/6 or 1/2; yet might always leave a certain excess one +way or the other, which would also become more definite as the trials +went on; thus showing that the die or penny did not satisfy the +mathematical hypothesis. Buffon is said to have tossed a coin 4040 +times, obtaining 1992 heads and 2048 tails; a pupil of De Morgan tossed +4092 times, obtaining 2048 heads and 2044 tails.</p><p><span class='pagenum'>[Pg 315]<a name="Page_315" id="Page_315"></a></span></p> + +<p>There are other important cases in which probability is estimated and +numerically expressed, although statistical evidence directly bearing +upon the point in question cannot be obtained; as in betting upon a +race; or in the prices of stocks and shares, which are supposed to +represent the probability of their paying, or continuing to pay, a +certain rate of interest. But the judgment of experts in such matters is +certainly based upon experience; and great pains are taken to make the +evidence as definite as possible by comparing records of speed, or by +financial estimates; though something must still be allowed for reports +of the condition of horses, or of the prospects of war, harvests, <i>etc.</i></p> + +<p>However, where statistical evidence is obtainable, no one dreams of +estimating probability by the quantity of his belief. Insurance offices, +dealing with fire, shipwreck, death, accident, <i>etc.</i>, prepare elaborate +statistics of these events, and regulate their rates accordingly. Apart +from statistics, at what rate ought the lives of men aged 40 to be +insured, in order to leave a profit of 5 per cent. upon £1000 payable at +each man's death? Is 'quantity of belief' a sufficient basis for doing +this sum?</p> + +<p><a name="chap_20_sect_4" id="chap_20_sect_4"></a>§ 4. The ground of probability is experience, then, and, whenever +possible, statistics; which are a kind of induction. It has indeed been +urged that induction is itself based upon probability; that the +subtlety, complexity and secrecy of nature are such, that we are never +quite sure that we fully know even what we have observed; and that, as +for laws, the conditions of the universe at large may at any moment be +completely changed; so that all imperfect inductions, including the law +of causation itself, are only probable. But, clearly, this doctrine +turns upon another ambiguity in the word 'probable.' It may be used in +the sense of 'less than absolutely certain'; and such doubtless is the +condition of all human knowledge, in comparison with the comprehensive +intuition of arch-<span class='pagenum'>[Pg 316]<a name="Page_316" id="Page_316"></a></span>angels: or it may mean 'less than certain according +to <i>our</i> standard of certainty,' that is, in comparison with the law of +causation and its derivatives.</p> + +<p>We may suppose some one to object that "by this relative standard even +empirical laws cannot be called 'only probable' as long as we 'know no +exception to them'; for that is all that can be said for the boasted law +of causation; and that, accordingly, we can frame no fraction to +represent their probability. That 'all swans are white' was at one time, +from this point of view, not probable but certain; though we now know it +to be false. It would have been an indecorum to call it only probable as +long as no other-coloured swan had been discovered; not merely because +the quantity of belief amounted to certainty, but because the number of +events (seeing a swan) and the number of their happenings in a certain +way (being white) were equal, and therefore the evidence amounted to 1 +or certainty." But, in fact, such an empirical law is only probable; and +the estimate of its probability must be based on the number of times +that similar laws have been found liable to exceptions. Albinism is of +frequent occurrence; and it is common to find closely allied varieties +of animals differing in colour. Had the evidence been duly weighed, it +could never have seemed more than probable that 'all swans are white.' +But what law, approaching the comprehensiveness of the law of causation, +presents any exceptions?</p> + +<p>Supposing evidence to be ultimately nothing but accumulated experience, +the amount of it in favour of causation is incomparably greater than the +most that has ever been advanced to show the probability of any other +kind of event; and every relation of events which is shown to have the +marks of causation obtains the support of that incomparably greater body +of evidence. Hence the only way in which causation can be called +probable, for us, is by considering it as the upward limit (1) to <span class='pagenum'>[Pg 317]<a name="Page_317" id="Page_317"></a></span>which +the series of probabilities tends; as impossibility is the downward +limit (0). Induction, 'humanly speaking,' does not rest on probability; +but the probability of concrete events (not of mere mathematical +abstractions like the falling of absolutely true dice) rests on +induction and, therefore, on causation. The inductive evidence +underlying an estimate of probability may be of three kinds: (<i>a</i>) +direct statistics of the events in question; as when we find that, at +the age of 20, the average expectation of life is 39-40 years. This is +an empirical law, and, if we do not know the causes of any event, we +must be content with an empirical law. But (<i>b</i>) if we do know the +causes of an event, and the causes which may prevent its happening, and +can estimate the comparative frequency of their occurring, we may deduce +the probability that the effect (that is, the event in question) will +occur. Or (<i>c</i>) we may combine these two methods, verifying each by +means of the other. Now either the method (<i>b</i>) or (<i>a fortiori</i>) the +method (<i>c</i>) (both depending on causation) is more trustworthy than the +method (<i>a</i>) by itself.</p> + +<p>But, further, a merely empirical statistical law will only be true as +long as the causes influencing the event remain the same. A die may be +found to turn ace once in six throws, on the average, in close +accordance with mathematical theory; but if we load it on that facet the +results will be very different. So it is with the expectation of life, +or fire, or shipwreck. The increased virulence of some epidemic such as +influenza, an outbreak of anarchic incendiarism, a moral epidemic of +over-loading ships, may deceive the hopes of insurance offices. Hence we +see, again, that probability depends upon causation, not causation upon +probability.</p> + +<p>That uncertainty of an event which arises not from ignorance of the law +of its cause, but from our not knowing whether the cause itself does or +does not occur at any particular time, is Contingency.</p><p><span class='pagenum'>[Pg 318]<a name="Page_318" id="Page_318"></a></span></p> + +<p><a name="chap_20_sect_5" id="chap_20_sect_5"></a>§ 5. The nature of an average supposes deviations from it. Deviations +from an average, or "errors," are assumed to conform to the law (1) that +the greater errors are less frequent than the smaller, so that most +events approximate to the average; and (2) that errors have no "bias," +but are equally frequent and equally great in both directions from the +mean, so that they are scattered symmetrically. Hence their distribution +may be expressed by some such figure as the following:</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/fig_11.png" width="600" height="321" alt="Fig. 11." title="" /> +<span class="caption smcap">Fig. 11.</span> +</div> + +<p>Here <i>o</i> is the average event, and <i>oy</i> represents the number of average +events. Along <i>ox</i>, in either direction, deviations are measured. At <i>p</i> +the amount of error or deviation is <i>op</i>; and the number of such +deviations is represented by the line or ordinate <i>pa</i>. At <i>s</i> the +deviation is <i>os</i>; and the number of such deviations is expressed by +<i>sb</i>. As the deviations grow greater, the number of them grows less. On +the other side of <i>o</i>, toward <i>-x</i>, at distances, <i>op'</i>, <i>os'</i> (equal to +<i>op</i>, <i>os</i>) the lines <i>p'a'</i>, <i>s'b'</i> represent the numbers of those +errors (equal to <i>pa</i>, <i>sb</i>).</p> + +<p>If <i>o</i> is the average height of the adult men of a nation, (say) 5 ft. 6 +in., <i>s'</i> and <i>s</i> may stand for 5 ft. and 6 ft.; <span class='pagenum'>[Pg 319]<a name="Page_319" id="Page_319"></a></span>men of 4 ft. 6 in. lie +further toward <i>-x</i>, and men of 6 ft. 6 in. further toward <i>x</i>. There +are limits to the stature of human beings (or to any kind of animal or +plant) in both directions, because of the physical conditions of +generation and birth. With such events the curve <i>b'yb</i> meets the +abscissa at some point in each direction; though where this occurs can +only be known by continually measuring dwarfs and giants. But in +throwing dice or tossing coins, whilst the average occurrence of ace is +once in six throws, and the average occurrence of 'tail' is once in two +tosses, there is no necessary limit to the sequences of ace or of 'tail' +that may occur in an infinite number of trials. To provide for such +cases the curve is drawn as if it never touched the abscissa.</p> + +<p>That some such figure as that given above describes a frequent +characteristic of an average with the deviations from it, may be shown +in two ways: (1) By arranging the statistical results of any homogeneous +class of measurements; when it is often found that they do, in fact, +approximately conform to the figure; that very many events are near the +average; that errors are symmetrically distributed on either side, and +that the greater errors are the rarer. (2) By mathematical demonstration +based upon the supposition that each of the events in question is +influenced, more or less, by a number of unknown conditions common to +them all, and that these conditions are independent of one another. For +then, in rare cases, all the conditions will operate favourably in one +way, and the men will be tall; or in the opposite way, and the men will +be short; in more numerous cases, many of the conditions will operate in +one direction, and will be partially cancelled by a few opposing them; +whilst in still more cases opposed conditions will approximately balance +one another and produce the average event or something near it. The +results will then conform to the above figure.</p><p><span class='pagenum'>[Pg 320]<a name="Page_320" id="Page_320"></a></span></p> + +<p>From the above assumption it follows that the symmetrical curve +describes only a 'homogeneous class' of measurements; that is, a class +no portion of which is much influenced by conditions peculiar to itself. +If the class is not homogeneous, because some portion of it is subject +to <i>peculiar</i> conditions, the curve will show a hump on one side or the +other. Suppose we are tabulating the ages at which Englishmen die who +have reached the age of 20, we may find that the greatest number die at +39 (19 years being the average expectation of life at 20) and that as +far as that age the curve upwards is regular, and that beyond the age of +39 it begins to descend regularly, but that on approaching 45 it bulges +out some way before resuming its regular descent—thus:</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/fig_12.png" width="600" height="322" alt="Fig. 12." title="" /> +<span class="caption smcap">Fig. 12.</span> +</div> + +<p>Such a hump in the curve might be due to the presence of a considerable +body of teetotalers, whose longevity was increased by the peculiar +condition of abstaining from alcohol, and whose average age was 45, 6 +years more than the average for common men.</p> + +<p>Again, if the group we are measuring be subject to selection (such as +British soldiers, for which profession all volunteers below a certain +height—say,<span class='pagenum'>[Pg 321]<a name="Page_321" id="Page_321"></a></span> 5 ft. 5 in.—are rejected), the curve will fall steeply on +one side, thus:</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/fig_13.png" width="600" height="309" alt="Fig. 13." title="" /> +<span class="caption smcap">Fig. 13.</span> +</div> + +<p>If, above a certain height, volunteers are also rejected, the curve will +fall abruptly on both sides. The average is supposed to be 5 ft. 8 in.</p> + +<p>The distribution of events is described by 'some such curve' as that +given in Fig. 11; but different groups of events may present figures or +surfaces in which the slopes of the curves are very different, namely, +more or less steep; and if the curve is very steep, the figure runs into +a peak; whereas, if the curve is gradual, the figure is comparatively +flat. In the latter case, where the figure is flat, fewer events will +closely cluster about the average, and the deviations will be greater.</p> + +<p>Suppose that we know nothing of a given event except that it belongs to +a certain class or series, what can we venture to infer of it from our +knowledge of the series? Let the event be the cephalic index of an +Englishman. The cephalic index is the breadth of a skull × 100 and +divided by the length of it; <i>e.g.</i> if a skull is 8 in. long and 6 in. +broad, (6×100)/8=75. We know that the average English skull has an index +of 78. The skull <span class='pagenum'>[Pg 322]<a name="Page_322" id="Page_322"></a></span>of the given individual, therefore, is more likely to +have that index than any other. Still, many skulls deviate from the +average, and we should like to know what is the probable error in this +case. The probable error is the measurement that divides the deviations +from the average in either direction into halves, so that there are as +many events having a greater deviation as there are events having a less +deviation. If, in Fig. 11 above, we have arranged the measurements of +the cephalic index of English adult males, and if at <i>o</i> (the average or +mean) the index is 78, and if the line <i>pa</i> divides the right side of +the fig. into halves, then <i>op</i> is the probable error. If the +measurement at <i>p</i> is 80, the probable error is 2. Similarly, on the +left hand, the probable error is <i>op'</i>, and the measurement at <i>p'</i> is +76. We may infer, then, that the skull of the man before us is more +likely to have an index of 78 than any other; if any other, it is +equally likely to lie between 80 and 76, or to lie outside them; but as +the numbers rise above 80 to the right, or fall below 76 to the left, it +rapidly becomes less and less likely that they describe this skull.</p> + +<p>In such cases as heights of men or skull measurements, where great +numbers of specimens exist, the average will be actually presented by +many of them; but if we take a small group, such as the measurements of +a college class, it may happen that the average height (say, 5 ft. 8 +in.) is not the actual height of any one man. Even then there will +generally be a closer cluster of the actual heights about that number +than about any other. Still, with very few cases before us, it may be +better to take the median than the average. The median is that event on +either side of which there are equal numbers of deviations. One +advantage of this procedure is that it may save time and trouble. To +find approximately the average height of a class, arrange the men in +order of height, take the middle one and measure him. A further +advantage of <span class='pagenum'>[Pg 323]<a name="Page_323" id="Page_323"></a></span>this method is that it excludes the influence of +extraordinary deviations. Suppose we have seven cephalic indices, from +skeletons found in the same barrow, 75½, 76, 78, 78, 79, 80½, 86. +The average is 79; but this number is swollen unduly by the last +measurement; and the median, 78, is more fairly representative of the +series; that is to say, with a greater number of skulls the average +would probably have been nearer 78.</p> + +<p>To make a single measurement of a phenomenon does not give one much +confidence. Another measurement is made; and then, if there is no +opportunity for more, one takes the mean or average of the two. But why? +For the result may certainly be worse than the first measurement. +Suppose that the events I am measuring are in fact fairly described by +Fig. II, although (at the outset) I know nothing about them; and that my +first measurement gives <i>p</i>, and my second <i>s</i>; the average of them is +worse than <i>p</i>. Still, being yet ignorant of the distribution of these +events, I do rightly in taking the average. For, as it happens, ¾ of +the events lie to the left of <i>p</i>; so that if the first trial gives <i>p</i>, +then the average of <i>p</i> and any subsequent trial that fell nearer than +(say) <i>s'</i> on the opposite side, would be better than <i>p</i>; and since +deviations greater than <i>s'</i> are rare, the chances are nearly 3 to 1 +that the taking of an average will improve the observation. Only if the +first trial give <i>o</i>, or fall within a little more than ½<i>p</i> on +either side of <i>o</i>, will the chances be against any improvement by +trying again and taking an average. Since, therefore, we cannot know the +position of our first trial in relation to <i>o</i>, it is always prudent to +try again and take the average; and the more trials we can make and +average, the better is the result. The average of a number of +observations is called a "Reduced Observation."</p> + +<p>We may have reason to believe that some of our measurements are better +than others because they have <span class='pagenum'>[Pg 324]<a name="Page_324" id="Page_324"></a></span>been taken by a better trained observer, +or by the same observer in a more deliberate way, or with better +instruments, and so forth. If so, such observations should be +'weighted,' or given more importance in our calculations; and a simple +way of doing this is to count them twice or oftener in taking the +average.</p> + +<p><a name="chap_20_sect_6" id="chap_20_sect_6"></a>§ 6. These considerations have an important bearing upon the +interpretation of probabilities. The average probability for any +<i>general class</i> or series of events cannot be confidently applied to any +<i>one instance</i> or to any <i>special class</i> of instances, since this one, +or this special class, may exhibit a striking error or deviation; it +may, in fact, be subject to special causes. Within the class whose +average is first taken, and which is described by general characters as +'a man,' or 'a die,' or 'a rifle shot,' there may be classes marked by +special characters and determined by special influences. Statistics +giving the average for 'mankind' may not be true of 'civilised men,' or +of any still smaller class such as 'Frenchmen.' Hence life-insurance +offices rely not merely on statistics of life and death in general, but +collect special evidence in respect of different ages and sexes, and +make further allowance for teetotalism, inherited disease, <i>etc</i>. +Similarly with individual cases: the average expectation for a class, +whether general or special, is only applicable to any particular case if +that case is adequately described by the class characters. In England, +for example, the average expectation of life for males at 20 years of +age is 39.40; but at 60 it is still 13.14, and at 73 it is 7.07; at 100 +it's 1.61. Of men 20 years old those who live more or less than 39.40 +years are deviations or errors; but there are a great many of them. To +insure the life of a single man at 20, in the expectation of his dying +at 60, would be a mere bet, if we had no special knowledge of him; the +safety of an insurance office lies in having so many clients that +opposite deviations cancel one another: the more <span class='pagenum'>[Pg 325]<a name="Page_325" id="Page_325"></a></span>clients the safer the +business. It is quite possible that a hundred men aged 20 should be +insured in one week and all of them die before 25; this would be +ruinous, if others did not live to be 80 or 90.</p> + +<p>Not only in such a practical affair as insurance, but in matters purely +scientific, the minute and subtle peculiarities of individuals have +important consequences. Each man has a certain cast of mind, character, +physique, giving a distinctive turn to all his actions even when he +tries to be normal. In every employment this determines his Personal +Equation, or average deviation from the normal. The term Personal +Equation is used chiefly in connection with scientific observation, as +in Astronomy. Each observer is liable to be a little wrong, and this +error has to be allowed for and his observations corrected accordingly.</p> + +<p>The use of the term 'expectation,' and of examples drawn from insurance +and gambling, may convey the notion that probability relates entirely to +future events; but if based on laws and causes, it can have no reference +to point of time. As long as conditions are the same, events will be the +same, whether we consider uniformities or averages. We may therefore +draw probable inferences concerning the past as well as the future, +subject to the same hypothesis, that the causes affecting the events in +question were the same and similarly combined. On the other hand, if we +know that conditions bearing on the subject of investigation, have +changed since statistics were collected, or were different at some time +previous to the collection of evidence, every probable inference based +on those statistics must be corrected by allowing for the altered +conditions, whether we desire to reason forwards or backwards in time.</p> + +<p><a name="chap_20_sect_7" id="chap_20_sect_7"></a>§ 7. The rules for the combination of probabilities are as follows:</p> + +<p>(1) If two events or causes do not concur, the probability of one or the +other occurring is the sum of the <span class='pagenum'>[Pg 326]<a name="Page_326" id="Page_326"></a></span>separate probabilities. A die cannot +turn up both ace and six; but the probability in favour of each is 1/6: +therefore, the probability in favour of one or the other is 1/3. Death +can hardly occur from both burning and drowning: if 1 in 1000 is burned +and 2 in 1000 are drowned, the probability of being burned or drowned is +3/1000.</p> + +<p>(2) If two events are independent, having neither connection nor +repugnance, the probability of their concurring is found by multiplying +together the separate probabilities of each occurring. If in walking +down a certain street I meet A once in four times, and B once in three +times, I ought (by mere chance) to meet both once in twelve times: for +in twelve occasions I meet B four times; but once in four I meet A.</p> + +<p>This is a very important rule in scientific investigation, since it +enables us to detect the presence of causation. For if the coincidence +of two events is more or less frequent than it would be if they were +entirely independent, there is either connection or repugnance between +them. If, <i>e.g.</i>, in walking down the street I meet both A and B oftener +than once in twelve times, they may be engaged in similar business, +calling them from their offices at about the same hour. If I meet them +both less often than once in twelve times, they may belong to the same +office, where one acts as a substitute for the other. Similarly, if in a +multitude of throws a die turns six oftener than once in six times, it +is not a fair one: that is, there is a cause favouring the turning of +six. If of 20,000 people 500 see apparitions and 100 have friends +murdered, the chance of any man having both experiences is 1/8000; but +if each lives on the average 300,000 hours, the chance of both events +occurring in the same hour is 1/2400000000. If the two events occur in +the same hour oftener than this, there is more than a chance +coincidence.</p> + +<p>The more minute a cause of connection or repugnance between events, the +longer the series of trials or instances <span class='pagenum'>[Pg 327]<a name="Page_327" id="Page_327"></a></span>necessary to bring out its +influence: the less a die is loaded, the more casts must be made before +it can be shown that a certain side tends to recur oftener than once in +six.</p> + +<p>(3) The rule for calculating the probability of a dependent event is the +same as the above; for the concurrence of two independent events is +itself dependent upon each of them occurring. My meeting with both A and +B in the street is dependent on my walking there and on my meeting one +of them. Similarly, if A is sometimes a cause of B (though liable to be +frustrated), and B sometimes of C (C and B having no causes independent +of B and A respectively), the occurrence of C is dependent on that of B, +and that again on the occurrence of A. Hence we may state the rule: If +two events are dependent each on another, so that if one occur the +second may (or may not), and if the second a third; whilst the third +never occurs without the second, nor the second without the first; the +probability that if the first occur the third will, is found by +multiplying together the fractions expressing the probability that the +first is a mark of the second and the second of the third.</p> + +<p>Upon this principle the value of hearsay evidence or tradition +deteriorates, and generally the cogency of any argument based upon the +combination of approximate generalisations dependent on one another or +"self-infirmative." If there are two witnesses, A and B, of whom A saw +an event, whilst B only heard A relate it (and is therefore dependent on +A), what credit is due to B's recital? Suppose the probability of each +man's being correct as to what he says he saw, or heard, is 3/4: then +(3/4 × 3/4 = 9/16) the probability that B's story is true is a little +more than 1/2. For if in 16 attestations A is wrong 4 times, B can only +be right in 3/4 of the remainder, or 9 times in 16. Again, if we have +the Approximate Generalisations, 'Most attempts to reduce wages are met +by <span class='pagenum'>[Pg 328]<a name="Page_328" id="Page_328"></a></span>strikes,' and 'Most strikes are successful,' and learn, on +statistical inquiry, that in every hundred attempts to reduce wages +there are 80 strikes, and that 70 p.c. of the strikes are successful, +then 56 p.c. of attempts to reduce wages are unsuccessful.