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| committer | Roger Frank <rfrank@pglaf.org> | 2025-10-14 20:03:43 -0700 |
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diff --git a/35421-h/35421-h.htm b/35421-h/35421-h.htm new file mode 100644 index 0000000..6b748e2 --- /dev/null +++ b/35421-h/35421-h.htm @@ -0,0 +1,19685 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" + "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> +<!-- $Id: header.txt 236 2009-12-07 18:57:00Z vlsimpson $ --> + +<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> + <head> + <meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1" /> + <meta http-equiv="Content-Style-Type" content="text/css" /> + <title> + The Project Gutenberg eBook of A System of Logic: Ratiocinative and Inductive, Vol. II, by John Stuart Mill. + </title> + <style type="text/css"> + +body { + margin-left: 10%; + margin-right: 10%; +} + + h1,h2,h3,h4,h5,h6 { + text-align: center; /* all headings centered */ + clear: both; +} + +p { + margin-top: .75em; + text-align: justify; + margin-bottom: .75em; +} + +p.newsection { + margin-top: 2em; +} + +hr { + width: 33%; + margin-top: 2em; + margin-bottom: 2em; + margin-left: auto; + margin-right: auto; + clear: both; +} +hr.tb { + width:45%; +} +hr.chap { + width:65%; +} +hr.full { + width:95%; +} + +table { + margin-left: auto; + margin-right: auto; +} + +.pagenum { /* uncomment the next line for invisible page numbers */ + /* visibility: hidden; */ + position: absolute; + left: 92%; + font-size: smaller; + text-align: right; + font-style: normal; +} /* page numbers */ + +.linenum { + position: absolute; + top: auto; + left: 4%; +} /* poetry number */ + +.blockquot { + margin-left: 5%; + margin-right: 10%; +} + +.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; + color: black; + 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;} + +/* Images */ +.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 */ +.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; +} + +/* Poetry */ +.poem { + margin-left:10%; + margin-right:10%; + text-align: left; +} + +.poem br {display: none;} + +.poem .stanza {margin: 1em 0em 1em 0em;} + +.poem span.i0 { + display: block; + margin-left: 0em; + padding-left: 3em; + text-indent: -3em; +} + +.poem span.i2 { + display: block; + margin-left: 2em; + padding-left: 3em; + text-indent: -3em; +} + +.poem span.i4 { + display: block; + margin-left: 4em; + padding-left: 3em; + text-indent: -3em; +} + +/* Non-headings that display like them */ +div.likeheading1 { + text-align:center; + margin-bottom: 2em; + font-weight: bold; + font-size:200%; +} +div.likeheading2 { + text-align:center; + margin-bottom: 2em; + font-weight: bold; + font-size:150%; +} +div.likeheading3 { + text-align:center; + margin-bottom: 2em; + font-weight: bold; + font-size:120%; +} + +div.tocbook { + margin-top:2em; + margin-bottom:0.5em; + font-weight:bold; + font-size:120%; +} + +div.tocchapter { + margin-top:1.5em; + margin-bottom:1.5em; +} + +div.wider td { + padding-left:1em; + padding-right:1em; +} + +div.wider0 td { + padding-left:0.2em; + padding-right:0.2em; +} + </style> + </head> +<body> + + +<pre> + +The Project Gutenberg EBook of A System of Logic: Ratiocinative and +Inductive, by John Stuart Mill + +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: A System of Logic: Ratiocinative and Inductive + 7th Edition, Vol. II + +Author: John Stuart Mill + +Release Date: February 27, 2011 [EBook #35421] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK A SYSTEM OF LOGIC, VOL II *** + + + + +Produced by David Clarke, Stephen H. Sentoff and the Online +Distributed Proofreading Team at https://www.pgdp.net (This +file was produced from images generously made available +by The Internet Archive/Canadian Libraries) + + + + + + +</pre> + + + +<p class="center"> +A<br /> +SYSTEM OF LOGIC<br /> +<br /> +RATIOCINATIVE AND INDUCTIVE</p> +<hr class="tb" /> +<p class="center"> +VOL. II. +</p> + + + +<hr class="chap" /> +<h1> +A<br /> +SYSTEM OF LOGIC<br /> +<br /> +RATIOCINATIVE AND INDUCTIVE<br /> +</h1> +<div class="likeheading2"> +BEING A CONNECTED VIEW OF THE<br /> +PRINCIPLES OF EVIDENCE<br /> +AND THE<br /> +METHODS OF SCIENTIFIC INVESTIGATION<br /> +</div> +<div class="likeheading3">BY</div> + +<div class="likeheading2">JOHN STUART MILL</div> + +<hr class="tb" /> +<div class="likeheading2"> +IN TWO VOLUMES<br /> +<br /> +VOL. II.</div> +<div class="likeheading2"> +SEVENTH EDITION</div> + +<p class="center"> +LONDON:<br /> +LONGMANS, GREEN, READER, AND DYER<br /> +<br /> +MDCCCLXVIII +</p> + + + + +<hr class="chap" /> +<p><span class="pagenum"><a name="Page_v" id="Page_v">[Pg v]</a></span></p> +<h2> +CONTENTS<br /> +OF<br /> +THE SECOND VOLUME.<br /> +</h2> + +<div class="center"> +<table border="0" cellpadding="4" cellspacing="0" summary=""> +<tr><td></td><td><div class="tocbook"><a href="#BOOK_III">BOOK III.</a><br /> +ON INDUCTION.—(<i>Continued.</i>)</div></td></tr> + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XIV">Chapter XIV.</a></span> <i>Of the Limits to the Explanation of Laws of +Nature; and of Hypotheses.</i></div></td></tr> + + +<tr><td align="right" valign="top" style="width:3em;">§ <a href="#BOOK_III_CHAPTER_XIV_1">1.</a></td><td align="left">Can all the sequences in nature be resolvable into one law?</td><td align="right" valign="top"><a href="#Page_3">3</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XIV_2">2.</a></td><td align="left">Ultimate laws cannot be less numerous than the distinguishable feelings of our nature</td><td align="right" valign="top"><a href="#Page_4">4</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XIV_3">3.</a></td><td align="left">In what sense ultimate facts can be explained</td><td align="right" valign="top"><a href="#Page_7">7</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XIV_4">4.</a></td><td align="left">The proper use of scientific hypotheses</td><td align="right" valign="top"><a href="#Page_8">8</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XIV_5">5.</a></td><td align="left">Their indispensableness</td><td align="right" valign="top"><a href="#Page_16">16</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XIV_6">6.</a></td><td align="left">Legitimate, how distinguished from illegitimate hypotheses</td><td align="right" valign="top"><a href="#Page_18">18</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XIV_7">7.</a></td><td align="left">Some inquiries apparently hypothetical are really inductive</td><td align="right" valign="top"><a href="#Page_25">25</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XV">Chapter XV.</a></span> <i>Of Progressive Effects; and of the Continued +Action of Causes.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_III_CHAPTER_XV_1">1.</a></td><td align="left">How a progressive effect results from the simple continuance of the cause</td><td align="right" valign="top"><a href="#Page_29">29</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XV_2">2.</a></td><td align="left">—and from the progressiveness of the cause</td><td align="right" valign="top"><a href="#Page_33">33</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XV_3">3.</a></td><td align="left">Derivative laws generated from a single ultimate law</td><td align="right" valign="top"><a href="#Page_36">36</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XVI">Chapter XVI.</a></span> <i>Of Empirical Laws.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_III_CHAPTER_XVI_1">1.</a></td><td align="left">Definition of an empirical law</td><td align="right" valign="top"><a href="#Page_38">38</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XVI_2">2.</a></td><td align="left">Derivative laws commonly depend on collocations</td><td align="right" valign="top"><a href="#Page_39">39</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XVI_3">3.</a></td><td align="left">The collocations of the permanent causes are not reducible to any law</td><td align="right" valign="top"><a href="#Page_41">41</a></td></tr> +<tr><td align="right" valign="top"><span class="pagenum"><a name="Page_vi" id="Page_vi">[Pg vi]</a></span><a href="#BOOK_III_CHAPTER_XVI_4">4.</a></td><td align="left">Hence empirical laws cannot be relied on beyond the limits of actual experience</td><td align="right" valign="top"><a href="#Page_41">41</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XVI_5">5.</a></td><td align="left">Generalizations which rest only on the Method of Agreement can only be received as empirical laws</td><td align="right" valign="top"><a href="#Page_43">43</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XVI_6">6.</a></td><td align="left">Signs from which an observed uniformity of sequence may be presumed to be resolvable</td><td align="right" valign="top"><a href="#Page_44">44</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XVI_7">7.</a></td><td align="left">Two kinds of empirical laws</td><td align="right" valign="top"><a href="#Page_47">47</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XVII">Chapter XVII.</a></span> <i>Of Chance, and its Elimination.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_III_CHAPTER_XVII_1">1.</a></td><td align="left">The proof of empirical laws depends on the theory of chance</td><td align="right" valign="top"><a href="#Page_49">49</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XVII_2">2.</a></td><td align="left">Chance defined and characterized</td><td align="right" valign="top"><a href="#Page_50">50</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XVII_3">3.</a></td><td align="left">The elimination of chance</td><td align="right" valign="top"><a href="#Page_55">55</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XVII_4">4.</a></td><td align="left">Discovery of residual phenomena by eliminating chance</td><td align="right" valign="top"><a href="#Page_57">57</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XVII_5">5.</a></td><td align="left">The doctrine of chances</td><td align="right" valign="top"><a href="#Page_59">59</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XVIII">Chapter XVIII.</a></span> <i>Of the Calculation of Chances.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_III_CHAPTER_XVIII_1">1.</a></td><td align="left">Foundation of the doctrine of chances, as taught by mathematics</td><td align="right" valign="top"><a href="#Page_61">61</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XVIII_2">2.</a></td><td align="left">The doctrine tenable</td><td align="right" valign="top"><a href="#Page_63">63</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XVIII_3">3.</a></td><td align="left">On what foundation it really rests</td><td align="right" valign="top"><a href="#Page_64">64</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XVIII_4">4.</a></td><td align="left">Its ultimate dependence on causation</td><td align="right" valign="top"><a href="#Page_68">68</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XVIII_5">5.</a></td><td align="left">Theorem of the doctrine of chances which relates to the cause of a given event</td><td align="right" valign="top"><a href="#Page_72">72</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XVIII_6">6.</a></td><td align="left">How applicable to the elimination of chance</td><td align="right" valign="top"><a href="#Page_74">74</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XIX">Chapter XIX.</a></span> <i>Of the Extension of Derivative Laws to Adjacent +Cases.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_III_CHAPTER_XIX_1">1.</a></td><td align="left">Derivative laws, when not casual, are almost always contingent on collocations</td><td align="right" valign="top"><a href="#Page_78">78</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XIX_2">2.</a></td><td align="left">On what grounds they can be extended to cases beyond the bounds of actual experience</td><td align="right" valign="top"><a href="#Page_80">80</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XIX_3">3.</a></td><td align="left">Those cases must be adjacent cases</td><td align="right" valign="top"><a href="#Page_82">82</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XX">Chapter XX.</a></span> <i>Of Analogy.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_III_CHAPTER_XX_1">1.</a></td><td align="left">Various senses of the word analogy</td><td align="right" valign="top"><a href="#Page_86">86</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XX_2">2.</a></td><td align="left">Nature of analogical evidence</td><td align="right" valign="top"><a href="#Page_87">87</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XX_3">3.</a></td><td align="left">On what circumstances its value depends</td><td align="right" valign="top"><a href="#Page_91">91</a></td></tr> + + +<tr><td><span class="pagenum"><a name="Page_vii" id="Page_vii">[Pg vii]</a></span></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XXI">Chapter XXI.</a></span> <i>Of the Evidence of the Law of Universal +Causation.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_III_CHAPTER_XXI_1">1.</a></td><td align="left">The law of causality does not rest on an instinct</td><td align="right" valign="top"><a href="#Page_95">95</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXI_2">2.</a></td><td align="left">But on an induction by simple enumeration</td><td align="right" valign="top"><a href="#Page_100">100</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXI_3">3.</a></td><td align="left">In what cases such induction is allowable</td><td align="right" valign="top"><a href="#Page_102">102</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXI_4">4.</a></td><td align="left">The universal prevalence of the law of causality, on what grounds admissible</td><td align="right" valign="top"><a href="#Page_105">105</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XXII">Chapter XXII.</a></span> <i>Of Uniformities of Coexistence not dependent +on Causation.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_III_CHAPTER_XXII_1">1.</a></td><td align="left">Uniformities of coexistence which result from laws of sequence</td><td align="right" valign="top"><a href="#Page_110">110</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXII_2">2.</a></td><td align="left">The properties of Kinds are uniformities of coexistence</td><td align="right" valign="top"><a href="#Page_111">111</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXII_3">3.</a></td><td align="left">Some are derivative, others ultimate</td><td align="right" valign="top"><a href="#Page_113">113</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXII_4">4.</a></td><td align="left">No universal axiom of coexistence</td><td align="right" valign="top"><a href="#Page_114">114</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXII_5">5.</a></td><td align="left">The evidence of uniformities of coexistence, how measured</td><td align="right" valign="top"><a href="#Page_117">117</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXII_6">6.</a></td><td align="left">When derivative, their evidence is that of empirical laws</td><td align="right" valign="top"><a href="#Page_117">117</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXII_7">7.</a></td><td align="left">So also when ultimate</td><td align="right" valign="top"><a href="#Page_119">119</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXII_8">8.</a></td><td align="left">The evidence stronger in proportion as the law is more general</td><td align="right" valign="top"><a href="#Page_120">120</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXII_9">9.</a></td><td align="left">Every distinct Kind must be examined</td><td align="right" valign="top"><a href="#Page_121">121</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XXIII">Chapter XXIII.</a></span> <i>Of Approximate Generalizations, and Probable +Evidence.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_III_CHAPTER_XXIII_1">1.</a></td><td align="left">The inferences called probable, rest on approximate generalizations</td><td align="right" valign="top"><a href="#Page_124">124</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXIII_2">2.</a></td><td align="left">Approximate generalizations less useful in science than in life</td><td align="right" valign="top"><a href="#Page_124">124</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXIII_3">3.</a></td><td align="left">In what cases they may be resorted to</td><td align="right" valign="top"><a href="#Page_126">126</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXIII_4">4.</a></td><td align="left">In what manner proved</td><td align="right" valign="top"><a href="#Page_127">127</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXIII_5">5.</a></td><td align="left">With what precautions employed</td><td align="right" valign="top"><a href="#Page_130">130</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXIII_6">6.</a></td><td align="left">The two modes of combining probabilities</td><td align="right" valign="top"><a href="#Page_131">131</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXIII_7">7.</a></td><td align="left">How approximate generalizations may be converted into accurate generalizations equivalent to them</td><td align="right" valign="top"><a href="#Page_136">136</a></td></tr> + + +<tr><td><span class="pagenum"><a name="Page_viii" id="Page_viii">[Pg viii]</a></span></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XXIV">Chapter XXIV.</a></span> <i>Of the Remaining Laws of Nature.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_III_CHAPTER_XXIV_1">1.</a></td><td align="left">Propositions which assert mere existence</td><td align="right" valign="top"><a href="#Page_139">139</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXIV_2">2.</a></td><td align="left">Resemblance, considered as a subject of science</td><td align="right" valign="top"><a href="#Page_141">141</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXIV_3">3.</a></td><td align="left">The axioms and theorems of mathematics comprise the principal laws of resemblance</td><td align="right" valign="top"><a href="#Page_143">143</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXIV_4">4.</a></td><td align="left">—and those of order in place, and rest on induction by simple enumeration</td><td align="right" valign="top"><a href="#Page_145">145</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXIV_5">5.</a></td><td align="left">The propositions of arithmetic affirm the modes of formation of some given number</td><td align="right" valign="top"><a href="#Page_146">146</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXIV_6">6.</a></td><td align="left">Those of algebra affirm the equivalence of different modes of formation of numbers generally</td><td align="right" valign="top"><a href="#Page_151">151</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXIV_7">7.</a></td><td align="left">The propositions of geometry are laws of outward nature</td><td align="right" valign="top"><a href="#Page_154">154</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXIV_8">8.</a></td><td align="left">Why geometry is almost entirely deductive</td><td align="right" valign="top"><a href="#Page_156">156</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXIV_9">9.</a></td><td align="left">Function of mathematical truths in the other sciences, and limits of that function</td><td align="right" valign="top"><a href="#Page_158">158</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_III_CHAPTER_XXV">Chapter XXV.</a></span> <i>Of the Grounds of Disbelief.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_III_CHAPTER_XXV_1">1.</a></td><td align="left">Improbability and impossibility</td><td align="right" valign="top"><a href="#Page_161">161</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXV_2">2.</a></td><td align="left">Examination of Hume's doctrine of miracles</td><td align="right" valign="top"><a href="#Page_162">162</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXV_3">3.</a></td><td align="left">The degrees of improbability correspond to differences in the nature of the generalization with which an assertion conflicts</td><td align="right" valign="top"><a href="#Page_166">166</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXV_4">4.</a></td><td align="left">A fact is not incredible because the chances are against it</td><td align="right" valign="top"><a href="#Page_170">170</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXV_5">5.</a></td><td align="left">Are coincidences less credible than other facts?</td><td align="right" valign="top"><a href="#Page_172">172</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_III_CHAPTER_XXV_6">6.</a></td><td align="left">An opinion of Laplace examined</td><td align="right" valign="top"><a href="#Page_175">175</a></td></tr> + + +<tr><td></td><td><div class="tocbook"><a href="#BOOK_IV">BOOK IV.</a><br /> +OF OPERATIONS SUBSIDIARY TO INDUCTION.</div></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_IV_CHAPTER_I">Chapter I.</a></span> <i>Of Observation and Description.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_IV_CHAPTER_I_1">1.</a></td><td align="left">Observation, how far a subject of logic</td><td align="right" valign="top"><a href="#Page_183">183</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_I_2">2.</a></td><td align="left">A great part of what seems observation is really inference</td><td align="right" valign="top"><a href="#Page_184">184</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_I_3">3.</a></td><td align="left">The description of an observation affirms more than is contained in the observation</td><td align="right" valign="top"><a href="#Page_187">187</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_I_4">4.</a></td><td align="left">—namely an agreement among phenomena; and the comparison of phenomena to ascertain such agreements is a preliminary to induction</td><td align="right" valign="top"><a href="#Page_190">190</a></td></tr> + + +<tr><td><span class="pagenum"><a name="Page_ix" id="Page_ix">[Pg ix]</a></span></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_IV_CHAPTER_II">Chapter II.</a></span> <i>Of Abstraction, or the Formation of +Conceptions.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_IV_CHAPTER_II_1">1.</a></td><td align="left">The comparison which is a preliminary to induction implies general conceptions</td><td align="right" valign="top"><a href="#Page_193">193</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_II_2">2.</a></td><td align="left">—but these need not be pre-existent</td><td align="right" valign="top"><a href="#Page_194">194</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_II_3">3.</a></td><td align="left">A general conception, originally the result of a comparison, becomes itself the type of comparison</td><td align="right" valign="top"><a href="#Page_198">198</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_II_4">4.</a></td><td align="left">What is meant by appropriate conceptions</td><td align="right" valign="top"><a href="#Page_200">200</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_II_5">5.</a></td><td align="left">—and by clear conceptions</td><td align="right" valign="top"><a href="#Page_203">203</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_II_6">6.</a></td><td align="left">Further illustration of the subject</td><td align="right" valign="top"><a href="#Page_205">205</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_IV_CHAPTER_III">Chapter III.</a></span> <i>Of Naming, as subsidiary to Induction.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_IV_CHAPTER_III_1">1.</a></td><td align="left">The fundamental property of names as an instrument of thought</td><td align="right" valign="top"><a href="#Page_209">209</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_III_2">2.</a></td><td align="left">Names are not indispensable to induction</td><td align="right" valign="top"><a href="#Page_210">210</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_III_3">3.</a></td><td align="left">In what manner subservient to it</td><td align="right" valign="top"><a href="#Page_211">211</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_III_4">4.</a></td><td align="left">General names not a mere contrivance to economize the use of language</td><td align="right" valign="top"><a href="#Page_213">213</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_IV_CHAPTER_IV">Chapter IV.</a></span> <i>Of the Requisites of a Philosophical Language, +and the Principles of Definition.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_IV_CHAPTER_IV_1">1.</a></td><td align="left">First requisite of philosophical language, a steady and determinate meaning for every general name</td><td align="right" valign="top"><a href="#Page_215">215</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_IV_2">2.</a></td><td align="left">Names in common use have often a loose connotation</td><td align="right" valign="top"><a href="#Page_215">215</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_IV_3">3.</a></td><td align="left">—which the logician should fix, with as little alteration as possible</td><td align="right" valign="top"><a href="#Page_218">218</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_IV_4">4.</a></td><td align="left">Why definition is often a question not of words but of things</td><td align="right" valign="top"><a href="#Page_220">220</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_IV_5">5.</a></td><td align="left">How the logician should deal with the transitive applications of words</td><td align="right" valign="top"><a href="#Page_224">224</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_IV_6">6.</a></td><td align="left">Evil consequences of casting off any portion of the customary connotation of words</td><td align="right" valign="top"><a href="#Page_229">229</a></td></tr> + + +<tr><td><span class="pagenum"><a name="Page_x" id="Page_x">[Pg x]</a></span></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_IV_CHAPTER_V">Chapter V.</a></span> <i>On the Natural History of the Variations in +the Meaning of Terms.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_IV_CHAPTER_V_1">1.</a></td><td align="left">How circumstances originally accidental become incorporated into the meaning of words</td><td align="right" valign="top"><a href="#Page_236">236</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_V_2">2.</a></td><td align="left">—and sometimes become the whole meaning</td><td align="right" valign="top"><a href="#Page_238">238</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_V_3">3.</a></td><td align="left">Tendency of words to become generalized</td><td align="right" valign="top"><a href="#Page_240">240</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_V_4">4.</a></td><td align="left">—and to become specialized</td><td align="right" valign="top"><a href="#Page_243">243</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_IV_CHAPTER_VI">Chapter VI.</a></span> <i>The Principles of a Philosophical Language +further considered.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_IV_CHAPTER_VI_1">1.</a></td><td align="left">Second requisite of philosophical language, a name for every important meaning</td><td align="right" valign="top"><a href="#Page_248">248</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_VI_2">2.</a></td><td align="left">—viz. first, an accurate descriptive terminology</td><td align="right" valign="top"><a href="#Page_248">248</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_VI_3">3.</a></td><td align="left">—secondly, a name for each of the more important results of scientific abstraction</td><td align="right" valign="top"><a href="#Page_252">252</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_VI_4">4.</a></td><td align="left">—thirdly, a nomenclature, or system of the names of Kinds</td><td align="right" valign="top"><a href="#Page_255">255</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_VI_5">5.</a></td><td align="left">Peculiar nature of the connotation of names which belong to a nomenclature</td><td align="right" valign="top"><a href="#Page_257">257</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_VI_6">6.</a></td><td align="left">In what cases language may, and may not, be used mechanically</td><td align="right" valign="top"><a href="#Page_259">259</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_IV_CHAPTER_VII">Chapter VII.</a></span> <i>Of Classification, as subsidiary to +Induction.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_IV_CHAPTER_VII_1">1.</a></td><td align="left">Classification as here treated of, wherein different from the classification implied in naming</td><td align="right" valign="top"><a href="#Page_266">266</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_VII_2">2.</a></td><td align="left">Theory of natural groups</td><td align="right" valign="top"><a href="#Page_267">267</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_VII_3">3.</a></td><td align="left">Are natural groups given by type, or by definition?</td><td align="right" valign="top"><a href="#Page_271">271</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_VII_4">4.</a></td><td align="left">Kinds are natural groups</td><td align="right" valign="top"><a href="#Page_274">274</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_VII_5">5.</a></td><td align="left">How the names of Kinds should be constructed</td><td align="right" valign="top"><a href="#Page_280">280</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_IV_CHAPTER_VIII">Chapter VIII.</a></span> <i>Of Classification by Series.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_IV_CHAPTER_VIII_1">1.</a></td><td align="left">Natural groups should be arranged in a natural series</td><td align="right" valign="top"><a href="#Page_284">284</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_VIII_2">2.</a></td><td align="left">The arrangement should follow the degrees of the main phenomenon</td><td align="right" valign="top"><a href="#Page_285">285</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_VIII_3">3.</a></td><td align="left">—which implies the assumption of a type-species</td><td align="right" valign="top"><a href="#Page_287">287</a></td></tr> +<tr><td align="right" valign="top"><span class="pagenum"><a name="Page_xi" id="Page_xi">[Pg xi]</a></span><a href="#BOOK_IV_CHAPTER_VIII_4">4.</a></td><td align="left">How the divisions of the series should be determined</td><td align="right" valign="top"><a href="#Page_288">288</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_IV_CHAPTER_VIII_5">5.</a></td><td align="left">Zoology affords the completest type of scientific classification</td><td align="right" valign="top"><a href="#Page_289">289</a></td></tr> + + +<tr><td></td><td><div class="tocbook"><a href="#BOOK_V">BOOK V.</a><br /> +ON FALLACIES.</div></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_V_CHAPTER_I">Chapter I.</a></span> <i>Of Fallacies in General.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_V_CHAPTER_I_1">1.</a></td><td align="left">Theory of fallacies a necessary part of logic</td><td align="right" valign="top"><a href="#Page_295">295</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_I_2">2.</a></td><td align="left">Casual mistakes are not fallacies</td><td align="right" valign="top"><a href="#Page_297">297</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_I_3">3.</a></td><td align="left">The moral sources of erroneous opinion, how related to the intellectual</td><td align="right" valign="top"><a href="#Page_297">297</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_V_CHAPTER_II">Chapter II.</a></span> <i>Classification of Fallacies.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_V_CHAPTER_II_1">1.</a></td><td align="left">On what criteria a classification of fallacies should be grounded</td><td align="right" valign="top"><a href="#Page_301">301</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_II_2">2.</a></td><td align="left">The five classes of fallacies</td><td align="right" valign="top"><a href="#Page_302">302</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_II_3">3.</a></td><td align="left">The reference of a fallacy to one or another class is sometimes arbitrary</td><td align="right" valign="top"><a href="#Page_305">305</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_V_CHAPTER_III">Chapter III.</a></span> <i>Fallacies of Simple Inspection, or à priori +Fallacies.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_V_CHAPTER_III_1">1.</a></td><td align="left">Character of this class of Fallacies</td><td align="right" valign="top"><a href="#Page_309">309</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_III_2">2.</a></td><td align="left">Natural prejudice of mistaking subjective laws for objective, exemplified in popular superstitions</td><td align="right" valign="top"><a href="#Page_310">310</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_III_3">3.</a></td><td align="left">Natural prejudices, that things which we think of together must exist together, and that what is inconceivable must be false</td><td align="right" valign="top"><a href="#Page_314">314</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_III_4">4.</a></td><td align="left">Natural prejudice, of ascribing objective existence to abstractions</td><td align="right" valign="top"><a href="#Page_321">321</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_III_5">5.</a></td><td align="left">Fallacy of the Sufficient Reason</td><td align="right" valign="top"><a href="#Page_322">322</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_III_6">6.</a></td><td align="left">Natural prejudice, that the differences in nature correspond to the distinctions in language</td><td align="right" valign="top"><a href="#Page_325">325</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_III_7">7.</a></td><td align="left">Prejudice, that a phenomenon cannot have more than one cause</td><td align="right" valign="top"><a href="#Page_329">329</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_III_8">8.</a></td><td align="left">Prejudice, that the conditions of a phenomenon must resemble the phenomenon</td><td align="right" valign="top"><a href="#Page_332">332</a></td></tr> + + +<tr><td><span class="pagenum"><a name="Page_xii" id="Page_xii">[Pg xii]</a></span></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_V_CHAPTER_IV">Chapter IV.</a></span> <i>Fallacies of Observation.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_V_CHAPTER_IV_1">1.</a></td><td align="left">Non-observation, and Mal-observation</td><td align="right" valign="top"><a href="#Page_341">341</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_IV_2">2.</a></td><td align="left">Non-observation of instances, and non-observation of circumstances</td><td align="right" valign="top"><a href="#Page_341">341</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_IV_3">3.</a></td><td align="left">Examples of the former</td><td align="right" valign="top"><a href="#Page_342">342</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_IV_4">4.</a></td><td align="left">—and of the latter</td><td align="right" valign="top"><a href="#Page_347">347</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_IV_5">5.</a></td><td align="left">Mal-observation characterized and exemplified</td><td align="right" valign="top"><a href="#Page_352">352</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_V_CHAPTER_V">Chapter V.</a></span> <i>Fallacies of Generalization.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_V_CHAPTER_V_1">1.</a></td><td align="left">Character of the class</td><td align="right" valign="top"><a href="#Page_356">356</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_V_2">2.</a></td><td align="left">Certain kinds of generalization must always be groundless</td><td align="right" valign="top"><a href="#Page_356">356</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_V_3">3.</a></td><td align="left">Attempts to resolve phenomena radically different into the same</td><td align="right" valign="top"><a href="#Page_357">357</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_V_4">4.</a></td><td align="left">Fallacy of mistaking empirical for causal laws</td><td align="right" valign="top"><a href="#Page_359">359</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_V_5">5.</a></td><td align="left"><i>Post hoc, ergo propter hoc</i>; and the deductive fallacy corresponding to it</td><td align="right" valign="top"><a href="#Page_364">364</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_V_6">6.</a></td><td align="left">Fallacy of False Analogies</td><td align="right" valign="top"><a href="#Page_366">366</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_V_7">7.</a></td><td align="left">Function of metaphors in reasoning</td><td align="right" valign="top"><a href="#Page_373">373</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_V_8">8.</a></td><td align="left">How fallacies of generalization grow out of bad classification</td><td align="right" valign="top"><a href="#Page_375">375</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_V_CHAPTER_VI">Chapter VI.</a></span> <i>Fallacies of Ratiocination.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_V_CHAPTER_VI_1">1.</a></td><td align="left">Introductory Remarks</td><td align="right" valign="top"><a href="#Page_377">377</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_VI_2">2.</a></td><td align="left">Fallacies in the conversion and æquipollency of propositions</td><td align="right" valign="top"><a href="#Page_377">377</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_VI_3">3.</a></td><td align="left">Fallacies in the syllogistic process</td><td align="right" valign="top"><a href="#Page_379">379</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_VI_4">4.</a></td><td align="left">Fallacy of changing the premises</td><td align="right" valign="top"><a href="#Page_379">379</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_V_CHAPTER_VII">Chapter VII.</a></span> <i>Fallacies of Confusion.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_V_CHAPTER_VII_1">1.</a></td><td align="left">Fallacy of Ambiguous Terms</td><td align="right" valign="top"><a href="#Page_384">384</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_VII_2">2.</a></td><td align="left">Fallacy of Petitio Principii</td><td align="right" valign="top"><a href="#Page_396">396</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_V_CHAPTER_VII_3">3.</a></td><td align="left">Fallacy of Ignoratio Elenchi</td><td align="right" valign="top"><a href="#Page_405">405</a></td></tr> + + +<tr><td><span class="pagenum"><a name="Page_xiii" id="Page_xiii">[Pg xiii]</a></span></td><td><div class="tocbook"><a href="#BOOK_VI">BOOK VI.</a><br /> +ON THE LOGIC OF THE MORAL SCIENCES.</div></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_VI_CHAPTER_I">Chapter I.</a></span> <i>Introductory Remarks.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_VI_CHAPTER_I_1">1.</a></td><td align="left">The backward state of the Moral Sciences can only be remedied by applying to them the methods of Physical Science, duly extended and generalized</td><td align="right" valign="top"><a href="#Page_413">413</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_I_2">2.</a></td><td align="left">How far this can be attempted in the present work</td><td align="right" valign="top"><a href="#Page_415">415</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_VI_CHAPTER_II">Chapter II.</a></span> <i>Of Liberty and Necessity.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_VI_CHAPTER_II_1">1.</a></td><td align="left">Are human actions subject to the law of causality?</td><td align="right" valign="top"><a href="#Page_417">417</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_II_2">2.</a></td><td align="left">The doctrine commonly called Philosophical Necessity, in what sense true</td><td align="right" valign="top"><a href="#Page_418">418</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_II_3">3.</a></td><td align="left">Inappropriateness and pernicious effect of the term Necessity</td><td align="right" valign="top"><a href="#Page_420">420</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_II_4">4.</a></td><td align="left">A motive not always the anticipation of a pleasure or a pain</td><td align="right" valign="top"><a href="#Page_424">424</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_VI_CHAPTER_III">Chapter III.</a></span> <i>That there is, or may be, a Science of +Human Nature.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_VI_CHAPTER_III_1">1.</a></td><td align="left">There may be sciences which are not exact sciences</td><td align="right" valign="top"><a href="#Page_426">426</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_III_2">2.</a></td><td align="left">To what scientific type the Science of Human Nature corresponds</td><td align="right" valign="top"><a href="#Page_429">429</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_VI_CHAPTER_IV">Chapter IV.</a></span> <i>Of the Laws of Mind.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_VI_CHAPTER_IV_1">1.</a></td><td align="left">What is meant by Laws of Mind</td><td align="right" valign="top"><a href="#Page_432">432</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_IV_2">2.</a></td><td align="left">Is there a science of Psychology?</td><td align="right" valign="top"><a href="#Page_433">433</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_IV_3">3.</a></td><td align="left">The principal investigations of Psychology characterized</td><td align="right" valign="top"><a href="#Page_435">435</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_IV_4">4.</a></td><td align="left">Relation of mental facts to physical conditions</td><td align="right" valign="top"><a href="#Page_440">440</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_VI_CHAPTER_V">Chapter V.</a></span> <i>Of Ethology, or the Science of the Formation of +Character.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_VI_CHAPTER_V_1">1.</a></td><td align="left">The Empirical Laws of Human Nature</td><td align="right" valign="top"><a href="#Page_445">445</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_V_2">2.</a></td><td align="left">—are merely approximate generalizations. The universal laws are those of the formation of character</td><td align="right" valign="top"><a href="#Page_447">447</a></td></tr> +<tr><td align="right" valign="top"><span class="pagenum"><a name="Page_xiv" id="Page_xiv">[Pg xiv]</a></span><a href="#BOOK_VI_CHAPTER_V_3">3.</a></td><td align="left">The laws of the formation of character cannot be ascertained by observation and experiment</td><td align="right" valign="top"><a href="#Page_449">449</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_V_4">4.</a></td><td align="left">—but must be studied deductively</td><td align="right" valign="top"><a href="#Page_454">454</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_V_5">5.</a></td><td align="left">The Principles of Ethology are the <i>axiomata media</i> of mental science</td><td align="right" valign="top"><a href="#Page_455">455</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_V_6">6.</a></td><td align="left">Ethology characterized</td><td align="right" valign="top"><a href="#Page_459">459</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_VI_CHAPTER_VI">Chapter VI.</a></span> <i>General Considerations on the Social Science.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_VI_CHAPTER_VI_1">1.</a></td><td align="left">Are Social Phenomena a subject of Science?</td><td align="right" valign="top"><a href="#Page_461">461</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_VI_2">2.</a></td><td align="left">Of what nature the Social Science must be</td><td align="right" valign="top"><a href="#Page_463">463</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_VI_CHAPTER_VII">Chapter VII.</a></span> <i>Of the Chemical, or Experimental, Method in the +Social Science.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_VI_CHAPTER_VII_1">1.</a></td><td align="left">Characters of the mode of thinking which deduces political doctrines from specific experience</td><td align="right" valign="top"><a href="#Page_466">466</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_VII_2">2.</a></td><td align="left">In the Social Science experiments are impossible</td><td align="right" valign="top"><a href="#Page_468">468</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_VII_3">3.</a></td><td align="left">—the Method of Difference inapplicable</td><td align="right" valign="top"><a href="#Page_469">469</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_VII_4">4.</a></td><td align="left">—and the Methods of Agreement, and of Concomitant Variations, inconclusive</td><td align="right" valign="top"><a href="#Page_471">471</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_VII_5">5.</a></td><td align="left">The Method of Residues also inconclusive, and presupposes Deduction</td><td align="right" valign="top"><a href="#Page_472">472</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_VI_CHAPTER_VIII">Chapter VIII.</a></span> <i>Of the Geometrical, or Abstract Method.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_VI_CHAPTER_VIII_1">1.</a></td><td align="left">Characters of this mode of thinking</td><td align="right" valign="top"><a href="#Page_476">476</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_VIII_2">2.</a></td><td align="left">Examples of the Geometrical Method</td><td align="right" valign="top"><a href="#Page_478">478</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_VIII_3">3.</a></td><td align="left">The interest-philosophy of the Bentham school</td><td align="right" valign="top"><a href="#Page_479">479</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_VI_CHAPTER_IX">Chapter IX.</a></span> <i>Of the Physical, or Concrete Deductive Method.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_VI_CHAPTER_IX_1">1.</a></td><td align="left">The Direct and Inverse Deductive Methods</td><td align="right" valign="top"><a href="#Page_486">486</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_IX_2">2.</a></td><td align="left">Difficulties of the Direct Deductive Method in the Social Science</td><td align="right" valign="top"><a href="#Page_489">489</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_IX_3">3.</a></td><td align="left">To what extent the different branches of sociological speculation can be studied apart. Political Economy characterized</td><td align="right" valign="top"><a href="#Page_492">492</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_IX_4">4.</a></td><td align="left">Political Ethology, or the science of national character</td><td align="right" valign="top"><a href="#Page_497">497</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_IX_5">5.</a></td><td align="left">The Empirical Laws of the Social Science</td><td align="right" valign="top"><a href="#Page_500">500</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_IX_6">6.</a></td><td align="left">The Verification of the Social Science</td><td align="right" valign="top"><a href="#Page_502">502</a></td></tr> + + +<tr><td><span class="pagenum"><a name="Page_xv" id="Page_xv">[Pg xv]</a></span></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_VI_CHAPTER_X">Chapter X.</a></span> <i>Of the Inverse Deductive, or Historical Method.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_VI_CHAPTER_X_1">1.</a></td><td align="left">Distinction between the general Science of Society, and special sociological inquiries</td><td align="right" valign="top"><a href="#Page_506">506</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_X_2">2.</a></td><td align="left">What is meant by a State of Society?</td><td align="right" valign="top"><a href="#Page_506">506</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_X_3">3.</a></td><td align="left">The Progressiveness of Man and Society</td><td align="right" valign="top"><a href="#Page_508">508</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_X_4">4.</a></td><td align="left">The laws of the succession of states of society can only be ascertained by the Inverse Deductive Method</td><td align="right" valign="top"><a href="#Page_511">511</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_X_5">5.</a></td><td align="left">Social Statics, or the science of the Coexistences of Social Phenomena</td><td align="right" valign="top"><a href="#Page_513">513</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_X_6">6.</a></td><td align="left">Social Dynamics, or the science of the Successions of Social Phenomena</td><td align="right" valign="top"><a href="#Page_521">521</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_X_7">7.</a></td><td align="left">Outlines of the Historical Method</td><td align="right" valign="top"><a href="#Page_522">522</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_X_8">8.</a></td><td align="left">Future prospects of Sociological Inquiry</td><td align="right" valign="top"><a href="#Page_525">525</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_VI_CHAPTER_XI">Chapter XI.</a></span> <i>Additional Elucidations of the Science of History.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_VI_CHAPTER_XI_1">1.</a></td><td align="left">The subjection of historical facts to uniform laws is verified by statistics</td><td align="right" valign="top"><a href="#Page_529">529</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_XI_2">2.</a></td><td align="left">—does not imply the insignificance of moral causes</td><td align="right" valign="top"><a href="#Page_532">532</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_XI_3">3.</a></td><td align="left">—nor the inefficacy of the characters of individuals and of the acts of governments</td><td align="right" valign="top"><a href="#Page_535">535</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_XI_4">4.</a></td><td align="left">The historical importance of eminent men and of the policy of governments illustrated</td><td align="right" valign="top"><a href="#Page_540">540</a></td></tr> + + +<tr><td></td><td><div class="tocchapter"><span class="smcap"><a href="#BOOK_VI_CHAPTER_XII">Chapter XII.</a></span> <i>Of the Logic of Practice, or Art; including +Morality and Policy.</i></div></td></tr> + + + +<tr><td align="right" valign="top">§ <a href="#BOOK_VI_CHAPTER_XII_1">1.</a></td><td align="left">Morality not a science, but an Art</td><td align="right" valign="top"><a href="#Page_544">544</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_XII_2">2.</a></td><td align="left">Relation between rules of art and the theorems of the corresponding science</td><td align="right" valign="top"><a href="#Page_544">544</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_XII_3">3.</a></td><td align="left">What is the proper function of rules of art?</td><td align="right" valign="top"><a href="#Page_546">546</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_XII_4">4.</a></td><td align="left">Art cannot be Deductive</td><td align="right" valign="top"><a href="#Page_548">548</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_XII_5">5.</a></td><td align="left">Every Art consists of truths of Science, arranged in the order suitable for some practical use</td><td align="right" valign="top"><a href="#Page_549">549</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_XII_6">6.</a></td><td align="left">Teleology, or the Doctrine of Ends</td><td align="right" valign="top"><a href="#Page_550">550</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_XII_7">7.</a></td><td align="left">Necessity of an ultimate standard, or first principle of Teleology</td><td align="right" valign="top"><a href="#Page_552">552</a></td></tr> +<tr><td align="right" valign="top"><a href="#BOOK_VI_CHAPTER_XII_8">8.</a></td><td align="left">Conclusion</td><td align="right" valign="top"><a href="#Page_554">554</a></td></tr> +</table></div> + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_1" id="Page_1">[Pg 1]</a></span></p> +<h2><a name="BOOK_III" id="BOOK_III"></a>BOOK III.<br /> +<i>CONTINUED.</i><br /> +OF INDUCTION.</h2> + + +<p><span class="pagenum"><a name="Page_2" id="Page_2">[Pg 2]</a></span></p> +<blockquote><p>"In such cases the inductive and deductive methods of inquiry may be +said to go hand in hand, the one verifying the conclusions deduced by +the other; and the combination of experiment and theory, which may thus +be brought to bear in such cases, forms an engine of discovery +infinitely more powerful than either taken separately. This state of any +department of science is perhaps of all others the most interesting, and +that which promises the most to research."—<span class="smcap">Sir J. Herschel</span>, <i>Discourse +on the Study of Natural Philosophy</i>.</p></blockquote> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_3" id="Page_3">[Pg 3]</a></span></p> +<h3><a name="BOOK_III_CHAPTER_XIV" id="BOOK_III_CHAPTER_XIV"></a>CHAPTER XIV.<br /> +OF THE LIMITS TO THE EXPLANATION OF LAWS OF NATURE; AND OF HYPOTHESES.</h3> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XIV_1">§ 1.</a> The preceding considerations have led us to recognise a distinction +between two kinds of laws, or observed uniformities in nature: ultimate +laws, and what may be termed derivative laws. Derivative laws are such +as are deducible from, and may, in any of the modes which we have +pointed out, be resolved into, other and more general ones. Ultimate +laws are those which cannot. We are not sure that any of the +uniformities with which we are yet acquainted are ultimate laws; but we +know that there must be ultimate laws; and that every resolution of a +derivative law into more general laws, brings us nearer to them.</p> + +<p>Since we are continually discovering that uniformities, not previously +known to be other than ultimate, are derivative, and resolvable into +more general laws; since (in other words) we are continually discovering +the explanation of some sequence which was previously known only as a +fact; it becomes an interesting question whether there are any necessary +limits to this philosophical operation, or whether it may proceed until +all the uniform sequences in nature are resolved into some one universal +law. For this seems, at first sight, to be the ultimatum towards which +the progress of induction, by the Deductive Method resting on a basis of +observation and experiment, is tending. Projects of this kind were +universal in the infancy of philosophy; any speculations which held out +a less brilliant prospect, being in those early times deemed not worth +pursuing. And the idea receives so much apparent countenance from the +nature of the most remarkable achievements of modern science, that +speculators are even now frequently <span class="pagenum"><a name="Page_4" id="Page_4">[Pg 4]</a></span>appearing, who profess either to +have solved the problem, or to suggest modes in which it may one day be +solved. Even where pretensions of this magnitude are not made, the +character of the solutions which are given or sought of particular +classes of phenomena, often involves such conceptions of what +constitutes explanation, as would render the notion of explaining all +phenomena whatever by means of some one cause or law, perfectly +admissible.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XIV_2">§ 2.</a> It is therefore useful to remark, that the ultimate Laws of Nature +cannot possibly be less numerous than the distinguishable sensations or +other feelings of our nature;—those, I mean, which are distinguishable +from one another in quality, and not merely in quantity or degree. For +example; since there is a phenomenon <i>sui generis</i>, called colour, which +our consciousness testifies to be not a particular degree of some other +phenomenon, as heat or odour or motion, but intrinsically unlike all +others, it follows that there are ultimate laws of colour; that though +the facts of colour may admit of explanation, they never can be +explained from laws of heat or odour alone, or of motion alone, but that +however far the explanation may be carried, there will always remain in +it a law of colour. I do not mean that it might not possibly be shown +that some other phenomenon, some chemical or mechanical action for +example, invariably precedes, and is the cause of, every phenomenon of +colour. But though this, if proved, would be an important extension of +our knowledge of nature, it would not explain how or why a motion, or a +chemical action, can produce a sensation of colour; and however diligent +might be our scrutiny of the phenomena, whatever number of hidden links +we might detect in the chain of causation terminating in the colour, the +last link would still be a law of colour, not a law of motion, nor of +any other phenomenon whatever. Nor does this observation apply only to +colour, as compared with any other of the great classes of sensations; +it applies to every particular colour, as compared with others. White +colour can in no manner be explained exclusively by the laws of the +production of red colour. In any attempt to explain it, we cannot <span class="pagenum"><a name="Page_5" id="Page_5">[Pg 5]</a></span>but +introduce, as one element of the explanation, the proposition that some +antecedent or other produces the sensation of white.</p> + +<p>The ideal limit, therefore, of the explanation of natural phenomena +(towards which as towards other ideal limits we are constantly tending, +without the prospect of ever completely attaining it) would be to show +that each distinguishable variety of our sensations, or other states of +consciousness, has only one sort of cause; that, for example, whenever +we perceive a white colour, there is some one condition or set of +conditions which is always present, and the presence of which always +produces in us that sensation. As long as there are several known modes +of production of a phenomenon, (several different substances, for +instance, which have the property of whiteness, and between which we +cannot trace any other resemblance,) so long it is not impossible that +one of these modes of production may be resolved into another, or that +all of them may be resolved into some more general mode of production +not hitherto recognised. But when the modes of production are reduced to +one, we cannot, in point of simplification, go any further. This one may +not, after all, be the ultimate mode; there may be other links to be +discovered between the supposed cause and the effect; but we can only +further resolve the known law, by introducing some other law hitherto +unknown; which will not diminish the number of ultimate laws.</p> + +<p>In what cases, accordingly, has science been most successful in +explaining phenomena, by resolving their complex laws into laws of +greater simplicity and generality? Hitherto chiefly in cases of the +propagation of various phenomena through space: and, first and +principally, the most extensive and important of all facts of that +description, the fact of motion. Now this is exactly what might be +expected from the principles here laid down. Not only is motion one of +the most universal of all phenomena, it is also (as might be expected +from that circumstance) one of those which, apparently at least, are +produced in the greatest number of ways; but the phenomenon itself is +always, to our sensations, the same in every respect but degree. +<span class="pagenum"><a name="Page_6" id="Page_6">[Pg 6]</a></span>Differences of duration, or of velocity, are evidently differences in +degree only; and differences of direction in space, which alone has any +semblance of being a distinction in kind, entirely disappear (so far as +our sensations are concerned) by a change in our own position; indeed +the very same motion appears to us, according to our position, to take +place in every variety of direction, and motions in every different +direction to take place in the same. And again, motion in a straight +line and in a curve are no otherwise distinct than that the one is +motion continuing in the same direction, the other is motion which at +each instant changes its direction. There is, therefore, according to +the principles I have stated, no absurdity in supposing that all motion +may be produced in one and the same way; by the same kind of cause. +Accordingly, the greatest achievements in physical science have +consisted in resolving one observed law of the production of motion into +the laws of other known modes of production, or the laws of several such +modes into one more general mode; as when the fall of bodies to the +earth, and the motions of the planets, were brought under the one law of +the mutual attraction of all particles of matter; when the motions said +to be produced by magnetism were shown to be produced by electricity; +when the motions of fluids in a lateral direction, or even contrary to +the direction of gravity, were shown to be produced by gravity; and the +like. There is an abundance of distinct causes of motion still +unresolved into one another; gravitation, heat, electricity, chemical +action, nervous action, and so forth; but whether the efforts of the +present generation of savans to resolve all these different modes of +production into one, are ultimately successful or not, the attempt so to +resolve them is perfectly legitimate. For though these various causes +produce, in other respects, sensations intrinsically different, and are +not, therefore, capable of being resolved into one another, yet in so +far as they all produce motion, it is quite possible that the immediate +antecedent of the motion may in all these different cases be the same; +nor is it impossible that these various agencies themselves may, as the +new doctrines assert, all of them have for their own immediate +antecedent, modes of molecular motion.</p> + +<p><span class="pagenum"><a name="Page_7" id="Page_7">[Pg 7]</a></span></p><p>We need not extend our illustration to other cases, as for instance to +the propagation of light, sound, heat, electricity, &c. through space, +or any of the other phenomena which have been found susceptible of +explanation by the resolution of their observed laws into more general +laws. Enough has been said to display the difference between the kind of +explanation and resolution of laws which is chimerical, and that of +which the accomplishment is the great aim of science; and to show into +what sort of elements the resolution must be effected, if at all.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XIV_3">§ 3.</a> As, however, there is scarcely any one of the principles of a true +method of philosophizing which does not require to be guarded against +errors on both sides, I must enter a caveat against another +misapprehension, of a kind directly contrary to the preceding. M. Comte, +among other occasions on which he has condemned, with some asperity, any +attempt to explain phenomena which are "evidently primordial," (meaning, +apparently, no more than that every peculiar phenomenon must have at +least one peculiar and therefore inexplicable law,) has spoken of the +attempt to furnish any explanation of the colour belonging to each +substance, "la couleur élémentaire propre à chaque substance," as +essentially illusory. "No one," says he, "in our time attempts to +explain the particular specific gravity of each substance or of each +structure. Why should it be otherwise as to the specific colour, the +notion of which is undoubtedly no less primordial?"<a name="FNanchor_1_1" id="FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a></p> + +<p>Now although, as he elsewhere observes, a colour must always remain a +different thing from a weight or a sound, varieties of colour might +nevertheless follow, or correspond to, given varieties of weight, or +sound, or some other phenomenon as different as these are from colour +itself. It is one question what a thing is, and another what it depends +on; and though to ascertain the conditions of an elementary phenomenon +is not to obtain any new insight into the nature of <span class="pagenum"><a name="Page_8" id="Page_8">[Pg 8]</a></span>the phenomenon +itself, that is no reason against attempting to discover the conditions. +The interdict against endeavouring to reduce distinctions of colour to +any common principle, would have held equally good against a like +attempt on the subject of distinctions of sound; which nevertheless have +been found to be immediately preceded and caused by distinguishable +varieties in the vibrations of elastic bodies: though a sound, no doubt, +is quite as different as a colour is from any motion of particles, +vibratory or otherwise. We might add, that, in the case of colours, +there are strong positive indications that they are not ultimate +properties of the different kinds of substances, but depend on +conditions capable of being superinduced upon all substances; since +there is no substance which cannot, according to the kind of light +thrown upon it, be made to assume almost any colour; and since almost +every change in the mode of aggregation of the particles of the same +substance, is attended with alterations in its colour, and in its +optical properties generally.</p> + +<p>The real defect in the attempts which have been made to account for +colours by the vibrations of a fluid, is not that the attempt itself is +unphilosophical, but that the existence of the fluid, and the fact of +its vibratory motion, are not proved; but are assumed, on no other +ground than the facility they are supposed to afford of explaining the +phenomena. And this consideration leads to the important question of the +proper use of scientific hypotheses; the connexion of which with the +subject of the explanation of the phenomena of nature, and of the +necessary limits to that explanation, needs not be pointed out.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XIV_4">§ 4.</a> An hypothesis is 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. If the hypothesis relates to the +cause, or mode of production of a phenomenon, it will serve, <span class="pagenum"><a name="Page_9" id="Page_9">[Pg 9]</a></span>if +admitted, to explain such facts as are found capable of being deduced +from it. And this explanation is the purpose of many, if not most, +hypotheses. Since explaining, in the scientific sense, means resolving +an uniformity which is not a law of causation, into the laws of +causation from which it results, or a complex law of causation into +simpler and more general ones from which it is capable of being +deductively inferred; if there do not exist any known laws which fulfil +this requirement, we may feign or imagine some which would fulfil it; +and this is making an hypothesis.</p> + +<p>An hypothesis being a mere supposition, there are no other limits to +hypotheses than those of the human imagination; we may, if we please, +imagine, by way of accounting for an effect, some cause of a kind +utterly unknown, and acting according to a law altogether fictitious. +But as hypotheses of this sort would not have any of the plausibility +belonging to those which ally themselves by analogy with known laws of +nature, and besides would not supply the want which arbitrary hypotheses +are generally invented to satisfy, by enabling the imagination to +represent to itself an obscure phenomenon in a familiar light; there is +probably no hypothesis in the history of science in which both the agent +itself and the law of its operation were fictitious. Either the +phenomenon assigned as the cause is real, but the law according to which +it acts, merely supposed; or the cause is fictitious, but is supposed to +produce its effects according to laws similar to those of some known +class of phenomena. An instance of the first kind is afforded by the +different suppositions made respecting the law of the planetary central +force, anterior to the discovery of the true law, that the force varies +as the inverse square of the distance; which also suggested itself to +Newton, in the first instance, as an hypothesis, and was verified by +proving that it led deductively to Kepler's laws. Hypotheses of the +second kind are such as the vortices of Descartes, which were +fictitious, but were supposed to obey the known laws of rotatory motion; +or the two rival hypotheses respecting the nature of light, the one +ascribing the phenomena to a fluid emitted from all luminous bodies, the +other (now generally received) attributing <span class="pagenum"><a name="Page_10" id="Page_10">[Pg 10]</a></span>them to vibratory motions +among the particles of an ether pervading all space. Of the existence of +either fluid there is no evidence, save the explanation they are +calculated to afford of some of the phenomena; but they are supposed to +produce their effects according to known laws; the ordinary laws of +continued locomotion in the one case, and in the other, those of the +propagation of undulatory movements among the particles of an elastic +fluid.</p> + +<p>According to the foregoing remarks, hypotheses are invented to enable +the Deductive Method to be earlier applied to phenomena. But<a name="FNanchor_2_2" id="FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a> in order +to discover the cause of any phenomenon by the Deductive Method, the +process must consist of three parts; induction, ratiocination, and +verification. Induction, (the place of which, however, may be supplied +by a prior deduction,) to ascertain the laws of the causes; +ratiocination, to compute from those laws, how the causes will operate +in the particular combination known to exist in the case in hand; +verification, by comparing this calculated effect with the actual +phenomenon. No one of these three parts of the process can be dispensed +with. In the deduction which proves the identity of gravity with the +central force of the solar system, all the three are found. First, it is +proved from the moon's motions, that the earth attracts her with a force +varying as the inverse square of the distance. This (though partly +dependent on prior deductions) corresponds to the first, or purely +inductive, step, the ascertainment of the law of the cause. Secondly, +from this law, and from the knowledge previously obtained of the moon's +mean distance from the earth, and of the actual amount of her deflexion +from the tangent, it is ascertained with what rapidity the earth's +attraction would cause the moon to fall, if she were no further off, and +no more acted upon by extraneous forces, than terrestrial bodies are: +that is the second step, the ratiocination. Finally, this calculated +velocity being compared with the observed velocity with which all heavy +bodies fall, by mere gravity, towards the surface of the earth, (sixteen +feet in the first second, forty-eight <span class="pagenum"><a name="Page_11" id="Page_11">[Pg 11]</a></span>in the second, and so forth, in +the ratio of the odd numbers, 1, 3, 5, &c.,) the two quantities are +found to agree. The order in which the steps are here presented, was not +that of their discovery; but it is their correct logical order, as +portions of the proof that the same attraction of the earth which causes +the moon's motion, causes also the fall of heavy bodies to the earth: a +proof which is thus complete in all its parts.</p> + +<p>Now, the Hypothetical Method suppresses the first of the three steps, +the induction to ascertain the law; and contents itself with the other +two operations, ratiocination and verification; the law which is +reasoned from, being assumed, instead of proved.</p> + +<p>This process may evidently be legitimate on one supposition, namely, if +the nature of the case be such that the final step, the verification, +shall amount to, and fulfil the conditions of, a complete induction. We +want to be assured that the law we have hypothetically assumed is a true +one; and its leading deductively to true results will afford this +assurance, provided the case be such that a false law cannot lead to a +true result; provided no law, except the very one which we have assumed, +can lead deductively to the same conclusions which that leads to. And +this proviso is often realized. For example, in the very complete +specimen of deduction which we just cited, the original major premise of +the ratiocination, the law of the attractive force, was ascertained in +this mode; by this legitimate employment of the Hypothetical Method. +Newton began by an assumption, that the force which at each instant +deflects a planet from its rectilineal course, and makes it describe a +curve round the sun, is a force tending directly towards the sun. He +then proved that if this be so, the planet will describe, as we know by +Kepler's first law that it does describe, equal areas in equal times; +and, lastly, he proved that if the force acted in any other direction +whatever, the planet would not describe equal areas in equal times. It +being thus shown that no other hypothesis would accord with the facts, +the assumption was proved; the hypothesis became an inductive truth. Not +only <span class="pagenum"><a name="Page_12" id="Page_12">[Pg 12]</a></span>did Newton ascertain by this hypothetical process the direction of +the deflecting force; he proceeded in exactly the same manner to +ascertain the law of variation of the quantity of that force. He assumed +that the force varied inversely as the square of the distance; showed +that from this assumption the remaining two of Kepler's laws might be +deduced; and finally, that any other law of variation would give results +inconsistent with those laws, and inconsistent, therefore, with the real +motions of the planets, of which Kepler's laws were known to be a +correct expression.</p> + +<p>I have said that in this case the verification fulfils the conditions of +an induction: but an induction of what sort? On examination we find that +it conforms to the canon of the Method of Difference. It affords the two +instances, A B C, <i>a b c</i>, and B C, <i>b c</i>. A represents central force; A +B C, the planets <i>plus</i> a central force; B C, the planets apart from a +central force. The planets with a central force give <i>a</i>, areas +proportional to the times; the planets without a central force give <i>b +c</i> (a set of motions) without <i>a</i>, or with something else instead of +<i>a</i>. This is the Method of Difference in all its strictness. It is true, +the two instances which the method requires are obtained in this case, +not by experiment, but by a prior deduction. But that is of no +consequence. It is immaterial what is the nature of the evidence from +which we derive the assurance that A B C will produce <i>a b c</i>, and B C +only <i>b c</i>; it is enough that we have that assurance. In the present +case, a process of reasoning furnished Newton with the very instances, +which, if the nature of the case had admitted of it, he would have +sought by experiment.</p> + +<p>It is thus perfectly possible, and indeed is a very common occurrence, +that what was an hypothesis at the beginning of the inquiry, becomes a +proved law of nature before its close. But in order that this should +happen, we must be able, either by deduction or experiment, to obtain +<i>both</i> the instances which the Method of Difference requires. That we +are able from the hypothesis to deduce the known facts, gives only the +affirmative instance, A B C, <i>a b c</i>. It is equally necessary that we +should be able to obtain, as Newton did, the negative <span class="pagenum"><a name="Page_13" id="Page_13">[Pg 13]</a></span>instance B C, <i>b +c</i>; by showing that no antecedent, except the one assumed in the +hypothesis, would in conjunction with B C produce <i>a</i>.</p> + +<p>Now it appears to me that this assurance cannot be obtained, when the +cause assumed in the hypothesis is an unknown cause, imagined solely to +account for <i>a</i>. When we are only seeking to determine the precise law +of a cause already ascertained, or to distinguish the particular agent +which is in fact the cause, among several agents of the same kind, one +or other of which it is already known to be, we may then obtain the +negative instance. An inquiry, which of the bodies of the solar system +causes by its attraction some particular irregularity in the orbit or +periodic time of some satellite or comet, would be a case of the second +description. Newton's was a case of the first. If it had not been +previously known that the planets were hindered from moving in straight +lines by some force tending towards the interior of their orbit, though +the exact direction was doubtful; or if it had not been known that the +force increased in some proportion or other as the distance diminished, +and diminished as it increased; Newton's argument would not have proved +his conclusion. These facts, however, being already certain, the range +of admissible suppositions was limited to the various possible +directions of a line, and the various possible numerical relations +between the variations of the distance, and the variations of the +attractive force: now among these it was easily shown that different +suppositions could not lead to identical consequences.</p> + +<p>Accordingly, Newton could not have performed his second great scientific +operation, that of identifying terrestrial gravity with the central +force of the solar system, by the same hypothetical method. When the law +of the moon's attraction had been proved from the data of the moon +itself, then on finding the same law to accord with the phenomena of +terrestrial gravity, he was warranted in adopting it as the law of those +phenomena likewise; but it would not have been allowable for him, +without any lunar data, to assume that the moon was attracted towards +the earth with a force as the inverse square <span class="pagenum"><a name="Page_14" id="Page_14">[Pg 14]</a></span>of the distance, merely +because that ratio would enable him to account for terrestrial gravity: +for it would have been impossible for him to prove that the observed law +of the fall of heavy bodies to the earth could not result from any +force, save one extending to the moon, and proportional to the inverse +square.</p> + +<p>It appears, then, to be a condition of a genuinely scientific +hypothesis, that it be not destined always to remain an hypothesis, but +be of such a nature as to be either proved or disproved by comparison +with observed facts. This condition is fulfilled when the effect is +already known to depend on the very cause supposed, and the hypothesis +relates only to the precise mode of dependence; the law of the variation +of the effect according to the variations in the quantity or in the +relations of the cause. With these may be classed the hypotheses which +do not make any supposition with regard to causation, but only with +regard to the law of correspondence between facts which accompany each +other in their variations, though there may be no relation of cause and +effect between them. Such were the different false hypotheses which +Kepler made respecting the law of the refraction of light. It was known +that the direction of the line of refraction varied with every variation +in the direction of the line of incidence, but it was not known how; +that is, what changes of the one corresponded to the different changes +of the other. In this case any law, different from the true one, must +have led to false results. And, lastly, we must add to these, all +hypothetical modes of merely representing, or <i>describing</i>, phenomena; +such as the hypothesis of the ancient astronomers that the heavenly +bodies moved in circles; the various hypotheses of excentrics, +deferents, and epicycles, which were added to that original hypothesis; +the nineteen false hypotheses which Kepler made and abandoned respecting +the form of the planetary orbits; and even the doctrine in which he +finally rested, that those orbits are ellipses, which was but an +hypothesis like the rest until verified by facts.</p> + +<p>In all these cases, verification is proof; if the supposition accords +with the phenomena there needs no other evidence <span class="pagenum"><a name="Page_15" id="Page_15">[Pg 15]</a></span>of it. But in order +that this may be the case, I conceive it to be necessary, when the +hypothesis relates to causation, that the supposed cause should not only +be a real phenomenon, something actually existing in nature, but should +be already known to exercise, or at least to be capable of exercising, +an influence of some sort over the effect. In any other case, it is no +evidence of the truth of the hypothesis that we are able to deduce the +real phenomena from it.</p> + +<p>Is it, then, never allowable, in a scientific hypothesis, to assume a +cause; but only to ascribe an assumed law to a known cause? I do not +assert this. I only say, that in the latter case alone can the +hypothesis be received as true merely because it explains the phenomena: +in the former case it is only useful by suggesting a line of +investigation which may possibly terminate in obtaining real proof. For +this purpose, as is justly remarked by M. Comte, it is indispensable +that the cause suggested by the hypothesis should be in its own nature +susceptible of being proved by other evidence. This seems to be the +philosophical import of Newton's maxim, (so often cited with approbation +by subsequent writers,) that the cause assigned for any phenomenon must +not only be such as if admitted would explain the phenomenon, but must +also be a <i>vera causa</i>. What he meant by a <i>vera causa</i> Newton did not +indeed very explicitly define; and Dr. Whewell, who dissents from the +propriety of any such restriction upon the latitude of framing +hypotheses, has had little difficulty in showing<a name="FNanchor_3_3" id="FNanchor_3_3"></a><a href="#Footnote_3_3" class="fnanchor">[3]</a> that his conception +of it was neither precise nor consistent with itself: accordingly his +optical theory was a signal instance of the violation of his own rule. +It is certainly not necessary that the cause assigned should be a cause +already known; else how could we ever become acquainted with any new +cause? But what is true in the maxim is, that the cause, though not +known previously, should be capable of being known thereafter; that its +existence should be capable of being detected, and its connexion with +the effect ascribed to it should be susceptible of being proved, <span class="pagenum"><a name="Page_16" id="Page_16">[Pg 16]</a></span>by +independent evidence. The hypothesis, by suggesting observations and +experiments, puts us on the road to that independent evidence if it be +really attainable; and till it be attained, the hypothesis ought not to +count for more than a conjecture.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XIV_5">§ 5.</a> This function, however, of hypotheses, is one which must be +reckoned absolutely indispensable in science. When Newton said, +"Hypotheses non fingo," he did not mean that he deprived himself of the +facilities of investigation afforded by assuming in the first instance +what he hoped ultimately to be able to prove. Without such assumptions, +science could never have attained its present state: they are necessary +steps in the progress to something more certain; and nearly everything +which is now theory was once hypothesis. Even in purely experimental +science, some inducement is necessary for trying one experiment rather +than another; and though it is abstractedly possible that all the +experiments which have been tried, might have been produced by the mere +desire to ascertain what would happen in certain circumstances, without +any previous conjecture as to the result; yet, in point of fact, those +unobvious, delicate, and often cumbrous and tedious processes of +experiment, which have thrown most light upon the general constitution +of nature, would hardly ever have been undertaken by the persons or at +the time they were, unless it had seemed to depend on them whether some +general doctrine or theory which had been suggested, but not yet proved, +should be admitted or not. If this be true even of merely experimental +inquiry, the conversion of experimental into deductive truths could +still less have been effected without large temporary assistance from +hypotheses. The process of tracing regularity in any complicated, and at +first sight confused set of appearances, is necessarily tentative: we +begin by making any supposition, even a false one, to see what +consequences will follow from it; and by observing how these differ from +the real phenomena, we learn what corrections to make in our assumption. +The simplest supposition which accords with the more obvious facts, is +the best to begin with; because <span class="pagenum"><a name="Page_17" id="Page_17">[Pg 17]</a></span>its consequences are the most easily +traced. This rude hypothesis is then rudely corrected, and the operation +repeated; and the comparison of the consequences deducible from the +corrected hypothesis, with the observed facts, suggests still further +correction, until the deductive results are at last made to tally with +the phenomena. "Some fact is as yet little understood, or some law is +unknown: we frame on the subject an hypothesis as accordant as possible +with the whole of the data already possessed; and the science, being +thus enabled to move forward freely, always ends by leading to new +consequences capable of observation, which either confirm or refute, +unequivocally, the first supposition." Neither induction nor deduction +would enable us to understand even the simplest phenomena, "if we did +not often commence by anticipating on the results; by making a +provisional supposition, at first essentially conjectural, as to some of +the very notions which constitute the final object of the inquiry."<a name="FNanchor_4_4" id="FNanchor_4_4"></a><a href="#Footnote_4_4" class="fnanchor">[4]</a> +Let any one watch the manner in which he himself unravels a complicated +mass of evidence; let him observe how, for instance, he elicits the true +history of any occurrence from the involved statements of one or of many +witnesses: he will find that he does not take all the items of evidence +into his mind at once, and attempt to weave them together: he +extemporises, from a few of the particulars, a first rude theory of the +mode in which the facts took place, and then looks at the other +statements one by one, to try whether they can be reconciled with that +provisional theory, or what alterations or additions it requires to make +it square with them. In this way, which has been justly compared to the +Methods of Approximation of mathematicians, we arrive, by means of +hypotheses, at conclusions not hypothetical.<a name="FNanchor_5_5" id="FNanchor_5_5"></a><a href="#Footnote_5_5" class="fnanchor">[5]</a></p> + + +<p><span class="pagenum"><a name="Page_18" id="Page_18">[Pg 18]</a></span></p><p class="newsection"><a name="BOOK_III_CHAPTER_XIV_6">§ 6.</a> It is perfectly consistent with the spirit of the method, to +assume in this provisional manner not only an hypothesis <span class="pagenum"><a name="Page_19" id="Page_19">[Pg 19]</a></span>respecting the +law of what we already know to be the cause, but an hypothesis +respecting the cause itself. It is allowable, useful, and often even +necessary, to begin by asking ourselves what cause <i>may</i> have produced +the effect, in order that we may know in what direction to look out for +evidence to determine whether it actually <i>did</i>. The vortices of +Descartes would have been a perfectly legitimate hypothesis, if it had +been possible, by any mode of exploration which we could entertain the +hope of ever possessing, to bring the reality of the vortices, as a fact +in nature, conclusively to the test of observation. The hypothesis was +vicious, simply because it could not lead to any course of investigation +capable of converting it from an hypothesis into a proved fact. It might +chance to be <i>dis</i>proved, either by some want of correspondence with the +phenomena it purported to explain, or (as actually happened) by some +extraneous fact. "The free passage of comets through the spaces in which +these vortices should have been, convinced men that these vortices did +not exist."<a name="FNanchor_6_6" id="FNanchor_6_6"></a><a href="#Footnote_6_6" class="fnanchor">[6]</a> But the hypothesis would have been false, though no such +direct evidence of its falsity had been procurable. Direct evidence of +its truth there could not be.</p> + +<p>The prevailing hypothesis of a luminiferous ether, in other respects not +without analogy to that of Descartes, is not in its own nature entirely +cut off from the possibility of direct evidence in its favour. It is +well known that the difference between the calculated and the observed +times of the periodical return of Encke's comet, has led to a conjecture +that a medium capable of opposing resistance to motion is diffused +through space. If this surmise should be confirmed, in the course of +ages, by the gradual accumulation of a similar variance in the case of +the other bodies of the solar system, the luminiferous ether would have +made a considerable advance towards the character of a <i>vera causa</i>, +since the existence would have been ascertained of a great cosmical +agent, possessing some of the attributes which the hypothesis assumes; +though there would still remain many difficulties, and the +identification of the <span class="pagenum"><a name="Page_20" id="Page_20">[Pg 20]</a></span>ether with the resisting medium would even, I +imagine, give rise to new ones. At present, however, this supposition +cannot be looked upon as more than a conjecture; the existence of the +ether still rests on the possibility of deducing from its assumed laws a +considerable number of the phenomena of light; and this evidence I +cannot regard as conclusive, because we cannot have, in the case of such +an hypothesis, the assurance that if the hypothesis be false it must +lead to results at variance with the true facts.</p> + +<p>Accordingly, most thinkers of any degree of sobriety allow, that an +hypothesis of this kind is not to be received as probably true because +it accounts for all the known phenomena; since this is a condition +sometimes fulfilled tolerably well by two conflicting hypotheses; while +there are probably a thousand more which are equally possible, but +which, for want of anything analogous in our experience, our minds are +unfitted to conceive. But it seems to be thought that an hypothesis of +the sort in question is entitled to a more favourable reception, if, +besides accounting for all the facts previously known, it has led to the +anticipation and prediction of others which experience afterwards +verified; as the undulatory theory of light led to the prediction, +subsequently realized by experiment, that two luminous rays might meet +each other in such a manner as to produce darkness. Such predictions and +their fulfilment are, indeed, well calculated to impress the uninformed, +whose faith in science rests solely on similar coincidences between its +prophecies and what comes to pass. But it is strange that any +considerable stress should be laid upon such a coincidence by persons of +scientific attainments. If the laws of the propagation of light accord +with those of the vibrations of an elastic fluid in as many respects as +is necessary to make the hypothesis afford a correct expression of all +or most of the phenomena known at the time, it is nothing strange that +they should accord with each other in one respect more. Though twenty +such coincidences should occur, they would not prove the reality of the +undulatory ether; it would not follow that the phenomena of light were +results of the laws of elastic fluids, but <span class="pagenum"><a name="Page_21" id="Page_21">[Pg 21]</a></span>at most that they are +governed by laws partially identical with these; which, we may observe, +is already certain, from the fact that the hypothesis in question could +be for a moment tenable.<a name="FNanchor_7_7" id="FNanchor_7_7"></a><a href="#Footnote_7_7" class="fnanchor">[7]</a> Cases may be cited, even in our imperfect +acquaintance with nature, where agencies that we have good reason to +consider as radically distinct, produce their effects, or some of their +effects, according to laws which are identical. The law, for example, of +the inverse square of the distance, is the measure of the intensity not +only of gravitation, but (it is believed) of illumination, and of heat +diffused from a centre. Yet no one looks upon this identity as proving +similarity in the mechanism by which the three kinds of phenomena are +produced.</p> + +<p>According to Dr. Whewell, the coincidence of results predicted from an +hypothesis, with facts afterwards observed, amounts to a conclusive +proof of the truth of the theory. "If I copy a long series of letters, +of which the last half dozen are concealed, and if I guess these aright, +as is found to be the case when they are afterwards uncovered, this must +be because I have made out the import of the inscription. To say, that +because I have copied all that I could see, it is nothing strange that I +should guess those which I cannot see, would be absurd, without +supposing such a ground for guessing."<a name="FNanchor_8_8" id="FNanchor_8_8"></a><a href="#Footnote_8_8" class="fnanchor">[8]</a> If any one, from examining the +greater part of a long inscription, can interpret the characters so that +the inscription gives a rational meaning in a known language, there is a +strong presumption that his interpretation is correct; but I do not +think the presumption much increased by his being able to guess the few +remaining letters without seeing them: for we should naturally expect +(when the nature of the case excludes <span class="pagenum"><a name="Page_22" id="Page_22">[Pg 22]</a></span>chance) that even an erroneous +interpretation which accorded with all the visible parts of the +inscription would accord also with the small remainder; as would be the +case, for example, if the inscription had been designedly so contrived +as to admit of a double sense. I assume that the uncovered characters +afford an amount of coincidence too great to be merely casual: otherwise +the illustration is not a fair one. No one supposes the agreement with +the phenomena of light with the theory of undulations to be merely +fortuitous. It must arise from the actual identity of some of the laws +of undulations with some of those of light: and if there be that +identity, it is reasonable to suppose that its consequences would not +end with the phenomena which first suggested the identification, nor be +even confined to such phenomena as were known at the time. But it does +not follow, because some of the laws agree with those of undulations, +that there are any actual undulations; no more than it followed because +some (though not so many) of the same laws agreed with those of the +projection of particles, that there was actual emission of particles. +Even the undulatory hypothesis does not account for all the phenomena of +light. The natural colours of objects, the compound nature of the solar +ray, the absorption of light, and its chemical and vital action, the +hypothesis leaves as mysterious as it found them; and some of these +facts are, at least apparently, more reconcileable with the emission +theory than with that of Young and Fresnel. Who knows but that some +third hypothesis, including all these phenomena, may in time leave the +undulatory theory as far behind as that has left the theory of Newton +and his successors?</p> + +<p>To the statement, that the condition of accounting for all the known +phenomena is often fulfilled equally well by two conflicting hypotheses, +Dr. Whewell makes answer that he knows "of no such case in the history +of science, where the phenomena are at all numerous and complicated."<a name="FNanchor_9_9" id="FNanchor_9_9"></a><a href="#Footnote_9_9" class="fnanchor">[9]</a> +Such an affirmation, by a writer of Dr. Whewell's minute acquaintance +with the history of science, would carry great authority, if he <span class="pagenum"><a name="Page_23" id="Page_23">[Pg 23]</a></span>had +not, a few pages before, taken pains to refute it,<a name="FNanchor_10_10" id="FNanchor_10_10"></a><a href="#Footnote_10_10" class="fnanchor">[10]</a> by maintaining +that even the exploded scientific hypotheses might always, or almost +always, have been so modified as to make them correct representations of +the phenomena. The hypothesis of vortices, he tells us, was, by +successive modifications, brought to coincide in its results with the +Newtonian theory and with the facts. The vortices did not indeed explain +all the phenomena which the Newtonian theory was ultimately found to +account for, such as the precession of the equinoxes; but this +phenomenon was not, at the time, in the contemplation of either party, +as one of the facts to be accounted for. All the facts which they did +contemplate, we may believe on Dr. Whewell's authority to have accorded +as accurately with the Cartesian hypothesis, in its finally improved +state, as with Newton's.</p> + +<p>But it is not, I conceive, a valid reason for accepting any given +hypothesis, that we are unable to imagine any other which will account +for the facts. There is no necessity for supposing that the true +explanation must be one which, with only our present experience, we +could imagine. Among the natural agents with which we are acquainted, +the vibrations of an elastic fluid may be the only one whose laws bear a +close resemblance to those of light; but we cannot tell that there does +not exist an unknown cause, other than an elastic ether diffused through +space, yet producing effects identical in some respects with those which +would result from the undulations of such an ether. To assume that no +such cause can exist, appears to me an extreme case of assumption +without evidence.</p> + +<p>I do not mean to condemn those who employ themselves in working out into +detail this sort of hypotheses; it is useful to ascertain what are the +known phenomena, to the laws of which those of the subject of inquiry +bear the greatest, or even a great analogy, since this may suggest (as +in the case of the luminiferous ether it actually did) experiments to +determine whether the analogy which goes so far does not <span class="pagenum"><a name="Page_24" id="Page_24">[Pg 24]</a></span>extend still +further. But that, in doing this, we should imagine ourselves to be +seriously inquiring whether the hypothesis of an ether, an electric +fluid, or the like, is true; that we should fancy it possible to obtain +the assurance that the phenomena are produced in that way and no other; +seems to me, I confess, unworthy of the present improved conceptions of +the methods of physical science. And at the risk of being charged with +want of modesty, I cannot help expressing astonishment that a +philosopher of Dr. Whewell's abilities and attainments should have +written an elaborate treatise on the philosophy of induction, in which +he recognises absolutely no mode of induction except that of trying +hypothesis after hypothesis until one is found which fits the phenomena; +which one, when found, is to be assumed as true, with no other +reservation than that if on re-examination it should appear to assume +more than is needful for explaining the phenomena, the superfluous part +of the assumption should be cut off. And this without the slightest +distinction between the cases in which it may be known beforehand that +two different hypotheses cannot lead to the same result, and those in +which, for aught we can ever know, the range of suppositions, all +equally consistent with the phenomena, may be infinite.<a name="FNanchor_11_11" id="FNanchor_11_11"></a><a href="#Footnote_11_11" class="fnanchor">[11]</a></p> + + +<p><span class="pagenum"><a name="Page_25" id="Page_25">[Pg 25]</a></span></p><p class="newsection"><a name="BOOK_III_CHAPTER_XIV_7">§ 7.</a> It is necessary, before quitting the subject of hypotheses, to +guard against the appearance of reflecting upon the scientific value of +several branches of physical inquiry, which, though only in their +infancy, I hold to be strictly inductive. There is a great difference +between inventing agencies to account for classes of phenomena, and +endeavouring, in conformity with known laws, to conjecture what former +collocations of known agents may have given birth to individual facts +still in existence. The latter is the legitimate operation of inferring +from an observed effect, the existence, in time past, of a cause similar +to that by which we know it to be produced in all cases in which we have +actual experience of its origin. This, for example, is the scope of the +inquiries of geology; and they are no more illogical or visionary than +judicial inquiries, which also aim at discovering a past event by +inference from those of its effects which still subsist. As we can +ascertain whether a man was murdered or died a natural death, from the +indications exhibited by the corpse, the presence or absence of signs of +struggling on the ground or on the adjacent objects, the <span class="pagenum"><a name="Page_26" id="Page_26">[Pg 26]</a></span>marks of +blood, the footsteps of the supposed murderers, and so on, proceeding +throughout on uniformities ascertained by a perfect induction without +any mixture of hypothesis; so if we find, on and beneath the surface of +our planet, masses exactly similar to deposits from water, or to results +of the cooling of matter melted by fire, we may justly conclude that +such has been their origin; and if the effects, though similar in kind, +are on a far larger scale than any which are now produced, we may +rationally, and without hypothesis, conclude either that the causes +existed formerly with greater intensity, or that they have operated +during an enormous length of time. Further than this no geologist of +authority has, since the rise of the present enlightened school of +geological speculation, attempted to go.</p> + +<p>In many geological inquiries it doubtless happens that though the laws +to which the phenomena are ascribed are known laws, and the agents known +agents, those agents are not known to have been present in the +particular case. In the speculation respecting the igneous origin of +trap or granite, the fact does not admit of direct proof, that those +substances have been actually subjected to intense heat. But the same +thing might be said of all judicial inquiries which proceed on +circumstantial evidence. We can conclude that a man was murdered, though +it is not proved by the testimony of eye-witnesses that some person who +had the intention of murdering him was present on the spot. It is +enough, for most purposes, if no other known cause could have generated +the effects shown to have been produced.</p> + +<p>The celebrated speculation of Laplace concerning the origin of the earth +and planets, participates essentially in the inductive character of +modern geological theory. The speculation is, that the atmosphere of the +sun originally extended to the present limits of the solar system; from +which, by the process of cooling, it has contracted to its present +dimensions; and since, by the general principles of mechanics, the +rotation of the sun and of its accompanying atmosphere must increase in +rapidity as its volume diminishes, <span class="pagenum"><a name="Page_27" id="Page_27">[Pg 27]</a></span>the increased centrifugal force +generated by the more rapid rotation, overbalancing the action of +gravitation, has caused the sun to abandon successive rings of vaporous +matter, which are supposed to have condensed by cooling, and to have +become the planets. There is in this theory no unknown substance +introduced on supposition, nor any unknown property or law ascribed to a +known substance. The known laws of matter authorize us to suppose that a +body which is constantly giving out so large an amount of heat as the +sun is, must be progressively cooling, and that, by the process of +cooling, it must contract; if, therefore, we endeavour, from the present +state of that luminary, to infer its state in a time long past, we must +necessarily suppose that its atmosphere extended much farther than at +present, and we are entitled to suppose that it extended as far as we +can trace effects such as it might naturally leave behind it on +retiring; and such the planets are. These suppositions being made, it +follows from known laws that successive zones of the solar atmosphere +might be abandoned; that these would continue to revolve round the sun +with the same velocity as when they formed part of its substance; and +that they would cool down, long before the sun itself, to any given +temperature, and consequently to that at which the greater part of the +vaporous matter of which they consisted would become liquid or solid. +The known law of gravitation would then cause them to agglomerate in +masses, which would assume the shape our planets actually exhibit; would +acquire, each about its own axis, a rotatory movement; and would in that +state revolve, as the planets actually do, about the sun, in the same +direction with the sun's rotation, but with less velocity, because in +the same periodic time which the sun's rotation occupied when his +atmosphere extended to that point. There is thus, in Laplace's theory, +nothing, strictly speaking, hypothetical: it is an example of legitimate +reasoning from a present effect to a possible past cause, according to +the known laws of that cause. The theory therefore is, as I have said, +of a similar character to the theories of geologists; but considerably +inferior <span class="pagenum"><a name="Page_28" id="Page_28">[Pg 28]</a></span>to them in point of evidence. Even if it were proved (which it +is not) that the conditions necessary for determining the breaking off +of successive rings would certainly occur; there would still be a much +greater chance of error in assuming that the existing laws of nature are +the same which existed at the origin of the solar system, than in merely +presuming (with geologists) that those laws have lasted through a few +revolutions and transformations of a single one among the bodies of +which that system is composed.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_29" id="Page_29">[Pg 29]</a></span></p> +<h3><a name="BOOK_III_CHAPTER_XV" id="BOOK_III_CHAPTER_XV"></a>CHAPTER XV.<br /> +OF PROGRESSIVE EFFECTS; AND OF THE CONTINUED ACTION OF CAUSES.</h3> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XV_1">§ 1.</a> In the last four chapters we have traced the general outlines of +the theory of the generation of derivative laws from ultimate ones. In +the present chapter our attention will be directed to a particular case +of the derivation of laws from other laws, but a case so general, and so +important, as not only to repay, but to require, a separate examination. +This is, the case of a complex phenomenon resulting from one simple law, +by the continual addition of an effect to itself.</p> + +<p>There are some phenomena, some bodily sensations for example, which are +essentially instantaneous, and whose existence can only be prolonged by +the prolongation of the existence of the cause by which they are +produced. But most phenomena are in their own nature permanent; having +begun to exist, they would exist for ever unless some cause intervened +having a tendency to alter or destroy them. Such, for example, are all +the facts or phenomena which we call bodies. Water, once produced, will +not of itself relapse into a state of hydrogen and oxygen; such a change +requires some agent having the power of decomposing the compound. Such, +again, are the positions in space, and the movements, of bodies. No +object at rest alters its position without the intervention of some +conditions extraneous to itself; and when once in motion, no object +returns to a state of rest, or alters either its direction or its +velocity, unless some new external conditions are superinduced. It, +therefore, perpetually happens that a temporary cause gives rise to a +permanent effect. The contact of iron with moist air for a few hours, +produces a rust which may endure for centuries; or a projectile <span class="pagenum"><a name="Page_30" id="Page_30">[Pg 30]</a></span>force +which launches a cannon ball into space, produces a motion which would +continue for ever unless some other force counteracted it.</p> + +<p>Between the two examples which we have here given, there is a difference +worth pointing out. In the former (in which the phenomenon produced is a +substance, and not a motion of a substance), since the rust remains for +ever and unaltered unless some new cause supervenes, we may speak of the +contact of air a hundred years ago as even the proximate cause of the +rust which has existed from that time until now. But when the effect is +motion, which is itself a change, we must use a different language. The +permanency of the effect is now only the permanency of a series of +changes. The second foot, or inch, or mile of motion, is not the mere +prolonged duration of the first foot, or inch, or mile, but another fact +which succeeds, and which may in some respects be very unlike the +former, since it carries the body through a different region of space. +Now, the original projectile force which set the body moving is the +remote cause of all its motion, however long continued, but the +proximate cause of no motion except that which took place at the first +instant. The motion at any subsequent instant is proximately caused by +the motion which took place at the instant preceding. It is on that, and +not on the original moving cause, that the motion at any given moment +depends. For, suppose that the body passes through some resisting +medium, which partially counteracts the effect of the original impulse, +and retards the motion: this counteraction (it needs scarcely here be +repeated) is as strict an example of obedience to the law of the +impulse, as if the body had gone on moving with its original velocity; +but the motion which results is different, being now a compound of the +effects of two causes acting in contrary directions, instead of the +single effect of one cause. Now, what cause does the body obey in its +subsequent motion? The original cause of motion, or the actual motion at +the preceding instant? The latter: for when the object issues from the +resisting medium, it continues moving, not with its original, but with +its retarded velocity. The motion having once been diminished, <span class="pagenum"><a name="Page_31" id="Page_31">[Pg 31]</a></span>all that +which follows is diminished. The effect changes, because the cause which +it really obeys, the proximate cause, the real cause in fact, has +changed. This principle is recognised by mathematicians when they +enumerate among the causes by which the motion of a body is at any +instant determined, the <i>force generated</i> by the previous motion; an +expression which would be absurd if taken to imply that this "force" was +an intermediate link between the cause and the effect, but which really +means only the previous motion itself, considered as a cause of further +motion. We must, therefore, if we would speak with perfect precision, +consider each link in the succession of motions as the effect of the +link preceding it. But if, for the convenience of discourse, we speak of +the whole series as one effect, it must be as an effect produced by the +original impelling force; a permanent effect produced by an +instantaneous cause, and possessing the property of self-perpetuation.</p> + +<p>Let us now suppose that the original agent or cause, instead of being +instantaneous, is permanent. Whatever effect has been produced up to a +given time, would (unless prevented by the intervention of some new +cause) subsist permanently, even if the cause were to perish. Since, +however, the cause does not perish, but continues to exist and to +operate, it must go on producing more and more of the effect; and +instead of an uniform effect, we have a progressive series of effects, +arising from the accumulated influence of a permanent cause. Thus, the +contact of iron with the atmosphere causes a portion of it to rust; and +if the cause ceased, the effect already produced would be permanent, but +no further effect would be added. If, however, the cause, namely, +exposure to moist air, continues, more and more of the iron becomes +rusted, until all which is exposed is converted into a red powder, when +one of the conditions of the production of rust, namely, the presence of +unoxidized iron, has ceased, and the effect cannot any longer be +produced. Again, the earth causes bodies to fall towards it, that is, +the existence of the earth at a given instant, causes an unsupported +body to move towards it at the succeeding instant: and if the earth were +<span class="pagenum"><a name="Page_32" id="Page_32">[Pg 32]</a></span>annihilated, as much of the effect as is already produced would +continue; the object would go on moving in the same direction, with its +acquired velocity, until intercepted by some body or deflected by some +other force. The earth, however, not being annihilated, goes on +producing in the second instant an effect similar and of equal amount +with the first, which two effects being added together, there results an +accelerated velocity; and this operation being repeated at each +successive instant, the mere permanence of the cause, though without +increase, gives rise to a constant progressive increase of the effect, +so long as all the conditions, negative and positive, of the production +of that effect, continue to be realized.</p> + +<p>It is obvious that this state of things is merely a case of the +Composition of Causes. A cause which continues in action, must on a +strict analysis be considered as a number of causes exactly similar, +successively introduced, and producing by their combination the sum of +the effects which they would severally produce if they acted singly. The +progressive rusting of the iron is in strictness the sum of the effects +of many particles of air acting in succession upon corresponding +particles of iron. The continued action of the earth upon a falling body +is equivalent to a series of forces, applied in successive instants, +each tending to produce a certain constant quantity of motion; and the +motion at each instant is the sum of the effects of the new force +applied at the preceding instant, and the motion already acquired. In +each instant, a fresh effect, of which gravity is the proximate cause, +is added to the effect of which it was the remote cause: or (to express +the same thing in another manner) the effect produced by the earth's +influence at the instant last elapsed, is added to the sum of the +effects of which the remote causes were the influences exerted by the +earth at all the previous instants since the motion began. The case, +therefore, comes under the principle of a concurrence of causes +producing an effect equal to the sum of their separate effects. But as +the causes come into play not all at once, but successively, and as the +effect at each instant is the sum of the effects of those causes only +which have come into action up to <span class="pagenum"><a name="Page_33" id="Page_33">[Pg 33]</a></span>that instant, the result assumes the +form of an ascending series; a succession of sums, each greater than +that which preceded it; and we have thus a progressive effect from the +continued action of a cause.</p> + +<p>Since the continuance of the cause influences the effect only by adding +to its quantity, and since the addition takes place according to a fixed +law (equal quantities in equal times), the result is capable of being +computed on mathematical principles. In fact, this case, being that of +infinitesimal increments, is precisely the case which the differential +calculus was invented to meet. The questions, what effect will result +from the continual addition of a given cause to itself, and what amount +of the cause, being continually added to itself, will produce a given +amount of the effect, are evidently mathematical questions, and to be +treated, therefore, deductively. If, as we have seen, cases of the +Composition of Causes are seldom adapted for any other than deductive +investigation, this is especially true in the case now examined, the +continual composition of a cause with its own previous effects; since +such a case is peculiarly amenable to the deductive method, while the +undistinguishable manner in which the effects are blended with one +another and with the causes, must make the treatment of such an instance +experimentally, still more chimerical than in any other case.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XV_2">§ 2.</a> We shall next advert to a rather more intricate operation of the +same principle, namely, when the cause does not merely continue in +action, but undergoes, during the same time, a progressive change in +those of its circumstances which contribute to determine the effect. In +this case, as in the former, the total effect goes on accumulating by +the continual addition of a fresh effect to that already produced, but +it is no longer by the addition of equal quantities in equal times; the +quantities added are unequal, and even the quality may now be different. +If the change in the state of the permanent cause be progressive, the +effect will go through a double series of changes, arising partly from +the accumulated action of the cause, and partly from the changes in its +action. The effect <span class="pagenum"><a name="Page_34" id="Page_34">[Pg 34]</a></span>is still a progressive effect, produced however, not +by the mere continuance of a cause, but by its continuance and its +progressiveness combined.</p> + +<p>A familiar example is afforded by the increase of the temperature as +summer advances, that is, as the sun draws nearer to a vertical +position, and remains a greater number of hours above the horizon. This +instance exemplifies in a very interesting manner the twofold operation +on the effect, arising from the continuance of the cause, and from its +progressive change. When once the sun has come near enough to the +zenith, and remains above the horizon long enough, to give more warmth +during one diurnal rotation than the counteracting cause, the earth's +radiation, can carry off, the mere continuance of the cause would +progressively increase the effect, even if the sun came no nearer and +the days grew no longer; but in addition to this, a change takes place +in the accidents of the cause (its series of diurnal positions), tending +to increase the quantity of the effect. When the summer solstice has +passed, the progressive change in the cause begins to take place the +reverse way; but, for some time, the accumulating effect of the mere +continuance of the cause exceeds the effect of the changes in it, and +the temperature continues to increase.</p> + +<p>Again, the motion of a planet is a progressive effect, produced by +causes at once permanent and progressive. The orbit of a planet is +determined (omitting perturbations) by two causes: first, the action of +the central body, a permanent cause, which alternately increases and +diminishes as the planet draws nearer to or goes further from its +perihelion, and which acts at every point in a different direction; and, +secondly, the tendency of the planet to continue moving in the direction +and with the velocity which it has already acquired. This force also +grows greater as the planet draws nearer to its perihelion, because as +it does so its velocity increases; and less, as it recedes from its +perihelion: and this force as well as the other acts at each point in a +different direction, because at every point the action of the central +force, by deflecting the planet from its previous direction, alters the +line in which it tends to continue moving. The motion at each instant is +determined <span class="pagenum"><a name="Page_35" id="Page_35">[Pg 35]</a></span>by the amount and direction of the motion, and the amount +and direction of the sun's action, at the previous instant: and if we +speak of the entire revolution of the planet as one phenomenon (which, +as it is periodical and similar to itself, we often find it convenient +to do,) that phenomenon is the progressive effect of two permanent and +progressive causes, the central force and the acquired motion. Those +causes happening to be progressive in the particular way which is called +periodical, the effect necessarily is so too; because the quantities to +be added together returning in a regular order, the same sums must also +regularly return.</p> + +<p>This example is worthy of consideration also in another respect. Though +the causes themselves are permanent, and independent of all conditions +known to us, the changes which take place in the quantities and +relations of the causes are actually caused by the periodical changes in +the effects. The causes, as they exist at any moment, having produced a +certain motion, that motion, becoming itself a cause, reacts upon the +causes, and produces a change in them. By altering the distance and +direction of the central body relatively to the planet, and the +direction and quantity of the force in the direction of the tangent, it +alters the elements which determine the motion at the next succeeding +instant. This change renders the next motion somewhat different; and +this difference, by a fresh reaction upon the causes, renders the next +motion again different, and so on. The original state of the causes +might have been such, that this series of actions modified by reactions +would not have been periodical. The sun's action, and the original +impelling force, might have been in such a ratio to one another, that +the reaction of the effect would have been such as to alter the causes +more and more, without ever bringing them back to what they were at any +former time. The planet would then have moved in a parabola, or an +hyperbola, curves not returning into themselves. The quantities of the +two forces were, however, originally such, that the successive reactions +of the effect bring back the causes, after a certain time, to what they +were before; and from that time all the variations continue to recur +again and again in the same periodical order, <span class="pagenum"><a name="Page_36" id="Page_36">[Pg 36]</a></span>and must so continue +while the causes subsist and are not counteracted.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XV_3">§ 3.</a> In all cases of progressive effects, whether arising from the +accumulation of unchanging or of changing elements, there is an +uniformity of succession not merely between the cause and the effect, +but between the first stages of the effect and its subsequent stages. +That a body <i>in vacuo</i> falls sixteen feet in the first second, +forty-eight in the second, and so on in the ratio of the odd numbers, is +as much an uniform sequence as that when the supports are removed the +body falls. The sequence of spring and summer is as regular and +invariable as that of the approach of the sun and spring: but we do not +consider spring to be the cause of summer; it is evident that both are +successive effects of the heat received from the sun, and that, +considered merely in itself, spring might continue for ever, without +having the slightest tendency to produce summer. As we have so often +remarked, not the conditional, but the unconditional invariable +antecedent is termed the cause. That which would not be followed by the +effect unless something else had preceded, is not the cause, however +invariable the sequence may in fact be.</p> + +<p>It is in this way that most of those uniformities of succession are +generated, which are not cases of causation. When a phenomenon goes on +increasing, or periodically increases and diminishes, or goes through +any continued and unceasing process of variation reducible to an uniform +rule or law of succession, we do not on this account presume that any +two successive terms of the series are cause and effect. We presume the +contrary; we expect to find that the whole series originates either from +the continued action of fixed causes, or from causes which go through a +corresponding process of continuous change. A tree grows from half an +inch high to a hundred feet; and some trees will generally grow to that +height, unless prevented by some counteracting cause. But we do not call +the seedling the cause of the full-grown tree; the invariable antecedent +it certainly is, and we know very imperfectly on what other antecedents +the sequence is contingent, but we are convinced that it <span class="pagenum"><a name="Page_37" id="Page_37">[Pg 37]</a></span>is contingent +on something; because the homogeneousness of the antecedent with the +consequent, the close resemblance of the seedling to the tree in all +respects except magnitude, and the graduality of the growth, so exactly +resembling the progressively accumulating effect produced by the long +action of some one cause, leave no possibility of doubting that the +seedling and the tree are two terms in a series of that description, the +first term of which is yet to seek. The conclusion is further confirmed +by this, that we are able to prove by strict induction the dependence of +the growth of the tree, and even of the continuance of its existence, +upon the continued repetition of certain processes of nutrition, the +rise of the sap, the absorptions and exhalations by the leaves, &c.; and +the same experiments would probably prove to us that the growth of the +tree is the accumulated sum of the effects of these continued processes, +were we not, for want of sufficiently microscopic eyes, unable to +observe correctly and in detail what those effects are.</p> + +<p>This supposition by no means requires that the effect should not, during +its progress, undergo many modifications besides those of quantity, or +that it should not sometimes appear to undergo a very marked change of +character. This may be either because the unknown cause consists of +several component elements or agents, whose effects, accumulating +according to different laws, are compounded in different proportions at +different periods in the existence of the organized being; or because, +at certain points in its progress, fresh causes or agencies come in, or +are evolved, which intermix their laws with those of the prime agent.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_38" id="Page_38">[Pg 38]</a></span></p> +<h3><a name="BOOK_III_CHAPTER_XVI" id="BOOK_III_CHAPTER_XVI"></a>CHAPTER XVI.<br /> +OF EMPIRICAL LAWS.</h3> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVI_1">§ 1.</a> Scientific inquirers give the name of Empirical Laws to those +uniformities which observation or experiment has shown to exist, but on +which they hesitate to rely in cases varying much from those which have +been actually observed, for want of seeing any reason <i>why</i> such a law +should exist. It is implied, therefore, in the notion of an empirical +law, that it is not an ultimate law; that if true at all, its truth is +capable of being, and requires to be, accounted for. It is a derivative +law, the derivation of which is not yet known. To state the explanation, +the <i>why</i>, of the empirical law, would be to state the laws from which +it is derived; the ultimate causes on which it is contingent. And if we +knew these, we should also know what are its limits; under what +conditions it would cease to be fulfilled.</p> + +<p>The periodical return of eclipses, as originally ascertained by the +persevering observation of the early eastern astronomers, was an +empirical law, until the general laws of the celestial motions had +accounted for it. The following are empirical laws still waiting to be +resolved into the simpler laws from which they are derived. The local +laws of the flux and reflux of the tides in different places: the +succession of certain kinds of weather to certain appearances of sky: +the apparent exceptions to the almost universal truth that bodies expand +by increase of temperature: the law that breeds, both animal and +vegetable, are improved by crossing: that gases have a strong tendency +to permeate animal membranes: that substances containing a very high +proportion of nitrogen (such as hydrocyanic acid and morphia) are +powerful poisons: that when different metals are fused together, the +alloy is harder than the various elements: that the number of <span class="pagenum"><a name="Page_39" id="Page_39">[Pg 39]</a></span>atoms of +acid required to neutralize one atom of any base, is equal to the number +of atoms of oxygen in the base: that the solubility of substances in one +another, depends<a name="FNanchor_12_12" id="FNanchor_12_12"></a><a href="#Footnote_12_12" class="fnanchor">[12]</a> (at least in some degree) on the similarity of +their elements.</p> + +<p>An empirical law, then, is an observed uniformity, presumed to be +resolvable into simpler laws, but not yet resolved into them. The +ascertainment of the empirical laws of phenomena often precedes by a +long interval the explanation of those laws by the Deductive Method; and +the verification of a deduction usually consists in the comparison of +its results with empirical laws previously ascertained.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVI_2">§ 2.</a> From a limited number of ultimate laws of causation, there are +necessarily generated a vast number of derivative uniformities, both of +succession and of coexistence. Some are laws of succession or of +coexistence between different effects of the same cause: of these we had +examples in the last chapter. Some are laws of succession between +effects and their remote causes; resolvable into the laws which connect +each with the intermediate link. Thirdly, when causes act together and +compound their effects, the laws of those causes generate the +fundamental law of the effect, namely, that it depends on the +coexistence of those causes. And, finally, the order of succession or of +coexistence which obtains among effects, necessarily depends on their +causes. If they are effects of the same cause, it depends on the laws of +that cause; if on different causes, it depends on the laws of those +causes severally, and on the circumstances which determine their +coexistence. If we <span class="pagenum"><a name="Page_40" id="Page_40">[Pg 40]</a></span>inquire further when and how the causes will +coexist, that, again, depends on <i>their</i> causes: and we may thus trace +back the phenomena higher and higher, until the different series of +effects meet in a point, and the whole is shown to have depended +ultimately on some common cause; or until, instead of converging to one +point, they terminate in different points, and the order of the effects +is proved to have arisen from the collocation of some of the primeval +causes, or natural agents. For example, the order of succession and of +coexistence among the heavenly motions, which is expressed by Kepler's +laws, is derived from the coexistence of two primeval causes, the sun, +and the original impulse or projectile force belonging to each +planet.<a name="FNanchor_13_13" id="FNanchor_13_13"></a><a href="#Footnote_13_13" class="fnanchor">[13]</a> Kepler's laws are resolved into the laws of these causes and +the fact of their coexistence.</p> + +<p>Derivative laws, therefore, do not depend solely on the ultimate laws +into which they are resolvable: they mostly depend on those ultimate +laws, and an ultimate fact; namely, the mode of coexistence of some of +the component elements of the universe. The ultimate laws of causation +might be the same as at present, and yet the derivative laws completely +different, if the causes coexisted in different proportions, or with any +difference in those of their relations by which the effects are +influenced. If, for example, the sun's attraction, and the original +projectile force, had existed in some other ratio to one another than +they did (and we know of no reason why this should not have been the +case), the derivative laws of the heavenly motions might have been quite +different from what they are. The proportions which exist happen to be +such as to produce regular elliptical motions; any other proportions +would have produced different ellipses, or circular, or parabolic, or +hyperbolic motions, but still regular ones; because the effects of each +of the agents accumulate according to an uniform law; and two regular +series of quantities, when their corresponding terms are added, must +produce a regular series of some sort, whatever the quantities +themselves are.</p> + + +<p><span class="pagenum"><a name="Page_41" id="Page_41">[Pg 41]</a></span></p><p class="newsection"><a name="BOOK_III_CHAPTER_XVI_3">§ 3.</a> Now this last-mentioned element in the resolution of a derivative +law, the element which is not a law of causation, but a collocation of +causes, cannot itself be reduced to any law. There is (as formerly +remarked<a name="FNanchor_14_14" id="FNanchor_14_14"></a><a href="#Footnote_14_14" class="fnanchor">[14]</a>) no uniformity, no <i>norma</i>, principle, or rule, perceivable +in the distribution of the primeval natural agents through the universe. +The different substances composing the earth, the powers that pervade +the universe, stand in no constant relation to one another. One +substance is more abundant than others, one power acts through a larger +extent of space than others, without any pervading analogy that we can +discover. We not only do not know of any reason why the sun's attraction +and the force in the direction of the tangent coexist in the exact +proportion they do, but we can trace no coincidence between it and the +proportions in which any other elementary powers in the universe are +intermingled. The utmost disorder is apparent in the combination of the +causes; which is consistent with the most regular order in their +effects; for when each agent carries on its own operations according to +an uniform law, even the most capricious combination of agencies will +generate a regularity of some sort; as we see in the kaleidoscope, where +any casual arrangement of coloured bits of glass produces by the laws of +reflection a beautiful regularity in the effect.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVI_4">§ 4.</a> In the above considerations lies the justification of the limited +degree of reliance which scientific inquirers are accustomed to place in +empirical laws.</p> + +<p>A derivative law which results wholly from the operation of some one +cause, will be as universally true as the laws of the cause itself; that +is, it will always be true except where some one of those effects of the +cause, on which the derivative law depends, is defeated by a +counteracting cause. But when the derivative law results not from +different effects of one cause, but from effects of several causes, we +cannot be certain that it will be true under any variation in the mode +of coexistence <span class="pagenum"><a name="Page_42" id="Page_42">[Pg 42]</a></span>of those causes, or of the primitive natural agents on +which the causes ultimately depend. The proposition that coal beds rest +on certain descriptions of strata exclusively, though true on the earth +so far as our observation has reached, cannot be extended to the moon or +the other planets, supposing coal to exist there; because we cannot be +assured that the original constitution of any other planet was such as +to produce the different depositions in the same order as in our globe. +The derivative law in this case depends not solely on laws, but on a +collocation; and collocations cannot be reduced to any law.</p> + +<p>Now it is the very nature of a derivative law which has not yet been +resolved into its elements, in other words, an empirical law, that we do +not know whether it results from the different effects of one cause, or +from effects of different causes. We cannot tell whether it depends +wholly on laws, or partly on laws and partly on a collocation. If it +depends on a collocation, it will be true in all the cases in which that +particular collocation exists. But, since we are entirely ignorant, in +case of its depending on a collocation, what the collocation is, we are +not safe in extending the law beyond the limits of time and place in +which we have actual experience of its truth. Since within those limits +the law has always been found true, we have evidence that the +collocations, whatever they are, on which it depends, do really exist +within those limits. But, knowing of no rule or principle to which the +collocations themselves conform, we cannot conclude that because a +collocation is proved to exist within certain limits of place or time, +it will exist beyond those limits. Empirical laws, therefore, can only +be received as true within the limits of time and place in which they +have been found true by observation: and not merely the limits of time +and place, but of time, place, and circumstance: for since it is the +very meaning of an empirical law that we do not know the ultimate laws +of causation on which it is dependent, we cannot foresee, without actual +trial, in what manner or to what extent the introduction of any new +circumstance may affect it.</p> + + +<p><span class="pagenum"><a name="Page_43" id="Page_43">[Pg 43]</a></span></p><p class="newsection"><a name="BOOK_III_CHAPTER_XVI_5">§ 5.</a> But how are we to know that an uniformity, ascertained by +experience, is only an empirical law? Since, by the supposition, we have +not been able to resolve it into any other laws, how do we know that it +is not an ultimate law of causation?</p> + +<p>I answer, that no generalization amounts to more than an empirical law +when the only proof on which it rests is that of the Method of +Agreement. For it has been seen that by that method alone we never can +arrive at causes. The utmost that the Method of Agreement can do is, to +ascertain the whole of the circumstances common to all cases in which a +phenomenon is produced: and this aggregate includes not only the cause +of the phenomenon, but all phenomena with which it is connected by any +derivative uniformity, whether as being collateral effects of the same +cause, or effects of any other cause which, in all the instances we have +been able to observe, coexisted with it. The method affords no means of +determining which of these uniformities are laws of causation, and which +are merely derivative laws, resulting from those laws of causation and +from the collocation of the causes. None of them, therefore, can be +received in any other character than that of derivative laws, the +derivation of which has not been traced; in other words, empirical laws: +in which light, all results obtained by the Method of Agreement (and +therefore almost all truths obtained by simple observation without +experiment) must be considered, until either confirmed by the Method of +Difference, or explained deductively, in other words accounted for <i>à +priori</i>.</p> + +<p>These empirical laws may be of greater or less authority, according as +there is reason to presume that they are resolvable into laws only, or +into laws and collocations together. The sequences which we observe in +the production and subsequent life of an animal or a vegetable, resting +on the Method of Agreement only, are mere empirical laws; but though the +antecedents in those sequences may not be the causes of the consequents, +both the one and the other are doubtless, in the main, successive stages +of a progressive effect originating in a <span class="pagenum"><a name="Page_44" id="Page_44">[Pg 44]</a></span>common cause, and therefore +independent of collocations. The uniformities, on the other hand, in the +order of superposition of strata on the earth, are empirical laws of a +much weaker kind, since they not only are not laws of causation, but +there is no reason to believe that they depend on any common cause: all +appearances are in favour of their depending on the particular +collocation of natural agents which at some time or other existed on our +globe, and from which no inference can be drawn as to the collocation +which exists or has existed in any other portion of the universe.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVI_6">§ 6.</a> Our definition of an empirical law including not only those +uniformities which are not known to be laws of causation, but also those +which are, provided there be reason to presume that they are not +ultimate laws; this is the proper place to consider by what signs we may +judge that even if an observed uniformity be a law of causation, it is +not an ultimate but a derivative law.</p> + +<p>The first sign is, if between the antecedent <i>a</i> and the consequent <i>b</i> +there be evidence of some intermediate link; some phenomenon of which we +can surmise the existence, though from the imperfection of our senses or +of our instruments we are unable to ascertain its precise nature and +laws. If there be such a phenomenon (which may be denoted by the letter +<i>x</i>), it follows that even if <i>a</i> be the cause of <i>b</i>, it is but the +remote cause, and that the law, <i>a</i> causes <i>b</i>, is resolvable into at +least two laws, <i>a</i> causes <i>x</i>, and <i>x</i> causes <i>b</i>. This is a very +frequent case, since the operations of nature mostly take place on so +minute a scale, that many of the successive steps are either +imperceptible, or very indistinctly perceived.</p> + +<p>Take, for example, the laws of the chemical composition of substances; +as that hydrogen and oxygen being combined, water is produced. All we +see of the process is, that the two gases being mixed in certain +proportions, and heat or electricity being applied, an explosion takes +place, the gases disappear, and water remains. There is no doubt about +the law, or about its being a law of causation. But between the +antecedent (the gases in a state of mechanical mixture, <span class="pagenum"><a name="Page_45" id="Page_45">[Pg 45]</a></span>heated or +electrified), and the consequent (the production of water), there must +be an intermediate process which we do not see. For if we take any +portion whatever of the water, and subject it to analysis, we find that +it always contains hydrogen and oxygen; nay, the very same proportions +of them, namely, two thirds, in volume, of hydrogen, and one third +oxygen. This is true of a single drop; it is true of the minutest +portion which our instruments are capable of appreciating. Since, then, +the smallest perceptible portion of the water contains both those +substances, portions of hydrogen and oxygen smaller than the smallest +perceptible must have come together in every such minute portion of +space; must have come closer together than when the gases were in a +state of mechanical mixture, since (to mention no other reasons) the +water occupies far less space than the gases. Now, as we cannot see this +contact or close approach of the minute particles, we cannot observe +with what circumstances it is attended, or according to what laws it +produces its effects. The production of water, that is, of the sensible +phenomena which characterize the compound, may be a very remote effect +of those laws. There may be innumerable intervening links; and we are +sure that there must be some. Having full proof that corpuscular action +of some kind takes place previous to any of the great transformations in +the sensible properties of substances, we can have no doubt that the +laws of chemical action, as at present known, are not ultimate but +derivative laws; however ignorant we may be, and even though we should +for ever remain ignorant, of the nature of the laws of corpuscular +action from which they are derived.</p> + +<p>In like manner, all the processes of vegetative life, whether in the +vegetable properly so called or in the animal body, are corpuscular +processes. Nutrition is the addition of particles to one another, +sometimes merely replacing other particles separated and excreted, +sometimes occasioning an increase of bulk or weight, so gradual, that +only after a long continuance does it become perceptible. Various +organs, by means of peculiar vessels, secrete from the blood, fluids, +the component <span class="pagenum"><a name="Page_46" id="Page_46">[Pg 46]</a></span>particles of which must have been in the blood, but which +differ from it most widely both in mechanical properties and in chemical +composition. Here, then, are abundance of unknown links to be filled up; +and there can be no doubt that the laws of the phenomena of vegetative +or organic life are derivative laws, dependent on properties of the +corpuscles, and of those elementary tissues which are comparatively +simple combinations of corpuscles.</p> + +<p>The first sign, then, from which a law of causation, though hitherto +unresolved, may be inferred to be a derivative law, is any indication of +the existence of an intermediate link or links between the antecedent +and the consequent. The second is, when the antecedent is an extremely +complex phenomenon, and its effects therefore, probably, in part at +least, compounded of the effects of its different elements; since we +know that the case in which the effect of the whole is not made up of +the effects of its parts, is exceptional, the Composition of Causes +being by far the more ordinary case.</p> + +<p>We will illustrate this by two examples, in one of which the antecedent +is the sum of many homogeneous, in the other of heterogeneous, parts. +The weight of a body is made up of the weights of its minute particles: +a truth which astronomers express in its most general terms, when they +say that bodies, at equal distances, gravitate to one another in +proportion to their quantity of matter. All true propositions, +therefore, which can be made concerning gravity, are derivative laws; +the ultimate law into which they are all resolvable being, that every +particle of matter attracts every other. As our second example, we may +take any of the sequences observed in meteorology: for instance, a +diminution of the pressure of the atmosphere (indicated by a fall of the +barometer) is followed by rain. The antecedent is here a complex +phenomenon, made up of heterogeneous elements; the column of the +atmosphere over any particular place consisting of two parts, a column +of air, and a column of aqueous vapour mixed with it; and the change in +the two together manifested by a fall of the barometer, and followed by +rain, must be either a <span class="pagenum"><a name="Page_47" id="Page_47">[Pg 47]</a></span>change in one of these, or in the other, or in +both. We might, then, even in the absence of any other evidence, form a +reasonable presumption, from the invariable presence of both these +elements in the antecedent, that the sequence is probably not an +ultimate law, but a result of the laws of the two different agents; a +presumption only to be destroyed when we had made ourselves so well +acquainted with the laws of both, as to be able to affirm that those +laws could not by themselves produce the observed result.</p> + +<p>There are but few known cases of succession from very complex +antecedents, which have not either been actually accounted for from +simpler laws, or inferred with great probability (from the ascertained +existence of intermediate links of causation not yet understood) to be +capable of being so accounted for. It is, therefore, highly probable +that all sequences from complex antecedents are thus resolvable, and +that ultimate laws are in all cases comparatively simple. If there were +not the other reasons already mentioned for believing that the laws of +organized nature are resolvable into simpler laws, it would be almost a +sufficient reason that the antecedents in most of the sequences are so +very complex.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVI_7">§ 7.</a> In the preceding discussion we have recognised two kinds of +empirical laws: those known to be laws of causation, but presumed to be +resolvable into simpler laws; and those not known to be laws of +causation at all. Both these kinds of laws agree in the demand which +they make for being explained by deduction, and agree in being the +appropriate means of verifying such deduction, since they represent the +experience with which the result of the deduction must be compared. They +agree, further, in this, that until explained, and connected with the +ultimate laws from which they result, they have not attained the highest +degree of certainty of which laws are susceptible. It has been shown on +a former occasion that laws of causation which are derivative, and +compounded of simpler laws, are not only, as the nature of the case +implies, less general, but even less certain, than the <span class="pagenum"><a name="Page_48" id="Page_48">[Pg 48]</a></span>simpler laws +from which they result; not in the same degree to be relied on as +universally true. The inferiority of evidence, however, which attaches +to this class of laws, is trifling, compared with that which is inherent +in uniformities not known to be laws of causation at all. So long as +these are unresolved, we cannot tell on how many collocations, as well +as laws, their truth may be dependent; we can never, therefore, extend +them with any confidence to cases in which we have not assured +ourselves, by trial, that the necessary collocation of causes, whatever +it may be, exists. It is to this class of laws alone that the property, +which philosophers usually consider as characteristic of empirical laws, +belongs in all its strictness; the property of being unfit to be relied +on beyond the limits of time, place, and circumstance, in which the +observations have been made. These are empirical laws in a more emphatic +sense; and when I employ that term (except where the context manifestly +indicates the reverse) I shall generally mean to designate those +uniformities only, whether of succession or of coexistence, which are +not known to be laws of causation.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_49" id="Page_49">[Pg 49]</a></span></p> +<h3><a name="BOOK_III_CHAPTER_XVII" id="BOOK_III_CHAPTER_XVII"></a>CHAPTER XVII.<br /> +OF CHANCE AND ITS ELIMINATION.</h3> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVII_1">§ 1.</a> Considering then as empirical laws only those observed uniformities +respecting which the question whether they are laws of causation must +remain undecided until they can be explained deductively, or until some +means are found of applying the Method of Difference to the case, it has +been shown in the preceding chapter, that until an uniformity can, in +one or the other of these modes, be taken out of the class of empirical +laws, and brought either into that of laws of causation or of the +demonstrated results of laws of causation, it cannot with any assurance +be pronounced true beyond the local and other limits within which it has +been found so by actual observation. It remains to consider how we are +to assure ourselves of its truth even within those limits; after what +quantity of experience a generalization which rests solely on the Method +of Agreement, can be considered sufficiently established, even as an +empirical law. In a former chapter, when treating of the Methods of +Direct Induction, we expressly reserved this question,<a name="FNanchor_15_15" id="FNanchor_15_15"></a><a href="#Footnote_15_15" class="fnanchor">[15]</a> and the time +is now come for endeavouring to solve it.</p> + +<p>We found that the Method of Agreement has the defect of not proving +causation, and can therefore only be employed for the ascertainment of +empirical laws. But we also found that besides this deficiency, it +labours under a characteristic imperfection, tending to render uncertain +even such conclusions as it is in itself adapted to prove. This +imperfection arises from Plurality of Causes. Although two or more cases +in which the phenomenon <i>a</i> has been met with, may have no common +antecedent except A, this does not prove that there <span class="pagenum"><a name="Page_50" id="Page_50">[Pg 50]</a></span>is any connexion +between <i>a</i> and A, since <i>a</i> may have many causes, and may have been +produced, in these different instances, not by anything which the +instances had in common, but by some of those elements in them which +were different. We nevertheless observed, that in proportion to the +multiplication of instances pointing to A as the antecedent, the +characteristic uncertainty of the method diminishes, and the existence +of a law of connexion between A and <i>a</i> more nearly approaches to +certainty. It is now to be determined, after what amount of experience +this certainty may be deemed to be practically attained, and the +connexion between A and <i>a</i> may be received as an empirical law.</p> + +<p>This question may be otherwise stated in more familiar terms:—After how +many and what sort of instances may it be concluded, that an observed +coincidence between two phenomena is not the effect of chance?</p> + +<p>It is of the utmost importance for understanding the logic of induction, +that we should form a distinct conception of what is meant by chance, +and how the phenomena which common language ascribes to that abstraction +are really produced.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVII_2">§ 2.</a> Chance is usually spoken of in direct antithesis to law; whatever +(it is supposed) cannot be ascribed to any law, is attributed to chance. +It is, however, certain, that whatever happens is the result of some +law; is an effect of causes, and could have been predicted from a +knowledge of the existence of those causes, and from their laws. If I +turn up a particular card, that is a consequence of its place in the +pack. Its place in the pack was a consequence of the manner in which the +cards were shuffled, or of the order in which they were played in the +last game; which, again, were effects of prior causes. At every stage, +if we had possessed an accurate knowledge of the causes in existence, it +would have been abstractedly possible to foretell the effect.</p> + +<p>An event occurring by chance, may be better described as a coincidence +from which we have no ground to infer an uniformity: the occurrence of a +phenomenon in certain circumstances, <span class="pagenum"><a name="Page_51" id="Page_51">[Pg 51]</a></span>without our having reason on that +account to infer that it will happen again in those circumstances. This, +however, when looked closely into, implies that the enumeration of the +circumstances is not complete. Whatever the fact be, since it has +occurred once, we may be sure that if <i>all</i> the same circumstances were +repeated, it would occur again; and not only if all, but there is some +particular portion of those circumstances, on which the phenomenon is +invariably consequent. With most of them, however, it is not connected +in any permanent manner: its conjunction with those is said to be the +effect of chance, to be merely casual. Facts casually conjoined are +separately the effects of causes, and therefore of laws; but of +different causes, and causes not connected by any law.</p> + +<p>It is incorrect, then, to say that any phenomenon is produced by chance; +but we may say that two or more phenomena are conjoined by chance, that +they coexist or succeed one another only by chance: meaning that they +are in no way related through causation; that they are neither cause and +effect, nor effects of the same cause, nor effects of causes between +which there subsists any law of coexistence, nor even effects of the +same collocation of primeval causes.</p> + +<p>If the same casual coincidence never occurred a second time, we should +have an easy test for distinguishing such from the coincidences which +are the results of a law. As long as the phenomena had been found +together only once, so long, unless we knew some more general laws from +which the coincidence might have resulted, we could not distinguish it +from a casual one; but if it occurred twice, we should know that the +phenomena so conjoined must be in some way connected through their +causes.</p> + +<p>There is, however, no such test. A coincidence may occur again and +again, and yet be only casual. Nay, it would be inconsistent with what +we know of the order of nature, to doubt that every casual coincidence +will sooner or later be repeated, as long as the phenomena between which +it occurred do not cease to exist, or to be reproduced. The recurrence, +therefore, of the same coincidence more than once, or even its frequent +<span class="pagenum"><a name="Page_52" id="Page_52">[Pg 52]</a></span>recurrence, does not prove that it is an instance of any law; does not +prove that it is not casual, or, in common language, the effect of +chance.</p> + +<p>And yet, when a coincidence cannot be deduced from known laws, nor +proved by experiment to be itself a case of causation, the frequency of +its occurrence is the only evidence from which we can infer that it is +the result of a law. Not, however, its absolute frequency. The question +is not whether the coincidence occurs often or seldom, in the ordinary +sense of those terms; but whether it occurs more often than chance will +account for; more often than might rationally be expected if the +coincidence were casual. We have to decide, therefore, what degree of +frequency in a coincidence, chance will account for. And to this there +can be no general answer. We can only state the principle by which the +answer must be determined: the answer itself will be different in every +different case.</p> + +<p>Suppose that one of the phenomena, A, exists always, and the other +phenomenon, B, only occasionally: it follows that every instance of B +will be an instance of its coincidence with A, and yet the coincidence +will be merely casual, not the result of any connexion between them. The +fixed stars have been constantly in existence since the beginning of +human experience, and all phenomena that have come under human +observation have, in every single instance, coexisted with them; yet +this coincidence, though equally invariable with that which exists +between any of those phenomena and its own cause, does not prove that +the stars are its cause, nor that they are in anywise connected with it. +As strong a case of coincidence, therefore, as can possibly exist, and a +much stronger one in point of mere frequency than most of those which +prove laws, does not here prove a law: why? because, since the stars +exist always, they <i>must</i> coexist with every other phenomenon, whether +connected with them by causation or not. The uniformity, great though it +be, is no greater than would occur on the supposition that no such +connexion exists.</p> + +<p>On the other hand, suppose that we were inquiring whether <span class="pagenum"><a name="Page_53" id="Page_53">[Pg 53]</a></span>there be any +connexion between rain and any particular wind. Rain, we know, +occasionally occurs with every wind; therefore the connexion, if it +exists, cannot be an actual law; but still, rain may be connected with +some particular wind through causation; that is, though they cannot be +always effects of the same cause (for if so they would regularly +coexist), there may be some causes common to the two, so that in so far +as either is produced by those common causes, they will, from the laws +of the causes, be found to coexist. How, then, shall we ascertain this? +The obvious answer is, by observing whether rain occurs with one wind +more frequently than with any other. That, however, is not enough; for +perhaps that one wind blows more frequently than any other; so that its +blowing more frequently in rainy weather is no more than would happen, +although it had no connexion with the causes of rain, provided it were +not connected with causes adverse to rain. In England, westerly winds +blow during about twice as great a portion of the year as easterly. If, +therefore, it rains only twice as often with a westerly, as with an +easterly wind, we have no reason to infer that any law of nature is +concerned in the coincidence. If it rains more than twice as often, we +may be sure that some law is concerned; either there is some cause in +nature which, in this climate, tends to produce both rain and a westerly +wind, or a westerly wind has itself some tendency to produce rain. But +if it rains less than twice as often, we may draw a directly opposite +inference: the one, instead of being a cause, or connected with causes, +of the other, must be connected with causes adverse to it, or with the +absence of some cause which produces it; and though it may still rain +much oftener with a westerly wind than with an easterly, so far would +this be from proving any connexion between the phenomena, that the +connexion proved would be between rain and an easterly wind, to which, +in mere frequency of coincidence, it is less allied.</p> + +<p>Here, then, are two examples: in one, the greatest possible frequency of +coincidence, with no instance whatever to the contrary, does not prove +that there is any law; in the other, a much less frequency of +coincidence, even when non-coincidence <span class="pagenum"><a name="Page_54" id="Page_54">[Pg 54]</a></span>is still more frequent, does +prove that there is a law. In both cases the principle is the same. In +both we consider the positive frequency of the phenomena themselves, and +how great frequency of coincidence that must of itself bring about, +without supposing any connexion between them, provided there be no +repugnance; provided neither be connected with any cause tending to +frustrate the other. If we find a greater frequency of coincidence than +this, we conclude that there is some connexion; if a less frequency, +that there is some repugnance. In the former case, we conclude that one +of the phenomena can under some circumstances cause the other, or that +there exists something capable of causing them both; in the latter, that +one of them, or some cause which produces one of them, is capable of +counteracting the production of the other. We have thus to deduct from +the observed frequency of coincidence, as much as may be the effect of +chance, that is, of the mere frequency of the phenomena themselves; and +if anything remains, what does remain is the residual fact which proves +the existence of a law.</p> + +<p>The frequency of the phenomena can only be ascertained within definite +limits of space and time; depending as it does on the quantity and +distribution of the primeval natural agents, of which we can know +nothing beyond the boundaries of human observation, since no law, no +regularity, can be traced in it, enabling us to infer the unknown from +the known. But for the present purpose this is no disadvantage, the +question being confined within the same limits as the data. The +coincidences occurred in certain places and times, and within those we +can estimate the frequency with which such coincidences would be +produced by chance. If, then, we find from observation that A exists in +one case out of every two, and B in one case out of every three; then if +there be neither connexion nor repugnance between them, or between any +of their causes, the instances in which A and B will both exist, that is +to say will coexist, will be one case in every six. For A exists in +three cases out of six: and B, existing in one case out of every three +without <span class="pagenum"><a name="Page_55" id="Page_55">[Pg 55]</a></span>regard to the presence or absence of A, will exist in one case +out of those three. There will therefore be, of the whole number of +cases, two in which A exists without B; one case of B without A; two in +which neither B nor A exists, and one case out of six in which they both +exist. If then, in point of fact, they are found to coexist oftener than +in one case out of six; and, consequently, A does not exist without B so +often as twice in three times, nor B without A so often as once in every +twice; there is some cause in existence which tends to produce a +conjunction between A and B.</p> + +<p>Generalizing the result, we may say, that if A occurs in a larger +proportion of the cases where B is, than of the cases where B is not; +then will B also occur in a larger proportion of the cases where A is, +than of the cases where A is not; and there is some connexion, through +causation, between A and B. If we could ascend to the causes of the two +phenomena, we should find, at some stage, either proximate or remote, +some cause or causes common to both; and if we could ascertain what +these are, we could frame a generalization which would be true without +restriction of place or time: but until we can do so, the fact of a +connexion between the two phenomena remains an empirical law.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVII_3">§ 3.</a> Having considered in what manner it may be determined whether any +given conjunction of phenomena is casual, or the result of some law; to +complete the theory of chance, it is necessary that we should now +consider those effects which are partly the result of chance and partly +of law, or, in other words, in which the effects of casual conjunctions +of causes are habitually blended in one result with the effects of a +constant cause.</p> + +<p>This is a case of Composition of Causes; and the peculiarity of it is, +that instead of two or more causes intermixing their effects in a +regular manner with those of one another, we have now one constant +cause, producing an effect which is successively modified by a series of +variable causes. Thus, as summer advances, the approach of the sun to a +vertical <span class="pagenum"><a name="Page_56" id="Page_56">[Pg 56]</a></span>position tends to produce a constant increase of temperature; +but with this effect of a constant cause, there are blended the effects +of many variable causes, winds, clouds, evaporation, electric agencies +and the like, so that the temperature of any given day depends in part +on these fleeting causes, and only in part on the constant cause. If the +effect of the constant cause is always accompanied and disguised by +effects of variable causes, it is impossible to ascertain the law of the +constant cause in the ordinary manner, by separating it from all other +causes and observing it apart. Hence arises the necessity of an +additional rule of experimental inquiry.</p> + +<p>When the action of a cause A is liable to be interfered with, not +steadily by the same cause or causes, but by different causes at +different times, and when these are so frequent, or so indeterminate, +that we cannot possibly exclude all of them from any experiment, though +we may vary them; our resource is, to endeavour to ascertain what is the +effect of all the variable causes taken together. In order to do this, +we make as many trials as possible, preserving A invariable. The results +of these different trials will naturally be different, since the +indeterminate modifying causes are different in each: if, then, we do +not find these results to be progressive, but, on the contrary, to +oscillate about a certain point, one experiment giving a result a little +greater, another a little less, one a result tending a little more in +one direction, another a little more in the contrary direction; while +the average or middle point does not vary, but different sets of +experiments (taken in as great a variety of circumstances as possible) +yield the same mean, provided only they be sufficiently numerous; then +that mean or average result, is the part, in each experiment, which is +due to the cause A, and is the effect which would have been obtained if +A could have acted alone: the variable remainder is the effect of +chance, that is, of causes the coexistence of which with the cause A was +merely casual. The test of the sufficiency of the induction in this case +is, when any increase of the number of trials from which the average is +struck, does not materially alter the average.</p> + +<p><span class="pagenum"><a name="Page_57" id="Page_57">[Pg 57]</a></span></p><p>This kind of elimination, in which we do not eliminate any one +assignable cause, but the multitude of floating unassignable ones, may +be termed the Elimination of Chance. We afford an example of it when we +repeat an experiment, in order, by taking the mean of different results, +to get rid of the effects of the unavoidable errors of each individual +experiment. When there is no permanent cause such as would produce a +tendency to error peculiarly in one direction, we are warranted by +experience in assuming that the errors on one side will, in a certain +number of experiments, about balance the errors on the contrary side. We +therefore repeat the experiment, until any change which is produced in +the average of the whole by further repetition, falls within limits of +error consistent with the degree of accuracy required by the purpose we +have in view.<a name="FNanchor_16_16" id="FNanchor_16_16"></a><a href="#Footnote_16_16" class="fnanchor">[16]</a></p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVII_4">§ 4.</a> In the supposition hitherto made, the effect of the constant cause +A has been assumed to form so great and conspicuous a part of the +general result, that its existence never could be a matter of +uncertainty, and the object of the eliminating process was only to +ascertain <i>how much</i> is attributable to that cause; what is its exact +law. Cases, however, occur in which the effect of a constant cause is so +small, compared with that of some of the changeable causes with which +<span class="pagenum"><a name="Page_58" id="Page_58">[Pg 58]</a></span>it is liable to be casually conjoined, that of itself it escapes +notice, and the very existence of any effect arising from a constant +cause is first learnt, by the process which in general serves only for +ascertaining the quantity of that effect. This case of induction may be +characterized as follows. A given effect is known to be chiefly, and not +known not to be wholly, determined by changeable causes. If it be wholly +so produced, then if the aggregate be taken of a sufficient number of +instances, the effects of these different causes will cancel one +another. If, therefore, we do not find this to be the case, but, on the +contrary, after such a number of trials has been made that no further +increase alters the average result, we find that average to be, not +zero, but some other quantity, about which, though small in comparison +with the total effect, the effect nevertheless oscillates, and which is +the middle point in its oscillation; we may conclude this to be the +effect of some constant cause: which cause, by some of the methods +already treated of, we may hope to detect. This may be called <i>the +discovery of a residual phenomenon by eliminating the effects of +chance</i>.</p> + +<p>It is in this manner, for example, that loaded dice may be discovered. +Of course no dice are so clumsily loaded that they must always throw +certain numbers; otherwise the fraud would be instantly detected. The +loading, a constant cause, mingles with the changeable causes which +determine what cast will be thrown in each individual instance. If the +dice were not loaded, and the throw were left to depend entirely on the +changeable causes, these in a sufficient number of instances would +balance one another, and there would be no preponderant number of throws +of any one kind. If, therefore, after such a number of trials that no +further increase of their number has any material effect upon the +average, we find a preponderance in favour of a particular throw; we may +conclude with assurance that there is some constant cause acting in +favour of that throw, or in other words, that the dice are not fair; and +the exact amount of the unfairness. In a similar manner, what is called +the diurnal variation of the barometer, which is very small compared +with the variations <span class="pagenum"><a name="Page_59" id="Page_59">[Pg 59]</a></span>arising from the irregular changes in the state of +the atmosphere, was discovered by comparing the average height of the +barometer at different hours of the day. When this comparison was made, +it was found that there was a small difference, which on the average was +constant, however the absolute quantities might vary, and which +difference, therefore, must be the effect of a constant cause. This +cause was afterwards ascertained, deductively, to be the rarefaction of +the air, occasioned by the increase of temperature as the day advances.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVII_5">§ 5.</a> After these general remarks on the nature of chance, we are +prepared to consider in what manner assurance may be obtained that a +conjunction between two phenomena, which has been observed a certain +number of times, is not casual, but a result of causation, and to be +received therefore as one of the uniformities of nature, though (until +accounted for <i>à priori</i>) only as an empirical law.