</p> + +<p>Of course this method of calculation cannot be quantitatively applied if +no statistics are obtainable, as in the testimony of witnesses; and even +if an average numerical value could be attached to the evidence of a +certain class of witnesses, it would be absurd to apply it to the +evidence of any particular member of the class without taking account of +his education, interest in the case, prejudice, or general capacity. +Still, the numerical illustration of the rapid deterioration of hearsay +evidence, when less than quite veracious, puts us on our guard against +rumour. To retail rumour may be as bad as to invent an original lie.</p> + +<p>(4) If an event may coincide with two or more other independent events, +the probability that they will together be a sign of it, is found by +multiplying together the fractions representing the improbability that +each is a sign of it, and subtracting the product from unity.</p> + +<p>This is the rule for estimating the cogency of circumstantial evidence +and analogical evidence; or, generally, for combining approximate +generalisations "self-corroboratively." If, for example, each of two +independent circumstances, A and B, indicates a probability of 6 to 1 in +favour of a certain event; taking 1 to represent certainty, 1-6/7 is the +improbability of the event, notwithstanding each circumstance. Then 1/7 +× 1/7 = 1/49, the improbability of both proving it. Therefore the +probability of the event is 48 to 1. The matter may be plainer if put +thus: A's indication is right 6 times in 7, or 42 in 49; in the +remaining 7 times in 49, B's indication will be right 6 times. +Therefore, together they will be right 48 times in 49. If each of two +witnesses is truthful 6 times in 7, one or the other will be truthful 48 +times in 49. But they will not be <span class='pagenum'>[Pg 329]<a name="Page_329" id="Page_329"></a></span>believed unless they agree; and in +the 42 cases of A being right, B will contradict him 6 times; so that +they only concur in being right 36 times. In the remaining 7 times in +which A is wrong, B will contradict him 6 times, and once they will both +be wrong. It does not follow that when both are wrong they will concur; +for they may tell very different stories and still contradict one +another.</p> + +<p>If in an analogical argument there were 8 points of comparison, 5 for +and 3 against a certain inference, and the probability raised by each +point could be quantified, the total value of the evidence might be +estimated by doing similar sums for and against, and subtracting the +unfavourable from the favourable total.</p> + +<p>When approximate generalisations that have not been precisely quantified +combine their evidence, the cogency of the argument increases in the +same way, though it cannot be made so definite. If it be true that most +poets are irritable, and also that most invalids are irritable, a still +greater proportion will be irritable of those who are both invalids and +poets.</p> + +<p>On the whole, from the discussion of probabilities there emerge four +principal cautions as to their use: Not to make a pedantic parade of +numerical probability, where the numbers have not been ascertained; Not +to trust to our feeling of what is likely, if statistics can be +obtained; Not to apply an average probability to special classes or +individuals without inquiring whether they correspond to the average +type; and Not to trust to the empirical probability of events, if their +causes can be discovered and made the basis of reasoning which the +empirical probability may be used to verify.</p> + +<p>The reader who wishes to pursue this subject further should read a work +to which the foregoing chapter is greatly indebted, Dr. Venn's <i>Logic of +Chance</i>.</p><p><span class='pagenum'>[Pg 330]<a name="Page_330" id="Page_330"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_XXI" id="CHAPTER_XXI"></a>CHAPTER XXI</h2> + +<h3>DIVISION AND CLASSIFICATION</h3> + + +<p><a name="chap_21_sect_1" id="chap_21_sect_1"></a>§ 1. Classification, in its widest sense, is a mental grouping of facts +or phenomena according to their resemblances and differences, so as best +to serve some purpose. A "mental grouping": for although in museums we +often see the things themselves arranged in classes, yet such an +arrangement only contains specimens representing a classification. The +classification itself may extend to innumerable objects most of which +have never been seen at all. Extinct animals, for example, are +classified from what we know of their fossils; and some of the fossils +may be seen arranged in a museum; but the animals themselves have +disappeared for many ages.</p> + +<p>Again, things are classed according to their resemblances and +differences: that is to say, those that most closely resemble one +another are classed together on that ground; and those that differ from +one another in important ways, are distributed into other classes. The +more the things differ, the wider apart are their classes both in +thought and in the arrangements of a museum. If their differences are +very great, as with animals, vegetables and minerals, the classing of +them falls to different departments of thought or science, and is often +represented in different museums, zoological, botanical, mineralogical.</p> + +<p>We must not, however, suppose that there is only one way of classifying +things. The same objects may be <span class='pagenum'>[Pg 331]<a name="Page_331" id="Page_331"></a></span>classed in various ways according to +the purpose in view. For gardening, we are usually content to classify +plants into trees, shrubs, flowers, grasses and weeds; the ordinary +crops of English agriculture are distinguished, in settling their +rotation, into white and green; the botanist divides the higher plants +into gymnosperms and angiosperms, and the latter into monocotyledons and +dicotyledons. The principle of resemblance and difference is recognised +in all these cases; but what resemblances or differences are important +depends upon the purpose to be served.</p> + +<p>Purposes are either (α) special or practical, as in gardening or +hunting, or (β) general or scientific, as in Botany or Zoology. The +scientific purpose is merely knowledge; it may indeed subserve all +particular or practical ends, but has no other end than knowledge +directly in view. And whilst, even for knowledge, different +classifications may be suitable for different lines of inquiry, in +Botany and Zoology the Morphological Classification is that which gives +the most general and comprehensive knowledge (see Huxley, <i>On the +Classification of Animals</i>, ch. 1). Most of what a logician says about +classification is applicable to the practical kind; but the scientific +(often called 'Natural Classification'), as the most thorough and +comprehensive, is what he keeps most constantly before him.</p> + +<p>Scientific classification comes late in human history, and at first +works over earlier classifications which have been made by the growth of +intelligence, of language, and of the practical arts. Even in the +distinctions recognised by animals, may be traced the grounds of +classification: a cat does not confound a dog with one of its own +species, nor water with milk, nor cabbage with fish. But it is in the +development of language that the progress of instinctive classification +may best be seen. The use of general names implies the recognition of +classes of things corre<span class='pagenum'>[Pg 332]<a name="Page_332" id="Page_332"></a></span>sponding to them, which form their denotation, +and whose resembling qualities, so far as recognised, form their +connotation; and such names are of many degrees of generality. The use +of abstract names shows that the objects classed have also been +analysed, and that their resembling qualities have been recognised +amidst diverse groups of qualities.</p> + +<p>Of the classes marked by popular language it is worth while to +distinguish two sorts (<i>cf.</i> <a href="#chap_19_sect_4">chap. xix. § 4</a>): Kinds, and those having +but few points of agreement.</p> + +<p>But the popular classifications, made by language and the primitive +arts, are very imperfect. They omit innumerable things which have not +been found useful or noxious, or have been inconspicuous, or have not +happened to occur in the region inhabited by those who speak a +particular language; and even things recognised and named may have been +very superficially examined, and therefore wrongly classed, as when a +whale or porpoise is called a fish, or a slowworm is confounded with +snakes. A scientific classification, on the other hand, aims at the +utmost comprehensiveness, ransacking the whole world from the depths of +the earth to the remotest star for new objects, and scrutinising +everything with the aid of crucible and dissecting knife, microscope and +spectroscope, to find the qualities and constitution of everything, in +order that it may be classed among those things with which it has most +in common and distinguished from those other things from which it +differs. A scientific classification continually grows more +comprehensive, more discriminative, more definitely and systematically +coherent. Hence the uses of classification may be easily perceived.</p> + +<p><a name="chap_21_sect_2" id="chap_21_sect_2"></a>§ 2. The first use of classification is the better understanding of the +facts of Nature (or of any sphere of practice); for understanding +consists in perceiving and comprehending the likeness and difference of +things, in assimilating and distinguishing them; and, in carrying <span class='pagenum'>[Pg 333]<a name="Page_333" id="Page_333"></a></span>out +this process systematically, new correlations of properties are +continually disclosed. Thus classification is closely analogous to +explanation. Explanation has been shown (<a href="#chap_19_sect_5">chap. xix. § 5</a>) to consist in +the discovery of the laws or causes of changes in Nature; and laws and +causes imply similarity, or like changes under like conditions: in the +same way classification consists in the discovery of resemblances in the +things that undergo change. We may say (subject to subsequent +qualifications) that Explanation deals with Nature in its dynamic, +Classification in its static aspect. In both cases we have a feeling of +relief. When the cause of any event is pointed out, or an object is +assigned its place in a system of classes, the gaping wonder, or +confusion, or perplexity, occasioned by an unintelligible thing, or by a +multitude of such things, is dissipated. Some people are more than +others susceptible of this pleasure and fastidious about its purity.</p> + +<p>A second use of classification is to aid the memory. It strengthens +memory, because one of the conditions of our recollecting things is, +that they resemble what we last thought of; so that to be accustomed to +study and think of things in classes must greatly facilitate +recollection. But, besides this, a classification enables us easily to +run over all the contrasted and related things that we want to think of. +Explanation and classification both tend to rationalise the memory, and +to organise the mind in correspondence with Nature.</p> + +<p>Every one knows how a poor mind is always repeating itself, going by +rote through the same train of words, ideas, actions; and that such a +mind is neither interesting nor practical. It is not practical, because +the circumstances of life are rarely exactly repeated, so that for a +present purpose it is rarely enough to remember only one former case; we +need several, that by comparing (perhaps automatically) their +resemblances and differences with the one before us, we may select a +course of action, <span class='pagenum'>[Pg 334]<a name="Page_334" id="Page_334"></a></span>or a principle, or a parallel, suited to our +immediate needs. Greater fertility and flexibility of thought seem +naturally to result from the practice of explanation and classification. +But it must be honestly added, that the result depends upon the spirit +in which such study is carried on; for if we are too fond of finality, +too eager to believe that we have already attained a greater precision +and comprehension than are in fact attainable, nothing can be more +petrific than 'science,' and our last state may be worse than the first. +Of this, students of Logic have often furnished examples.</p> + +<p><a name="chap_21_sect_3" id="chap_21_sect_3"></a>§ 3. Classification may be either Deductive or Inductive; that is to +say, in the formation of classes, as in the proof of propositions, we +may, on the whole, proceed from the more to the less, or from the less +to the more general; not that these two processes are entirely +independent.</p> + +<p>If we begin with some large class, such as 'Animal,' and subdivide it +deductively into Vertebrate and Invertebrate, yet the principle of +division (namely, central structure) has first been reached by a +comparison of examples and by generalisation; if, on the other hand, +beginning with individuals, we group them inductively into classes, and +these again into wider ones (as dogs, rats, horses, whales and monkeys +into mammalia) we are guided both in special cases by hypotheses as to +the best grounds of resemblance, and throughout by the general principle +of classification—to associate things that are alike and to separate +things that are unlike. This principle holds implicitly a place in +classification similar to that of causation in explanation; both are +principles of intelligence. Here, then, as in proof, induction is +implied in deduction, and deduction in induction. Still, the two modes +of procedure may be usefully distinguished: in deduction, we proceed +from the idea of a whole to its parts, from general to special; in +induction, from special (or particular) to general, from parts to the +idea of a whole.</p><p><span class='pagenum'>[Pg 335]<a name="Page_335" id="Page_335"></a></span></p> + +<p><a name="chap_21_sect_4" id="chap_21_sect_4"></a>§ 4. The process of Deductive Classification, or Formal Division, may be +represented thus:</p> + +<div class="figcenter" style="width: 300px;"> +<img src="images/page335.png" width="300" height="128" alt="" title="" /> +</div> + +<p>Given any class (A) to be divided:</p> + +<p>1. Select one important character, attribute, or quality (B), not common +to all the individuals comprehended in the class, as the basis of +division (<i>fundamentum divisionis</i>).</p> + +<p>2. Proceed by Dichotomy; that is, cut the given class into two, one +having the selected attribute (say, B), the other not having it (b). +This, like all formal processes, assumes the principles of Contradiction +and Excluded Middle, that 'No A is both B and not-B,' and that 'Every A +is either B or not-B' (<a href="#chap_6_sect_3">chap. vi. § 3</a>); and if these principles are not +true, or not applicable, the method fails.</p> + +<p>When a class is thus subdivided, it may be called, in relation to its +subclasses, a Genus; and in relation to it, the subclasses may be called +Species: thus—genus A, species AB and Ab, <i>etc.</i></p> + +<p>3. Proceed gradually in the order of the importance of characters; that +is, having divided the given class, subdivide on the same principle the +two classes thence arising; and so again and again, step by step, until +all the characters are exhausted: <i>Divisio ne fiat per saltum</i>.</p> + +<p>Suppose we were to attempt an exhaustive classification of things by +this method, we must begin with 'All Things,' and divide them (say) into +phenomenal and not-phenomenal, and then subdivide phenomena, and so on, +thus:</p><p><span class='pagenum'>[Pg 336]<a name="Page_336" id="Page_336"></a></span></p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/page336.png" width="600" height="324" alt="" title="" /> +</div> + +<p class="noindent">Having subdivided 'Simple' by all possible characters, we must then go +back and similarly subdivide Not-phenomenal, Unextended, Not-resistant, +Not-gravitating, and Compound. Now, if we knew all possible characters, +and the order of their importance, we might prepare <i>a priori</i> a +classification of all possible things; at least, of all things that come +under the principles of Contradiction and Excluded Middle. Many of our +compartments might contain nothing actual; there may, for example, be +nothing that is not phenomenal to some mind, or nothing that is extended +and not-resistant (no vacuum), and so forth. This would imply a breach +of the rule, that the dividing quality be not common to the whole class; +but, in fact, doubts have been, and are, seriously entertained whether +these compartments are filled or not. If they are not, we have concepts +representing nothing, which have been generated by the mere force of +grammatical negation, or by the habit of thinking according to the +principle of Excluded Middle; and, on the strength of these empty +concepts, we have been misled into dividing by an attribute, which +(being universal) cannot be a <i>fundamentum <span class='pagenum'>[Pg 337]<a name="Page_337" id="Page_337"></a></span>divisionis</i>. But though in +such a classification places might be empty, there would be a place for +everything; for whatever did not come into some positive class (such as +Gravitating) must fall under one of the negative classes (the 'Nots') +that run down the right-hand side of the Table and of its subdivisions.</p> + +<p>This is the ideal of classification. Unfortunately we have to learn what +characters or attributes are possible, by experience and comparison; we +are far from knowing them all: and we do not know the order of their +importance; nor are we even clear what 'important' means in this +context, whether 'widely prevalent,' or 'ancient,' or 'causally +influential,' or 'indicative of others.' Hence, in classifying actual +things, we must follow the inductive method of beginning with +particulars, and sorting them according to their likeness and difference +as discovered by investigation. The exceptional cases, in which +deduction is really useful, occur where certain limits to the number and +combination of qualities happen to be known, as they may be in human +institutions, or where there are mathematical conditions. Thus, we might +be able to classify orders of Architecture, or the classical metres and +stanzas of English poetry; though, in fact, these things are too free, +subtle and complex for deductive treatment: for do not the Arts grow +like trees? The only sure cases are mathematical; as we may show that +there are possible only three kinds of plane triangles, four conic +sections, five regular solids.</p> + +<p><a name="chap_21_sect_5" id="chap_21_sect_5"></a>§ 5. The rules for <i>testing</i> a Division are as follows:</p> + +<p>1. Each Sub-class, or Species, should comprise less than the Class, or +Genus, to be divided. This provides that the division shall be a real +one, and not based upon an attribute common to the whole class; that, +therefore, the first rule for making a division shall have been adhered +to. But, as in <a href="#chap_21_sect_4">§ 4</a>, we are here met by a logical difficulty. Suppose +that the class to be divided is A, and that we attempt to divide upon +the attribute B, into AB and Ab; <span class='pagenum'>[Pg 338]<a name="Page_338" id="Page_338"></a></span>is this a true division, if we do not +know any A that is not B? As far as our knowledge extends, we have not +divided A at all. On the other hand, our knowledge of concrete things is +never exhaustive; so that, although we know of no A that is not B, it +may yet exist, and we have seen that it is a logical caution not to +assume what we do not know. In a deductive classification, at least, it +seems better to regard every attribute as a possible ground of division. +Hence, in the above division of 'All Things,'—'Not-phenomenal,' +'Extended-Not-resistant,' 'Resistant-Not-gravitating,' appear as +negative classes (that is, classes based on the negation of an +attribute), although their real existence may be doubtful. But, if this +be justifiable, we must either rewrite the first test of a division +thus: 'Each sub-class should <i>possibly</i> comprise less than the class to +be divided'; or else we must confine the test to (<i>a</i>) thoroughly +empirical divisions, as in dividing Colour into Red and Not-red, where +we know that both sub-classes are real; and (<i>b</i>) divisions under +demonstrable conditions—as in dividing the three kinds of triangles by +the quality equilateral, we know that it is only applicable to +acute-angled triangles, and do not attempt to divide the right-angled or +obtuse-angled by it.</p> + +<p>2. The Sub-classes taken together should be equal to the Class to be +divided: the sum of the Species constitutes the Genus. This provides +that the division shall be exhaustive; which dichotomy always secures, +according to the principle of Excluded Middle; because whatever is not +in the positive class, must be in the negative: Red and Not-red include +all colours.</p> + +<p>3. The Sub-classes must be opposed or mutually exclusive: Species must +not overlap. This again is secured by dichotomy, according to the +principle of Contradiction, provided the division be made upon one +attribute at a time. But, if we attempt to divide simultaneously upon +two attributes, as 'Musicians' upon 'nationality' and<span class='pagenum'>[Pg 339]<a name="Page_339" id="Page_339"></a></span> 'method,' we get +what is called a Cross-division, thus 'German Musicians.' 'Not-German,' +'Classical,' 'Not-Classical;' for these classes may overlap, the same +men sometimes appearing in two groups—Bach in 'German' and 'Classical,' +Pergolesi in 'Not-German' and 'Classical.' If, however, we divide +Musicians upon these attributes successively, cross division will be +avoided, thus:</p> + +<div class="figcenter" style="width: 400px;"> +<img src="images/page339.png" width="400" height="124" alt="" title="" /> +</div> + +<p>Here no Musician will be found in two classes, <i>unless</i> he has written +works in two styles, <i>or unless</i> there are works whose style is +undecided. This "unless—or unless" may suggest caution in using +dichotomy as a short cut to the classification of realities.</p> + +<p>4. No Sub-class must include anything that is not comprised in the class +to be divided: the Genus comprises all the Species. We must not divide +Dogs into fox-terriers and dog-fish.</p> + +<p><a name="chap_21_sect_6" id="chap_21_sect_6"></a>§ 6. The process of Inductive Classification may be represented thus:</p> + +<p>Given any multitude of individuals to be classified:</p> + +<p>(1) Place together in groups (or in thought) those things that have in +common the most, the most widely diffused and the most important +qualities.</p> + +<p>(2) Connect those groups which have, as groups, the greater resemblance, +and separate those that have the greater difference.</p> + +<p>(3) Demarcate, as forming higher or more general classes, those groups +of groups that have important characters in common; and, if possible, on +the same principle, form these higher classes into classes higher still: +that is to say, graduate the classification upwards.</p><p><span class='pagenum'>[Pg 340]<a name="Page_340" id="Page_340"></a></span></p> + +<p>Whilst in Division the terms 'Genus' and 'Species' are entirely relative +to one another and have no fixed positions in a gradation of classes, it +has been usual, in Inductive Classification, to confine the term +'Species' to classes regarded as lowest in the scale, to give the term +'Genera' to classes on the step above, and at each higher step to find +some new term such as 'Tribe,' 'Order,' 'Sub-kingdom,' 'Kingdom'; as may +be seen by turning to any book on Botany or Zoology. If, having fixed +our Species, we find them subdivisible, it is usual to call the +Sub-species 'Varieties.'</p> + +<p>Suppose an attempt to classify by this method the objects in a +sitting-room. We see at a glance carpets, mats, curtains, grates, +fire-irons, coal-scuttles, chairs, sofas, tables, books, pictures, +musical instruments, <i>etc.</i> These may be called 'Species.' Carpets and +mats go together; so do chairs and sofas; so do grates, fire-irons, and +coal-scuttles and so on. These greater groups, or higher classes, are +'Genera.' Putting together carpets, mats and curtains as +'warmth-fabrics'; chairs, sofas and tables as 'supports'; books, +pictures and musical instruments as 'means of culture'; these groups we +may call Orders. Sum up the whole as, from the housewife's point of +view, 'furniture.' If we then subdivide some of the species, as books +into poetry, novels, travels, <i>etc.</i>, these Sub-species may be +considered 'Varieties.'</p> + +<p>A Classification thus made, may be tested by the same rules as those +given for testing a Division; but if it does not stand the test, we must +not infer that the classification is a bad one. If the best possible, it +is good, though formally imperfect: whatever faults are found must then +be charged upon the 'matter,' which is traditionally perverse and +intractable. If, for example, there is a hammock in the room, it must be +classed not with the curtains as a warmth-fabric, but with the sofas as +a support; and books and pictures may be classed as, in a peculiar +sense, means of culture, though all the objects in the room may <span class='pagenum'>[Pg 341]<a name="Page_341" id="Page_341"></a></span>have +been modified and assorted with a view to gratifying and developing good +taste.</p> + +<p><a name="chap_21_sect_7" id="chap_21_sect_7"></a>§ 7. The difficulty of classifying natural objects is very great. It is +not enough to consider their external appearance: exhaustive knowledge +of their internal structure is necessary, and of the functions of every +part of their structure. This is a matter of immense research, and has +occupied many of the greatest minds for very many years. The following +is a tabular outline of the classification of the</p> + + +<div class="figcenter" style="width: 600px;"> +<img src="images/page341.png" width="600" height="691" alt="" title="" /> +</div> +<p><span class='pagenum'>[Pg 342]<a name="Page_342" id="Page_342"></a></span></p> + +<p>As there is not space enough to tabulate such a classification in full, +I have developed at each step the most interesting groups: Vertebrates, +Mammalia, Monodelphia Carnivora, Digitigrada, Felidæ, Lion. Most of the +other groups in each grade are also subdivisible, though some of them +contain far fewer sub-classes than others.