</p> + +<p>We will suppose the strongest case, namely, that the phenomenon B has +never been observed except in conjunction with A. Even then, the +probability that they are connected is not measured by the total number +of instances in which they have been found together, but by the excess +of that number above the number due to the absolute frequency of A. If, +for example, A exists always, and therefore coexists with everything, no +number of instances of its coexistence with B would prove a connexion; +as in our example of the fixed stars. If A be a fact of such common +occurrence that it may be presumed to be present in half of all the +cases that occur, and therefore in half the cases in which B occurs, it +is only the proportional excess above half, that is to be reckoned as +evidence towards proving a connexion between A and B.</p> + +<p>In addition to the question, What is the number of coincidences which, +on an average of a great multitude of trials, may be expected to arise +from chance alone? there is also another question, namely, Of what +extent of deviation from that average is the occurrence credible, from +chance alone, in some <span class="pagenum"><a name="Page_60" id="Page_60">[Pg 60]</a></span>number of instances smaller than that required +for striking a fair average? It is not only to be considered what is the +general result of the chances in the long run, but also what are the +extreme limits of variation from the general result, which may +occasionally be expected as the result of some smaller number of +instances.</p> + +<p>The consideration of the latter question, and any consideration of the +former beyond that already given to it, belong to what mathematicians +term the doctrine of chances, or, in a phrase of greater pretension, the +Theory of Probabilities.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_61" id="Page_61">[Pg 61]</a></span></p> +<h3><a name="BOOK_III_CHAPTER_XVIII" id="BOOK_III_CHAPTER_XVIII"></a>CHAPTER XVIII.<br /> +OF THE CALCULATION OF CHANCES.</h3> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVIII_1">§ 1.</a> "Probability," says Laplace,<a name="FNanchor_17_17" id="FNanchor_17_17"></a><a href="#Footnote_17_17" class="fnanchor">[17]</a> "has reference partly to our +ignorance, partly to our knowledge. We know that among three or more +events, one, and only one, must happen; but there is nothing leading us +to believe that any one of them will happen rather than the others. In +this state of indecision, it is impossible for us to pronounce with +certainty on their occurrence. It is, however, probable that any one of +these events, selected at pleasure, will not take place; because we +perceive several cases, all equally possible, which exclude its +occurrence, and only one which favours it.</p> + +<p>"The theory of chances consists in reducing all events of the same kind +to a certain number of cases equally possible, that is, such that we are +<i>equally undecided</i> as to their existence; and in determining the number +of these cases which are favourable to the event of which the +probability is sought. The ratio of that number to the number of all the +possible cases, is the measure of the probability; which is thus a +fraction, having for its numerator the number of cases favourable to the +event, and for its denominator the number of all the cases which are +possible."</p> + +<p>To a calculation of chances, then, according to Laplace, two things are +necessary: we must know that of several events some one will certainly +happen, and no more than one; and we must not know, nor have any reason +to expect, that it will be one of these events rather than another. It +has been contended that these are not the only requisites, and that +Laplace has overlooked, in the general theoretical statement, a +necessary part of the foundation of the doctrine of chances. <span class="pagenum"><a name="Page_62" id="Page_62">[Pg 62]</a></span>To be able +(it has been said) to pronounce two events equally probable, it is not +enough that we should know that one or the other must happen, and should +have no grounds for conjecturing which. Experience must have shown that +the two events are of equally frequent occurrence. Why, in tossing up a +halfpenny, do we reckon it equally probable that we shall throw cross or +pile? Because we know that in any great number of throws, cross and pile +are thrown about equally often; and that the more throws we make, the +more nearly the equality is perfect. We may know this if we please by +actual experiment; or by the daily experience which life affords of +events of the same general character; or deductively, from the effect of +mechanical laws on a symmetrical body acted upon by forces varying +indefinitely in quantity and direction. We may know it, in short, either +by specific experience, or on the evidence of our general knowledge of +nature. But, in one way or the other, we must know it, to justify us in +calling the two events equally probable; and if we knew it not, we +should proceed as much at haphazard in staking equal sums on the result, +as in laying odds.</p> + +<p>This view of the subject was taken in the first edition of the present +work: but I have since become convinced, that the theory of chances, as +conceived by Laplace and by mathematicians generally, has not the +fundamental fallacy which I had ascribed to it.</p> + +<p>We must remember that the probability of an event is not a quality of +the event itself, but a mere name for the degree of ground which we, or +some one else, have for expecting it. The probability of an event to one +person is a different thing from the probability of the same event to +another, or to the same person after he has acquired additional +evidence. The probability to me, that an individual of whom I know +nothing but his name, will die within the year, is totally altered by my +being told, the next minute, that he is in the last stage of a +consumption. Yet this makes no difference in the event itself, nor in +any of the causes on which it depends. Every event is in itself certain, +not probable: if we knew all, we should either know positively that it +will happen, or positively <span class="pagenum"><a name="Page_63" id="Page_63">[Pg 63]</a></span>that it will not. But its probability to us +means the degree of expectation of its occurrence, which we are +warranted in entertaining by our present evidence.</p> + +<p>Bearing this in mind, I think it must be admitted, that even when we +have no knowledge whatever to guide our expectations, except the +knowledge that what happens must be some one of a certain number of +possibilities, we may still reasonably judge, that one supposition is +more probable <i>to us</i> than another supposition; and if we have any +interest at stake, we shall best provide for it by acting conformably to +that judgment.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVIII_2">§ 2.</a> Suppose that we are required to take a ball from a box, of which we +only know that it contains balls both black and white, and none of any +other colour. We know that the ball we select will be either a black or +a white ball; but we have no ground for expecting black rather than +white, or white rather than black. In that case, if we are obliged to +make a choice, and to stake something on one or the other supposition, +it will, as a question of prudence, be perfectly indifferent which; and +we shall act precisely as we should have acted if we had known +beforehand that the box contained an equal number of black and white +balls. But though our conduct would be the same, it would not be founded +on any surmise that the balls were in fact thus equally divided; for we +might, on the contrary, know, by authentic information, that the box +contained ninety-nine balls of one colour, and only one of the other; +still, if we are not told which colour has only one, and which has +ninety-nine, the drawing of a white and of a black ball will be equally +probable to us; we shall have no reason for staking anything on the one +event rather than on the other; the option between the two will be a +matter of indifference; in other words it will be an even chance.</p> + +<p>But let it now be supposed that instead of two there are three +colours—white, black, and red; and that we are entirely ignorant of the +proportion in which they are mingled. We should then have no reason for +expecting one more than <span class="pagenum"><a name="Page_64" id="Page_64">[Pg 64]</a></span>another, and if obliged to bet, should venture +our stake on red, white, or black, with equal indifference. But should +we be indifferent whether we betted for or against some one colour, as, +for instance, white? Surely not. From the very fact that black and red +are each of them separately equally probable to us with white, the two +together must be twice as probable. We should in this case expect +not-white rather than white, and so much rather, that we would lay two +to one upon it. It is true, there might for aught we knew be more white +balls than black and red together; and if so, our bet would, if we knew +more, be seen to be a disadvantageous one. But so also, for aught we +knew, might there be more red balls than black and white, or more black +balls than white and red, and in such case the effect of additional +knowledge would be to prove to us that our bet was more advantageous +than we had supposed it to be. There is in the existing state of our +knowledge a rational probability of two to one against white; a +probability fit to be made a basis of conduct. No reasonable person +would lay an even wager in favour of white, against black and red; +though against black alone, or red alone, he might do so without +imprudence.</p> + +<p>The common theory, therefore, of the calculation of chances, appears to +be tenable. Even when we know nothing except the number of the possible +and mutually excluding contingencies, and are entirely ignorant of their +comparative frequency, we may have grounds, and grounds numerically +appreciable, for acting on one supposition rather than on another; and +this is the meaning of Probability.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVIII_3">§ 3.</a> The principle, however, on which the reasoning proceeds, is +sufficiently evident. It is the obvious one, that when the cases which +exist are shared among several kinds, it is impossible that <i>each</i> of +those kinds should be a majority of the whole: on the contrary, there +must be a majority against each kind, except one at most; and if any +kind has more than its share in proportion to the total number, the +others collectively must have less. Granting this axiom, and assuming +that we have no ground for selecting any one kind <span class="pagenum"><a name="Page_65" id="Page_65">[Pg 65]</a></span>as more likely than +the rest to surpass the average proportion, it follows that we cannot +rationally presume this of any; which we should do, if we were to bet in +favour of it, receiving less odds than in the ratio of the number of the +other kinds. Even, therefore, in this extreme case of the calculation of +probabilities, which does not rest on special experience at all, the +logical ground of the process is our knowledge, such knowledge as we +then have, of the laws governing the frequency of occurrence of the +different cases; but in this case the knowledge is limited to that +which, being universal and axiomatic, does not require reference to +specific experience, or to any considerations arising out of the special +nature of the problem under discussion.</p> + +<p>Except, however, in such cases as games of chance, where the very +purpose in view requires ignorance instead of knowledge, I can conceive +no case in which we ought to be satisfied with such an estimate of +chances as this; an estimate founded on the absolute minimum of +knowledge respecting the subject. It is plain that, in the case of the +coloured balls, a very slight ground of surmise that the white balls +were really more numerous than either of the other colours, would +suffice to vitiate the whole of the calculations made in our previous +state of indifference. It would place us in that position of more +advanced knowledge, in which the probabilities, to us, would be +different from what they were before; and in estimating these new +probabilities we should have to proceed on a totally different set of +data, furnished no longer by mere counting of possible suppositions, but +by specific knowledge of facts. Such data it should always be our +endeavour to obtain; and in all inquiries, unless on subjects equally +beyond the range of our means of knowledge and our practical uses, they +may be obtained, if not good, at least better than none at all.<a name="FNanchor_18_18" id="FNanchor_18_18"></a><a href="#Footnote_18_18" class="fnanchor">[18]</a></p> + +<p><span class="pagenum"><a name="Page_66" id="Page_66">[Pg 66]</a></span></p><p>It is obvious, too, that even when the probabilities are derived from +observation and experiment, a very slight improvement in the data, by +better observations, or by taking into fuller consideration the special +circumstances of the case, is of more use than the most elaborate +application of the calculus to probabilities founded on the data in +their previous state of inferiority. The neglect of this obvious +reflection has given rise to misapplications of the calculus of +probabilities which have made it the real opprobrium of mathematics. It +is sufficient to refer to the applications made of it to the credibility +of witnesses, and to the correctness of the verdicts of juries. In +regard to the first, common sense would dictate that it is impossible to +strike a general average of the veracity, and other qualifications for +true testimony, of mankind, or of any class of them; and even if it were +possible, the employment of it for such a purpose implies a +misapprehension of the use of averages: which serve indeed to protect +those whose interest is at stake, against mistaking the general result +of large masses of instances, but are of extremely small value as +grounds of expectation in any one individual instance, unless the case +be one of those in which the great majority of individual instances do +not differ much from the average. In the case of a witness, persons of +common sense would draw their conclusions from the degree of consistency +of his statements, his conduct under cross-examination, and the relation +of the case itself to his interests, his partialities, and his mental +<span class="pagenum"><a name="Page_67" id="Page_67">[Pg 67]</a></span>capacity, instead of applying so rude a standard (even if it were +capable of being verified) as the ratio between the number of true and +the number of erroneous statements which he may be supposed to make in +the course of his life.</p> + +<p>Again, on the subject of juries, or other tribunals, some mathematicians +have set out from the proposition that the judgment of any one judge, or +juryman, is, at least in some small degree, more likely to be right than +wrong, and have concluded that the chance of a number of persons +concurring in a wrong verdict is diminished, the more the number is +increased; so that if the judges are only made sufficiently numerous, +the correctness of the judgment may be reduced almost to certainty. I +say nothing of the disregard shown to the effect produced on the moral +position of the judges by multiplying their numbers; the virtual +destruction of their individual responsibility, and weakening of the +application of their minds to the subject. I remark only the fallacy of +reasoning from a wide average, to cases necessarily differing greatly +from any average. It may be true that taking all causes one with +another, the opinion of any one of the judges would be oftener right +than wrong; but the argument forgets that in all but the more simple +cases, in all cases in which it is really of much consequence what the +tribunal is, the proposition might probably be reversed; besides which, +the cause of error, whether arising from the intricacy of the case or +from some common prejudice or mental infirmity, if it acted upon one +judge, would be extremely likely to affect all the others in the same +manner, or at least a majority, and thus render a wrong instead of a +right decision more probable, the more the number was increased.</p> + +<p>These are but samples of the errors frequently committed by men who, +having made themselves familiar with the difficult formulæ which algebra +affords for the estimation of chances under suppositions of a complex +character, like better to employ those formulæ in computing what are the +probabilities to a person half informed about a case, than to look out +for means of being better informed. Before applying the doctrine of +chances to any scientific purpose, the foundation <span class="pagenum"><a name="Page_68" id="Page_68">[Pg 68]</a></span>must be laid for an +evaluation of the chances, by possessing ourselves of the utmost +attainable amount of positive knowledge. The knowledge required is that +of the comparative frequency with which the different events in fact +occur. For the purposes, therefore, of the present work, it is allowable +to suppose, that conclusions respecting the probability of a fact of a +particular kind, rest on our knowledge of the proportion between the +cases in which facts of that kind occur, and those in which they do not +occur: this knowledge being either derived from specific experiment, or +deduced from our knowledge of the causes in operation which tend to +produce, compared with those which tend to prevent, the fact in +question.</p> + +<p>Such calculation of chances is grounded on an induction; and to render +the calculation legitimate, the induction must be a valid one. It is not +less an induction, though it does not prove that the event occurs in all +cases of a given description, but only that out of a given number of +such cases, it occurs in about so many. The fraction which +mathematicians use to designate the probability of an event, is the +ratio of these two numbers; the ascertained proportion between the +number of cases in which the event occurs, and the sum of all the cases, +those in which it occurs and in which it does not occur taken together. +In playing at cross and pile, the description of cases concerned are +throws, and the probability of cross is one-half, because if we throw +often enough, cross is thrown about once in every two throws. In the +cast of a die, the probability of ace is one-sixth; not simply because +there are six possible throws, of which ace is one, and because we do +not know any reason why one should turn up rather than another; though I +have admitted the validity of this ground in default of a better; but +because we do actually know, either by reasoning or by experience, that +in a hundred, or a million of throws, ace is thrown about one-sixth of +that number, or once in six times.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVIII_4">§ 4.</a> I say, "either by reasoning or by experience;" meaning specific +experience. But in estimating probabilities, it is not a matter of +indifference from which of these two <span class="pagenum"><a name="Page_69" id="Page_69">[Pg 69]</a></span>sources we derive our assurance. +The probability of events as calculated from their mere frequency in +past experience, affords a less secure basis for practical guidance, +than their probability as deduced from an equally accurate knowledge of +the frequency of occurrence of their causes.</p> + +<p>The generalization, that an event occurs in ten out of every hundred +cases of a given description, is as real an induction as if the +generalization were that it occurs in all cases. But when we arrive at +the conclusion by merely counting instances in actual experience, and +comparing the number of cases in which A has been present with the +number in which it has been absent, the evidence is only that of the +method of Agreement, and the conclusion amounts only to an empirical +law. We can make a step beyond this when we can ascend to the causes on +which the occurrence of A or its non-occurrence will depend, and form an +estimate of the comparative frequency of the causes favourable and of +those unfavourable to the occurrence. These are data of a higher order, +by which the empirical law derived from a mere numerical comparison of +affirmative and negative instances will be either corrected or +confirmed, and in either case we shall obtain a more correct measure of +probability than is given by that numerical comparison. It has been well +remarked that in the kind of examples by which the doctrine of chances +is usually illustrated, that of balls in a box, the estimate of +probabilities is supported by reasons of causation, stronger than +specific experience. "What is the reason that in a box where there are +nine black balls and one white, we expect to draw a black ball nine +times as much (in other words, nine times as often, frequency being the +gauge of intensity in expectation) as a white? Obviously because the +local conditions are nine times as favourable, because the hand may +alight in nine places and get a black ball, while it can only alight in +one place and find a white ball; just for the same reason that we do not +expect to succeed in finding a friend in a crowd, the conditions in +order that we and he should come together being many and difficult. This +of course would not hold to the same extent were the white balls of +smaller size than the black, neither would the probability remain the +<span class="pagenum"><a name="Page_70" id="Page_70">[Pg 70]</a></span>same: the larger ball would be much more likely to meet the hand."<a name="FNanchor_19_19" id="FNanchor_19_19"></a><a href="#Footnote_19_19" class="fnanchor">[19]</a></p> + +<p>It is, in fact, evident, that when once causation is admitted as an +universal law, our expectation of events can only be rationally grounded +on that law. To a person who recognises that every event depends on +causes, a thing's having happened once is a reason for expecting it to +happen again, only because proving that there exists, or is liable to +exist, a cause adequate to produce it.<a name="FNanchor_20_20" id="FNanchor_20_20"></a><a href="#Footnote_20_20" class="fnanchor">[20]</a> The frequency of the +particular event, apart from all surmise respecting its cause, can give +rise to no other induction than that <i>per enumerationem simplicem</i>; and +the precarious inferences derived from this, are superseded, and +disappear from the field, as soon as the principle of causation makes +its appearance there.</p> + +<p>Notwithstanding, however, the abstract superiority of an estimate of +probability grounded on causes, it is a fact that in almost all cases in +which chances admit of estimation sufficiently <span class="pagenum"><a name="Page_71" id="Page_71">[Pg 71]</a></span>precise to render their +numerical appreciation of any practical value, the numerical data are +not drawn from knowledge of the causes, but from experience of the +events themselves. The probabilities of life at different ages, or in +different climates; the probabilities of recovery from a particular +disease; the chances of the birth of male or female offspring; the +chances of the destruction of houses or other property by fire; the +chances of the loss of a ship in a particular voyage; are deduced from +bills of mortality, returns from hospitals, registers of births, of +shipwrecks, &c., that is, from the observed frequency not of the causes, +but of the effects. The reason is, that in all these classes of facts, +the causes are either not amenable to direct observation at all, or not +with the requisite precision, and we have no means of judging of their +frequency except from the empirical law afforded by the frequency of the +effects. The inference does not the less depend on causation alone. We +reason from an effect to a similar effect by passing through the cause. +If the actuary of an insurance office infers from his tables that among +a hundred persons now living, of a particular age, five on the average +will attain the age of seventy, his inference is legitimate, not for the +simple reason that this is the proportion who have lived till seventy in +times past, but because the fact of their having so lived shows that +this is the proportion existing, at that place and time, between the +causes which prolong life to the age of seventy, and those tending to +bring it to an earlier close.<a name="FNanchor_21_21" id="FNanchor_21_21"></a><a href="#Footnote_21_21" class="fnanchor">[21]</a></p> + + +<p><span class="pagenum"><a name="Page_72" id="Page_72">[Pg 72]</a></span></p><p class="newsection"><a name="BOOK_III_CHAPTER_XVIII_5">§ 5.</a> From the preceding principles it is easy to deduce the +demonstration of that theorem of the doctrine of probabilities, which is +the foundation of its application to inquiries for ascertaining the +occurrence of a given event, or the reality of an individual fact. The +signs or evidences by which a fact is usually proved, are some of its +consequences: and the inquiry hinges upon determining what cause is most +likely to have produced a given effect. The theorem applicable to such +investigations is the Sixth Principle in Laplace's <i>Essai Philosophique +sur les Probabilités</i>, which is described by him as the "fundamental +principle of that branch of the Analysis of Chances, which consists in +ascending from events to their causes."<a name="FNanchor_22_22" id="FNanchor_22_22"></a><a href="#Footnote_22_22" class="fnanchor">[22]</a></p> + +<p>Given an effect to be accounted for, and there being several causes +which might have produced it, but of the presence of which in the +particular case nothing is known; the probability that the effect was +produced by any one of these causes <i>is as the antecedent probability of +the cause, multiplied by the probability that the cause, if it existed, +would have produced the given effect</i>.</p> + +<p>Let M be the effect, and A, B, two causes, by either of which it might +have been produced. To find the probability that it was produced by the +one and not by the other, ascertain which of the two is most likely to +have existed, and which of them, if it did exist, was most likely to +produce the effect M: the probability sought is a compound of these two +probabilities.</p> + +<p><span class="smcap">Case I.</span> Let the causes be both alike in the second respect; either A or +B, when it exists, being supposed equally likely (or equally certain) to +produce M; but let A be in itself twice as likely as B to exist, that +is, twice as <span class="pagenum"><a name="Page_73" id="Page_73">[Pg 73]</a></span>frequent a phenomenon. Then it is twice as likely to have +existed in this case, and to have been the cause which produced M.</p> + +<p>For, since A exists in nature twice as often as B; in any 300 cases in +which one or other existed, A has existed 200 times and B 100. But +either A or B must have existed wherever M is produced: therefore in 300 +times that M is produced, A was the producing cause 200 times, B only +100, that is, in the ratio of 2 to 1. Thus, then, if the causes are +alike in their capacity of producing the effect, the probability as to +which actually produced it, is in the ratio of their antecedent +probabilities.</p> + +<p><span class="smcap">Case II.</span> Reversing the last hypothesis, let us suppose that the causes +are equally frequent, equally likely to have existed, but not equally +likely, if they did exist, to produce M: that in three times in which A +occurs, it produces that effect twice, while B, in three times, produces +it only once. Since the two causes are equally frequent in their +occurrence; in every six times that either one or the other exists, A +exists three times and B three times. A, of its three times, produces M +in two; B, of its three times, produces M in one. Thus, in the whole six +times, M is only produced thrice; but of that thrice it is produced +twice by A, once only by B. Consequently, when the antecedent +probabilities of the causes are equal, the chances that the effect was +produced by them are in the ratio of the probabilities that if they did +exist they would produce the effect.</p> + +<p><span class="smcap">Case III.</span> The third case, that in which the causes are unlike in both +respects, is solved by what has preceded. For, when a quantity depends +on two other quantities, in such a manner that while either of them +remains constant it is proportional to the other, it must necessarily be +proportional to the product of the two quantities, the product being the +only function of the two which obeys that law of variation. Therefore, +the probability that M was produced by either cause, is as the +antecedent probability of the cause, multiplied by the probability that +if it existed it would produce M. Which was to be demonstrated.</p> + +<p><span class="pagenum"><a name="Page_74" id="Page_74">[Pg 74]</a></span></p><p>Or we may prove the third case as we proved the first and second. Let A +be twice as frequent as B; and let them also be unequally likely, when +they exist, to produce M: let A produce it twice in four times, B thrice +in four times. The antecedent probability of A is to that of B as 2 to +1; the probabilities of their producing M are as 2 to 3; the product of +these ratios is the ratio of 4 to 3: and this will be the ratio of the +probabilities that A or B was the producing cause in the given instance. +For, since A is twice as frequent as B, out of twelve cases in which one +or other exists, A exists in 8 and B in 4. But of its eight cases, A, by +the supposition, produces M in only 4, while B of its four cases +produces M in 3. M, therefore, is only produced at all in seven of the +twelve cases; but in four of these it is produced by A, in three by B; +hence, the probabilities of its being produced by A and by B are as 4 to +3, and are expressed by the fractions 4/7 and 3/7. Which was to be +demonstrated.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XVIII_6">§ 6.</a> It remains to examine the bearing of the doctrine of chances on the +peculiar problem which occupied us in the preceding chapter, namely, how +to distinguish coincidences which are casual from those which are the +result of law; from those in which the facts which accompany or follow +one another are somehow connected through causation.</p> + +<p>The doctrine of chances affords means by which, if we knew the <i>average</i> +number of coincidences to be looked for between two phenomena connected +only casually, we could determine how often any given deviation from +that average will occur by chance. If the probability of any casual +coincidence, considered in itself, be 1/<i>m</i>, the probability that the +same coincidence will be repeated <i>n</i> times in succession is 1/<i>m</i><sup>n</sup>. +For example, in one throw of a die the probability of ace being 1/6; the +probability of throwing ace twice in succession will be 1 divided by the +square of 6, or 1/36. For ace is <span class="pagenum"><a name="Page_75" id="Page_75">[Pg 75]</a></span>thrown at the first throw once in six, +or six in thirty-six times, and of those six, the die being cast again, +ace will be thrown but once; being altogether once in thirty-six times. +The chance of the same cast three times successively is, by a similar +reasoning, 1/6<sup>3</sup> or 1/216: that is, the event will happen, on a large +average, only once in two hundred and sixteen throws.</p> + +<p>We have thus a rule by which to estimate the probability that any given +series of coincidences arises from chance; provided we can measure +correctly the probability of a single coincidence. If we can obtain an +equally precise expression for the probability that the same series of +coincidences arises from causation, we should only have to compare the +numbers. This however, can rarely be done. Let us see what degree of +approximation can practically be made to the necessary precision.</p> + +<p>The question falls within Laplace's sixth principle, just demonstrated. +The given fact, that is to say, the series of coincidences, may have +originated either in a casual conjunction of causes, or in a law of +nature. The probabilities, therefore, that the fact originated in these +two modes, are as their antecedent probabilities, multiplied by the +probabilities that if they existed they would produce the effect. But +the particular combination of chances, if it occurred, or the law of +nature if real, would certainly produce the series of coincidences. The +probabilities, therefore, that the coincidences are produced by the two +causes in question, are as the antecedent probabilities of the causes. +One of these, the antecedent probability of the combination of mere +chances which would produce the given result, is an appreciable +quantity. The antecedent probability of the other supposition may be +susceptible of a more or less exact estimation, according to the nature +of the case.</p> + +<p>In some cases, the coincidence, supposing it to be the result of +causation at all, must be the result of a known cause: as the succession +of aces, if not accidental, must arise from the loading of the die. In +such cases we may be able to <span class="pagenum"><a name="Page_76" id="Page_76">[Pg 76]</a></span>form a conjecture as to the antecedent +probability of such a circumstance, from the characters of the parties +concerned, or other such evidence; but it would be impossible to +estimate that probability with anything like numerical precision. The +counter-probability, however, that of the accidental origin of the +coincidence, dwindling so rapidly as it does at each new trial; the +stage is soon reached at which the chance of unfairness in the die, +however small in itself, must be greater than that of a casual +coincidence: and on this ground, a practical decision can generally be +come to without much hesitation, if there be the power of repeating the +experiment.</p> + +<p>When, however, the coincidence is one which cannot be accounted for by +any known cause, and the connexion between the two phenomena, if +produced by causation, must be the result of some law of nature hitherto +unknown; which is the case we had in view in the last chapter; then, +though the probability of a casual coincidence may be capable of +appreciation, that of the counter-supposition, the existence of an +undiscovered law of nature, is clearly unsusceptible of even an +approximate valuation. In order to have the data which such a case would +require, it would be necessary to know what proportion of all the +individual sequences or coexistences occurring in nature are the result +of law, and what proportion are mere casual coincidences. It being +evident that we cannot form any plausible conjecture as to this +proportion, much less appreciate it numerically, we cannot attempt any +precise estimation of the comparative probabilities. But of this we are +sure, that the detection of an unknown law of nature—of some previously +unrecognised constancy of conjunction among phenomena—is no uncommon +event. If, therefore, the number of instances in which a coincidence is +observed, over and above that which would arise on the average from the +mere concurrence of chances, be such that so great an amount of +coincidences from accident alone would be an extremely uncommon event; +we have reason to conclude that the coincidence is the effect of +causation, and may be received (subject to correction from further +experience) as an empirical law. Further than this, in point of +precision, we <span class="pagenum"><a name="Page_77" id="Page_77">[Pg 77]</a></span>cannot go; nor, in most cases, is greater precision +required, for the solution of any practical doubt.<a name="FNanchor_23_23" id="FNanchor_23_23"></a><a href="#Footnote_23_23" class="fnanchor">[23]</a></p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_78" id="Page_78">[Pg 78]</a></span></p> +<h3><a name="BOOK_III_CHAPTER_XIX" id="BOOK_III_CHAPTER_XIX"></a>CHAPTER XIX.<br /> +OF THE EXTENSION OF DERIVATIVE LAWS TO ADJACENT CASES.</h3> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XIX_1">§ 1.</a> We have had frequent occasion to notice the inferior generality of +derivative laws, compared with the ultimate laws from which they are +derived. This inferiority, which affects not only the extent of the +propositions themselves, but their degree of certainty within that +extent, is most conspicuous in the uniformities of coexistence and +sequence obtaining between effects which depend ultimately on different +primeval causes. Such uniformities will only obtain where there exists +the same collocation of those primeval causes. If the collocation +varies, though the laws themselves remain the same, a totally different +set of derivative uniformities may, and generally will, be the result.</p> + +<p>Even where the derivative uniformity is between different effects of the +same cause, it will by no means obtain as universally as the law of the +cause itself. If <i>a</i> and <i>b</i> accompany or succeed one another as effects +of the cause A, it by no means follows that A is the only cause which +can produce them, or that if there be another cause, as B, capable of +producing <i>a</i>, it must produce <i>b</i> likewise. The conjunction therefore +of <i>a</i> and <i>b</i> perhaps does not hold universally, but only in the +instances in which <i>a</i> arises from A. When it is produced by a cause +other than A, <i>a</i> and <i>b</i> may be dissevered. Day (for example) is always +in our experience followed by night; but day is not the cause of night; +both are successive effects of a common cause, the periodical passage of +the spectator into and out of the earth's shadow, consequent on the +earth's rotation, and on the illuminating property of the sun. If, +therefore, day is ever produced by a different cause or set of causes +from this, day will not, or at least may not, be followed <span class="pagenum"><a name="Page_79" id="Page_79">[Pg 79]</a></span>by night. On +the sun's own surface, for instance, this may be the case.</p> + +<p>Finally, even when the derivative uniformity is itself a law of +causation (resulting from the combination of several causes), it is not +altogether independent of collocations. If a cause supervenes, capable +of wholly or partially counteracting the effect of any one of the +conjoined causes, the effect will no longer conform to the derivative +law. While, therefore, each ultimate law is only liable to frustration +from one set of counteracting causes, the derivative law is liable to it +from several. Now, the possibility of the occurrence of counteracting +causes which do not arise from any of the conditions involved in the law +itself, depends on the original collocations.</p> + +<p>It is true that (as we formerly remarked) laws of causation, whether +ultimate or derivative, are, in most cases, fulfilled even when +counteracted; the cause produces its effect, though that effect is +destroyed by something else. That the effect may be frustrated, is, +therefore, no objection to the universality of laws of causation. But it +is fatal to the universality of the sequences or coexistences of +effects, which compose the greater part of the derivative laws flowing +from laws of causation. When, from the law of a certain combination of +causes, there results a certain order in the effects; as from the +combination of a single sun with the rotation of an opaque body round +its axis, there results, on the whole surface of that opaque body, an +alternation of day and night; then if we suppose one of the combined +causes counteracted, the rotation stopped, the sun extinguished, or a +second sun superadded, the truth of that particular law of causation is +in no way affected; it is still true that one sun shining on an opaque +revolving body will alternately produce day and night; but since the sun +no longer does shine on such a body, the derivative uniformity, the +succession of day and night on the given planet, is no longer true. +Those derivative uniformities, therefore, which are not laws of +causation, are (except in the rare case of their depending on one cause +alone, not on a combination of causes,) always more or less <span class="pagenum"><a name="Page_80" id="Page_80">[Pg 80]</a></span>contingent +on collocations; and are hence subject to the characteristic infirmity +of empirical laws, that of being admissible only where the collocations +are known by experience to be such as are requisite for the truth of the +law, that is, only within the conditions of time and place confirmed by +actual observation.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XIX_2">§ 2.</a> This principle, when stated in general terms, seems clear and +indisputable; yet many of the ordinary judgments of mankind, the +propriety of which is not questioned, have at least the semblance of +being inconsistent with it. On what grounds, it may be asked, do we +expect that the sun will rise to-morrow? To-morrow is beyond the limits +of time comprehended in our observations. They have extended over some +thousands of years past, but they do not include the future. Yet we +infer with confidence that the sun will rise to-morrow; and nobody +doubts that we are entitled to do so. Let us consider what is the +warrant for this confidence.</p> + +<p>In the example in question, we know the causes on which the derivative +uniformity depends. They are, the sun giving out light, the earth in a +state of rotation and intercepting light. The induction which shows +these to be the real causes, and not merely prior effects of a common +cause, being complete; the only circumstances which could defeat the +derivative law are such as would destroy or counteract one or other of +the combined causes. While the causes exist, and are not counteracted, +the effect will continue. If they exist and are not counteracted +to-morrow, the sun will rise to-morrow.</p> + +<p>Since the causes, namely the sun and the earth, the one in the state of +giving out light, the other in a state of rotation, will exist until +something destroys them; all depends on the probabilities of their +destruction, or of their counteraction. We know by observation (omitting +the inferential proofs of an existence for thousands of ages anterior), +that these phenomena have continued for (say) five thousand years. +Within that time there has existed no cause sufficient to <span class="pagenum"><a name="Page_81" id="Page_81">[Pg 81]</a></span>diminish them +appreciably; nor which has counteracted their effect in any appreciable +degree. The chance, therefore, that the sun may not rise to-morrow, +amounts to the chance that some cause, which has not manifested itself +in the smallest degree during five thousand years, will exist to-morrow +in such intensity as to destroy the sun or the earth, the sun's light or +the earth's rotation, or to produce an immense disturbance in the effect +resulting from those causes.</p> + +<p>Now, if such a cause will exist to-morrow, or at any future time, some +cause, proximate or remote, of that cause must exist now, and must have +existed during the whole of the five thousand years. If, therefore, the +sun do not rise to-morrow, it will be because some cause has existed, +the effects of which though during five thousand years they have not +amounted to a perceptible quantity, will in one day become overwhelming. +Since this cause has not been recognised during such an interval of +time, by observers stationed on our earth, it must, if it exist, be +either some agent whose effects develop themselves gradually and very +slowly, or one which existed in regions beyond our observation, and is +now on the point of arriving in our part of the universe. Now all causes +which we have experience of, act according to laws incompatible with the +supposition that their effects, after accumulating so slowly as to be +imperceptible for five thousand years, should start into immensity in a +single day. No mathematical law of proportion between an effect and the +quantity or relations of its cause, could produce such contradictory +results. The sudden development of an effect of which there was no +previous trace, always arises from the coming together of several +distinct causes, not previously conjoined; but if such sudden +conjunction is destined to take place, the causes, or <i>their</i> causes, +must have existed during the entire five thousand years; and their not +having once come together during that period, shows how rare that +particular combination is. We have, therefore, the warrant of a rigid +induction for considering it probable, in a degree undistinguishable +from certainty, that the known conditions requisite for the sun's rising +will exist to-morrow.</p> + + +<p><span class="pagenum"><a name="Page_82" id="Page_82">[Pg 82]</a></span></p><p class="newsection"><a name="BOOK_III_CHAPTER_XIX_3">§ 3.</a> But this extension of derivative laws, not causative, beyond the +limits of observation, can only be to <i>adjacent</i> cases. If instead of +to-morrow we had said this day twenty thousand years, the inductions +would have been anything but conclusive. That a cause which, in +opposition to very powerful causes, produced no perceptible effect +during five thousand years, should produce a very considerable one by +the end of twenty thousand, has nothing in it which is not in conformity +with our experience of causes. We know many agents, the effect of which +in a short period does not amount to a perceptible quantity, but by +accumulating for a much longer period becomes considerable. Besides, +looking at the immense multitude of the heavenly bodies, their vast +distances, and the rapidity of the motion of such of them as are known +to move, it is a supposition not at all contradictory to experience that +some body may be in motion towards us, or we towards it, within the +limits of whose influence we have not come during five thousand years, +but which in twenty thousand more may be producing effects upon us of +the most extraordinary kind. Or the fact which is capable of preventing +sunrise may be, not the cumulative effect of one cause, but some new +combination of causes; and the chances favourable to that combination, +though they have not produced it once in five thousand years, may +produce it once in twenty thousand. So that the inductions which +authorize us to expect future events, grow weaker and weaker the further +we look into the future, and at length become inappreciable.</p> + +<p>We have considered the probabilities of the sun's rising to-morrow, as +derived from the real laws, that is, from the laws of the causes on +which that uniformity is dependent. Let us now consider how the matter +would have stood if the uniformity had been known only as an empirical +law; if we had not been aware that the sun's light, and the earth's +rotation (or the sun's motion), were the causes on which the periodical +occurrence of daylight depends. We could have extended this empirical +law to cases adjacent in time, though not to so great a distance of time +as we can now. Having evidence that the effects had remained unaltered +and been punctually conjoined <span class="pagenum"><a name="Page_83" id="Page_83">[Pg 83]</a></span>for five thousand years, we could infer +that the unknown causes on which the conjunction is dependent had +existed undiminished and uncounteracted during the same period. The same +conclusions, therefore, would follow as in the preceding case; except +that we should only know that during five thousand years nothing had +occurred to defeat perceptibly this particular effect; while, when we +know the causes, we have the additional assurance, that during that +interval no such change has been noticeable in the causes themselves, as +by any degree of multiplication or length of continuance could defeat +the effect.</p> + +<p>To this must be added, that when we know the causes, we may be able to +judge whether there exists any known cause capable of counteracting +them; while as long as they are unknown, we cannot be sure but that if +we did know them, we could predict their destruction from causes +actually in existence. A bedridden savage, who had never seen the +cataract of Niagara, but who lived within hearing of it, might imagine +that the sound he heard would endure for ever; but if he knew it to be +the effect of a rush of waters over a barrier of rock which is +progressively wearing away, he would know that within a number of ages +which may be calculated, it will be heard no more. In proportion, +therefore, to our ignorance of the causes on which the empirical law +depends, we can be less assured that it will continue to hold good; and +the farther we look into futurity, the less improbable is it that some +one of the causes, whose coexistence gives rise to the derivative +uniformity, may be destroyed or counteracted. With every prolongation of +time, the chances multiply of such an event, that is to say, its +non-occurrence hitherto becomes a less guarantee of its not occurring +within the given time. If, then, it is only to cases which in point of +time are adjacent (or nearly adjacent) to those which we have actually +observed, that <i>any</i> derivative law, not of causation, can be extended +with an assurance equivalent to certainty, much more is this true of a +merely empirical law. Happily, for the purposes of life it is to such +cases alone that we can almost ever have occasion to extend them.</p> + +<p><span class="pagenum"><a name="Page_84" id="Page_84">[Pg 84]</a></span></p><p>In respect of place, it might seem that a merely empirical law could +not be extended even to adjacent cases; that we could have no assurance +of its being true in any place where it has not been specially observed. +The past duration of a cause is a guarantee for its future existence, +unless something occurs to destroy it; but the existence of a cause in +one or any number of places, is no guarantee for its existence in any +other place, since there is no uniformity in the collocations of +primeval causes. When, therefore, an empirical law is extended beyond +the local limits within which it has been found true by observation, the +cases to which it is thus extended must be such as are presumably within +the influence of the same individual agents. If we discover a new planet +within the known bounds of the solar system (or even beyond those +bounds, but indicating its connexion with the system by revolving round +the sun), we may conclude, with great probability, that it revolves on +its axis. For all the known planets do so; and this uniformity points to +some common cause, antecedent to the first records of astronomical +observation: and though the nature of this cause can only be matter of +conjecture, yet if it be, as is not unlikely, and as Laplace's theory +supposes, not merely the same kind of cause, but the same individual +cause (such as an impulse given to all the bodies at once), that cause, +acting at the extreme points of the space occupied by the sun and +planets, is likely, unless defeated by some counteracting cause, to have +acted at every intermediate point, and probably somewhat beyond; and +therefore acted, in all probability, upon the supposed newly-discovered +planet.</p> + +<p>When, therefore, effects which are always found conjoined, can be traced +with any probability to an identical (and not merely a similar) origin, +we may with the same probability extend the empirical law of their +conjunction to all places within the extreme local boundaries within +which the fact has been observed; subject to the possibility of +counteracting causes in some portion of the field. Still more +confidently may we do so when the law is not merely empirical; when the +phenomena which we find conjoined are effects of ascertained <span class="pagenum"><a name="Page_85" id="Page_85">[Pg 85]</a></span>causes, +from the laws of which the conjunction of their effects is deducible. In +that case, we may both extend the derivative uniformity over a larger +space, and with less abatement for the chance of counteracting causes. +The first, because instead of the local boundaries of our observation of +the fact itself, we may include the extreme boundaries of the +ascertained influence of its causes. Thus the succession of day and +night, we know, holds true of all the bodies of the solar system except +the sun itself; but we know this only because we are acquainted with the +causes: if we were not, we could not extend the proposition beyond the +orbits of the earth and moon, at both extremities of which we have the +evidence of observation for its truth. With respect to the probability +of counteracting causes, it has been seen that this calls for a greater +abatement of confidence, in proportion to our ignorance of the causes on +which the phenomena depend. On both accounts, therefore, a derivative +law which we know how to resolve, is susceptible of a greater extension +to cases adjacent in place, than a merely empirical law.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_86" id="Page_86">[Pg 86]</a></span></p> +<h3><a name="BOOK_III_CHAPTER_XX" id="BOOK_III_CHAPTER_XX"></a>CHAPTER XX.<br /> +OF ANALOGY.</h3> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XX_1">§ 1.</a> The word Analogy, as the name of a mode of reasoning, is generally +taken for some kind of argument supposed to be of an inductive nature, +but not amounting to a complete induction. There is no word, however, +which is used more loosely, or in a greater variety of senses, than +Analogy. It sometimes stands for arguments which may be examples of the +most rigorous Induction. Archbishop Whately, for instance, following +Ferguson and other writers, defines Analogy conformably to its primitive +acceptation, that which was given to it by mathematicians, Resemblance +of Relations. In this sense, when a country which has sent out colonies +is termed the mother country, the expression is analogical, signifying +that the colonies of a country stand in the same <i>relation</i> to her in +which children stand to their parents. And if any inference be drawn +from this resemblance of relations, as, for instance, that obedience or +affection is due from colonies to the mother country, this is called +reasoning by analogy. Or if it be argued that a nation is most +beneficially governed by an assembly elected by the people, from the +admitted fact that other associations for a common purpose, such as +joint-stock companies, are best managed by a committee chosen by the +parties interested; this, too, is an argument from analogy in the +preceding sense, because its foundation is, not that a nation is like a +joint stock company, or Parliament like a board of directors, but that +Parliament stands in the same <i>relation</i> to the nation in which a board +of directors stands to a joint stock company. Now, in an argument of +this nature, there is no inherent inferiority of conclusiveness. Like +other arguments from resemblance, it may amount to nothing, or it may be +a perfect and conclusive induction. The circumstance <span class="pagenum"><a name="Page_87" id="Page_87">[Pg 87]</a></span>in which the two +cases resemble, may be capable of being shown to be the <i>material</i> +circumstance; to be that on which all the consequences, necessary to be +taken into account in the particular discussion, depend. In the example +last given, the resemblance is one of relation; the <i>fundamentum +relationis</i> being the management by a few persons, of affairs in which a +much greater number are interested along with them. Now, some may +contend that this circumstance which is common to the two cases, and the +various consequences which follow from it, have the chief share in +determining all the effects which make up what we term good or bad +administration. If they can establish this, their argument has the force +of a rigorous induction; if they cannot, they are said to have failed in +proving the analogy between the two cases; a mode of speech which +implies that when the analogy can be proved, the argument founded on it +cannot be resisted.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XX_2">§ 2.</a> It is on the whole more usual, however, to extend the name of +analogical evidence to arguments from any sort of resemblance, provided +they do not amount to a complete induction: without peculiarly +distinguishing resemblance of relations. Analogical reasoning, in this +sense, may be reduced to the following formula:—Two things resemble +each other in one or more respects; a certain proposition is true of the +one; therefore it is true of the other. But we have nothing here by +which to discriminate analogy from induction, since this type will serve +for all reasoning from experience. In the strictest induction, equally +with the faintest analogy, we conclude because A resembles B in one or +more properties, that it does so in a certain other property. The +difference is, that in the case of a complete induction it has been +previously shown, by due comparison of instances, that there is an +invariable conjunction between the former property or properties and the +latter property; but in what is called analogical reasoning, no such +conjunction has been made out. There have been no opportunities of +putting in practice the Method of Difference, or even the Method of +Agreement; but we <span class="pagenum"><a name="Page_88" id="Page_88">[Pg 88]</a></span>conclude (and that is all which the argument of +analogy amounts to) that a fact <i>m</i>, known to be true of A, is more +likely to be true of B if B agrees with A in some of its properties +(even though no connexion is known to exist between <i>m</i> and those +properties), than if no resemblance at all could be traced between B and +any other thing known to possess the attribute <i>m</i>.</p> + +<p>To this argument it is of course requisite, that the properties common +to A with B shall be merely not known to be connected with <i>m</i>; they +must not be properties known to be unconnected with it. If, either by +processes of elimination, or by deduction from previous knowledge of the +laws of the properties in question, it can be concluded that they have +nothing to do with <i>m</i>, the argument of analogy is put out of court. The +supposition must be that <i>m</i> is an effect really dependent on some +property of A, but we know not on which. We cannot point out any of the +properties of A, which is the cause of <i>m</i>, or united with it by any +law. After rejecting all which we know to have nothing to do with it, +there remain several between which we are unable to decide: of which +remaining properties, B possesses one or more. This accordingly, we +consider as affording grounds, of more or less strength, for concluding +by analogy that B possesses the attribute <i>m</i>.</p> + +<p>There can be no doubt that every such resemblance which can be pointed +out between B and A, affords some degree of probability, beyond what +would otherwise exist, in favour of the conclusion drawn from it. If B +resembled A in all its ultimate properties, its possessing the attribute +<i>m</i> would be a certainty, not a probability: and every resemblance which +can be shown to exist between them, places it by so much the nearer to +that point. If the resemblance be in an ultimate property, there will be +resemblance in all the derivative properties dependent on that ultimate +property, and of these <i>m</i> may be one. If the resemblance be in a +derivative property, there is reason to expect resemblance in the +ultimate property on which it depends, and in the other derivative +properties dependent on the same ultimate property. Every resemblance +<span class="pagenum"><a name="Page_89" id="Page_89">[Pg 89]</a></span>which can be shown to exist, affords ground for expecting an indefinite +number of other resemblances: the particular resemblance sought will, +therefore, be oftener found among things thus known to resemble, than +among things between which we know of no resemblance.<a name="FNanchor_24_24" id="FNanchor_24_24"></a><a href="#Footnote_24_24" class="fnanchor">[24]</a></p> + +<p>For example, I might infer that there are probably inhabitants in the +moon, because there are inhabitants on the earth, in the sea, and in the +air: and this is the evidence of analogy. The circumstance of having +inhabitants is here assumed not to be an ultimate property, but (as is +reasonable to suppose) a consequence of other properties; and depending, +therefore, in the case of the earth, on some of its properties as a +portion of the universe, but on which of those properties we know not. +Now the moon resembles the earth in being a solid, opaque, nearly +spherical substance, appearing to contain, or to have contained, active +volcanoes; receiving heat and light from the sun, in about the same +quantity as our earth; revolving on its axis; composed of materials +which gravitate, and obeying all the various laws resulting from that +property. And I think no one will deny that if this were all that was +known of the moon, the existence of inhabitants in that luminary would +derive from these various resemblances to the earth, a greater degree of +probability than it would otherwise have: though the amount of the +augmentation it would be useless to attempt to estimate.</p> + +<p>If, however, every resemblance proved between B and A, in any point not +known to be immaterial with respect to <i>m</i>, <span class="pagenum"><a name="Page_90" id="Page_90">[Pg 90]</a></span>forms some additional +reason for presuming that B has the attribute <i>m</i>; it is clear, <i>è +contra</i>, that every dissimilarity which can be proved between them, +furnishes a counter-probability of the same nature on the other side. It +is not indeed unusual that different ultimate properties should, in some +particular instances, produce the same derivative property; but on the +whole it is certain that things which differ in their ultimate +properties, will differ at least as much in the aggregate of their +derivative properties, and that the differences which are unknown will +on the average of cases bear some proportion to those which are known. +There will, therefore, be a competition between the known points of +agreement and the known points of difference in A and B; and according +as the one or the other may be deemed to preponderate, the probability +derived from analogy will be for or against B's having the property <i>m</i>. +The moon, for instance, agrees with the earth in the circumstances +already mentioned; but differs in being smaller, in having its surface +more unequal, and apparently volcanic throughout, in having, at least on +the side next the earth, no atmosphere sufficient to refract light, no +clouds, and (it is therefore concluded) no water. These differences, +considered merely as such, might perhaps balance the resemblances, so +that analogy would afford no presumption either way. But considering +that some of the circumstances which are wanting on the moon are among +those which, on the earth, are found to be indispensable conditions of +animal life, we may conclude that if that phenomenon does exist in the +moon, (or at all events on the nearer side,) it must be as an effect of +causes totally different from those on which it depends here; as a +consequence, therefore, of the moon's differences from the earth, not of +the points of agreement. Viewed in this light, all the resemblances +which exist become presumptions against, not in favour of, the moon's +being inhabited. Since life cannot exist there in the manner in which it +exists here, the greater the resemblance of the lunar world to the +terrestrial in other respects, the less reason we have to believe that +it can contain life.</p> + +<p>There are, however, other bodies in our system, between <span class="pagenum"><a name="Page_91" id="Page_91">[Pg 91]</a></span>which and the +earth there is a much closer resemblance; which possess an atmosphere, +clouds, consequently water (or some fluid analogous to it), and even +give strong indications of snow in their polar regions; while the cold, +or heat, though differing greatly on the average from ours, is, in some +parts at least of those planets, possibly not more extreme than in some +regions of our own which are habitable. To balance these agreements, the +ascertained differences are chiefly in the average light and heat, +velocity of rotation, density of material, intensity of gravity, and +similar circumstances of a secondary kind. With regard to these planets, +therefore, the argument of analogy gives a decided preponderance in +favour of their resembling the earth in any of its derivative +properties, such as that of having inhabitants; though, when we consider +how immeasurably multitudinous are those of their properties which we +are entirely ignorant of, compared with the few which we know, we can +attach but trifling weight to any considerations of resemblance in which +the known elements bear so inconsiderable a proportion to the unknown.</p> + +<p>Besides the competition between analogy and diversity, there may be a +competition of conflicting analogies. The new case may be similar in +some of its circumstances to cases in which the fact <i>m</i> exists, but in +others to cases in which it is known not to exist. Amber has some +properties in common with vegetable, others with mineral products. A +painting of unknown origin, may resemble, in certain of its characters, +known works of a particular master, but in others it may as strikingly +resemble those of some other painter. A vase may bear some analogy to +works of Grecian, and some to those of Etruscan, or Egyptian art. We are +of course supposing that it does not possess any quality which has been +ascertained, by a sufficient induction, to be a conclusive mark either +of the one or of the other.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XX_3">§ 3.</a> Since the value of an analogical argument inferring one resemblance +from other resemblances without any antecedent evidence of a connexion +between them, depends on the extent of ascertained resemblance, compared +first with the <span class="pagenum"><a name="Page_92" id="Page_92">[Pg 92]</a></span>amount of ascertained difference, and next with the +extent of the unexplored region of unascertained properties; it follows +that where the resemblance is very great, the ascertained difference +very small, and our knowledge of the subject-matter tolerably extensive, +the argument from analogy may approach in strength very near to a valid +induction. If, after much observation of B, we find that it agrees with +A in nine out of ten of its known properties, we may conclude with a +probability of nine to one, that it will possess any given derivative +property of A. If we discover, for example, an unknown animal or plant, +resembling closely some known one in the greater number of the +properties we observe in it, but differing in some few, we may +reasonably expect to find in the unobserved remainder of its properties, +a general agreement with those of the former; but also a difference +corresponding proportionately to the amount of observed diversity.</p> + +<p>It thus appears that the conclusions derived from analogy are only of +any considerable value, when the case to which we reason is an adjacent +case; adjacent, not as before, in place or time, but in circumstances. +In the case of effects of which the causes are imperfectly or not at all +known, when consequently the observed order of their occurrence amounts +only to an empirical law, it often happens that the conditions which +have coexisted whenever the effect was observed, have been very +numerous. Now if a new case presents itself, in which all these +conditions do not exist, but the far greater part of them do, some one +or a few only being wanting, the inference that the effect will occur, +notwithstanding this deficiency of complete resemblance to the cases in +which it has been observed, may, though of the nature of analogy, +possess a high degree of probability. It is hardly necessary to add +that, however considerable this probability may be, no competent +inquirer into nature will rest satisfied with it when a complete +induction is attainable; but will consider the analogy as a mere +guide-post, pointing out the direction in which more rigorous +investigations should be prosecuted.</p> + +<p>It is in this last respect that considerations of analogy have <span class="pagenum"><a name="Page_93" id="Page_93">[Pg 93]</a></span>the +highest scientific value. The cases in which analogical evidence affords +in itself any very high degree of probability, are, as we have observed, +only those in which the resemblance is very close and extensive; but +there is no analogy, however faint, which may not be of the utmost value +in suggesting experiments or observations that may lead to more positive +conclusions. When the agents and their effects are out of the reach of +further observation and experiment, as in the speculations already +alluded to respecting the moon and planets, such slight probabilities +are no more than an interesting theme for the pleasant exercise of +imagination; but any suspicion, however slight, that sets an ingenious +person at work to contrive an experiment, or affords a reason for trying +one experiment rather than another, may be of the greatest benefit to +science.</p> + +<p>On this ground, though I cannot accept as positive doctrines any of +those scientific hypotheses which are unsusceptible of being ultimately +brought to the test of actual induction, such, for instance, as the two +theories of light, the emission theory of the last century, and the +undulatory theory which predominates in the present, I am yet unable to +agree with those who consider such hypotheses to be worthy of entire +disregard. As is well said by Hartley (and concurred in by a thinker in +general so diametrically opposed to Hartley's opinions as Dugald +Stewart), "any hypothesis which has so much plausibility as to explain a +considerable number of facts, helps us to digest these facts in proper +order, to bring new ones to light, and make <i>experimenta crucis</i> for the +sake of future inquirers."<a name="FNanchor_25_25" id="FNanchor_25_25"></a><a href="#Footnote_25_25" class="fnanchor">[25]</a> If an hypothesis both explains known +facts, and has led to the prediction of others previously unknown, and +since verified by experience, the laws of the phenomenon which is the +subject of inquiry must bear at least a great similarity to those of the +class of phenomena to which the hypothesis assimilates it; and since the +analogy which extends so far may probably extend farther, nothing is +more <span class="pagenum"><a name="Page_94" id="Page_94">[Pg 94]</a></span>likely to suggest experiments tending to throw light upon the real +properties of the phenomenon, than the following out such an hypothesis. +But to this end it is by no means necessary that the hypothesis be +mistaken for a scientific truth. On the contrary, that illusion is in +this respect, as in every other, an impediment to the progress of real +knowledge, by leading inquirers to restrict themselves arbitrarily to +the particular hypothesis which is most accredited at the time, instead +of looking out for every class of phenomena between the laws of which +and those of the given phenomenon any analogy exists, and trying all +such experiments as may tend to the discovery of ulterior analogies +pointing in the same direction.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_95" id="Page_95">[Pg 95]</a></span></p> +<h3><a name="BOOK_III_CHAPTER_XXI" id="BOOK_III_CHAPTER_XXI"></a>CHAPTER XXI.<br /> +OF THE EVIDENCE OF THE LAW OF UNIVERSAL CAUSATION.</h3> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXI_1">§ 1.</a> We have now completed our review of the logical processes by which +the laws, or uniformities, of the sequence of phenomena, and those +uniformities in their coexistence which depend on the laws of their +sequence, are ascertained or tested. As we recognised in the +commencement, and have been enabled to see more clearly in the progress +of the investigation, the basis of all these logical operations is the +law of causation. The validity of all the Inductive Methods depends on +the assumption that every event, or the beginning of every phenomenon, +must have some cause; some antecedent, on the existence of which it is +invariably and unconditionally consequent. In the Method of Agreement +this is obvious; that method avowedly proceeding on the supposition that +we have found the true cause as soon as we have negatived every other. +The assertion is equally true of the Method of Difference. That method +authorizes us to infer a general law from two instances; one, in which A +exists together with a multitude of other circumstances, and B follows; +another, in which, A being removed, and all other circumstances +remaining the same, B is prevented. What, however, does this prove? It +proves that B, in the particular instance, cannot have had any other +cause than A; but to conclude from this that A was the cause, or that A +will on other occasions be followed by B, is only allowable on the +assumption that B must have some cause; that among its antecedents in +any single instance in which it occurs, there must be one which has the +capacity of producing it at other times. This being admitted, it is seen +that in the case in question that antecedent can be <span class="pagenum"><a name="Page_96" id="Page_96">[Pg 96]</a></span>no other than A; +but, that if it be no other than A it must be A, is not proved, by these +instances at least, but taken for granted. There is no need to spend +time in proving that the same thing is true of the other Inductive +Methods. The universality of the law of causation is assumed in them +all.</p> + +<p>But is this assumption warranted? Doubtless (it may be said) <i>most</i> +phenomena are connected as effects with some antecedent or cause, that +is, are never produced unless some assignable fact has preceded them; +but the very circumstance that complicated processes of induction are +sometimes necessary, shows that cases exist in which this regular order +of succession is not apparent to our unaided apprehension. If, then, the +processes which bring these cases within the same category with the +rest, require that we should assume the universality of the very law +which they do not at first sight appear to exemplify, is not this a +<i>petitio principii</i>? Can we prove a proposition, by an argument which +takes it for granted? And if not so proved, on what evidence does it +rest?</p> + +<p>For this difficulty, which I have purposely stated in the strongest +terms it will admit of, the school of metaphysicians who have long +predominated in this country find a ready salvo. They affirm, that the +universality of causation is a truth which we cannot help believing; +that the belief in it is an instinct, one of the laws of our believing +faculty. As the proof of this, they say, and they have nothing else to +say, that everybody does believe it; and they number it among the +propositions, rather numerous in their catalogue, which may be logically +argued against, and perhaps cannot be logically proved, but which are of +higher authority than logic, and so essentially inherent in the human +mind, that even he who denies them in speculation, shows by his habitual +practice that his arguments make no impression upon himself.</p> + +<p>Into the merits of this question, considered as one of psychology, it +would be foreign to my purpose to enter here: but I must protest against +adducing, as evidence of the truth of a fact in external nature, the +disposition, however strong or <span class="pagenum"><a name="Page_97" id="Page_97">[Pg 97]</a></span>however general, of the human mind to +believe it. Belief is not proof, and does not dispense with the +necessity of proof. I am aware, that to ask for evidence of a +proposition which we are supposed to believe instinctively, is to expose +oneself to the charge of rejecting the authority of the human faculties; +which of course no one can consistently do, since the human faculties +are all which any one has to judge by: and inasmuch as the meaning of +the word evidence is supposed to be, something which when laid before +the mind, induces it to believe; to demand evidence when the belief is +ensured by the mind's own laws, is supposed to be appealing to the +intellect against the intellect. But this, I apprehend, is a +misunderstanding of the nature of evidence. By evidence is not meant +anything and everything which produces belief. There are many things +which generate belief besides evidence. A mere strong association of +ideas often causes a belief so intense as to be unshakeable by +experience or argument. Evidence is not that which the mind does or must +yield to, but that which it ought to yield to, namely, that, by yielding +to which, its belief is kept conformable to fact. There is no appeal +from the human faculties generally, but there is an appeal from one +human faculty to another; from the judging faculty, to those which take +cognizance of fact, the faculties of sense and consciousness. The +legitimacy of this appeal is admitted whenever it is allowed that our +judgments ought to be conformable to fact. To say that belief suffices +for its own justification is making opinion the test of opinion; it is +denying the existence of any outward standard, the conformity of an +opinion to which constitutes its truth. We call one mode of forming +opinions right and another wrong, because the one does, and the other +does not, tend to make the opinion agree with the fact—to make people +believe what really is, and expect what really will be. Now a mere +disposition to believe, even if supposed instinctive, is no guarantee +for the truth of the thing believed. If, indeed, the belief ever +amounted to an irresistible necessity, there would then be no <i>use</i> in +appealing from it, because there would be no possibility of altering it. +But even then the <span class="pagenum"><a name="Page_98" id="Page_98">[Pg 98]</a></span>truth of the belief would not follow; it would only +follow that mankind were under a permanent necessity of believing what +might possibly not be true; in other words, that a case might occur in +which our senses or consciousness, if they could be appealed to, might +testify one thing, and our reason believe another. But in fact there is +no such permanent necessity. There is no proposition of which it can be +asserted that every human mind must eternally and irrevocably believe +it. Many of the propositions of which this is most confidently stated, +great numbers of human beings have disbelieved. The things which it has +been supposed that nobody could possibly help believing, are +innumerable; but no two generations would make out the same catalogue of +them. One age or nation believes implicitly what to another seems +incredible and inconceivable; one individual has not a vestige of a +belief which another deems to be absolutely inherent in humanity. There +is not one of these supposed instinctive beliefs which is really +inevitable. It is in the power of every one to cultivate habits of +thought which make him independent of them. The habit of philosophical +analysis, (of which it is the surest effect to enable the mind to +command, instead of being commanded by, the laws of the merely passive +part of its own nature,) by showing to us that things are not +necessarily connected in fact because their ideas are connected in our +minds, is able to loosen innumerable associations which reign +despotically over the undisciplined or early-prejudiced mind. And this +habit is not without power even over those associations which the school +of which I have been speaking regard as connate and instinctive. I am +convinced that any one accustomed to abstraction and analysis, who will +fairly exert his faculties for the purpose, will, when his imagination +has once learnt to entertain the notion, find no difficulty in +conceiving that in some one for instance of the many firmaments into +which sidereal astronomy now divides the universe, events may succeed +one another at random, without any fixed law; nor can anything in our +experience, or in our mental nature, constitute a sufficient, or indeed +any, reason for believing that this is nowhere the case.</p> + +<p><span class="pagenum"><a name="Page_99" id="Page_99">[Pg 99]</a></span></p><p>Were we to suppose (what it is perfectly possible to imagine) that the +present order of the universe were brought to an end, and that a chaos +succeeded in which there was no fixed succession of events, and the past +gave no assurance of the future; if a human being were miraculously kept +alive to witness this change, he surely would soon cease to believe in +any uniformity, the uniformity itself no longer existing. If this be +admitted, the belief in uniformity either is not an instinct, or it is +an instinct conquerable, like all other instincts, by acquired +knowledge.</p> + +<p>But there is no need to speculate on what might be, when we have +positive and certain knowledge of what has been. It is not true as a +matter of fact, that mankind have always believed that all the +successions of events were uniform and according to fixed laws. The +Greek philosophers, not even excepting Aristotle, recognised Chance and +Spontaneity (<i>τύχη</i> and <i>τὸ αὐτομάτον</i>) as among the +agents in nature; in other words, they believed that to that extent +there was no guarantee that the past had been similar to itself, or that +the future would resemble the past. Even now a full half of the +philosophical world, including the very same metaphysicians who contend +most for the instinctive character of the belief in uniformity, consider +one important class of phenomena, volitions, to be an exception to the +uniformity, and not governed by a fixed law.<a name="FNanchor_26_26" id="FNanchor_26_26"></a><a href="#Footnote_26_26" class="fnanchor">[26]</a></p> + + +<p><span class="pagenum"><a name="Page_100" id="Page_100">[Pg 100]</a></span></p><p class="newsection"><a name="BOOK_III_CHAPTER_XXI_2">§ 2.</a> As was observed in a former place,<a name="FNanchor_27_27" id="FNanchor_27_27"></a><a href="#Footnote_27_27" class="fnanchor">[27]</a> the belief we entertain in +the universality, throughout nature, of the law of cause and effect, is +itself an instance of induction; and by no means one of the earliest +which any of us, or which mankind in general, can have made. We arrive +at this universal law, by generalization from many laws of inferior +generality. We should never have had the notion of causation (in the +philosophical meaning of the term) as a condition of all phenomena, +unless many cases of causation, or in other words, many partial +uniformities of sequence, had previously become familiar. The more +obvious of the particular uniformities suggest, and give evidence of, +the general uniformity, and the general uniformity, once established, +enables us to prove the remainder of the particular uniformities of +which it is made up. As, however, all rigorous processes of induction +presuppose the general uniformity, our knowledge of the particular +uniformities from which it was first inferred was not, of course, +derived from rigorous induction, but from the loose and uncertain mode +of induction <i>per enumerationem simplicem</i>: and the law of universal +causation, being collected <span class="pagenum"><a name="Page_101" id="Page_101">[Pg 101]</a></span>from results so obtained, cannot itself rest +on any better foundation.</p> + +<p>It would seem, therefore, that induction <i>per enumerationem simplicem</i> +not only is not necessarily an illicit logical process, but is in +reality the only kind of induction possible; since the more elaborate +process depends for its validity on a law, itself obtained in that +inartificial mode. Is there not then an inconsistency in contrasting the +looseness of one method with the rigidity of another, when that other is +indebted to the looser method for its own foundation?</p> + +<p>The inconsistency, however, is only apparent. Assuredly, if induction by +simple enumeration were an invalid process, no process grounded on it +could be valid; just as no reliance could be placed on telescopes, if we +could not trust our eyes. But though a valid process, it is a fallible +one, and fallible in very different degrees: if therefore we can +substitute for the more fallible forms of the process, an operation +grounded on the same process in a less fallible form, we shall have +effected a very material improvement. And this is what scientific +induction does.</p> + +<p>A mode of concluding from experience must be pronounced untrustworthy, +when subsequent experience refuses to confirm it. According to this +criterion, induction by simple enumeration—in other words, +generalization of an observed fact from the mere absence of any known +instance to the contrary—affords in general a precarious and unsafe +ground of assurance; for such generalizations are incessantly +discovered, on further experience, to be false. Still, however, it +affords some assurance, sufficient, in many cases, for the ordinary +guidance of conduct. It would be absurd to say, that the generalizations +arrived at by mankind in the outset of their experience, such as these, +Food nourishes, Fire burns, Water drowns, were unworthy of reliance.<a name="FNanchor_28_28" id="FNanchor_28_28"></a><a href="#Footnote_28_28" class="fnanchor">[28]</a> +There is a scale of trustworthiness in <span class="pagenum"><a name="Page_102" id="Page_102">[Pg 102]</a></span>the results of the original +unscientific Induction; and on this diversity (as observed in the fourth +chapter of the present book) depend the rules for the improvement of the +process. The improvement consists in correcting one of these +inartificial generalizations by means of another. As has been already +pointed out, this is all that art can do. To test a generalization, by +showing that it either follows from, or conflicts with, some stronger +induction, some generalization resting on a broader foundation of +experience, is the beginning and end of the logic of Induction.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXI_3">§ 3.</a> Now the precariousness of the method of simple enumeration is in an +inverse ratio to the largeness of the generalization. The process is +delusive and insufficient, exactly in proportion as the subject-matter +of the observation is special and limited in extent. As the sphere +widens, this unscientific method becomes less and less liable to +mislead; and the most universal class of truths, the law of causation +for instance, and the principles of number and of geometry, are duly and +satisfactorily proved by that method alone, nor are they susceptible of +any other proof.</p> + +<p>With respect to the whole class of generalizations of which we have +recently treated, the uniformities which depend on causation, the truth +of the remark just made follows by obvious inference from the principles +laid down in the preceding chapters. When a fact has been observed a +certain number of times to be true, and is not in any instance known <span class="pagenum"><a name="Page_103" id="Page_103">[Pg 103]</a></span>to +be false; if we at once affirm that fact as an universal truth or law of +nature, without testing it by any of the four methods of induction, nor +deducing it from other known laws, we shall in general err grossly: but +we are perfectly justified in affirming it as an empirical law, true +within certain limits of time, place, and circumstance, provided the +number of coincidences be greater than can with any probability be +ascribed to chance. The reason for not extending it beyond those limits +is, that the fact of its holding true within them may be a consequence +of collocations, which cannot be concluded to exist in one place because +they exist in another; or may be dependent on the accidental absence of +counteracting agencies, which any variation of time, or the smallest +change of circumstances, may possibly bring into play. If we suppose, +then, the subject-matter of any generalization to be so widely diffused +that there is no time, no place, and no combination of circumstances, +but must afford an example either of its truth or of its falsity, and if +it be never found otherwise than true, its truth cannot depend on any +collocations, unless such as exist at all times and places; nor can it +be frustrated by any counteracting agencies, unless by such as never +actually occur. It is, therefore, an empirical law coextensive with all +human experience; at which point the distinction between empirical laws +and laws of nature vanishes, and the proposition takes its place among +the most firmly established as well as largest truths accessible to +science.</p> + +<p>Now, the most extensive in its subject-matter of all generalizations +which experience warrants, respecting the sequences and coexistences of +phenomena, is the law of causation. It stands at the head of all +observed uniformities, in point of universality, and therefore (if the +preceding observations are correct) in point of certainty. And if we +consider, not what mankind would have been justified in believing in the +infancy of their knowledge, but what may rationally be believed in its +present more advanced state, we shall find ourselves warranted in +considering this fundamental law, though itself obtained by induction +from particular laws of causation, as not less certain, but on the +contrary, more so, than any of those from which it <span class="pagenum"><a name="Page_104" id="Page_104">[Pg 104]</a></span>was drawn. It adds +to them as much proof as it receives from them. For there is probably no +one even of the best established laws of causation which is not +sometimes counteracted, and to which, therefore, apparent exceptions do +not present themselves, which would have necessarily and justly shaken +the confidence of mankind in the universality of those laws, if +inductive processes founded on the universal law had not enabled us to +refer those exceptions to the agency of counteracting causes, and +thereby reconcile them with the law with which they apparently conflict. +Errors, moreover, may have slipped into the statement of any one of the +special laws, through inattention to some material circumstance: and +instead of the true proposition, another may have been enunciated, false +as an universal law, though leading, in all cases hitherto observed, to +the same result. To the law of causation, on the contrary, we not only +do not know of any exception, but the exceptions which limit or +apparently invalidate the special laws, are so far from contradicting +the universal one, that they confirm it; since in all cases which are +sufficiently open to our observation, we are able to trace the +difference of result, either to the absence of a cause which had been +present in ordinary cases, or to the presence of one which had been +absent.</p> + +<p>The law of cause and effect, being thus certain, is capable of imparting +its certainty to all other inductive propositions which can be deduced +from it; and the narrower inductions may be regarded as receiving their +ultimate sanction from that law, since there is no one of them which is +not rendered more certain than it was before, when we are able to +connect it with that larger induction, and to show that it cannot be +denied, consistently with the law that everything which begins to exist +has a cause. And hence we are justified in the seeming inconsistency, of +holding induction by simple enumeration to be good for proving this +general truth, the foundation of scientific induction, and yet refusing +to rely on it for any of the narrower inductions. I fully admit that if +the law of causation were unknown, generalization in the more obvious +cases of uniformity in phenomena would nevertheless <span class="pagenum"><a name="Page_105" id="Page_105">[Pg 105]</a></span>be possible, and +though in all cases more or less precarious, and in some extremely so, +would suffice to constitute a certain measure of probability: but what +the amount of this probability might be, we are dispensed from +estimating, since it never could amount to the degree of assurance which +the proposition acquires, when, by the application to it of the Four +Methods, the supposition of its falsity is shown to be inconsistent with +the Law of Causation. We are therefore logically entitled, and, by the +necessities of scientific Induction, required, to disregard the +probabilities derived from the early rude method of generalizing, and to +consider no minor generalization as proved except so far as the law of +causation confirms it, nor probable except so far as it may reasonably +be expected to be so confirmed.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXI_4">§ 4.</a> The assertion, that our inductive processes assume the law of +causation, while the law of causation is itself a case of induction, is +a paradox, only on the old theory of reasoning, which supposes the +universal truth, or major premise, in a ratiocination, to be the real +proof of the particular truths which are ostensibly inferred from it. +According to the doctrine maintained in the present treatise,<a name="FNanchor_29_29" id="FNanchor_29_29"></a><a href="#Footnote_29_29" class="fnanchor">[29]</a> the +major premise is not the proof of the conclusion, but is itself proved, +along with the conclusion from the same evidence. "All men are mortal" +is not the proof that Lord Palmerston is mortal; but our past experience +of mortality authorizes us to infer <i>both</i> the general truth and the +particular fact, and the one with exactly the same degree of assurance +as the other. The mortality of Lord Palmerston is not an inference from +the mortality of all men, but from the experience which proves the +mortality of all men; and is a correct inference from experience, if +that general truth is so too. This relation between our general beliefs +and their particular applications holds equally true in the more +comprehensive case which we are now discussing. Any new fact of +causation inferred by induction, is rightly inferred, if no other +objection can be made to the inference than can be <span class="pagenum"><a name="Page_106" id="Page_106">[Pg 106]</a></span>made to the general +truth that every event has a cause. The utmost certainty which can be +given to a conclusion arrived at in the way of inference, stops at this +point. When we have ascertained that the particular conclusion must +stand or fall with the general uniformity of the laws of nature—that it +is liable to no doubt except the doubt whether every event has a +cause—we have done all that can be done for it. The strongest assurance +we can obtain of any theory respecting the cause of a given phenomenon, +is that the phenomenon has either that cause or none.</p> + +<p>The latter supposition might have been an admissible one in a very early +period of our study of nature. But we have been able to perceive that in +the stage which mankind have now reached, the generalization which gives +the Law of Universal Causation has grown into a stronger and better +induction, one deserving of greater reliance, than any of the +subordinate generalizations. We may even, I think, go a step further +than this, and regard the certainty of that great induction as not +merely comparative, but, for all practical purposes, absolute.</p> + +<p>The considerations which, as I apprehend, give, at the present day, to +the proof of the law of uniformity of succession as true of all +phenomena without exception, this character of completeness and +conclusiveness, are the following:—First, that we now know it directly +to be true of far the greatest number of phenomena; that there are none +of which we know it not to be true, the utmost that can be said being, +that of some we cannot positively from direct evidence affirm its truth; +while phenomenon after phenomenon, as they become better known to us, +are constantly passing from the latter class into the former; and in all +cases in which that transition has not yet taken place, the absence of +direct proof is accounted for by the rarity or the obscurity of the +phenomena, our deficient means of observing them, or the logical +difficulties arising from the complication of the circumstances in which +they occur; insomuch that, notwithstanding as rigid a dependence on +given conditions as exists in the case of any other phenomenon, it was +not likely that we should be better <span class="pagenum"><a name="Page_107" id="Page_107">[Pg 107]</a></span>acquainted with those conditions +than we are. Besides this first class of considerations, there is a +second, which still further corroborates the conclusion. Although there +are phenomena the production and changes of which elude all our attempts +to reduce them universally to any ascertained law; yet in every such +case, the phenomenon, or the objects concerned in it, are found in some +instances to obey the known laws of nature. The wind, for example, is +the type of uncertainty and caprice, yet we find it in some cases +obeying with as much constancy as any phenomenon in nature the law of +the tendency of fluids to distribute themselves so as to equalize the +pressure on every side of each of their particles; as in the case of the +trade winds, and the monsoons. Lightning might once have been supposed +to obey no laws; but since it has been ascertained to be identical with +electricity, we know that the very same phenomenon in some of its +manifestations is implicitly obedient to the action of fixed causes. I +do not believe that there is now one object or event in all our +experience of nature, within the bounds of the solar system at least, +which has not either been ascertained by direct observation to follow +laws of its own, or been proved to be closely similar to objects and +events which, in more familiar manifestations, or on a more limited +scale, follow strict laws: our inability to trace the same laws on a +larger scale and in the more recondite instances, being accounted for by +the number and complication of the modifying causes, or by their +inaccessibility to observation.</p> + +<p>The progress of experience, therefore, has dissipated the doubt which +must have rested on the universality of the law of causation while there +were phenomena which seemed to be <i>sui generis</i>, not subject to the same +laws with any other class of phenomena, and not as yet ascertained to +have peculiar laws of their own. This great generalization, however, +might reasonably have been, as it in fact was, acted on as a probability +of the highest order, before there were sufficient grounds for receiving +it as a certainty. For, whatever has been found true in innumerable +instances, and never found to be false <span class="pagenum"><a name="Page_108" id="Page_108">[Pg 108]</a></span>after due examination in any, we +are safe in acting on as universal provisionally, until an undoubted +exception appears; provided the nature of the case be such that a real +exception could scarcely have escaped our notice. When every phenomenon +that we ever knew sufficiently well to be able to answer the question, +had a cause on which it was invariably consequent, it was more rational +to suppose that our inability to assign the causes of other phenomena +arose from our ignorance, than that there were phenomena which were +uncaused, and which happened to be exactly those which we had hitherto +had no sufficient opportunity of studying.</p> + +<p>It must, at the same time, be remarked, that the reasons for this +reliance do not hold in circumstances unknown to us, and beyond the +possible range of our experience. In distant parts of the stellar +regions, where the phenomena may be entirely unlike those with which we +are acquainted, it would be folly to affirm confidently that this +general law prevails, any more than those special ones which we have +found to hold universally on our own planet. The uniformity in the +succession of events, otherwise called the law of causation, must be +received not as a law of the universe, but of that portion of it only +which is within the range of our means of sure observation, with a +reasonable degree of extension to adjacent cases. To extend it further +is to make a supposition without evidence, and to which, in the absence +of any ground from experience for estimating its degree of probability, +it would be idle to attempt to assign any.<a name="FNanchor_30_30" id="FNanchor_30_30"></a><a href="#Footnote_30_30" class="fnanchor">[30]</a></p> + +<p><span class="pagenum"><a name="Page_109" id="Page_109">[Pg 109]</a></span></p> + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_110" id="Page_110">[Pg 110]</a></span></p> +<h3><a name="BOOK_III_CHAPTER_XXII" id="BOOK_III_CHAPTER_XXII"></a>CHAPTER XXII.<br /> +OF UNIFORMITIES OF COEXISTENCE NOT DEPENDENT ON CAUSATION.</h3> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXII_1">§ 1.</a> The order of the occurrence of phenomena in time, is either +successive or simultaneous; the uniformities, therefore, which obtain in +their occurrence, are either uniformities of succession or of +coexistence. Uniformities of succession are all comprehended under the +law of causation and its consequences. Every phenomenon has a cause, +which it invariably follows; and from this are derived other invariable +sequences among the successive stages of the same effect, as well as +between the effects resulting from causes which invariably succeed one +another.</p> + +<p>In the same manner with these derivative uniformities of succession, a +great variety of uniformities of coexistence also take their rise. +Coordinate effects of the same cause naturally coexist with one another. +High water at any point on the earth's surface, and high water at the +point diametrically opposite to it, are effects uniformly simultaneous, +resulting from the direction in which the combined attractions of the +sun and moon act upon the waters of the ocean. An eclipse of the sun to +us, and an eclipse of the earth to a spectator situated in the moon, are +in like manner phenomena invariably coexistent; and their coexistence +can equally be deduced from the laws of their production.</p> + +<p>It is an obvious question, therefore, whether all the uniformities of +coexistence among phenomena may not be accounted for in this manner. And +it cannot be doubted that between phenomena which are themselves +effects, the coexistences must necessarily depend on the causes of those +phenomena. If they are effects immediately or remotely of the same +cause, they cannot coexist except by virtue of some laws or properties +of <span class="pagenum"><a name="Page_111" id="Page_111">[Pg 111]</a></span>that cause: if they are effects of different causes, they cannot +coexist unless it be because their causes coexist; and the uniformity of +coexistence, if such there be, between the effects, proves that those +particular causes, within the limits of our observation, have uniformly +been coexistent.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXII_2">§ 2.</a> But these same considerations compel us to recognise that there +must be one class of coexistences which cannot depend on causation; the +coexistences between the ultimate properties of things—those properties +which are the causes of all phenomena, but are not themselves caused by +any phenomenon, and a cause for which could only be sought by ascending +to the origin of all things. Yet among these ultimate properties there +are not only coexistences, but uniformities of coexistence. General +propositions may be, and are, formed, which assert that whenever certain +properties are found, certain others are found along with them. We +perceive an object; say, for instance, water. We recognise it to be +water, of course by certain of its properties. Having recognised it, we +are able to affirm of it innumerable other properties; which we could +not do unless it were a general truth, a law or uniformity in nature, +that the set of properties by which we identify the substance as water, +always have those other properties conjoined with them.</p> + +<p>In a former place,<a name="FNanchor_31_31" id="FNanchor_31_31"></a><a href="#Footnote_31_31" class="fnanchor">[31]</a> it has been explained in some detail what is +meant by the Kinds of objects; those classes which differ from one +another not by a limited and definite, but by an indefinite and unknown, +number of distinctions. To this we have now to add, that every +proposition by which anything is asserted of a Kind, affirms an +uniformity of coexistence. Since we know nothing of Kinds but their +properties, the Kind, to us, <i>is</i> the set of properties by which it is +identified, and which must of course be sufficient to distinguish it +from every other kind.<a name="FNanchor_32_32" id="FNanchor_32_32"></a><a href="#Footnote_32_32" class="fnanchor">[32]</a> In affirming anything, therefore, of a Kind, +<span class="pagenum"><a name="Page_112" id="Page_112">[Pg 112]</a></span>we are affirming something to be uniformly coexistent with the +properties by which the kind is recognised; and that is the sole meaning +of the assertion.</p> + +<p>Among the uniformities of coexistence which exist in nature, may hence +be numbered all the properties of Kinds. The whole of these, however, +are not independent of causation, but only a portion of them. Some are +ultimate properties, others derivative; of some, no cause can be +assigned, but others are manifestly dependent on causes. Thus, pure +atmospheric air is a Kind, and one of its most unequivocal properties is +its gaseous form: this property, however, has for its cause the presence +of a certain quantity of latent heat; and if that heat could be taken +away (as has been done from so many gases in Faraday's experiments), the +gaseous form would doubtless disappear, together with numerous other +properties which depend on, or are caused by, that property.</p> + +<p>In regard to all substances which are chemical compounds, and which +therefore may be regarded as products of the juxtaposition of substances +different in Kind from themselves, there is considerable reason to +presume that the specific properties of the compound are consequent, as +effects, on some of the properties of the elements, though little +progress has yet been made in tracing any invariable relation between +the latter and the former. Still more strongly will a similar +presumption exist, when the object itself, as in the case of organized +beings, is no primeval agent, but an effect, which depends on a cause or +causes for its very existence. The Kinds therefore which are called in +chemistry simple substances, or elementary natural agents, are the only +ones, any of whose properties can with <span class="pagenum"><a name="Page_113" id="Page_113">[Pg 113]</a></span>certainty be considered +ultimate; and of these the ultimate properties are probably much more +numerous that we at present recognise, since every successful instance +of the resolution of the properties of their compounds into simpler +laws, generally leads to the recognition of properties in the elements +distinct from any previously known. The resolution of the laws of the +heavenly motions, established the previously unknown ultimate property +of a mutual attraction between all bodies: the resolution, so far as it +has yet proceeded, of the laws of crystallization, of chemical +composition, electricity, magnetism, &c., points to various polarities, +ultimately inherent in the particles of which bodies are composed; the +comparative atomic weights of different kinds of bodies were ascertained +by resolving, into more general laws, the uniformities observed in the +proportions in which substances combine with one another; and so forth. +Thus although every resolution of a complex uniformity into simpler and +more elementary laws has an apparent tendency to diminish the number of +the ultimate properties, and really does remove many properties from the +list; yet, (since the result of this simplifying process is to trace up +an ever greater variety of different effects to the same agents,) the +further we advance in this direction, the greater number of distinct +properties we are forced to recognise in one and the same object: the +coexistences of which properties must accordingly be ranked among the +ultimate generalities of nature.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXII_3">§ 3.</a> There are, therefore, only two kinds of propositions which assert +uniformity of coexistence between properties. Either the properties +depend on causes, or they do not. If they do, the proposition which +affirms them to be coexistent is a derivative law of coexistence between +effects, and until resolved into the laws of causation on which it +depends, is an empirical law, and to be tried by the principles of +induction to which such laws are amenable. If, on the other hand, the +properties do not depend on causes, but are ultimate properties; then if +it be true that they invariably coexist, they must all be ultimate +properties of one and the same Kind; and it is of <span class="pagenum"><a name="Page_114" id="Page_114">[Pg 114]</a></span>these only that the +coexistences can be classed as a peculiar sort of laws of nature.</p> + +<p>When we affirm that all crows are black, or that all negroes have woolly +hair, we assert an uniformity of coexistence. We assert that the +property of blackness, or of having woolly hair, invariably coexists +with the properties which, in common language, or in the scientific +classification that we adopt, are taken to constitute the class crow, or +the class negro. Now, supposing blackness to be an ultimate property of +black objects, or woolly hair an ultimate property of the animals which +possess it; supposing that these properties are not results of +causation, are not connected with antecedent phenomena by any law; then +if all crows are black, and all negroes have woolly hair, these must be +ultimate properties of the Kind <i>crow</i>, or <i>negro</i>, or of some Kind +which includes them. If, on the contrary, blackness or woolly hair be an +effect depending on causes, these general propositions are manifestly +empirical laws; and all that has already been said respecting that class +of generalizations may be applied without modification to these.</p> + +<p>Now, we have seen that in the case of all compounds—of all things, in +short, except the elementary substances and primary powers of +nature—the presumption is, that the properties do really depend upon +causes; and it is impossible in any case whatever to be certain that +they do not. We therefore should not be safe in claiming for any +generalization respecting the coexistence of properties, a degree of +certainty to which, if the properties should happen to be the result of +causes, it would have no claim. A generalization respecting coexistence, +or in other words respecting the properties of Kinds, may be an ultimate +truth, but it may, also, be merely a derivative one; and since, if so, +it is one of those derivative laws which are neither laws of causation, +nor have been resolved into the laws of causation on which they depend, +it can possess no higher degree of evidence than belongs to an empirical +law.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXII_4">§ 4.</a> This conclusion will be confirmed by the consideration <span class="pagenum"><a name="Page_115" id="Page_115">[Pg 115]</a></span>of one +great deficiency, which precludes the application to the ultimate +uniformities of coexistence, of a system of rigorous scientific +induction, such as the uniformities in the succession of phenomena have +been found to admit of. The basis of such a system is wanting: there is +no general axiom, standing in the same relation to the uniformities of +coexistence as the law of causation does to those of succession. The +Methods of Induction applicable to the ascertainment of causes and +effects, are grounded on the principle that everything which has a +beginning must have some cause or other; that among the circumstances +which actually existed at the time of its commencement, there is +certainly some one combination, on which the effect in question is +unconditionally consequent, and on the repetition of which it would +certainly again recur. But in an inquiry whether some kind (as crow) +universally possesses a certain property (as blackness), there is no +room for any assumption analogous to this. We have no previous certainty +that the property must have something which constantly coexists with it; +must have an invariable coexistent, in the same manner as an event must +have an invariable antecedent. When we feel pain, we must be in some +circumstances under which if exactly repeated we should always feel +pain. But when we are conscious of blackness, it does not follow that +there is something else present of which blackness is a constant +accompaniment. There is, therefore, no room for elimination; no Method +of Agreement or Difference, or of Concomitant Variations (which is but a +modification either of the Method of Agreement or of the Method of +Difference). We cannot conclude that the blackness we see in crows must +be an invariable property of crows, merely because there is nothing else +present of which it can be an invariable property. We therefore inquire +into the truth of a proposition like "All crows are black," under the +same disadvantage as if, in our inquiries into causation, we were +compelled to let in, as one of the possibilities, that the effect may in +that particular instance have arisen without any cause at all.</p> + +<p>To overlook this grand distinction was, as it seems to me, the capital +error in Bacon's view of inductive philosophy. <span class="pagenum"><a name="Page_116" id="Page_116">[Pg 116]</a></span>The principle of +elimination, that great logical instrument which he had the immense +merit of first bringing into general use, he deemed applicable in the +same sense, and in as unqualified a manner, to the investigation of the +coexistences, as to that of the successions of phenomena. He seems to +have thought that as every event has a cause, or invariable antecedent, +so every property of an object has an invariable coexistent, which he +called its Form: and the examples he chiefly selected for the +application and illustration of his method, were inquiries into such +Forms; attempts to determine in what else all those objects resembled, +which agreed in some one general property, as hardness or softness, +dryness or moistness, heat or coldness. Such inquiries could lead to no +result. The objects seldom have any such circumstances in common. They +usually agree in the one point inquired into, and in nothing else. A +great proportion of the properties which, so far as we can conjecture, +are the likeliest to be really ultimate, would seem to be inherently +properties of many different Kinds of things, not allied in any other +respect. And as for the properties which, being effects of causes, we +are able to give some account of, they have generally nothing to do with +the ultimate resemblances or diversities in the objects themselves, but +depend on some outward circumstances, under the influence of which any +objects whatever are capable of manifesting those properties; as is +emphatically the case with those favourite subjects of Bacon's +scientific inquiries, hotness and coldness; as well as with hardness and +softness, solidity and fluidity, and many other conspicuous qualities.</p> + +<p>In the absence, then, of any universal law of coexistence, similar to +the universal law of causation which regulates sequence, we are thrown +back upon the unscientific induction of the ancients, <i>per enumerationem +simplicem, ubi non reperitur instantia contradictoria</i>. The reason we +have for believing that all crows are black, is simply that we have seen +and heard of many black crows, and never one of any other colour. It +remains to be considered how far this evidence can reach, and how we are +to measure its strength in any given case.</p> + + +<p><span class="pagenum"><a name="Page_117" id="Page_117">[Pg 117]</a></span></p><p class="newsection"><a name="BOOK_III_CHAPTER_XXII_5">§ 5.</a> It sometimes happens that a mere change in the mode of verbally +enunciating a question, though nothing is really added to the meaning +expressed, is of itself a considerable step towards its solution. This, +I think, happens in the present instance. The degree of certainty of any +generalization which rests on no other evidence than the agreement, so +far as it goes, of all past observation, is but another phrase for the +degree of improbability that an exception, if any existed, could have +hitherto remained unobserved. The reason for believing that all crows +are black, is measured by the improbability that crows of any other +colour should have existed to the present time without our being aware +of it. Let us state the question in this last mode, and consider what is +implied in the supposition that there may be crows which are not black, +and under what conditions we can be justified in regarding this as +incredible.</p> + +<p>If there really exist crows which are not black, one of two things must +be the fact. Either the circumstance of blackness, in all crows hitherto +observed, must be, as it were, an accident, not connected with any +distinction of Kind; or if it be a property of Kind, the crows which are +not black must be a new Kind, a Kind hitherto overlooked, though coming +under the same general description by which crows have hitherto been +characterized. The first supposition would be proved true if we were to +discover casually a white crow among black ones, or if it were found +that black crows sometimes turn white. The second would be shown to be +the fact if in Australia or Central Africa a species or a race of white +or grey crows were found to exist.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXII_6">§ 6.</a> The former of these suppositions necessarily implies that the +colour is an effect of causation. If blackness, in the crows in which it +has been observed, be not a property of Kind, but can be present or +absent without any difference generally in the properties of the object; +then it is not an ultimate fact in the individuals themselves, but is +certainly dependent on a cause. There are, no doubt, many properties +which vary from individual to individual of the same Kind, <span class="pagenum"><a name="Page_118" id="Page_118">[Pg 118]</a></span>even the +same <i>infima species</i>, or lowest Kind. Some flowers may be either white +or red, without differing in any other respect. But these properties are +not ultimate; they depend on causes. So far as the properties of a thing +belong to its own nature, and do not arise from some cause extrinsic to +it, they are always the same in the same Kind. Take, for instance, all +simple substances and elementary powers; the only things of which we are +certain that some at least of their properties are really ultimate. +Colour is generally esteemed the most variable of all properties: yet we +do not find that sulphur is sometimes yellow and sometimes white, or +that it varies in colour at all, except so far as colour is the effect +of some extrinsic cause, as of the sort of light thrown upon it, the +mechanical arrangement of the particles, (as after fusion) &c. We do not +find that iron is sometimes fluid and sometimes solid at the same +temperature; gold sometimes malleable and sometimes brittle; that +hydrogen will sometimes combine with oxygen and sometimes not; or the +like. If from simple substances we pass to any of their definite +compounds, as water, lime, or sulphuric acid, there is the same +constancy in their properties. When properties vary from individual to +individual, it is either in the case of miscellaneous aggregations, such +as atmospheric air or rock, composed of heterogeneous substances, and +not constituting or belonging to any real Kind,<a name="FNanchor_33_33" id="FNanchor_33_33"></a><a href="#Footnote_33_33" class="fnanchor">[33]</a> or it is in the case +of organic beings. In them, indeed, there is variability in a high +degree. Animals of the same species and race, human beings of the same +age, sex, and country, will be most different, for example, in face and +figure. But organized beings (from the extreme complication of the laws +by which they are regulated) being more eminently modifiable, that is, +liable to be influenced by a greater number and variety of causes, than +any other phenomena whatever; having also themselves had a beginning, +and therefore a cause; there is reason to believe that <span class="pagenum"><a name="Page_119" id="Page_119">[Pg 119]</a></span>none of their +properties are ultimate, but all of them derivative, and produced by +causation. And the presumption is confirmed, by the fact that the +properties which vary from one individual to another, also generally +vary more or less at different times in the same individual; which +variation, like any other event, supposes a cause, and implies, +consequently, that the properties are not independent of causation.</p> + +<p>If, therefore, blackness be merely accidental in crows, and capable of +varying while the Kind remains the same, its presence or absence is +doubtless no ultimate fact, but the effect of some unknown cause: and in +that case the universality of the experience that all crows are black is +sufficient proof of a common cause, and establishes the generalization +as an empirical law. Since there are innumerable instances in the +affirmative, and hitherto none at all in the negative, the causes on +which the property depends must exist everywhere in the limits of the +observations which have been made; and the proposition may be received +as universal within those limits, and with the allowable degree of +extension to adjacent cases.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXII_7">§ 7.</a> If, in the second place, the property, in the instances in which it +has been observed, is not an effect of causation, it is a property of +Kind; and in that case the generalization can only be set aside by the +discovery of a new Kind of crow. That, however, a peculiar Kind, not +hitherto discovered, should exist in nature, is a supposition so often +realized, that it cannot be considered at all improbable. We have +nothing to authorize us in attempting to limit the Kinds of things which +exist in nature. The only unlikelihood would be that a new Kind should +be discovered in localities which there was previously reason to believe +had been thoroughly explored; and even this improbability depends on the +degree of conspicuousness of the difference between the newly-discovered +Kind and all others, since new Kinds of minerals, plants, and even +animals, previously overlooked or confounded with known species, are +still continually detected in the most frequented situations. On this +second ground, therefore, as well as <span class="pagenum"><a name="Page_120" id="Page_120">[Pg 120]</a></span>on the first, the observed +uniformity of coexistence can only hold good as an empirical law, within +the limits not only of actual observation, but of an observation as +accurate as the nature of the case required. And hence it is that (as +remarked in an early chapter of the present Book) we so often give up +generalizations of this class at the first summons. If any credible +witness stated that he had seen a white crow, under circumstances which +made it not incredible that it should have escaped notice previously, we +should give full credence to the statement.</p> + +<p>It appears, then, that the uniformities which obtain in the coexistence +of phenomena,—those which we have reason to consider as ultimate, no +less than those which arise from the laws of causes yet undetected—are +entitled to reception only as empirical laws; are not to be presumed +true except within the limits of time, place, and circumstance, in which +the observations were made, or except in cases strictly adjacent.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXII_8">§ 8.</a> We have seen in the last chapter that there is a point of +generality at which empirical laws become as certain as laws of nature, +or rather, at which there is no longer any distinction between empirical +laws and laws of nature. As empirical laws approach this point, in other +words, as they rise in their degree of generality, they become more +certain; their universality may be more strongly relied on. For, in the +first place, if they are results of causation (which, even in the class +of uniformities treated of in the present chapter, we never can be +certain that they are not) the more general they are, the greater is +proved to be the space over which the necessary collocations prevail, +and within which no causes exist capable of counteracting the unknown +causes on which the empirical law depends. To say that anything is an +invariable property of some very limited class of objects, is to say +that it invariably accompanies some very numerous and complex group of +distinguishing properties; which, if causation be at all concerned in +the matter, argues a combination of many causes, and therefore a great +liability to counteraction; while the comparatively narrow range of the +<span class="pagenum"><a name="Page_121" id="Page_121">[Pg 121]</a></span>observations renders it impossible to predict to what extent unknown +counteracting causes may be distributed throughout nature. But when a +generalization has been found to hold good of a very large proportion of +all things whatever, it is already proved that nearly all the causes +which exist in nature have no power over it; that very few changes in +the combination of causes can effect it; since the greater number of +possible combinations must have already existed in some one or other of +the instances in which it has been found true. If, therefore, any +empirical law is a result of causation, the more general it is, the more +it may be depended on. And even if it be no result of causation, but an +ultimate coexistence, the more general it is, the greater amount of +experience it is derived from, and the greater therefore is the +probability that if exceptions had existed, some would already have +presented themselves.</p> + +<p>For these reasons, it requires much more evidence to establish an +exception to one of the more general empirical laws than to the more +special ones. We should not have any difficulty in believing that there +might be a new Kind of crow; or a new kind of bird resembling a crow in +the properties hitherto considered distinctive of that Kind. But it +would require stronger proof to convince us of the existence of a Kind +of crow having properties at variance with any generally recognised +universal property of birds; and a still higher degree if the properties +conflict with any recognised universal property of animals. And this is +conformable to the mode of judgment recommended by the common sense and +general practice of mankind, who are more incredulous as to any +novelties in nature, according to the degree of generality of the +experience which these novelties seem to contradict.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXII_9">§ 9.</a> Still, however, even these greater generalizations, which embrace +comprehensive Kinds, containing under them a great number and variety of +<i>infimæ species</i>, are only empirical laws, resting on induction by +simple enumeration merely, and not on any process of elimination, a +process wholly inapplicable to this sort of case. Such generalizations, +therefore, <span class="pagenum"><a name="Page_122" id="Page_122">[Pg 122]</a></span>ought to be grounded on an examination of all the <i>infimæ +species</i> comprehended in them, and not of a portion only. We cannot +conclude (where causation is not concerned), because a proposition is +true of a number of things resembling one another only in being animals, +that it is therefore true of all animals. If, indeed, anything be true +of species which differ more from one another than either differs from a +third, (especially if that third species occupies in most of its known +properties a position between the two former,) there is some probability +that the same thing will also be true of that intermediate species; for +it is often, though by no means universally, found, that there is a sort +of parallelism in the properties of different Kinds, and that their +degree of unlikeness in one respect bears some proportion to their +unlikeness in others. We see this parallelism in the properties of the +different metals; in those of sulphur, phosphorus, and carbon; of +chlorine, iodine, and bromine; in the natural orders of plants and +animals, &c. But there are innumerable anomalies and exceptions to this +sort of conformity; if indeed the conformity itself be anything but an +anomaly and an exception in nature.</p> + +<p>Universal propositions, therefore, respecting the properties of superior +Kinds, unless grounded on proved or presumed connexion by causation, +ought not to be hazarded except after separately examining every known +sub-kind included in the larger Kind. And even then such generalizations +must be held in readiness to be given up on the occurrence of some new +anomaly, which, when the uniformity is not derived from causation, can +never, even in the case of the most general of these empirical laws, be +considered very improbable. Thus all the universal propositions which it +has been attempted to lay down respecting simple substances, or +concerning any of the classes which have been formed among simple +substances, (and the attempt has been often made,) have, with the +progress of experience, either faded into inanity, or been proved to be +erroneous; and each Kind of simple substance remains with its own +collection of properties apart from the rest, saving a certain +parallelism with a few other Kinds, the most similar <span class="pagenum"><a name="Page_123" id="Page_123">[Pg 123]</a></span>to itself. In +organized beings, indeed, there are abundance of propositions +ascertained to be universally true of superior genera, to many of which +the discovery hereafter of any exceptions must be regarded as extremely +improbable. But these, as already observed, are, we have every reason to +believe, properties dependent on causation.</p> + +<p>Uniformities of coexistence, then, not only when they are consequences +of laws of succession, but also when they are ultimate truths, must be +ranked, for the purpose of logic, among empirical laws; and are amenable +in every respect to the same rules with those unresolved uniformities +which are known to be dependent on causation.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_124" id="Page_124">[Pg 124]</a></span></p> +<h3><a name="BOOK_III_CHAPTER_XXIII" id="BOOK_III_CHAPTER_XXIII"></a>CHAPTER XXIII.<br /> +OF APPROXIMATE GENERALIZATIONS, AND PROBABLE EVIDENCE.</h3> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIII_1">§ 1.</a> In our inquiries into the nature of the inductive process, we must +not confine our notice to such generalizations from experience as +profess to be universally true. There is a class of inductive truths +avowedly not universal; in which it is not pretended that the predicate +is always true of the subject; but the value of which, as +generalizations, is nevertheless extremely great. An important portion +of the field of inductive knowledge does not consist of universal +truths, but of approximations to such truths; and when a conclusion is +said to rest on probable evidence, the premises it is drawn from are +usually generalizations of this sort.</p> + +<p>As every certain inference respecting a particular case, implies that +there is ground for a general proposition, of the form, Every A is B; so +does every probable inference suppose that there is ground for a +proposition of the form, Most A are B: and the degree of probability of +the inference in an average case, will depend on the proportion between +the number of instances existing in nature which accord with the +generalization, and the number of those which conflict with it.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIII_2">§ 2.</a> Propositions in the form, Most A are B, are of a very different +degree of importance in science, and in the practice of life. To the +scientific inquirer they are valuable chiefly as materials for, and +steps towards, universal truths. The discovery of these is the proper +end of science: its work is not done if it stops at the proposition that +a majority of A are B, without circumscribing that majority by some +common <span class="pagenum"><a name="Page_125" id="Page_125">[Pg 125]</a></span>character, fitted to distinguish them from the minority. +Independently of the inferior precision of such imperfect +generalizations, and the inferior assurance with which they can be +applied to individual cases, it is plain that, compared with exact +generalizations, they are almost useless as means of discovering +ulterior truths by way of deduction. We may, it is true, by combining +the proposition Most A are B, with an universal proposition, Every B is +C, arrive at the conclusion that Most A are C. But when a second +proposition of the approximate kind is introduced,—or even when there +is but one, if that one be the major premise,—nothing can in general be +positively concluded. When the major is Most B are D, then, even if the +minor be Every A is B, we cannot infer that most A are D, or with any +certainty that even some A are D. Though the majority of the class B +have the attribute signified by D, the whole of the sub-class A may +belong to the minority.<a name="FNanchor_34_34" id="FNanchor_34_34"></a><a href="#Footnote_34_34" class="fnanchor">[34]</a></p> + +<p>Though so little use can be made, in science, of approximate +generalizations, except as a stage on the road to something better, for +practical guidance they are often all we have to rely on. Even when +science has really determined the universal laws of any phenomenon, not +only are those laws generally too much encumbered with conditions to be +adapted for every-day use, but the cases which present themselves in +life are too complicated, and our decisions require to be taken too +rapidly, to admit of waiting till the existence of a phenomenon can be +proved by what have been scientifically ascertained to be universal +marks of it. To be indecisive and reluctant to act, because we have not +evidence of a perfectly conclusive character to act on, is a defect +sometimes incident to scientific minds, but which, wherever it exists, +renders them unfit for practical emergencies. If we would succeed in +action, we must judge by indications which, though they do not +<span class="pagenum"><a name="Page_126" id="Page_126">[Pg 126]</a></span>generally mislead us, sometimes do; and must make up, as far as +possible, for the incomplete conclusiveness of any one indication, by +obtaining others to corroborate it. The principles of induction +applicable to approximate generalization are therefore a not less +important subject of inquiry, than the rules for the investigation of +universal truths; and might reasonably be expected to detain us almost +as long, were it not that these principles are mere corollaries from +those which have been already treated of.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIII_3">§ 3.</a> There are two sorts of cases in which we are forced to guide +ourselves by generalizations of the imperfect form, Most A are B. The +first is, when we have no others; when we have not been able to carry +our investigation of the laws of the phenomena any farther; as in the +following propositions: Most dark-eyed persons have dark hair; Most +springs contain mineral substances; Most stratified formations contain +fossils. The importance of this class of generalizations is not very +great; for, though it frequently happens that we see no reason why that +which is true of most individuals of a class is not true of the +remainder, nor are able to bring the former under any general +description which can distinguish them from the latter, yet if we are +willing to be satisfied with propositions of a less degree of +generality, and to break down the class A into subclasses, we may +generally obtain a collection of propositions exactly true. We do not +know why most wood is lighter than water, nor can we point out any +general property which discriminates wood that is lighter than water +from that which is heavier. But we know exactly what species are the one +and what the other. And if we meet with a specimen not conformable to +any known species (the only case in which our previous knowledge affords +no other guidance than the approximate generalization), we can generally +make a specific experiment, which is a surer resource.</p> + +<p>It often happens, however, that the proposition, Most A are B, is not +the ultimatum of our scientific progress, though the knowledge we +possess beyond it cannot conveniently be brought to bear upon the +particular instance. In such a case <span class="pagenum"><a name="Page_127" id="Page_127">[Pg 127]</a></span>we know well enough what +circumstances distinguish the portion of A which has the attribute B +from the portion which has it not, but have no means, or have not time, +to examine whether those characteristic circumstances exist or not in +the individual case. This is the situation we are generally in when the +inquiry is of the kind called moral, that is, of the kind which has in +view to predict human actions. To enable us to affirm anything +universally concerning the actions of classes of human beings, the +classification must be grounded on the circumstances of their mental +culture and habits, which in an individual case are seldom exactly +known; and classes grounded on these distinctions would never precisely +accord with those into which mankind are divided for social purposes. +All propositions which can be framed respecting the actions of human +beings as ordinarily classified, or as classified according to any kind +of outward indications, are merely approximate. We can only say, Most +persons of a particular age, profession, country, or rank in society, +have such and such qualities; or, Most persons when placed in certain +circumstances act in such and such a way. Not that we do not often know +well enough on what causes the qualities depend, or what sort of persons +they are who act in that particular way; but we have seldom the means of +knowing whether any individual person has been under the influence of +those causes, or is a person of that particular sort. We could replace +the approximate generalizations by propositions universally true; but +these would hardly ever be capable of being applied to practice. We +should be sure of our majors, but we should not be able to get minors to +fit: we are forced, therefore, to draw our conclusions from coarser and +more fallible indications.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIII_4">§ 4.</a> Proceeding now to consider, what is to be regarded as sufficient +evidence of an approximate generalization; we can have no difficulty in +at once recognising that when admissible at all, it is admissible only +as an empirical law. Propositions of the form, Every A is B, are not +necessarily laws of causation, or ultimate uniformities of coexistence; +propositions like Most A are B <i>cannot</i> be so. Propositions <span class="pagenum"><a name="Page_128" id="Page_128">[Pg 128]</a></span>hitherto +found true in every observed instance, may yet be no necessary +consequence of laws of causation, or of ultimate uniformities, and +unless they are so, may, for aught we know, be false beyond the limits +of actual observation: still more evidently must this be the case with +propositions which are only true in a mere majority of the observed +instances.</p> + +<p>There is some difference, however, in the degree of certainty of the +proposition, Most A are B, according as that approximate generalization +composes the whole of our knowledge of the subject, or not. Suppose, +first, that the former is the case. We know only that most A are B, not +why they are so, nor in what respect those which are, differ from those +which are not. How then did we learn that most A are B? Precisely in the +manner in which we should have learnt, had such happened to be the fact, +that all A are B. We collected a number of instances sufficient to +eliminate chance, and having done so, compared the number of instances +in the affirmative with the number in the negative. The result, like +other unresolved derivative laws, can be relied on solely within the +limits not only of place and time, but also of circumstance, under which +its truth has been actually observed; for as we are supposed to be +ignorant of the causes which make the proposition true, we cannot tell +in what manner any new circumstance might perhaps affect it. The +proposition, Most judges are inaccessible to bribes, would be found true +of Englishmen, Frenchmen, Germans, North Americans, and so forth; but if +on this evidence alone we extended the assertion to Orientals, we should +step beyond the limits, not only of place but of circumstance, within +which the fact had been observed, and should let in possibilities of the +absence of the determining causes, or the presence of counteracting +ones, which might be fatal to the approximate generalization.</p> + +<p>In the case where the approximate proposition is not the ultimatum of +our scientific knowledge, but only the most available form of it for +practical guidance; where we know, not only that most A have the +attribute B, but also the causes of B, or some properties by which the +portion of A which has that attribute is distinguished from the portion +which has it <span class="pagenum"><a name="Page_129" id="Page_129">[Pg 129]</a></span>not; we are rather more favourably situated than in the +preceding case. For we have now a double mode of ascertaining whether it +be true that most A are B; the direct mode, as before, and an indirect +one, that of examining whether the proposition admits of being deduced +from the known cause, or from any known criterion, of B. Let the +question, for example, be whether most Scotchmen can read? We may not +have observed, or received the testimony of others respecting, a +sufficient number and variety of Scotchmen to ascertain this fact; but +when we consider that the cause of being able to read is the having been +taught it, another mode of determining the question presents itself, +namely, by inquiring whether most Scotchmen have been sent to schools +where reading is effectually taught. Of these two modes, sometimes one +and sometimes the other is the more available. In some cases, the +frequency of the effect is the more accessible to that extensive and +varied observation which is indispensable to the establishment of an +empirical law; at other times, the frequency of the causes, or of some +collateral indications. It commonly happens that neither is susceptible +of so satisfactory an induction as could be desired, and that the +grounds on which the conclusion is received are compounded of both. Thus +a person may believe that most Scotchmen can read, because, so far as +his information extends, most Scotchmen have been sent to school, and +most Scotch schools teach reading effectually; and also because most of +the Scotchmen whom he has known or heard of, could read; though neither +of these two sets of observations may by itself fulfil the necessary +conditions of extent and variety.</p> + +<p>Although the approximate generalization may in most cases be +indispensable for our guidance, even when we know the cause, or some +certain mark, of the attribute predicated; it needs hardly be observed +that we may always replace the uncertain indication by a certain one, in +any case in which we can actually recognise the existence of the cause +or mark. For example, an assertion is made by a witness, and the +question is, whether to believe it. If we do not look to any of the +individual circumstances of the case, we have nothing <span class="pagenum"><a name="Page_130" id="Page_130">[Pg 130]</a></span>to direct us but +the approximate generalization, that truth is more common than +falsehood, or, in other words, that most persons, on most occasions, +speak truth. But if we consider in what circumstances the cases where +truth is spoken differ from those in which it is not, we find, for +instance, the following: the witness's being an honest person or not; +his being an accurate observer or not; his having an interest to serve +in the matter or not. Now, not only may we be able to obtain other +approximate generalizations respecting the degree of frequency of these +various possibilities, but we may know which of them is positively +realized in the individual case. That the witness has or has not an +interest to serve, we perhaps know directly; and the other two points +indirectly, by means of marks; as, for example, from his conduct on some +former occasion; or from his reputation, which, though a very uncertain +mark, affords an approximate generalization (as, for instance, Most +persons who are believed to be honest by those with whom they have had +frequent dealings, are really so) which approaches nearer to an +universal truth than the approximate general proposition with which we +set out, viz. Most persons on most occasions speak truth.</p> + +<p>As it seems unnecessary to dwell further on the question of the evidence +of approximate generalizations, we shall proceed to a not less important +topic, that of the cautions to be observed in arguing from these +incompletely universal propositions to particular cases.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIII_5">§ 5.</a> So far as regards the direct application of an approximate +generalization to an individual instance, this question presents no +difficulty. If the proposition, Most A are B, has been established, by a +sufficient induction, as an empirical law, we may conclude that any +particular A is B with a probability proportioned to the preponderance +of the number of affirmative instances over the number of exceptions. If +it has been found practicable to attain numerical precision in the data, +a corresponding degree of precision may be given to the evaluation of +the chances of error in the conclusion. If it can be established as an +empirical law that nine out of every ten A are B, <span class="pagenum"><a name="Page_131" id="Page_131">[Pg 131]</a></span>there will be one +chance in ten of error in assuming that any A, not individually known to +us, is a B: but this of course holds only within the limits of time, +place, and circumstance, embraced in the observations, and therefore +cannot be counted on for any sub-class or variety of A (or for A in any +set of external circumstances) which were not included in the average. +It must be added, that we can guide ourselves by the proposition, Nine +out of every ten A are B, only in cases of which we know nothing except +that they fall within the class A. For if we know, of any particular +instance <i>i</i>, not only that it falls under A, but to what species or +variety of A it belongs, we shall generally err in applying to <i>i</i> the +average struck for the whole genus, from which the average corresponding +to that species alone would, in all probability, materially differ. And +so if <i>i</i>, instead of being a particular sort of instance, is an +instance known to be under the influence of a particular set of +circumstances. The presumption drawn from the numerical proportions in +the whole genus would probably, in such a case, only mislead. A general +average should only be applied to cases which are neither known, nor can +be presumed, to be other than average cases. Such averages, therefore, +are commonly of little use for the practical guidance of any affairs but +those which concern large numbers. Tables of the chances of life are +useful to insurance offices, but they go a very little way towards +informing any one of the chances of his own life, or any other life in +which he is interested, since almost every life is either better or +worse than the average. Such averages can only be considered as +supplying the first term in a series of approximations; the subsequent +terms proceeding on an appreciation of the circumstances belonging to +the particular case.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIII_6">§ 6.</a> From the application of a single approximate generalization to +individual cases, we proceed to the application of two or more of them +together to the same case.</p> + +<p>When a judgment applied to an individual instance is grounded on two +approximate generalizations taken in conjunction, the propositions may +co-operate towards the result <span class="pagenum"><a name="Page_132" id="Page_132">[Pg 132]</a></span>in two different ways. In the one, each +proposition is separately applicable to the case in hand, and our object +in combining them is to give to the conclusion in that particular case +the double probability arising from the two propositions separately. +This may be called joining two probabilities by way of Addition; and the +result is a probability greater than either. The other mode is, when +only one of the propositions is directly applicable to the case, the +second being only applicable to it by virtue of the application of the +first. This is joining two probabilities by way of Ratiocination or +Deduction; the result of which is a less probability than either. The +type of the first argument is, Most A are B; most C are B; this thing is +both an A and a C; therefore it is probably a B. The type of the second +is, Most A are B; most C are A; this is a C; therefore it is probably an +A, therefore it is probably a B. The first is exemplified when we prove +a fact by the testimony of two unconnected witnesses; the second, when +we adduce only the testimony of one witness that he has heard the thing +asserted by another. Or again, in the first mode it may be argued that +the accused committed the crime, because he concealed himself, and +because his clothes were stained with blood; in the second, that he +committed it because he washed or destroyed his clothes, which is +supposed to render it probable that they were stained with blood. +Instead of only two links, as in these instances, we may suppose chains +of any length. A chain of the former kind was termed by Bentham<a name="FNanchor_35_35" id="FNanchor_35_35"></a><a href="#Footnote_35_35" class="fnanchor">[35]</a> a +self-corroborative chain of evidence; the second, a self-infirmative +chain.</p> + +<p>When approximate generalizations are joined by way of addition, we may +deduce from the theory of probabilities laid down in a former chapter, +in what manner each of them adds to the probability of a conclusion +which has the warrant of them all.</p> + +<p>In the early editions of this treatise, the joint probability arising +from the sum of two independent probabilities was estimated in the +following manner. If, on an average, two of <span class="pagenum"><a name="Page_133" id="Page_133">[Pg 133]</a></span>every three As are Bs, and +three of every four Cs are Bs, the probability that something which is +both an A and a C is a B, will be more than two in three, or than three +in four. Of every twelve things which are As, all except four are Bs by +the supposition; and if the whole twelve, and consequently those four, +have the characters of C likewise, three of these will be Bs on that +ground. Therefore, out of twelve which are both As and Cs, eleven are +Bs. To state the argument in another way; a thing which is both an A and +a C, but which is not a B, is found in only one of three sections of the +class A, and in only one of four sections of the class C; but this +fourth of C being spread over the whole of A indiscriminately, only +one-third part of it (or one-twelfth of the whole number) belongs to the +third section of A; therefore a thing which is not a B occurs only once, +among twelve things which are both As and Cs. The argument would in the +language of the doctrine of chances, be thus expressed: the chance that +an A is not a B is 1/3, the chance that a C is not a B is 1/4; hence if +the thing be both an A and a C, the chance is 1/3 of 1/4 = 1/12.</p> + +<p>It has, however, been pointed out to me by a mathematical friend, that +in this statement the evaluation of the chances is erroneous. The +correct mode of setting out the possibilities is as follows. If the +thing (let us call it T) which is both an A and a C, is a B, something +is true which is only true twice in every thrice, and something else +which is only true thrice in every four times. The first fact being true +eight times in twelve, and the second being true six times in every +eight, and consequently six times in those eight; both facts will be +true only six times in twelve. On the other hand if T, although it is +both an A and a C, is not a B, something is true which is only true once +in every thrice, and something else which is only true once in every +four times. The former being true four times out of twelve, and the +latter once in every four, and therefore once in those four; both are +only true in one case out of twelve. So that T is a B six times in +twelve, and T is not a B, only once: making the comparative +probabilities, not eleven to one, as I had previously made them, but six +to one.</p> + +<p>It may be asked, what happens in the remaining cases? <span class="pagenum"><a name="Page_134" id="Page_134">[Pg 134]</a></span>since in this +calculation seven out of twelve cases seem to have exhausted the +possibilities. If T is a B in only six cases of every twelve, and a +not-B in only one, what is it in the other five? The only supposition +remaining for those cases is that it is neither a B nor not a B, which +is impossible. But this impossibility merely proves that the state of +things supposed in the hypothesis does not exist in those cases. They +are cases that do not furnish anything which is both an A and a C.</p> + +<p>To make this intelligible, we will substitute for our symbols a concrete +case. Let there be two witnesses, M and N, whose probabilities of +veracity correspond with the ratios of the preceding example: M speaks +truth twice in every thrice, N thrice in every four times. The question +is, what is the probability that a statement, in which they both concur, +will be true. The cases may be classed as follows. Both the witnesses +will speak truly six in every twelve times; both falsely once in twelve +times. Therefore, if they both agree in an assertion, it will be true +six times, for once that it will be false. What happens in the remaining +cases is here evident; there will be five cases in every twelve in which +the witnesses will not agree. M will speak truth and N falsehood in two +cases of every twelve; N will speak truth and M falsehood in three +cases, making in all five. In these cases, however, the witnesses will +not agree in their testimony. But disagreement between them is excluded +by the supposition. There are, therefore, only seven cases which are +within the conditions of the hypothesis; of which seven, veracity exists +in six, and falsehood in one. Resuming our former symbols, in five cases +out of twelve T is not both an A and a C, but an A only, or a C only. +The cases in which it is both are only seven, in six of which it is a B, +in one not a B, making the chance six to one, or 6/7 and 1/7 +respectively.</p> + +<p>In this correct, as in the former incorrect computation, it is of course +presupposed that the probabilities arising from A and C are independent +of each other. There must not be any such connexion between A and C, +that when a thing belongs to the one class it will therefore belong to +the other, or even <span class="pagenum"><a name="Page_135" id="Page_135">[Pg 135]</a></span>have a greater chance of doing so. Otherwise the +not-Bs which are Cs may be, most or even all of them, identical with the +not-Bs which are As; in which last case the probability arising from A +and C together will be no greater than that arising from A alone.</p> + +<p>When approximate generalizations are joined together in the other mode, +that of deduction, the degree of probability of the inference, instead +of increasing, diminishes at each step. From two such premises as Most A +are B, Most B are C, we cannot with certainty conclude that even a +single A is C; for the whole of the portion of A which in any way falls +under B, may perhaps be comprised in the exceptional part of it. Still, +the two propositions in question afford an appreciable probability that +any given A is C, provided the average on which the second proposition +is grounded, was taken fairly with reference to the first; provided the +proposition, Most B are C, was arrived at in a manner leaving no +suspicion that the probability arising from it is otherwise than fairly +distributed over the section of B which belongs to A. For though the +instances which are A <i>may</i> be all in the minority, they may, also, be +all in the majority; and the one possibility is to be set against the +other. On the whole, the probability arising from the two propositions +taken together, will be correctly measured by the probability arising +from the one, abated in the ratio of that arising from the other. If +nine out of ten Swedes have light hair, and eight out of nine +inhabitants of Stockholm are Swedes, the probability arising from these +two propositions, that any given inhabitant of Stockholm is +light-haired, will amount to eight in ten; though it is rigorously +possible that the whole Swedish population of Stockholm might belong to +that tenth section of the people of Sweden who are an exception to the +rest.</p> + +<p>If the premises are known to be true not of a bare majority, but of +nearly the whole, of their respective subjects, we may go on joining one +such proposition to another for several steps, before we reach a +conclusion not presumably true even of a majority. The error of the +conclusion will amount to the aggregate of the errors of all the +premises. <span class="pagenum"><a name="Page_136" id="Page_136">[Pg 136]</a></span>Let the proposition, Most A are B, be true of nine in ten; +Most B are C, of eight in nine: then not only will one A in ten not be +C, because not B, but even of the nine-tenths which are B, only +eight-ninths will be C: that is, the cases of A which are C will be only +8/9 of 9/10, or four-fifths. Let us now add Most C are D, and suppose +this to be true of seven cases out of eight; the proportion of A which +is D will be only 7/8 of 8/9 of 9/10, or 7/10. Thus the probability +progressively dwindles. The experience, however, on which our +approximate generalizations are grounded, has so rarely been subjected +to, or admits of, accurate numerical estimation, that we cannot in +general apply any measurement to the diminution of probability which +takes place at each illation; but must be content with remembering that +it does diminish at every step, and that unless the premises approach +very nearly indeed to being universally true, the conclusion after a +very few steps is worth nothing. A hearsay of a hearsay, or an argument +from presumptive evidence depending not on immediate marks but on marks +of marks, is worthless at a very few removes from the first stage.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIII_7">§ 7.</a> There are, however, two cases in which reasonings depending on +approximate generalizations may be carried to any length we please with +as much assurance, and are as strictly scientific, as if they were +composed of universal laws of nature. But these cases are exceptions of +the sort which are currently said to prove the rule. The approximate +generalizations are as suitable, in the cases in question, for purposes +of ratiocination, as if they were complete generalizations, because they +are capable of being transformed into complete generalizations exactly +equivalent.</p> + +<p>First: If the approximate generalization is of the class in which our +reason for stopping at the approximation is not the impossibility, but +only the inconvenience, of going further; if we are cognizant of the +character which distinguishes the cases that accord with the +generalization from those which are exceptions to it; we may then +substitute for the approximate proposition, an universal proposition +with a <span class="pagenum"><a name="Page_137" id="Page_137">[Pg 137]</a></span>proviso. The proposition, Most persons who have uncontrolled +power employ it ill, is a generalization of this class, and may be +transformed into the following:—All persons who have uncontrolled power +employ it ill, provided they are not persons of unusual strength of +judgment and rectitude of purpose. The proposition, carrying the +hypothesis or proviso with it, may then be dealt with no longer as an +approximate, but as an universal proposition; and to whatever number of +steps the reasoning may reach, the hypothesis, being carried forward to +the conclusion, will exactly indicate how far that conclusion is from +being applicable universally. If in the course of the argument other +approximate generalizations are introduced, each of them being in like +manner expressed as an universal proposition with a condition annexed, +the sum of all the conditions will appear at the end as the sum of all +the errors which affect the conclusion. Thus, to the proposition last +cited, let us add the following:—All absolute monarchs have +uncontrolled power, unless their position is such that they need the +active support of their subjects (as was the case with Queen Elizabeth, +Frederick of Prussia, and others). Combining these two propositions, we +can deduce from them an universal conclusion, which will be subject to +both the hypotheses in the premises; All absolute monarchs employ their +power ill, unless their position makes them need the active support of +their subjects, or unless they are persons of unusual strength of +judgment and rectitude of purpose. It is of no consequence how rapidly +the errors in our premises accumulate, if we are able in this manner to +record each error, and keep an account of the aggregate as it swells up.</p> + +<p>Secondly: there is a case in which approximate propositions, even +without our taking note of the conditions under which they are not true +of individual cases, are yet, for the purposes of science, universal +ones; namely, in the inquiries which relate to the properties not of +individuals, but of multitudes. The principal of these is the science of +politics, or of human society. This science is principally concerned +with the actions not of solitary individuals, but of masses; with the +fortunes not of single persons, but of communities.</p> + +<p><span class="pagenum"><a name="Page_138" id="Page_138">[Pg 138]</a></span></p><p>For the statesman, therefore, it is generally enough to know that +<i>most</i> persons act or are acted upon in a particular way; since his +speculations and his practical arrangements refer almost exclusively to +cases in which the whole community, or some large portion of it, is +acted upon at once, and in which, therefore, what is done or felt by +<i>most</i> persons determines the result produced by or upon the body at +large. He can get on well enough with approximate generalizations on +human nature, since what is true approximately of all individuals is +true absolutely of all masses. And even when the operations of +individual men have a part to play in his deductions, as when he is +reasoning of kings, or other single rulers, still, as he is providing +for indefinite duration, involving an indefinite succession of such +individuals, he must in general both reason and act as if what is true +of most persons were true of all.</p> + +<p>The two kinds of considerations above adduced are a sufficient +refutation of the popular error, that speculations on society and +government, as resting on merely probable evidence, must be inferior in +certainty and scientific accuracy to the conclusions of what are called +the exact sciences, and less to be relied on in practice. There are +reasons enough why the moral sciences must remain inferior to at least +the more perfect of the physical: why the laws of their more complicated +phenomena cannot be so completely deciphered, nor the phenomena +predicted with the same degree of assurance. But though we cannot attain +to so many truths, there is no reason that those we can attain should +deserve less reliance, or have less of a scientific character. Of this +topic, however, I shall treat more systematically in the concluding +Book, to which place any further consideration of it must be deferred.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_139" id="Page_139">[Pg 139]</a></span></p> +<h3><a name="BOOK_III_CHAPTER_XXIV" id="BOOK_III_CHAPTER_XXIV"></a>CHAPTER XXIV.<br /> +OF THE REMAINING LAWS OF NATURE.</h3> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIV_1">§ 1.</a> In the First Book, we found that all the assertions which can be +conveyed by language, express some one or more of five different things: +Existence; Order in Place; Order in Time; Causation; and +Resemblance.<a name="FNanchor_36_36" id="FNanchor_36_36"></a><a href="#Footnote_36_36" class="fnanchor">[36]</a> Of these, Causation, in our view of the subject, not +being fundamentally different from Order in Time, the five species of +possible assertions are reduced to four. The propositions which affirm +Order in Time, in either of its two modes, Coexistence and Succession, +have formed, thus far, the subject of the present Book. And we have now +concluded the exposition, so far as it falls within the limits assigned +to this work, of the nature of the evidence on which these propositions +rest, and the processes of investigation by which they are ascertained +and proved. There remain three classes of facts: Existence, Order in +Place, and Resemblance; in regard to which the same questions are now to +be resolved.</p> + +<p>Regarding the first of these, very little needs be said. Existence in +general, is a subject not for our science, but for metaphysics. To +determine what things can be recognised as really existing, +independently of our own sensible or other impressions, and in what +meaning the term is, in that case, predicated of them, belongs to the +consideration of "Things in themselves," from which, throughout this +work, we have as much as possible kept aloof. Existence, so far as Logic +is concerned about it, has reference only to phenomena; to actual, or +possible, states of external or internal consciousness, in ourselves or +others. Feelings of sensitive beings, or possibilities of having such +feelings, are the only things the existence <span class="pagenum"><a name="Page_140" id="Page_140">[Pg 140]</a></span>of which can be a subject +of logical induction, because the only things of which the existence in +individual cases can be a subject of experience.</p> + +<p>It is true that a thing is said by us to exist, even when it is absent, +and therefore is not and cannot be perceived. But even then, its +existence is to us only another word for our conviction that we should +perceive it on a certain supposition; namely, if we were in the needful +circumstances of time and place, and endowed with the needful perfection +of organs. My belief that the Emperor of China exists, is simply my +belief that if I were transported to the imperial palace or some other +locality in Pekin, I should see him. My belief that Julius Cæsar +existed, is my belief that I should have seen him if I had been present +in the field of Pharsalia, or in the senate-house at Rome. When I +believe that stars exist beyond the utmost range of my vision, though +assisted by the most powerful telescopes yet invented, my belief, +philosophically expressed, is, that with still better telescopes, if +such existed, I could see them, or that they may be perceived by beings +less remote from them in space, or whose capacities of perception are +superior to mine.</p> + +<p>The existence, therefore, of a phenomenon, is but another word for its +being perceived, or for the inferred possibility of perceiving it. When +the phenomenon is within the range of present observation, by present +observation we assure ourselves of its existence; when it is beyond that +range, and is therefore said to be absent, we infer its existence from +marks or evidences. But what can these evidences be? Other phenomena; +ascertained by induction to be connected with the given phenomenon, +either in the way of succession or of coexistence. The simple existence, +therefore, of an individual phenomenon, when not directly perceived, is +inferred from some inductive law of succession or coexistence: and is +consequently not amenable to any peculiar inductive principles. We prove +the existence of a thing, by proving that it is connected by succession +or coexistence with some known thing.</p> + +<p>With respect to <i>general</i> propositions of this class, that is, <span class="pagenum"><a name="Page_141" id="Page_141">[Pg 141]</a></span>which +affirm the bare fact of existence, they have a peculiarity which renders +the logical treatment of them a very easy matter; they are +generalizations which are sufficiently proved by a single instance. That +ghosts, or unicorns, or sea-serpents exist, would be fully established +if it could be ascertained positively that such things had been even +once seen. Whatever has once happened, is capable of happening again; +the only question relates to the conditions under which it happens.</p> + +<p>So far, therefore, as relates to simple existence, the Inductive Logic +has no knots to untie. And we may proceed to the remaining two of the +great classes into which facts have been divided; Resemblance, and Order +in Space.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIV_2">§ 2.</a> Resemblance and its opposite, except in the case in which they +assume the names of Equality and Inequality, are seldom regarded as +subjects of science; they are supposed to be perceived by simple +apprehension; by merely applying our senses or directing our attention +to the two objects at once, or in immediate succession. And this +simultaneous, or virtually simultaneous, application of our faculties to +the two things which are to be compared, does necessarily constitute the +ultimate appeal, wherever such application is practicable. But, in most +cases, it is not practicable: the objects cannot be brought so close +together that the feeling of their resemblance (at least a complete +feeling of it) directly arises in the mind. We can only compare each of +them with some third object, capable of being transported from one to +the other. And besides, even when the objects can be brought into +immediate juxtaposition, their resemblance or difference is but +imperfectly known to us, unless we have compared them minutely, part by +part. Until this has been done, things in reality very dissimilar often +appear undistinguishably alike. Two lines of very unequal length will +appear about equal when lying in different directions; but place them +parallel, with their farther extremities even, and if we look at the +nearer extremities, their inequality becomes a matter of direct +perception.</p> + +<p><span class="pagenum"><a name="Page_142" id="Page_142">[Pg 142]</a></span></p><p>To ascertain whether, and in what, two phenomena resemble or differ, is +not always, therefore, so easy a thing as it might at first appear. When +the two cannot be brought into juxtaposition, or not so that the +observer is able to compare their several parts in detail, he must +employ the indirect means of reasoning and general propositions. When we +cannot bring two straight lines together, to determine whether they are +equal, we do it by the physical aid of a foot rule applied first to one +and then to the other, and the logical aid of the general proposition or +formula, "Things which are equal to the same thing are equal to one +another." The comparison of two things through the intervention of a +third thing, when their direct comparison is impossible, is the +appropriate scientific process for ascertaining resemblances and +dissimilarities, and is the sum total of what Logic has to teach on the +subject.