</p> + +<p>To see the true character of this classification, we must consider that +it is based chiefly upon knowledge of existing animals. Some extinct +animals, known by their fossils, find places in it; for others new +places have been made. But it represents, on the whole, a cross-section, +or cross-sections of Nature as developing in time; and, in order to give +a just view of the relations of animals, it must be seen in the light of +other considerations. The older systems of classification, and the rules +for making them, seem to have assumed that an actual system of classes, +or of what Mill calls 'Kinds,' exists in nature, and that the relations +of Kinds in this system are determined by quantity of resemblance in +co-inherent qualities, as the ground of their affinity.</p> + +<p><a name="chap_21_sect_8" id="chap_21_sect_8"></a>§ 8. Darwin's doctrine of the origin of species affects the conception +of natural classification in several ways, (1) If all living things are +blood-relations, modified in the course of ages according to their +various conditions of life, 'affinity' must mean 'nearness of common +descent'; and it seems irrational to propose a classification upon any +other basis. We have to consider the Animal (or the Vegetable) Kingdom +as a family tree, exhibiting a long line of ancestors, and (descended +from them) all sorts of cousins, first, second, third, <i>etc.</i>, perhaps +once, twice, or oftener 'removed.' Animals in the relation of first +cousins must be classed as nearer than second cousins, and so on.</p> + +<p>But, if we accept this principle, and are able to trace relationship, it +may not lead to the same results as would be reached by simply relying +upon the present 'quantity <span class='pagenum'>[Pg 343]<a name="Page_343" id="Page_343"></a></span>of resemblance,' unless we understand this +in a very particular way. For the most obvious features of an animal may +have been recently acquired; which often happens with those characters +that adapt an animal to its habits of life, as the wings of a bat, or +the fish-like shape of a dolphin; or as in cases of 'mimicry.' Some +butterflies, snakes, <i>etc.</i>, have grown to resemble closely, in a +superficial way, other butterflies and snakes, from which a stricter +investigation widely separates them; and this superficial resemblance is +probably a recent acquisition, for the sake of protection; the imitated +butterflies being nauseous, and the imitated snakes poisonous. On the +other hand, ancient and important traits of structure may, in some +species, have dwindled into inconspicuous survivals or be still found +only in the embryo; so that only great knowledge and sagacity can +identify them; yet upon ancient traits, though hidden, classification +depends. The seal seems nearer allied to the porpoise than to the tiger, +the shrew nearer to the mouse than to the hedgehog; and the Tasmanian +wolf looks more like a true wolf, the Tasmanian devil more like a +badger, than like a kangaroo: yet the seal is nearer akin to the tiger, +the shrew to the hedgehog, and the Tasmanian flesh-eaters are marsupial, +like the kangaroo. To overcome this difficulty we must understand the +resemblance upon which classification is based to include resemblance of +Causation, that is, the fact itself of descent from common ancestors. +For organic beings, all other rules of classification are subordinate to +one: trace the genealogy of every form.</p> + +<p>By this rule we get a definite meaning for the phrase 'important or +fundamental attribute' as determining organic classes; namely, most +ancient, or 'best serving to indicate community of origin.' Grades of +classification will be determined by such fundamental characters, and +may correspond approximately to the more general types (now extinct) +from which existing animals have descended.</p><p><span class='pagenum'>[Pg 344]<a name="Page_344" id="Page_344"></a></span></p> + +<p>(2) By the hypothesis of development the fixity of species is +discredited. The lowest grade of a classification is made up not of +well-defined types unchanging from age to age, but of temporary species, +often connected by uncertain and indistinct varieties: some of which +may, in turn, if the conditions of their existence alter, undergo such +changes as to produce new species. Hence the notion that Kinds exist in +organic nature must be greatly modified. During a given period of a few +thousand years, Kinds may be recognised, because, under such conditions +as now prevail in the world, that period of time is insufficient to +bring about great changes. But, if it be true that lions, tigers, and +leopards have had a common ancestor, from whose type they have gradually +diverged, it is plain that their present distinctness results only from +the death of intermediate specimens and the destruction of intermediate +varieties. Were it possible to restore, by the evidence of fossils, all +the ranks of the great processions that have descended from the common +ancestor, there would nowhere occur a greater difference than between +offspring and parents; and the appearance of Kinds existing in nature, +which is so striking in a museum or zoological garden, would entirely +vanish.</p> + +<p>A classification, then, as formerly observed, represents a cross-section +of nature as developing in time: could we begin at the beginning and +follow this development down the course of time, we should find no +classes, but an ever-moving, changing, spreading, branching continuum. +It may be represented thus: Suppose an animal (or plant) A, extending +over a certain geographical area, subject to different influences and +conditions of climate, food, hill and plain, wood and prairie, enemies +and rivals, and undergoing modifications here and there in adaptation to +the varying conditions of life: then varieties appear. These varieties, +diverging more and more, become distinct species (AB, AC, AD, AX). Some +of these species, the <span class='pagenum'>[Pg 345]<a name="Page_345" id="Page_345"></a></span>more widely diffused, again produce varieties; +which, in turn become species (ABE, ABF, ADG, ADH). From these, again, +ABE, ABFI, ABFJ, AC, ADHK, ADHL, ADHM, the extant species, descend.</p> + +<div class="figcenter" style="width: 500px;"> +<img src="images/page345.png" width="500" height="195" alt="" title="" /> +</div> + +<p>If in this age a classifier appears, he finds seven living species, +which can be grouped into four genera (ABE, ABF, AC, ADH), and these +again into three Families (AB, AC, AD), all forming one Order. But the +animals which were their ancestors are all extinct. If the fossils of +any of them—say AB, ADG and AX—can be found, he has three more +species, one more genus (ADG), and one more family (AX). For AC, which +has persisted unchanged, and AX, which has become extinct, are both of +them Families, each represented by only one species. It seems necessary +to treat such ancient types as species on a level with extant forms; but +the naturalist draws our attention to their archaic characteristics, and +tries to explain their places in the order of evolution and their +relationships.</p> + +<p>But now suppose that he could find a fossil specimen of every generation +(hundreds of thousands of generations), from ABFI, <i>etc.</i>, up to A; +then, as each generation would only differ from the preceding as +offspring from parents, he would be unable at any point to distinguish a +species; <span class='pagenum'>[Pg 346]<a name="Page_346" id="Page_346"></a></span>at most, he would observe a slightly marked variety. ABFI and +ABFJ would grow more and more alike, until they became indistinguishable +in ABF; ABF and ABE would merge into AB; AB, AC, AD and AX would merge +into A. Hence, the appearance of species is due to our taking +cross-sections of time, or comparing forms that belong to periods remote +from one another (like AX, ADG, and ADHK, or AD, ADH and ADHK), and this +appearance of species depends upon the destruction of ancestral +intermediate forms.</p> + +<p>(3) The hypothesis of development modifies the logical character of +classification: it no longer consists in a direct induction of +co-inherent characters, but is largely a deduction of these from the +characters of earlier forms, together with the conditions of variation; +in other words, the definition of a species must, with the progress of +science, cease to be a mere empirical law of co-inherence and become a +derivative law of Causation. But this was already implied in the +position that causation is the fundamental principle of the explanation +of concrete things; and accordingly, the derivative character of species +or kinds extends beyond organic nature.</p> + +<p><a name="chap_21_sect_9" id="chap_21_sect_9"></a>§ 9. The classification of inorganic bodies also depends on causation. +There is the physical classification into Solids, Liquids, and Gases. +But these states of matter are dependent on temperature; at different +temperatures, the same body may exist in all three states. They cannot +therefore be defined as solid, liquid, or gaseous absolutely, but only +within certain degrees of temperature, and therefore as dependent upon +causation. Similarly, the geological classification of rocks, according +to relative antiquity (primary, secondary, tertiary, with their +subdivisions), and mode of formation (igneous and aqueous), rests upon +causation; and so does the chemical classification of compound bodies +according to the elements that enter into them in definite proportions. +Hence, only the <span class='pagenum'>[Pg 347]<a name="Page_347" id="Page_347"></a></span>classification of the elements themselves (amongst +concrete things), at present, depends largely upon empirical +Coinherence. If the elements remain irresolvable into anything simpler, +the definitions of the co-inherent characters that distinguish them must +be reckoned amongst the ultimate Uniformities of Nature. But if a +definite theory of their origin both generally and severally, whether +out of ether-vortices, or groups of electric corpuscles, or whatnot, +shall ever gain acceptance, similarity of genesis or causation will +naturally be the leading consideration in classifying the chemical +elements. To find common principles of causation, therefore, constitutes +the verification of every Natural Classification. The ultimate +explanation of nature is always causation; the Law of Causation is the +backbone of the system of Experience.</p><p><span class='pagenum'>[Pg 348]<a name="Page_348" id="Page_348"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_XXII" id="CHAPTER_XXII"></a>CHAPTER XXII</h2> + +<h3>NOMENCLATURE, DEFINITION, PREDICABLES</h3> + + +<p><a name="chap_22_sect_1" id="chap_22_sect_1"></a>§ 1. Precision of thought needs precision of language for the recording +of such thought and for communicating it to others. We can often +remember with great vividness persons, things, landscapes, changes and +actions of persons or things, without the aid of language (though words +are often mixed with such trains of imagery), and by this means may form +judgments and inferences in particular cases; but for general notions, +judgments and inferences, not merely about this or that man, or thing, +but about all men or all kinds of things, we need something besides the +few images we can form of them from observation. Even if we possess +generic images, say, of 'horse' or 'cat' (that is, images formed, like +composite photographs, by a coalescence of the images of all the horses +or cats we have seen, so that their common properties stand out and +their differences frustrate and cancel one another), these are useless +for precise thought; for the generic image will not correspond with the +general appearance of horse or cat, unless we have had proportional +experience of all varieties and have been impartially interested in all; +and, besides, what we want for general thought is not a generic image of +the appearance of things, though it were much more definite and fairly +representative than such images ever are, but a general representation +of their important characters; which may be connected with internal +organs, such as none but an anatomist ever sees. We require a <span class='pagenum'>[Pg 349]<a name="Page_349" id="Page_349"></a></span>symbol +connected with the general character of a thing, or quality, or process, +as scientifically determined, whose representative truth may be trusted +in ordinary cases, or may be verified whenever doubt arises. Such +symbols are for most purposes provided by language; Mathematics and +Chemistry have their own symbols.</p> + +<p><a name="chap_22_sect_2" id="chap_22_sect_2"></a>§ 2. First there should be "a name for every important meaning": (<i>a</i>) A +Nomenclature, or system of the names of all classes of objects, adapted +to the use of each science. Thus, in Geology there are names for classes +of rocks and strata, in Chemistry for the elements and their compounds, +in Zoology and Botany for the varieties and species of animals and +plants, their genera, families and orders.</p> + +<p>To have such names, however, is not the whole aim in forming a +scientific language; it is desirable that they should be systematically +significant, and even elegant. Names, like other instruments, ought to +be efficient, and the efficiency of names consists in conveying the most +meaning with the least effort. In Botany and Zoology this result is +obtained by giving to each species a composite name which includes that +of the genus to which it belongs. The species of Felidæ given in <a href="#chap_17_sect_7">chap. +xvii. § 7</a>, are called <i>Felis leo</i> (lion), <i>Felis tigris</i> (tiger), <i>Felis +leopardus</i> (leopard), <i>Felis concolor</i> (puma), <i>Felis lyncus</i> (European +lynx), <i>Felis catus</i> (wild cat). In Chemistry, the nomenclature is +extremely efficient. Names of the simpler compounds are formed by +combining the names of the elements that enter into them; as Hydrogen +Chloride, Hydrogen Sulphide, Carbon Dioxide; and these can be given +still more briefly and efficiently in symbols, as HCl, H<sub>2</sub>S, CO<sub>2</sub>. +The symbolic letters are usually initials of the names of the elements: +as C = Carbon, S = Sulphur; sometimes of the Latin name, when the common +name is English, as Fe = Iron. Each letter represents a fixed quantity +of the element for which it stands, <i>viz.</i>, the atomic weight. The +number written below a symbol on the right-hand side <span class='pagenum'>[Pg 350]<a name="Page_350" id="Page_350"></a></span>shows how many +atoms of the element denoted enter into a molecule of the compound.</p> + +<p>(<i>b</i>) A Terminology is next required, in order to describe and define +the things that constitute the classes designated by the nomenclature, +and to describe and explain their actions.</p> + +<p>(i) A name for every integral part of an object, as head, limb, +vertebra, heart, nerve, tendon; stalk, leaf, corolla, stamen, pistil; +plinth, frieze, <i>etc.</i> (ii) A name for every metaphysical part or +abstract quality of an object, and for its degrees and modes; as +extension, figure, solidity, weight; rough, smooth, elastic, friable; +the various colours, red, blue, yellow, in all their shades and +combinations and so with sounds, smells, tastes, temperatures. The terms +of Geometry are employed to describe the modes of figure, as angular, +curved, square, elliptical; and the terms of Arithmetic to express the +degrees of weight, elasticity, temperature, pitch of sound. When other +means fail, qualities are suggested by the names of things which exhibit +them in a salient way; figures by such terms as amphitheatre, bowl-like, +pear-shaped, egg-shaped; colours by lias-blue, sky-blue, gentian-blue, +peacock-blue; and similarly with sounds, smells and tastes. It is also +important to express by short terms complex qualities, as harmony, +fragrance, organisation, sex, symmetry, stratification.</p> + +<p>(iii) In the explanation of Nature we further require suitable names for +processes and activities: as deduction, conversion, verification, +addition, integration, causation, tendency, momentum, gravitation, +aberration, refraction, conduction, affinity, combination, germination, +respiration, attention, association, development.</p> + +<p>There may sometimes be a difficulty in distinguishing the terms which +stand for qualities from those that express activities, since all +qualities imply activities: weight, for example, implies gravitation; +and the quality heat is also a kind of motion. The distinction aimed at +lies be<span class='pagenum'>[Pg 351]<a name="Page_351" id="Page_351"></a></span>tween a quality as perceived by means of an effect upon our +senses (as weight is resistance to our effort in lifting; heat, a +sensation when we approach fire), and that property of a body which is +conceived to account for its energy (as gravitation that brings a body +to the ground, or physical heat that expands an iron bar or works an +engine). The former class of words, expressing qualities, are chiefly +used in description: the latter class, expressing activities, are +chiefly needed in explanation. They correspond respectively, like +classification and explanation, with the static and dynamic aspects of +Nature.</p> + +<p>The terms of ordinary language fall into the same classes as those of +science: they stand for things, classes of things, parts, or qualities, +or activities of things; but they are far less precise in their +signification. As long as popular thought is vague its language must be +vague; nor is it desirable too strictly to correct the language whilst +the thought is incorrigible. Much of the effect of poetry and eloquence +depends upon the elasticity and indirect suggestiveness of common terms. +Even in reasoning upon some subjects, it is a mistake to aim at an +unattainable precision. It is better to be vaguely right than exactly +wrong. In the criticism of manners, of fine art, or of literature, in +politics, religion and moral philosophy, what we are anxious to say is +often far from clear to ourselves; and it is better to indicate our +meaning approximately, or as we feel about it, than to convey a false +meaning, or to lose the warmth and colour that are the life of such +reflections. It is hard to decide whether more harm has been done by +sophists who take a base advantage of the vagueness of common terms, or +by honest paralogists (if I may use the word) who begin by deceiving +themselves with a plausible definiteness of expression, and go on to +propagate their delusions amongst followers eager for systematic insight +but ignorant of the limits of its possibility.</p><p><span class='pagenum'>[Pg 352]<a name="Page_352" id="Page_352"></a></span></p> + +<p><a name="chap_22_sect_3" id="chap_22_sect_3"></a>§ 3. A Definition is necessary (if possible) for every scientific name. +To define a name is to give a precise statement of its meaning or +connotation. The name to be defined is the subject of a proposition, +whose predicate is a list of the fundamental qualities common to the +things or processes which the subject denotes, and on account of +possessing which qualities this name is given to them.</p> + +<p>Thus, a curve is a line of which no part is straight. The momentum of a +moving body is the product of its mass and its velocity (these being +expressed in numbers of certain units). Nitrogen is a transparent +colourless gas, atomic weight 14, specific gravity .9713, not readily +combining, <i>etc.</i> A lion is a monodelphian mammal, predatory, walking on +its toes, of nocturnal habits, with a short rounded head and muzzle; +dental formula: Incisors (3-3)/(3-3), canines (1-1)/(1/1), præmolars +(3-3)/(2-2), molars (1-1)/(1-1) = 30; four toes on the hind and five on +the fore foot, retractile claws, prickly tongue, light and muscular in +build, about 9½ feet from muzzle to tip of tail, tawny in colour, the +males maned, with a tufted tail. If anything answers to this +description, it is called a lion; if not, not: for this is the meaning +of the name.</p> + +<p>For ordinary purposes, it may suffice to give an Incomplete Definition; +that is, a list of qualities not exhaustive, but containing enough to +identify the things denoted by the given name; as if we say that a lion +is 'a large tawny beast of prey with a tufted tail.' Such purposes may +also be served by a Description; which is technically, a proposition +mentioning properties sufficient to distinguish the things denoted, but +not the properties that enter into the definition; as if nitrogen be +indicated as the gas that constitutes 4/5 of the atmosphere.</p> + +<p><a name="chap_22_sect_4" id="chap_22_sect_4"></a>§ 4. The rules for testing a Definition are: I.—As to its Contents— +<span class='pagenum'>[Pg 353]<a name="Page_353" id="Page_353"></a></span></p> +<p>(1) +It must state the whole connotation of the name to be defined.</p> + +<p>(2) It must not include any quality derivative from the connotation. +Such a quality is called a Proprium. A breach of this rule can do no +positive harm, but it is a departure from scientific economy. There is +no need to state in the definition what can be derived from it; and +whatever can be derived by causation, or by mathematical demonstration, +should be exhibited in that manner.</p> + +<p>(3) It must not mention any circumstance that is not a part of the +connotation, even though it be universally found in the things denoted. +Such a circumstance, if not derivable from the connotation, is called an +Accident. That, for example, the lion at present only inhabits the Old +World, is an accident: if a species otherwise like a lion were found in +Brazil, it would not be refused the name of lion on the score of +locality. Whilst, however, the rules of Logic have forbidden the +inclusion of proprium or accident in a definition, in fact the +definitions of Natural History often mention such attributes when +characteristic. Indeed, definitions of superordinate classes—Families +and Orders—not infrequently give qualities as generally found in the +subordinate classes, and at the same time mention exceptional cases in +which they do not occur.</p> + +<p>II.—As to its Expression—</p> + +<p>(4) A Definition must not include the very term to be defined, nor any +cognate. In defining 'lion' we must not repeat 'lion,' nor use +'leonine'; it would elucidate nothing.</p> + +<p>(5) It must not be put in vague language.</p> + +<p>(6) It must not be in a negative form, if a positive form be obtainable. +We must not be content to say that a lion is 'no vegetarian,' or 'no +lover of daylight.' To define a curve as a line 'always changing its +direction' may be better than as 'in no part straight.'</p> + +<p><a name="chap_22_sect_5" id="chap_22_sect_5"></a>§ 5. The process of determining a Definition is insepar<span class='pagenum'>[Pg 354]<a name="Page_354" id="Page_354"></a></span>able from +classification. We saw that classification consists in distributing +things into groups according to their likenesses and differences, +regarding as a class those individuals which have most qualities in +common. In doing so we must, of course, recognise the common qualities +or points of likeness; and to enumerate these is to define the name of +the class. If we discover the qualities upon which a class is based by +direct observation and induction, by the same method we discover the +definition of its name.</p> + +<p>We saw also that classification is not merely the determination of +isolated groups of things, but a systematic arrangement of such groups +in relation to one another. Hence, again, Definitions are not +independent, but relative to one another; and, of course, in the same +way as classes are relative. That is to say, as a class is placed in +subordination to higher or more comprehensive groups, so the definition +of its name is subordinate to that of their names; and as a class stands +in contrast with co-ordinate classes (those that are in the same degree +of subordination to the same higher groups), so the definition of its +name is in contrast or co-ordination with the definitions of their +names. Lion is subordinate to <i>Felis</i>, to Digitigrade, to Carnivore and +so on up to Animal; and, beyond the Animal Kingdom, to Phenomenon; it is +co-ordinate with tiger, puma, <i>etc.</i>; and more remotely it is +co-ordinate with dog, jackal, wolf, which come under <i>Canis</i>—a genus +co-ordinate with <i>Felis</i>. The definition of lion, therefore, is +subordinate to that of <i>Felis</i>, and to all above it up to Phenomenon; +and is co-ordinate with that of tiger, and with all species in the same +grade. This is the ground of the old method of definition <i>per genus et +differentiam</i>.</p> + +<p>The genus being the next class above any species, the <i>differentia</i> or +Difference consists of the qualities which mark that species in addition +to those that mark the genus, and which therefore distinguish it from +all other <span class='pagenum'>[Pg 355]<a name="Page_355" id="Page_355"></a></span>species of the same genus. In the above definition of lion, +for example, all the properties down to "light and muscular in build" +are generic, that is, are possessed by the whole genus, <i>Felis</i>; and the +remaining four (size, colour, tufted tail, and mane in the male) are the +Difference or specific properties, because in those points the lion +contrasts with the other species of that genus. Differences may be +exhibited thus:</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td> </td><td align='center'><i>Lion.</i></td><td align='center'><i>Tiger.</i></td></tr> +<tr><td align='left' class="smcap">Size:</td><td align='left'>about 9½ feet from nose to tip of tail.</td><td align='left'>About 10 feet.</td></tr> +<tr><td align='left' class="smcap">Colour:</td><td align='left'>tawny.</td><td align='left'>Warm tawny, striped with black.</td></tr> +<tr><td align='left' class="smcap">Tail:</td><td align='left'>tufted.</td><td align='left'>Tapering.</td></tr> +<tr><td align='left' class="smcap">Mane:</td><td align='left'>present in the male.</td><td align='left'>Both sexes maneless.</td></tr> +</table></div> + + +<p>There are other differences in the shape of the skull. In defining lion, +then, it would have been enough to mention the genus and the properties +making up the Difference; because the properties of the genus may be +found by turning to the definition of the genus; and, on the principle +of economy, whatever it is enough to do it is right to do. To define 'by +genus and difference' is a point of elegance, when the genus is known; +but the only way of knowing it is to compare the individuals comprised +in it and in co-ordinate genera, according to the methods of scientific +classification. It may be added that, as the genus represents ancestral +derivation, the predication of genus in a definition indicates the +remote causes of the phenomena denoted by the name defined. And this way +of defining corresponds with the method of double naming by genus and +species: <i>Felis leo</i>, <i>Felis tigris</i>, <i>etc.</i>; <i>Vanessa Atalanta</i>, +<i>Vanessa Io</i>, <i>etc.</i></p> + +<p>The so-called Genetic Definition, chiefly used in Mathematics, is a rule +for constructing that which a name denotes, in such a way as to ensure +its possessing the tributes connoted by the name. Thus, for a circle:<span class='pagenum'>[Pg 356]<a name="Page_356" id="Page_356"></a></span> +Take any point and, at any constant distance from it, trace a line +returning into itself. In Chemistry a genetic definition of any compound +might be given in the form of directions for the requisite synthesis of +elements.</p> + +<p><a name="chap_22_sect_6" id="chap_22_sect_6"></a>§ 6. The chief difficulty in the definition of scientific names consists +in determining exactly the nature of the things denoted by them, as in +classifying plants and animals. If organic species are free growths, +continually changing, however gradually, according as circumstances give +some advantage to one form over others, we may expect to find such +species branching into varieties, which differ considerably from one +another in some respects, though not enough to constitute distinct +species. This is the case; and, consequently, there arises some +uncertainty in collecting from all the varieties those attributes which +are common to the species as a whole; and, therefore, of course, +uncertainty in defining the species. The same difficulty may occur in +defining a genus, on account of the extent to which some of its species +differ from others, whilst having enough of the common character to +deter the classifier from forming a distinct genus on their account. On +the other hand the occurrence of numerous intermediate varieties may +make it difficult to distinguish genera or species at all. Even the +Kingdoms of plants and animals are hard to discriminate at the lowest +levels of organisation. Now, where there is a difficulty of +classification there must be a corresponding difficulty of definition.</p> + +<p>It has been proposed in such cases to substitute a Type for a +Definition; to select some variety of a species, or species of a genus, +as exhibiting its character in an eminent degree, and to regard other +groups as belonging to the same species or genus, according as they +agree more with this type than with other types representing other +species or genera. But the selection of one group as typical implies a +recognition of its attributes as prevailing generally (though not +universally) throughout the species or genus; <span class='pagenum'>[Pg 357]<a name="Page_357" id="Page_357"></a></span>and to recognise these +attributes and yet refuse to enumerate them in a definition, seems to be +no great gain. To enumerate the attributes of the type as an Approximate +Definition of the species or genus, true of <i>most</i> of the groups +constituting the species or genus, answers the same purpose, is more +explicit, and can mislead no one who really attends to the exposition. +An approximate definition is, indeed, less misleading than the +indication of a type; for the latter method seems to imply that the +group which is now typical has a greater permanence or reality than its +co-ordinate groups; whereas, for aught we know, one of the outside +varieties or species may even now be superseding and extinguishing it. +But the statement of a definition as approximate, is an honest +confession that both the definition and the classification are (like a +provisional hypothesis) merely the best account we can give of the +matter according to our present knowledge.</p> + +<p><a name="chap_22_sect_7" id="chap_22_sect_7"></a>§ 7. The limits of Definition are twofold: (<i>a</i>) A name whose meaning +cannot be analysed cannot be defined. This limitation meets us only in +dealing with the names of the metaphysical parts or simple qualities of +objects under the second requisite of a Terminology. Resistance and +weight, colour and its modes, many names of sounds, tastes, smells, heat +and cold—in fact, whatever stands for an unanalysable perception, +cannot be made intelligible to any one who has not had experience of the +facts denoted; they cannot be defined, but only exemplified. A sort of +genetic definition may perhaps be attempted, as if we say that colour is +the special sensation of the cones of the retina, or that blue is the +sensation produced by a ray of light vibrating about 650,000,000,000,000 +times a second; but such expressions can give no notion of our meaning +to a blind man, or to any one who has never seen a blue object. Nor can +we explain what heat is like, or the smell of tobacco, to those who have +never experienced them; nor the sound of C 128 to one who knows nothing +of the musical scale.</p><p><span class='pagenum'>[Pg 358]<a name="Page_358" id="Page_358"></a></span></p> + +<p>If we distinguish the property of an object from the sensation it +excites in us, we may define any simple property as 'the power of +producing the sensation'; the colour of a flower as the power of +exciting the sensation of colour in us. Still, this gives no information +to the blind nor to the colour-blind. Abstract names may be defined by +defining the corresponding concrete: the definition of 'human nature' is +the same as of 'man.' But if the corresponding concrete be a simple +sensation (as blue), this being indefinable, the abstract (blueness) is +also indefinable.</p> + +<p>(<i>b</i>) The second limit of Definition is the impossibility of exhausting +infinity, which would be necessary in order to convey the meaning of the +name of any individual thing or person. For, as we saw in <a href="#CHAPTER_IV">chap. iv.</a>, if +in attempting to define a proper name we stop short of infinity, our +list of qualities or properties may possibly be found in two +individuals, and then it becomes the definition of a class-name or +general name, however small the actual class. Hence we can only give a +Description of that which a proper name denotes, enumerating enough of +its properties to distinguish it from everything else as far as our +knowledge goes.</p> + +<p><a name="chap_22_sect_8" id="chap_22_sect_8"></a>§ 8. The five Predicables (Species, Genus, Difference, Proprium, +Accident) may best be discussed in connection with Classification and +Definition; and in giving an account of Classification, most of what has +to be said about them has been anticipated. Their name, indeed, connects +them with the doctrine of Propositions; for Predicables are terms that +may be predicated, classified according to their connotative relation to +the subject of a proposition (that is, according to the relation in +which their connotation stands to the connotation of the subject): +nevertheless, the significance of the relations of such predicates to a +subject is derivative from the general doctrine of classification.</p> + +<p>For example, in the proposition 'X is Y,' Y must be one of the five +sorts of predicables in relation to X; but <span class='pagenum'>[Pg 359]<a name="Page_359" id="Page_359"></a></span>of what sort, depends upon +what X (the subject) is, or means. The subject of the proposition must +be either a definition, or a general connotative name, or a singular +name.</p> + +<p>If X be a definition, Y must be a species; for nothing but a general +name can be predicated of a definition: and, strictly speaking, it is +only in relation to a definition (as subject) that species can be a +predicable; when it is called <i>Species predicabilis</i> (1).</p> + +<p>If X be a connotative name, it is itself a species (<i>Species +subjicibilis</i>); and the place of the subject of a proposition is the +usual one for species. The predicate, Y, may then be related to the +species in three different ways. First, it may be a definition, exactly +equivalent to the species;—in fact, nothing else than the species in an +explicit form, the analysis of its connotation. Secondly, the predicate +may be, or connote, some <i>part only</i> of the definition or connotation of +the species; and then it is either genus (2), or difference (3). +Thirdly, the predicate may connote <i>no part</i> of the definition, and then +it is either derivable from it, being a proprium (4), or not derivable +from it, being an accident (5). These points of doctrine will be +expanded and illustrated in subsequent pages.</p> + +<p>If X be a singular name, deriving connotation from its constituent terms +(<a href="#chap_4_sect_2">chap. iv. § 2</a>), as 'The present Emperor of China,' it may be treated as +a <i>Species subjicibilis</i>. Then that he is 'an absolute monarch,' +predicates a genus; because that is a genus of 'Emperor,' a part of the +singular name that gives it connotation. That he wears a yellow robe is +a proprium, derivable from the ceremonial of his court. That he is +thirty years of age is an accident.</p> + +<p>But if X be a proper name, having no connotation, Y must always be an +accident; since there can then be no definition of X, and therefore +neither species, genus, difference, nor proprium. Hence, that 'John Doe +is a man' is an accidental proposition: 'man' is not here a <i>Species +</i><span class='pagenum'>[Pg 360]<a name="Page_360" id="Page_360"></a></span><i>predicabilis</i>; for the name might have been given to a dog or a +mountain. That is what enables the proposition to convey information: it +would be useless if the proper name implied 'humanity.'</p> + +<p>'Species' is most frequently used (as in Zoology) for the <i>class +denoted</i> by a general name; but in Logic it is better to treat it as a +general name used connotatively for the attributes possessed in common +by the things denoted, and on account of which they are regarded as a +class: it is sometimes called the Essence (<a href="#chap_22_sect_9">§ 9</a>). In this connotative +sense, a species is implicitly what the definition is explicitly; and +therefore the two are always simply convertible. Thus, 'A plane +triangle' (species) is 'a figure enclosed by three straight lines' +(definition): clearly we may equally say, 'A figure enclosed by three +straight lines is a plane triangle.' It is a simple identity.</p> + +<p>A genus is also commonly viewed denotatively, as a class containing +smaller classes, its species; but in Logic it is, again, better to treat +it connotatively, as a name whose definition is part of the definition +of a given species.</p> + +<p>A difference is the remainder of the definition of any species after +subtracting a given genus. Hence, the genus and difference together make +up the species; whence the method of definition <i>per genus et +differentiam</i> (<i>ante</i>, <a href="#chap_22_sect_5">§ 5</a>).</p> + +<p>Whilst in Botany and Zoology the species is fixed at the lowest step of +the classification (varieties not being reckoned as classes), and the +genus is also fixed on the step next above it, in Logic these +predicables are treated as movable up and down the ladder: any lower +class being species in relation to any higher; which higher class, +wherever taken, thus becomes a genus. Lion may logically be regarded as +a species of digitigrade, or mammal, or animal; and then each of these +is a genus as to lion: or, again, digitigrade may be regarded as a +species of mammal, or mammal as a species of animal. The highest class, +how<span class='pagenum'>[Pg 361]<a name="Page_361" id="Page_361"></a></span>ever, is never a species; wherefore it is called a <i>Summum Genus</i>: +and the lowest class is never a genus; wherefore it is called an <i>Infima +Species</i>. Between these two any step may be either species or genus, +according to the relation in which it is viewed to other classes, and is +then called Subaltern. The <i>summum genus</i>, again, may be viewed in +relation to a <i>given</i> universe or <i>suppositio</i> (that is, any limited +area of existence now the object of attention), or to the <i>whole</i> +universe. If we take the animal kingdom as our <i>suppositio</i>, Animal is +the <i>summum genus</i>; but if we take the whole universe, 'All things' is +the <i>summum genus</i>.</p> + +<p>"Porphyry's tree" is used to illustrate this doctrine. It begins with a +<i>summum genus</i>, 'Substance,' and descends by adding differences, step by +step, to the <i>infima species</i>, 'Man.' It also illustrates Division by +Dichotomy.</p> + +<div class="figcenter" style="width: 300px;"> +<img src="images/page361.png" width="300" height="632" alt="" title="" /> +</div> + +<p><span class='pagenum'>[Pg 362]<a name="Page_362" id="Page_362"></a></span>Beginning with 'Substance,' as <i>summum genus</i>, and adding the +difference 'Corporeal,' we frame the species 'Body.' Taking 'Body' as +the genus and adding the difference 'Animate,' we frame the species +'Living Body;' and so on till 'Man' is reached; which, being <i>infima +species</i>, is only subdivisible into individuals. But the division of Man +into individuals involves a change of principle; it is a division of the +denotation, not an increase of the connotation as in the earlier steps. +Only one side of each dichotomy is followed out in the 'tree': if the +other side had been taken, Incorporeal Substance would be 'Spirit'; +which might be similarly subdivided.</p> + +<p>Genus and species, then, have a double relation. In denotation the genus +includes the species; in connotation the species includes the genus. +Hence the doctrine that by increasing the connotation of a name we +decrease its denotation: if, for example, to the definition of 'lion' we +add 'inhabiting Africa,' Asiatic lions are no longer denoted by it. On +the other hand, if we use a name to denote objects that it did not +formerly apply to, some of the connotation must be dropped: if, for +example, the name 'lion' be used to include 'pumas,' the tufted tail and +mane can no longer be part of the meaning of the word; since pumas have +not these properties.</p> + +<p>This doctrine is logically or formally true, but it may not always be +true in fact. It is logically true; because wherever we add to the +connotation of a name, it is possible that some things to which it +formerly applied are now excluded from its denotation, though we may not +know of any such things. Still, as a matter of fact, an object may be +discovered to have a property previously unknown, and this property may +be fundamental and co-extensive with the denotation of its name, or even +more widely prevalent. The discovery that the whale is a mammal did not +limit the class 'whale'; nor did the discovery that lions, dogs, wolves, +<i>etc.</i>, walk upon their toes, affect the application of any of these +names.</p><p><span class='pagenum'>[Pg 363]<a name="Page_363" id="Page_363"></a></span></p> + +<p>Similarly, the extension of a name to things not previously denoted by +it, may not in fact alter its definition; for the extension may be made +on the very ground that the things now first denoted by it have been +found to have the properties enumerated in its definition, as when the +name 'mammal' was applied to whales, dolphins, <i>etc.</i> If, however, +'mammal' had formerly been understood to apply only to land animals, so +that its definition included (at least, popularly) the quality of +'living on the land,' this part of the connotation was of course lost +when the denotation came to include certain aquatic animals.</p> + +<p>A proprium is an attribute derived from the definition: being either +(<i>a</i>) implied in it, or deducible from it, as 'having its three angles +equal to two right angles' may be proved from the definition of a +triangle; or (<i>b</i>) causally dependent on it, as being 'dangerous to +flocks' results from the nature of a wolf, and as 'moving in an ellipse' +results from the nature of a planet in its relation to the sun.</p> + +<p>An accident is a property accompanying the defining attributes without +being deducible from them. The word suggests that such a property is +merely 'accidental,' or there 'by chance'; but it only means that we do +not understand the connection.</p> + +<p>Proprium and Accident bear the same relation to one another as +Derivative and Empirical Laws: the predication of a proprium is a +derivative law, and the predication of an accident is an empirical law. +Both accidents and empirical laws present problems, the solution of +which consists in reducing them, respectively, to propria and derivative +laws. Thus the colour of animals was once regarded as an accident for +which no reason could be given; but now the colour of animals is +regarded as an effect of their nature and habits, the chief determinants +of it being the advantage of concealment; whilst in other cases, as +among brightly coloured insects and snakes, the determinant may be the +advantage of advertising their <span class='pagenum'>[Pg 364]<a name="Page_364" id="Page_364"></a></span>own noxiousness. If such reasoning is +sound, colour is a proprium (and if so, it cannot <i>logically</i> be +included in a definition; but it is better to be judicious than formal).</p> + +<p>If the colour of animals is a proprium, we must recognise a distinction +between Inseparable and Separable Propria, according as they do, or do +not, always accompany the essence: for mankind is regarded as one +species; but each colour, white, black or yellow, is separable from it +under different climatic conditions; whilst tigers are everywhere +coloured and striped in much the same way; so that we may consider their +colouring as inseparable, in spite of exceptional specimens black or +white or clouded.</p> + +<p>The same distinction may be drawn between accidents. 'Inhabiting Asia' +is an Inseparable Accident of tiger, but a Separable Accident of lion. +Even the occasional characteristics and occupations of individuals are +sometimes called separable accidents of the species; as, of man, being +colour-blind, carpentering, or running.</p> + +<p>A proprium in the original signification of the term <span title='[Greek: hidion]'>ἴδιον</span> was peculiar +to a species, never found with any other, and was therefore convertible +with the subject; but this restriction is no longer insisted on.</p> + +<p><a name="chap_22_sect_9" id="chap_22_sect_9"></a>§ 9. Any predication of a genus, difference or definition, is a verbal, +analytic, or essential proposition: and any predication of a proprium or +accident, is a real, synthetic, or accidental proposition (<a href="#chap_5_sect_6">chap. v. § 6</a>). A proposition is called verbal or analytic when the predicate is a +part, or the whole, of the meaning of the subject; and the subject being +species, a genus or difference is part, and a definition is the whole, +of its meaning or connotation. Hence such a proposition has also been +called explicative. Again, a proposition is called real or synthetic +when the predicate is no part of the meaning of the subject; and, the +subject being species, a proprium or accident is no part of its meaning +or connotation. Hence such a proposition has been called ampliative.</p><p><span class='pagenum'>[Pg 365]<a name="Page_365" id="Page_365"></a></span></p> + +<p>As to Essential and Accidental, these terms are derived from the +doctrine of Realism. Realists maintain that the essence of a thing, or +that which makes a thing to be what (or of what kind) it is, also makes +everything else of the same kind to be what it is. The essence, they +say, is not proper to each thing or separately inherent in it, but is an +'Universal' common to all things of that kind. Some hold that the +universal nature of things of any kind is an Idea existing (apart from +the things) in the intelligible world, invisible to mortal eye and only +accessible to thought; whence the Idea is called a noumenon: that only +the Idea is truly real, and that the things (say, trees, bedsteads and +cities) which appear to us in sense-perception, and which therefore are +called phenomena, only exist by participating in, or imitating, the Idea +of each kind of them. The standard of this school bears the legend +<i>Universalia ante rem</i>.</p> + +<p>But others think that the Universal does not exist apart from particular +things, but is their present essence; gives them actuality as individual +substances; "informs" them, or is their formal cause, and thus makes +them to be what they are of their kind according to the definition: the +universal lion is in all lions, and is not merely similar, but identical +in all; for thus the Universal Reason thinks and energises in Nature. +This school inscribes upon its banners, <i>Universalia in re</i>.</p> + +<p>To define anything, then, is to discover its essence, whether +transcendent or immanent; and to predicate the definition, or any part +of it (genus or difference), is to enounce an essential proposition. But +a proprium, being no part of a definition, though it always goes along +with it, does not show what a thing is; nor of course does an accident; +so that to predicate either of these is to enounce an accidental +proposition.</p> + +<p>Another school of Metaphysicians denies the existence of Universal Ideas +or Forms; the real things, according to <span class='pagenum'>[Pg 366]<a name="Page_366" id="Page_366"></a></span>them, are individuals; which, +so far as any of them resemble one another, are regarded as forming +classes; and the only Universal is the class-name, which is applied +universally in the same sense. Hence, they are called Nominalists. The +sense in which any name is applied, they say, is derived from a +comparison of the individuals, and by abstraction of the properties they +have in common; and thus the definition is formed. <i>Universalia post +rem</i> is their motto. Some Nominalists, however, hold that, though +Universals do not exist in nature, they do in our minds, as Abstract +Ideas or Concepts; and that to define a term is to analyse the concept +it stands for; whence, these philosophers are called Conceptualists.</p> + +<p>Such questions belong to Metaphysics rather than to Logic; and the +foregoing is a commonplace account of a subject upon every point of +which there is much difference of opinion.</p> + +<p><a name="chap_22_sect_10" id="chap_22_sect_10"></a>§ 10. The doctrine of the Predicaments, or Categories, is so interwoven +with the history of speculation and especially of Logic that, though its +vitality is exhausted, it can hardly be passed over unmentioned. The +predicaments of Aristotle are the heads of a classification of terms as +possible predicates of a particular thing or individual. Hamilton +(<i>Logic</i>: Lect. xi.) has given a classification of them; which, if it +cannot be found in Aristotle, is an aid to the memory, and may be thrown +into a table thus:</p> + + + +<div class='center'> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td align='left'>Substance</td><td> </td><td align='left' title='[Greek: ousia]'>οὐσία</td><td align='right'>(1)</td></tr> +<tr><td> </td></tr> +<tr><td align='left'></td><td align='left'>[Quantity</td><td align='left' title='[Greek: poson]'>ποσόν</td><td align='right'>(2)</td></tr> +<tr><td align='right'>[Attribute]—</td><td align='left'>[Quality</td><td align='left' title='[Greek: poion]'>ποιόν</td><td align='right'>(3)</td></tr> +<tr><td align='left'></td><td align='left'>[Relation</td><td align='left' title='[Greek: pros ti]'>πρόσ τι</td><td align='right'>(4)</td></tr> +<tr><td> </td></tr> +<tr><td align='left'></td><td align='left'>[Where</td><td align='left' title='[Greek: pou]'>ποῡ</td><td align='right'>(5)</td></tr> +<tr><td align='left'></td><td align='left'>[When</td><td align='left' title='[Greek: pote]'>πότε</td><td align='right'>(6)</td></tr> +<tr><td align='left'></td><td align='left'>[Action</td><td align='left' title='[Greek: poiein]'>ποιεῑν</td><td align='right'>(7)</td></tr> +<tr><td align='left'>[Modes of Relation]</td><td align='left'>[Passion</td><td align='left' title='[Greek: paschein]'>πάσχειν</td><td align='right'>(8)</td></tr> +<tr><td align='left'></td><td align='left'>[Posture</td><td align='left' title='[Greek: keisthai]'>κεῑσθαι</td><td align='right'>(9)</td></tr> +<tr><td align='left'></td><td align='left'>[Habit</td><td align='left' title='[Greek: echein]'>ἔχειν</td><td align='right'>(10)</td></tr> +</table></div> + + +<p><span class='pagenum'>[Pg 367]<a name="Page_367" id="Page_367"></a></span>Taking a particular thing or individual, as 'Socrates,' this is +Substance in the proper sense of the word, and can never be a predicate, +but is the subject of all predicates. We may assert of him (1) Substance +in the secondary sense (species or genus) that he is a man or an animal; +(2) Quantity, of such a height or weight; (3) Quality, fair or dark; (4) +Relation, shorter or taller than Xanthippe; (5) Where, at Athens; (6) +When, two thousand and odd years ago; (7) Action, that he questions or +pleads; (8) Passion, that he is answered or condemned; (9) Posture, that +he sits or stands; (10) Habit, that he is clothed or armed.</p> + +<p>Thus illustrated (<i>Categoriæ</i>: c. 4), the predicaments seem to be a list +of topics, generally useful for the analysis and description of an +individual, but wanting in the scientific qualities of rational +arrangement, derivation and limitation. Why are there just these heads, +and just so many? It has been suggested that they were determined by +grammatical forms: for Substance is expressed by a substantive; +Quantity, Quality and Relation are adjectival; Where and When, +adverbial; and the remaining four are verbal. It is true that the parts +of speech were not systematically discriminated until some years after +Aristotle's time; but, as they existed, they may have unconsciously +influenced his selection and arrangement of the predicaments. Where a +principle is so obscure one feels glad of any clue to it (<i>cf.