</p> + +<p>An undue extension of this remark induced Locke to consider reasoning +itself as nothing but the comparison of two ideas through the medium of +a third, and knowledge as the perception of the agreement or +disagreement of two ideas: doctrines which the Condillac school blindly +adopted, without the qualifications and distinctions with which they +were studiously guarded by their illustrious author. Where, indeed, the +agreement or disagreement (otherwise called resemblance or +dissimilarity) of any two things is the very matter to be determined, as +is the case particularly in the sciences of quantity and extension; +there, the process by which a solution, if not attainable by direct +perception, must be indirectly sought, consists in comparing these two +things through the medium of a third. But this is far from being true of +all inquiries. The knowledge that bodies fall to the ground is not a +perception of agreement or disagreement, but of a series of physical +occurrences, a succession of sensations. Locke's definitions of +knowledge and of reasoning required to be limited to our knowledge of, +and reasoning about, resemblances. Nor, even when thus restricted, are +the propositions strictly correct; since the comparison is not made, as +he represents, between the ideas of the two phenomena, but between <span class="pagenum"><a name="Page_143" id="Page_143">[Pg 143]</a></span>the +phenomena themselves. This mistake has been pointed out in an earlier +part of our inquiry,<a name="FNanchor_37_37" id="FNanchor_37_37"></a><a href="#Footnote_37_37" class="fnanchor">[37]</a> and we traced it to an imperfect conception of +what takes place in mathematics, where very often the comparison is +really made between the ideas, without any appeal to the outward senses; +only, however, because in mathematics a comparison of the ideas is +strictly equivalent to a comparison of the phenomena themselves. Where, +as in the case of numbers, lines, and figures, our idea of an object is +a complete picture of the object, so far as respects the matter in hand; +we can, of course, learn from the picture, whatever could be learnt from +the object itself by mere contemplation of it as it exists at the +particular instant when the picture is taken. No mere contemplation of +gunpowder would ever teach us that a spark would make it explode, nor, +consequently, would the contemplation of the idea of gunpowder do so: +but the mere contemplation of a straight line shows that it cannot +inclose a space: accordingly the contemplation of the idea of it will +show the same. What takes place in mathematics is thus no argument that +the comparison is between the ideas only. It is always, either +indirectly or directly, a comparison of the phenomena.</p> + +<p>In cases in which we cannot bring the phenomena to the test of direct +inspection at all, or not in a manner sufficiently precise, but must +judge of their resemblance by inference from other resemblances or +dissimilarities more accessible to observation, we of course require, as +in all cases of ratiocination, generalizations or formulæ applicable to +the subject. We must reason from laws of nature; from the uniformities +which are observable in the fact of likeness or unlikeness.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIV_3">§ 3.</a> Of these laws or uniformities, the most comprehensive are those +supplied by mathematics; the axioms relating to equality, inequality, +and proportionality, and the various theorems thereon founded. And these +are the only Laws of Resemblance which require to be, or which can be, +treated apart. It is true there are innumerable other <span class="pagenum"><a name="Page_144" id="Page_144">[Pg 144]</a></span>theorems which +affirm resemblances among phenomena; as that the angle of the reflection +of light is <i>equal</i> to its angle of incidence (equality being merely +exact resemblance in magnitude). Again, that the heavenly bodies +describe <i>equal</i> areas in equal times; and that their periods of +revolution are <i>proportional</i> (another species of resemblance) to the +sesquiplicate powers of their distances from the centre of force. These +and similar propositions affirm resemblances, of the same nature with +those asserted in the theorems of mathematics; but the distinction is, +that the propositions of mathematics are true of all phenomena whatever, +or at least without distinction of origin; while the truths in question +are affirmed only of special phenomena, which originate in a certain +way; and the equalities, proportionalities, or other resemblances, which +exist between such phenomena, must necessarily be either derived from, +or identical with, the law of their origin—the law of causation on +which they depend. The equality of the areas described in equal times by +the planets, is <i>derived</i> from the laws of the causes; and, until its +derivation was shown, it was an empirical law. The equality of the +angles of reflexion and incidence is <i>identical</i> with the law of the +cause; for the cause is the incidence of a ray of light upon a +reflecting surface, and the equality in question is the very law +according to which that cause produces its effects. This class, +therefore, of the uniformities of resemblance between phenomena, are +inseparable, in fact and in thought, from the laws of the production of +those phenomena: and the principles of induction applicable to them are +no other than those of which we have treated in the preceding chapters +of this Book.</p> + +<p>It is otherwise with the truths of mathematics. The laws of equality and +inequality between spaces, or between numbers, have no connexion with +laws of causation. That the angle of reflexion is equal to the angle of +incidence, is a statement of the mode of action of a particular cause; +but that when two straight lines intersect each other the opposite +angles are equal, is true of all such lines and angles, by whatever +cause produced. That the squares of the periodic times of the planets +are proportional to the cubes of their distances from <span class="pagenum"><a name="Page_145" id="Page_145">[Pg 145]</a></span>the sun, is an +uniformity derived from the laws of the causes (or forces) which produce +the planetary motions; but that the square of any number is four times +the square of half the number, is true independently of any cause. The +only laws of resemblance, therefore, which we are called upon to +consider independently of causation, belong to the province of +mathematics.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIV_4">§ 4.</a> The same thing is evident with respect to the only one remaining of +our five categories, Order in Place. The order in place, of the effects +of a cause, is (like everything else belonging to the effects) a +consequence of the laws of that cause. The order in place, or, as we +have termed it, the collocation, of the primeval causes, is (as well as +their resemblance) in each instance an ultimate fact, in which no laws +or uniformities are traceable. The only remaining general propositions +respecting order in place, and the only ones which have nothing to do +with causation, are some of the truths of geometry; laws through which +we are able, from the order in place of certain points, lines, or +spaces, to infer the order in place of others which are connected with +the former in some known mode; quite independently of the particular +nature of those points, lines, or spaces, in any other respect than +position or magnitude, as well as independently of the physical cause +from which in any particular case they happen to derive their origin.</p> + +<p>It thus appears that mathematics is the only department of science into +the methods of which it still remains to inquire. And there is the less +necessity that this inquiry should occupy us long, as we have already, +in the Second Book, made considerable progress in it. We there remarked, +that the directly inductive truths of mathematics are few in number; +consisting of the axioms, together with certain propositions concerning +existence, tacitly involved in most of the so-called definitions. And we +gave what appeared conclusive reasons for affirming that these original +premises, from which the remaining truths of the science are deduced, +are, notwithstanding all appearances to the contrary, results of +observation and experience; founded, <span class="pagenum"><a name="Page_146" id="Page_146">[Pg 146]</a></span>in short, on the evidence of the +senses. That things equal to the same thing are equal to one another, +and that two straight lines which have once intersected one another +continue to diverge, are inductive truths; resting, indeed, like the law +of universal causation, only on induction <i>per enumerationem simplicem</i>; +on the fact that they have been perpetually perceived to be true, and +never once found to be false. But, as we have seen in a recent chapter +that this evidence, in the case of a law so completely universal as the +law of causation, amounts to the fullest proof, so is this even more +evidently true of the general propositions to which we are now +adverting; because, as a perception of their truth in any individual +case whatever, requires only the simple act of looking at the objects in +a proper position, there never could have been in their case (what, for +a long period, there were in the case of the law of causation) instances +which were apparently, though not really, exceptions to them. Their +infallible truth was recognised from the very dawn of speculation; and +as their extreme familiarity made it impossible for the mind to conceive +the objects under any other law, they were, and still are, generally +considered as truths recognised by their own evidence, or by instinct.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIV_5">§ 5.</a> There is something which seems to require explanation, in the fact +that the immense multitude of truths (a multitude still as far from +being exhausted as ever) comprised in the mathematical sciences, can be +elicited from so small a number of elementary laws. One sees not, at +first, how it is that there can be room for such an infinite variety of +true propositions, on subjects apparently so limited.</p> + +<p>To begin with the science of number. The elementary or ultimate truths +of this science are the common axioms concerning equality, namely, +"Things which are equal to the same thing are equal to one another," and +"Equals added to equals make equal sums," (no other axioms are +required,<a name="FNanchor_38_38" id="FNanchor_38_38"></a><a href="#Footnote_38_38" class="fnanchor">[38]</a>) <span class="pagenum"><a name="Page_147" id="Page_147">[Pg 147]</a></span>together with the definitions of the various numbers. +Like other so-called definitions, these are composed of two things, the +explanation of a name, and the assertion of a fact: of which the latter +alone can form a first principle or premise of a science. The fact +asserted in the definition of a number is a physical fact. Each of the +numbers two, three, four, &c., denotes physical phenomena, and connotes +a physical property of those phenomena. Two, for instance, denotes all +pairs of things, and twelve all dozens of things, connoting what makes +them pairs, or dozens; and that which makes them so is something +physical; since it cannot be denied that two apples are physically +distinguishable from three apples, two horses from one horse, and so +forth: that they are a different visible and tangible phenomenon. I am +not undertaking to say what the difference is; it is enough that there +is a difference of which the senses can take cognizance. And although a +hundred and two horses are not so easily distinguished from a hundred +and three, as two horses are from three—though in most positions the +senses do not perceive any difference—yet they may be so placed that a +difference will be perceptible, or else we should never have +distinguished them, and given them different names. Weight is +confessedly a physical property of things; yet small differences between +great weights are as imperceptible to the senses in most situations, as +small differences between great numbers; and are only put in evidence by +placing the two objects in a peculiar position—namely, in the opposite +scales of a delicate balance.</p> + +<p><span class="pagenum"><a name="Page_148" id="Page_148">[Pg 148]</a></span></p><p>What, then, is that which is connoted by a name of number? Of course +some property belonging to the agglomeration of things which we call by +the name; and that property is, the characteristic manner in which the +agglomeration is made up of, and may be separated into, parts. I will +endeavour to make this more intelligible by a few explanations.</p> + +<p>When we call a collection of objects <i>two</i>, <i>three</i>, or <i>four</i>, they are +not two, three, or four in the abstract; they are two, three, or four +things of some particular kind; pebbles, horses, inches, pounds weight. +What the name of number connotes is, the manner in which single objects +of the given kind must be put together, in order to produce that +particular aggregate. If the aggregate be of pebbles, and we call it +<i>two</i>, the name implies that, to compose the aggregate, one pebble must +be joined to one pebble. If we call it <i>three</i>, one and one and one +pebble must be brought together to produce it, or else one pebble must +be joined to an aggregate of the kind called <i>two</i>, already existing. +The aggregate which we call <i>four</i>, has a still greater number of +characteristic modes of formation. One and one and one and one pebble +may be brought together; or two aggregates of the kind called <i>two</i> may +be united; or one pebble may be added to an aggregate of the kind called +<i>three</i>. Every succeeding number in the ascending series, may be formed +by the junction of smaller numbers in a progressively greater variety of +ways. Even limiting the parts to two, the number may be formed, and +consequently may be divided, in as many different ways as there are +numbers smaller than itself; and, if we admit of threes, fours, &c., in +a still greater variety. Other modes of arriving at the same aggregate +present themselves, not by the union of smaller, but by the +dismemberment of larger aggregates. Thus, <i>three pebbles</i> may be formed +by taking away one pebble from an aggregate of four; <i>two pebbles</i>, by +an equal division of a similar aggregate; and so on.</p> + +<p>Every arithmetical proposition; every statement of the result of an +arithmetical operation; is a statement of one of the modes of formation +of a given number. It affirms <span class="pagenum"><a name="Page_149" id="Page_149">[Pg 149]</a></span>that a certain aggregate might have been +formed by putting together certain other aggregates, or by withdrawing +certain portions of some aggregate; and that, by consequence, we might +reproduce those aggregates from it, by reversing the process.</p> + +<p>Thus, when we say that the cube of 12 is 1728, what we affirm is this: +that if, having a sufficient number of pebbles or of any other objects, +we put them together into the particular sort of parcels or aggregates +called twelves; and put together these twelves again into similar +collections; and, finally, make up twelve of these largest parcels; the +aggregate thus formed will be such a one as we call 1728; namely, that +which (to take the most familiar of its modes of formation) may be made +by joining the parcel called a thousand pebbles, the parcel called seven +hundred pebbles, the parcel called twenty pebbles, and the parcel called +eight pebbles.</p> + +<p>The converse proposition, that the cube root of 1728 is 12, asserts that +this large aggregate may again be decomposed into the twelve twelves of +twelves of pebbles which it consists of.</p> + +<p>The modes of formation of any number are innumerable; but when we know +one mode of formation of each, all the rest may be determined +deductively. If we know that <i>a</i> is formed from <i>b</i> and <i>c</i>, <i>b</i> from +<i>a</i> and <i>e</i>, <i>c</i> from <i>d</i> and <i>f</i>, and so forth, until we have included +all the numbers of any scale we choose to select, (taking care that for +each number the mode of formation be really a distinct one, not bringing +us round again to the former numbers, but introducing a new number,) we +have a set of propositions from which we may reason to all the other +modes of formation of those numbers from one another. Having established +a chain of inductive truths connecting together all the numbers of the +scale, we can ascertain the formation of any one of those numbers from +any other by merely travelling from one to the other along the chain. +Suppose that we know only the following modes of formation: 6 = 4 + 2, 4 += 7 - 3, 7 = 5 + 2, 5 = 9 - 4. We could determine how 6 may be formed +from 9. For 6 = 4 + 2 = 7 - 3 + 2 = 5 + 2 - 3 + 2 = 9 - 4 + 2 - 3 + 2. +It may therefore be formed by <span class="pagenum"><a name="Page_150" id="Page_150">[Pg 150]</a></span>taking away 4 and 3, and adding 2 and 2. +If we know besides that 2 + 2 = 4, we obtain 6 from 9 in a simpler mode, +by merely taking away 3.</p> + +<p>It is sufficient, therefore, to select one of the various modes of +formation of each number, as a means of ascertaining all the rest. And +since things which are uniform, and therefore simple, are most easily +received and retained by the understanding, there is an obvious +advantage in selecting a mode of formation which shall be alike for all; +in fixing the connotation of names of number on one uniform principle. +The mode in which our existing numerical nomenclature is contrived +possesses this advantage, with the additional one, that it happily +conveys to the mind two of the modes of formation of every number. Each +number is considered as formed by the addition of an unit to the number +next below it in magnitude, and this mode of formation is conveyed by +the place which it occupies in the series. And each is also considered +as formed by the addition of a number of units less than ten, and a +number of aggregates each equal to one of the successive powers of ten; +and this mode of its formation is expressed by its spoken name, and by +its numerical character.</p> + +<p>What renders arithmetic the type of a deductive science, is the +fortunate applicability to it of a law so comprehensive as "The sums of +equals are equals:" or (to express the same principle in less familiar +but more characteristic language), Whatever is made up of parts, is made +up of the parts of those parts. This truth, obvious to the senses in all +cases which can be fairly referred to their decision, and so general as +to be coextensive with nature itself, being true of all sorts of +phenomena, (for all admit of being numbered,) must be considered an +inductive truth, or law of nature, of the highest order. And every +arithmetical operation is an application of this law, or of other laws +capable of being deduced from it. This is our warrant for all +calculations. We believe that five and two are equal to seven, on the +evidence of this inductive law, combined with the definitions of those +numbers. We arrive at that conclusion (as all know who remember how they +first <span class="pagenum"><a name="Page_151" id="Page_151">[Pg 151]</a></span>learned it) by adding a single unit at a time: 5 + 1 = 6, +therefore 5 + 1 + 1 = 6 + 1 = 7: and again 2 = 1 + 1, therefore 5 + 2 = +5 + 1 + 1 = 7.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIV_6">§ 6.</a> Innumerable as are the true propositions which can be formed +concerning particular numbers, no adequate conception could be gained, +from these alone, of the extent of the truths composing the science of +number. Such propositions as we have spoken of are the least general of +all numerical truths. It is true that even these are coextensive with +all nature: the properties of the number four are true of all objects +that are divisible into four equal parts, and all objects are either +actually or ideally so divisible. But the propositions which compose the +science of algebra are true, not of a particular number, but of all +numbers; not of all things under the condition of being divided in a +particular way, but of all things under the condition of being divided +in any way—of being designated by a number at all.</p> + +<p>Since it is impossible for different numbers to have any of their modes +of formation completely in common, it is a kind of paradox to say, that +all propositions which can be made concerning numbers relate to their +modes of formation from other numbers, and yet that there are +propositions which are true of all numbers. But this very paradox leads +to the real principle of generalization concerning the properties of +numbers. Two different numbers cannot be formed in the same manner from +the same numbers; but they may be formed in the same manner from +different numbers; as nine is formed from three by multiplying it into +itself, and sixteen is formed from four by the same process. Thus there +arises a classification of modes of formation, or in the language +commonly used by mathematicians, a classification of Functions. Any +number, considered as formed from any other number, is called a function +of it; and there are as many kinds of functions as there are modes of +formation. The simple functions are by no means numerous, most functions +being formed by the combination of several of the operations which form +simple functions, or by successive repetitions of some one of those +<span class="pagenum"><a name="Page_152" id="Page_152">[Pg 152]</a></span>operations. The simple functions of any number <i>x</i> are all reducible to +the following forms: <i>x + a</i>, <i>x - a</i>, <i>a x</i>, <i>x/a</i>, <i>x<sup>a</sup></i>, +<i><sup>a</sup>√<span style="border-top:1px black solid;">x</span></i>, log. <i>x</i> (to the base <i>a</i>), and the same expressions varied by +putting <i>x</i> for <i>a</i> and <i>a</i> for <i>x</i>, wherever that substitution would +alter the value: to which perhaps ought to be added sin <i>x</i>, and arc +(sin = <i>x</i>). All other functions of <i>x</i> are formed by putting some one +or more of the simple functions in the place of <i>x</i> or <i>a</i>, and +subjecting them to the same elementary operations.</p> + +<p>In order to carry on general reasonings on the subject of Functions, we +require a nomenclature enabling us to express any two numbers by names +which, without specifying what particular numbers they are, shall show +what function each is of the other; or, in other words, shall put in +evidence their mode of formation from one another. The system of general +language called algebraical notation does this. The expressions <i>a</i> and +<i>a</i><sup>2</sup> + 3<i>a</i> denote, the one any number, the other the number formed +from it in a particular manner. The expressions <i>a</i>, <i>b</i>, <i>n</i>, and (<i>a</i> + +<i>b</i>)<sup><i>n</i></sup>, denote any three numbers, and a fourth which is formed from +them in a certain mode.</p> + +<p>The following may be stated as the general problem of the algebraical +calculus: F being a certain function of a given number, to find what +function F will be of any function of that number. For example, a +binomial <i>a</i> + <i>b</i> is a function of its two parts <i>a</i> and <i>b</i>, and the +parts are, in their turn, functions of <i>a + b</i>: now (<i>a</i> + <i>b</i>)<sup><i>n</i></sup> is a +certain function of the binomial; what function will this be of <i>a</i> and +<i>b</i>, the two parts? The answer to this question is the binomial theorem. +The formula (<i>a</i> + <i>b</i>)<sup><i>n</i></sup> = <i>a</i><sup><i>n</i></sup> + (<i>n</i> / 1) <i>a</i><sup><i>n</i> - 1</sup> <i>b</i> + ((<i>n</i>·(<i>n</i> - 1)) / +(1·2)) <i>a</i><sup><i>n</i> - 2</sup> <i>b</i><sup>2</sup> + &c., shows in what manner the number which is +formed by multiplying <i>a</i> + <i>b</i> into itself <i>n</i> times, might be formed +without that process, directly from <i>a</i>, <i>b</i>, and <i>n</i>. And of this +nature are all the theorems of the science of number. They assert the +identity of the result of different modes of formation. They affirm that +some mode of formation from <i>x</i>, and some mode of <span class="pagenum"><a name="Page_153" id="Page_153">[Pg 153]</a></span>formation from a +certain function of <i>x</i>, produce the same number.</p> + +<p>Besides these general theorems of formulæ, what remains in the +algebraical calculus is the resolution of equations. But the resolution +of an equation is also a theorem. If the equation be <i>x</i><sup>2</sup> + <i>ax</i> = <i>b</i>, +the resolution of this equation, viz. <i>x</i> = -(1/2) <i>a</i> ± √<span style="border-top:1px black solid;">(1/4)<i>a</i><sup>2</sup> + <i>b</i></span>, is a general proposition, which may be regarded as an +answer to the question, If <i>b</i> is a certain function of <i>x</i> and <i>a</i> +(namely <i>x</i><sup>2</sup> + <i>ax</i>), what function is <i>x</i> of <i>b</i> and <i>a</i>? The +resolution of equations is, therefore, a mere variety of the general +problem as above stated. The problem is—Given a function, what function +is it of some other function? And in the resolution of an equation, the +question is, to find what function of one of its own functions the +number itself is.</p> + +<p>Such as above described, is the aim and end of the calculus. As for its +processes, every one knows that they are simply deductive. In +demonstrating an algebraical theorem, or in resolving an equation, we +travel from the <i>datum</i> to the <i>quæsitum</i> by pure ratiocination; in +which the only premises introduced, besides the original hypotheses, are +the fundamental axioms already mentioned—that things equal to the same +thing are equal to one another, and that the sums of equal things are +equal. At each step in the demonstration or in the calculation, we apply +one or other of these truths, or truths deducible from them, as, that +the differences, products, &c., of equal numbers are equal.</p> + +<p>It would be inconsistent with the scale of this work, and not necessary +to its design, to carry the analysis of the truths and processes of +algebra any farther; which is also the less needful, as the task has +been, to a very great extent, performed by other writers. Peacock's +Algebra, and Dr. Whewell's <i>Doctrine of Limits</i>, are full of instruction +on the subject. The profound treatises of a truly philosophical +mathematician, Professor De Morgan, should be studied by every one who +desires to comprehend the evidence of mathematical truths, and the +meaning of the obscurer processes of the calculus; and the speculations +of M. Comte, in his <i>Cours de Philosophie <span class="pagenum"><a name="Page_154" id="Page_154">[Pg 154]</a></span>Positive</i>, on the philosophy +of the higher branches of mathematics, are among the many valuable gifts +for which philosophy is indebted to that eminent thinker.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIV_7">§ 7.</a> If the extreme generality, and remoteness not so much from sense as +from the visual and tactual imagination, of the laws of number, renders +it a somewhat difficult effort of abstraction to conceive those laws as +being in reality physical truths obtained by observation; the same +difficulty does not exist with regard to the laws of extension. The +facts of which those laws are expressions, are of a kind peculiarly +accessible to the senses, and suggesting eminently distinct images to +the fancy. That geometry is a strictly physical science would doubtless +have been recognised in all ages, had it not been for the illusions +produced by two circumstances. One of these is the characteristic +property, already noticed, of the facts of geometry, that they may be +collected from our ideas or mental pictures of objects as effectually as +from the objects themselves. The other is, the demonstrative character +of geometrical truths; which was at one time supposed to constitute a +radical distinction between them and physical truths, the latter, as +resting on merely probable evidence, being deemed essentially uncertain +and unprecise. The advance of knowledge has, however, made it manifest +that physical science, in its better understood branches, is quite as +demonstrative as geometry. The task of deducing its details from a few +comparatively simple principles is found to be anything but the +impossibility it was once supposed to be; and the notion of the superior +certainty of geometry is an illusion, arising from the ancient prejudice +which, in that science, mistakes the ideal data from which we reason, +for a peculiar class of realities, while the corresponding ideal data of +any deductive physical science are recognised as what they really are, +mere hypotheses.</p> + +<p>Every theorem in geometry is a law of external nature, and might have +been ascertained by generalizing from observation and experiment, which +in this case resolve themselves into comparison and measurement. But it +was found practicable, <span class="pagenum"><a name="Page_155" id="Page_155">[Pg 155]</a></span>and being practicable, was desirable, to deduce +these truths by ratiocination from a small number of general laws of +nature, the certainty and universality of which are obvious to the most +careless observer, and which compose the first principles and ultimate +premises of the science. Among these general laws must be included the +same two which we have noticed as ultimate principles of the Science of +Number also, and which are applicable to every description of quantity; +viz. The sums of equals are equal, and Things which are equal to the +same thing are equal to one another; the latter of which may be +expressed in a manner more suggestive of the inexhaustible multitude of +its consequences, by the following terms: Whatever is equal to any one +of a number of equal magnitudes, is equal to any other of them. To these +two must be added, in geometry, a third law of equality, namely, that +lines, surfaces, or solid spaces, which can be so applied to one another +as to coincide, are equal. Some writers have asserted that this law of +nature is a mere verbal definition; that the expression "equal +magnitudes" <i>means</i> nothing but magnitudes which can be so applied to +one another as to coincide. But in this opinion I cannot agree. The +equality of two geometrical magnitudes cannot differ fundamentally in +its nature from the equality of two weights, two degrees of heat, or two +portions of duration, to none of which would this pretended definition +of equality be suitable. None of these things can be so applied to one +another as to coincide, yet we perfectly understand what we mean when we +call them equal. Things are equal in magnitude, as things are equal in +weight, when they are felt to be exactly similar in respect of the +attribute in which we compare them: and the application of the objects +to each other in the one case, like the balancing them with a pair of +scales in the other, is but a mode of bringing them into a position in +which our senses can recognise deficiencies of exact resemblance that +would otherwise escape our notice.</p> + +<p>Along with these three general principles or axioms, the remainder of +the premises of geometry consists of the so-called definitions, that is +to say, propositions asserting the real <span class="pagenum"><a name="Page_156" id="Page_156">[Pg 156]</a></span>existence of the various +objects therein designated, together with some one property of each. In +some cases more than one property is commonly assumed, but in no case is +more than one necessary. It is assumed that there are such things in +nature as straight lines, and that any two of them setting out from the +same point, diverge more and more without limit. This assumption, (which +includes and goes beyond Euclid's axiom that two straight lines cannot +inclose a space,) is as indispensable in geometry, and as evident, +resting on as simple, familiar, and universal observation, as any of the +other axioms. It is also assumed that straight lines diverge from one +another in different degrees; in other words, that there are such things +as angles, and that they are capable of being equal or unequal. It is +assumed that there is such a thing as a circle, and that all its radii +are equal; such things as ellipses, and that the sums of the focal +distances are equal for every point in an ellipse; such things as +parallel lines, and that those lines are everywhere equally distant.<a name="FNanchor_39_39" id="FNanchor_39_39"></a><a href="#Footnote_39_39" class="fnanchor">[39]</a></p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIV_8">§ 8.</a> It is a matter of more than curiosity to consider, to what +peculiarity of the physical truths which are the subject of geometry, it +is owing that they can all be deduced from so <span class="pagenum"><a name="Page_157" id="Page_157">[Pg 157]</a></span>small a number of +original premises: why it is that we can set out from only one +characteristic property of each kind of phenomenon, and with that and +two or three general truths relating to equality, can travel from mark +to mark until we obtain a vast body of derivative truths, to all +appearance extremely unlike those elementary ones.</p> + +<p>The explanation of this remarkable fact seems to lie in the following +circumstances. In the first place, all questions of position and figure +may be resolved into questions of magnitude. The position and figure of +any object are determined, by determining the position of a sufficient +number of points in it; and the position of any point may be determined +by the magnitude of three rectangular co-ordinates, that is, of the +perpendiculars drawn from the point to three planes at right angles to +one another, arbitrarily selected. By this transformation of all +questions of quality into questions only of quantity, geometry is +reduced to the single problem of the measurement of magnitudes, that is, +the ascertainment of the equalities which exist between them. Now when +we consider that by one of the general axioms, any equality, when +ascertained, is proof of as many other equalities as there are other +things equal to either of the two equals; and that by another of those +axioms, any ascertained equality is proof of the equality of as many +pairs of magnitudes as can be formed by the numerous operations which +resolve themselves into the addition of the equals to themselves or to +other equals; we cease to wonder that in proportion as a science is +conversant about equality, it should afford a more copious supply of +marks of marks; and that the sciences of number and extension, which are +conversant with little else than equality, should be the most deductive +of all the sciences.</p> + +<p>There are also two or three of the principal laws of space or extension +which are unusually fitted for rendering one position or magnitude a +mark of another, and thereby contributing to render the science largely +deductive. First; the magnitudes of inclosed spaces, whether superficial +or solid, are completely determined by the magnitudes of the lines <span class="pagenum"><a name="Page_158" id="Page_158">[Pg 158]</a></span>and +angles which bound them. Secondly, the length of any line, whether +straight or curve, is measured (certain other things being given) by the +angle which it subtends, and <i>vice versâ</i>. Lastly, the angle which any +two straight lines make with each other at an inaccessible point, is +measured by the angles they severally make with any third line we choose +to select. By means of these general laws, the measurement of all lines, +angles, and spaces whatsoever might be accomplished by measuring a +single straight line and a sufficient number of angles; which is the +plan actually pursued in the trigonometrical survey of a country; and +fortunate it is that this is practicable, the exact measurement of long +straight lines being always difficult, and often impossible, but that of +angles very easy. Three such generalizations as the foregoing afford +such facilities for the indirect measurement of magnitudes, (by +supplying us with known lines or angles which are marks of the magnitude +of unknown ones, and thereby of the spaces which they inclose,) that it +is easily intelligible how from a few data we can go on to ascertain the +magnitude of an indefinite multitude of lines, angles, and spaces, which +we could not easily, or could not at all, measure by any more direct +process.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXIV_9">§ 9.</a> Such are the few remarks which it seemed necessary to make in this +place, respecting the laws of nature which are the peculiar subject of +the sciences of number and extension. The immense part which those laws +take in giving a deductive character to the other departments of +physical science, is well known; and is not surprising, when we consider +that all causes operate according to mathematical laws. The effect is +always dependent on, or is a function of, the quantity of the agent; and +generally of its position also. We cannot, therefore, reason respecting +causation, without introducing considerations of quantity and extension +at every step; and if the nature of the phenomena admits of our +obtaining numerical data of sufficient accuracy, the laws of quantity +become the grand instrument for calculating forward to an effect, or +backward to a cause. That in all other sciences, as well as in +<span class="pagenum"><a name="Page_159" id="Page_159">[Pg 159]</a></span>geometry, questions of quality are scarcely ever independent of +questions of quantity, may be seen from the most familiar phenomena. +Even when several colours are mixed on a painter's palette, the +comparative quantity of each entirely determines the colour of the +mixture.</p> + +<p>With this mere suggestion of the general causes which render +mathematical principles and processes so predominant in those deductive +sciences which afford precise numerical data, I must, on the present +occasion, content myself: referring the reader who desires a more +thorough acquaintance with the subject, to the first two volumes of M. +Comte's systematic work.</p> + +<p>In the same work, and more particularly in the third volume, are also +fully discussed the limits of the applicability of mathematical +principles to the improvement of other sciences. Such principles are +manifestly inapplicable, where the causes on which any class of +phenomena depend are so imperfectly accessible to our observation, that +we cannot ascertain, by a proper induction, their numerical laws; or +where the causes are so numerous, and intermixed in so complex a manner +with one another, that even supposing their laws known, the computation +of the aggregate effect transcends the powers of the calculus as it is, +or is likely to be; or lastly, where the causes themselves are in a +state of perpetual fluctuation; as in physiology, and still more, if +possible, in the social science. The mathematical solutions of physical +questions become progressively more difficult and imperfect, in +proportion as the questions divest themselves of their abstract and +hypothetical character, and approach nearer to the degree of +complication actually existing in nature; insomuch that beyond the +limits of astronomical phenomena, and of those most nearly analogous to +them, mathematical accuracy is generally obtained "at the expense of the +reality of the inquiry:" while even in astronomical questions, +"notwithstanding the admirable simplicity of their mathematical +elements, our feeble intelligence becomes incapable of following out +effectually the logical combinations of the laws on which the phenomena +are dependent, as soon as we attempt to take into simultaneous +<span class="pagenum"><a name="Page_160" id="Page_160">[Pg 160]</a></span>consideration more than two or three essential influences."<a name="FNanchor_40_40" id="FNanchor_40_40"></a><a href="#Footnote_40_40" class="fnanchor">[40]</a> Of +this, the problem of the Three Bodies has already been cited, more than +once, as a remarkable instance; the complete solution of so +comparatively simple a question having vainly tried the skill of the +most profound mathematicians. We may conceive, then, how chimerical +would be the hope that mathematical principles could be advantageously +applied to phenomena dependent on the mutual action of the innumerable +minute particles of bodies, as those of chemistry, and still more, of +physiology; and for similar reasons those principles remain inapplicable +to the still more complex inquiries, the subjects of which are phenomena +of society and government.</p> + +<p>The value of mathematical instruction as a preparation for those more +difficult investigations, consists in the applicability not of its +doctrines, but of its method. Mathematics will ever remain the most +perfect type of the Deductive Method in general; and the applications of +mathematics to the deductive branches of physics, furnish the only +school in which philosophers can effectually learn the most difficult +and important portion of their art, the employment of the laws of +simpler phenomena for explaining and predicting those of the more +complex. These grounds are quite sufficient for deeming mathematical +training an indispensable basis of real scientific education, and +regarding (according to the <i>dictum</i> which an old but unauthentic +tradition ascribes to Plato) one who is <i>ἀγεωμέτρητος</i>, as +wanting in one of the most essential qualifications for the successful +cultivation of the higher branches of philosophy.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_161" id="Page_161">[Pg 161]</a></span></p> +<h3><a name="BOOK_III_CHAPTER_XXV" id="BOOK_III_CHAPTER_XXV"></a>CHAPTER XXV.<br /> +OF THE GROUNDS OF DISBELIEF.</h3> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXV_1">§ 1.</a> The method of arriving at general truths, or general propositions +fit to be believed, and the nature of the evidence on which they are +grounded, have been discussed, as far as space and the writer's +faculties permitted, in the twenty-four preceding chapters. But the +result of the examination of evidence is not always belief, nor even +suspension of judgment; it is sometimes disbelief. The philosophy, +therefore, of induction and experimental inquiry is incomplete, unless +the grounds not only of belief, but of disbelief, are treated of; and to +this topic we shall devote one, and the final, chapter.</p> + +<p>By disbelief is not here to be understood the mere absence of belief. +The ground for abstaining from belief is simply the absence or +insufficiency of proof; and in considering what is sufficient evidence +to support any given conclusion, we have already, by implication, +considered what evidence is not sufficient for the same purpose. By +disbelief is here meant, not the state of mind in which we form no +opinion concerning a subject, but that in which we are fully persuaded +that some opinion is not true; insomuch that if evidence, even of great +apparent strength, (whether grounded on the testimony of others or on +our own supposed perceptions,) were produced in favour of the opinion, +we should believe that the witnesses spoke falsely, or that they, or we +ourselves if we were the direct percipients, were mistaken.</p> + +<p>That there are such cases, no one is likely to dispute. Assertions for +which there is abundant positive evidence are often disbelieved, on +account of what is called their improbability, or impossibility. And the +question for consideration is <span class="pagenum"><a name="Page_162" id="Page_162">[Pg 162]</a></span>what, in the present case, these words +mean, and how far and in what circumstances the properties which they +express are sufficient grounds for disbelief.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXV_2">§ 2.</a> It is to be remarked in the first place, that the positive evidence +produced in support of an assertion which is nevertheless rejected on +the score of impossibility or improbability, is never such as amounts to +full proof. It is always grounded on some approximate generalization. +The fact may have been asserted by a hundred witnesses; but there are +many exceptions to the universality of the generalization that what a +hundred witnesses affirm is true. We may seem to ourselves to have +actually seen the fact: but, that we really see what we think we see, is +by no means an universal truth; our organs may have been in a morbid +state; or we may have inferred something, and imagined that we perceived +it. The evidence, then, in the affirmative being never more than an +approximate generalization, all will depend on what the evidence in the +negative is. If that also rests on an approximate generalization, it is +a case for comparison of probabilities. If the approximate +generalizations leading to the affirmative are, when added together, +less strong, or in other words, farther from being universal, than the +approximate generalizations which support the negative side of the +question, the proposition is said to be improbable, and is to be +disbelieved provisionally. If however an alleged fact be in +contradiction, not to any number of approximate generalizations, but to +a completed generalization grounded on a rigorous induction, it is said +to be impossible, and is to be disbelieved totally.</p> + +<p>This last principle, simple and evident as it appears, is the doctrine +which, on the occasion of an attempt to apply it to the question of the +credibility of miracles, excited so violent a controversy. Hume's +celebrated doctrine, that nothing is credible which is contradictory to +experience, or at variance with laws of nature, is merely this very +plain and harmless proposition, that whatever is contradictory to a +complete induction is incredible. That such a maxim as this should +either be accounted a dangerous heresy, or mistaken for a great and +<span class="pagenum"><a name="Page_163" id="Page_163">[Pg 163]</a></span>recondite truth, speaks ill for the state of philosophical speculation +on such subjects.</p> + +<p>But does not (it may be asked) the very statement of the proposition +imply a contradiction? An alleged fact, according to this theory, is not +to be believed if it contradict a complete induction. But it is +essential to the completeness of an induction that it shall not +contradict any known fact. Is it not then a <i>petitio principii</i> to say, +that the fact ought to be disbelieved because the induction opposed to +it is complete? How can we have a right to declare the induction +complete, while facts, supported by credible evidence, present +themselves in opposition to it?</p> + +<p>I answer, we have that right whenever the scientific canons of induction +give it to us; that is, whenever the induction <i>can</i> be complete. We +have it, for example, in a case of causation in which there has been an +<i>experimentum crucis</i>. If an antecedent A, superadded to a set of +antecedents in all other respects unaltered, is followed by an effect B +which did not exist before, A is, in that instance at least, the cause +of B, or an indispensable part of its cause; and if A be tried again +with many totally different sets of antecedents and B still follows, +then it is the whole cause. If these observations or experiments have +been repeated so often, and by so many persons, as to exclude all +supposition of error in the observer, a law of nature is established; +and so long as this law is received as such, the assertion that on any +particular occasion A took place, and yet B did not follow, <i>without any +counteracting cause</i>, must be disbelieved. Such an assertion is not to +be credited on any less evidence than what would suffice to overturn the +law. The general truths, that whatever has a beginning has a cause, and +that when none but the same causes exist, the same effects follow, rest +on the strongest inductive evidence possible; the proposition that +things affirmed by even a crowd of respectable witnesses are true, is +but an approximate generalization; and—even if we fancy we actually saw +or felt the fact which is in contradiction to the law—what a human +being can see is no more than a set of appearances; from which the real +nature of the phenomenon is merely an inference, and in this inference +<span class="pagenum"><a name="Page_164" id="Page_164">[Pg 164]</a></span>approximate generalizations usually have a large share. If, therefore, +we make our election to hold by the law, no quantity of evidence +whatever ought to persuade us that there has occurred anything in +contradiction to it. If, indeed, the evidence produced is such that it +is more likely that the set of observations and experiments on which the +law rests should have been inaccurately performed or incorrectly +interpreted, than that the evidence in question should be false, we may +believe the evidence; but then we must abandon the law. And since the +law was received on what seemed a complete induction, it can only be +rejected on evidence equivalent; namely, as being inconsistent not with +any number of approximate generalizations, but with some other and +better established law of nature. This extreme case, of a conflict +between two supposed laws of nature, has probably never actually +occurred where, in the process of investigating both the laws, the true +canons of scientific induction had been kept in view; but if it did +occur, it must terminate in the total rejection of one of the supposed +laws. It would prove that there must be a flaw in the logical process by +which either one or the other was established: and if there be so, that +supposed general truth is no truth at all. We cannot admit a proposition +as a law of nature, and yet believe a fact in real contradiction to it. +We must disbelieve the alleged fact, or believe that we were mistaken in +admitting the supposed law.</p> + +<p>But in order that any alleged fact should be contradictory to a law of +causation, the allegation must be, not simply that the cause existed +without being followed by the effect, for that would be no uncommon +occurrence; but that this happened in the absence of any adequate +counteracting cause. Now in the case of an alleged miracle, the +assertion is the exact opposite of this. It is, that the effect was +defeated, not in the absence, but in consequence of a counteracting +cause, namely, a direct interposition of an act of the will of some +being who has power over nature; and in particular of a Being, whose +will being assumed to have endowed all the causes with the powers by +which they produce their effects, may well be supposed able to +counteract them. A miracle (as was justly <span class="pagenum"><a name="Page_165" id="Page_165">[Pg 165]</a></span>remarked by Brown<a name="FNanchor_41_41" id="FNanchor_41_41"></a><a href="#Footnote_41_41" class="fnanchor">[41]</a>) is no +contradiction to the law of cause and effect; it is a new effect, +supposed to be produced by the introduction of a new cause. Of the +adequacy of that cause, if present, there can be no doubt; and the only +antecedent improbability which can be ascribed to the miracle, is the +improbability that any such cause existed.</p> + +<p>All, therefore, which Hume has made out, and this he must be considered +to have made out, is, that (at least in the imperfect state of our +knowledge of natural agencies, which leaves it always possible that some +of the physical antecedents may have been hidden from us,) no evidence +can prove a miracle to any one who did not previously believe the +existence of a being or beings with supernatural power; or who believes +himself to have full proof that the character of the Being whom he +recognises, is inconsistent with his having seen fit to interfere on the +occasion in question.</p> + +<p>If we do not already believe in supernatural agencies, no miracle can +prove to us their existence. The miracle itself, considered merely as an +extraordinary fact, may be satisfactorily certified by our senses or by +testimony; but nothing can ever prove that it is a miracle: there is +still another possible hypothesis, that of its being the result of some +unknown natural cause: and this possibility cannot be so completely shut +out, as to leave no alternative but that of admitting the existence and +intervention of a being superior to nature. Those, however, who already +believe in such a being, have two hypotheses to choose from, a +supernatural and an unknown natural agency; and they have to judge which +of the two is the most probable in the particular case. In forming this +judgment, an important element of the question will be the conformity of +the result to the laws of the supposed agent, that is, to the character +of the Deity as they conceive it. But, with the knowledge which we now +possess of the general uniformity of the course of nature, religion, +following in the wake of science, has been compelled to acknowledge the +government of the <span class="pagenum"><a name="Page_166" id="Page_166">[Pg 166]</a></span>universe as being on the whole carried on by general +laws, and not by special interpositions. To whoever holds this belief, +there is a general presumption against any supposition of divine agency +not operating through general laws, or in other words, there is an +antecedent improbability in every miracle, which, in order to outweigh +it, requires an extraordinary strength of antecedent probability derived +from the special circumstances of the case.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXV_3">§ 3.</a> It appears from what has been said, that the assertion that a cause +has been defeated of an effect which is connected with it by a +completely ascertained law of causation, is to be disbelieved or not, +according to the probability or improbability that there existed in the +particular instance an adequate counteracting cause. To form an estimate +of this, is not more difficult than of other probabilities. With regard +to all <i>known</i> causes capable of counteracting the given causes, we have +generally some previous knowledge of the frequency or rarity of their +occurrence, from which we may draw an inference as to the antecedent +improbability of their having been present in any particular case. And +neither in respect to known or unknown causes are we required to +pronounce on the probability of their existing in nature, but only of +their having existed at the time and place at which the transaction is +alleged to have happened. We are seldom, therefore, without the means +(when the circumstances of the case are at all known to us) of judging +how far it is likely that such a cause should have existed at that time +and place without manifesting its presence by some other marks, and (in +the case of an unknown cause) without having hitherto manifested its +existence in any other instance. According as this circumstance, or the +falsity of the testimony, appears more improbable, that is, conflicts +with an approximate generalization of a higher order, we believe the +testimony, or disbelieve it; with a stronger or a weaker degree of +conviction, according to the preponderance: at least until we have +sifted the matter further.</p> + +<p>So much, then, for the case in which the alleged fact conflicts, <span class="pagenum"><a name="Page_167" id="Page_167">[Pg 167]</a></span>or +appears to conflict, with a real law of causation. But a more common +case, perhaps, is that of its conflicting with uniformities of mere +coexistence, not proved to be dependent on causation: in other words, +with the properties of Kinds. It is with these uniformities principally, +that the marvellous stories related by travellers are apt to be at +variance: as of men with tails, or with wings, and (until confirmed by +experience) of flying fish; or of ice, in the celebrated anecdote of the +Dutch travellers and the King of Siam. Facts of this description, facts +previously unheard of but which could not from any known law of +causation be pronounced impossible, are what Hume characterizes as not +contrary to experience, but merely unconformable to it; and Bentham, in +his treatise on Evidence, denominates them facts disconformable <i>in +specie</i>, as distinguished from such as are disconformable <i>in toto</i> or +in <i>degree</i>.</p> + +<p>In a case of this description, the fact asserted is the existence of a +new Kind; which in itself is not in the slightest degree incredible, and +only to be rejected if the improbability that any variety of object +existing at the particular place and time should not have been +discovered sooner, be greater than that of error or mendacity in the +witnesses. Accordingly, such assertions, when made by credible persons, +and of unexplored places, are not disbelieved, but at most regarded as +requiring confirmation from subsequent observers; unless the alleged +properties of the supposed new Kind are at variance with known +properties of some larger kind which includes it; or in other words, +unless, in the new Kind which is asserted to exist, some properties are +said to have been found disjoined from others which have always been +known to accompany them; as in the case of Pliny's men, or any other +kind of animal of a structure different from that which has always been +found to coexist with animal life. On the mode of dealing with any such +case, little needs be added to what has been said on the same topic in +the twenty-second chapter.<a name="FNanchor_42_42" id="FNanchor_42_42"></a><a href="#Footnote_42_42" class="fnanchor">[42]</a> When the uniformities of coexistence +which the alleged fact <span class="pagenum"><a name="Page_168" id="Page_168">[Pg 168]</a></span>would violate, are such as to raise a strong +presumption of their being the result of causation, the fact which +conflicts with them is to be disbelieved; at least provisionally, and +subject to further investigation. When the presumption amounts to a +virtual certainty, as in the case of the general structure of organized +beings, the only question requiring consideration is whether, in +phenomena so little understood, there may not be liabilities to +counteraction from causes hitherto unknown; or whether the phenomena may +not be capable of originating in some other way, which would produce a +different set of derivative uniformities. Where (as in the case of the +flying fish, or the ornithorhynchus) the generalization to which the +alleged fact would be an exception is very special and of limited range, +neither of the above suppositions can be deemed very improbable; and it +is generally, in the case of such alleged anomalies, wise to suspend our +judgment, pending the subsequent inquiries which will not fail to +confirm the assertion if it be true. But when the generalization is very +comprehensive, embracing a vast number and variety of observations, and +covering a considerable province of the domain of nature; then, for +reasons which have been fully explained, such an empirical law comes +near to the certainty of an ascertained law of causation: and any +alleged exception to it cannot be admitted, unless on the evidence of +some law of causation proved by a still more complete induction.</p> + +<p>Such uniformities in the course of nature as do not bear marks of being +the results of causation, are, as we have already seen, admissible as +universal truths with a degree of credence proportioned to their +generality. Those which are true of all things whatever, or at least +which are totally independent of the varieties of Kinds, namely, the +laws of number and extension, to which we may add the law of causation +itself, are probably the only ones, an exception to which is absolutely +and permanently incredible. Accordingly, it is to assertions supposed to +be contradictory to these laws, or to some others coming near to them in +generality, that the word impossibility (at least <i>total</i> impossibility) +seems to be generally confined. Violations of other laws, of special +laws of causation <span class="pagenum"><a name="Page_169" id="Page_169">[Pg 169]</a></span>for instance, are said, by persons studious of +accuracy in expression, to be impossible <i>in the circumstances of the +case</i>; or impossible unless some cause had existed which did not exist +in the particular case.<a name="FNanchor_43_43" id="FNanchor_43_43"></a><a href="#Footnote_43_43" class="fnanchor">[43]</a> Of no assertion, not in contradiction to +some of these very general laws, will more than improbability be +asserted by any cautious person; and improbability not of the highest +degree, unless the time and place in which the fact is said to have +occurred, render it almost certain that the anomaly, if real, could not +have been overlooked by other observers. Suspension of judgment is in +all other cases the resource of the judicious inquirer; provided the +testimony in favour of the anomaly presents, when well sifted, no +suspicious circumstances.</p> + +<p>But the testimony is scarcely ever found to stand that test, in cases in +which the anomaly is not real. In the instances on record in which a +great number of witnesses, of good reputation and scientific +acquirements, have testified to the truth of something which has turned +out untrue, there have almost always been circumstances which, to a keen +observer who had taken due pains to sift the matter, would have rendered +the testimony untrustworthy. There have generally been means of +accounting for the impression on the senses or minds of the alleged +percipients, by fallacious appearances; or some epidemic delusion, +propagated by the contagious influence of popular feeling, has been +concerned in the case; or some strong <span class="pagenum"><a name="Page_170" id="Page_170">[Pg 170]</a></span>interest has been +implicated—religious zeal, party feeling, vanity, or at least the +passion for the marvellous, in persons strongly susceptible of it. When +none of these or similar circumstances exist to account for the apparent +strength of the testimony; and where the assertion is not in +contradiction either to those universal laws which know no counteraction +or anomaly, or to the generalizations next in comprehensiveness to them, +but would only amount, if admitted, to the existence of an unknown cause +or an anomalous Kind, in circumstances not so thoroughly explored but +that it is credible that things hitherto unknown may still come to +light; a cautious person will neither admit nor reject the testimony, +but will wait for confirmation at other times and from other unconnected +sources. Such ought to have been the conduct of the King of Siam when +the Dutch travellers affirmed to him the existence of ice. But an +ignorant person is as obstinate in his contemptuous incredulity as he is +unreasonably credulous. Anything unlike his own narrow experience he +disbelieves, if it flatters no propensity; any nursery tale is swallowed +implicitly by him if it does.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXV_4">§ 4.</a> I shall now advert to a very serious misapprehension of the +principles of the subject, which has been committed by some of the +writers against Hume's Essay on Miracles, and by Bishop Butler before +them, in their anxiety to destroy what appeared to them a formidable +weapon of assault against the Christian religion; and the effect of +which is entirely to confound the doctrine of the Grounds of Disbelief. +The mistake consists in overlooking the distinction between (what may be +called) improbability before the fact, and improbability after it; or +(since, as Mr. Venn remarks, the distinction of past and future is not +the material circumstance) between the improbability of a mere guess +being right, and the improbability of an alleged fact being true.</p> + +<p>Many events are altogether improbable to us, before they have happened, +or before we are informed of their happening, which are not in the least +incredible when we are informed of them, because not contrary to any, +even approximate, induction. <span class="pagenum"><a name="Page_171" id="Page_171">[Pg 171]</a></span>In the cast of a perfectly fair die, the +chances are five to one against throwing ace, that is, ace will be +thrown on an average only once in six throws. But this is no reason +against believing that ace was thrown on a given occasion, if any +credible witness asserts it; since though ace is only thrown once in six +times, <i>some</i> number which is only thrown once in six times must have +been thrown if the die was thrown at all. The improbability, then, or in +other words, the unusualness, of any fact, is no reason for disbelieving +it, if the nature of the case renders it certain that either that or +something equally improbable, that is, equally unusual, did happen. Nor +is this all: for even if the other five sides of the die were all twos, +or all threes, yet as ace would still on the average come up once in +every six throws, its coming up in a given throw would be not in any way +contradictory to experience. If we disbelieved all facts which had the +chances against them beforehand, we should believe hardly anything. We +are told that A. B. died yesterday: the moment before we were so told, +the chances against his having died on that day may have been ten +thousand to one; but since he was certain to die at some time or other, +and when he died must necessarily die on some particular day, while the +preponderance of chances is very great against every day in particular, +experience affords no ground for discrediting any testimony which may be +produced to the event's having taken place on a given day.</p> + +<p>Yet it has been considered, by Dr. Campbell and others, as a complete +answer to Hume's doctrine (that things are incredible which are +<i>contrary</i> to the uniform course of experience), that we do not +disbelieve, merely because the chances were against them, things in +strict <i>conformity</i> to the uniform course of experience; that we do not +disbelieve an alleged fact merely because the combination of causes on +which it depends occurs only once in a certain number of times. It is +evident that whatever is shown by observation, or can be proved from +laws of nature, to occur in a certain proportion (however small) of the +whole number of possible cases, is not contrary to experience; though we +are right in disbelieving it, if some other supposition respecting the +matter in question involves on the <span class="pagenum"><a name="Page_172" id="Page_172">[Pg 172]</a></span>whole a less departure from the +ordinary course of events. Yet, on such grounds as this have able +writers been led to the extraordinary conclusion, that nothing supported +by credible testimony ought ever to be disbelieved.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXV_5">§ 5.</a> We have considered two species of events, commonly said to be +improbable; one kind which are in no way extraordinary, but which, +having an immense preponderance of chances against them, are improbable +until they are affirmed, but no longer; another kind which, being +contrary to some recognised law of nature, are incredible on any amount +of testimony except such as would be sufficient to shake our belief in +the law itself. But between these two classes of events, there is an +intermediate class, consisting of what are commonly termed Coincidences: +in other words, those combinations of chances which present some +peculiar and unexpected regularity, assimilating them, in so far, to the +results of law. As if, for example, in a lottery of a thousand tickets, +the numbers should be drawn in the exact order of what are called the +natural numbers, 1, 2, 3, &c. We have still to consider the principles +of evidence applicable to this case: whether there is any difference +between coincidences and ordinary events, in the amount of testimony or +other evidence necessary to render them credible.</p> + +<p>It is certain, that on every rational principle of expectation, a +combination of this peculiar sort may be expected quite as often as any +other given series of a thousand numbers; that with perfectly fair dice, +sixes will be thrown twice, thrice, or any number of times in +succession, quite as often in a thousand or a million throws, as any +other succession of numbers fixed upon beforehand; and that no judicious +player would give greater odds against the one series than against the +other. Notwithstanding this, there is a general disposition to regard +the one as much more improbable than the other, and as requiring much +stronger evidence to make it credible. Such is the force of this +impression, that it has led some thinkers to the conclusion, that nature +has greater difficulty in producing regular combinations than irregular +ones; or in other <span class="pagenum"><a name="Page_173" id="Page_173">[Pg 173]</a></span>words, that there is some general tendency of things, +some law, which prevents regular combinations from occurring, or at +least from occurring so often as others. Among these thinkers may be +numbered D'Alembert; who, in an Essay on Probabilities to be found in +the fifth volume of his <i>Mélanges</i>, contends that regular combinations, +though equally probable according to the mathematical theory with any +others, are physically less probable. He appeals to common sense, or in +other words, to common impressions; saying, if dice thrown repeatedly in +our presence gave sixes every time, should we not, before the number of +throws had reached ten, (not to speak of thousands of millions,) be +ready to affirm, with the most positive conviction, that the dice were +false?</p> + +<p>The common and natural impression is in favour of D'Alembert: the +regular series would be thought much more unlikely than an irregular. +But this common impression is, I apprehend, merely grounded on the fact, +that scarcely anybody remembers to have ever seen one of these peculiar +coincidences: the reason of which is simply that no one's experience +extends to anything like the number of trials, within which that or any +other given combination of events can be expected to happen. The chance +of sixes on a single throw of two dice being 1/36, the chance of sixes +ten times in succession is 1 divided by the tenth power of 36; in other +words, such a concurrence is only likely to happen once in +3,656,158,440,062,976 trials, a number which no dice-player's experience +comes up to a millionth part of. But if, instead of sixes ten times, any +other given succession of ten throws had been fixed upon, it would have +been exactly as unlikely that in any individual's experience that +particular succession had ever occurred; although this does not <i>seem</i> +equally improbable, because no one could possibly have remembered +whether it had occurred or not, and because the comparison is tacitly +made, not between sixes ten times and any one particular series of +throws, but between all regular and all irregular successions taken +together.</p> + +<p>That (as D'Alembert says) if the succession of sixes was actually thrown +before our eyes, we should ascribe it not to <span class="pagenum"><a name="Page_174" id="Page_174">[Pg 174]</a></span>chance, but to unfairness +in the dice, is unquestionably true. But this arises from a totally +different principle. We should then be considering, not the probability +of the fact in itself, but the comparative probability with which, when +it is known to have happened, it may be referred to one or to another +cause. The regular series is not at all less likely than the irregular +one to be brought about by chance, but it is much more likely than the +irregular one to be produced by design; or by some general cause +operating through the structure of the dice. It is the nature of casual +combinations to produce a repetition of the same event, as often and no +oftener than any other series of events. But it is the nature of general +causes to reproduce, in the same circumstances, always the same event. +Common sense and science alike dictate that, all other things being the +same, we should rather attribute the effect to a cause which if real +would be very likely to produce it, than to a cause which would be very +unlikely to produce it. According to Laplace's sixth theorem, which we +demonstrated in a former chapter, the difference of probability arising +from the superior <i>efficacy</i> of the constant cause, unfairness in the +dice, would after a very few throws far outweigh any antecedent +probability which there could be against its existence.</p> + +<p>D'Alembert should have put the question in another manner. He should +have supposed that we had ourselves previously tried the dice, and knew +by ample experience that they were fair. Another person then tries them +in our absence, and assures us that he threw sixes ten times in +succession. Is the assertion credible or not? Here the effect to be +accounted for is not the occurrence itself, but the fact of the +witness's asserting it. This may arise either from its having really +happened, or from some other cause. What we have to estimate is the +comparative probability of these two suppositions.</p> + +<p>If the witness affirmed that he had thrown any other series of numbers, +supposing him to be a person of veracity, and tolerable accuracy, and to +profess that he took particular notice, we should believe him. But the +ten sixes are exactly <span class="pagenum"><a name="Page_175" id="Page_175">[Pg 175]</a></span>as likely to have been really thrown as the other +series. If, therefore, this assertion is less credible than the other, +the reason must be, not that it is less likely than the other to be made +truly, but that it is more likely than the other to be made falsely.</p> + +<p>One reason obviously presents itself why what is called a coincidence, +should be oftener asserted falsely than an ordinary combination. It +excites wonder. It gratifies the love of the marvellous. The motives, +therefore, to falsehood, one of the most frequent of which is the desire +to astonish, operate more strongly in favour of this kind of assertion +than of the other kind. Thus far there is evidently more reason for +discrediting an alleged coincidence, than a statement in itself not more +probable, but which if made would not be thought remarkable. There are +cases, however, in which the presumption on this ground would be the +other way. There are some witnesses who, the more extraordinary an +occurrence might appear, would be the more anxious to verify it by the +utmost carefulness of observation before they would venture to believe +it, and still more before they would assert it to others.</p> + + +<p class="newsection"><a name="BOOK_III_CHAPTER_XXV_6">§ 6.</a> Independently, however, of any peculiar chances of mendacity +arising from the nature of the assertion, Laplace contends, that merely +on the general ground of the fallibility of testimony, a coincidence is +not credible on the same amount of testimony on which we should be +warranted in believing an ordinary combination of events. In order to do +justice to his argument, it is necessary to illustrate it by the example +chosen by himself.</p> + +<p>If, says Laplace, there were one thousand tickets in a box, and one only +has been drawn out, then if an eye-witness affirms that the number drawn +was 79, this, though the chances were 999 in 1000 against it, is not on +that account the less credible; its credibility is equal to the +antecedent probability of the witness's veracity. But if there were in +the box 999 black balls and only one white, and the witness affirms that +the white ball was drawn, the case according to Laplace is very +<span class="pagenum"><a name="Page_176" id="Page_176">[Pg 176]</a></span>different: the credibility of his assertion is but a small fraction of +what it was in the former case; the reason of the difference being as +follows.</p> + +<p>The witnesses of whom we are speaking must, from the nature of the case, +be of a kind whose credibility falls materially short of certainty: let +us suppose, then, the credibility of the witness in the case in question +to be 9/10; that is, let us suppose that in every ten statements which +the witness makes, nine on an average are correct, and one incorrect. +Let us now suppose that there have taken place a sufficient number of +drawings to exhaust all the possible combinations, the witness deposing +in every one. In one case out of every ten in all these drawings he will +actually have made a false announcement. But in the case of the thousand +tickets these false announcements will have been distributed impartially +over all the numbers, and of the 999 cases in which No. 79 was not +drawn, there will have been only one case in which it was announced. On +the contrary, in the case of the thousand balls, (the announcement being +always either "black" or "white,") if white was not drawn, and there was +a false announcement, that false announcement <i>must</i> have been white; +and since by the supposition there was a false announcement once in +every ten times, white will have been announced falsely in one tenth +part of all the cases in which it was not drawn, that is, in one tenth +part of 999 cases out of every thousand. White, then, is drawn, on an +average, exactly as often as No. 79, but it is announced, without having +been really drawn, 999 times as often as No. 79; the announcement +therefore requires a much greater amount of testimony to render it +credible.<a name="FNanchor_44_44" id="FNanchor_44_44"></a><a href="#Footnote_44_44" class="fnanchor">[44]</a></p> + +<p><span class="pagenum"><a name="Page_177" id="Page_177">[Pg 177]</a></span></p><p>To make this argument valid it must of course be supposed, that the +announcements made by the witness are average specimens of his general +veracity and accuracy; or, at least, that they are neither more nor less +so in the case of the black and white balls, than in the case of the +thousand tickets. This assumption, however, is not warranted. A person +is far less likely to mistake, who has only one form of error to guard +against, than if he had 999 different errors to avoid. For instance, in +the example chosen, a messenger who might make a mistake once in ten +times in reporting the number drawn in a lottery, might not err once in +a thousand times if sent simply to observe whether a ball was black or +white. Laplace's argument therefore is faulty even as applied to his own +case. Still less can that case be received as completely representing +all cases of coincidence. Laplace has so contrived his example, that +though black answers to 999 distinct possibilities, and white only to +one, the witness has nevertheless no bias which can make him prefer +black to white. The witness did not know that there were 999 black balls +in the box and only one white; or if he did, Laplace has taken care to +make all the 999 cases so undistinguishably alike, that there is hardly +a possibility of any cause of falsehood or error operating in favour of +any of them, which would not operate in the same manner if there were +only one. Alter this supposition, and the whole argument falls to the +ground. Let the balls, for instance, be numbered, and let the white ball +be No. 79. Considered in respect of their colour, there are but two +things which the witness can be interested in asserting, or can have +dreamt or hallucinated, or has to choose from if he answers at random, +viz. black and white: but considered in respect of the numbers attached +to them, there are a thousand: and if his interest or error happens to +be connected with the numbers, though the only assertion he makes is +about the colour, the case becomes precisely assimilated to that of the +thousand tickets. Or instead of the balls suppose a lottery, with 1000 +tickets and but one prize, and that I hold No. 79, and being interested +only in that, ask the witness not what was the number drawn, but whether +it was 79 or some other. There are now only <span class="pagenum"><a name="Page_178" id="Page_178">[Pg 178]</a></span>two cases, as in Laplace's +example; yet he surely would not say that if the witness answered 79, +the assertion would be in an enormous proportion less credible, than if +he made the same answer to the same question asked in the other way. If, +for instance, (to put a case supposed by Laplace himself,) he has staked +a large sum on one of the chances, and thinks that by announcing its +occurrence he shall increase his credit; he is equally likely to have +betted on any one of the 999 numbers which are attached to black balls, +and so far as the chances of mendacity from this cause are concerned, +there will be 999 times as many chances of his announcing black falsely, +as white.</p> + +<p>Or suppose a regiment of 1000 men, 999 Englishmen and one Frenchman, and +that of these one man has been killed, and it is not known which. I ask +the question, and the witness answers, the Frenchman. This was not only +as improbable <i>à priori</i>, but is in itself as singular a circumstance, +as remarkable a coincidence, as the drawing of the white ball: yet we +should believe the statement as readily, as if the answer had been John +Thompson. Because though the 999 Englishmen were all alike in the point +in which they differed from the Frenchman, they were not, like the 999 +black balls, undistinguishable in every other respect; but being all +different, they admitted as many chances of interest or error, as if +each man had been of a different nation; and if a lie was told or a +mistake made, the misstatement was as likely to fall on any Jones or +Thompson of the set, as on the Frenchman.</p> + +<p>The example of a coincidence selected by D'Alembert, that of sixes +thrown on a pair of dice ten times in succession, belongs to this sort +of cases rather than to such as Laplace's. The coincidence is here far +more remarkable, because of far rarer occurrence, than the drawing of +the white ball. But though the improbability of its really occurring is +greater, the superior probability of its being announced falsely cannot +be established with the same evidence. The announcement "black" +represented 999 cases, but the witness may not have known this, and if +he did, the 999 cases are so exactly alike, that there is <span class="pagenum"><a name="Page_179" id="Page_179">[Pg 179]</a></span>really only +one set of possible causes of mendacity corresponding to the whole. The +announcement "sixes <i>not</i> drawn ten times," represents, and is known by +the witness to represent, a great multitude of contingencies, every one +of which being unlike every other, there may be a different and a fresh +set of causes of mendacity corresponding to each.</p> + +<p>It appears to me, therefore, that Laplace's doctrine is not strictly +true of any coincidences, and is wholly inapplicable to most: and that +to know whether a coincidence does or does not require more evidence to +render it credible than an ordinary event, we must refer, in every +instance, to first principles, and estimate afresh what is the +probability that the given testimony would have been delivered in that +instance, supposing the fact which it asserts not to be true.</p> + +<p>With these remarks we close the discussion of the Grounds of Disbelief; +and along with it, such exposition as space admits, and as the writer +has it in his power to furnish, of the Logic of Induction.</p> + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"><p><a name="Footnote_1_1" id="Footnote_1_1"></a><a href="#FNanchor_1_1"><span class="label">[1]</span></a> <i>Cours de Philosophie Positive</i>, ii. 656.</p></div> + +<div class="footnote"><p><a name="Footnote_2_2" id="Footnote_2_2"></a><a href="#FNanchor_2_2"><span class="label">[2]</span></a> Vide supra, <span title="See Vol. I.">book iii. ch. xi.</span></p></div> + +<div class="footnote"><p><a name="Footnote_3_3" id="Footnote_3_3"></a><a href="#FNanchor_3_3"><span class="label">[3]</span></a> <i>Philosophy of Discovery</i>, pp. 185 et seqq.</p></div> + +<div class="footnote"><p><a name="Footnote_4_4" id="Footnote_4_4"></a><a href="#FNanchor_4_4"><span class="label">[4]</span></a> <i>Philosophie Positive</i>, ii. 434-437.</p></div> + +<div class="footnote"><p><a name="Footnote_5_5" id="Footnote_5_5"></a><a href="#FNanchor_5_5"><span class="label">[5]</span></a> As an example of legitimate hypothesis according to the +test here laid down, has been justly cited that of Broussais, who, +proceeding on the very rational principle that every disease must +originate in some definite part or other of the organism, boldly assumed +that certain fevers, which not being known to be local were called +constitutional, had their origin in the mucous membrane of the +alimentary canal. The supposition was indeed, as is now generally +admitted, erroneous; but he was justified in making it, since by +deducing the consequences of the supposition, and comparing them with +the facts of those maladies, he might be certain of disproving his +hypothesis if it was ill founded, and might expect that the comparison +would materially aid him in framing another more conformable to the +phenomena. +</p><p> +The doctrine now universally received, that the earth is a natural +magnet, was originally an hypothesis of the celebrated Gilbert. +</p><p> +Another hypothesis, to the legitimacy of which no objection can lie, and +which is well calculated to light the path of scientific inquiry, is +that suggested by several recent writers, that the brain is a voltaic +pile, and that each of its pulsations is a discharge of electricity +through the system. It has been remarked that the sensation felt by the +hand from the beating of a brain, bears a strong resemblance to a +voltaic shock. And the hypothesis, if followed to its consequences, +might afford a plausible explanation of many physiological facts, while +there is nothing to discourage the hope that we may in time sufficiently +understand the conditions of voltaic phenomena to render the truth of +the hypothesis amenable to observation and experiment. +</p><p> +The attempt to localize, in different regions of the brain, the physical +organs of our different mental faculties and propensities, was, on the +part of its original author, a legitimate example of a scientific +hypothesis; and we ought not, therefore, to blame him for the extremely +slight grounds on which he often proceeded, in an operation which could +only be tentative, though we may regret that materials barely sufficient +for a first rude hypothesis should have been hastily worked up into the +vain semblance of a science. If there be really a connexion between the +scale of mental endowments and the various degrees of complication in +the cerebral system, the nature of that connexion was in no other way so +likely to be brought to light as by framing, in the first instance, an +hypothesis similar to that of Gall. But the verification of any such +hypothesis is attended, from the peculiar nature of the phenomena, with +difficulties which phrenologists have not shown themselves even +competent to appreciate, much less to overcome. +</p><p> +Mr. Darwin's remarkable speculation on the Origin of Species is another +unimpeachable example of a legitimate hypothesis. What he terms "natural +selection" is not only a <i>vera causa</i>, but one proved to be capable of +producing effects of the same kind with those which the hypothesis +ascribes to it: the question of possibility is entirely one of degree. +It is unreasonable to accuse Mr. Darwin (as has been done) of violating +the rules of Induction. The rules of Induction are concerned with the +conditions of Proof. Mr. Darwin has never pretended that his doctrine +was proved. He was not bound by the rules of Induction, but by those of +Hypothesis. And these last have seldom been more completely fulfilled. +He has opened a path of inquiry full of promise, the results of which +none can foresee. And is it not a wonderful feat of scientific knowledge +and ingenuity to have rendered so bold a suggestion, which the first +impulse of every one was to reject at once, admissible and discussable, +even as a conjecture?