</i> Grote's +<i>Aristotle</i>, c. 3, and Zeller's <i>Aristotle</i>, c. 6). But whatever the +origin and original meaning of the predicaments, they were for a long +time regarded as a classification of things; and it is in this sense +that Mill criticises them (<i>Logic</i>: Bk. I. c. 3).</p> + +<p>If, however, the predicaments are heads of a classification of terms +predicable, we may expect to find some connection with the predicables; +and, in fact, secondary Substances are species and genus; whilst the +remaining nine forms are generally accidents. But, again, we may <span class='pagenum'>[Pg 368]<a name="Page_368" id="Page_368"></a></span>expect +some agreement between them and the fundamental forms of predication +(<i>ante</i>, <a href="#chap_1_sect_5">chap. i. § 5</a>, and <a href="#chap_2_sect_4">chap. ii § 4</a>): Substance, whether as the +foundation of attributes, or as genus and species, implies the +predication of co-inherence, which is one mode of <i>Co-existence</i>. +Quantity is predicated as equality (or inequality) a mode of <i>Likeness</i>; +and the other mode of <i>Likeness</i> is involved in the predication of +Quality. Relation, indeed, is the abstract of all predication, and ought +not to appear in a list along with special forms of itself. 'Where' is +position, or <i>Co-existence</i> in space; and 'When' is position in time, or +<i>Succession</i>. Action and Passion are the most interesting aspect of +<i>Causation</i>. Posture and Habit are complex modes of <i>Co-existence</i>, but +too specialised to have any philosophic value. Now, I do not pretend +that this is what Aristotle meant and was trying to say: but if +Likeness, Co-existence, Succession and Causation are fundamental forms +of predication, a good mind analysing the fact of predication is likely +to happen upon them in one set of words or another.</p> + +<p>By Kant the word 'Category' has been appropriated to the highest forms +of judgment, such as Unity, Reality, Substance, and Cause, under which +the understanding reduces phenomena to order and thereby constitutes +Nature. This change of meaning has not been made without a certain +continuity of thought; for forms of judgment are modes of predication. +But besides altering the lists of categories and greatly improving it, +Kant has brought forward under an old title a doctrine so original and +suggestive that it has extensively influenced the subsequent history of +Philosophy. At the same time, and probably as a result of the vogue of +the Kantian philosophy, the word 'category' has been vulgarised as a +synonym for 'class,' just as 'predicament' long ago passed from +Scholastic Logic into common use as a synonym for 'plight.' A minister +is said to be 'in a predicament,' or to fall under the 'category of +impostors.'</p><p><span class='pagenum'>[Pg 369]<a name="Page_369" id="Page_369"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_XXIII" id="CHAPTER_XXIII"></a>CHAPTER XXIII</h2> + +<h3>DEFINITION OF COMMON TERMS</h3> + + +<p><a name="chap_23_sect_1" id="chap_23_sect_1"></a>§ 1. Ordinary words may need definition, if in the course of exposition +or argument their meaning is liable to be mistaken. But as definition +cannot give one the sense of a popular word for all occasions of its +use, it is an operation of great delicacy. Fixity of meaning in the use +of single words is contrary to the genius of the common vocabulary; +since each word, whilst having a certain predominant character, must be +used with many shades of significance, in order to express the different +thoughts and feelings of multitudes of men in endlessly diversified +situations; and its force, whenever it is used, is qualified by the +other words with which it is connected in a sentence, by its place in +the construction of the sentence, by the emphasis, or by the pitch of +its pronunciation compared with the other words.</p> + +<p>Clearly, the requisite of a scientific language, 'that every word shall +have one meaning well defined,' is too exacting for popular language; +because the other chief requisite of scientific language cannot be +complied with, 'that there be no important meaning without a name.' +'Important meanings,' or what seem such, are too numerous to be thus +provided for; and new ones are constantly arising, as each of us pursues +his business or his pleasure, his meditations or the excursions of his +fancy. It is impossible to have a separate term for each meaning; and, +therefore, the terms we have must admit of variable application.</p><p><span class='pagenum'>[Pg 370]<a name="Page_370" id="Page_370"></a></span></p> + +<p>An attempt to introduce new words is generally disgusting. Few men have +mastered the uses of half the words already to be found in our classics. +Much more would be lost than gained by doubling the dictionary. It is +true that, at certain stages in the growth of a people, a need may be +widely felt for the adoption of new words: such, in our own case, was +the period of the Tudors and early Stuarts. Many fresh words, chiefly +from the Latin, then appeared in books, were often received with +reprobation and derision, sometimes disappeared again, sometimes +established their footing in the language: see <i>The Art of English +Poetry</i> (ascribed to Puttenham), Book III. chap. 4, and Ben Jonson's +<i>Poetaster</i>, Act. V. sc. I. Good judges did not know whether a word was +really called for: even Shakespeare thought 'remuneration' and +'accommodate' ridiculous. But such national exigencies rarely arise; and +in our own time great authors distinguish themselves by the plastic +power with which they make common words convey uncommon meanings.</p> + +<p>Fluid, however, as popular language is and ought to be, it may be +necessary for the sake of clear exposition, or to steady the course of +an argument, to avoid either sophistry or unintentional confusion, that +words should be defined and discriminated; and we must discuss the means +of doing so.</p> + +<p><a name="chap_23_sect_2" id="chap_23_sect_2"></a>§ 2. Scientific method is applicable, with some qualifications, to the +definition of ordinary words. Classification is involved in any problem +of definition: at least, if our object is to find a meaning that shall +be generally acceptable and intelligible. No doubt two disputants may, +for their own satisfaction, adopt any arbitrary definition of a word +important in their controversy; or, any one may define a word as he +pleases, at the risk of being misunderstood, provided he has no +fraudulent intention. But in exposition or argument addressed to the +public, where words are used in some of their ordinary senses, it should +<span class='pagenum'>[Pg 371]<a name="Page_371" id="Page_371"></a></span>be recognised that the meaning of each one involves that of many +others. For language has grown with the human mind, as representing its +knowledge of the world: this knowledge consists of the resemblances and +differences of things and of the activities of things, that is, of +classes and causes; and as there is such order in the world, so there +must be in language: language, therefore, embodies an irregular +classification of things with their attributes and relations according +to our knowledge and beliefs. The best attempt (known to me) to carry +out this view is contained in Roget's <i>Thesaurus</i>, which is a +classification of English words according to their meanings: founded, as +the author tells us, on the models of Zoology and Botany, it has some of +the requisites of a Logical Dictionary.</p> + +<p>Popular language, indeed, having grown up with a predominantly practical +purpose, represents a very imperfect classification philosophically +considered. Things, or aspects, or processes of things, that have +excited little interest, have often gone unnamed: so that scientific +discoverers are obliged, for scientific purposes, to invent thousands of +new names. Strong interests, on the other hand, give such a colour to +language, that, where they enter, it is difficult to find any +indifferent expressions. <i>Consistency</i> being much prized, though often +the part of a blockhead, <i>inconsistency</i> implies not merely the absence +of the supposed virtue, but a positive vice: <i>Beauty</i> being attractive +and <i>ugliness</i> the reverse, if we invent a word for that which is +neither, 'plainness,' it at once becomes tinged with the ugly. We seem +to love beauty and morality so much as to be almost incapable of +signifying their absence without expressing aversion.</p> + +<p>Again, the erroneous theories of mankind have often found their way into +popular speech, and their terms have remained there long after the +rejection of the beliefs they embodied: as—lunatic, augury, divination, +spell, exorcism: though, to be sure, such words may often be <span class='pagenum'>[Pg 372]<a name="Page_372" id="Page_372"></a></span>turned to +good account, besides the interest of preserving their original sense. +Language is a record as well as an index of ideas.</p> + +<p>Language, then, being essentially classificatory, any attempt to +ascertain the meaning of a word, far from neglecting its relations to +others, should be directed toward elucidating them.</p> + +<p>Every word belongs to a group, and this group to some other larger +group. A group is sometimes formed by derivation, at least so far as +different meanings are marked merely by inflections, as <i>short</i>, +<i>shorter</i>, <i>shorten</i>, <i>shortly</i>; but, for the most part, is a conflux of +words from many different sources. <i>Repose</i>, <i>depose</i>, <i>suppose</i>, +<i>impose</i>, <i>propose</i>, are not nearly connected in meaning; but are +severally allied in sense much more closely with words philologically +remote. Thus <i>repose</i> is allied with <i>rest</i>, <i>sleep</i>, <i>tranquillity</i>; +<i>disturbance</i>, <i>unrest</i>, <i>tumult</i>; whilst <i>depose</i> is, in one sense, +allied with <i>overthrow</i>, <i>dismiss</i>, <i>dethrone</i>; <i>restore</i>, <i>confirm</i>, +<i>establish</i>; and, in another sense, with <i>declare</i>, <i>attest</i>, <i>swear</i>, +<i>prove</i>, <i>etc.</i> Groups of words, in fact, depend on their meanings, just +as the connection of scientific names follows the resemblance in +character of the things denoted.</p> + +<p>Words, accordingly, stand related to one another, for the most part, +though very irregularly, as genus, species, and co-ordinate species. +Taking <i>repose</i> as a genus, we have as species of it, though not exactly +co-ordinate with one another, <i>tranquillity</i> with a mental differentia +(repose of mind), <i>rest</i>, whether of mind or body, <i>sleep</i>, with the +differentia of unconsciousness (privative). Synonyms are species, or +varieties, wherever any difference can be detected in them; and to +discriminate them we must first find the generic meaning; for which +there may, or may not, be a single word. Thus, <i>equality</i>, <i>sameness</i>, +<i>likeness</i>, <i>similarity</i>, <i>resemblance</i>, <i>identity</i>, are synonyms; but, +if we attend to the ways in which they are actually used, perhaps none +of them <span class='pagenum'>[Pg 373]<a name="Page_373" id="Page_373"></a></span>can claim to be a genus in relation to the rest. If so, we must +resort to a compound term for the genus, such as 'absence of some sort +of difference.' Then <i>equality</i> is absence of difference in quantity; +<i>sameness</i> is often absence of difference in quality, though the usage +is not strict: <i>likeness</i>, <i>similarity</i>, and <i>resemblance</i>, in their +actual use, perhaps, cannot be discriminated; unless <i>likeness</i> be the +more concrete, <i>similarity</i> the more abstract; but they may all be used +compatibly with the recognition of more or less difference in the things +compared, and even imply this. <i>Identity</i> is the absence of difference +of origin, a continuity of existence, with so much sameness from moment +to moment as is compatible with changes in the course of nature; so that +egg, caterpillar, chrysalis, butterfly may be identical for the run of +an individual life, in spite of differences quantitative and +qualitative, as truly as a shilling that all the time lies in a drawer.</p> + +<p>Co-ordinate Species, when positive, have the least contrariety; but +there are also opposites, namely, negatives, contradictories and fuller +contraries. These may be regarded as either co-ordinate genera or the +species of co-ordinate genera. Thus, <i>repose</i> being a genus, +<i>not-repose</i> is by dichotomy a co-ordinate genus and is a negative and +contradictory; then <i>activity</i> (implying an end in view), <i>motion</i> +(limited to matter), <i>disturbance</i> (implying changes from a state of +calm), <i>tumult</i>, <i>etc.</i>, are co-ordinate species of <i>not-repose</i>, and +are therefore co-ordinate opposites, or contraries, of the species of +<i>repose</i>.</p> + +<p>As for correlative words, like <i>master and slave</i>, <i>husband and wife</i>, +<i>etc.</i>, it may seem far-fetched to compare them with the sexes of the +same species of plants or animals; but there is this resemblance between +the two cases, that sexual names are correlative, as 'lioness,' and that +one sex of a species, like a correlative name, cannot be defined without +implying the other; for if a distinctive attribute of one sex be +mentioned (as the lion's mane), it is implied <span class='pagenum'>[Pg 374]<a name="Page_374" id="Page_374"></a></span>that the other wants it, +and apart from this implication the species is not defined: just as the +definition of 'master' implies a 'slave' to obey.</p> + +<p>Common words, less precise than the terms of a scientific nomenclature, +differ from them also in this, that the same word may occur in different +genera. Thus, <i>sleep</i> is a species of <i>repose</i> as above; but it is also +a species of <i>unconsciousness</i>, with co-ordinate species <i>swoon</i>, +<i>hypnotic state</i>, <i>etc.</i> In fact, every word stands under as many +distinct genera, at least, as there are simple or indefinable qualities +to be enumerated in its definition.</p> + +<p><a name="chap_23_sect_3" id="chap_23_sect_3"></a>§ 3. Partially similar to a scientific nomenclature, ordinary language +has likewise a terminology for describing things according to their +qualities and structure. Such is the function of all the names of +colours, sounds, tastes, contrasts of temperature, of hardness, of +pleasantness; in short, of all descriptive adjectives, and all names for +the parts and processes of things. Any word connoting a quality may be +used to describe many very different things, as long as they agree in +that quality.</p> + +<p>But the quality connoted by a word, and treated as always the same +quality, is often only analogically the same. We speak of a <i>great</i> +storm, a <i>great</i> man, a <i>great</i> book; but <i>great</i> is in each case not +only relative, implying small, and leaving open the possibility that +what we call great is still smaller than something else of its kind, but +it is also predicated with reference to some quality or qualities, which +may be very different in the several cases of its application. If the +book is prized for wisdom, or for imagination, its greatness lies in +that quality; if the man is distinguished for influence, or for courage, +his greatness is of that nature; if the storm is remarkable for +violence, or for duration, its greatness depends on that fact. The word +<i>great</i>, therefore, is not used for these things in the same sense, but +only analogically and elliptically. Similarly with good, pure, free, +strong, rich, and <span class='pagenum'>[Pg 375]<a name="Page_375" id="Page_375"></a></span>so on. 'Rest' has not the same meaning in respect of +a stone and of an animal, nor 'strong' in respect of thought and muscle, +nor 'sweet' in respect of sugar and music. But here we come to the +border between literal and figurative use; every one sees that +figurative epithets are analogical; but by custom any figurative use may +become literal.</p> + +<p>Again, many general names of widely different meaning, are brought +together in describing any concrete object, as an animal, or a +landscape, or in defining any specific term. This is the sense of the +doctrine, that any concrete thing is a conflux of generalities or +universals: it may at least be considered in this way; though it seems +more natural to say, that an object presents these different aspects to +a spectator, who, fully to comprehend it, must classify it in every +aspect.</p> + +<p><a name="chap_23_sect_4" id="chap_23_sect_4"></a>§ 4. The process of seeking a definition may be guided by the following +maxims:</p> + +<p>(1) Find the usage of good modern authors; that is (as they rarely +define a word explicitly), consider what in various relations they use +it to denote; from which uses its connotation may be collected.</p> + +<p>(2) But if this process yield no satisfactory result, make a list of the +things denoted, and of those denoted by the co-ordinate and opposite +words; and observe the qualities in which the things denoted agree, and +in which they differ from those denoted by the contraries and opposites. +If 'civilisation' is to be defined, make lists of civilised peoples, of +semi-civilised, of barbarous, and of savage: now, what things are common +to civilised peoples and wanting in the others respectively? This is an +exercise worth attempting. If poetry is to be defined, survey some +typical examples of what good critics recognise as poetry, and compare +them with examples of bad 'poetry,' literary prose, oratory, and +science. Having determined the characteristics of each kind, arrange +them opposite one <span class='pagenum'>[Pg 376]<a name="Page_376" id="Page_376"></a></span>another in parallel columns. Whoever tries to define +by this method a few important, frequently occurring words, will find +his thoughts the clearer for it, and will collect by the way much +information which may be more valuable than the definition itself, +should he ever find one.</p> + +<p>(3) If the genus of a word to be defined is already known, the process +may be shortened. Suppose the genus of poetry to be <i>belles lettres</i> +(that is, 'appealing to good taste'), this suffices to mark it off from +science; but since literary prose and oratory are also <i>belles lettres</i>, +we must still seek the differentia of poetry by a comparison of it with +these co-ordinate species. A compound word often exhibits genus and +difference upon its face: as 're-turn,' 'inter-penetrate,' +'tuning-fork,' 'cricket-bat'; but the two last would hardly be +understood without inspection or further description. And however a +definition be discovered, it is well to state it <i>per genus et +differentiam</i>.</p> + +<p>(4) In defining any term we should avoid encroaching upon the meaning of +any of the co-ordinate terms; for else their usefulness is lessened: as +by making 'law' include 'custom,' or 'wealth' include 'labour' or +'culture.'</p> + +<p>(5) If two or more terms happen to be exactly synonymous, it may be +possible (and, if so, it is a service to the language) to divert one of +them to any neighbouring meaning that has no determinate expression. +Thus, Wordsworth and Coleridge took great pains to distinguish between +Imagination and Fancy, which had become in common usage practically +equivalent; and they sought to limit 'imagination' to an order of poetic +effect, which (they said) had prevailed during the Elizabethan age, but +had been almost lost during the Gallo-classic, and which it was their +mission to restore. Co-ordinate terms often tend to coalesce and become +synonymous, or one almost supersedes the other, to the consequent +impoverishment of our speech. At present <i>proposition</i> (that something +is <span class='pagenum'>[Pg 377]<a name="Page_377" id="Page_377"></a></span>the fact) has almost driven out <i>proposal</i> (that it is desirable to +co-operate in some action). Even good writers and speakers, by their own +practice, encourage this confusion: they submit to Parliament certain +'propositions' (proposals for legislation), or even make 'a proposition +of marriage.' Definition should counteract such a tendency.</p> + +<p>(6) We must avoid the temptation to extend the denotation of a word so +far as to diminish or destroy its connotation; or to increase its +connotation so much as to render it no longer applicable to things which +it formerly denoted: we should neither unduly generalise, nor unduly +specialise, a term. Is it desirable to define <i>education</i> so as to +include the 'lessons of experience'; or is it better to restrict it as +implying a personal educator? If any word implies blame or praise, we +are apt to extend it to everything we hate or approve. But <i>coward</i> +cannot be so defined as to include all bullies, nor <i>noble</i> so as to +include every honest man, without some loss in distinctness of thought.</p> + +<p>The same impulses make us specialise words; for, if two words express +approval, we wish to apply both to whatever we admire and to refuse both +to whatever displeases us. Thus, a man may resolve to call no one great +who is not good: greatness, according to him, connotes goodness: whence +it follows that (say) Napoleon I. was not great. Another man is +disgusted with greatness: according to him, good and great are mutually +exclusive classes, sheep and goats, as in Gray's wretched clench: +"Beneath the good how far, yet far above the great." In feet, however +'good' and 'great' are descriptive terms, sometimes applicable to the +same object, sometimes to different: but 'great' is the wider term and +applicable to goodness itself and also to badness; whereas by making +'great' connote goodness it becomes the narrower term. And as we have +seen (<a href="#chap_23_sect_3">§ 3</a>), such epithets may be applicable to objects on account of +different qualities: <i>good</i> is not predicated on the same ground of a +man and of a horse.</p><p><span class='pagenum'>[Pg 378]<a name="Page_378" id="Page_378"></a></span></p> + +<p>(7) In defining any word, it is desirable to bear in mind its +derivation, and to preserve the connection of meaning with its origin; +unless there are preponderant reasons for diverting it, grounded on our +need of the word to express a certain sense, and the greater difficulty +of finding any other word for the same purpose. It is better to lean to +the classical than to the vulgar sense of 'indifferent,' 'impertinent,' +'aggravating,' 'phenomenal.'</p> + +<p>(8) Rigorous definition should not be attempted where the subject does +not admit of it. Some kinds of things are so complex in their qualities, +and each quality may manifest itself in so many degrees without ever +admitting of exact measurement, that we have no means of marking them +off precisely from other things nearly allied, similarly complex and +similarly variable. If so we cannot precisely define their names. +Imagination and fancy are of this nature, civilisation and barbarism, +poetry and other kinds of literary expression. As to poetry, some think +it only exists in metre, but hardly maintain that the metre must be +strictly regular: if not, how much irregularity of rhythm is admissible? +Others regard a certain mood of impassioned imagination as the essence +of poetry; but they have never told us how great intensity of this mood +is requisite. We also hear that poetry is of such a nature that the +enjoyment of it is an end in itself; but as it is not maintained that +poetry must be wholly impersuasive or uninstructive, there seems to be +no means of deciding what amount or prominence of persuasion or +instruction would transfer the work to the region of oratory or science. +Such cases make the method of defining by the aid of a type really +useful: the difficulty can hardly be got over without pointing to +typical examples of each meaning, and admitting that there may be many +divergences and unclassifiable instances on the border between allied +meanings.</p> + +<p><a name="chap_23_sect_5" id="chap_23_sect_5"></a>§ 5. As science began from common knowledge, the <span class='pagenum'>[Pg 379]<a name="Page_379" id="Page_379"></a></span>terms of the common +vocabulary have often been adopted into the sciences, and many are still +found there: such as weight, mass, work, attraction, repulsion, +diffusion, reflection, absorption, base, salt, and so forth. In the more +exact sciences, the vague popular associations with such words are +hardly an inconvenience: since those addicted to such studies do not +expect to master them without undergoing special discipline; and, having +precisely defined the terms, they acquire the habit of thinking with +them according to their assigned signification in those investigations +to which they are appropriate. It is in the Social Sciences, especially +Economics and Ethics, that the use of popular terminology is at once +unavoidable and prejudicial. For the subject-matters, industry and the +conduct of life, are every man's business; and, accordingly, have always +been discussed with a consciousness of their direct practical bearing +upon public and private interests, and therefore in the common language, +in order that everybody may as far as possible benefit by whatever light +can be thrown upon them. The general practice of Economists and +Moralists, however, shows that, in their judgment, the good derived from +writing in the common vocabulary outweighs the evil: though it is +sometimes manifest that they themselves have been misled by +extra-scientific meanings. To reduce the evil as much as possible, the +following precautions seem reasonable:</p> + +<p>(1) To try to find and adopt the central meaning of the word (say rent +or money) in its current or traditionary applications: so as to lessen +in the greater number of cases the jar of conflicting associations. But +if the central popular meaning does not correspond with the scientific +conception to be expressed, it may be better to invent a new term.</p> + +<p>(2) To define the term with sufficient accuracy to secure its clear and +consistent use for scientific purposes.