</p></div> + +<div class="footnote"><p><a name="Footnote_6_6" id="Footnote_6_6"></a><a href="#FNanchor_6_6"><span class="label">[6]</span></a> Whewell's <i>Phil. of Discovery</i>, pp. 275, 276.</p></div> + +<div class="footnote"><p><a name="Footnote_7_7" id="Footnote_7_7"></a><a href="#FNanchor_7_7"><span class="label">[7]</span></a> What has most contributed to accredit the hypothesis of a +physical medium for the conveyance of light, is the certain fact that +light <i>travels</i>, (which cannot be proved of gravitation,) that its +communication is not instantaneous, but requires time, and that it is +intercepted (which gravitation is not) by intervening objects. These are +analogies between its phenomena and those of the mechanical motion of a +solid or fluid substance. But we are not entitled to assume that +mechanical motion is the only power in nature capable of exhibiting +those attributes.</p></div> + +<div class="footnote"><p><a name="Footnote_8_8" id="Footnote_8_8"></a><a href="#FNanchor_8_8"><span class="label">[8]</span></a> <i>Phil. of Disc.</i> p. 274.</p></div> + +<div class="footnote"><p><a name="Footnote_9_9" id="Footnote_9_9"></a><a href="#FNanchor_9_9"><span class="label">[9]</span></a> P. 271.</p></div> + +<div class="footnote"><p><a name="Footnote_10_10" id="Footnote_10_10"></a><a href="#FNanchor_10_10"><span class="label">[10]</span></a> P. 251 and the whole of Appendix G.</p></div> + +<div class="footnote"><p><a name="Footnote_11_11" id="Footnote_11_11"></a><a href="#FNanchor_11_11"><span class="label">[11]</span></a> In Dr. Whewell's latest version of his theory (<i>Philosophy +of Discovery</i>, p. 331) he makes a concession respecting the medium of +the transmission of light, which, taken in conjunction with the rest of +his doctrine on the subject, is not, I confess, very intelligible to me, +but which goes far towards removing, if it does not actually remove, the +whole of the difference between us. He is contending, against Sir +William Hamilton, that all matter has weight. Sir William, in proof of +the contrary, cited the luminiferous ether, and the calorific and +electric fluids, "which," he said, "we can neither denude of their +character of substance, nor clothe with the attribute of weight." "To +which," continues Dr. Whewell, "my reply is, that precisely because I +cannot clothe these agents with the attribute of Weight, I <i>do</i> denude +them of the character of Substance. They are not substances, but +agencies. These Imponderable Agents, are not properly called +Imponderable Fluids. This I conceive that I have proved." Nothing can be +more philosophical. But if the luminiferous ether is not matter, and +fluid matter too, what is the meaning of its undulations? Can an agency +undulate? Can there be alternate motion forward and backward of the +particles of an agency? And does not the whole mathematical theory of +the undulations imply them to be material? Is it not a series of +deductions from the known properties of elastic fluids? <i>This</i> opinion +of Dr. Whewell reduces the undulations to a figure of speech, and the +undulatory theory to the proposition which all must admit, that the +transmission of light takes place according to laws which present a very +striking and remarkable agreement with those of undulations. If Dr. +Whewell is prepared to stand by this doctrine, I have no difference with +him on the subject. +</p><p> +Since this chapter was written, the hypothesis of the luminiferous ether +has acquired a great accession of apparent strength, by being adopted +into the new doctrine of the Conservation of Force, as affording a +mechanism by which to explain the mode of production not of light only, +but of heat, and probably of all the other so-called imponderable +agencies. In the present immature stage of the great speculation in +question, I would not undertake to define the ultimate relation of the +hypothetical fluid to it; but I must remark that the essential part of +the new theory, the reciprocal convertibility and interchangeability of +these great cosmic agencies, is quite independent of the molecular +motions which have been imagined as the immediate causes of those +different manifestations and of their substitutions for one another; and +the former doctrine by no means necessarily carries the latter with it. +I confess that the entire theory of the vibrations of the ether, and the +movements which these vibrations are supposed to communicate to the +particles of solid bodies, seems to me at present the weakest part of +the new system, tending rather to weigh down than to prop up those of +its doctrines which rest on real scientific induction.</p></div> + +<div class="footnote"><p><a name="Footnote_12_12" id="Footnote_12_12"></a><a href="#FNanchor_12_12"><span class="label">[12]</span></a> Thus, water, of which eight-ninths in weight are oxygen, +dissolves most bodies which contain a high proportion of oxygen, such as +all the nitrates, (which have more oxygen than any others of the common +salts,) most of the sulphates, many of the carbonates, &c. Again, bodies +largely composed of combustible elements, like hydrogen and carbon, are +soluble in bodies of similar composition; rosin, for instance, will +dissolve in alcohol, tar in oil of turpentine. This empirical +generalization is far from being universally true; no doubt because it +is a remote, and therefore easily defeated, result of general laws too +deep for us at present to penetrate; but it will probably in time +suggest processes of inquiry, leading to the discovery of those laws.</p></div> + +<div class="footnote"><p><a name="Footnote_13_13" id="Footnote_13_13"></a><a href="#FNanchor_13_13"><span class="label">[13]</span></a> Or (according to Laplace's theory) the sun and the sun's +rotation.</p></div> + +<div class="footnote"><p><a name="Footnote_14_14" id="Footnote_14_14"></a><a href="#FNanchor_14_14"><span class="label">[14]</span></a> Supra, <span title="See Vol. I.">book iii. ch. v. § 7</span>.</p></div> + +<div class="footnote"><p><a name="Footnote_15_15" id="Footnote_15_15"></a><a href="#FNanchor_15_15"><span class="label">[15]</span></a> Supra, <span title="See Vol. I.">book iii. ch. x. § 2</span>.</p></div> + +<div class="footnote"><p><a name="Footnote_16_16" id="Footnote_16_16"></a><a href="#FNanchor_16_16"><span class="label">[16]</span></a> In the preceding discussion, the <i>mean</i> is spoken of as if +it were exactly the same thing with the <i>average</i>. But the mean for +purposes of inductive inquiry, is not the average, or arithmetical mean, +though in a familiar illustration of the theory the difference may be +disregarded. If the deviations on one side of the average are much more +numerous than those on the other (these last being fewer but greater), +the effect due to the invariable cause, as distinct from the variable +ones, will not coincide with the average, but will be either below or +above the average, whichever be the side on which the greatest number of +the instances are found. This follows from a truth, ascertained both +inductively and deductively, that small deviations from the true central +point are greatly more frequent than large ones. The mathematical law +is, "that the most probable determination of one or more invariable +elements from observation is that in which <i>the sum of the squares</i> of +the individual aberrations," or deviations, "<i>shall be the least +possible</i>." See this principle stated, and its grounds popularly +explained, by Sir John Herschel, in his review of Quetelet on +Probabilities, <i>Essays</i>, pp. 395 <i>et seq.</i></p></div> + +<div class="footnote"><p><a name="Footnote_17_17" id="Footnote_17_17"></a><a href="#FNanchor_17_17"><span class="label">[17]</span></a> <i>Essai Philosophique sur les Probabilités</i>, fifth Paris +Edition, p. 7.</p></div> + +<div class="footnote"><p><a name="Footnote_18_18" id="Footnote_18_18"></a><a href="#FNanchor_18_18"><span class="label">[18]</span></a> It even appears to me that the calculation of chances, +where there are no data grounded either on special experience or on +special inference, must, in an immense majority of cases, break down, +from sheer impossibility of assigning any principle by which to be +guided in setting out the list of possibilities. In the case of the +coloured balls we have no difficulty in making the enumeration, because +we ourselves determine what the possibilities shall be. But suppose a +case more analogous to those which occur in nature: instead of three +colours, let there be in the box all possible colours: we being supposed +ignorant of the comparative frequency with which different colours occur +in nature, or in the productions of art. How is the list of cases to be +made out? Is every distinct shade to count as a colour? If so, is the +test to be a common eye, or an educated eye, a painter's for instance? +On the answer to these questions would depend whether the chances +against some particular colour would be estimated at ten, twenty, or +perhaps five hundred to one. While if we knew from experience that the +particular colour occurs on an average a certain number of times in +every hundred or thousand, we should not require to know anything either +of the frequency or of the number of the other possibilities.</p></div> + +<div class="footnote"><p><a name="Footnote_19_19" id="Footnote_19_19"></a><a href="#FNanchor_19_19"><span class="label">[19]</span></a> <i>Prospective Review</i> for February 1850.</p></div> + +<div class="footnote"><p><a name="Footnote_20_20" id="Footnote_20_20"></a><a href="#FNanchor_20_20"><span class="label">[20]</span></a> "If this be not so, why do we feel so much more +probability added by the first instance, than by any single subsequent +instance? Why, except that the first instance gives us its possibility +(a cause <i>adequate</i> to it), while every other only gives us the +frequency of its conditions? If no reference to a cause be supposed, +possibility would have no meaning; yet it is clear, that, antecedent to +its happening, we might have supposed the event impossible, <i>i.e.</i>, have +believed that there was no physical energy really existing in the world +equal to producing it.... After the first time of happening, which is, +then, more important to the whole probability than any other single +instance (because proving the possibility), the <i>number</i> of times +becomes important as an index to the intensity or extent of the cause, +and its independence of any particular time. If we took the case of a +tremendous leap, for instance, and wished to form an estimate of the +probability of its succeeding a certain number of times; the first +instance, by showing its possibility (before doubtful) is of the most +importance; but every succeeding leap shows the power to be more +perfectly under control, greater and more invariable, and so increases +the probability; and no one would think of reasoning in this case +straight from one instance to the next, without referring to the +physical energy which each leap indicated. Is it not then clear that we +do not ever" (let us rather say, that we do not in an advanced state of +our knowledge) "conclude directly from the happening of an event to the +probability of its happening again; but that we refer to the cause, +regarding the past cases as an index to the cause, and the cause as our +guide to the future?"—<i>Ibid.</i></p></div> + +<div class="footnote"><p><a name="Footnote_21_21" id="Footnote_21_21"></a><a href="#FNanchor_21_21"><span class="label">[21]</span></a> The writer last quoted says that the valuation of chances +by comparing the number of cases in which the event occurs with the +number in which it does not occur, "would generally be wholly +erroneous," and "is not the true theory of probability." It is at least +that which forms the foundation of insurance, and of all those +calculations of chances in the business of life which experience so +abundantly verifies. The reason which the reviewer gives for rejecting +the theory, is that it "would regard an event as certain which had +hitherto never failed; which is exceedingly far from the truth, even for +a very large number of constant successes." This is not a defect in a +particular theory, but in any theory of chances. No principle of +evaluation can provide for such a case as that which the reviewer +supposes. If an event has never once failed, in a number of trials +sufficient to eliminate chance, it really has all the certainty which +can be given by an empirical law: it <i>is</i> certain during the continuance +of the same collocation of causes which existed during the observations. +If it ever fails, it is in consequence of some change in that +collocation. Now, no theory of chances will enable us to infer the +future probability of an event from the past, if the causes in +operation, capable of influencing the event, have intermediately +undergone a change.</p></div> + +<div class="footnote"><p><a name="Footnote_22_22" id="Footnote_22_22"></a><a href="#FNanchor_22_22"><span class="label">[22]</span></a> Pp. 18, 19. The theorem is not stated by Laplace in the +exact terms in which I have stated it; but the identity of import of the +two modes of expression is easily demonstrable.</p></div> + +<div class="footnote"><p><a name="Footnote_23_23" id="Footnote_23_23"></a><a href="#FNanchor_23_23"><span class="label">[23]</span></a> For a fuller treatment of the many interesting questions +raised by the theory of probabilities, I may now refer to a recent work +by Mr. Venn, Fellow of Caius College, Cambridge, "The Logic of Chance;" +one of the most thoughtful and philosophical treatises on any subject +connected with Logic and Evidence, which have been produced in this or +any other country for many years. Some criticisms contained in it have +been very useful to me in revising the corresponding chapters of the +present work. In several of Mr. Venn's opinions, however, I do not +agree. What these are will be obvious to any reader of Mr. Venn's work +who is also a reader of this.</p></div> + +<div class="footnote"><p><a name="Footnote_24_24" id="Footnote_24_24"></a><a href="#FNanchor_24_24"><span class="label">[24]</span></a> There was no greater foundation for this than for Newton's +celebrated conjecture that the diamond was combustible. He grounded his +guess on the very high refracting power of the diamond, comparatively to +its density; a peculiarity which had been observed to exist in +combustible substances; and on similar grounds he conjectured that +water, though not combustible, contained a combustible ingredient. +Experiment having subsequently shown that in both instances he guessed +right, the prophecy is considered to have done great honour to his +scientific sagacity; but it is to this day uncertain whether the guess +was, in truth, what there are so many examples of in the history of +science, a farsighted anticipation of a law afterwards to be discovered. +The progress of science has not hitherto shown ground for believing that +there is any real connexion between combustibility and a high refracting +power.</p></div> + +<div class="footnote"><p><a name="Footnote_25_25" id="Footnote_25_25"></a><a href="#FNanchor_25_25"><span class="label">[25]</span></a> Hartley's <i>Observations on Man</i>, vol. i. p. 16. The +passage is not in Priestley's curtailed edition.</p></div> + +<div class="footnote"><p><a name="Footnote_26_26" id="Footnote_26_26"></a><a href="#FNanchor_26_26"><span class="label">[26]</span></a> I am happy to be able to quote the following excellent +passage from Mr. Baden Powell's <i>Essay on the Inductive Philosophy</i>, in +confirmation, both in regard to history and to doctrine, of the +statement made in the text. Speaking of the "conviction of the universal +and permanent uniformity of nature," Mr. Powell says (pp. 98-100), +</p><p> +"We may remark that this idea, in its proper extent, is by no means one +of popular acceptance or natural growth. Just so far as the daily +experience of every one goes, so far indeed he comes to embrace a +certain persuasion of this kind, but merely to this limited extent, that +what is going on around him at present, in his own narrow sphere of +observation, will go on in like manner in future. The peasant believes +that the sun which rose to-day will rise again to-morrow; that the seed +put into the ground will be followed in due time by the harvest this +year as it was last year, and the like; but has no notion of such +inferences in subjects beyond his immediate observation. And it should +be observed that each class of persons, in admitting this belief within +the limited range of his own experience, though he doubt or deny it in +everything beyond, is, in fact, bearing unconscious testimony to its +universal truth. Nor, again, is it only among the <i>most</i> ignorant that +this limitation is put upon the truth. There is a very general +propensity to believe that everything beyond common experience, or +especially ascertained laws of nature, is left to the dominion of chance +or fate or arbitrary intervention; and even to object to any attempted +explanation by physical causes, if conjecturally thrown out for an +apparently unaccountable phenomenon. +</p><p> +"The precise doctrine of the <i>generalization</i> of this idea of the +uniformity of nature, so far from being obvious, natural, or intuitive, +is utterly beyond the attainment of the many. In all the extent of its +universality it is characteristic of the philosopher. It is clearly the +result of philosophic cultivation and training, and by no means the +spontaneous offspring of any primary principle naturally inherent in the +mind, as some seem to believe. It is no mere vague persuasion taken up +without examination, as a common prepossession to which we are always +accustomed; on the contrary, all common prejudices and associations are +against it. It is pre-eminently <i>an acquired idea</i>. It is not attained +without deep study and reflection. The best informed philosopher is the +man who most firmly believes it, even in opposition to received notions; +its acceptance depends on the extent and profoundness of his inductive +studies."</p></div> + +<div class="footnote"><p><a name="Footnote_27_27" id="Footnote_27_27"></a><a href="#FNanchor_27_27"><span class="label">[27]</span></a> Supra, <span title="See Vol. I.">book iii. ch. iii. § 1</span>.</p></div> + +<div class="footnote"><p><a name="Footnote_28_28" id="Footnote_28_28"></a><a href="#FNanchor_28_28"><span class="label">[28]</span></a> It deserves remark, that these early generalizations did +not, like scientific inductions, presuppose causation. What they did +presuppose, was <i>uniformity</i> in physical facts. But the observers were +as ready to presume uniformity in the coexistences of facts as in the +sequences. On the other hand, they never thought of assuming that this +uniformity was a principle pervading all nature: their generalizations +did not imply that there was uniformity in everything, but only that as +much uniformity as existed within their observation, existed also beyond +it. The induction, Fire burns, does not require for its validity that +all nature should observe uniform laws, but only that there should be +uniformity in one particular class of natural phenomena: the effects of +fire on the senses and on combustible substances. And uniformity to this +extent was not assumed, anterior to the experience, but proved by the +experience. The same observed instances which proved the narrower truth, +proved as much of the wider one as corresponded to it. It is from losing +sight of this fact, and considering the law of causation in its full +extent as necessarily presupposed in the very earliest generalizations, +that persons have been led into the belief that the law of causation is +known <i>à priori</i>, and is not itself a conclusion from experience.</p></div> + +<div class="footnote"><p><a name="Footnote_29_29" id="Footnote_29_29"></a><a href="#FNanchor_29_29"><span class="label">[29]</span></a> <span title="See Vol. I.">Book ii. chap. iii.</span></p></div> + +<div class="footnote"><p><a name="Footnote_30_30" id="Footnote_30_30"></a><a href="#FNanchor_30_30"><span class="label">[30]</span></a> One of the most rising thinkers of the new generation in +France, M. Taine (who has given, in the Revue des Deux Mondes, the most +masterly analysis, at least in one point of view, ever made of the +present work), though he rejects, on this and similar points of +psychology, the intuition theory in its ordinary form, nevertheless +assigns to the law of causation, and to some other of the most universal +laws, that certainty beyond the bounds of human experience, which I have +not been able to accord to them. He does this on the faith of our +faculty of abstraction, in which he seems to recognise an independent +source of evidence, not indeed disclosing truths not contained in our +experience, but affording an assurance which experience cannot give, of +the universality of those which it does contain. By abstraction M. Taine +seems to think that we are able, not merely to analyse that part of +nature which we see, and exhibit apart the elements which pervade it, +but to distinguish such of them as are elements of the system of nature +considered as a whole, not incidents belonging to our limited +terrestrial experience. I am not sure that I fully enter into M. Taine's +meaning; but I confess I do not see how any mere abstract conception, +elicited by our minds from our experience, can be evidence of an +objective fact in universal Nature, beyond what the experience itself +bears witness of; or how, in the process of interpreting in general +language the testimony of experience, the limitations of the testimony +itself can be cast off.</p></div> + +<div class="footnote"><p><a name="Footnote_31_31" id="Footnote_31_31"></a><a href="#FNanchor_31_31"><span class="label">[31]</span></a> <span title="See Vol. I.">Book i. chap. vii.</span></p></div> + +<div class="footnote"><p><a name="Footnote_32_32" id="Footnote_32_32"></a><a href="#FNanchor_32_32"><span class="label">[32]</span></a> In some cases, a Kind is sufficiently identified by some +one remarkable property: but most commonly several are required; each +property considered singly, being a joint property of that and of other +Kinds. The colour and brightness of the diamond are common to it with +the paste from which false diamonds are made; its octohedral form is +common to it with alum, and magnetic iron ore; but the colour and +brightness and the form together, identify its Kind; that is, are a mark +to us that it is combustible; that when burnt it produces carbonic acid; +that it cannot be cut with any known substance; together with many other +ascertained properties, and the fact that there exist an indefinite +number still unascertained.</p></div> + +<div class="footnote"><p><a name="Footnote_33_33" id="Footnote_33_33"></a><a href="#FNanchor_33_33"><span class="label">[33]</span></a> This doctrine of course assumes that the allotropic forms +of what is chemically the same substance are so many different Kinds; +and such, in the sense in which the word Kind is used in this treatise, +they really are.</p></div> + +<div class="footnote"><p><a name="Footnote_34_34" id="Footnote_34_34"></a><a href="#FNanchor_34_34"><span class="label">[34]</span></a> Mr. De Morgan, in his <i>Formal Logic</i>, makes the just +remark, that from two such premises as Most A are B, and Most A are C, +we may infer with certainty that some B are C. But this is the utmost +limit of the conclusions which can be drawn from two approximate +generalizations, when the precise degree of their approximation to +universality is unknown or undefined.</p></div> + +<div class="footnote"><p><a name="Footnote_35_35" id="Footnote_35_35"></a><a href="#FNanchor_35_35"><span class="label">[35]</span></a> <i>Rationale of Judicial Evidence</i>, vol. iii. p. 224.</p></div> + +<div class="footnote"><p><a name="Footnote_36_36" id="Footnote_36_36"></a><a href="#FNanchor_36_36"><span class="label">[36]</span></a> Supra, <span title="See Vol. I.">vol. i. p. 115</span>.</p></div> + +<div class="footnote"><p><a name="Footnote_37_37" id="Footnote_37_37"></a><a href="#FNanchor_37_37"><span class="label">[37]</span></a> Supra, <span title="See Vol. I.">book i. ch. v. § 1</span>, and <span title="See Vol. I.">book ii. ch. v. § 5</span>.</p></div> + +<div class="footnote"><p><a name="Footnote_38_38" id="Footnote_38_38"></a><a href="#FNanchor_38_38"><span class="label">[38]</span></a> The axiom, "Equals subtracted from equals leave equal +differences," may be demonstrated from the two axioms in the text. If A += <i>a</i> and B = <i>b</i>, A - B = <i>a - b</i>. For if not, let A - B = <i>a - b + c</i>. +Then since B = <i>b</i>, adding equals to equals, A = <i>a + c</i>. But A = <i>a</i>. +Therefore <i>a = a + c</i>, which is impossible. +</p><p> +This proposition having been demonstrated, we may, by means of it, +demonstrate the following: "If equals be added to unequals, the sums are +unequal." If A = <i>a</i> and B not = <i>b</i>, A + B is not = <i>a + b</i>. For +suppose it be so. Then, since A = <i>a</i> and A + B = <i>a + b</i>, subtracting +equals from equals, B = <i>b</i>; which is contrary to the hypothesis. +</p><p> +So again, it may be proved that two things, one of which is equal and +the other unequal to a third thing, are unequal to one another. If A = +<i>a</i> and A not = B, neither is <i>a</i> = B. For suppose it to be equal. Then +since A = <i>a</i> and <i>a</i> = B, and since things equal to the same thing are +equal to one another, A = B: which is contrary to the hypothesis.</p></div> + +<div class="footnote"><p><a name="Footnote_39_39" id="Footnote_39_39"></a><a href="#FNanchor_39_39"><span class="label">[39]</span></a> Geometers have usually preferred to define parallel lines +by the property of being in the same plane and never meeting. This, +however, has rendered it necessary for them to assume, as an additional +axiom, some other property of parallel lines; and the unsatisfactory +manner in which properties for that purpose have been selected by Euclid +and others has always been deemed the opprobrium of elementary geometry. +Even as a verbal definition, equidistance is a fitter property to +characterize parallels by, since it is the attribute really involved in +the signification of the name. If to be in the same plane and never to +meet were all that is meant by being parallel, we should feel no +incongruity in speaking of a curve as parallel to its asymptote. The +meaning of parallel lines is, lines which pursue exactly the same +direction, and which, therefore, neither draw nearer nor go farther from +one another; a conception suggested at once by the contemplation of +nature. That the lines will never meet is of course included in the more +comprehensive proposition that they are everywhere equally distant. And +that any straight lines which are in the same plane and not equidistant +will certainly meet, may be demonstrated in the most rigorous manner +from the fundamental property of straight lines assumed in the text, +viz. that if they set out from the same point, they diverge more and +more without limit.</p></div> + +<div class="footnote"><p><a name="Footnote_40_40" id="Footnote_40_40"></a><a href="#FNanchor_40_40"><span class="label">[40]</span></a> <i>Philosophie Positive</i>, iii. 414-416.</p></div> + +<div class="footnote"><p><a name="Footnote_41_41" id="Footnote_41_41"></a><a href="#FNanchor_41_41"><span class="label">[41]</span></a> See the two remarkable notes (A) and (F), appended to his +<i>Inquiry into the Relation of Cause and Effect</i>.</p></div> + +<div class="footnote"><p><a name="Footnote_42_42" id="Footnote_42_42"></a><a href="#FNanchor_42_42"><span class="label">[42]</span></a> Supra, pp. <a href="#Page_119">119</a>, <a href="#Page_120">120</a>.</p></div> + +<div class="footnote"><p><a name="Footnote_43_43" id="Footnote_43_43"></a><a href="#FNanchor_43_43"><span class="label">[43]</span></a> A writer to whom I have several times referred, gives as +the definition of an impossibility, that which there exists in the world +no cause adequate to produce. This definition does not take in such +impossibilities as these—that two and two should make five; that two +straight lines should inclose a space; or that anything should begin to +exist without a cause. I can think of no definition of impossibility +comprehensive enough to include all its varieties, except the one which +I have given: viz. An impossibility is that, the truth of which would +conflict with a complete induction, that is, with the most conclusive +evidence which we possess of universal truth. +</p><p> +As to the reputed impossibilities which rest on no other grounds than +our ignorance of any cause capable of producing the supposed effects; +very few of them are certainly impossible, or permanently incredible. +The facts of travelling seventy miles an hour, painless surgical +operations, and conversing by instantaneous signals between London and +New York, held a high place, not many years ago, among such +impossibilities.</p></div> + +<div class="footnote"><p><a name="Footnote_44_44" id="Footnote_44_44"></a><a href="#FNanchor_44_44"><span class="label">[44]</span></a> Not, however, as might at first sight appear, 999 times as +much. A complete analysis of the cases shows that (always assuming the +veracity of the witness to be 9/10) in 10,000 drawings, the drawing of +No. 79 will occur nine times, and be announced incorrectly once; the +credibility therefore of the announcement of No. 79 is 9/10; while the +drawing of a white ball will occur nine times, and be announced +incorrectly 999 times. The credibility therefore of the announcement of +white is 9/1008, and the ratio of the two 1008:10; the one announcement +being thus only about a hundred times more credible than the other, +instead of 999 times.</p></div> +</div> + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_181" id="Page_181">[Pg 181]</a></span></p> +<h2><a name="BOOK_IV" id="BOOK_IV"></a>BOOK IV.<br /> +OF OPERATIONS SUBSIDIARY TO INDUCTION.</h2> + + +<blockquote><p><span class="pagenum"><a name="Page_182" id="Page_182">[Pg 182]</a></span></p><p>"Clear and distinct ideas are terms which, though familiar and frequent +in men's mouths, I have reason to think every one who uses does not +perfectly understand. And possibly it is but here and there one who +gives himself the trouble to consider them so far as to know what he +himself or others precisely mean by them; I have, therefore, in most +places, chose to put determinate or determined, instead of clear and +distinct, as more likely to direct men's thoughts to my meaning in this +matter."—<span class="smcap">Locke's</span> <i>Essay on the Human Understanding</i>; Epistle to the +Reader.</p></blockquote> + +<blockquote><p>"Il ne peut y avoir qu'une méthode parfaite, qui est la <i>méthode +naturelle</i>; on nomme ainsi un arrangement dans lequel les êtres du même +genre seraient plus voisins entre eux que ceux de tous les autres +genres; les genres du même ordre, plus que ceux de tous les autres +ordres; et ainsi de suite. Cette méthode est l'idéal auquel l'histoire +naturelle doit tendre; car il est évident que si l'on y parvenait, l'on +aurait l'expression exacte et complète de la nature entière."—<span class="smcap">Cuvier</span>, +<i>Règne Animal</i>, Introduction.</p></blockquote> + +<blockquote><p>"Deux grandes notions philosophiques dominent la théorie fondamentale de +la méthode naturelle proprement dite, savoir la formation des groupes +naturels, et ensuite leur succession hiérarchique."—<span class="smcap">Comte</span>, <i>Cours de +Philosophie Positive</i>, 42me leçon.</p></blockquote> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_183" id="Page_183">[Pg 183]</a></span></p> +<h3><a name="BOOK_IV_CHAPTER_I" id="BOOK_IV_CHAPTER_I"></a>CHAPTER I.<br /> +OF OBSERVATION AND DESCRIPTION.</h3> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_I_1">§ 1.</a> The inquiry which occupied us in the two preceding books, has +conducted us to what appears a satisfactory solution of the principal +problem of Logic, according to the conception I have formed of the +science. We have found, that the mental process with which Logic is +conversant, the operation of ascertaining truths by means of evidence, +is always, even when appearances point to a different theory of it, a +process of induction. And we have particularized the various modes of +induction, and obtained a clear view of the principles to which it must +conform, in order to lead to results which can be relied on.</p> + +<p>The consideration of Induction, however, does not end with the direct +rules for its performance. Something must be said of those other +operations of the mind, which are either necessarily presupposed in all +induction, or are instrumental to the more difficult and complicated +inductive processes. The present book will be devoted to the +consideration of these subsidiary operations: among which our attention +must first be given to those, which are indispensable preliminaries to +all induction whatsoever.</p> + +<p>Induction being merely the extension to a class of cases, of something +which has been observed to be true in certain individual instances of +the class; the first place among the operations subsidiary to induction, +is claimed by Observation. This is not, however, the place to lay down +rules for making good observers; nor is it within the competence of +Logic to do so, but of the art of intellectual Education. Our business +with observation is only in its connexion with the appropriate problem +of logic, the estimation of evidence. We have to <span class="pagenum"><a name="Page_184" id="Page_184">[Pg 184]</a></span>consider, not how or +what to observe, but under what conditions observation is to be relied +on; what is needful, in order that the fact, supposed to be observed, +may safely be received as true.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_I_2">§ 2.</a> The answer to this question is very simple, at least in its first +aspect. The sole condition is, that what is supposed to have been +observed shall really have been observed; that it be an observation, not +an inference. For in almost every act of our perceiving faculties, +observation and inference are intimately blended. What we are said to +observe is usually a compound result, of which one-tenth may be +observation, and the remaining nine-tenths inference.</p> + +<p>I affirm, for example, that I hear a man's voice. This would pass, in +common language, for a direct perception. All, however, which is really +perception, is that I hear a sound. That the sound is a voice, and that +voice the voice of a man, are not perceptions but inferences. I affirm, +again, that I saw my brother at a certain hour this morning. If any +proposition concerning a matter of fact would commonly be said to be +known by the direct testimony of the senses, this surely would be so. +The truth, however, is far otherwise. I only saw a certain coloured +surface; or rather I had the kind of visual sensations which are usually +produced by a coloured surface; and from these as marks, known to be +such by previous experience, I concluded that I saw my brother. I might +have had sensations precisely similar, when my brother was not there. I +might have seen some other person so nearly resembling him in +appearance, as, at the distance, and with the degree of attention which +I bestowed, to be mistaken for him. I might have been asleep, and have +dreamed that I saw him; or in a state of nervous disorder, which brought +his image before me in a waking hallucination. In all these modes, many +have been led to believe that they saw persons well known to them, who +were dead or far distant. If any of these suppositions had been true, +the affirmation that I saw my brother would have been erroneous; but +whatever was matter of direct perception, namely the visual sensations, +would have been real. The inference only <span class="pagenum"><a name="Page_185" id="Page_185">[Pg 185]</a></span>would have been ill grounded; +I should have ascribed those sensations to a wrong cause.</p> + +<p>Innumerable instances might be given, and analysed in the same manner, +of what are vulgarly called errors of sense. There are none of them +properly errors of sense; they are erroneous inferences from sense. When +I look at a candle through a multiplying glass, I see what seems a dozen +candles instead of one: and if the real circumstances of the case were +skilfully disguised, I might suppose that there were really that number; +there would be what is called an optical deception. In the kaleidoscope +there really is that deception: when I look through the instrument, +instead of what is actually there, namely a casual arrangement of +coloured fragments, the appearance presented is that of the same +combination several times repeated in symmetrical arrangement round a +point. The delusion is of course effected by giving me the same +sensations which I should have had if such a symmetrical combination had +really been presented to me. If I cross two of my fingers, and bring any +small object, a marble for instance, into contact with both, at points +not usually touched simultaneously by one object, I can hardly, if my +eyes are shut, help believing that there are two marbles instead of one. +But it is not my touch in this case, nor my sight in the other, which is +deceived; the deception, whether durable or only momentary, is in my +judgment. From my senses I have only the sensations, and those are +genuine. Being accustomed to have those or similar sensations when, and +only when, a certain arrangement of outward objects is present to my +organs, I have the habit of instantly, when I experience the sensations, +inferring the existence of that state of outward things. This habit has +become so powerful, that the inference, performed with the speed and +certainty of an instinct, is confounded with intuitive perceptions. When +it is correct, I am unconscious that it ever needed proof; even when I +know it to be incorrect, I cannot without considerable effort abstain +from making it. In order to be aware that it is not made by instinct but +by an acquired habit, I am obliged to reflect on the slow process +through which I learnt to judge by the eye of many things <span class="pagenum"><a name="Page_186" id="Page_186">[Pg 186]</a></span>which I now +appear to perceive directly by sight; and on the reverse operation +performed by persons learning to draw, who with difficulty and labour +divest themselves of their acquired perceptions, and learn afresh to see +things as they appear to the eye.</p> + +<p>It would be easy to prolong these illustrations, were there any need to +expatiate on a topic so copiously exemplified in various popular works. +From the examples already given, it is seen sufficiently, that the +individual facts from which we collect our inductive generalizations are +scarcely ever obtained by observation alone. Observation extends only to +the sensations by which we recognise objects; but the propositions which +we make use of, either in science or in common life, relate mostly to +the objects themselves. In every act of what is called observation, +there is at least one inference—from the sensations to the presence of +the object; from the marks or diagnostics, to the entire phenomenon. And +hence, among other consequences, follows the seeming paradox, that a +general proposition collected from particulars is often more certainly +true than any one of the particular propositions from which, by an act +of induction, it was inferred. For, each of those particular (or rather +singular) propositions involved an inference, from the impression on the +senses to the fact which caused that impression: and this inference may +have been erroneous in any one of the instances, but cannot well have +been erroneous in all of them, provided their number was sufficient to +eliminate chance. The conclusion, therefore, that is, the general +proposition, may deserve more complete reliance than it would be safe to +repose in any one of the inductive premises.</p> + +<p>The logic of observation, then, consists solely in a correct +discrimination between that, in a result of observation, which has +really been perceived, and that which is an inference from the +perception. Whatever portion is inference, is amenable to the rules of +induction already treated of, and requires no further notice here: the +question for us in this place is, when all which is inference is taken +away, what remains. There remains, in the first place, the mind's own +feelings or states of <span class="pagenum"><a name="Page_187" id="Page_187">[Pg 187]</a></span>consciousness, namely, its outward feelings or +sensations, and its inward feelings—its thoughts, emotions, and +volitions. Whether anything else remains, or all else is inference from +this; whether the mind is capable of directly perceiving or apprehending +anything except states of its own consciousness—is a problem of +metaphysics not to be discussed in this place. But after excluding all +questions on which metaphysicians differ, it remains true, that for most +purposes the discrimination we are called upon practically to exercise +is that between sensations or other feelings, of our own or of other +people, and inferences drawn from them. And on the theory of Observation +this is all which seems necessary to be said for the purposes of the +present work.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_I_3">§ 3.</a> If, in the simplest observation, or in what passes for such, there +is a large part which is not observation but something else; so in the +simplest description of an observation, there is, and must always be, +much more asserted than is contained in the perception itself. We cannot +describe a fact, without implying more than the fact. The perception is +only of one individual thing; but to describe it is to affirm a +connexion between it and every other thing which is either denoted or +connoted by any of the terms used. To begin with an example, than which +none can be conceived more elementary: I have a sensation of sight, and +I endeavour to describe it by saying that I see something white. In +saying this, I do not solely affirm my sensation; I also class it. I +assert a resemblance between the thing I see, and all things which I and +others are accustomed to call white. I assert that it resembles them in +the circumstance in which they all resemble one another, in that which +is the ground of their being called by the name. This is not merely one +way of describing an observation, but the only way. If I would either +register my observation for my own future use, or make it known for the +benefit of others, I must assert a resemblance between the fact which I +have observed and something else. It is inherent in a description, to be +the statement of a resemblance, or resemblances.</p> + +<p><span class="pagenum"><a name="Page_188" id="Page_188">[Pg 188]</a></span></p><p>We thus see that it is impossible to express in words any result of +observation, without performing an act possessing what Dr. Whewell +considers to be characteristic of Induction. There is always something +introduced which was not included in the observation itself; some +conception common to the phenomenon with other phenomena to which it is +compared. An observation cannot be spoken of in language at all without +declaring more than that one observation; without assimilating it to +other phenomena already observed and classified. But this identification +of an object—this recognition of it as possessing certain known +characteristics—has never been confounded with Induction. It is an +operation which precedes all induction, and supplies it with its +materials. It is a perception of resemblances, obtained by comparison.</p> + +<p>These resemblances are not always apprehended directly, by merely +comparing the object observed with some other present object, or with +our recollection of an object which is absent. They are often +ascertained through intermediate marks, that is, deductively. In +describing some new kind of animal, suppose me to say that it measures +ten feet in length, from the forehead to the extremity of the tail. I +did not ascertain this by the unassisted eye. I had a two-foot rule +which I applied to the object, and, as we commonly say, measured it; an +operation which was not wholly manual, but partly also mathematical, +involving the two propositions, Five times two is ten, and Things which +are equal to the same thing are equal to one another. Hence, the fact +that the animal is ten feet long is not an immediate perception, but a +conclusion from reasoning; the minor premises alone being furnished by +observation of the object. Nevertheless, this is called an observation +or a description of the animal, not an induction respecting it.</p> + +<p>To pass at once from a very simple to a very complex example: I affirm +that the earth is globular. The assertion is not grounded on direct +perception; for the figure of the earth cannot, by us, be directly +perceived, though the assertion would not be true unless circumstances +could be supposed under which its truth could be so perceived. That the +form <span class="pagenum"><a name="Page_189" id="Page_189">[Pg 189]</a></span>of the earth is globular is inferred from certain marks, as for +instance from this, that its shadow thrown upon the moon is circular; or +this, that on the sea, or any extensive plain, our horizon is always a +circle; either of which marks is incompatible with any other than a +globular form. I assert further, that the earth is that particular kind +of globe which is termed an oblate spheroid; because it is found by +measurement in the direction of the meridian, that the length on the +surface of the earth which subtends a given angle at its centre, +diminishes as we recede from the equator and approach the poles. But +these propositions, that the earth is globular, and that it is an oblate +spheroid, assert, each of them, an individual fact; in its own nature +capable of being perceived by the senses when the requisite organs and +the necessary position are supposed, and only not actually perceived +because those organs and that position are wanting. This identification +of the earth, first as a globe, and next as an oblate spheroid, which, +if the fact could have been seen, would have been called a description +of the figure of the earth, may without impropriety be so called when, +instead of being seen, it is inferred. But we could not without +impropriety call either of these assertions an induction from facts +respecting the earth. They are not general propositions collected from +particular facts, but particular facts deduced from general +propositions. They are conclusions obtained deductively, from premises +originating in induction: but of these premises some were not obtained +by observation of the earth, nor had any peculiar reference to it.</p> + +<p>If, then, the truth respecting the figure of the earth is not an +induction, why should the truth respecting the figure of the earth's +orbit be so? The two cases only differ in this, that the form of the +orbit was not, like the form of the earth itself, deduced by +ratiocination from facts which were marks of ellipticity, but was got at +by boldly guessing that the path was an ellipse, and finding afterwards, +on examination, that the observations were in harmony with the +hypothesis. According to Dr. Whewell, however, this process of guessing +and verifying our guesses is not only induction, but the whole <span class="pagenum"><a name="Page_190" id="Page_190">[Pg 190]</a></span>of +induction: no other exposition can be given of that logical operation. +That he is wrong in the latter assertion, the whole of the preceding +book has, I hope, sufficiently proved; and that the process by which the +ellipticity of the planetary orbits was ascertained, is not induction at +all, was attempted to be shown in the second chapter of the same +book.<a name="FNanchor_1_45" id="FNanchor_1_45"></a><a href="#Footnote_1_45" class="fnanchor">[1]</a> We are now, however, prepared to go more into the heart of the +matter than at that earlier period of our inquiry, and to show, not +merely what the operation in question is not, but what it is.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_I_4">§ 4.</a> We observed, in the second chapter, that the proposition "the earth +moves in an ellipse," so far as it only serves for the colligation or +connecting together of actual observations, (that is, as it only affirms +that the observed positions of the earth may be correctly represented by +as many points in the circumference of an imaginary ellipse,) is not an +induction, but a description: it is an induction, only when it affirms +that the intermediate positions, of which there has been no direct +observation, would be found to correspond to the remaining points of the +same elliptic circumference. Now, though this real induction is one +thing, and the description another, we are in a very different condition +for making the induction before we have obtained the description, and +after it. For inasmuch as the description, like all other descriptions, +contains the assertion of a resemblance between the phenomenon described +and something else; in pointing out something which the series of +observed places of a planet resembles, it points out something in which +the several places themselves agree. If the series of places correspond +to as many points of an ellipse, the places themselves agree in being +situated in that ellipse. We have, therefore, by the same process which +gave us the description, obtained the requisites for an induction by the +Method of Agreement. The successive observed places of the earth being +considered as effects, and its motion as the cause which produces them, +we find that those effects, that is, those places, agree in the +circumstance of <span class="pagenum"><a name="Page_191" id="Page_191">[Pg 191]</a></span>being in an ellipse. We conclude that the remaining +effects, the places which have not been observed, agree in the same +circumstance, and that the <i>law</i> of the motion of the earth is motion in +an ellipse.</p> + +<p>The Colligation of Facts, therefore, by means of hypotheses, or, as Dr. +Whewell prefers to say, by means of Conceptions, instead of being, as he +supposes, Induction itself, takes its proper place among operations +subsidiary to Induction. All Induction supposes that we have previously +compared the requisite number of individual instances, and ascertained +in what circumstances they agree. The Colligation of Facts is no other +than this preliminary operation. When Kepler, after vainly endeavouring +to connect the observed places of a planet by various hypotheses of +circular motion, at last tried the hypothesis of an ellipse and found it +answer to the phenomena; what he really attempted, first unsuccessfully +and at last successfully, was to discover the circumstance in which all +the observed positions of the planet agreed. And when he in like manner +connected another set of observed facts, the periodic times of the +different planets, by the proposition that the squares of the times are +proportional to the cubes of the distances, what he did was simply to +ascertain the property in which the periodic times of all the different +planets agreed.</p> + +<p>Since, therefore, all that is true and to the purpose in Dr. Whewell's +doctrine of Conceptions might be fully expressed by the more familiar +term Hypothesis; and since his Colligation of Facts by means of +appropriate Conceptions, is but the ordinary process of finding by a +comparison of phenomena, in what consists their agreement or +resemblance; I would willingly have confined myself to those better +understood expressions, and persevered to the end in the same abstinence +which I have hitherto observed from ideological discussions; considering +the mechanism of our thoughts to be a topic distinct from and irrelevant +to the principles and rules by which the trustworthiness of the results +of thinking is to be estimated. Since, however, a work of such high +pretensions, and, it must also be said, of <span class="pagenum"><a name="Page_192" id="Page_192">[Pg 192]</a></span>so much real merit, has +rested the whole theory of Induction upon such ideological +considerations, it seems necessary for others who follow, to claim for +themselves and their doctrines whatever position may properly belong to +them on the same metaphysical ground. And this is the object of the +succeeding chapter.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_193" id="Page_193">[Pg 193]</a></span></p> +<h3><a name="BOOK_IV_CHAPTER_II" id="BOOK_IV_CHAPTER_II"></a>CHAPTER II.<br /> +OF ABSTRACTION, OR THE FORMATION OF CONCEPTIONS.</h3> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_II_1">§ 1.</a> The metaphysical inquiry into the nature and composition of what +have been called Abstract Ideas, or in other words, of the notions which +answer in the mind to classes and to general names, belongs not to +Logic, but to a different science, and our purpose does not require that +we should enter upon it here. We are only concerned with the universally +acknowledged fact, that such notions or conceptions do exist. The mind +can conceive a multitude of individual things as one assemblage or +class; and general names do really suggest to us certain ideas or mental +representations, otherwise we could not use the names with consciousness +of a meaning. Whether the idea called up by a general name is composed +of the various circumstances in which all the individuals denoted by the +name agree, and of no others, (which is the doctrine of Locke, Brown, +and the Conceptualists;) or whether it be the idea of some one of those +individuals, clothed in its individualizing peculiarities, but with the +accompanying knowledge that those peculiarities are not properties of +the class, (which is the doctrine of Berkeley, Mr. Bailey,<a name="FNanchor_2_46" id="FNanchor_2_46"></a><a href="#Footnote_2_46" class="fnanchor">[2]</a> and the +modern Nominalists;) or whether (as held by Mr. James <span class="pagenum"><a name="Page_194" id="Page_194">[Pg 194]</a></span>Mill) the idea of +the class is that of a miscellaneous assemblage of individuals belonging +to the class; or whether, finally, (what appears to be the truest +opinion,) it be any one or any other of all these, according to the +accidental circumstances of the case; certain it is, that <i>some</i> idea or +mental conception is suggested by a general name, whenever we either +hear it or employ it with consciousness of a meaning. And this, which we +may call if we please a general idea, <i>represents</i> in our minds the +whole class of things to which the name is applied. Whenever we think or +reason concerning the class, we do so by means of this idea. And the +voluntary power which the mind has, of attending to one part of what is +present to it at any moment, and neglecting another part, enables us to +keep our reasonings and conclusions respecting the class unaffected by +anything in the idea or mental image which is not really, or at least +which we do not really believe to be, common to the whole class.<a name="FNanchor_3_47" id="FNanchor_3_47"></a><a href="#Footnote_3_47" class="fnanchor">[3]</a></p> + +<p>There are, then, such things as general conceptions, or conceptions by +means of which we can think generally: and when we form a set of +phenomena into a class, that is, when we compare them with one another +to ascertain in what they agree, some general conception is implied in +this mental operation. And inasmuch as such a comparison is a necessary +preliminary to Induction, it is most true that Induction could not go on +without general conceptions.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_II_2">§ 2.</a> But it does not therefore follow that these general conceptions +must have existed in the mind previously to the comparison. It is not a +law of our intellect, that in comparing things with each other and +taking note of their agreement we merely recognise as realized in the +outward world something that we already had in our minds. The conception +originally found its way to us as the <i>result</i> of such a comparison. It +was obtained (in metaphysical phrase) by <i>abstraction</i> from individual +things. These things may be things which we perceived or thought of on +former occasions, <span class="pagenum"><a name="Page_195" id="Page_195">[Pg 195]</a></span>but they may also be the things which we are +perceiving or thinking of on the very occasion. When Kepler compared the +observed places of the planet Mars, and found that they agreed in being +points of an elliptic circumference, he applied a general conception +which was already in his mind, having been derived from his former +experience. But this is by no means universally the case. When we +compare several objects and find them to agree in being white, or when +we compare the various species of ruminating animals and find them to +agree in being cloven-footed, we have just as much a general conception +in our minds as Kepler had in his: we have the conception of "a white +thing," or the conception of "a cloven-footed animal." But no one +supposes that we necessarily bring these conceptions with us, and +<i>superinduce</i> them (to adopt Dr. Whewell's expression) upon the facts: +because in these simple cases everybody sees that the very act of +comparison which ends in our connecting the facts by means of the +conception, may be the source from which we derive the conception +itself. If we had never seen any white object or had never seen any +cloven-footed animal before, we should at the same time and by the same +mental act acquire the idea, and employ it for the colligation of the +observed phenomena. Kepler, on the contrary, really had to bring the +idea with him, and superinduce it upon the facts; he could not evolve it +out of them: if he had not already had the idea, he would not have been +able to acquire it by a comparison of the planet's positions. But this +inability was a mere accident: the idea of an ellipse could have been +acquired from the paths of the planets as effectually as from anything +else, if the paths had not happened to be invisible. If the planet had +left a visible track, and we had been so placed that we could see it at +the proper angle, we might have abstracted our original idea of an +ellipse from the planetary orbit. Indeed, every conception which can be +made the instrument for connecting a set of facts, might have been +originally evolved from those very facts. The conception is a conception +<i>of</i> something; and that which it is a conception of, is really <i>in</i> the +facts, and might, under some supposable circumstances, or by some +supposable extension <span class="pagenum"><a name="Page_196" id="Page_196">[Pg 196]</a></span>of the faculties which we actually possess, have +been detected in them. And not only is this always in itself possible, +but it actually happens, in almost all cases in which the obtaining of +the right conception is a matter of any considerable difficulty. For if +there be no new conception required; if one of those already familiar to +mankind will serve the purpose, the accident of being the first to whom +the right one occurs, may happen to almost anybody; at least in the case +of a set of phenomena which the whole scientific world are engaged in +attempting to connect. The honour, in Kepler's case, was that of the +accurate, patient, and toilsome calculations by which he compared the +results that followed from his different guesses, with the observations +of Tycho Brahe; but the merit was very small of guessing an ellipse; the +only wonder is that men had not guessed it before, nor could they have +failed to do so if there had not existed an obstinate <i>à priori</i> +prejudice that the heavenly bodies must move, if not in a circle, in +some combination of circles.</p> + +<p>The really difficult cases are those in which the conception destined to +create light and order out of darkness and confusion, has to be sought +for among the very phenomena which it afterwards serves to arrange. Why, +according to Dr. Whewell himself, did the ancients fail in discovering +the laws of mechanics, that is, of equilibrium and of the communication +of motion? Because they had not, or at least had not clearly, the ideas +or conceptions of pressure and resistance, momentum, and uniform and +accelerating force. And whence could they have obtained these ideas, +except from the very facts of equilibrium and motion? The tardy +development of several of the physical sciences, for example of optics, +electricity, magnetism, and the higher generalizations of chemistry, he +ascribes to the fact that mankind had not yet possessed themselves of +the Idea of Polarity, that is, the idea of opposite properties in +opposite directions. But what was there to suggest such an idea, until, +by a separate examination of several of these different branches of +knowledge, it was shown that the facts of each of them did present, in +some instances <span class="pagenum"><a name="Page_197" id="Page_197">[Pg 197]</a></span>at least, the curious phenomenon of opposite properties +in opposite directions? The thing was superficially manifest only in two +cases, those of the magnet, and of electrified bodies; and there the +conception was encumbered with the circumstance of material poles, or +fixed points in the body itself, in which points this opposition of +properties seemed to be inherent. The first comparison and abstraction +had led only to this conception of poles; and if anything corresponding +to that conception had existed in the phenomena of chemistry or optics, +the difficulty now justly considered so great, would have been extremely +small. The obscurity rose from the fact, that the polarities in +chemistry and optics were distinct species, though of the same genus, +with the polarities in electricity and magnetism: and that in order to +assimilate the phenomena to one another, it was necessary to compare a +polarity without poles, such for instance as is exemplified in the +polarization of light, and the polarity with (apparent) poles, which we +see in the magnet; and to recognise that these polarities, while +different in many other respects, agree in the one character which is +expressed by the phrase, opposite properties in opposite directions. +From the result of such a comparison it was that the minds of scientific +men formed this new general conception: between which, and the first +confused feeling of an analogy between some of the phenomena of light +and those of electricity and magnetism, there is a long interval, filled +up by the labours and more or less sagacious suggestions of many +superior minds.</p> + +<p>The conceptions, then, which we employ for the colligation and +methodization of facts, do not develop themselves from within, but are +impressed upon the mind from without; they are never obtained otherwise +than by way of comparison and abstraction, and, in the most important +and the most numerous cases, are evolved by abstraction from the very +phenomena which it is their office to colligate. I am far, however, from +wishing to imply that it is not often a very difficult thing to perform +this process of abstraction well, or that the success of an inductive +operation does not, in many cases, principally depend on the skill with +which we perform it. Bacon was <span class="pagenum"><a name="Page_198" id="Page_198">[Pg 198]</a></span>quite justified in designating as one of +the principal obstacles to good induction, general conceptions wrongly +formed, "notiones temerè à rebus abstractæ:" to which Dr. Whewell adds, +that not only does bad abstraction make bad induction, but that in order +to perform induction well, we must have abstracted well; our general +conceptions must be "clear" and "appropriate" to the matter in hand.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_II_3">§ 3.</a> In attempting to show what the difficulty in this matter really is, +and how it is surmounted, I must beg the reader, once for all, to bear +this in mind; that although in discussing the opinions of a different +school of philosophy, I am willing to adopt their language, and to +speak, therefore, of connecting facts through the instrumentality of a +conception, this technical phraseology means neither more nor less than +what is commonly called comparing the facts with one another and +determining in what they agree. Nor has the technical expression even +the advantage of being metaphysically correct. The facts are not +<i>connected</i>, except in a merely metaphorical acceptation of the term. +The <i>ideas</i> of the facts may become connected, that is, we may be led to +think of them together; but this consequence is no more than what may be +produced by any casual association. What really takes place, is, I +conceive, more philosophically expressed by the common word Comparison, +than by the phrases "to connect" or "to superinduce." For, as the +general conception is itself obtained by a comparison of particular +phenomena, so, when obtained, the mode in which we apply it to other +phenomena is again by comparison. We compare phenomena with each other +to get the conception, and we then compare those and other phenomena +<i>with</i> the conception. We get the conception of an animal (for instance) +by comparing different animals, and when we afterwards see a creature +resembling an animal, we compare it with our general conception of an +animal; and if it agrees with that general conception, we include it in +the class. The conception becomes the type of comparison.</p> + +<p>And we need only consider what comparison is, to see that where the +objects are more than two, and still more when <span class="pagenum"><a name="Page_199" id="Page_199">[Pg 199]</a></span>they are an indefinite +number, a type of some sort is an indispensable condition of the +comparison. When we have to arrange and classify a great number of +objects according to their agreements and differences, we do not make a +confused attempt to compare all with all. We know that two things are as +much as the mind can easily attend to at a time, and we therefore fix +upon one of the objects, either at hazard or because it offers in a +peculiarly striking manner some important character, and, taking this as +our standard, compare it with one object after another. If we find a +second object which presents a remarkable agreement with the first, +inducing us to class them together, the question instantly arises, in +what particular circumstances do they agree? and to take notice of these +circumstances is already a first stage of abstraction, giving rise to a +general conception. Having advanced thus far, when we now take in hand a +third object we naturally ask ourselves the question, not merely whether +this third object agrees with the first, but whether it agrees with it +in the same circumstances in which the second did? in other words, +whether it agrees with the general conception which has been obtained by +abstraction from the first and second? Thus we see the tendency of +general conceptions, as soon as formed, to substitute themselves as +types, for whatever individual objects previously answered that purpose +in our comparisons. We may, perhaps, find that no considerable number of +other objects agree with this first general conception; and that we must +drop the conception, and beginning again with a different individual +case, proceed by fresh comparisons to a different general conception. +Sometimes, again, we find that the same conception will serve, by merely +leaving out some of its circumstances; and by this higher effort of +abstraction, we obtain a still more general conception; as in the case +formerly referred to, the scientific world rose from the conception of +poles to the general conception of opposite properties in opposite +directions; or as those South-Sea islanders, whose conception of a +quadruped had been abstracted from hogs (the only animals of that +description which they had seen), when they afterwards compared that +conception with other quadrupeds, dropped some of the <span class="pagenum"><a name="Page_200" id="Page_200">[Pg 200]</a></span>circumstances, +and arrived at the more general conception which Europeans associate +with the term.</p> + +<p>These brief remarks contain, I believe, all that is well-grounded in the +doctrine, that the conception by which the mind arranges and gives unity +to phenomena must be furnished by the mind itself, and that we find the +right conception by a tentative process, trying first one and then +another until we hit the mark. The conception is not furnished <i>by</i> the +mind until it has been furnished <i>to</i> the mind; and the facts which +supply it are sometimes extraneous facts, but more often the very facts +which we are attempting to arrange by it. It is quite true, however, +that in endeavouring to arrange the facts, at whatever point we begin, +we never advance three steps without forming a general conception, more +or less distinct and precise; and that this general conception becomes +the clue which we instantly endeavour to trace through the rest of the +facts, or rather, becomes the standard with which we thenceforth compare +them. If we are not satisfied with the agreements which we discover +among the phenomena by comparing them with this type, or with some still +more general conception which by an additional stage of abstraction we +can form from the type; we change our path, and look out for other +agreements: we recommence the comparison from a different +starting-point, and so generate a different set of general conceptions. +This is the tentative process which Dr. Whewell speaks of; and which has +not unnaturally suggested the theory, that the conception is supplied by +the mind itself: since the different conceptions which the mind +successively tries, it either already possessed from its previous +experience, or they were supplied to it in the first stage of the +corresponding act of comparison; so that, in the subsequent part of the +process, the conception manifested itself as something compared with the +phenomena, not evolved from them.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_II_4">§ 4.</a> If this be a correct account of the instrumentality of general +conceptions in the comparison which necessarily precedes Induction, we +shall easily be able to translate into our own language what Dr. Whewell +means by saying that conceptions, <span class="pagenum"><a name="Page_201" id="Page_201">[Pg 201]</a></span>to be subservient to Induction, must +be "clear" and "appropriate."</p> + +<p>If the conception corresponds to a real agreement among the phenomena; +if the comparison which we have made of a set of objects has led us to +class them according to real resemblances and differences; the +conception which does this cannot fail to be appropriate, for some +purpose or other. The question of appropriateness is relative to the +particular object we have in view. As soon as, by our comparison, we +have ascertained some agreement, something which can be predicated in +common of a number of objects; we have obtained a basis on which an +inductive process is capable of being founded. But the agreements, or +the ulterior consequences to which those agreements lead, may be of very +different degrees of importance. If, for instance, we only compare +animals according to their colour, and class those together which are +coloured alike, we form the general conceptions of a white animal, a +black animal, &c., which are conceptions legitimately formed; and if an +induction were to be attempted concerning the causes of the colours of +animals, this comparison would be the proper and necessary preparation +for such an induction, but would not help us towards a knowledge of the +laws of any other of the properties of animals: while if, with Cuvier, +we compare and class them according to the structure of the skeleton, +or, with Blainville, according to the nature of their outward +integuments, the agreements and differences which are observable in +these respects are not only of much greater importance in themselves, +but are marks of agreements and differences in many other important +particulars of the structure and mode of life of the animals. If, +therefore, the study of their structure and habits be our object, the +conceptions generated by these last comparisons are far more +"appropriate" than those generated by the former. Nothing, other than +this, can be meant by the appropriateness of a conception.</p> + +<p>When Dr. Whewell says that the ancients, or the schoolmen, or any modern +inquirers, missed discovering the real law of a phenomenon because they +applied to it an inappropriate instead of an appropriate conception; he +can only mean that <span class="pagenum"><a name="Page_202" id="Page_202">[Pg 202]</a></span>in comparing various instances of the phenomenon, to +ascertain in what those instances agreed, they missed the important +points of agreement; and fastened upon such as were either imaginary, +and not agreements at all, or if real agreements, were comparatively +trifling, and had no connexion with the phenomenon, the law of which was +sought.</p> + +<p>Aristotle, philosophizing on the subject of motion, remarked that +certain motions apparently take place spontaneously; bodies fall to the +ground, flame ascends, bubbles of air rise in water, &c.: and these he +called natural motions; while others not only never take place without +external incitement, but even when such incitement is applied, tend +spontaneously to cease; which, to distinguish them from the former, he +called violent motions. Now, in comparing the so-called natural motions +with one another, it appeared to Aristotle that they agreed in one +circumstance, namely, that the body which moved (or seemed to move) +spontaneously, was moving <i>towards its own place</i>; meaning thereby the +place from whence it originally came, or the place where a great +quantity of matter similar to itself was assembled. In the other class +of motions, as when bodies are thrown up in the air, they are, on the +contrary, moving <i>from</i> their own place. Now, this conception of a body +moving towards its own place may justly be considered inappropriate; +because, though it expresses a circumstance really found in some of the +most familiar instances of motion apparently spontaneous, yet, first, +there are many other cases of such motion, in which that circumstance is +absent: the motion, for instance, of the earth and planets. Secondly, +even when it is present, the motion, on closer examination, would often +be seen not to be spontaneous: as, when air rises in water, it does not +rise by its own nature, but is pushed up by the superior weight of the +water which presses upon it. Finally, there are many cases in which the +spontaneous motion takes place in the contrary direction to what the +theory considers as the body's own place; for instance, when a fog rises +from a lake, or when water dries up. The agreement, therefore, which +Aristotle selected as his principle of classification, did not extend to +all cases of the phenomenon he <span class="pagenum"><a name="Page_203" id="Page_203">[Pg 203]</a></span>wanted to study, spontaneous motion; +while it did include cases of the absence of the phenomenon, cases of +motion not spontaneous. The conception was hence "inappropriate." We may +add that, in the case in question, no conception would be appropriate; +there is no agreement which runs through all the cases of spontaneous or +apparently spontaneous motion and no others: they cannot be brought +under one law: it is a case of Plurality of Causes.<a name="FNanchor_4_48" id="FNanchor_4_48"></a><a href="#Footnote_4_48" class="fnanchor">[4]</a></p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_II_5">§ 5.</a> So much for the first of Dr. Whewell's conditions, that conceptions +must be appropriate. The second is, that they shall be "clear:" and let +us consider what this implies. Unless the conception corresponds to a +real agreement, it has a worse defect than that of not being clear; it +is not applicable to the case at all. Among the phenomena, therefore, +which we are attempting to connect by means of the conception, we must +suppose that there really is an agreement, and that the conception is a +conception of that agreement. In order, then, that it may be clear, the +only requisite is, that we shall know exactly in what the agreement +consists; that it shall have been carefully observed, and accurately +remembered. We are said not to have a clear conception of the +resemblance among a set of objects, when we have only a general <span class="pagenum"><a name="Page_204" id="Page_204">[Pg 204]</a></span>feeling +that they resemble, without having analysed their resemblance, or +perceived in what points it consists, and fixed in our memory an exact +recollection of those points. This want of clearness, or, as it may be +otherwise called, this vagueness, in the general conception, may be +owing either to our having no accurate knowledge of the objects +themselves, or merely to our not having carefully compared them. Thus a +person may have no clear idea of a ship because he has never seen one, +or because he remembers but little, and that faintly, of what he has +seen. Or he may have a perfect knowledge and remembrance of many ships +of various kinds, frigates among the rest, but he may have no clear but +only a confused idea of a frigate, because he has never been told, and +has not compared them sufficiently to have remarked and remembered, in +what particular points a frigate differs from some other kind of ship.</p> + +<p>It is not, however, necessary, in order to have clear ideas, that we +should know all the common properties of the things which we class +together. That would be to have our conception of the class complete as +well as clear. It is sufficient if we never class things together +without knowing exactly why we do so,—without having ascertained +exactly what agreements we are about to include in our conception; and +if, after having thus fixed our conception, we never vary from it, never +include in the class anything which has not those common properties, nor +exclude from it anything which has. A clear conception means a +determinate conception; one which does not fluctuate, which is not one +thing to-day and another to-morrow, but remains fixed and invariable, +except when, from the progress of our knowledge, or the correction of +some error, we consciously add to it or alter it. A person of clear +ideas, is a person who always knows in virtue of what properties his +classes are constituted; what attributes are connoted by his general +names.</p> + +<p>The principal requisites, therefore, of clear conceptions, are habits of +attentive observation, an extensive experience, and a memory which +receives and retains an exact image of what is observed. And in +proportion as any one has the habit of <span class="pagenum"><a name="Page_205" id="Page_205">[Pg 205]</a></span>observing minutely and comparing +carefully a particular class of phenomena, and an accurate memory for +the results of the observation and comparison, so will his conceptions +of that class of phenomena be clear; provided he has the indispensable +habit, (naturally, however, resulting from those other endowments,) of +never using general names without a precise connotation.</p> + +<p>As the clearness of our conceptions chiefly depends on the <i>carefulness</i> +and <i>accuracy</i> of our observing and comparing faculties, so their +appropriateness, or rather the chance we have of hitting upon the +appropriate conception in any case, mainly depends on the <i>activity</i> of +the same faculties. He who by habit, grounded on sufficient natural +aptitude, has acquired a readiness in accurately observing and comparing +phenomena, will perceive so many more agreements and will perceive them +so much more rapidly than other people, that the chances are much +greater of his perceiving, in any instance, the agreement on which the +important consequences depend.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_II_6">§ 6.</a> It is of so much importance that the part of the process of +investigating truth, discussed in this chapter, should be rightly +understood, that I think it is desirable to restate the results we have +arrived at, in a somewhat different mode of expression.</p> + +<p>We cannot ascertain general truths, that is, truths applicable to +classes, unless we have formed the classes in such a manner that general +truths can be affirmed of them. In the formation of any class, there is +involved a conception of it as a class, that is, a conception of certain +circumstances as being those which characterize the class, and +distinguish the objects composing it from all other things. When we know +exactly what these circumstances are, we have a clear idea (or +conception) of the class, and of the meaning of the general name which +designates it. The primary condition implied in having this clear idea, +is that the class be really a class; that it correspond to a real +distinction; that the things it includes really do agree with one +another in certain particulars, and differ, in those same particulars, +from all other things. A person without <span class="pagenum"><a name="Page_206" id="Page_206">[Pg 206]</a></span>clear ideas, is one who +habitually classes together, under the same general names, things which +have no common properties, or none which are not possessed also by other +things; or who, if the usage of other people prevents him from actually +misclassing things, is unable to state to himself the common properties +in virtue of which he classes them rightly.</p> + +<p>But it is not the sole requisite of classification that the classes +should be real classes, framed by a legitimate mental process. Some +modes of classing things are more valuable than others for human uses, +whether of speculation or of practice; and our classifications are not +well made, unless the things which they bring together not only agree +with each other in something which distinguishes them from all other +things, but agree with each other and differ from other things in the +very circumstances which are of primary importance for the purpose +(theoretical or practical) which we have in view, and which constitutes +the problem before us. In other words, our conceptions, though they may +be clear, are not <i>appropriate</i> for our purpose, unless the properties +we comprise in them are those which will help us towards what we wish to +understand—<i>i. e.</i>, either those which go deepest into the nature of +the things, if our object be to understand that, or those which are most +closely connected with the particular property which we are endeavouring +to investigate.</p> + +<p>We cannot, therefore, frame good general conceptions beforehand. That +the conception we have obtained is the one we want, can only be known +when we have done the work for the sake of which we wanted it; when we +completely understand the general character of the phenomena, or the +conditions of the particular property with which we concern ourselves. +General conceptions formed without this thorough knowledge, are Bacon's +"notiones temerè à rebus abstractæ." Yet such premature conceptions we +must be continually making up, in our progress to something better. They +are an impediment to the progress of knowledge, only when they are +permanently acquiesced in. When it has become our habit to group things +in wrong classes—in groups which either are not really classes, having +no distinctive points of agreement (absence of <i>clear</i> <span class="pagenum"><a name="Page_207" id="Page_207">[Pg 207]</a></span>ideas), or which +are not classes of which anything important to our purpose can be +predicated (absence of <i>appropriate</i> ideas); and when, in the belief +that these badly made classes are those sanctioned by Nature, we refuse +to exchange them for others, and cannot or will not make up our general +conceptions from any other elements; in that case all the evils which +Bacon ascribes to his "notiones temerè abstractæ" really occur. This was +what the ancients did in physics, and what the world in general does in +morals and politics to the present day.</p> + +<p>It would thus, in my view of the matter, be an inaccurate mode of +expression to say, that obtaining appropriate conceptions is a condition +precedent to generalization. Throughout the whole process of comparing +phenomena with one another for the purpose of generalization, the mind +is trying to make up a conception; but the conception which it is trying +to make up is that of the really important point of agreement in the +phenomena. As we obtain more knowledge of the phenomena themselves, and +of the conditions on which their important properties depend, our views +on this subject naturally alter; and thus we advance from a less to a +more "appropriate" general conception, in the progress of our +investigations.</p> + +<p>We ought not, at the same time, to forget that the really important +agreement cannot always be discovered by mere comparison of the very +phenomena in question, without the aid of a conception acquired +elsewhere; as in the case, so often referred to, of the planetary +orbits.</p> + +<p>The search for the agreement of a set of phenomena is in truth very +similar to the search for a lost or hidden object. At first we place +ourselves in a sufficiently commanding position, and cast our eyes round +us, and if we can see the object it is well; if not, we ask ourselves +mentally what are the places in which it may be hid, in order that we +may there search for it: and so on, until we imagine the place where it +really is. And here too we require to have had a previous conception, or +knowledge, of those different places. As in this familiar process, so in +the philosophical operation which <span class="pagenum"><a name="Page_208" id="Page_208">[Pg 208]</a></span>it illustrates, we first endeavour to +find the lost object or recognise the common attribute, without +conjecturally invoking the aid of any previously acquired conception, or +in other words, of any hypothesis. Having failed in this, we call upon +our imagination for some hypothesis of a possible place, or a possible +point of resemblance, and then look, to see whether the facts agree with +the conjecture.</p> + +<p>For such cases something more is required than a mind accustomed to +accurate observation and comparison. It must be a mind stored with +general conceptions, previously acquired, of the sorts which bear +affinity to the subject of the particular inquiry. And much will also +depend on the natural strength and acquired culture of what has been +termed the scientific imagination; on the faculty possessed of mentally +arranging known elements into new combinations, such as have not yet +been observed in nature, though not contradictory to any known laws.</p> + +<p>But the variety of intellectual habits, the purposes which they serve, +and the modes in which they may be fostered and cultivated, are +considerations belonging to the Art of Education: a subject far wider +than Logic, and which this treatise does not profess to discuss. Here, +therefore, the present chapter may properly close.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_209" id="Page_209">[Pg 209]</a></span></p> +<h3><a name="BOOK_IV_CHAPTER_III" id="BOOK_IV_CHAPTER_III"></a>CHAPTER III.<br /> +OF NAMING, AS SUBSIDIARY TO INDUCTION.</h3> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_III_1">§ 1.</a> It does not belong to the present undertaking to dwell on the +importance of language as a medium of human intercourse, whether for +purposes of sympathy or of information. Nor does our design admit of +more than a passing allusion to that great property of names, on which +their functions as an intellectual instrument are, in reality, +ultimately dependent; their potency as a means of forming, and of +riveting, associations among our other ideas: a subject on which an able +thinker<a name="FNanchor_5_49" id="FNanchor_5_49"></a><a href="#Footnote_5_49" class="fnanchor">[5]</a> has thus written:—</p> + +<p>"Names are impressions of sense, and as such take the strongest hold on +the mind, and of all other impressions can be most easily recalled and +retained in view. They therefore serve to give a point of attachment to +all the more volatile objects of thought and feeling. Impressions that +when passed might be dissipated for ever, are, by their connexion with +language, always within reach. Thoughts, of themselves, are perpetually +slipping out of the field of immediate mental vision; but the name +abides with us, and the utterance of it restores them in a moment. Words +are the custodiers of every product of mind less impressive than +themselves. All extensions of human knowledge, all new generalizations, +are fixed and spread, even unintentionally, by the use of words. The +child growing up learns, along with the vocables of his mother-tongue, +that things which he would have believed to be different, are, in +important points, the same. Without any formal instruction, the language +in which we grow up teaches us all the common philosophy of the age. It +directs us to observe and know things which we should have overlooked; +<span class="pagenum"><a name="Page_210" id="Page_210">[Pg 210]</a></span>it supplies us with classifications ready made, by which things are +arranged (as far as the light of by-gone generations admits) with the +objects to which they bear the greatest total resemblance. The number of +general names in a language, and the degree of generality of those +names, afford a test of the knowledge of the era, and of the +intellectual insight which is the birthright of any one born into it."</p> + +<p>It is not, however, of the functions of Names, considered generally, +that we have here to treat, but only of the manner and degree in which +they are directly instrumental to the investigation of truth; in other +words, to the process of induction.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_III_2">§ 2.</a> Observation and Abstraction, the operations which formed the +subject of the two foregoing chapters, are conditions indispensable to +induction; there can be no induction where they are not. It has been +imagined that Naming is also a condition equally indispensable. There +are thinkers who have held that language is not solely, according to a +phrase generally current, <i>an</i> instrument of thought, but <i>the</i> +instrument: that names, or something equivalent to them, some species of +artificial signs, are necessary to reasoning; that there could be no +inference, and consequently no induction, without them. But if the +nature of reasoning was correctly explained in the earlier part of the +present work, this opinion must be held to be an exaggeration, though of +an important truth. If reasoning be from particulars to particulars, and +if it consist in recognising one fact as a mark of another, or a mark of +a mark of another, nothing is required to render reasoning possible, +except senses and association: senses to perceive that two facts are +conjoined; association, as the law by which one of those two facts +raises up the idea of the other.<a name="FNanchor_6_50" id="FNanchor_6_50"></a><a href="#Footnote_6_50" class="fnanchor">[6]</a> For these mental phenomena, as well +as for the <span class="pagenum"><a name="Page_211" id="Page_211">[Pg 211]</a></span>belief or expectation which follows, and by which we +recognise as having taken place, or as about to take place, that of +which we have perceived a mark, there is evidently no need of language. +And this inference of one particular fact from another is a case of +induction. It is of this sort of induction that brutes are capable: it +is in this shape that uncultivated minds make almost all their +inductions, and that we all do so in the cases in which familiar +experience forces our conclusions upon us without any active process of +inquiry on our part, and in which the belief or expectation follows the +suggestion of the evidence, with the promptitude and certainty of an +instinct.<a name="FNanchor_7_51" id="FNanchor_7_51"></a><a href="#Footnote_7_51" class="fnanchor">[7]</a></p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_III_3">§ 3.</a> But though inference of an inductive character is possible without +the use of signs, it could never, without them, be carried much beyond +the very simple cases which we have just described, and which form, in +all probability, the limit of the reasonings of those animals to whom +conventional language is unknown. Without language, or something +equivalent to it, there could only be as much reasoning from experience +as can take place without the aid of general propositions. Now, though +in strictness we may reason from past experience to a fresh individual +case without the intermediate stage of a general proposition, yet +without general propositions we should seldom remember what past +experience we have had, and scarcely ever what conclusions that +experience will warrant. The division of the inductive process into two +parts, the first ascertaining what is a mark of the given fact, the +second whether in the new case that mark exists, <span class="pagenum"><a name="Page_212" id="Page_212">[Pg 212]</a></span>is natural, and +scientifically indispensable. It is, indeed, in a majority of cases, +rendered necessary by mere distance of time. The experience by which we +are to guide our judgments may be other people's experience, little of +which can be communicated to us otherwise than by language: when it is +our own, it is generally experience long past; unless, therefore, it +were recorded by means of artificial signs, little of it (except in +cases involving our intenser sensations or emotions, or the subjects of +our daily and hourly contemplation) would be retained in the memory. It +is hardly necessary to add, that when the inductive inference is of any +but the most direct and obvious nature—when it requires several +observations or experiments, in varying circumstances, and the +comparison of one of these with another—it is impossible to proceed a +step, without the artificial memory which words bestow. Without words, +we should, if we had often seen A and B in immediate and obvious +conjunction, expect B whenever we saw A; but to discover their +conjunction when not obvious, or to determine whether it is really +constant or only casual, and whether there is reason to expect it under +any given change of circumstances, is a process far too complex to be +performed without some contrivance to make our remembrance of our own +mental operations accurate. Now, language is such a contrivance. When +that instrument is called to our aid, the difficulty is reduced to that +of making our remembrance of the meaning of words accurate. This being +secured, whatever passes through our minds may be remembered accurately, +by putting it carefully into words, and committing the words either to +writing or to memory.</p> + +<p>The function of Naming, and particularly of General Names, in Induction, +may be recapitulated as follows. Every inductive inference which is good +at all, is good for a whole class of cases: and, that the inference may +have any better warrant of its correctness than the mere clinging +together of two ideas, a process of experimentation and comparison is +necessary; in which the whole class of cases must be brought to view, +and some uniformity in the course of nature evolved and ascertained, +since the existence of such an uniformity <span class="pagenum"><a name="Page_213" id="Page_213">[Pg 213]</a></span>is required as a +justification for drawing the inference in even a single case. This +uniformity, therefore, may be ascertained once for all; and if, being +ascertained, it can be remembered, it will serve as a formula for +making, in particular cases, all such inferences as the previous +experience will warrant. But we can only secure its being remembered, or +give ourselves even a chance of carrying in our memory any considerable +number of such uniformities, by registering them through the medium of +permanent signs; which (being, from the nature of the case, signs not of +an individual fact, but of an uniformity, that is, of an indefinite +number of facts similar to one another) are general signs; universals; +general names, and general propositions.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_III_4">§ 4.</a> And here I cannot omit to notice an oversight committed by some +eminent thinkers; who have said that the cause of our using general +names is the infinite multitude of individual objects, which, making it +impossible to have a name for each, compels us to make one name serve +for many. This is a very limited view of the function of general names. +Even if there were a name for every individual object, we should require +general names as much as we now do. Without them we could not express +the result of a single comparison, nor record any one of the +uniformities existing in nature; and should be hardly better off in +respect to Induction than if we had no names at all. With none but names +of individuals, (or in other words, proper names,) we might, by +pronouncing the name, suggest the idea of the object, but we could not +assert any proposition; except the unmeaning ones formed by predicating +two proper names one of another. It is only by means of general names +that we can convey any information, predicate any attribute, even of an +individual, much more of a class. Rigorously speaking we could get on +without any other general names than the abstract names of attributes; +all our propositions might be of the form "such an individual object +possesses such an attribute," or "such an attribute is always (or never) +conjoined with such another attribute." In fact, however, <span class="pagenum"><a name="Page_214" id="Page_214">[Pg 214]</a></span>mankind have +always given general names to objects as well as attributes, and indeed +before attributes: but the general names given to objects imply +attributes, derive their whole meaning from attributes; and are chiefly +useful as the language by means of which we predicate the attributes +which they connote.</p> + +<p>It remains to be considered what principles are to be adhered to in +giving general names, so that these names, and the general propositions +in which they fill a place, may conduce most to the purposes of +Induction.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_215" id="Page_215">[Pg 215]</a></span></p> +<h3><a name="BOOK_IV_CHAPTER_IV" id="BOOK_IV_CHAPTER_IV"></a>CHAPTER IV.<br /> +OF THE REQUISITES OF A PHILOSOPHICAL LANGUAGE, AND THE PRINCIPLES OF DEFINITION.</h3> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_IV_1">§ 1.</a> In order that we may possess a language perfectly suitable for the +investigation and expression of general truths, there are two principal, +and several minor, requisites. The first is, that every general name +should have a meaning, steadily fixed, and precisely determined. When, +by the fulfilment of this condition, such names as we possess are fitted +for the due performance of their functions, the next requisite, and the +second in order of importance, is that we should possess a name wherever +one is needed; wherever there is anything to be designated by it, which +it is of importance to express.</p> + +<p>The former of these requisites is that to which our attention will be +exclusively directed in the present chapter.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_IV_2">§ 2.</a> Every general name, then, must have a certain and knowable meaning. +Now the meaning (as has so often been explained) of a general +connotative name, resides in the connotation; in the attribute on +account of which, and to express which, the name is given. Thus, the +name animal being given to all things which possess the attributes of +sensation and voluntary motion, the word connotes those attributes +exclusively, and they constitute the whole of its meaning. If the name +be abstract, its denotation is the same with the connotation of the +corresponding concrete: it designates directly the attribute, which the +concrete term implies. To give a precise meaning to general names is, +then, to fix with steadiness the attribute or attributes connoted by +each concrete general name, and denoted by the corresponding abstract. +Since abstract names, in the order of their creation, <span class="pagenum"><a name="Page_216" id="Page_216">[Pg 216]</a></span>do not precede +but follow concrete ones, as is proved by the etymological fact that +they are almost always derived from them; we may consider their meaning +as determined by, and dependent on, the meaning of their concrete: and +thus the problem of giving a distinct meaning to general language, is +all included in that of giving a precise connotation to all concrete +general names.</p> + +<p>This is not difficult in the case of new names; of the technical terms +created by scientific inquirers for the purposes of science or art. But +when a name is in common use, the difficulty is greater; the problem in +this case not being that of choosing a convenient connotation for the +name, but of ascertaining and fixing the connotation with which it is +already used. That this can ever be a matter of doubt, is a sort of +paradox. But the vulgar (including in that term all who have not +accurate habits of thought) seldom know exactly what assertion they +intend to make, what common property they mean to express, when they +apply the same name to a number of different things. All which the name +expresses with them, when they predicate it of an object, is a confused +feeling of resemblance between that object and some of the other things +which they have been accustomed to denote by the name. They have applied +the name Stone to various objects previously seen; they see a new +object, which appears to them somewhat like the former, and they call it +a stone, without asking themselves in what respect it is like, or what +mode or degree of resemblance the best authorities, or even they +themselves, require as a warrant for using the name. This rough general +impression of resemblance is, however, made up of particular +circumstances of resemblance; and into these it is the business of the +logician to analyse it; to ascertain what points of resemblance among +the different things commonly called by the name, have produced in the +common mind this vague feeling of likeness; have given to the things the +similarity of aspect, which has made them a class, and has caused the +same name to be bestowed upon them.</p> + +<p>But though general names are imposed by the vulgar <span class="pagenum"><a name="Page_217" id="Page_217">[Pg 217]</a></span>without any more +definite connotation than that of a vague resemblance; general +propositions come in time to be made, in which predicates are applied to +those names, that is, general assertions are made concerning the <i>whole</i> +of the things which are denoted by the name. And since by each of these +propositions some attribute, more or less precisely conceived, is of +course predicated, the ideas of these various attributes thus become +associated with the name, and in a sort of uncertain way it comes to +connote them; there is a hesitation to apply the name in any new case in +which any of the attributes familiarly predicated of the class do not +exist. And thus, to common minds, the propositions which they are in the +habit of hearing or uttering concerning a class, make up in a loose way +a sort of connotation for the class-name. Let us take, for instance, the +word Civilized. How few could be found, even among the most educated +persons, who would undertake to say exactly what the term Civilized +connotes. Yet there is a feeling in the minds of all who use it, that +they are using it with a meaning; and this meaning is made up, in a +confused manner, of everything which they have heard or read that +civilized men, or civilized communities, are, or may be expected to be.</p> + +<p>It is at this stage, probably, in the progress of a concrete name, that +the corresponding abstract name generally comes into use. Under the +notion that the concrete name must of course convey a meaning, or in +other words, that there is some property common to all things which it +denotes, people give a name to this common property; from the concrete +Civilized, they form the abstract Civilization. But since most people +have never compared the different things which are called by the +concrete name, in such a manner as to ascertain what properties these +things have in common, or whether they have any; each is thrown back +upon the marks by which he himself has been accustomed to be guided in +his application of the term: and these, being merely vague hearsays and +current phrases, are not the same in any two persons, nor in the same +person at different times. Hence the word (as Civilization, for example) +which professes to be the designation of the <span class="pagenum"><a name="Page_218" id="Page_218">[Pg 218]</a></span>unknown common property, +conveys scarcely to any two minds the same idea. No two persons agree in +the things they predicate of it; and when it is itself predicated of +anything, no other person knows, nor does the speaker himself know with +precision, what he means to assert. Many other words which could be +named, as the word <i>honour</i>, or the word <i>gentleman</i>, exemplify this +uncertainty still more strikingly.</p> + +<p>It needs scarcely be observed, that general propositions of which no one +can tell exactly what they assert, cannot possibly have been brought to +the test of a correct induction. Whether a name is to be used as an +instrument of thinking, or as a means of communicating the result of +thought, it is imperative to determine exactly the attribute or +attributes which it is to express: to give it, in short, a fixed and +ascertained connotation.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_IV_3">§ 3.</a> It would, however, be a complete misunderstanding of the proper +office of a logician in dealing with terms already in use, if we were to +think that because a name has not at present an ascertained connotation, +it is competent to any one to give it such a connotation at his own +choice. The meaning of a term actually in use is not an arbitrary +quantity to be fixed, but an unknown quantity to be sought.</p> + +<p>In the first place, it is obviously desirable to avail ourselves, as far +as possible, of the associations already connected with the name; not +enjoining the employment of it in a manner which conflicts with all +previous habits, and especially not so as to require the rupture of +those strongest of all associations between names, which are created by +familiarity with propositions in which they are predicated of one +another. A philosopher would have little chance of having his example +followed, if he were to give such a meaning to his terms as should +require us to call the North American Indians a civilized people, or the +higher classes in France or England savages; or to say that civilized +people live by hunting, and savages by agriculture. Were there no other +reason, the extreme difficulty of effecting so complete a revolution in +<span class="pagenum"><a name="Page_219" id="Page_219">[Pg 219]</a></span>speech would be more than a sufficient one. The endeavour should be, +that all generally received propositions into which the term enters, +should be at least as true after its meaning is fixed, as they were +before; and that the concrete name, therefore, should not receive such a +connotation as shall prevent it from denoting things which, in common +language, it is currently affirmed of. The fixed and precise connotation +which it receives, should not be in deviation from, but in agreement (as +far as it goes) with, the vague and fluctuating connotation which the +term already had.</p> + +<p>To fix the connotation of a concrete name, or the denotation of the +corresponding abstract, is to define the name. When this can be done +without rendering any received assertions inadmissible, the name can be +defined in accordance with its received use, which is vulgarly called +defining not the name but the thing. What is meant by the improper +expression of defining a thing, (or rather a class of things—for nobody +talks of defining an individual,) is to define the name, subject to the +condition that it shall denote those things. This, of course, supposes a +comparison of the things, feature by feature and property by property, +to ascertain what attributes they agree in; and not unfrequently an +operation strictly inductive, for the purpose of ascertaining some +unobvious agreement, which is the cause of the obvious agreements.</p> + +<p>For, in order to give a connotation to a name, consistently with its +denoting certain objects, we have to make our selection from among the +various attributes in which those objects agree. To ascertain in what +they do agree is, therefore, the first logical operation requisite. When +this has been done as far as is necessary or practicable, the question +arises, which of these common attributes shall be selected to be +associated with the name. For if the class which the name denotes be a +Kind, the common properties are innumerable; and even if not, they are +often extremely numerous. Our choice is first limited by the preference +to be given to properties which are well known, and familiarly +predicated of the class; but even these are often too numerous to be all +included in the definition, and, besides, the properties most generally +known may <span class="pagenum"><a name="Page_220" id="Page_220">[Pg 220]</a></span>not be those which serve best to mark out the class from all +others. We should therefore select from among the common properties, (if +among them any such are to be found,) those on which it has been +ascertained by experience, or proved by deduction, that many others +depend; or at least which are sure marks of them, and from whence, +therefore, many others will follow by inference. We thus see that to +frame a good definition of a name already in use, is not a matter of +choice but of discussion, and discussion not merely respecting the usage +of language, but respecting the properties of things, and even the +origin of those properties. And hence every enlargement of our knowledge +of the objects to which the name is applied, is liable to suggest an +improvement in the definition. It is impossible to frame a perfect set +of definitions on any subject, until the theory of the subject is +perfect: and as science makes progress, its definitions are also +progressive.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_IV_4">§ 4.</a> The discussion of Definitions, in so far as it does not turn on the +use of words but on the properties of things, Dr. Whewell calls the +Explication of Conceptions. The act of ascertaining, better than before, +in what particulars any phenomena which are classed together agree, he +calls in his technical phraseology, unfolding the general conception in +virtue of which they are so classed. Making allowance for what appears +to me the darkening and misleading tendency of this mode of expression, +several of his remarks are so much to the purpose, that I shall take the +liberty of transcribing them.</p> + +<p>He observes,<a name="FNanchor_8_52" id="FNanchor_8_52"></a><a href="#Footnote_8_52" class="fnanchor">[8]</a> that many of the controversies which have had an +important share in the formation of the existing body of science, have +"assumed the form of a battle of Definitions. For example, the inquiry +concerning the laws of falling bodies, led to the question whether the +proper definition of a <i>uniform force</i> is that it generates a velocity +proportional to the <i>space</i> from rest, or to the <i>time</i>. The controversy +of the <i>vis viva</i> was what was the proper definition of the <i>measure of +force</i>. A <span class="pagenum"><a name="Page_221" id="Page_221">[Pg 221]</a></span>principal question in the classification of minerals is, what +is the definition of a <i>mineral species</i>. Physiologists have endeavoured +to throw light on their subject by defining <i>organization</i>, or some +similar term." Questions of the same nature are still open respecting +the definitions of Specific Heat, Latent Heat, Chemical Combination, and +Solution.</p> + +<p>"It is very important for us to observe, that these controversies have +never been questions of insulated and <i>arbitrary</i> definitions, as men +seem often tempted to imagine them to have been. In all cases there is a +tacit assumption of some proposition which is to be expressed by means +of the definition, and which gives it its importance. The dispute +concerning the definition thus acquires a real value, and becomes a +question concerning true and false. Thus in the discussion of the +question, What is a uniform force? it was taken for granted that gravity +is a uniform force. In the debate of the <i>vis viva</i>, it was assumed that +in the mutual action of bodies the whole effect of the force is +unchanged. In the zoological definition of species, (that it consists of +individuals which have, or may have, sprung from the same parents,) it +is presumed that individuals so related resemble each other more than +those which are excluded by such a definition; or, perhaps, that species +so defined have permanent and definite differences. A definition of +organization, or of some other term, which was not employed to express +some principle, would be of no value.</p> + +<p>"The establishment, therefore, of a right definition of a term, may be a +useful step in the explication of our conceptions; but this will be the +case then only when we have under our consideration some proposition in +which the term is employed. For then the question really is, how the +conception shall be understood and defined in order that the proposition +may be true.</p> + +<p>"To unfold our conceptions by means of definitions has never been +serviceable to science, except when it has been associated with an +immediate use of the definitions. The endeavour to define a Uniform +Force was combined with the assertion that gravity is a uniform force: +the attempt to <span class="pagenum"><a name="Page_222" id="Page_222">[Pg 222]</a></span>define Accelerating Force was immediately followed by +the doctrine that accelerating forces may be compounded: the process of +defining Momentum was connected with the principle that momenta gained +and lost are equal: naturalists would have given in vain the definition +of Species which we have quoted, if they had not also given the +characters of species so separated.... Definition may be the best mode +of explaining our conception, but that which alone makes it worth while +to explain it in any mode, is the opportunity of using it in the +expression of truth. When a definition is propounded to us as a useful +step in knowledge, we are always entitled to ask what principle it +serves to enunciate."</p> + +<p>In giving, then, an exact connotation to the phrase, "an uniform force," +the condition was understood, that the phrase should continue to denote +gravity. The discussion, therefore, respecting the definition, resolved +itself into this question, What is there of an uniform nature in the +motions produced by gravity? By observations and comparisons, it was +found, that what was uniform in those motions was the ratio of the +velocity acquired to the time elapsed; equal velocities being added in +equal times. An uniform force, therefore, was defined, a force which +adds equal velocities in equal times. So, again, in defining momentum. +It was already a received doctrine, that when two objects impinge upon +one another, the momentum lost by the one is equal to that gained by the +other. This proportion it was deemed necessary to preserve, not from the +motive (which operates in many other cases) that it was firmly fixed in +popular belief; for the proposition in question had never been heard of +by any but the scientifically instructed. But it was felt to contain a +truth: even a superficial observation of the phenomena left no doubt +that in the propagation of motion from one body to another, there was +something of which the one body gained precisely what the other lost; +and the word momentum had been invented to express this unknown +something. The settlement, therefore, of the definition of momentum, +involved the determination of the question, What is that of <span class="pagenum"><a name="Page_223" id="Page_223">[Pg 223]</a></span>which a +body, when it sets another body in motion, loses exactly as much as it +communicates? And when experiment had shown that this <i>something</i> was +the product of the velocity of the body by its mass, or quantity of +matter, this became the definition of momentum.</p> + +<p>The following remarks,<a name="FNanchor_9_53" id="FNanchor_9_53"></a><a href="#Footnote_9_53" class="fnanchor">[9]</a> therefore, are perfectly just: "The business +of definition is part of the business of discovery.... To define, so +that our definition shall have any scientific value, requires no small +portion of that sagacity by which truth is detected.... When it has been +clearly seen what ought to be our definition, it must be pretty well +known what truth we have to state. The definition, as well as the +discovery, supposes a decided step in our knowledge to have been made. +The writers on Logic, in the middle ages, made Definition the last stage +in the progress of knowledge; and in this arrangement at least, the +history of science, and the philosophy derived from the history, confirm +their speculative views." For in order to judge finally how the name +which denotes a class may best be defined, we must know all the +properties common to the class, and all the relations of causation or +dependence among those properties.</p> + +<p>If the properties which are fittest to be selected as marks of other +common properties are also obvious and familiar, and especially if they +bear a great part in producing that general air of resemblance which was +the original inducement to the formation of the class, the definition +will then be most felicitous. But it is often necessary to define the +class by some property not familiarly known, provided that property be +the best mark of those which are known. M. de Blainville, for instance, +founded his definition of life on the process of decomposition and +recomposition which incessantly takes place in every living body, so +that the particles composing it are never for two instants the same. +This is by no means one of the most obvious properties of living bodies; +it might escape altogether the notice of an unscientific observer. Yet +great authorities (independently of M. de Blainville, who is himself <span class="pagenum"><a name="Page_224" id="Page_224">[Pg 224]</a></span>a +first-rate authority) have thought that no other property so well +answers the conditions required for the definition.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_IV_5">§ 5.</a> Having laid down the principles which ought for the most part to be +observed in attempting to give a precise connotation to a term in use, I +must now add, that it is not always practicable to adhere to those +principles, and that even when practicable, it is occasionally not +desirable.</p> + +<p>Cases in which it is impossible to comply with all the conditions of a +precise definition of a name in agreement with usage, occur very +frequently. There is often no one connotation capable of being given to +a word, so that it shall still denote everything it is accustomed to +denote; or that all the propositions into which it is accustomed to +enter, and which have any foundation in truth, shall remain true. +Independently of accidental ambiguities, in which the different meanings +have no connexion with one another; it continually happens that a word +is used in two or more senses derived from each other, but yet radically +distinct. So long as a term is vague, that is, so long as its +connotation is not ascertained and permanently fixed, it is constantly +liable to be applied by <i>extension</i> from one thing to another, until it +reaches things which have little, or even no, resemblance to those which +were first designated by it.</p> + +<p>Suppose, says Dugald Stewart, in his <i>Philosophical Essays</i>,<a name="FNanchor_10_54" id="FNanchor_10_54"></a><a href="#Footnote_10_54" class="fnanchor">[10]</a> "that +the letters A, B, C, D, E, denote a series of objects; that A possesses +some one quality in common with B; B a quality in common with C; C a +quality in common with D; D a quality in common with E; while at the +same time, no quality can be found which belongs in common to any +<i>three</i> objects in the series. Is it not conceivable, that the affinity +between A and B may produce a transference of the name of the first to +the second; and that, in consequence of the other affinities which +connect the remaining objects together, the same name may pass in +succession from B to C; from C to D; and from D to E? In this manner, a +common <span class="pagenum"><a name="Page_225" id="Page_225">[Pg 225]</a></span>appellation will arise between A and E, although the two objects +may, in their nature and properties, be so widely distant from each +other, that no stretch of imagination can conceive how the thoughts were +led from the former to the latter. The transitions, nevertheless, may +have been all so easy and gradual, that, were they successfully detected +by the fortunate ingenuity of a theorist, we should instantly recognise, +not only the verisimilitude, but the truth of the conjecture: in the +same way as we admit, with the confidence of intuitive conviction, the +certainty of the well-known etymological process which connects the +Latin preposition <i>e</i> or <i>ex</i> with the English substantive <i>stranger</i>, +the moment that the intermediate links of the chain are submitted to our +examination."<a name="FNanchor_11_55" id="FNanchor_11_55"></a><a href="#Footnote_11_55" class="fnanchor">[11]</a></p> + +<p>The applications which a word acquires by this gradual extension of it +from one set of objects to another, Stewart, adopting an expression from +Mr. Payne Knight, calls its <i>transitive</i> applications; and after briefly +illustrating such of them as are the result of local or casual +associations, he proceeds as follows:<a name="FNanchor_12_56" id="FNanchor_12_56"></a><a href="#Footnote_12_56" class="fnanchor">[12]</a>—</p> + +<p>"But although by far the greater part of the transitive or derivative +applications of words depend on casual and unaccountable caprices of the +feelings or the fancy, there are certain cases in which they open a very +interesting field of philosophical speculation. Such are those, in which +an analogous transference of the corresponding term may be remarked +universally, or very generally, in other languages; and in which, of +course, the uniformity of the result must be ascribed to the essential +principles of the human frame. Even in such cases, however, it will by +no means be always found, on <span class="pagenum"><a name="Page_226" id="Page_226">[Pg 226]</a></span>examination, that the various applications +of the same term have arisen from any common quality or qualities in the +objects to which they relate. In the greater number of instances, they +may be traced to some natural and universal associations of ideas, +founded in the common faculties, common organs, and common condition of +the human race.... According to the different degrees of intimacy and +strength in the associations on which the <i>transitions</i> of language are +founded, very different effects may be expected to arise. Where the +association is slight and casual, the several meanings will remain +distinct from each other, and will often, in process of time, assume the +appearance of capricious varieties in the use of the same arbitrary +sign. <i>Where the association is so natural and habitual as to become +virtually indissoluble, the transitive meanings will coalesce in one +complex conception; and every new transition will become a more +comprehensive generalization of the term in question.</i>"</p> + +<p>I solicit particular attention to the law of mind expressed in the last +sentence, and which is the source of the perplexity so often experienced +in detecting these transitions of meaning. Ignorance of that law is the +shoal on which some of the most powerful intellects which have adorned +the human race have been stranded. The inquiries of Plato into the +definitions of some of the most general terms of moral speculation are +characterized by Bacon as a far nearer approach to a true inductive +method than is elsewhere to be found among the ancients, and are, +indeed, almost perfect examples of the preparatory process of comparison +and abstraction: but, from being unaware of the law just mentioned, he +often wasted the powers of this great logical instrument on inquiries in +which it could realize no result, since the phenomena, whose common +properties he so elaborately endeavoured to detect, had not really any +common properties. Bacon himself fell into the same error in his +speculations on the nature of heat, in which he evidently confounded +under the name hot, classes of phenomena which had no property in +common. Stewart certainly overstates the matter when he speaks of "a +prejudice which has descended <span class="pagenum"><a name="Page_227" id="Page_227">[Pg 227]</a></span>to modern times from the scholastic ages, +that when a word admits of a variety of significations, these different +significations must all be species of the same genus, and must +consequently include some essential idea common to every individual to +which the generic term can be applied:"<a name="FNanchor_13_57" id="FNanchor_13_57"></a><a href="#Footnote_13_57" class="fnanchor">[13]</a> for both Aristotle and his +followers were well aware that there are such things as ambiguities of +language, and delighted in distinguishing them. But they never suspected +ambiguity in the cases where (as Stewart remarks) the association on +which the transition of meaning was founded is so natural and habitual, +that the two meanings blend together in the mind, and a real transition +becomes an apparent generalization. Accordingly they wasted infinite +pains in endeavouring to find a definition which would serve for several +distinct meanings at once: as in an instance noticed by Stewart himself, +that of "causation; the ambiguity of the word which, in the Greek +language, corresponds to the English word <i>cause</i>, having suggested to +them the vain attempt of tracing the common idea which, in the case of +any <i>effect</i>, belongs to the <i>efficient</i>, to the <i>matter</i>, to the +<i>form</i>, and to the <i>end</i>. The idle generalities" (he adds) "we meet with +in other philosophers, about the ideas of the <i>good</i>, the <i>fit</i>, and the +<i>becoming</i>, have taken their rise from the same undue influence of +popular epithets on the speculations of the learned."<a name="FNanchor_14_58" id="FNanchor_14_58"></a><a href="#Footnote_14_58" class="fnanchor">[14]</a></p> + +<p>Among the words which have undergone so many successive transitions of +meaning that every trace of a property common to all the things they are +applied to, or at least common and also peculiar to those things, has +been lost, Stewart considers the word Beautiful to be one. And (without +attempting to decide a question which in no respect belongs to logic) I +cannot but feel, with him, considerable doubt, whether the word +beautiful connotes the same property when we speak of a beautiful +colour, a beautiful face, a beautiful scene, a beautiful character, and +a beautiful poem. The word was doubtless extended from one of these +objects <span class="pagenum"><a name="Page_228" id="Page_228">[Pg 228]</a></span>to another on account of a resemblance between them, or more +probably, between the emotions they excited; and, by this progressive +extension, it has at last reached things very remote from those objects +of sight to which there is no doubt that it was first appropriated; and +it is at least questionable whether there is now any property common to +all the things which, consistently with usage, may be called beautiful, +except the property of agreeableness, which the term certainly does +connote, but which cannot be all that people usually intend to express +by it, since there are many agreeable things which are never called +beautiful. If such be the case, it is impossible to give to the word +Beautiful any fixed connotation, such that it shall denote all the +objects which in common use it now denotes, but no others. A fixed +connotation, however, it ought to have; for, so long as it has not, it +is unfit to be used as a scientific term, and is a perpetual source of +false analogies and erroneous generalizations.</p> + +<p>This, then, constitutes a case in exemplification of our remark, that +even when there is a property common to all the things denoted by a +name, to erect that property into the definition and exclusive +connotation of the name is not always desirable. The various things +called beautiful unquestionably resemble one another in being agreeable; +but to make this the definition of beauty, and so extend the word +Beautiful to all agreeable things, would be to drop altogether a portion +of meaning which the word really, though indistinctly, conveys, and to +do what depends on us towards causing those qualities of the objects +which the word previously, though vaguely, pointed at, to be overlooked +and forgotten. It is better, in such a case, to give a fixed connotation +to the term by restricting, than by extending its use; rather excluding +from the epithet Beautiful some things to which it is commonly +considered applicable, than leaving out of its connotation any of the +qualities by which, though occasionally lost sight of, the general mind +may have been habitually guided in the commonest and most interesting +applications of the term. For there is no question that <span class="pagenum"><a name="Page_229" id="Page_229">[Pg 229]</a></span>when people +call anything beautiful, they think they are asserting more than that it +is merely agreeable. They think they are ascribing a peculiar <i>sort</i> of +agreeableness, analogous to that which they find in some other of the +things to which they are accustomed to apply the same name. If, +therefore, there be any peculiar sort of agreeableness which is common +though not to all, yet to the principal things which are called +beautiful, it is better to limit the denotation of the term to those +things, than to leave that kind of quality without a term to connote it, +and thereby divert attention from its peculiarities.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_IV_6">§ 6.</a> The last remark exemplifies a rule of terminology, which is of +great importance, and which has hardly yet been recognised as a rule, +but by a few thinkers of the present century. In attempting to rectify +the use of a vague term by giving it a fixed connotation, we must take +care not to discard (unless advisedly, and on the ground of a deeper +knowledge of the subject) any portion of the connotation which the word, +in however indistinct a manner, previously carried with it. For +otherwise language loses one of its inherent and most valuable +properties, that of being the conservator of ancient experience; the +keeper-alive of those thoughts and observations of former ages, which +may be alien to the tendencies of the passing time. This function of +language is so often overlooked or undervalued, that a few observations +on it appear to be extremely required.</p> + +<p>Even when the connotation of a term has been accurately fixed, and still +more if it has been left in the state of a vague unanalysed feeling of +resemblance; there is a constant tendency in the word, through familiar +use, to part with a portion of its connotation. It is a well-known law +of the mind, that a word originally associated with a very complex +cluster of ideas, is far from calling up all those ideas in the mind, +every time the word is used: it calls up only one or two, from which the +mind runs on by fresh associations to another set of ideas, without +waiting for the suggestion of the remainder of the complex cluster. If +this were not the case, processes of <span class="pagenum"><a name="Page_230" id="Page_230">[Pg 230]</a></span>thought could not take place with +anything like the rapidity which we know they possess. Very often, +indeed, when we are employing a word in our mental operations, we are so +far from waiting until the complex idea which corresponds to the meaning +of the word is consciously brought before us in all its parts, that we +run on to new trains of ideas by the other associations which the mere +word excites, without having realized in our imagination any part +whatever of the meaning: thus using the word, and even using it well and +accurately, and carrying on important processes of reasoning by means of +it, in an almost mechanical manner; so much so, that some +metaphysicians, generalizing from an extreme case, have fancied that all +reasoning is but the mechanical use of a set of terms according to a +certain form. We may discuss and settle the most important interests of +towns or nations, by the application of general theorems or practical +maxims previously laid down, without having had consciously suggested to +us, once in the whole process, the houses and green fields, the thronged +market-places and domestic hearths, of which not only those towns and +nations consist, but which the words town and nation confessedly mean.</p> + +<p>Since, then, general names come in this manner to be used (and even to +do a portion of their work well) without suggesting to the mind the +whole of their meaning, and often with the suggestion of a very small, +or no part at all of that meaning; we cannot wonder that words so used +come in time to be no longer capable of suggesting any other of the +ideas appropriated to them, than those with which the association is +most immediate and strongest, or most kept up by the incidents of life: +the remainder being lost altogether; unless the mind, by often +consciously dwelling on them, keeps up the association. Words naturally +retain much more of their meaning to persons of active imagination, who +habitually represent to themselves things in the concrete, with the +detail which belongs to them in the actual world. To minds of a +different description, the only antidote to this corruption of language +is predication. The habit of predicating of the name, all the various +properties which it originally connoted, <span class="pagenum"><a name="Page_231" id="Page_231">[Pg 231]</a></span>keeps up the association +between the name and those properties.</p> + +<p>But in order that it may do so, it is necessary that the predicates +should themselves retain their association with the properties which +they severally connote. For the propositions cannot keep the meaning of +the words alive, if the meaning of the propositions themselves should +die. And nothing is more common than for propositions to be mechanically +repeated, mechanically retained in the memory, and their truth +undoubtingly assented to and relied on, while yet they carry no meaning +distinctly home to the mind; and while the matter of fact or law of +nature which they originally expressed is as much lost sight of, and +practically disregarded, as if it never had been heard of at all. In +those subjects which are at the same time familiar and complicated, and +especially in those which are so in as great a degree as moral and +social subjects are, it is a matter of common remark how many important +propositions are believed and repeated from habit, while no account +could be given, and no sense is practically manifested, of the truths +which they convey. Hence it is, that the traditional maxims of old +experience, though seldom questioned, have often so little effect on the +conduct of life; because their meaning is never, by most persons, really +felt, until personal experience has brought it home. And thus also it is +that so many doctrines of religion, ethics, and even politics, so full +of meaning and reality to first converts, have manifested (after the +association of that meaning with the verbal formulas has ceased to be +kept up by the controversies which accompanied their first introduction) +a tendency to degenerate rapidly into lifeless dogmas; which tendency, +all the efforts of an education expressly and skilfully directed to +keeping the meaning alive, are barely sufficient to counteract.</p> + +<p>Considering, then, that the human mind, in different generations, +occupies itself with different things, and in one age is led by the +circumstances which surround it to fix more of its attention upon one of +the properties of a thing, in another age upon another; it is natural +and inevitable that in <span class="pagenum"><a name="Page_232" id="Page_232">[Pg 232]</a></span>every age a certain portion of our recorded and +traditional knowledge, not being continually suggested by the pursuits +and inquiries with which mankind are at that time engrossed, should fall +asleep, as it were, and fade from the memory. It would be in danger of +being totally lost, if the propositions or formulas, the results of the +previous experience, did not remain, as forms of words it may be, but of +words that once really conveyed, and are still supposed to convey, a +meaning: which meaning, though suspended, may be historically traced, +and when suggested, may be recognised by minds of the necessary +endowments as being still matter of fact, or truth. While the formulas +remain, the meaning may at any time revive; and as on the one hand the +formulas progressively lose the meaning they were intended to convey, +so, on the other, when this forgetfulness has reached its height and +begun to produce obvious consequences, minds arise which from the +contemplation of the formulas rediscover the truth, when truth it was, +which was contained in them, and announce it again to mankind, not as a +discovery, but as the meaning of that which they have been taught, and +still profess to believe.</p> + +<p>Thus there is a perpetual oscillation in spiritual truths, and in +spiritual doctrines of any significance, even when not truths. Their +meaning is almost always in a process either of being lost or of being +recovered. Whoever has attended to the history of the more serious +convictions of mankind—of the opinions by which the general conduct of +their lives is, or as they conceive ought to be, more especially +regulated—is aware that even when recognising verbally the same +doctrines, they attach to them at different periods a greater or a less +quantity, and even a different kind, of meaning. The words in their +original acceptation connoted, and the propositions expressed, a +complication of outward facts and inward feelings, to different portions +of which the general mind is more particularly alive in different +generations of mankind. To common minds, only that portion of the +meaning is in each generation suggested, of which that generation +possesses the counterpart in its own habitual experience. <span class="pagenum"><a name="Page_233" id="Page_233">[Pg 233]</a></span>But the words +and propositions lie ready to suggest to any mind duly prepared the +remainder of the meaning. Such individual minds are almost always to be +found: and the lost meaning, revived by them, again by degrees works its +way into the general mind.</p> + +<p>The arrival of this salutary reaction may however be materially +retarded, by the shallow conceptions and incautious proceedings of mere +logicians. It sometimes happens that towards the close of the downward +period, when the words have lost part of their significance, and have +not yet begun to recover it, persons arise whose leading and favourite +idea is the importance of clear conceptions and precise thought, and the +necessity, therefore, of definite language. These persons, in examining +the old formulas, easily perceive that words are used in them without a +meaning; and if they are not the sort of persons who are capable of +rediscovering the lost signification, they naturally enough dismiss the +formula, and define the name without reference to it. In so doing they +fasten down the name to what it connotes in common use at the time when +it conveys the smallest quantity of meaning; and introduce the practice +of employing it, consistently and uniformly, according to that +connotation. The word in this way acquires an extent of denotation far +beyond what it had before; it becomes extended to many things to which +it was previously, in appearance capriciously, refused. Of the +propositions in which it was formerly used, those which were true in +virtue of the forgotten part of its meaning are now, by the clearer +light which the definition diffuses, seen not to be true according to +the definition; which, however, is the recognised and sufficiently +correct expression of all that is perceived to be in the mind of any one +by whom the term is used at the present day. The ancient formulas are +consequently treated as prejudices; and people are no longer taught as +before, though not to understand them, yet to believe that there is +truth in them. They no longer remain in the general mind surrounded by +respect, and ready at any time to suggest their original meaning. +Whatever truths they contain are not only, in these circumstances, +rediscovered far more slowly, but, when rediscovered, <span class="pagenum"><a name="Page_234" id="Page_234">[Pg 234]</a></span>the prejudice +with which novelties are regarded is now, in some degree at least, +against them, instead of being on their side.</p> + +<p>An example may make these remarks more intelligible. In all ages, except +where moral speculation has been silenced by outward compulsion, or +where the feelings which prompt to it still continue to be satisfied by +the traditional doctrines of an established faith, one of the subjects +which have most occupied the minds of thinking persons is the inquiry, +What is virtue? or, What is a virtuous character? Among the different +theories on the subject which have, at different times, grown up and +obtained partial currency, every one of which reflected as in the +clearest mirror, the express image of the age which gave it birth; there +was one, according to which virtue consists in a correct calculation of +our own personal interests, either in this world only, or also in +another. To make this theory plausible, it was of course necessary that +the only beneficial actions which people in general were accustomed to +see, or were therefore accustomed to praise, should be such as were, or +at least might without contradicting obvious facts be supposed to be, +the result of a prudential regard to self-interest; so that the words +really connoted no more, in common acceptation, than was set down in the +definition.</p> + +<p>Suppose, now, that the partisans of this theory had contrived to +introduce a consistent and undeviating use of the term according to this +definition. Suppose that they had seriously endeavoured, and had +succeeded in the endeavour, to banish the word disinterestedness from +the language; had obtained the disuse of all expressions attaching odium +to selfishness or commendation to self-sacrifice, or which implied +generosity or kindness to be anything but doing a benefit in order to +receive a greater personal advantage in return. Need we say, that this +abrogation of the old formulas for the sake of preserving clear ideas +and consistency of thought, would have been a great evil? while the very +inconsistency incurred by the coexistence of the formulas with +philosophical opinions which seemed to condemn them as absurdities, +operated as a <span class="pagenum"><a name="Page_235" id="Page_235">[Pg 235]</a></span>stimulus to the re-examination of the subject; and thus +the very doctrines originating in the oblivion into which a part of the +truth had fallen, were rendered indirectly, but powerfully, instrumental +to its revival.</p> + +<p>The doctrine of the Coleridge school, that the language of any people +among whom culture is of old date, is a sacred deposit, the property of +all ages, and which no one age should consider itself empowered to +alter—borders indeed, as thus expressed, on an extravagance; but it is +grounded on a truth, frequently overlooked by that class of logicians +who think more of having a clear than of having a comprehensive meaning; +and who perceive that every age is adding to the truths which it has +received from its predecessors, but fail to see that a counter process +of losing truths already possessed, is also constantly going on, and +requiring the most sedulous attention to counteract it. Language is the +depository of the accumulated body of experience to which all former +ages have contributed their part, and which is the inheritance of all +yet to come. We have no right to prevent ourselves from transmitting to +posterity a larger portion of this inheritance than we may ourselves +have profited by. However much we may be able to improve on the +conclusions of our forefathers, we ought to be careful not inadvertently +to let any of their premises slip through our fingers. It may be good to +alter the meaning of a word, but it is bad to let any part of the +meaning drop. Whoever seeks to introduce a more correct use of a term +with which important associations are connected, should be required to +possess an accurate acquaintance with the history of the particular +word, and of the opinions which in different stages of its progress it +served to express. To be qualified to define the name, we must know all +that has ever been known of the properties of the class of objects which +are, or originally were, denoted by it. For if we give it a meaning +according to which any proposition will be false which has ever been +generally held to be true, it is incumbent on us to be sure that we know +and have considered all which those, who believed the proposition, +understood by it.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_236" id="Page_236">[Pg 236]</a></span></p> +<h3><a name="BOOK_IV_CHAPTER_V" id="BOOK_IV_CHAPTER_V"></a>CHAPTER V.<br /> +ON THE NATURAL HISTORY OF THE VARIATIONS IN THE MEANING OF TERMS.</h3> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_V_1">§ 1.</a> It is not only in the mode which has now been pointed out, namely +by gradual inattention to a portion of the ideas conveyed, that words in +common use are liable to shift their connotation. The truth is, that the +connotation of such words is perpetually varying; as might be expected +from the manner in which words in common use acquire their connotation. +A technical term, invented for purposes of art or science, has, from the +first, the connotation given to it by its inventor; but a name which is +in every one's mouth before any one thinks of defining it, derives its +connotation only from the circumstances which are habitually brought to +mind when it is pronounced. Among these circumstances, the properties +common to the things denoted by the name, have naturally a principal +place; and would have the sole place, if language were regulated by +convention rather than by custom and accident. But besides these common +properties, which if they exist are <i>certainly</i> present whenever the +name is employed, any other circumstance may <i>casually</i> be found along +with it, so frequently as to become associated with it in the same +manner, and as strongly, as the common properties themselves. In +proportion as this association forms itself, people give up using the +name in cases in which those casual circumstances do not exist. They +prefer using some other name, or the same name with some adjunct, rather +than employ an expression which will call up an idea they do not want to +excite. The circumstance originally casual, thus becomes regularly a +part of the connotation of the word.</p> + +<p><span class="pagenum"><a name="Page_237" id="Page_237">[Pg 237]</a></span></p><p>It is this continual incorporation of circumstances originally +accidental, into the permanent signification of words, which is the +cause that there are so few exact synonymes. It is this also which +renders the dictionary meaning of a word, by universal remark so +imperfect an exponent of its real meaning. The dictionary meaning is +marked out in a broad, blunt way, and probably includes all that was +originally necessary for the correct employment of the term; but in +process of time so many collateral associations adhere to words, that +whoever should attempt to use them with no other guide than the +dictionary, would confound a thousand nice distinctions and subtle +shades of meaning which dictionaries take no account of; as we notice in +the use of a language in conversation or writing by a foreigner not +thoroughly master of it. The history of a word, by showing the causes +which determine its use, is in these cases a better guide to its +employment than any definition; for definitions can only show its +meaning at the particular time, or at most the series of its successive +meanings, but its history may show the law by which the succession was +produced. The word <i>gentleman</i>, for instance, to the correct employment +of which a dictionary would be no guide, originally meant simply a man +born in a certain rank. From this it came by degrees to connote all such +qualities or adventitious circumstances as were usually found to belong +to persons of that rank. This consideration at once explains why in one +of its vulgar acceptations it means any one who lives without labour, in +another without manual labour, and in its more elevated signification it +has in every age signified the conduct, character, habits, and outward +appearance, in whomsoever found, which, according to the ideas of that +age, belonged or were expected to belong to persons born and educated in +a high social position.</p> + +<p>It continually happens that of two words, whose dictionary meanings are +either the same or very slightly different, one will be the proper word +to use in one set of circumstances, another in another, without its +being possible to show how the custom of so employing them originally +grew up. The accident <span class="pagenum"><a name="Page_238" id="Page_238">[Pg 238]</a></span>that one of the words was used and not the other +on a particular occasion or in a particular social circle, will be +sufficient to produce so strong an association between the word and some +speciality of circumstances, that mankind abandon the use of it in any +other case, and the speciality becomes part of its signification. The +tide of custom first drifts the word on the shore of a particular +meaning, then retires and leaves it there.</p> + +<p>An instance in point is the remarkable change which, in the English +language at least, has taken place in the signification of the word +<i>loyalty</i>. That word originally meant in English, as it still means in +the language from whence it came, fair, open dealing, and fidelity to +engagements; in that sense the quality it expressed was part of the +ideal chivalrous or knightly character. By what process, in England, the +term became restricted to the single case of fidelity to the throne, I +am not sufficiently versed in the history of courtly language to be able +to pronounce. The interval between a <i>loyal chevalier</i> and a loyal +subject is certainly great. I can only suppose that the word was, at +some period, the favourite term at court to express fidelity to the oath +of allegiance; until at length those who wished to speak of any other, +and as it was probably deemed, inferior sort of fidelity, either did not +venture to use so dignified a term, or found it convenient to employ +some other in order to avoid being misunderstood.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_V_2">§ 2.</a> Cases are not unfrequent in which a circumstance, at first casually +incorporated into the connotation of a word which originally had no +reference to it, in time wholly supersedes the original meaning, and +becomes not merely a part of the connotation, but the whole of it. This +is exemplified in the word pagan, <i>paganus</i>; which originally, as its +etymology imports, was equivalent to <i>villager</i>; the inhabitant of a +<i>pagus</i>, or village. At a particular era in the extension of +Christianity over the Roman empire, the adherents of the old religion, +and the villagers or country people, were nearly the <span class="pagenum"><a name="Page_239" id="Page_239">[Pg 239]</a></span>same body of +individuals, the inhabitants of the towns having been earliest +converted; as in our own day, and at all times, the greater activity of +social intercourse renders them the earliest recipients of new opinions +and modes, while old habits and prejudices linger longest among the +country people: not to mention that the towns were more immediately +under the direct influence of the government, which at that time had +embraced Christianity. From this casual coincidence, the word <i>paganus</i> +carried with it, and began more and more steadily to suggest, the idea +of a worshipper of the ancient divinities; until at length it suggested +that idea so forcibly that people who did not desire to suggest the idea +avoided using the word. But when <i>paganus</i> had come to connote +heathenism, the very unimportant circumstance, with reference to that +fact, of the place of residence, was soon disregarded in the employment +of the word. As there was seldom any occasion for making separate +assertions respecting heathens who lived in the country, there was no +need for a separate word to denote them; and pagan came not only to mean +heathen, but to mean that exclusively.</p> + +<p>A case still more familiar to most readers is that of the word <i>villain</i> +or <i>villein</i>. This term, as everybody knows, had in the middle ages a +connotation as strictly defined as a word could have, being the proper +legal designation for those persons who were the subjects of the less +onerous forms of feudal bondage. The scorn of the semibarbarous military +aristocracy for these their abject dependants, rendered the act of +likening any person to this class of people a mark of the greatest +contumely: the same scorn led them to ascribe to the same people all +manner of hateful qualities, which doubtless also, in the degrading +situation in which they were held, were often not unjustly imputed to +them. These circumstances combined to attach to the term villain, ideas +of crime and guilt in so forcible a manner, that the application of the +epithet even to those to whom it legally belonged became an affront, and +was abstained from whenever no affront was intended. From that time +guilt was part of the connotation; and soon became the whole <span class="pagenum"><a name="Page_240" id="Page_240">[Pg 240]</a></span>of it, +since mankind were not prompted by any urgent motive to continue making +a distinction in their language between bad men of servile station and +bad men of any other rank in life.</p> + +<p>These and similar instances in which the original signification of a +term is totally lost—another and an entirely distinct meaning being +first engrafted upon the former, and finally substituted for it—afford +examples of the double movement which is always taking place in +language: two counter-movements, one of Generalization, by which words +are perpetually losing portions of their connotation, and becoming of +less meaning and more general acceptation; the other of Specialization, +by which other, or even these same words, are continually taking on +fresh connotation; acquiring additional meaning, by being restricted in +their employment to a part only of the occasions on which they might +properly be used before. This double movement is of sufficient +importance in the natural history of language, (to which natural history +the artificial modifications ought always to have some degree of +reference,) to justify our dwelling a little longer on the nature of the +twofold phenomenon, and the causes to which it owes its existence.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_V_3">§ 3.</a> To begin with the movement of generalization. It is unnecessary to +dwell on the changes in the meaning of names which take place merely +from their being used ignorantly, by persons who, not having properly +mastered the received connotation of a word, apply it in a looser and +wider sense than belongs to it. This, however, is a real source of +alterations in the language; for when a word, from being often employed +in cases where one of the qualities which it connotes does not exist, +ceases to suggest that quality with certainty, then even those who are +under no mistake as to the proper meaning of the word, prefer expressing +that meaning in some other way, and leave the original word to its fate. +The word 'Squire as standing for an owner of a landed estate; Parson, as +denoting not the rector of the parish, but clergymen in general; Artist, +to denote only a painter or sculptor; are <span class="pagenum"><a name="Page_241" id="Page_241">[Pg 241]</a></span>cases in point.<a name="FNanchor_15_59" id="FNanchor_15_59"></a><a href="#Footnote_15_59" class="fnanchor">[15]</a> +Independently, however, of the generalization of names through their +ignorant misuse, there is a tendency in the same direction, consistently +with a perfect knowledge of their meaning; arising from the fact, that +the number of <span class="pagenum"><a name="Page_242" id="Page_242">[Pg 242]</a></span>things known to us, and of which we feel a desire to +speak, multiply faster than the names for them. Except on subjects for +which there has been constructed a scientific terminology, with which +unscientific persons do not meddle, great difficulty is generally found +in bringing a new name into use; and independently of that difficulty, +it is natural to prefer giving to a new object a name which at least +expresses its resemblance to something already known, since by +predicating of it a name entirely new we at first convey no information. +In this manner the name of a species often becomes the name of a genus; +as <i>salt</i>, for example, or <i>oil</i>; the former of which words originally +denoted only the muriate of soda, the latter, as its etymology +indicates, only olive oil; but which now denote large and diversified +classes of substances resembling these in some of their qualities, and +connote only those common qualities, instead of the whole of the +distinctive properties of olive oil and sea salt. The words <i>glass</i> and +<i>soap</i> are used by modern chemists in a similar manner, to denote genera +of which the substances vulgarly so called are single species. And it +often happens, as in those instances, that the term keeps its special +signification in addition to its more general one, and becomes +ambiguous, that is, two names instead of one.</p> + +<p>These changes, by which words in ordinary use become more and more +generalized, and less and less expressive, take place in a still greater +degree with the words which express the complicated phenomena of mind +and society. Historians, <span class="pagenum"><a name="Page_243" id="Page_243">[Pg 243]</a></span>travellers, and in general those who speak or +write concerning moral and social phenomena with which they are not +familiarly acquainted, are the great agents in this modification of +language. The vocabulary of all except unusually instructed as well as +thinking persons, is, on such subjects, eminently scanty. They have a +certain small set of words to which they are accustomed, and which they +employ to express phenomena the most heterogeneous, because they have +never sufficiently analysed the facts to which those words correspond in +their own country, to have attached perfectly definite ideas to the +words. The first English conquerors of Bengal, for example, carried with +them the phrase <i>landed proprietor</i> into a country where the rights of +individuals over the soil were extremely different in degree, and even +in nature, from those recognised in England. Applying the term with all +its English associations in such a state of things; to one who had only +a limited right they gave an absolute right, from another because he had +not an absolute right they took away all right, drove whole classes of +people to ruin and despair, filled the country with banditti, created a +feeling that nothing was secure, and produced, with the best intentions, +a disorganization of society which had not been produced in that country +by the most ruthless of its barbarian invaders. Yet the usage of persons +capable of so gross a misapprehension, determines the meaning of +language; and the words they thus misuse grow in generality, until the +instructed are obliged to acquiesce; and to employ those words (first +freeing them from vagueness by giving them a definite connotation) as +generic terms, subdividing the genera into species.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_V_4">§ 4.</a> While the more rapid growth of ideas than of names thus creates a +perpetual necessity for making the same names serve, even if +imperfectly, on a greater number of occasions; a counter-operation is +going on, by which names become on the contrary restricted to fewer +occasions, by taking on, as it were, additional connotation, from +circumstances not originally included in the meaning, but which have +become connected with it in the mind by some accidental cause. We <span class="pagenum"><a name="Page_244" id="Page_244">[Pg 244]</a></span>have +seen above, in the words <i>pagan</i> and <i>villain</i>, remarkable examples of +the specialization of the meaning of words from casual associations, as +well as of the generalization of it in a new direction, which often +follows.</p> + +<p>Similar specializations are of frequent occurrence in the history even +of scientific nomenclature. "It is by no means uncommon," says Dr. +Paris, in his <i>Pharmacologia</i>,<a name="FNanchor_16_60" id="FNanchor_16_60"></a><a href="#Footnote_16_60" class="fnanchor">[16]</a> "to find a word which is used to +express general characters subsequently become the name of a specific +substance in which such characters are predominant; and we shall find +that some important anomalies in nomenclature may be thus explained. The +term <i>Αρσενίκον</i>, from which the word Arsenic is derived, was an +ancient epithet applied to those natural substances which possessed +strong and acrimonious properties, and as the poisonous quality of +arsenic was found to be remarkably powerful, the term was especially +applied to Orpiment, the form in which this metal most usually occurred. +So the term <i>Verbena</i> (quasi <i>Herbena</i>) originally denoted all those +herbs that were held sacred on account of their being employed in the +rites of sacrifice, as we learn from the poets; but as <i>one</i> herb was +usually adopted upon these occasions, the word Verbena came to denote +that particular herb <i>only</i>, and it is transmitted to us to this day +under the same title, viz. Verbena or Vervain, and indeed until lately +it enjoyed the medical reputation which its sacred origin conferred upon +it, for it was worn suspended around the neck as an amulet. <i>Vitriol</i>, +in the original application of the word, denoted <i>any</i> crystalline body +with a certain degree of transparency (<i>vitrum</i>); it is hardly necessary +to observe that the term is now appropriated to a particular species: in +the same manner, Bark, which is a general term, is applied to express +<i>one</i> genus, and by way of eminence, it has the article <i>The</i> prefixed, +as <i>The</i> bark: the same observation will apply to the word Opium, which, +in its primitive sense, signifies <i>any</i> juice (<i>ὀπὸς</i>, <i>Succus</i>), +while it now only denotes <i>one</i> species, viz. that of the poppy. So, +again, <i>Elaterium</i> was used by Hippocrates to signify <span class="pagenum"><a name="Page_245" id="Page_245">[Pg 245]</a></span>various internal +applications, especially purgatives, of a violent and drastic nature +(from the word <i>ἐλαύνω</i>, <i>agito</i>, <i>moveo</i>, <i>stimulo</i>), but by +succeeding authors it was exclusively applied to denote the active +matter which subsides from the juice of the wild cucumber. The word +<i>Fecula</i>, again, originally meant to imply <i>any</i> substance which was +derived by spontaneous subsidence from a liquid (from <i>fæx</i>, the grounds +or settlement of <i>any</i> liquor); afterwards it was applied to Starch, +which is deposited in this manner by agitating the flour of wheat in +water; and lastly, it has been applied to a peculiar vegetable +principle, which, like starch, is insoluble in cold, but completely +soluble in boiling water, with which it forms a gelatinous solution. +This indefinite meaning of the word <i>fecula</i> has created numerous +mistakes in pharmaceutic chemistry; Elaterium, for instance, is said to +be <i>fecula</i>, and, in the original sense of the word, it is properly so +called, inasmuch as it is procured from a vegetable juice by spontaneous +subsidence, but in the limited and modern acceptation of the term, it +conveys an erroneous idea; for instead of the active principle of the +juice residing in <i>fecula</i>, it is a peculiar proximate principle, <i>sui +generis</i>, to which I have ventured to bestow the name of <i>Elatin</i>. For +the same reason, much doubt and obscurity involve the meaning of the +word <i>Extract</i>, because it is applied <i>generally</i> to any substance +obtained by the evaporation of a vegetable solution, and <i>specifically</i> +to a peculiar proximate principle, possessed of certain characters, by +which it is distinguished from every other elementary body."</p> + +<p>A generic term is always liable to become thus limited to a single +species, or even individual, if people have occasion to think and speak +of that individual or species much oftener than of anything else which +is contained in the genus. Thus by cattle, a stage-coachman will +understand horses; beasts, in the language of agriculturists, stands for +oxen; and birds, with some sportsmen, for partridges only. The law of +language which operates in these trivial instances, is the very same in +conformity to which the terms Θεός, Deus, and God, were +adopted from Polytheism by Christianity, to express the single object of +its own adoration. Almost all the terminology <span class="pagenum"><a name="Page_246" id="Page_246">[Pg 246]</a></span>of the Christian Church +is made up of words originally used in a much more general acceptation: +<i>Ecclesia</i>, Assembly; <i>Bishop</i>, Episcopus, Overseer; <i>Priest</i>, +Presbyter, Elder; <i>Deacon</i>, Diaconus, Administrator; <i>Sacrament</i>, a vow +of allegiance; <i>Evangelium</i>, good tidings; and some words, as +<i>Minister</i>, are still used both in the general and in the limited sense. +It would be interesting to trace the progress by which <i>author</i> came, in +its most familiar sense, to signify a writer, and <i>ποίητης</i>, or +maker, a poet.</p> + +<p>Of the incorporation into the meaning of a term, of circumstances +accidentally connected with it at some particular period, as in the case +of Pagan, instances might easily be multiplied. Physician (<i>φυσίκος</i>, or naturalist) became, in England, synonymous with a healer +of diseases, because until a comparatively late period medical +practitioners were the only naturalists. <i>Clerc</i>, or clericus, a +scholar, came to signify an ecclesiastic, because the clergy were for +many centuries the only scholars.</p> + +<p>Of all ideas, however, the most liable to cling by association to +anything with which they have ever been connected by proximity, are +those of our pleasures and pains, or of the things which we habitually +contemplate as sources of our pleasures or pains. The additional +connotation, therefore, which a word soonest and most readily takes on, +is that of agreeableness or painfulness, in their various kinds and +degrees: of being a good or bad thing; desirable or to be avoided; an +object of hatred, of dread, contempt, admiration, hope, or love. +Accordingly there is hardly a single name, expressive of any moral or +social fact calculated to call forth strong affections either of a +favourable or of a hostile nature, which does not carry with it +decidedly and irresistibly a connotation of those strong affections, or, +at the least, of approbation or censure; insomuch that to employ those +names in conjunction with others by which the contrary sentiments were +expressed, would produce the effect of a paradox, or even a +contradiction in terms. The baneful influence of a connotation thus +acquired, on the prevailing habits of thought, especially in morals and +politics, has been well pointed out on <span class="pagenum"><a name="Page_247" id="Page_247">[Pg 247]</a></span>many occasions by Bentham. It +gives rise to the fallacy of "question-begging names." The very property +which we are inquiring whether a thing possesses or not, has become so +associated with the name of the thing as to be part of its meaning, +insomuch that by merely uttering the name we assume the point which was +to be made out: one of the most frequent sources of apparently +self-evident propositions.</p> + +<p>Without any further multiplication of examples to illustrate the changes +which usage is continually making in the signification of terms, I shall +add, as a practical rule, that the logician, not being able to prevent +such transformations, should submit to them with a good grace when they +are irrevocably effected, and if a definition is necessary, define the +word according to its new meaning; retaining the former as a second +signification, if it is needed, and if there is any chance of being able +to preserve it either in the language of philosophy or in common use. +Logicians cannot <i>make</i> the meaning of any but scientific terms: that of +all other words is made by the collective human race. But logicians can +ascertain clearly what it is which, working obscurely, has guided the +general mind to a particular employment of a name; and when they have +found this, they can clothe it in such distinct and permanent terms, +that mankind shall see the meaning which before they only felt, and +shall not suffer it to be afterwards forgotten or misapprehended.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_248" id="Page_248">[Pg 248]</a></span></p> +<h3><a name="BOOK_IV_CHAPTER_VI" id="BOOK_IV_CHAPTER_VI"></a>CHAPTER VI.<br /> +THE PRINCIPLES OF A PHILOSOPHICAL LANGUAGE FURTHER CONSIDERED.</h3> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VI_1">§ 1.</a> We have, thus far, considered only one of the requisites of a +language adapted for the investigation of truth; that its terms shall +each of them convey a determinate and unmistakeable meaning. There are, +however, as we have already remarked, other requisites; some of them +important only in the second degree, but one which is fundamental, and +barely yields in point of importance, if it yields at all, to the +quality which we have already discussed at so much length. That the +language may be fitted for its purposes, not only should every word +perfectly express its meaning, but there should be no important meaning +without its word. Whatever we have occasion to think of often, and for +scientific purposes, ought to have a name appropriated to it.</p> + +<p>This requisite of philosophical language may be considered under three +different heads; that number of separate conditions being involved in +it.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VI_2">§ 2.</a> First: there ought to be all such names, as are needful for making +such a record of individual observations that the words of the record +shall exactly show what fact it is which has been observed. In other +words, there should be an accurate Descriptive Terminology.