</p> + +<p>(3) When a popular term has to be used in a sense that <span class='pagenum'>[Pg 380]<a name="Page_380" id="Page_380"></a></span>departs from the +ordinary one in such a way as to incur the danger of misunderstanding, +to qualify it by some adjunct or "interpretation-clause."</p> + +<p>The first of these rules is not always adhered to; and, in the progress +of a science, as subtler and more abstract relations are discovered +amongst the facts, the meaning of a term may have to be modified and +shifted further and further from its popular use. The term 'rent,' for +example, is used by economists, in such a sense that they have to begin +the discussion of the facts it denotes, by explaining that it does not +imply any actual payment by one man to another. Here, for most readers, +the meaning they are accustomed to, seems already to have entirely +disappeared. Difficulties may, however, be largely overcome by +qualifying the term in its various relations, as produce-rents, +ground-rents, customary rents, and so forth, (<i>Cf</i>. Dr. Keynes' <i>Scope +and Method of Political Economy</i>, chap. 5.)</p> + +<p><a name="chap_23_sect_6" id="chap_23_sect_6"></a>§ 6. Definitions affect the cogency of arguments in many ways, whether +we use popular or scientific language. If the definitions of our terms +are vague, or are badly abstracted from the facts denoted, all arguments +involving these terms are inconclusive. There can be no confidence in +reasoning with such terms; since, if vague, there is nothing to protect +us from ambiguity; or, if their meaning has been badly abstracted, we +may be led into absurdity—as if 'impudence' should be defined in such a +way as to confound it with honesty.</p> + +<p>Again, it is by definitions that we can best distinguish between Verbal +and Real Propositions. Whether a term predicated is implied in the +definition of the subject, or adds something to its meaning, deserves +our constant attention. We often persuade ourselves that statements are +profound and important, when, in fact, they are mere verbal +propositions. "It is just to give every man his due"; "the greater good +ought to be preferred to the <span class='pagenum'>[Pg 381]<a name="Page_381" id="Page_381"></a></span>less"; such dicta sound well—indeed, too +well! For 'a man's due' means nothing else than what it is just to give +him; and 'the greater good' may mean the one that ought to be preferred: +these, therefore, are Truisms. The investigation of a definition may be +a very valuable service to thought; but, once found, there is no merit +in repeating it. To put forward verbal or analytic propositions, or +truisms, as information (except, of course, in explaining terms to the +uninstructed), shows that we are not thinking what we say; for else we +must become aware of our own emptiness. Every step forward in knowledge +is expressed in a real or synthetic proposition; and it is only by means +of such propositions that information can be given (except as to the +meaning of words) or that an argument or train of reasoning can make any +progress.</p> + +<p>Opposed to a truism is a Contradiction in Terms; that is, the denying of +a subject something which it connotes (or which belongs to its +definition), or the affirming of it something whose absence it connotes +(or which is excluded by its definition). A verbal proposition is +necessarily true, because it is tautologous; a contradiction in terms is +necessarily false, because it is inconsistent. Yet, as a rhetorical +artifice, or figure, it may be effective: that 'the slave is not bound +to obey his master' may be a way of saying that there ought to be no +slaves; that 'property is theft,' is an uncompromising assertion of the +communistic ideal. Similarly a truism may have rhetorical value: that 'a +Negro is a man' has often been a timely reminder, or even that "a man's +a man." It is only when we fall into such contradiction or tautology by +lapse of thought, by not fully understanding our own words, that it +becomes absurd.</p> + +<p>Real Propositions comprise the predication of Propria and Accidentia. +Accidentia, implying a sort of empirical law, can only be established by +direct induction. But <span class='pagenum'>[Pg 382]<a name="Page_382" id="Page_382"></a></span>propria are deduced from (or rather by means of) +the definition with the help of real propositions, and this is what is +called 'arguing from a Definition.' Thus, if increasing capacity for +co-operation be a specific character of civilisation, 'great wealth' may +be considered as a proprium of civilised as compared with barbarous +nations. For co-operation is made most effectual by the division of +labour, and that this is the chief condition of producing wealth is a +real proposition. Such arguments from definitions concerning concrete +facts and causation require verification by comparing the conclusion +with the facts. The verification of this example is easy, if we do not +let ourselves be misled in estimating the wealth of barbarians by the +ostentatious "pearl and gold" of kings and nobles, where 99 per cent. of +the people live in penury and servitude. The wealth of civilisation is +not only great but diffused, and in its diffusion its greatness must be +estimated.</p> + +<p>To argue from a definition may be a process of several degrees of +complexity. The simplest case is the establishing of a proprium as the +direct consequence of some connoted attribute, as in the above example. +If the definition has been correctly abstracted from the particulars, +the particulars have the attributes summarised in the definition; and, +therefore, they have whatever can be shown to follow from those +attributes. But it frequently happens that the argument rests partly on +the qualities connoted by the class name and partly on many other facts.</p> + +<p>In Geometry, the proof of a theorem depends not only upon the definition +of the figure or figures directly concerned, but also upon one or more +axioms, and upon propria or constructions already established. Thus, in +Euclid's fifth Proposition, the proof that the angles at the base of an +isosceles triangle are equal, depends not only on the equality of the +opposite sides, but upon this <span class='pagenum'>[Pg 383]<a name="Page_383" id="Page_383"></a></span>together with the construction that shows +how from the greater of two lines a part may be cut off equal to the +less, the proof that triangles that can be conceived to coincide are +equal, and the axiom that if equals be taken from equals the remainders +are equal. Similarly, in Biology, if colouring favourable to concealment +is a proprium of carnivorous animals, it is not deducible merely from +their predatory character or any other attribute entering into the +definition of any species of them, but from their predatory character +together with the causes summarised in the phrase 'Natural Selection'; +that is, competition for a livelihood, and the destruction of those that +labour under any disadvantages, of which conspicuous colouring would be +one. The particular coloration of any given species, again, can only be +deduced by further considering its habitat (desert, jungle or +snowfield): a circumstance lying wholly outside the definition of the +species.</p> + +<p>The validity of an argument based partly or wholly on a definition +depends, in the first place, on the existence of things corresponding +with the definition—that is, having the properties connoted by the name +defined. If there are no such things as isosceles triangles, Euclid's +fifth Proposition is only formally true, like a theorem concerning the +fourth dimension of space: merely consistent with his other assumptions. +But if there be any triangles only approximately isosceles, the proof +applies to them, making allowance for their concrete imperfection: the +nearer their sides approach straightness and equality the more nearly +equal will the opposite angles be.</p> + +<p>Again, as to the things corresponding with terms defined, according to +Dr. Venn, their 'existence' may be understood in several senses: (1) +merely for the reason, like the pure genera and species of Porphyry's +tree; the sole condition of whose being is logical consistency: or (2) +for the imagination, like the giants and magicians of <span class='pagenum'>[Pg 384]<a name="Page_384" id="Page_384"></a></span>romance, the +heroes of tragedy and the fairies of popular superstition; whose +properties may be discussed, and verified by appeal to the right +documents and authorities (poems and ballads): or (3) for perception, +like plants, animals, stones and stars. Only the third class exist in +the proper sense of the word. But under a convention or hypothesis of +existence, we may argue from the definition of a fairy, or a demigod, or +a dragon, and deduce various consequences without absurdity, if we are +content with poetic consistency and the authority of myths and romances +as the test of truth.</p> + +<p>In the region of concrete objects, whose properties are causes, and +neither merely fictions nor determinations of space (as in Geometry), we +meet with another condition of the validity of any argument depending on +a definition: there must not only be objects corresponding to the +definition, but there must be no other causes counteracting those +qualities on whose agency our argument relies. Thus, though we may infer +from the quality of co-operation connoted by civilisation, that a +civilised country will be a wealthy one, this may not be found true of +such a country recently devastated by war or other calamity. Nor can +co-operation always triumph over disadvantageous circumstances. +Scandinavia is so poor in the gifts of nature favourable to industry, +that it is not wealthy in spite of civilisation: still, it is far +wealthier than it would be in the hands of a barbarous people. In short, +when arguing from a definition, we can only infer the <i>tendency</i> of any +causal characteristics included in it; the unqualified realisation of +such a tendency must depend upon the absence of counteracting causes. As +soon as we leave the region of pure conceptions and make any attempt to +bring our speculations home to the actual phenomena of nature or of +human life, the verification of every inference becomes an unremitting +obligation.</p><p><span class='pagenum'>[Pg 385]<a name="Page_385" id="Page_385"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="CHAPTER_XXIV" id="CHAPTER_XXIV"></a>CHAPTER XXIV</h2> + +<h3>FALLACIES</h3> + + +<p><a name="chap_24_sect_1" id="chap_24_sect_1"></a>§ 1. A Fallacy is any failure to fulfil the conditions of proof. If we +neglect or mistake the conditions of proof unintentionally, whether in +our private meditations or in addressing others, it is a Paralogism: but +if we endeavour to pass off upon others evidence or argument which we +know or suspect to be unsound, it is a Sophism.</p> + +<p>Fallacies, whether paralogisms or sophisms, may be divided into two +classes: (<i>a</i>) the Formal, or those that can be shown to conflict with +one or more of the truths of Logic, whether Deductive or Inductive; as +if we attempt to prove an universal affirmative in the Third Figure; or +to argue that, as the average expectation of life for males at the age +of 20 is 19½ years, therefore Alcibiades, being 20 years of age, will +die when he is 39½; (<i>b</i>) the Material, or those that cannot be +clearly exhibited as transgressions of any logical principle, but are +due to superficial inquiry or confused reasoning; as in adopting +premises on insufficient authority, or without examining the facts; or +in mistaking the point to be proved.</p> + +<p><a name="chap_24_sect_2" id="chap_24_sect_2"></a>§ 2. Formal Fallacies of Deduction and Induction are, all of them, +breaches of the rule 'not to go beyond the evidence.' As a detailed +account of them would be little else than a repetition of the foregoing +chapters, it may suffice to recall some of the places at which it is +easiest to go astray.</p> + +<p>(1) It is not uncommon to mistake the Contrary for the Contradictory, +as—A is not taller than B, ∴ he is shorter.</p><p><span class='pagenum'>[Pg 386]<a name="Page_386" id="Page_386"></a></span></p> + +<p>(2) To convert <i>A</i>. or <i>O</i>. simply, as—</p> + + +<div class="example"><span class="i0">All Money is Wealth ∴ All Wealth is Money;</span></div> + + +<p class="noindent">or—Some Wealth is not Money ∴ Some Money is not Wealth.</p> + +<p>In both these cases, Wealth, though undistributed in the convertend, is +distributed in the converse.</p> + +<p>(3) To attempt to syllogise with two premises containing four terms, as</p> + + +<div class="example"><span class="i1">The Papuans are savages;<br /></span> +<span class="i1">The Javanese are neighbours of the Papuans:<br /></span> +<span class="i0">∴ The Javanese are savages.</span></div> + + +<p class="noindent">Such an argument is excluded by the definition of a Syllogism, and +presents no formal evidence whatever. We should naturally assume that +any man who advanced it merely meant to raise some probability that +'neighbourhood is a sign of community of ideas and customs.' But, if so, +he should have been more explicit. There would, of course, be the same +failure of connection, if a fourth term were introduced into the +conclusion, instead of into the premises.</p> + +<p>(4) To distribute in the conclusion a term that was undistributed in the +premises (an error essentially the same as (2) above), <i>i.e.</i>, Illicit +process of the major or minor term, as—</p> + + +<div class="example"><span class="i1">Every rational agent is accountable;<br /></span> +<span class="i1">Brutes are not rational agents:<br /></span> +<span class="i0">∴ Brutes are not accountable.</span></div> + + +<p class="noindent">In this example (from Whately), an illegitimate mood of Fig. I., the +major term, 'accountable,' has suffered the illicit process; since, in +the premise, it is predicate of an affirmative proposition and, +therefore, undistributed; but, in the conclusion, it is predicate of a +negative proposition and, therefore, distributed. The fact that nearly +everybody would accept the conclusion as true, might lead one to +overlook the formal inconclusiveness of the proof.</p><p><span class='pagenum'>[Pg 387]<a name="Page_387" id="Page_387"></a></span></p> + +<p>Again,</p> + + +<div class="example"><span class="i1">All men are two-handed;<br /></span> +<span class="i1">All two-handed animals are cooking animals:<br /></span> +<span class="i0">∴ All cooking animals are men.</span></div> + + +<p class="noindent">Here we have Bramantip concluding in A.; and there is, formally, an +illicit process of the minor; though the conclusion is true; and the +evidence, such as it is, is materially adequate. ('Two-handed,' being a +peculiar differentia, is nugatory as a middle term, and may be cut out +of both premises; whilst 'cooking' is a proprium peculiar to the species +Man; so that these terms might be related in U., <i>All men are all +cookers</i>; whence, by conversion, <i>All cookers are men</i>.)</p> + +<p>(5) To omit to distribute the middle term in one or the other premise, +as—</p> + + +<div class="example"><span class="i1">All verbal propositions are self-evident;<br /></span> +<span class="i1">All axioms are self-evident:<br /></span> +<span class="i0">∴ All axioms are verbal propositions.</span></div> + + +<p class="noindent">This is an illegitimate mood in Fig. II.; in which, to give any +conclusion, one premise must be negative. It may serve as a formal +illustration of Undistributed Middle; though, as both premises are +verbal propositions, it is (materially) not syllogistic at all, but an +error of classification; a confounding of co-ordinate species by assuming +their identity because they have the generic attribute in common.</p> + +<p>(6) To simply convert an hypothetical proposition, as—</p> + + +<div class="example"><span class="i1">If trade is free, it prospers;<br /></span> +<span class="i0">∴ If trade prospers, it is free.</span></div> + + +<p class="noindent">This is similar to the simple conversion of the categorical A.; since it +takes for granted that the antecedent is co-extensive with the +consequent, or (in other words) that the freedom of trade is the sole +condition of, or (at least) inseparable from, its prosperity.</p><p><span class='pagenum'>[Pg 388]<a name="Page_388" id="Page_388"></a></span></p> + +<p>The same assumption is made if, in an hypothetical syllogism, we try to +ground an inference on the affirmation of the consequent or denial of +the antecedent, as—</p> + + +<div class="example"><span class="i0">If trade is free it prospers:<br /></span> +<span class="i1">It does prosper;<br /></span> +<span class="i0">∴ It is free.<br /></span> +<span class="i1">It is not free;<br /></span> +<span class="i0">∴ It does not prosper.</span></div> + + +<p class="noindent">Neither of these arguments is formally good; nor, of course, is either +of them materially valid, if it be possible for trade to prosper in +spite of protective tariffs.</p> + +<p>An important example of this fallacy is the prevalent notion, that if +the conclusion of an argument is true the premises must be trustworthy; +or, that if the premises are false the conclusion must be erroneous. +For, plainly, that—</p> + +<p>If the premises are true, the conclusion is true, is a hypothetical +proposition; and we argue justly—</p> + + +<div class="example"><span class="i1">The premises are true;<br /></span> +<span class="i0">∴ The conclusion is true;<br /></span> +<span class="i0">or, The conclusion is false;<br /></span> +<span class="i0">∴ The premises are false (or one of them is).</span></div> + + +<p class="noindent">This is valid for every argument that is formally correct; but that we +cannot trust the premises on the strength of the conclusion, nor reject +the conclusion because the premises are absurd, the following example +will show:</p> + + +<div class="example"><span class="i1">All who square the circle are great mathematicians;<br /></span> +<span class="i1">Newton squared the circle:<br /></span> +<span class="i0">∴ Newton was a great mathematician.</span></div> + + +<p class="noindent">The conclusion is true; but the premises are intolerable.</p> + +<p>How the taking of Contraries for Contradictories may vitiate Disjunctive +Syllogisms and Dilemmas has been sufficiently explained in the twelfth +chapter.</p> + +<p><a name="chap_24_sect_3" id="chap_24_sect_3"></a>§ 3. Formal Fallacies of Induction consist in supposing <span class='pagenum'>[Pg 389]<a name="Page_389" id="Page_389"></a></span>or inferring +Causation without attempting to prove it, or in pretending to prove it +without satisfying the Canons of observation and experiment: as—</p> + +<p>(1) To assign the Cause of anything that is not a concrete event: as, +<i>e.g.</i>, why two circles can touch only in one point. We should give the +'reason'; for this expression includes, besides evidence of causation, +the principles of formal deduction, logical and mathematical.</p> + +<p>(2) To argue, as if on inductive grounds, concerning the cause of the +Universe as a whole. This may be called the fallacy of transcendent +inference: since the Canons are only applicable to instances of events +that can be compared; they cannot deal with that which is in its nature +unique.</p> + +<p>(3) To mistake co-existent phenomena for cause and effect: as when a +man, wearing an amulet and escaping shipwreck, regards the amulet as the +cause of his escape. To prove his point, he must either get again into +exactly the same circumstances without his amulet, and be +drowned—according to the method of Difference; or, shirking the only +satisfactory test, and putting up with mere Agreement, he must show, +(<i>a</i>) that all who are shipwrecked and escape wear amulets, and (<i>b</i>) +that their cases agree in nothing else; and (<i>c</i>), by the Joint Method, +that all who are shipwrecked without amulets are drowned. And even if +his evidence, according to Agreement, seemed satisfactory at all these +points, it would still be fallacious to trust to it as proof of direct +causation; since we have seen that unaided observation is never +sufficient for this: it is only by experiment in prepared circumstances +that we can confidently trace sequence and the transfer of energy.</p> + +<p>There is the reverse error of mistaking causal connection for +independent co-existence: as if any one regards it as merely a curious +coincidence that great rivers generally flow past great towns. In this +case, however, the evi<span class='pagenum'>[Pg 390]<a name="Page_390" id="Page_390"></a></span>dence of connection does not depend merely upon +direct Induction.</p> + +<p>(4) <i>Post hoc, ergo propter hoc</i>: to accept the mere sequence of +phenomena, even though often repeated, as proving that the phenomena are +cause and effect, or connected by causation. This is a very natural +error: for although, the antecedents of a phenomenon being numerous, +most of them cannot be its cause, yet it is among them that the cause +must be sought. Indeed, if there is neither time nor opportunity for +analysis, it may seem better to accept any antecedent as a cause (or, at +least, as a sign) of an important event than to go without any guide. +And, accordingly, the vast and complicated learning of omens, augury, +horoscopy and prophetic dreams, relies upon this maxim; for whatever the +origin of such superstitions, a single coincidence in their favour +triumphantly confirms them. It is the besetting delusion of everybody +who has wishes or prejudices; that is, of all of us at some time or +other; for then we are ready to believe without evidence. The fallacy +consists in judging off-hand, without any attempt, either by logic or by +common sense, to eliminate the irrelevant antecedents; which may include +all the most striking and specious.</p> + +<p>(5) To regard the Co-Effects (whether simultaneous or successive) of a +common cause as standing in the direct relation of cause and effect. +Probably no one supposes that the falling of the mercury in his +thermometer causes the neighbouring lake to freeze. True, it is the +antecedent, and (within a narrow range of experience) may be the +invariable antecedent of the formation of ice; but, besides that the two +events are so unequal, every one is aware that there is another +antecedent, the fall of temperature, which causes both. To justify +inductively our belief in causation, the instances compared must agree, +or differ, in one circumstance only (besides the effect). The flowing +tide is an antecedent of the ebbing tide; it is <span class='pagenum'>[Pg 391]<a name="Page_391" id="Page_391"></a></span>invariably so, and is +equal to it; but it is not the cause of it: other circumstances are +present; and the moon is the chief condition of both flow and ebb. In +several instances, States that have grown outrageously luxurious have +declined in power: that luxury caused their downfall may seem obvious, +and capable of furnishing a moral lesson to the young. Hence other +important circumstances are overlooked, such as the institution of +slavery, the corruption and rapacity of officials and tax-gatherers, an +army too powerful for discipline; any or all of which may be present, +and sufficient to explain both the luxury and the ruin.</p> + +<p>(6) To mistake one condition of a phenomenon for the whole cause. To +speak of an indispensable condition of any phenomenon as the cause of +it, may be a mere conventional abbreviation; and in this way such a mode +of expression is common not only in popular but also in scientific +discussion. Thus we say that a temperature of 33° F. is a cause of the +melting of ice; although that ice melts at 33° F., must further depend +upon something in the nature of water; for every solid has its own +melting-point. As long, then, as we remember that 'cause,' used in this +sense, is only a convenient abbreviation, no harm is done; but, if we +forget it, fallacy may result: as when a man says that the cause of a +financial crisis was the raising of the rate of discount, neglecting the +other conditions of the market; whereas, in some circumstances, a rise +of the Bank-rate may increase public confidence and prevent a crisis.</p> + +<p>We have seen that the direct use of the Canons of Agreement and +Difference may only enable us to say that a certain antecedent is a +cause or an indispensable condition of the phenomenon under +investigation. If, therefore, it is important to find the whole cause, +we must either experiment directly upon the other conditions, or resort +to the Method of Residues and deductive reason<span class='pagenum'>[Pg 392]<a name="Page_392" id="Page_392"></a></span>ing; nor must we be +content, without showing (where such precision is possible) that the +alleged cause and the given phenomenon are equal.</p> + +<p>(7) To mistake a single consequence of a given cause for the whole +effect, is a corresponding error; and none so common. Nearly all the +mistakes of private conduct and of legislation are due to it: To cure +temporary lassitude by a stimulant, and so derange the liver; to +establish a new industry by protective duties, and thereby impoverish +the rest of the country; to gag the press, and so drive the discontented +into conspiracy; to build an alms-house, and thereby attract paupers +into the parish, raise the rates, and discourage industry.</p> + +<p>(8) To demand greater exactness in the estimate of causes or effects +than a given subject admits of. In the more complex sciences, Biology, +Psychology, Sociology, it is often impossible to be confident that all +the conditions of a given phenomenon have been assigned, or that all its +consequences have been traced. The causes of the origin of species and +of the great French Revolution have been carefully investigated, and +still we may doubt whether they have all been discovered, or whether +their comparative importance has been rightly determined; but it would +be very unreasonable to treat those things as miraculous and +unintelligible. We read in the <i>Ethics</i>, that a properly cultivated mind +knows what degree of precision is to be expected in each science. The +greatest possible precision is always to be sought; but what is possible +depends partly on the nature of the study and partly upon the state of +scientific preparation.</p> + +<p>(9) To treat an agent or condition remote in time as an unconditional +cause: for every moment of time gives an opportunity for new +combinations of forces and, therefore, for modifications of the effect. +Thus, although we often say that Napoleon's Russian expedition was the +cause of his downfall, yet the effect was subject to numerous <span class='pagenum'>[Pg 393]<a name="Page_393" id="Page_393"></a></span>further +conditions. Had the natives not burnt Moscow, had the winter been +exceptionally mild, had the Prussians and Austrians not risen against +him, the event might have been very different. It is rash to trace the +liberties of modern Europe to the battle of Marathon. Indeed, our powers +of perception are so unequal to the subtlety of nature, that even in +experimental science there is time for molecular changes to occur +between what we treat as a cause and the effect as we perceive it; and, +in such cases, the strictly unconditional cause has not been discovered.</p> + +<p>(10) To neglect the negative conditions to which a cause is subject. +When we say that water boils at 212° F., we mean "provided the pressure +be the same as that of the atmosphere at about the sea-level"; for under +a greater pressure water will not boil at that temperature, whilst under +less pressure it boils at a lower temperature. In the usual statement of +a law of causation, 'disturbing,' 'frustrating,' 'counteracting' +circumstances (that is, negative conditions) are supposed to be absent; +so that the strict statement of such a law, whether for a remote cause, +or for an immediate cause (when only positive conditions are included), +is that the agent or assemblage of conditions, <i>tends</i> to produce such +an effect, other conditions being favourable, or in the absence of +contrary forces.</p> + +<p>(11) It is needless to repeat what has already been said of other +fallacies that beset inductive proof; such as the neglect of a possible +plurality of causes where the effect has been vaguely conceived; the +extension of empirical laws beyond adjacent cases; the chief errors to +which the estimate of analogies and probabilities, or the application of +the principles of classification are liable; and the reliance upon +direct Induction where the aid of Deduction may be obtained, or upon +observation where experiment may be employed. As to formal fallacies +that may be avoided by adhering to the rules of logical method, this may +suffice.</p><p><span class='pagenum'>[Pg 394]<a name="Page_394" id="Page_394"></a></span></p> + +<p><a name="chap_24_sect_4" id="chap_24_sect_4"></a>§ 4. There remain many ways in which arguments fall short of a tolerable +standard of proof, though they cannot be exhibited as definite breaches +of logical principles. Logicians, therefore, might be excused from +discussing them; but out of the abundance of their pity for human +infirmity they usually describe and label the chief classes of these +'extra-logical fallacies,' and exhibit a few examples.</p> + +<p>We may adopt Whately's remark, that a fallacy lies either (1) in the +premises, or (2) in the conclusion, or (3) in the attempt to connect a +conclusion with the premises.</p> + +<p>(1) Now the premises of a sound argument must either be valid +deductions, or valid inductions, or particular observations, or axioms. +In an unsound argument, then, whose premises are supported by either +deduction or induction, the evidence may be reduced to logical rules; +and its failure is therefore a 'logical fallacy' such as we have already +discussed. It follows that an extra-logical fallacy of the premises must +lie in what cannot be reduced to rules of evidence, that is, in bad +observations (<a href="#chap_24_sect_5">§ 5</a>), or sham axioms (<a href="#chap_24_sect_6">§ 6</a>).</p> + +<p>(2) As to the conclusion, this can only be fallacious if some other +conclusion has been substituted for that which was to have been proved +(<a href="#chap_24_sect_7">§ 7</a>).</p> + +<p>(3) Fallacies in the connection between premises and conclusion, if all +the propositions are distinctly and explicitly stated, become manifest +upon applying the rules of Logic. Fallacies, therefore, which are not +thus manifest, and so are extra-logical, must depend upon some sort of +slurring, confusion, or ambiguity of thought or speech (<a href="#chap_24_sect_8">§ 8</a>).</p> + +<p><a name="chap_24_sect_5" id="chap_24_sect_5"></a>§ 5. Amongst Fallacies of Observation, Mill distinguishes (1) those of +Non-observation, where either instances of the presence or absence of +the phenomenon under investigation, or else some of the circumstances +constituting it or attending upon it, though important to the induction, +are <span class='pagenum'>[Pg 395]<a name="Page_395" id="Page_395"></a></span>overlooked. These errors are implied in the Formal Fallacies of +Induction already treated of in <a href="#chap_24_sect_3">§ 3</a> (paragraphs (3) to (7)).</p> + +<p>Mill's class (2) comprises fallacies of Malobservation. Malobservation +may be due to obtuseness or slowness of perception; and it is one +advantage of the physical sciences as means of education, that the +training involved in studying them tends to cure these defects—at +least, within their own range.</p> + +<p>But the occasion of error upon which Mill most insists, is our proneness +to substitute a hasty inference for a just representation of the fact +before us; as when a yachtsman, eager for marvels, sees a line of +porpoises and takes them for the sea-serpent. Every one knows what it is +to mistake a stranger for a friend, a leaf for a sparrow, one word for +another. The wonder is that we are not oftener wrong; considering how +small a part present sensation has in perception, and how much of every +object observed is supplied by a sort of automatic judgment. You see +something brown, which your perceptive mechanism classes with the +appearance of a cow at such a distance; and instantly all the other +properties of a cow are supplied from the resources of former +experience: but on getting nearer, it turns out to be a log of wood. It +is some protection against such errors to know that we are subject to +them; and the Logician fulfils his duty in warning us accordingly. But +the matter belongs essentially to Psychology; and whoever wishes to +pursue it will find a thorough explanation in Prof. Sully's volume on +<i>Illusions</i>.</p> + +<p>Another error is the accumulation of useless, irrelevant observations, +from which no proof of the point at issue can be derived. It has been +said that an important part of an inductive inquirer's equipment +consists in knowing what to observe. The study of any science educates +this faculty by showing us what observations have been effective in +similar cases; but something depends upon <span class='pagenum'>[Pg 396]<a name="Page_396" id="Page_396"></a></span>genius. Observation is +generally guided by hypotheses: he makes the right observations who can +frame the right hypotheses; whilst another overlooks things, or sees +them all awry, because he is confused and perverted by wishes, +prejudices or other false preconceptions; and still another gropes about +blindly, noting this and docketing that to no purpose, because he has no +hypothesis, or one so vague and ill-conceived that it sheds no light +upon his path.</p> + +<p><a name="chap_24_sect_6" id="chap_24_sect_6"></a>§ 6. The second kind of extra-logical Fallacy lying in the premises, +consists in offering as evidence some assertion entirely baseless or +nugatory, but expressed in such a way as to seem like a general truth +capable of subsuming the proposition in dispute: it is generally known +as <i>petitio principii</i>, or begging the question. The question may be +begged in three ways:</p> + +<p>(1) There are what Mill calls Fallacies <i>a priori</i>, mere assertions, +pretending to be self-evident, and often sincerely accepted as such by +the author and some infatuated disciples, but in which the cool +spectator sees either no sense at all, or palpable falsity. These sham +axioms are numerous; and probably every one is familiar with the +following examples: That circular motion is the most perfect; That every +body strives toward its natural place; That like cures like; That every +bane has its antidote; That what is true of our conceptions is true of +Nature; That pleasure is nothing but relief from pain; That the good, +the beautiful and the true are the same thing; That, in trade, whatever +is somewhere gained is somewhere lost; That only in agriculture does +nature assist man; That a man may do what he will with his own; That +some men are naturally born to rule and others to obey. Some of these +doctrines are specious enough; whilst, as to others, how they could ever +have been entertained arouses a wonder that can only be allayed by a +lengthy historical and psychological disquisition.</p> + +<p>(2) Verbal propositions offered as proof of some matter <span class='pagenum'>[Pg 397]<a name="Page_397" id="Page_397"></a></span>of fact. These +have, indeed, one attribute of axioms; they are self-evident to any one +who knows the language; but as they only dissect the meaning of words, +nothing but the meaning of words can be inferred from them. If anything +further is arrived at, it must be by the help of real propositions. How +common is such an argument as this: 'Lying is wrong, because it is +vicious'—the implied major premise being that 'what is vicious is +wrong.' All three propositions are verbal, and we merely learn from them +that lying is <i>called</i> vicious and wrong; and to make that knowledge +deterrent, it must be supplemented by a further premise, that 'whatever +is called wrong ought to be avoided.' This is a real proposition; but it +is much more difficult to prove it than 'that lying ought to be +avoided.' Still, such arguments, though bad Logic, often have a +rhetorical force: to call lying not only wrong but vicious, may be +dissuasive by accumulating associations of shame and ignominy.</p> + +<p>Definitions, being the most important of verbal propositions (since they +imply the possibility of as many other verbal propositions as there are +defining attributes and combinations of them), need to be watched with +especial care. If two disputants define the same word in different ways, +with each of the different attributes included in their several +definitions they may bring in a fresh set of real propositions as to the +agency or normal connection of that attribute. Hence their conclusions +about the things denoted by the word defined, diverge in all directions +and to any extent. And it is generally felt that a man who is allowed to +define his terms as he pleases, may prove anything to those who, through +ignorance or inadvertence, grant that the things that those terms stand +for have the attributes that figure in his definitions.</p> + +<p>(3) <i>Circulus in demonstrando</i>, the pretence of giving a reason for an +assertion, whilst in fact only repeating the assertion itself—generally +in other words. In such cases <span class='pagenum'>[Pg 398]<a name="Page_398" id="Page_398"></a></span>the original proposition is, perhaps, +really regarded as self-evident, but by force of habit a man says +'because'; and then, after vainly fumbling in his empty pocket for the +coin of reason, the habit of symbolic thinking in words only, without +reference to the facts, comes to his rescue, and he ends with a +paraphrase of the same assertion. Thus a man may try to prove the +necessity of Causation: 'Every event must have a cause; because an event +is a change of phenomena, and this implies a transformation of something +pre-existing; which can only have been possible, if there were forces in +operation capable of transforming it.' Or, again: 'We ought not to go to +war, because it is wrong to shed blood.' But, plainly, if war did not +imply bloodshed, the unlawfulness of this could be nothing against war. +The more serious any matter is, the more important it becomes either to +reason thoroughly about it, or to content ourselves with wholesome +assertions. How many 'arguments' are superfluous!</p> + +<p><a name="chap_24_sect_7" id="chap_24_sect_7"></a>§ 7. The Fallacy of surreptitious conclusion (<i>ignoratio elenchi</i>), the +mistaking or obscuring of the proposition really at issue, whilst +proving something else instead. This may be done by substituting a +particular proposition for an universal, or an universal for a +particular. Thus, he who attacks the practice of giving in charity must +not be content to show that it has, in this or that case, degraded the +recipient; who may have been exceptionally weak. Or, again, to dissuade +another from giving alms in a particular case, it is not enough to show +that the general tendency of almsgiving is injurious; for, by taking +pains in a particular case, the general tendency may often be +counteracted.</p> + +<p>Sometimes an argument establishing a wholly irrelevant conclusion is +substituted for an <i>argumentum ad rem</i>. Macaulay complains of those +apologists for Charles I. who try to defend him as a king, by urging +that he was a good judge of paintings and indulgent to his wife.</p><p><span class='pagenum'>[Pg 399]<a name="Page_399" id="Page_399"></a></span></p> + +<p>To this class of Fallacies belongs the <i>argumentum ad hominem</i>, which +consists in showing not that a certain proposition is true, but that +Critias ought to accept it in consistency with his other opinions. Thus: +'In every parish the cost of education ought to be paid out of the +rates: you, at least, have said that there can be no sound economy, +unless local expenses are defrayed from local funds.' But whether this +is a fallacy depends, as Whately observes, upon whether it is urged as +actually proving the point at issue, or merely as convicting the +opponent of inconsistency. In the latter case, the argument is quite +fair: whatever such a conclusion may be worth.</p> + +<p>Similarly with the <i>argumentum ad populum</i>: 'this measure is favourable +to such or such a class; let them vote for it.' An appeal to private +greed, however base, is not fallacious, as long as the interest of the +class is not <i>fraudulently</i> substituted for the good of the nation. And +much the same may be said for the <i>argumentum ad verecundiam</i>. When a +question of morals is debated as a question of honour among thieves, +there is no fallacy, if the moral issue is frankly repudiated. The +argument from authority is often brought under this head: 'such is the +opinion of Aristotle.' Although this does not establish the truth of any +proposition, it may be fairly urged as a reason for not hastily adopting +a contrary conclusion: that is, if the subject under discussion be one +as to which Aristotle (or whoever the authority may be) had materials +for forming a judgment.</p> + +<p>A negative use of this fallacy is very common. Some general doctrine, +such as Positivism, Transcendentalism, Utilitarianism, or Darwinism, is +held in common by a group of men; who, however, all judge independently, +and therefore are likely to differ in details. An opponent exhibits +their differences of opinion, and thereupon pretends to have refuted the +theory they agree in supporting. This is an <i>argumentum ad scholam</i>, and +pushes too far the <span class='pagenum'>[Pg 400]<a name="Page_400" id="Page_400"></a></span>demand for consistency. In fact it recoils upon the +sophist; for there is no sense in quoting men against one another, +unless both (or all) are acknowledged to speak with the authority of +learning and judgment, and therefore the general doctrine which they +hold in common is the more confirmed.</p> + +<p>This is an example of the paralogism of 'proving too much'; when a +disputant is so eager to refute an opponent as to lay down, or imply, +principles from which an easy inference destroys his own position. To +appeal to a principle of greater sweep than the occasion requires may +easily open the way to this pitfall: as if a man should urge that 'all +men are liars,' as the premise of an argument designed to show that +another's assertion is less credible than his own.</p> + +<p>A common form of <i>ignoratio elenchi</i> is that which Whately called the +'fallacy of objections': namely, to lay stress upon all the +considerations against any doctrine or proposal, without any attempt to +weigh them against the considerations in its favour; amongst which +should be reckoned all the considerations that tell against the +alternative doctrines or proposals. Incontestable demonstration can +rarely be expected even in science, outside of the Mathematics; and in +practical affairs, as Butler says, 'probability is the very guide of +life'; so that every conclusion depends upon the balance of evidence, +and to allow weight to only a part of it is an evasion of the right +issue.</p> + +<p><a name="chap_24_sect_8" id="chap_24_sect_8"></a>§ 8. Fallacies in the connection of premises and conclusion, that cannot +be detected by reducing the arguments to syllogistic form, must depend +upon some juggling with language to disguise their incoherence. They may +be generally described as Fallacies of Ambiguity, whether they turn upon +the use of the same word in different senses, or upon ellipsis. Thus it +may be argued that all works written in a classical language are +classical, and <span class='pagenum'>[Pg 401]<a name="Page_401" id="Page_401"></a></span>that, therefore, the history of Philosophy by Diogenes +Lærtius, being written in Greek, is a classic. Such ambiguities are +sometimes serious enough; sometimes are little better than jokes. For +jokes, as Whately observes, are often fallacies; and considered as a +propædeutic to the art of sophistry, punning deserves the ignominy that +has overtaken it.</p> + +<p>Fallacies of ellipsis usually go by learned names, as; (1) <i>a dicto +secundum quid ad dictum simpliciter</i>. It has been argued that since, +according to Ricardo, the value of goods depends solely upon the +quantity of labour necessary to produce them, the labourers who are +employed upon (say) cotton cloth ought to receive as wages the whole +price derived from its sale, leaving nothing for interest upon capital. +Ricardo, however, explained that by 'the quantity of labour necessary to +produce goods' he meant not only what is immediately applied to them, +but also the labour bestowed upon the implements and buildings with +which the immediate labour is assisted. Now these buildings and +implements are capital, the labour which produced them was paid for, and +it was far enough from Ricardo's mind to suppose that the capital which +assists present labour upon (say) cotton cloth has no claim to +remuneration out of the price of it. In this argument, then, the word +labour in the premise is used <i>secundum quid</i>, that is, with the +suppressed qualification of including past as well as present labour; +but in the conclusion labour is used <i>simpliciter</i> to mean present +labour only.</p> + +<p>(2) <i>A dicto secundum quid ad dictum secundum alterum quid</i>. It may be +urged that, since the tax on tea is uniform, therefore all consumers +contribute equally to the revenue for their enjoyment of it. But written +out fairly this argument runs thus: Since tea is taxed uniformly <i>4d. +per lb.</i>, all consumers pay equally for their enjoyment of it <i>whatever +quantity they use</i>. These qualifications introduced, nobody can be +deceived.</p><p><span class='pagenum'>[Pg 402]<a name="Page_402" id="Page_402"></a></span></p> + +<p>(3) <i>A dicto simpliciter ad dictum secundum quid</i>, also called <i>fallacia +accidentis</i>. Thus: To take interest upon a loan is perfectly just, +therefore, I do right to exact it from my own father in distress. The +popular answer to this sort of blunder is that 'circumstances alter +cases.' We commit this error in supposing that what is true of the +average is likely to be true of each case; as if one should say: 'The +offices are ready to insure my house [with thousands of others] against +fire at a rate per annum which will leave them heavy losers unless it +lasts a hundred years; so, as we are told not to take long views of +life, I shall not insure.'</p> + +<p>The Fallacy of Division and Composition consists in suggesting, or +assuming, that what is true of things severally denoted by a term is +true of them taken together. That every man is mortal is generally +admitted, but we cannot infer that, therefore, the human race will +become extinct. That the remote prospects of the race are tragic may be +plausibly argued, but not from that premise.</p> + +<p>Changing the Premises is a fallacy usually placed in this division; +although, instead of disguising different meanings under similar words, +it generally consists in using words or phrases ostensibly differing, as +if they were equivalent: those addressed being expected to renounce +their right to reduce the argument to strict forms of proof, as needless +pedantry in dealing with an author so palpably straightforward. If an +orator says—'Napoleon conquered Europe; in other words, he murdered +five millions of his fellow creatures'—and is allowed to go on, he may +infer from the latter of these propositions many things which the former +of them would hardly have covered. This is a sort of hyperbole, and +there is a corresponding meiosis, as: 'Mill <i>admits</i> that the Syllogism +is useful'; when, in fact, that is Mill's <i>contention</i>. It may be +supposed that, if a man be fool enough to be imposed upon by such +transparent colours, it serves him right; but this harsh <span class='pagenum'>[Pg 403]<a name="Page_403" id="Page_403"></a></span>judgment will +not be urged by any one who knows and considers the weaker brethren.</p> + +<p><a name="chap_24_sect_9" id="chap_24_sect_9"></a>§ 9. The above classification of Fallacies is a rearrangement of the +plans adopted by Whately and Mill. But Fallacies resemble other +spontaneous natural growths in not submitting to precise and definite +classification. The same blunders, looked at from different points of +view, may seem to belong to different groups. Thus, the example given +above to illustrate <i>fallacia accidentis</i>, 'that, since it is just to +take interest, it is right to exact it from one's own father,' may also +be regarded as <i>petitio principii</i>, if we consider the unconditional +statement of the premise—'to take interest upon a loan is perfectly +just'; for, surely, this is only conditionally true. Or, again, the +first example given of simple ambiguity—'that whatever is written in a +classical language is classical, <i>etc.</i>,' may, if we attend merely to +the major premise, be treated as a bad generalisation, an undue +extension of an inference, founded upon a simple enumeration of the +first few Greek and Latin works that one happened to remember.</p> + +<p>It must also be acknowledged that genuine wild fallacies, roaming the +jungle of controversy, are not so easily detected or evaded as specimens +seem to be when exhibited in a Logician's collection; where one surveys +them without fear, like a child at a menagerie. To assume the succinct +mode of statement that is most convenient for refutation, is not the +natural habit of these things. But to give reality to his account of +fallacies an author needs a large space, that he may quote no +inconsiderable part of literature ancient and modern.</p> + +<p>As to the means of avoiding fallacies, a general increase of sincerity +and candour amongst mankind may be freely recommended. With more honesty +there would be fewer bad arguments; but there is such a thing as +well-meaning incapacity that gets unaffectedly fogged in converting A., +and regards the refractoriness of O., as more than flesh <span class='pagenum'>[Pg 404]<a name="Page_404" id="Page_404"></a></span>and blood can +endure. Mere indulgence in figurative language, again, is a besetting +snare. "One of the fathers, in great severity called poesy <i>vinum +dæmonum</i>," says Bacon: himself too fanciful for a philosopher. Surely, +to use a simile for the discovery of truth is like studying beauty in +the bowl of a spoon.</p> + +<p>The study of the natural sciences trains and confirms the mind in a +habit of good reasoning, which is the surest preservative against +paralogism, as long as the terms in use are, like those of science, well +defined; and where they are ill defined, so that it is necessary to +guard against ambiguity, a thorough training in politics or metaphysics +may be useful. Logic seems to me to serve, in some measure, both these +purposes. The conduct of business, or experience, a sufficient time +being granted, is indeed the best teacher, but also the most austere and +expensive. In the seventeenth century some of the greatest philosophers +wrote <i>de intellectus emendatione</i>; and if their successors have given +over this very practical inquiry, the cause of its abandonment is not +success and satiety but despair. Perhaps the right mind is not to be +made by instruction, but can only be bred: a slow, haphazard process; +and meanwhile the rogue of a sophist may count on a steady supply of +dupes to amuse the tedium of many an age.</p> + +<p class="center"><b>FINIS.</b></p><p><span class='pagenum'>[Pg 405]<a name="Page_405" id="Page_405"></a></span></p> + + + +<hr style="width: 65%;" /> +<h2><a name="QUESTIONS" id="QUESTIONS"></a>QUESTIONS</h2> + +<p style="text-indent: -3em;"><i>The following questions are chiefly taken from public examination +papers: Civil Service</i> [S], <i>Oxford</i> [O], <i>Cambridge</i> [C], <i>London</i> [L].</p> + + +<h3>I. TERMS, ETC.</h3> + +<p style="text-indent: -3em;">1. What is a Term? Explain and illustrate the chief divisions of Terms. +What is meant by the Connotation of a Term? Illustrate. [S]</p> + +<p style="text-indent: -3em;">2. "The connotation and denotation of terms vary inversely." Examine +this assertion, explaining carefully the limits within which it is true, +if at all. [S]</p> + +<p style="text-indent: -3em;">3. Exemplify the false reasoning arising from the confusion of Contrary +and Contradictory Terms. [S]</p> + +<p style="text-indent: -3em;">4. Discuss the claims of the doctrine of Terms to be included in a +Logical System. Distinguish between a General and an Abstract Term. [S]</p> + +<p style="text-indent: -3em;">5. Explain and illustrate what is meant by the Denotation and +Connotation of a Term. What terms have both, and what have one only? [S]</p> + +<p style="text-indent: -3em;">6. Distinguish between Abstract and Concrete Names. To which of these +classes belong (<i>a</i>) adjectives, (<i>b</i>) names of states of consciousness? +Are any abstract names connotative? [S]</p> + +<p style="text-indent: -3em;">7. Distinguish between (<i>a</i>) Proper and Singular Terms, (<i>b</i>) Negative +and Privative, (<i>c</i>) Absolute and Relative. Illustrate.</p> + +<p style="text-indent: -3em;">8. What connection is there between the Connotation and the Relativity +of Names?</p><p><span class='pagenum'>[Pg 406]<a name="Page_406" id="Page_406"></a></span></p> + +<p style="text-indent: -3em;">9. Examine the logical relations between the following pairs of terms: +(<i>a</i>) happy and happiness; (<i>b</i>) happy and unhappy; (<i>c</i>) 'the juryman' +and 'the jury'; (<i>d</i>) parent and offspring.</p> + +<p class="noindent">Explain the technical words used in your answer. [C]</p> + +<p style="text-indent: -3em;">10. Distinguish between <i>name</i>; <i>part of speech</i>; <i>term</i>: and illustrate +by reference to the following—use, useful, usefully. [C]</p> + +<p style="text-indent: -3em;">11. Describe the nature of <i>Collective</i> terms; examine in particular any +difficulties in distinguishing between these and general or abstract +terms. [C]</p> + +<p style="text-indent: -3em;">12. Distinguish between <i>positive</i>, <i>negative</i>, and <i>privative</i> names. +Of what kind are the following, and why—parallel, alien, idle, unhappy? +What ambiguity is there in the use of such a term as "not-white"? [C]</p> + + +<h3>II. PROPOSITIONS AND IMMEDIATE INFERENCE.</h3> + +<p style="text-indent: -3em;">13. What is meant by (1) the Conversion, and (2) the Contra-position of +a proposition? Apply these processes, as far as admissible, to the +following:—</p> + +<div class="blockquot"><p class="noindent">(<i>a</i>) All invertebrates have cold blood.</p> + +<p class="noindent">(<i>b</i>) Some cold-blooded animals are not invertebrates.</p> + +<p class="noindent">(<i>c</i>) No wingless birds are songsters.</p> + +<p class="noindent">(<i>d</i>) Some winged birds are not songsters.</p></div> + +<p class="noindent">What can you infer from (<i>a</i>) and (<i>b</i>) jointly, and what from (<i>c</i>) and +(<i>d</i>) jointly? [S]</p> + +<p style="text-indent: -3em;">14. "The author actually supposes that, because Professor Fawcett denies +that all wealth is money, he denies that all money is wealth." Analyse +the differences of opinion implied in the above passage. [S]</p> + +<p style="text-indent: -3em;">15. Take any universal affirmative proposition; convert it by obversion +(contraposition); attach the negative particle to the predicate, and +again convert. Interpret the result exactly, and say whether it is or is +not equivalent to the original proposition. [S]</p><p><span class='pagenum'>[Pg 407]<a name="Page_407" id="Page_407"></a></span></p> + +<p style="text-indent: -3em;">16. What information about the term "solid body" can we derive from the +proposition, "No bodies which are not solids are crystals"? [S]</p> + +<p style="text-indent: -3em;">17. Discuss the proposal to treat all propositions as affirmative.</p> + +<p style="text-indent: -3em;">18. Convert the proposition "A is probably B." What information does the +proposition give us concerning B? [S]</p> + +<p style="text-indent: -3em;">19. Show in how many ways you can deny the following assertions: All +cathedral towns are all cities; Canterbury is the Metropolitan see. [S]</p> + +<p style="text-indent: -3em;">20. Explain the nature of a <i>hypothetical</i> (or conditional) proposition. +What do you consider the radical difference between it and a +categorical? [S]</p> + +<p style="text-indent: -3em;">21. What is the function of the <i>copula</i>? In what different manners has +it been treated? [S]</p> + +<p style="text-indent: -3em;">22. Convert "A killed C unjustly"; "All Knowledge is probably useful"; +"The exception proves the rule"; "Birds of a feather flock together." +[S]</p> + +<p style="text-indent: -3em;">23. What is modality? How are modals treated by (<i>a</i>) formal logic and +(<i>b</i>) by the theory of induction? [S]</p> + +<p style="text-indent: -3em;">24. What is the subject of an impersonal proposition? Give reasons for +your answer. [S]</p> + +<p style="text-indent: -3em;">25. Is the categorical proposition sufficiently described as referring a +thing or things to a class? [S]</p> + +<p style="text-indent: -3em;">26. Enumerate the cases in which the truth or falsity of one proposition +may be formally inferred from the truth or falsity of another. +Illustrate these cases, and give to each its technical name. [S]</p> + +<p style="text-indent: -3em;">27. Illustrate the relation of Immediate Inferences to the Laws of +Thought.</p> + +<p style="text-indent: -3em;">28. Explain what is meant by (<i>a</i>) Symbolic Logic; (<i>b</i>) the Logic of +Relatives. Describe some method of representing propositions by means +of diagrams; and indicate how far any particular theory of the import of +propositions is involved in such representation. [S]</p><p><span class='pagenum'>[Pg 408]<a name="Page_408" id="Page_408"></a></span></p> + +<p style="text-indent: -3em;">29. Explain the exact nature of the relation between two <i>Contradictory</i> +propositions; and define Conversion by Contraposition, determining what +kind of propositions admit of such conversion.</p> + +<p class="noindent">Give the contradictory and the contrapositive of each of the following +propositions:—</p> + +<div class="blockquot"><p class="noindent">(<i>a</i>) All equilateral triangles are equiangular;</p> + +<p class="noindent">(<i>b</i>) No vertebrate animal has jaws opening sideways;</p> + +<p class="noindent">(<i>c</i>) Wherever A and B are both present, either C or D is +also present. [S]</p></div> + +<p style="text-indent: -3em;">30. Define Obversion and Inversion, and apply these processes also to +the above three propositions.</p> + +<p style="text-indent: -3em;">31. Propositions can be understood either in extension or in intension. +Explain this, and discuss the relative value of the two interpretations. +[S]</p> + +<p style="text-indent: -3em;">32. Distinguish between real and verbal propositions; and explain the +importance of the distinction.</p> + +<p style="text-indent: -3em;">33. Illustrate the process called 'change of Relation.'</p> + + +<h3>III. SYLLOGISM AND MEDIATE INFERENCE.</h3> + +<p style="text-indent: -3em;">34. What is a Syllogism? Find, without reference to the mnemonic verses, +in what different ways it is possible to prove syllogistically the +conclusion <i>No S is P</i>; and show the equivalence between these different +ways. [S]</p> + +<p style="text-indent: -3em;">35. From what points of view can the syllogism be regarded</p> + +<div class="blockquot"><p class="noindent">(1) as being, (2) as not being, a <i>petitio principii</i>? [S]</p></div> + +<p style="text-indent: -3em;">36. What are the figures of syllogism? For what kind of arguments are +they severally adapted? [S]</p> + +<p style="text-indent: -3em;">37. What is meant by Mood and Figure? How can the validity of a Mood be +tested? Should there be four Figures or three? [S]</p><p><span class='pagenum'>[Pg 409]<a name="Page_409" id="Page_409"></a></span></p> + +<p style="text-indent: -3em;">38. Construct syllogisms in Camenes, Datisi and Baroco, and reduce them +to the corresponding moods of the first figure.</p> + +<p style="text-indent: -3em;">39. Explain the meaning of "ostensive" and "indirect" Reduction. Show +that any Mood of the second Figure may be reduced in either way.</p> + +<p style="text-indent: -3em;">40. Show that A cannot be proved except in the First Figure. Express the +following reasoning in as many syllogistic figures as you can: Some +theorists cannot be trusted, for they are unwise. [S]</p> + +<p style="text-indent: -3em;">41. Discuss the possibility of reducing the argument <i>a fortiori</i> to the +syllogistic form. [S]</p> + +<p style="text-indent: -3em;">42. Can a false conclusion be reached through true premises, or a true +conclusion through false premises? Give reasons for your answer. [S]</p> + +<p style="text-indent: -3em;">43. Can we under any circumstances infer a relation between X and Z from +the premises—</p> + + +<div class="example"><span class="i0">Some Y's are X's<br /></span> +<span class="i0">Some Y's are Z's? [S]</span></div> + + +<p style="text-indent: -3em;">44. Take an apparent syllogism subject to the fallacy of negative +premises, and inquire whether you can correct the reasoning by +converting one or both of the premises into the affirmative form. [S]</p> + +<p style="text-indent: -3em;">45. Enumerate the faults to which a syllogism is liable, giving +instances of each. [S]</p> + +<p style="text-indent: -3em;">46. State any Enthymeme, and expand it into (1) a Syllogism, (2) an +Epicheirema, (3) a Sorites; and give in each case the technical name of +the Mood or Order that results.</p> + +<p style="text-indent: -3em;">47. State any Disjunctive Syllogism, and change it (1) into a +Hypothetical, (2) into a Categorical; and discuss the loss or gain, in +cogency or significance involved in this process.</p><p><span class='pagenum'>[Pg 410]<a name="Page_410" id="Page_410"></a></span></p> + +<p style="text-indent: -3em;">48. Can the Syllogism be treated as merely a consequence of the "Laws of +Thought"? If not, why not; and what else does it imply?</p> + +<p style="text-indent: -3em;">49. Prove that with three given propositions (of the forms A., E., I., +O.) it is never possible to construct more than one valid syllogism. [C]</p> + +<p style="text-indent: -3em;">50. Distinguish between a Constructive and a Destructive Hypothetical +Syllogism; and show how one may be reduced to the other. [C]</p> + + +<h3>IV. INDUCTION, ETC.</h3> + +<p style="text-indent: -3em;">51. What constitutes a Valid Induction? Distinguish it from a legitimate +hypothesis. [S]</p> + +<p style="text-indent: -3em;">52. Is it possible to form true universal propositions about facts if we +have not actually observed all the individuals designated by the subject +of the proposition? If so, how? [S]</p> + +<p style="text-indent: -3em;">53. "Perfect induction is demonstrative and syllogistic; imperfect +induction is neither." Explain the difference between perfect and +imperfect induction, and examine the truth of this assertion. [S]</p> + +<p style="text-indent: -3em;">54. Why is it that one should not regard night as the cause, nor even as +a universal condition of day? Explain "cause" and "condition." [S]</p> + +<p style="text-indent: -3em;">55. What do you understand by an experiment? Can you say how many +experiments are required to establish (1) a fact, (2) a law of nature?</p> + +<p style="text-indent: -3em;">56. How would you define <i>antecedent</i>, <i>cause</i>, <i>effect</i>, <i>consequent</i>? +[S]</p> + +<p style="text-indent: -3em;">57. England is the richest country in the world, and has a gold +currency. Russia and India, in proportion to population, are poor +countries and have little or no gold currency. How far are such kind of +facts logically sufficient to prove that a gold currency is the cause of +a nation's wealth? [S]</p><p><span class='pagenum'>[Pg 411]<a name="Page_411" id="Page_411"></a></span></p> + +<p style="text-indent: -3em;">58. A man having been shot through the heart immediately falls dead. +Investigate the logical value of such a fact as proving that all men +shot through the heart will fall dead. [S]</p> + +<p style="text-indent: -3em;">59. Explain the process of induction called the Method of Difference, +and give some new instances of its application. How is it related to the +Method of Concomitant Variations? What is the Major Premise implied in +all these methods? [S]</p> + +<p style="text-indent: -3em;">59A. Examine the position, that the Canons of Experiment are useless, +because the work of preparing the experiments must have been done before +the canons can be applied.</p> + +<p style="text-indent: -3em;">60. Explain the logical cogency of experiments in the search for +physical causes. [S]</p> + +<p style="text-indent: -3em;">61. If the effects of A B C D are fully expressed by a b c d, and those +of B C D by b c d, what inductive inference can be drawn and on what +principle? State the canon according to which it is drawn. [S]</p> + +<p style="text-indent: -3em;">62. Compare the advantage of observation and experiment as means of +gaining data for Reasoning. [S]</p> + +<p style="text-indent: -3em;">63. Compare the cogency of different Inductive Methods, showing the kind +of evidence each requires, and the principle on which it is based. [S]</p> + +<p style="text-indent: -3em;">64. Compare the Canons of Agreement and Difference (1) as to the +difficulty of finding or preparing actual Instances for them, and (2) as +to their conclusiveness.</p> + +<p style="text-indent: -3em;">65. Describe what is meant by residual phenomena, and estimate their +value in inductive science. [S]</p> + +<p style="text-indent: -3em;">66. What is the argument from Analogy? How does it differ from (<i>a</i>) +Induction, (<i>b</i>) metaphorical argument? [S]</p> + +<p style="text-indent: -3em;">67. What are the various senses in which the word Analogy has been used? +Distinguish, giving instances, between good and bad analogies. [S]</p><p><span class='pagenum'>[Pg 412]<a name="Page_412" id="Page_412"></a></span></p> + +<p style="text-indent: -3em;">68. How do you distinguish between what Mill calls the Geometrical, +Physical, and Historical Methods?</p> + +<p style="text-indent: -3em;">68A. The Comparative Method is appealed to where direct evidence is +wanting. Explain this.</p> + +<p style="text-indent: -3em;">69. What is meant by a doctrine being unverifiable? If a conclusion +reached by deduction does not agree with the facts, where must we look +for error?</p> + +<p style="text-indent: -3em;">70. There are certain cases in which failure of verification is fatal to +a theory, and other cases in which it is of comparatively little +cogency. How would you distinguish between these classes of cases? [S]</p> + +<p style="text-indent: -3em;">71. Taking the "evolution," or any other proposed hypothesis, how should +one proceed (<i>a</i>) to show whether it satisfies the conditions of a +legitimate hypothesis sufficiently to entitle it to investigation, and +(<i>b</i>) to test it with a view to its acceptance or rejection as a truth +of science? [S]</p> + +<p style="text-indent: -3em;">72. What do you mean by saying that "a phenomenon has been +satisfactorily explained"?</p> + +<p style="text-indent: -3em;">73. Explain and illustrate the Historical Method of Sociological +inquiry. [S]</p> + +<p style="text-indent: -3em;">74. What is the relation of the theory of Probability to Logic? [S]</p> + +<p style="text-indent: -3em;">75. Explain and discuss the doctrine that Induction is based upon the +Theory of Probability. [S]</p> + +<p style="text-indent: -3em;">75A. What are the logical grounds of the Law of Error?</p> + +<p style="text-indent: -3em;">76. Explain the nature and use of Classification, the means to, and +tests of, its successful performance. [S]</p> + +<p style="text-indent: -3em;">77. What is Definition and what is its use? Mention various difficulties +that occur in the process, and show how they are to be met. [S]</p> + +<p style="text-indent: -3em;">78. Propose rules for a good Division and a good Definition, and +exemplify the breach of them. [S]</p> + +<p style="text-indent: -3em;">79. Examine the validity of the idea of Real Kinds. [O]</p> + +<p style="text-indent: -3em;">80. What kind of words are indefinable, and why? When do we define by +negation and by example? [S]</p><p><span class='pagenum'>[Pg 413]<a name="Page_413" id="Page_413"></a></span></p> + +<p style="text-indent: -3em;">81. Distinguish between the province and aims of classification and +(logical) division. Illustrate. [S]</p> + +<p style="text-indent: -3em;">82. What is an <i>infima species</i> or <i>species specialissima</i>? Compare the +use of the terms <i>genus</i> and <i>species</i> in Logic with that which is +common in speaking of animals or plants. [S]</p> + +<p style="text-indent: -3em;">83. How far does the formation of Definitions and Classifications +constitute the end of Science? [S]</p> + +<p style="text-indent: -3em;">84. Examine the methodological relations between Definition, +Classification and Nomenclature. [S]</p> + +<p style="text-indent: -3em;">85. Give instances of "Differentia," "Property," "Inseparable Accident"; +and examine, with reference to your instances, how far it is possible to +distinguish them. [S]</p> + + +<h3>V. MISCELLANEOUS.</h3> + +<p style="text-indent: -3em;">86. "People can reason without the help of Logic." Why is this not a +sufficient objection to the study? In your answer show distinctly why +Logic should be studied. [S]</p> + +<p style="text-indent: -3em;">87. What is the meaning of the assertion that Logic is concerned with +the form, and not with the matter, of thought? [S]</p> + +<p style="text-indent: -3em;">88. "Neither by deductive nor inductive reasoning can we add a tittle to +our implicit knowledge." (Jevons.) Explain and criticise. [S]</p> + +<p style="text-indent: -3em;">89. What is the logical foundation of the indirect method or <i>reductio +ad absurdum</i>? Is it applicable to non-mathematical subjects? [S]</p> + +<p style="text-indent: -3em;">90. On what grounds do we believe in the reality of an historical event? +[S]</p> + +<p style="text-indent: -3em;">91. "Facts are familiar theories." Explain and discuss this. [O]</p> + +<p style="text-indent: -3em;">92. Wherein lies the difficulty of proving a negative? [O]</p><p><span class='pagenum'>[Pg 414]<a name="Page_414" id="Page_414"></a></span></p> + +<p style="text-indent: -3em;">93. Can any limits be assigned to the possible unification of the +sciences? [O]</p> + +<p style="text-indent: -3em;">94. Are the results of inductive inference necessarily certain? [O]</p> + +<p style="text-indent: -3em;">95. The method of deductive science is hypothetical. Explain and +discuss. [O]</p> + +<p style="text-indent: -3em;">96. "The uniformity of Nature can never be more than a working +hypothesis." Explain and criticise.</p> + +<p style="text-indent: -3em;">97. "Without speculation there is no good and original observation." +Why? [O]</p> + +<p style="text-indent: -3em;">98. Can the provinces of induction and deduction be kept separate? [O]</p> + +<p style="text-indent: -3em;">99. How far is the relation of logical dependence identical with that of +causation? [O]</p> + +<p style="text-indent: -3em;">99A. Discuss the position that the forms of Logic are meaningless apart +from their application.</p> + +<p style="text-indent: -3em;">100. State in syllogistic form (mood and figure) the following +arguments:—</p> + +<div class="blockquot"><p class="noindent">(<i>a</i>) As polygamy is in many countries legal, we may infer +the variability of the moral standard.</p> + +<p class="noindent">(<i>b</i>) If gold is wealth, to export it diminishes the national +resources.</p> + +<p class="noindent">(<i>c</i>) If all good people are happy, unhappiness is an +indication of vice.</p> + +<p class="noindent">(<i>d</i>) One may be sure of the benefits of inuring young +children to cold, from the strength exhibited by all men and +women thus treated in infancy.</p> + +<p class="noindent">(<i>e</i>) Where there is no law, there is no injustice.</p> + +<p class="noindent">(<i>f</i>) "Dissimulation is but a faint kind of policy or wisdom; +for it asketh a strong wit and a strong heart to know when to +tell the truth, and to do it; therefore it is the weaker sort +of politicians that are the greatest dissemblers." (Bacon.)</p> + +<p class="noindent">(<i>g</i>) Money being a barren product, it is contrary to nature +to make it reproduce itself. Usury, therefore, is unnatural, +and, being unnatural, is unjustifiable.</p><p><span class='pagenum'>[Pg 415]<a name="Page_415" id="Page_415"></a></span></p> + +<p class="noindent">(<i>h</i>) The study of mathematics is essential to a complete +course of education, because it induces a habit of close and +regular reasoning. [S]</p></div> + +<p style="text-indent: -3em;">101. Explain and illustrate the following terms:—Subalternans, <i>Vera +Causa</i>, Plurality of Causes, Law of Nature, Empirical Law, <i>Summum +Genus</i>, Predicament, <i>Arbor Porphyriana</i>, Axiom, Universe of discourse +(<i>suppositio</i>), Antinomy, Dilemma, Realism, Dichotomy, etc.</p> + +<p style="text-indent: -3em;">102. Is there any distinction and, if so, what, between a complete +Description and an Explanation? [C]</p> + +<p style="text-indent: -3em;">103. On what principles have fallacies been classified? To what extent +do you think a satisfactory classification of Fallacies possible? [C]</p> + +<p style="text-indent: -3em;">104. Examine how far conceptions of Persistence and of Invariable +Concomitance of Properties are involved in the methodological +application of the conception of Cause.</p> + +<p style="text-indent: -3em;">104A. Inquire whether the two following propositions can be reconciled +with one another: (a) The same conjunction of antecedents is invariably +followed by the same consequent; (<i>b</i>) We never find the same +concurrence of phenomena a second time. [C]</p> + +<p style="text-indent: -3em;">105. Using the term Logic in a wide sense, so as to include Methodology, +inquire how far a Logic of Observation is possible, and show in what it +will consist. [C]</p> + +<p style="text-indent: -3em;">106. What is Proof?</p> + +<p class="noindent">Explain and discuss the following dicta:—(<i>a</i>) <i>Qui nimium probat, +nihil probat</i>: (<i>b</i>) A bad proof is worse than no proof; (<i>c</i>) The +exception proves the rule; (<i>d</i>) Negatives cannot be proved. [C]</p> + +<p style="text-indent: -3em;">107. Examine how far the rules of immediate and syllogistic inference +are modified by differences of interpretation of the categorical +proposition in respect of the existence of the subject. [S]</p><p><span class='pagenum'>[Pg 416]<a name="Page_416" id="Page_416"></a></span></p> + +<p style="text-indent: -3em;">108. "An effect is but the sum of all the partial causes, the +concurrence of which constitutes its existence." "The cause of an event +is its invariable and unconditional antecedent." Explain and compare +these two theories of causation. Does either alone exhaust the +scientific conception of cause? [S]</p> + +<p style="text-indent: -3em;">109. Under what logical conditions are statistical inferences +authorised, and what is the nature of their conclusions? [S]</p> + +<p style="text-indent: -3em;">110. Distinguish between Psychology, Metaphysics, and Logic; and discuss +briefly their mutual relations. [S]</p> + +<p style="text-indent: -3em;">111. All processes of inference in which the ultimate premises are +particular cases are equally induction.</p> + +<p class="noindent">Induction is an inverse deduction.</p> + +<p class="noindent">Explain and contrast these two theories of the relation of induction to +deduction. [S]</p> + +<p style="text-indent: -3em;">112. What are the Fallacies specially incident to Induction?—or to the +application of the theory of Probabilities? [S]</p> + +<p style="text-indent: -3em;">113. What is meant by the <i>personal error</i> (or <i>personal equation</i>) in +observation? Discuss its importance in different branches of knowledge. +[S]</p> + +<p style="text-indent: -3em;">114. Define and illustrate:—Paralogism, <i>ignoratio elenchi</i>, <i>fallacia +accidentis</i>, <i>argumentum ad verecundiam</i>, illicit process, undistributed +middle, etc.</p> + +<p style="text-indent: -3em;">115. State the three fundamental laws of thought, explain their meaning, +and consider how far they are independent of each other? [L]</p> + +<p style="text-indent: -3em;">116. Enumerate the "Heads of Predicables" and define their meaning. +Discuss their logical importance. [L]</p> + +<p style="text-indent: -3em;">117. Upon what grounds has it been asserted that the conclusion of a +syllogism is drawn, not from, but according to, the major premise? Are +they valid? [L]</p><p><span class='pagenum'>[Pg 417]<a name="Page_417" id="Page_417"></a></span></p> + +<p style="text-indent: -3em;">118. "Experiment is always preferable to observation." Why is this? +Explain from the example of any science how observation and experiment +supplement each other. [L]</p> + +<p style="text-indent: -3em;">119. What is a hypothesis? Distinguish between a working hypothesis and +an established hypothesis, so as to bring out the conditions on which +the latter depends. [L]</p> + +<p style="text-indent: -3em;">120. Explain how good scientific nomenclature and terminology are +connected with the purposes of good classification. [L]</p> + + + + +<hr style="width: 65%;" /> +<p class='center'><i>Printed in Great Britain by Hazell, Watson & Viney, Ld., London and +Aylesbury for Simpkin, Marshall, Hamilton, Kent & Co. Ltd.</i></p> + +<hr style="width: 65%;" /> + +<h3>Transcriber's Notes</h3> + +<p>The following corrections were made to the original text:</p> + +<p>Page 40: "inedequate" changed to "inadequate"</p> +<p>Page 42: "classily" changed to "classify"</p> +<p>Page 90: "alledging" changed to "alleging"</p> +<p>Page 128: missing comma added: "Camenes, Dimaris"</p> +<p>Page 141: "evalued" changed to "evaluated"</p> +<p>Page 147: "tellens" changed to "tollens": "and the Modus tollens"</p> +<p>Page 170: "impredictable" changed to "unpredictable"</p> +<p>Page 210: missing word 'a' added: "Sesostris conquered a great"</p> +<p>Page 307: "either" changed to "neither"</p> +<p>Page 315: "inductions" changed to "induction"</p> +<p>Page 401: "quality" changed to "quantity"</p> +<p>Page 401: "propœdeutic" changed to "propædeutic"</p> + + + + + + + + + + +<pre> + + + + + +End of the Project Gutenberg EBook of Logic, by Carveth Read + +*** END OF THIS PROJECT GUTENBERG EBOOK LOGIC *** + +***** This file should be named 18440-h.htm or 18440-h.zip ***** +This and all associated files of various formats will be found in: + http://www.gutenberg.org/1/8/4/4/18440/ + +Produced by Susan Skinner and the Online Distributed +Proofreading Team at http://www.pgdp.net + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. 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