</p> + +<p>The only things which we can observe directly being our own sensations, +or other feelings, a complete descriptive language would be one in which +there should be a name for every variety of elementary sensation or +feeling. Combinations of sensations or feelings may always be described, +if we have a name for each of the elementary feelings which compose +them; but brevity of description, and clearness <span class="pagenum"><a name="Page_249" id="Page_249">[Pg 249]</a></span>(which often depends +very much on brevity,) are greatly promoted by giving distinctive names +not to the elements alone, but also to all combinations which are of +frequent recurrence. On this occasion I cannot do better than quote from +Dr. Whewell<a name="FNanchor_17_61" id="FNanchor_17_61"></a><a href="#Footnote_17_61" class="fnanchor">[17]</a> some of the excellent remarks which he has made on this +important branch of our subject.</p> + +<p>"The meaning of [descriptive] technical terms can be fixed in the first +instance only by convention, and can be made intelligible only by +presenting to the senses that which the terms are to signify. The +knowledge of a colour by its name can only be taught through the eye. No +description can convey to a hearer what we mean by <i>apple-green</i> or +<i>French-grey</i>. It might, perhaps, be supposed that, in the first +example, the term <i>apple</i>, referring to so familiar an object, +sufficiently suggests the colour intended. But it may easily be seen +that this is not true; for apples are of many different hues of green, +and it is only by a conventional selection that we can appropriate the +term to one special shade. When this appropriation is once made, the +term refers to the sensation, and not to the parts of the term; for +these enter into the compound merely as a help to the memory, whether +the suggestion be a natural connexion as in 'apple-green,' or a casual +one as in 'French-grey.' In order to derive due advantage from technical +terms of this kind, they must be associated <i>immediately</i> with the +perception to which they belong; and not connected with it through the +vague usages of common language. The memory must retain the sensation; +and the technical word must be understood as directly as the most +familiar word, and more distinctly. When we find such terms as +<i>tin-white</i> or <i>pinchbeck-brown</i>, the metallic colour so denoted ought +to start up in our memory without delay or search.</p> + +<p>"This, which it is most important to recollect with respect to the +simpler properties of bodies, as colour and form, is no less true with +respect to more compound notions. In all cases the term is fixed to a +peculiar meaning by convention; <span class="pagenum"><a name="Page_250" id="Page_250">[Pg 250]</a></span>and the student, in order to use the +word, must be completely familiar with the convention, so that he has no +need to frame conjectures from the word itself. Such conjectures would +always be insecure, and often erroneous. Thus the term <i>papilionaceous</i> +applied to a flower is employed to indicate, not only a resemblance to a +butterfly, but a resemblance arising from five petals of a certain +peculiar shape and arrangement; and even if the resemblance were much +stronger than it is in such cases, yet, if it were produced in a +different way, as for example, by one petal, or two only, instead of a +'standard,' two 'wings,' and a 'keel' consisting of two parts more or +less united into one, we should be no longer justified in speaking of it +as a 'papilionaceous' flower."</p> + +<p>When, however, the thing named is, as in this last case, a combination +of simple sensations, it is not necessary, in order to learn the meaning +of the word, that the student should refer back to the sensations +themselves; it may be communicated to him through the medium of other +words; the terms, in short, may be defined. But the names of elementary +sensations, or elementary feelings of any sort, cannot be defined; nor +is there any mode of making their signification known but by making the +learner experience the sensation, or referring him, through some known +mark, to his remembrance of having experienced it before. Hence it is +only the impressions on the outward senses, or those inward feelings +which are connected in a very obvious and uniform manner with outward +objects, that are really susceptible of an exact descriptive language. +The countless variety of sensations which arise, for instance, from +disease, or from peculiar physiological states, it would be in vain to +attempt to name; for as no one can judge whether the sensation I have is +the same with his, the name cannot have, to us two, real community of +meaning. The same may be said, to a considerable extent, of purely +mental feelings. But in some of the sciences which are conversant with +external objects, it is scarcely possible to surpass the perfection to +which this quality of a philosophical language has been carried.</p> + +<p><span class="pagenum"><a name="Page_251" id="Page_251">[Pg 251]</a></span></p><p>"The formation<a name="FNanchor_18_62" id="FNanchor_18_62"></a><a href="#Footnote_18_62" class="fnanchor">[18]</a> of an exact and extensive descriptive language for +botany has been executed with a degree of skill and felicity, which, +before it was attained, could hardly have been dreamt of as attainable. +Every part of a plant has been named; and the form of every part, even +the most minute, has had a large assemblage of descriptive terms +appropriated to it, by means of which the botanist can convey and +receive knowledge of form and structure, as exactly as if each minute +part were presented to him vastly magnified. This acquisition was part +of the Linnæan reform.... 'Tournefort,' says Decandolle, 'appears to +have been the first who really perceived the utility of fixing the sense +of terms in such a way as always to employ the same word in the same +sense, and always to express the same idea by the same words; but it was +Linnæus who really created and fixed this botanical language, and this +is his fairest claim to glory, for by this fixation of language he has +shed clearness and precision over all parts of the science.'</p> + +<p>"It is not necessary here to give any detailed account of the terms of +botany. The fundamental ones have been gradually introduced, as the +parts of plants were more carefully and minutely examined. Thus the +flower was necessarily distinguished into the <i>calyx</i>, the <i>corolla</i>, +the <i>stamens</i>, and the <i>pistils</i>; the sections of the corolla were +termed <i>petals</i> by Columna; those of the calyx were called <i>sepals</i> by +Necker. Sometimes terms of greater generality were devised; as +<i>perianth</i>, to include the calyx and corolla, whether one or both of +these were present; <i>pericarp</i>, for the part enclosing the grain, of +whatever kind it be, fruit, nut, pod, &c. And it may easily be imagined, +that descriptive terms may, by definition and combination, become very +numerous and distinct. Thus leaves may be called <i>pinnatifid</i>, +<i>pinnatipartite</i>, <i>pinnatisect</i>, <i>pinnatilobate</i>, <i>palmatifid</i>, +<i>palmatipartite</i>, &c., and each of these words designates different +combinations of the modes and extent of the divisions of the leaf with +the divisions of its outline. <span class="pagenum"><a name="Page_252" id="Page_252">[Pg 252]</a></span>In some cases, arbitrary numerical +relations are introduced into the definition: thus, a leaf is called +<i>bilobate</i>, when it is divided into two parts by a notch; but if the +notch go to the middle of its length, it is <i>bifid</i>; if it go near the +base of the leaf, it is <i>bipartite</i>; if to the base, it is <i>bisect</i>. +Thus, too, a pod of a cruciferous plant is a <i>siliqua</i>, if it is four +times as long as it is broad, but if it be shorter than this it is a +<i>silicula</i>. Such terms being established, the form of the very complex +leaf or frond of a fern (Hymenophyllum Wilsoni) is exactly conveyed by +the following phrase:—'fronds rigid pinnate, pinnæ recurved +subunilateral, pinnatifid, the segments linear undivided or bifid +spinuloso-serrate.'</p> + +<p>"Other characters, as well as form, are conveyed with the like +precision: Colour by means of a classified scale of colours.... This was +done with most precision by Werner, and his scale of colours is still +the most usual standard of naturalists. Werner also introduced a more +exact terminology with regard to other characters which are important in +mineralogy, as lustre, hardness. But Mohs improved upon this step by +giving a numerical scale of hardness, in which talc is 1, gypsum 2, calc +spar 3, and so on.... Some properties, as specific gravity, by their +definition give at once a numerical measure; and others, as crystalline +form, require a very considerable array of mathematical calculation and +reasoning, to point out their relations and gradations."</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VI_3">§ 3.</a> Thus far of Descriptive Terminology, or of the language requisite +for placing on record our observation of individual instances. But when +we proceed from this to Induction, or rather to that comparison of +observed instances which is the preparatory step towards it, we stand in +need of an additional and a different sort of general names.</p> + +<p>Whenever, for purposes of Induction, we find it necessary to introduce +(in Dr. Whewell's phraseology) some new general conception; that is, +whenever the comparison of a set of phenomena leads to the recognition +in them of some common circumstance, which, our attention not having +been directed <span class="pagenum"><a name="Page_253" id="Page_253">[Pg 253]</a></span>to it on any former occasion, is to us a new phenomenon; +it is of importance that this new conception, or this new result of +abstraction, should have a name appropriated to it; especially if the +circumstance it involves be one which leads to many consequences, or +which is likely to be found also in other classes of phenomena. No +doubt, in most cases of the kind, the meaning might be conveyed by +joining together several words already in use. But when a thing has to +be often spoken of, there are more reasons than the saving of time and +space, for speaking of it in the most concise manner possible. What +darkness would be spread over geometrical demonstrations, if wherever +the word <i>circle</i> is used, the definition of a circle were inserted +instead of it. In mathematics and its applications, where the nature of +the processes demands that the attention should be strongly +concentrated, but does not require that it should be widely diffused, +the importance of concentration also in the expressions has always been +duly felt; and a mathematician no sooner finds that he shall often have +occasion to speak of the same two things together, than he at once +creates a term to express them whenever combined: just as, in his +algebraical operations, he substitutes for (<i>a<sup>m</sup></i> + <i>b<sup>n</sup></i>) <i>p</i>/<i>q</i>, or for +<i>a</i>/<i>b</i> + <i>b</i>/<i>c</i> + <i>c</i>/<i>d</i> + &c., the single letter P, Q, or S; not solely to +shorten his symbolical expressions, but to simplify the purely +intellectual part of his operations, by enabling the mind to give its +exclusive attention to the relation between the quantity S and the other +quantities which enter into the equation, without being distracted by +thinking unnecessarily of the parts of which S is itself composed.</p> + +<p>But there is another reason, in addition to that of promoting +perspicuity, for giving a brief and compact name to each of the more +considerable results of abstraction which are obtained in the course of +our intellectual phenomena. By naming them, we fix our attention upon +them; we keep them more constantly before the mind. The names are +remembered, and being remembered, suggest their definition; while if +instead of specific and characteristic names, the <span class="pagenum"><a name="Page_254" id="Page_254">[Pg 254]</a></span>meaning had been +expressed by putting together a number of other names, that particular +combination of words already in common use for other purposes would have +had nothing to make itself remembered by. If we want to render a +particular combination of ideas permanent in the mind, there is nothing +which clenches it like a name specially devoted to express it. If +mathematicians had been obliged to speak of "that to which a quantity, +in increasing or diminishing, is always approaching nearer, so that the +difference becomes less than any assignable quantity, but to which it +never becomes exactly equal," instead of expressing all this by the +simple phrase, "the limit of a quantity," we should probably have long +remained without most of the important truths which have been discovered +by means of the relation between quantities of various kinds and their +limits. If instead of speaking of <i>momentum</i>, it had been necessary to +say, "the product of the number of units of velocity in the velocity by +the number of units of mass in the mass," many of the dynamical truths +now apprehended by means of this complex idea would probably have +escaped notice, for want of recalling the idea itself with sufficient +readiness and familiarity. And on subjects less remote from the topics +of popular discussion, whoever wishes to draw attention to some new or +unfamiliar distinction among things, will find no way so sure as to +invent or select suitable names for the express purpose of marking it.</p> + +<p>A volume devoted to explaining what the writer means by civilization, +does not raise so vivid a conception of it as the single expression, +that Civilization is a different thing from Cultivation; the compactness +of that brief designation for the contrasted quality being an equivalent +for a long discussion. So, if we would impress forcibly upon the +understanding and memory the distinction between the two different +conceptions of a representative government, we cannot more effectually +do so than by saying that Delegation is not Representation. Hardly any +original thoughts on mental or social subjects ever make their way among +mankind, or assume their proper importance in the minds even of <span class="pagenum"><a name="Page_255" id="Page_255">[Pg 255]</a></span>their +inventors, until aptly-selected words or phrases have, as it were, +nailed them down and held them fast.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VI_4">§ 4.</a> Of the three essential parts of a philosophical language, we have +now mentioned two: a terminology suited for describing with precision +the individual facts observed; and a name for every common property of +any importance or interest, which we detect by comparing those facts: +including (as the concretes corresponding to those abstract terms) names +for the classes which we artificially construct in virtue of those +properties, or as many of them, at least, as we have frequent occasion +to predicate anything of.</p> + +<p>But there is a sort of classes, for the recognition of which no such +elaborate process is necessary; because each of them is marked out from +all others not by some one property, the detection of which may depend +on a difficult act of abstraction, but by its properties generally. I +mean, the Kinds of things, in the sense which, in this treatise, has +been specially attached to that term. By a Kind, it will be remembered, +we mean one of those classes which are distinguished from all others not +by one or a few definite properties, but by an unknown multitude of +them: the combination of properties on which the class is grounded, +being a mere index to an indefinite number of other distinctive +attributes. The class horse is a Kind, because the things which agree in +possessing the characters by which we recognise a horse, agree in a +great number of other properties, as we know, and, it cannot be doubted, +in many more than we know. Animal, again, is a Kind, because no +definition that could be given of the name animal could either exhaust +the properties common to all animals, or supply premises from which the +remainder of those properties could be inferred. But a combination of +properties which does not give evidence of the existence of any other +independent peculiarities, does not constitute a Kind. White horse, +therefore, is not a Kind; because horses which agree in whiteness, do +not agree in anything else, except the qualities common to all horses, +and whatever may be the causes or effects of that particular colour.</p> + +<p><span class="pagenum"><a name="Page_256" id="Page_256">[Pg 256]</a></span></p><p>On the principle that there should be a name for everything which we +have frequent occasion to make assertions about, there ought evidently +to be a name for every Kind; for as it is the very meaning of a Kind +that the individuals composing it have an indefinite multitude of +properties in common, it follows that, if not with our present +knowledge, yet with that which we may hereafter acquire, the Kind is a +subject to which there will have to be applied many predicates. The +third component element of a philosophical language, therefore, is that +there shall be a name for every Kind. In other words, there must not +only be a terminology, but also a nomenclature.</p> + +<p>The words Nomenclature and Terminology are employed by most authors +almost indiscriminately; Dr. Whewell being, as far as I am aware, the +first writer who has regularly assigned to the two words different +meanings. The distinction however which he has drawn between them being +real and important, his example is likely to be followed; and (as is apt +to be the case when such innovations in language are felicitously made) +a vague sense of the distinction is found to have influenced the +employment of the terms in common practice, before the expediency had +been pointed out of discriminating them philosophically. Every one would +say that the reform effected by Lavoisier and Guyton-Morveau in the +language of chemistry consisted in the introduction of a new +nomenclature, not of a new terminology. Linear, lanceolate, oval, or +oblong, serrated, dentate, or crenate leaves, are expressions forming +part of the terminology of botany, while the names "Viola odorata," and +"Ulex Europæus," belong to its nomenclature.</p> + +<p>A nomenclature may be defined, the collection of the names of all the +Kinds with which any branch of knowledge is conversant; or more +properly, of all the lowest Kinds, or <i>infimæ species</i>—those which may +be subdivided indeed, but not into Kinds, and which generally accord +with what in natural history are termed simply species. Science +possesses two splendid examples of a systematic nomenclature; that of +plants and animals, constructed by Linnæus and his successors, <span class="pagenum"><a name="Page_257" id="Page_257">[Pg 257]</a></span>and that +of chemistry, which we owe to the illustrious group of chemists who +flourished in France towards the close of the eighteenth century. In +these two departments, not only has every known species, or lowest Kind, +a name assigned to it, but when new lowest Kinds are discovered, names +are at once given to them on an uniform principle. In other sciences the +nomenclature is not at present constructed on any system, either because +the species to be named are not numerous enough to require one, (as in +geometry for example,) or because no one has yet suggested a suitable +principle for such a system, as in mineralogy; in which the want of a +scientifically constructed nomenclature is now the principal cause which +retards the progress of the science.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VI_5">§ 5.</a> A word which carries on its face that it belongs to a nomenclature, +seems at first sight to differ from other concrete general names in +this—that its meaning does not reside in its connotation, in the +attributes implied in it, but in its denotation, that is, in the +particular group of things which it is appointed to designate; and +cannot, therefore, be unfolded by means of a definition, but must be +made known in another way. This opinion, however, appears to me +erroneous. Words belonging to a nomenclature differ, I conceive, from +other words mainly in this, that besides the ordinary connotation, they +have a peculiar one of their own: besides connoting certain attributes, +they also connote that those attributes are distinctive of a Kind. The +term "peroxide of iron," for example, belonging by its form to the +systematic nomenclature of chemistry, bears on its face that it is the +name of a peculiar Kind of substance. It moreover connotes, like the +name of any other class, some portion of the properties common to the +class; in this instance the property of being a compound of iron and the +largest dose of oxygen with which iron will combine. These two things, +the fact of being such a compound, and the fact of being a Kind, +constitute the connotation of the name peroxide of iron. When we say of +the substance before us, that it is the peroxide of iron, we thereby +assert, first, that it is a compound of iron and a maximum of <span class="pagenum"><a name="Page_258" id="Page_258">[Pg 258]</a></span>oxygen, +and next, that the substance so composed is a peculiar Kind of +substance.</p> + +<p>Now, this second part of the connotation of any word belonging to a +nomenclature is as essential a portion of its meaning as the first part, +while the definition only declares the first: and hence the appearance +that the signification of such terms cannot be conveyed by a definition: +which appearance, however, is fallacious. The name Viola odorata denotes +a Kind, of which a certain number of characters, sufficient to +distinguish it, are enunciated in botanical works. This enumeration of +characters is surely, as in other cases, a definition of the name. No, +say some, it is not a definition, for the name Viola odorata does not +mean those characters; it means that particular group of plants, and the +characters are selected from among a much greater number, merely as +marks by which to recognise the group. But to this I reply, that the +name does not mean that group, for it would be applied to that group no +longer than while the group is believed to be an <i>infima species</i>; if it +were to be discovered that several distinct Kinds have been confounded +under this one name, no one would any longer apply the name Viola +odorata to the whole of the group, but would apply it, if retained at +all, to one only of the Kinds contained therein. What is imperative, +therefore, is not that the name shall denote one particular collection +of objects, but that it shall denote a Kind, and a lowest Kind. The form +of the name declares that, happen what will, it is to denote an <i>infima +species</i>; and that, therefore, the properties which it connotes, and +which are expressed in the definition, are to be connoted by it no +longer than while we continue to believe that those properties, when +found together, indicate a Kind, and that the whole of them are found in +no more than one Kind.</p> + +<p>With the addition of this peculiar connotation, implied in the form of +every word which belongs to a systematic nomenclature; the set of +characters which is employed to discriminate each Kind from all other +Kinds (and which is a real definition) constitutes as completely as in +any other case the whole meaning of the term. It is no objection to say +that (as is often the case in natural history) the set of characters +<span class="pagenum"><a name="Page_259" id="Page_259">[Pg 259]</a></span>may be changed, and another substituted as being better suited for the +purpose of distinction, while the word, still continuing to denote the +same group of things, is not considered to have changed its meaning. For +this is no more than may happen in the case of any other general name: +we may, in reforming its connotation, leave its denotation untouched; +and it is generally desirable to do so. The connotation, however, is not +the less for this the real meaning, for we at once apply the name +wherever the characters set down in the definition are found; and that +which exclusively guides us in applying the term, must constitute its +signification. If we find, contrary to our previous belief, that the +characters are not peculiar to one species, we cease to use the term +coextensively with the characters; but then it is because the other +portion of the connotation fails; the condition that the class must be a +Kind. The connotation, therefore, is still the meaning; the set of +descriptive characters is a true definition; and the meaning is +unfolded, not indeed (as in other cases) by the definition alone, but by +the definition and the form of the word taken together.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VI_6">§ 6.</a> We have now analysed what is implied in the two principal +requisites of a philosophical language; first, precision, or +definiteness, and secondly, completeness. Any further remarks on the +mode of constructing a nomenclature must be deferred until we treat of +Classification; the mode of naming the Kinds of things being necessarily +subordinate to the mode of arranging those Kinds into larger classes. +With respect to the minor requisites of terminology, some of them are +well stated and illustrated in the "Aphorisms concerning the Language of +Science," included in Dr. Whewell's <i>Philosophy of the Inductive +Sciences</i>. These, as being of secondary importance in the peculiar point +of view of Logic, I shall not further refer to, but shall confine my +observations to one more quality, which, next to the two already treated +of, appears to be the most valuable which the language of science can +possess. Of this quality a general notion may be conveyed by the +following aphorism:</p> + +<p><span class="pagenum"><a name="Page_260" id="Page_260">[Pg 260]</a></span></p><p>Whenever the nature of the subject permits our reasoning processes to +be, without danger, carried on mechanically, the language should be +constructed on as mechanical principles as possible; while in the +contrary case, it should be so constructed that there shall be the +greatest possible obstacles to a merely mechanical use of it.</p> + +<p>I am aware that this maxim requires much explanation, which I shall at +once proceed to give. And first, as to what is meant by using a language +mechanically. The complete or extreme case of the mechanical use of +language, is when it is used without any consciousness of a meaning, and +with only the consciousness of using certain visible or audible marks in +conformity to technical rules previously laid down. This extreme case is +nowhere realized except in the figures of arithmetic and the symbols of +algebra, a language unique in its kind, and approaching as nearly to +perfection, for the purposes to which it is destined, as can, perhaps, +be said of any creation of the human mind. Its perfection consists in +the completeness of its adaptation to a purely mechanical use. The +symbols are mere counters, without even the semblance of a meaning apart +from the convention which is renewed each time they are employed, and +which is altered at each renewal, the same symbol <i>a</i> or <i>x</i> being used +on different occasions to represent things which (except that, like all +things, they are susceptible of being numbered) have no property in +common. There is nothing, therefore, to distract the mind from the set +of mechanical operations which are to be performed upon the symbols, +such as squaring both sides of the equation, multiplying or dividing +them by the same or by equivalent symbols, and so forth. Each of these +operations, it is true, corresponds to a syllogism; represents one step +of a ratiocination relating not to the symbols, but to the things +signified by them. But as it has been found practicable to frame a +technical form, by conforming to which we can make sure of finding the +conclusion of the ratiocination, our end can be completely attained +without our ever thinking of anything but the symbols. Being thus +intended to work merely as mechanism, they have the qualities which +mechanism ought to have. They are of the least <span class="pagenum"><a name="Page_261" id="Page_261">[Pg 261]</a></span>possible bulk, so that +they take up scarcely any room, and waste no time in their manipulation; +they are compact, and fit so closely together that the eye can take in +the whole at once of almost every operation which they are employed to +perform.</p> + +<p>These admirable properties of the symbolical language of mathematics +have made so strong an impression on the minds of many thinkers, as to +have led them to consider the symbolical language in question as the +ideal type of philosophical language generally; to think that names in +general, or (as they are fond of calling them) signs, are fitted for the +purposes of thought in proportion as they can be made to approximate to +the compactness, the entire unmeaningness, and the capability of being +used as counters without a thought of what they represent, which are +characteristic of the <i>a</i> and <i>b</i>, the <i>x</i> and <i>y</i>, of algebra. This +notion has led to sanguine views of the acceleration of the progress of +science by means which, I conceive, cannot possibly conduce to that end, +and forms part of that exaggerated estimate of the influence of signs, +which has contributed in no small degree to prevent the real laws of our +intellectual operations from being rightly understood.</p> + +<p>In the first place, a set of signs by which we reason without +consciousness of their meaning, can be serviceable, at most, only in our +deductive operations. In our direct inductions we cannot for a moment +dispense with a distinct mental image of the phenomena, since the whole +operation turns on a perception of the particulars in which those +phenomena agree and differ. But, further, this reasoning by counters is +only suitable to a very limited portion even of our deductive processes. +In our reasonings respecting numbers, the only general principles which +we ever have occasion to introduce, are these, Things which are equal to +the same thing are equal to one another, and The sums or differences of +equal things are equal, with their various corollaries. Not only can no +hesitation ever arise respecting the applicability of these principles, +since they are true of all magnitudes whatever; but every possible +application of which they are susceptible, may <span class="pagenum"><a name="Page_262" id="Page_262">[Pg 262]</a></span>be reduced to a +technical rule; and such, in fact, the rules of the calculus are. But if +the symbols represent any other things than mere numbers, let us say +even straight or curve lines, we have then to apply theorems of geometry +not true of all lines without exception, and to select those which are +true of the lines we are reasoning about. And how can we do this unless +we keep completely in mind what particular lines these are? Since +additional geometrical truths may be introduced into the ratiocination +in any stage of its progress, we cannot suffer ourselves, during even +the smallest part of it, to use the names mechanically (as we use +algebraical symbols) without an image annexed to them. It is only after +ascertaining that the solution of a question concerning lines can be +made to depend on a previous question concerning numbers, or in other +words after the question has been (to speak technically) reduced to an +equation, that the unmeaning signs become available, and that the nature +of the facts themselves to which the investigation relates can be +dismissed from the mind. Up to the establishment of the equation, the +language in which mathematicians carry on their reasoning does not +differ in character from that employed by close reasoners on any other +kind of subject.</p> + +<p>I do not deny that every correct ratiocination, when thrown into the +syllogistic shape, is conclusive from the mere form of the expression, +provided none of the terms used be ambiguous; and this is one of the +circumstances which have led some writers to think that if all names +were so judiciously constructed and so carefully defined as not to admit +of any ambiguity, the improvement thus made in language would not only +give to the conclusions of every deductive science the same certainty +with those of mathematics, but would reduce all reasonings to the +application of a technical form, and enable their conclusiveness to be +rationally assented to after a merely mechanical process, as is +undoubtedly the case in algebra. But, if we except geometry, the +conclusions of which are already as certain and exact as they can be +made, there is no science but that of number, in which the practical +<span class="pagenum"><a name="Page_263" id="Page_263">[Pg 263]</a></span>validity of a reasoning can be apparent to any person who has looked +only at the form of the process. Whoever has assented to what was said +in the last Book concerning the case of the Composition of Causes, and +the still stronger case of the entire supersession of one set of laws by +another, is aware that geometry and algebra are the only sciences of +which the propositions are categorically true: the general propositions +of all other sciences are true only hypothetically, supposing that no +counteracting cause happens to interfere. A conclusion, therefore, +however correctly deduced, in point of form, from admitted laws of +nature, will have no other than an hypothetical certainty. At every step +we must assure ourselves that no other law of nature has superseded, or +intermingled its operation with, those which are the premises of the +reasoning; and how can this be done by merely looking at the words? We +must not only be constantly thinking of the phenomena themselves, but we +must be constantly studying them; making ourselves acquainted with the +peculiarities of every case to which we attempt to apply our general +principles.</p> + +<p>The algebraic notation, considered as a philosophical language, is +perfect in its adaptation to the subjects for which it is commonly +employed, namely those of which the investigations have already been +reduced to the ascertainment of a relation between numbers. But, +admirable as it is for its own purpose, the properties by which it is +rendered such are so far from constituting it the ideal model of +philosophical language in general, that the more nearly the language of +any other branch of science approaches to it, the less fit that language +is for its own proper functions. On all other subjects, instead of +contrivances to prevent our attention from being distracted by thinking +of the meaning of our signs, we ought to wish for contrivances to make +it impossible that we should ever lose sight of that meaning even for an +instant.</p> + +<p>With this view, as much meaning as possible should be thrown into the +formation of the word itself; the aids of derivation and analogy being +made available to keep alive a <span class="pagenum"><a name="Page_264" id="Page_264">[Pg 264]</a></span>consciousness of all that is signified +by it. In this respect those languages have an immense advantage which +form their compounds and derivatives from native roots, like the German, +and not from those of a foreign or dead language, as is so much the case +with English, French, and Italian: and the best are those which form +them according to fixed analogies, corresponding to the relations +between the ideas to be expressed. All languages do this more or less, +but especially, among modern European languages, the German; while even +that is inferior to the Greek, in which the relation between the meaning +of a derivative word and that of its primitive is in general clearly +marked by its mode of formation; except in the case of words compounded +with prepositions, which are often, in both those languages, extremely +anomalous.</p> + +<p>But all that can be done, by the mode of constructing words, to prevent +them from degenerating into sounds passing through the mind without any +distinct apprehension of what they signify, is far too little for the +necessity of the case. Words, however well constructed originally, are +always tending, like coins, to have their inscription worn off by +passing from hand to hand; and the only possible mode of reviving it is +to be ever stamping it afresh, by living in the habitual contemplation +of the phenomena themselves, and not resting in our familiarity with the +words that express them. If any one, having possessed himself of the +laws of phenomena as recorded in words, whether delivered to him +originally by others, or even found out by himself, is content from +thenceforth to live among these formulæ, to think exclusively of them, +and of applying them to cases as they arise, without keeping up his +acquaintance with the realities from which these laws were +collected—not only will he continually fail in his practical efforts, +because he will apply his formulæ without duly considering whether, in +this case and in that, other laws of nature do not modify or supersede +them; but the formulæ themselves will progressively lose their meaning +to him, and he will cease at last even to be capable of recognising with +certainty whether a case falls within the contemplation of his <span class="pagenum"><a name="Page_265" id="Page_265">[Pg 265]</a></span>formula +or not. It is, in short, as necessary, on all subjects not mathematical, +that the things on which we reason should be conceived by us in the +concrete, and "clothed in circumstances," as it is in algebra that we +should keep all individualizing peculiarities sedulously out of view.</p> + +<p>With this remark we close our observations on the Philosophy of +Language.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_266" id="Page_266">[Pg 266]</a></span></p> +<h3><a name="BOOK_IV_CHAPTER_VII" id="BOOK_IV_CHAPTER_VII"></a>CHAPTER VII.<br /> +OF CLASSIFICATION, AS SUBSIDIARY TO INDUCTION.</h3> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VII_1">§ 1.</a> There is, as has been frequently remarked in this work, a +classification of things, which is inseparable from the fact of giving +them general names. Every name which connotes an attribute, divides, by +that very fact, all things whatever into two classes, those which have +the attribute and those which have it not; those of which the name can +be predicated, and those of which it cannot. And the division thus made +is not merely a division of such things as actually exist, or are known +to exist, but of all such as may hereafter be discovered, and even of +all which can be imagined.</p> + +<p>On this kind of Classification we have nothing to add to what has +previously been said. The Classification which requires to be discussed +as a separate act of the mind, is altogether different. In the one, the +arrangement of objects in groups, and distribution of them into +compartments, is a mere incidental effect consequent on the use of names +given for another purpose, namely that of simply expressing some of +their qualities. In the other the arrangement and distribution are the +main object, and the naming is secondary to, and purposely conforms +itself to, instead of governing, that more important operation.</p> + +<p>Classification, thus regarded, is a contrivance for the best possible +ordering of the ideas of objects in our minds; for causing the ideas to +accompany or succeed one another in such a way as shall give us the +greatest command over our knowledge already acquired, and lead most +directly to the acquisition of more. The general problem of +Classification, in reference to these purposes, may be stated as +follows: To provide that things shall be thought of in such groups, and +<span class="pagenum"><a name="Page_267" id="Page_267">[Pg 267]</a></span>those groups in such an order, as will best conduce to the remembrance +and to the ascertainment of their laws.</p> + +<p>Classification thus considered, differs from classification in the wider +sense, in having reference to real objects exclusively, and not to all +that are imaginable: its object being the due co-ordination in our minds +of those things only, with the properties of which we have actually +occasion to make ourselves acquainted. But, on the other hand, it +embraces <i>all</i> really existing objects. We cannot constitute any one +class properly, except in reference to a general division of the whole +of nature; we cannot determine the group in which any one object can +most conveniently be placed, without taking into consideration all the +varieties of existing objects, all at least which have any degree of +affinity with it. No one family of plants or animals could have been +rationally constituted, except as part of a systematic arrangement of +all plants or animals; nor could such a general arrangement have been +properly made, without first determining the exact place of plants and +animals in a general division of nature.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VII_2">§ 2.</a> There is no property of objects which may not be taken, if we +please, as the foundation for a classification or mental grouping of +those objects; and in our first attempts we are likely to select for +that purpose properties which are simple, easily conceived, and +perceptible on a first view, without any previous process of thought. +Thus Tournefort's arrangement of plants was founded on the shape and +divisions of the corolla; and that which is commonly called the Linnæan +(though Linnæus also suggested another and more scientific arrangement) +was grounded chiefly on the number of the stamens and pistils.</p> + +<p>But these classifications, which are at first recommended by the +facility they afford of ascertaining to what class any individual +belongs, are seldom much adapted to the ends of that Classification +which is the subject of our present remarks. The Linnæan arrangement +answers the purpose of making us think together of all those kinds of +plants which possess the same number of stamens and pistils; but to +think of them <span class="pagenum"><a name="Page_268" id="Page_268">[Pg 268]</a></span>in that manner is of little use, since we seldom have +anything to affirm in common of the plants which have a given number of +stamens and pistils. If plants of the class Pentandria, order Monogynia, +agreed in any other properties, the habit of thinking and speaking of +the plants under a common designation would conduce to our remembering +those common properties so far as they were ascertained, and would +dispose us to be on the look-out for such of them as were not yet known. +But since this is not the case, the only purpose of thought which the +Linnæan classification serves is that of causing us to remember, better +than we should otherwise have done, the exact number of stamens and +pistils of every species of plants. Now, as this property is of little +importance or interest, the remembering it with any particular accuracy +is of no moment. And, inasmuch as, by habitually thinking of plants in +those groups, we are prevented from habitually thinking of them in +groups which have a greater number of properties in common, the effect +of such a classification, when systematically adhered to, upon our +habits of thought, must be regarded as mischievous.</p> + +<p>The ends of scientific classification are best answered, when the +objects are formed into groups respecting which a greater number of +general propositions can be made, and those propositions more important, +than could be made respecting any other groups into which the same +things could be distributed. The properties, therefore, according to +which objects are classified, should, if possible, be those which are +causes of many other properties: or at any rate, which are sure marks of +them. Causes are preferable, both as being the surest and most direct of +marks, and as being themselves the properties on which it is of most use +that our attention should be strongly fixed. But the property which is +the cause of the chief peculiarities of a class, is unfortunately seldom +fitted to serve also as the diagnostic of the class. Instead of the +cause, we must generally select some of its more prominent effects, +which may serve as marks of the other effects and of the cause.</p> + +<p>A classification thus formed is properly scientific or philosophical, +and is commonly called a Natural, in contradistinction <span class="pagenum"><a name="Page_269" id="Page_269">[Pg 269]</a></span>to a Technical +or Artificial, classification or arrangement. The phrase Natural +Classification seems most peculiarly appropriate to such arrangements as +correspond, in the groups which they form, to the spontaneous tendencies +of the mind, by placing together the objects most similar in their +general aspect: in opposition to those technical systems which, +arranging things according to their agreement in some circumstance +arbitrarily selected, often throw into the same group objects which in +the general aggregate of their properties present no resemblance, and +into different and remote groups, others which have the closest +similarity. It is one of the most valid recommendations of any +classification to the character of a scientific one, that it shall be a +natural classification in this sense also; for the test of its +scientific character is the number and importance of the properties +which can be asserted in common of all objects included in a group; and +properties on which the general aspect of the things depends, are, if +only on that ground, important, as well as, in most cases, numerous. +But, though a strong recommendation, this circumstance is not a <i>sine +quâ non</i>; since the most obvious properties of things may be of trifling +importance compared with others that are not obvious. I have seen it +mentioned as a great absurdity in the Linnæan classification, that it +places (which by the way it does not) the violet by the side of the oak: +it certainly dissevers natural affinities, and brings together things +quite as unlike as the oak and the violet are. But the difference, +apparently so wide, which renders the juxtaposition of those two +vegetables so suitable an illustration of a bad arrangement, depends, to +the common eye, mainly on mere size and texture; now if we made it our +study to adopt the classification which would involve the least peril of +similar <i>rapprochements</i>, we should return to the obsolete division into +trees, shrubs, and herbs, which though of primary importance with regard +to more general aspect, yet (compared even with so petty and unobvious a +distinction as that into dicotyledons and monocotyledons) answers to so +few differences in the other properties of plants, that a classification +founded on it (independently of the indistinctness of the lines of +demarcation) <span class="pagenum"><a name="Page_270" id="Page_270">[Pg 270]</a></span>would be as completely artificial and technical as the +Linnæan.</p> + +<p>Our natural groups, therefore, must often be founded not on the obvious, +but on the unobvious properties of things, when these are of greater +importance. But in such cases it is essential that there should be some +other property or set of properties, more readily recognisable by the +observer, which coexist with, and may be received as marks of, the +properties which are the real groundwork of the classification. A +natural arrangement, for example, of animals, must be founded in the +main on their internal structure, but (as has been justly remarked) it +would be absurd that we should not be able to determine the genus and +species of an animal without first killing it. On this ground, the +preference, among zoological classifications, is probably due to that of +M. de Blainville, founded on the differences in the external +integuments; differences which correspond, much more accurately than +might be supposed, to the really important varieties, both in the other +parts of the structure, and in the habits and history of the animals.</p> + +<p>This shows, more strongly than ever, how extensive a knowledge of the +properties of objects is necessary for making a good classification of +them. And as it is one of the uses of such a classification that by +drawing attention to the properties on which it is founded, and which if +the classification be good are marks of many others, it facilitates the +discovery of those others; we see in what manner our knowledge of +things, and our classification of them, tend mutually and indefinitely +to the improvement of each other.</p> + +<p>We said just now that the classification of objects should follow those +of their properties which indicate not only the most numerous, but also +the most important peculiarities. What is here meant by importance? It +has reference to the particular end in view; and the same objects, +therefore, may admit with propriety of several different +classifications. Each science or art forms its classification of things +according to the properties which fall within its special cognizance, or +of which it must take account in order to accomplish its <span class="pagenum"><a name="Page_271" id="Page_271">[Pg 271]</a></span>peculiar +practical end. A farmer does not divide plants, like a botanist, into +dicotyledonous and monocotyledonous, but into useful plants and weeds. A +geologist divides fossils, not like a zoologist, into families +corresponding to those of living species, but into fossils of the +secondary and of the tertiary periods, above the coal and below the +coal, &c. Whales are or are not fish, according to the purpose for which +we are considering them. "If we are speaking of the internal structure +and physiology of the animal, we must not call them fish; for in these +respects they deviate widely from fishes: they have warm blood, and +produce and suckle their young as land quadrupeds do. But this would not +prevent our speaking of the <i>whale fishery</i>, and calling such animals +<i>fish</i> on all occasions connected with this employment; for the +relations thus rising depend upon the animal's living in the water, and +being caught in a manner similar to other fishes. A plea that human laws +which mention fish do not apply to whales, would be rejected at once by +an intelligent judge."<a name="FNanchor_19_63" id="FNanchor_19_63"></a><a href="#Footnote_19_63" class="fnanchor">[19]</a></p> + +<p>These different classifications are all good, for the purposes of their +own particular departments of knowledge or practice. But when we are +studying objects not for any special practical end, but for the sake of +extending our knowledge of the whole of their properties and relations, +we must consider as the most important attributes, those which +contribute most, either by themselves or by their effects, to render the +things like one another, and unlike other things; which give to the +class composed of them the most marked individuality; which fill, as it +were, the largest space in their existence, and would most impress the +attention of a spectator who knew all their properties but was not +specially interested in any. Classes formed on this principle may be +called, in a more emphatic manner than any others, natural groups.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VII_3">§ 3.</a> On the subject of these groups Dr. Whewell lays <span class="pagenum"><a name="Page_272" id="Page_272">[Pg 272]</a></span>down a theory, +grounded on an important truth, which he has, in some respects, +expressed and illustrated very felicitously; but also, as it appears to +me, with some admixture of error. It will be advantageous, for both +these reasons, to extract the statement of his doctrine in the very +words he has used.</p> + +<p>"Natural groups," according to this theory,<a name="FNanchor_20_64" id="FNanchor_20_64"></a><a href="#Footnote_20_64" class="fnanchor">[20]</a> are "given by Type, not +by Definition." And this consideration accounts for that "indefiniteness +and indecision which we frequently find in the descriptions of such +groups, and which must appear so strange and inconsistent to any one who +does not suppose these descriptions to assume any deeper ground of +connexion than an arbitrary choice of the botanist. Thus in the family +of the rose-tree, we are told that the <i>ovules</i> are <i>very rarely</i> erect, +the <i>stigmata usually</i> simple. Of what use, it might be asked, can such +loose accounts be? To which the answer is, that they are not inserted in +order to distinguish the species, but in order to describe the family, +and the total relations of the ovules and the stigmata of the family are +better known by this general statement. A similar observation may be +made with regard to the Anomalies of each group, which occur so +commonly, that Mr. Lindley, in his <i>Introduction to the Natural System +of Botany</i>, makes the 'Anomalies' an article in each family. Thus, part +of the character of the Rosaceæ is, that they have alternate <i>stipulate</i> +leaves, and that the <i>albumen</i> is <i>obliterated</i>; but yet in <i>Lowea</i>, one +of the genera of this family, the stipulæ are <i>absent</i>; and the albumen +is <i>present</i> in another, <i>Neillia</i>. This implies, as we have already +seen, that the artificial character (or <i>diagnosis</i>, as Mr. Lindley +calls it,) is imperfect. It is, though very nearly, yet not exactly, +commensurate with the natural group: and hence in certain cases this +character is made to yield to the general weight of natural affinities.</p> + +<p>"These views,—of classes determined by characters which cannot be +expressed in words,—of propositions which state, not what happens in +all cases, but only usually,—of particulars <span class="pagenum"><a name="Page_273" id="Page_273">[Pg 273]</a></span>which are included in a +class, though they transgress the definition of it, may probably +surprise the reader. They are so contrary to many of the received +opinions respecting the use of definitions, and the nature of scientific +propositions, that they will probably appear to many persons highly +illogical and unphilosophical. But a disposition to such a judgment +arises in a great measure from this, that the mathematical and +mathematico-physical sciences have, in a great degree, determined men's +views of the general nature and form of scientific truth; while Natural +History has not yet had time or opportunity to exert its due influence +upon the current habits of philosophizing. The apparent indefiniteness +and inconsistency of the classifications and definitions of Natural +History belongs, in a far higher degree, to all other except +mathematical speculations; and the modes in which approximations to +exact distinctions and general truths have been made in Natural History, +may be worthy our attention, even for the light they throw upon the best +modes of pursuing truth of all kinds.</p> + +<p>"Though in a Natural group of objects a definition can no longer be of +any use as a regulative principle, classes are not therefore left quite +loose, without any certain standard or guide. The class is steadily +fixed, though not precisely limited; it is given, though not +circumscribed; it is determined, not by a boundary line without, but by +a central point within; not by what it strictly excludes, but by what it +eminently includes; by an example, not by a precept; in short, instead +of a Definition we have a Type for our director.</p> + +<p>"A Type is an example of any class, for instance a species of a genus, +which is considered as eminently possessing the character of the class. +All the species which have a greater affinity with this type-species +than with any others, form the genus, and are arranged about it, +deviating from it in various directions and different degrees. Thus a +genus may consist of several species which approach very near the type, +and of which the claim to a place with it is obvious; while there may be +other species which straggle further from this central <span class="pagenum"><a name="Page_274" id="Page_274">[Pg 274]</a></span>knot, and which +yet are clearly more connected with it than with any other. And even if +there should be some species of which the place is dubious, and which +appear to be equally bound to two generic types, it is easily seen that +this would not destroy the reality of the generic groups, any more than +the scattered trees of the intervening plain prevent our speaking +intelligibly of the distinct forests of two separate hills.</p> + +<p>"The type-species of every genus, the type-genus of every family, is, +then, one which possesses all the characters and properties of the genus +in a marked and prominent manner. The type of the Rose family has +alternate stipulate leaves, wants the albumen, has the ovules not erect, +has the stigmata simple, and besides these features, which distinguish +it from the exceptions or varieties of its class, it has the features +which make it prominent in its class. It is one of those which possess +clearly several leading attributes; and thus, though we cannot say of +any one genus that it <i>must</i> be the type of the family, or of any one +species that it <i>must</i> be the type of the genus, we are still not wholly +to seek; the type must be connected by many affinities with most of the +others of its group; it must be near the centre of the crowd, and not +one of the stragglers."</p> + +<p>In this passage (the latter part of which especially I cannot help +noticing as an admirable example of philosophic style) Dr. Whewell has +stated very clearly and forcibly, but (I think) without making all +necessary distinctions, one of the principles of a Natural +Classification. What this principle is, what are its limits, and in what +manner he seems to me to have overstepped them, will appear when we have +laid down another rule of Natural Arrangement, which appears to me still +more fundamental.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VII_4">§ 4.</a> The reader is by this time familiar with the general truth (which I +restate so often on account of the great confusion in which it is +commonly involved), that there are in nature distinctions of Kind; +distinctions not consisting in a <span class="pagenum"><a name="Page_275" id="Page_275">[Pg 275]</a></span>given number of definite properties, +<i>plus</i> the effects which follow from those properties, but running +through the whole nature, through the attributes generally, of the +things so distinguished. Our knowledge of the properties of a Kind is +never complete. We are always discovering, and expecting to discover, +new ones. Where the distinction between two classes of things is not one +of Kind, we expect to find their properties alike, except where there is +some reason for their being different. On the contrary, when the +distinction is in Kind, we expect to find the properties different +unless there be some cause for their being the same. All knowledge of a +Kind must be obtained by observation and experiment upon the Kind +itself; no inference respecting its properties from the properties of +things not connected with it by Kind, goes for more than the sort of +presumption usually characterized as an analogy, and generally in one of +its fainter degrees.</p> + +<p>Since the common properties of a true Kind, and consequently the general +assertions which can be made respecting it, or which are certain to be +made hereafter as our knowledge extends, are indefinite and +inexhaustible; and since the very first principle of natural +classification is that of forming the classes so that the objects +composing each may have the greatest number of properties in common; +this principle prescribes that every such classification shall recognise +and adopt into itself all distinctions of Kind, which exist among the +objects it professes to classify. To pass over any distinctions of Kind, +and substitute definite distinctions, which, however considerable they +may be, do not point to ulterior unknown differences, would be to +replace classes with more by classes with fewer attributes in common; +and would be subversive of the Natural Method of Classification.</p> + +<p>Accordingly all natural arrangements, whether the reality of the +distinction of Kinds was felt or not by their framers, have been led, by +the mere pursuit of their own proper end, to conform themselves to the +distinctions of Kind, so far as these had been ascertained at the time. +The Species of <span class="pagenum"><a name="Page_276" id="Page_276">[Pg 276]</a></span>Plants are not only real Kinds, but are probably,<a name="FNanchor_21_65" id="FNanchor_21_65"></a><a href="#Footnote_21_65" class="fnanchor">[21]</a> +all of them, real lowest Kinds, Infimæ Species; which if we were to +subdivide, as of course it is open to us to do, into subclasses, the +subdivision would necessarily be founded on <i>definite</i> distinctions, not +pointing (apart from what may be known of their causes or effects) to +any difference beyond themselves.</p> + +<p>In so far as a natural classification is grounded on real Kinds, its +groups are certainly not conventional; it is perfectly true that they do +not depend upon an arbitrary choice of the naturalist. But it does not +follow, nor, I conceive, is it true, that these classes are determined +by a type, and not by characters. To determine them by a type would be +as sure a way of missing the Kind, as if we were to select a set of +characters arbitrarily. They are determined by characters, but these are +not arbitrary. The problem is, to find a few definite characters which +point to the multitude of indefinite ones. Kinds are Classes between +which there is an impassable barrier; and what we have to seek is, marks +whereby we may determine on which side of the barrier an object takes +its place. The characters which will best do this should be chosen: if +they are also important in themselves, so much the better. When we have +selected the characters, we parcel out the objects according to those +characters, and not, I conceive, according to resemblance to a type. We +do not compose the species Ranunculus acris, of all plants which bear a +satisfactory degree of resemblance to a model-buttercup, but of those +which possess certain characters selected as marks by which we might +recognise the possibility of a common <span class="pagenum"><a name="Page_277" id="Page_277">[Pg 277]</a></span>parentage; and the enumeration of +those characters is the definition of the species.</p> + +<p>The question next arises, whether, as all Kinds must have a place among +the classes, so all the classes in a natural arrangement must be Kinds? +And to this I answer, certainly not. The distinctions of Kinds are not +numerous enough to make up the whole of a classification. Very few of +the genera of plants, or even of the families, can be pronounced with +certainty to be Kinds. The great distinctions of Vascular and Cellular, +Dicotyledonous or Exogenous and Monocotyledonous or Endogenous plants, +are perhaps differences of Kind; the lines of demarcation which divide +those classes seem (though even on this I would not pronounce +positively) to go through the whole nature of the plants. But the +different species of a genus, or genera of a family, usually have in +common only a limited number of characters. A Rose does not seem to +differ from a Rubus, or the Umbelliferæ from the Ranunculaceæ, in much +else than the characters botanically assigned to those genera or those +families. Unenumerated differences certainly do exist in some cases; +there are families of plants which have peculiarities of chemical +composition, or yield products having peculiar effects on the animal +economy. The Cruciferæ and Fungi contain an unusual proportion of +nitrogen; the Labiatæ are the chief sources of essential oils, the +Solaneæ are very commonly narcotic, &c. In these and similar cases there +are possibly distinctions of Kind; but it is by no means indispensable +that there should be. Genera and Families may be eminently natural, +though marked out from one another by properties limited in number; +provided those properties are important, and the objects contained in +each genus or family resemble each other more than they resemble +anything which is excluded from the genus or family.</p> + +<p>After the recognition and definition, then, of the <i>infimæ species</i>, the +next step is to arrange those <i>infimæ species</i> into larger groups: +making these groups correspond to Kinds wherever it is possible, but in +most cases without any such guidance. And in doing this it is true that +we are naturally <span class="pagenum"><a name="Page_278" id="Page_278">[Pg 278]</a></span>and properly guided, in most cases at least, by +resemblance to a type. We form our groups round certain selected Kinds, +each of which serves as a sort of exemplar of its group. But though the +groups are suggested by types, I cannot think that a group when formed +is <i>determined</i> by the type; that in deciding whether a species belongs +to the group, a reference is made to the type, and not to the +characters; that the characters "cannot be expressed in words." This +assertion is inconsistent with Dr. Whewell's own statement of the +fundamental principle of classification, namely, that "general +assertions shall be possible." If the class did not possess any +characters in common, what general assertions would be possible +respecting it? Except that they all resemble each other more than they +resemble anything else, nothing whatever could be predicated of the +class.</p> + +<p>The truth is, on the contrary, that every genus or family is framed with +distinct reference to certain characters, and is composed, first and +principally, of species which agree in possessing all those characters. +To these are added, as a sort of appendix, such other species, generally +in small number, as possess <i>nearly</i> all the properties selected; +wanting some of them one property, some another, and which, while they +agree with the rest <i>almost</i> as much as these agree with one another, do +not resemble in an equal degree any other group. Our conception of the +class continues to be grounded on the characters; and the class might be +defined, those things which <i>either</i> possess that set of characters, +<i>or</i> resemble the things that do so, more than they resemble anything +else.</p> + +<p>And this resemblance itself is not, like resemblance between simple +sensations, an ultimate fact, unsusceptible of analysis. Even the +inferior degree of resemblance is created by the possession of common +characters. Whatever resembles the genus Rose more than it resembles any +other genus, does so because it possesses a greater number of the +characters of that genus, than of the characters of any other genus. Nor +can there be any real difficulty in representing, by an enumeration of +characters, the nature and degree of the resemblance which is strictly +sufficient to include any object in <span class="pagenum"><a name="Page_279" id="Page_279">[Pg 279]</a></span>the class. There are always some +properties common to all things which are included. Others there often +are, to which some things, which are nevertheless included, are +exceptions. But the objects which are exceptions to one character are +not exceptions to another: the resemblance which fails in some +particulars must be made up for in others. The class, therefore, is +constituted by the possession of <i>all</i> the characters which are +universal, and <i>most</i> of those which admit of exceptions. If a plant had +the ovules erect, the stigmata divided, possessed the albumen, and was +without stipules, it possibly would not be classed among the Rosaceæ. +But it may want any one, or more than one of those characters, and not +be excluded. The ends of a scientific classification are better answered +by including it. Since it agrees so nearly, in its known properties, +with the sum of the characters of the class, it is likely to resemble +that class more than any other in those of its properties which are +still undiscovered.</p> + +<p>Not only, therefore, are natural groups, no less than any artificial +classes, determined by characters; they are constituted in contemplation +of, and by reason of, characters. But it is in contemplation not of +those characters only which are rigorously common to all the objects +included in the group, but of the entire body of characters, all of +which are found in most of those objects, and most of them in all. And +hence our conception of the class, the image in our minds which is +representative of it, is that of a specimen complete in all the +characters; most naturally a specimen which, by possessing them all in +the greatest degree in which they are ever found, is the best fitted to +exhibit clearly, and in a marked manner, what they are. It is by a +mental reference to this standard, not instead of, but in illustration +of, the definition of the class, that we usually and advantageously +determine whether any individual or species belongs to the class or not. +And this, as it seems to me, is the amount of truth contained in the +doctrine of Types.</p> + +<p>We shall see presently that where the classification is made for the +express purpose of a special inductive inquiry, it is not optional, but +necessary for fulfilling the conditions of a correct <span class="pagenum"><a name="Page_280" id="Page_280">[Pg 280]</a></span>Inductive Method, +that we should establish a type-species or genus, namely, the one which +exhibits in the most eminent degree the particular phenomenon under +investigation. But of this hereafter. It remains, for completing the +theory of natural groups, that a few words should be said on the +principles of the nomenclature adapted to them.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VII_5">§ 5.</a> A Nomenclature in science, is, as we have said, a system of the +names of Kinds. These names, like other class-names, are defined by the +enumeration of the characters distinctive of the class. The only merit +which a set of names can have beyond this, is to convey, by the mode of +their construction, as much information as possible: so that a person +who knows the thing, may receive all the assistance which the name can +give in remembering what he knows, while he who knows it not, may +receive as much knowledge respecting it as the case admits of, by merely +being told its name.</p> + +<p>There are two modes of giving to the name of a Kind this sort of +significance. The best, but which unfortunately is seldom practicable, +is when the word can be made to indicate, by its formation, the very +properties which it is designed to connote. The name of a Kind does not, +of course, connote all the properties of the Kind, since these are +inexhaustible, but such of them as are sufficient to distinguish it; +such as are sure marks of all the rest. Now, it is very rarely that one +property, or even any two or three properties, can answer this purpose. +To distinguish the common daisy from all other species of plants would +require the specification of many characters. And a name cannot, without +being too cumbrous for use, give indication, by its etymology or mode of +construction, of more than a very small number of these. The +possibility, therefore, of an ideally perfect Nomenclature, is probably +confined to the one case in which we are happily in possession of +something nearly approaching to it; the Nomenclature of elementary +Chemistry. The substances, whether simple or compound, with which +chemistry is conversant, are Kinds, and, as such, the properties which +distinguish each of them from the rest are innumerable; but in the case +of compound <span class="pagenum"><a name="Page_281" id="Page_281">[Pg 281]</a></span>substances (the simple ones are not numerous enough to +require a systematic nomenclature), there is one property, the chemical +composition, which is of itself sufficient to distinguish the Kind; and +is (with certain reservations not yet thoroughly understood) a sure mark +of all the other properties of the compound. All that was needful, +therefore, was to make the name of every compound express, on the first +hearing, its chemical composition; that is, to form the name of the +compound, in some uniform manner, from the names of the simple +substances which enter into it as elements. This was done, most +skilfully and successfully, by the French chemists. The only thing left +unexpressed by them was the exact proportion in which the elements were +combined; and even this, since the establishment of the atomic theory, +it has been found possible to express by a simple adaptation of their +phraseology.</p> + +<p>But where the characters which must be taken into consideration in order +sufficiently to designate the Kind, are too numerous to be all signified +in the derivation of the name, and where no one of them is of such +preponderant importance as to justify its being singled out to be so +indicated, we may avail ourselves of a subsidiary resource. Though we +cannot indicate the distinctive properties of the Kind, we may indicate +its nearest natural affinities, by incorporating into its name the name +of the proximate natural group of which it is one of the species. On +this principle is founded the admirable binary nomenclature of botany +and zoology. In this nomenclature the name of every species consists of +the name of the genus, or natural group next above it, with a word added +to distinguish the particular species. The last portion of the compound +name is sometimes taken from some <i>one</i> of the peculiarities in which +that species differs from others of the genus; as Clematis +<i>integrifolia</i>, Potentilla <i>alba</i>, Viola <i>palustris</i>, Artemisia +<i>vulgaris</i>; sometimes from a circumstance of an historical nature, as +Narcissus <i>poeticus</i>, Potentilla <i>tormentilla</i> (indicating that the +plant was formerly known by the latter name), Exacum <i>Candollii</i> (from +the fact that De Candolle was its first discoverer); and sometimes the +word is purely conventional, as Thlaspi <i>bursa-pastoris</i>, Ranunculus +<i>thora</i>; it is <span class="pagenum"><a name="Page_282" id="Page_282">[Pg 282]</a></span>of little consequence which; since the second, or as it +is usually called, the specific name, could at most express, +independently of convention, no more than a very small portion of the +connotation of the term. But by adding to this the name of the superior +genus, we may make the best amends we can for the impossibility of so +contriving the name as to express all the distinctive characters of the +Kind. We make it, at all events, express as many of those characters as +are common to the proximate natural group in which the Kind is included. +If even those common characters are so numerous or so little familiar as +to require a further extension of the same resource, we might, instead +of a binary, adopt a ternary nomenclature, employing not only the name +of the genus, but that of the next natural group in order of generality +above the genus, commonly called the Family. This was done in the +mineralogical nomenclature proposed by Professor Mohs. "The names framed +by him were not composed of two, but of three elements, designating +respectively the Species, the Genus, and the Order; thus he has such +species as <i>Rhombohedral Lime Haloide</i>, <i>Octohedral Fluor Haloide</i>, +<i>Prismatic Hal Baryte</i>."<a name="FNanchor_22_66" id="FNanchor_22_66"></a><a href="#Footnote_22_66" class="fnanchor">[22]</a> The binary construction, however, has been +found sufficient in botany and zoology, the only sciences in which this +general principle has hitherto been successfully adopted in the +construction of a nomenclature.</p> + +<p>Besides the advantage which this principle of nomenclature possesses, in +giving to the names of species the greatest quantity of independent +significance which the circumstances of the case admit of, it answers +the further end of immensely economizing the use of names, and +preventing an otherwise intolerable burden on the memory. When the names +of species become extremely numerous, some artifice (as Dr. Whewell<a name="FNanchor_23_67" id="FNanchor_23_67"></a><a href="#Footnote_23_67" class="fnanchor">[23]</a> +observes) becomes absolutely necessary to make it possible to recollect +or apply them. "The known species of plants, for example, were ten +thousand in the time of Linnæus, and are now probably sixty thousand. It +would be useless to endeavour to frame and employ separate names for +each of these species. <span class="pagenum"><a name="Page_283" id="Page_283">[Pg 283]</a></span>The division of the objects into a subordinated +system of classification enables us to introduce a Nomenclature which +does not require this enormous number of names. Each of the genera has +its name, and the species are marked by the addition of some epithet to +the name of the genus. In this manner about seventeen hundred generic +names, with a moderate number of specific names, were found by Linnæus +sufficient to designate with precision all the species of vegetables +known at his time." And though the number of generic names has since +greatly increased, it has not increased in anything like the proportion +of the multiplication of known species.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_284" id="Page_284">[Pg 284]</a></span></p> +<h3><a name="BOOK_IV_CHAPTER_VIII" id="BOOK_IV_CHAPTER_VIII"></a>CHAPTER VIII.<br /> +OF CLASSIFICATION BY SERIES.</h3> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VIII_1">§ 1.</a> Thus far, we have considered the principles of scientific +classification so far only as relates to the formation of natural +groups; and at this point most of those who have attempted a theory of +natural arrangement, including, among the rest, Dr. Whewell, have +stopped. There remains, however, another, and a not less important +portion of the theory, which has not yet, as far as I am aware, been +systematically treated of by any writer except M. Comte. This is, the +arrangement of the natural groups into a natural series.<a name="FNanchor_24_68" id="FNanchor_24_68"></a><a href="#Footnote_24_68" class="fnanchor">[24]</a></p> + +<p>The end of Classification, as an instrument for the investigation of +nature, is (as before stated) to make us think of those objects +together, which have the greatest number of important common properties; +and which therefore we have oftenest occasion, in the course of our +inductions, for taking into joint consideration. Our ideas of objects +are thus brought into the order most conducive to the successful +prosecution of inductive inquiries generally. But when the purpose is to +facilitate some particular inductive inquiry, more is required. To be +instrumental to that purpose, the classification must bring those +objects together, the simultaneous contemplation <span class="pagenum"><a name="Page_285" id="Page_285">[Pg 285]</a></span>of which is likely to +throw most light upon the particular subject. That subject being the +laws of some phenomenon or some set of connected phenomena; the very +phenomenon or set of phenomena in question must be chosen as the +groundwork of the classification.</p> + +<p>The requisites of a classification intended to facilitate the study of a +particular phenomenon, are, first, to bring into one class all Kinds of +things which exhibit that phenomenon, in whatever variety of forms or +degrees; and secondly, to arrange those Kinds in a series according to +the degree in which they exhibit it, beginning with those which exhibit +most of it, and terminating with those which exhibit least. The +principal example, as yet, of such a classification, is afforded by +comparative anatomy and physiology, from which, therefore, our +illustrations shall be taken.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VIII_2">§ 2.</a> The object being supposed to be, the investigation of the laws of +animal life; the first step, after forming the most distinct conception +of the phenomenon itself, possible in the existing state of our +knowledge, is to erect into one great class (that of animals) all the +known Kinds of beings where that phenomenon presents itself; in however +various combinations with other properties, and in however different +degrees. As some of these Kinds manifest the general phenomenon of +animal life in a very high degree, and others in an insignificant +degree, barely sufficient for recognition; we must, in the next place, +arrange the various Kinds in a series, following one another according +to the degrees in which they severally exhibit the phenomenon; beginning +therefore with man, and ending with the most imperfect kinds of +zoophytes.</p> + +<p>This is merely saying that we should put the instances, from which the +law is to be inductively collected, into the order which is implied in +one of the four Methods of Experimental Inquiry discussed in the +preceding Book; the fourth Method, that of Concomitant Variations. As +formerly remarked, this is often the only method to which recourse can +be had, with assurance of a true conclusion, in cases in which we have +but limited means of effecting, by artificial experiments, <span class="pagenum"><a name="Page_286" id="Page_286">[Pg 286]</a></span>a separation +of circumstances usually conjoined. The principle of the method is, that +facts which increase or diminish together, and disappear together, are +either cause and effect, or effects of a common cause. When it has been +ascertained that this relation really subsists between the variations, a +connexion between the facts themselves may be confidently laid down, +either as a law of nature or only as an empirical law, according to +circumstances.</p> + +<p>That the application of this Method must be preceded by the formation of +such a series as we have described, is too obvious to need being pointed +out; and the mere arrangement of a set of objects in a series, according +to the degrees in which they exhibit some fact of which we are seeking +the law, is too naturally suggested by the necessities of our inductive +operations, to require any lengthened illustration here. But there are +cases in which the arrangement required for the special purpose, becomes +the determining principle of the classification of the same objects for +general purposes. This will naturally and properly happen, when those +laws of the objects which are sought in the special inquiry enact so +principal a part in the general character and history of those +objects—exercise so much influence in determining all the phenomena of +which they are either the agents or the theatre—that all other +differences existing among the objects are fittingly regarded as mere +modifications of the one phenomenon sought; effects determined by the +co-operation of some incidental circumstance with the laws of that +phenomenon. Thus in the case of animated beings, the differences between +one class of animals and another may reasonably be considered as mere +modifications of the general phenomenon, animal life; modifications +arising either from the different degrees in which that phenomenon is +manifested in different animals, or from the intermixture of the effects +of incidental causes peculiar to the nature of each, with the effects +produced by the general laws of life; those laws still exercising a +predominant influence over the result. Such being the case, no other +inductive inquiry respecting animals can be successfully carried on, +except in subordination to the great inquiry into the universal <span class="pagenum"><a name="Page_287" id="Page_287">[Pg 287]</a></span>laws of +animal life. And the classification of animals best suited to that one +purpose, is the most suitable to all the other purposes of zoological +science.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VIII_3">§ 3.</a> To establish a classification of this sort, or even to apprehend it +when established, requires the power of recognising the essential +similarity of a phenomenon, in its minuter degrees and obscurer forms, +with what is called the <i>same</i> phenomenon in the greatest perfection of +its development; that is, of identifying with each other all phenomena +which differ only in degree, and in properties which we suppose to be +caused by difference of degree. In order to recognise this identity, or +in other words, this exact similarity of quality, the assumption of a +type-species is indispensable. We must consider as the type of the +class, that among the Kinds included in it, which exhibits the +properties constitutive of the class, in the highest degree; conceiving +the other varieties as instances of degeneracy, as it were, from that +type; deviations from it by inferior intensity of the characteristic +property or properties. For every phenomenon is best studied (<i>cæteris +paribus</i>) where it exists in the greatest intensity. It is there that +the effects which either depend on it, or depend on the same causes with +it, will also exist in the greatest degree. It is there, consequently, +and only there, that those effects of it, or joint effects with it, can +become fully known to us, so that we may learn to recognise their +smaller degrees, or even their mere rudiments, in cases in which the +direct study would have been difficult or even impossible. Not to +mention that the phenomenon in its higher degrees may be attended by +effects or collateral circumstances which in its smaller degrees do not +occur at all, requiring for their production in any sensible amount a +greater degree of intensity of the cause than is there met with. In man, +for example, (the species in which both the phenomenon of animal and +that of organic life exist in the highest degree,) many subordinate +phenomena develop themselves in the course of his animated existence, +which the inferior varieties of animals do not show. The knowledge of +these properties may nevertheless be of great avail towards <span class="pagenum"><a name="Page_288" id="Page_288">[Pg 288]</a></span>the +discovery of the conditions and laws of the general phenomenon of life, +which is common to man with those inferior animals. And they are, even, +rightly considered as properties of animated nature itself; because they +may evidently be affiliated to the general laws of animated nature; +because we may fairly presume that some rudiments or feeble degrees of +those properties would be recognised in all animals by more perfect +organs, or even by more perfect instruments, than ours; and because +those may be correctly termed properties of a class, which a thing +exhibits exactly in proportion as it belongs to the class, that is, in +proportion as it possesses the main attributes constitutive of the +class.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VIII_4">§ 4.</a> It remains to consider how the internal distribution of the series +may most properly take place: in what manner it should be divided into +Orders, Families, and Genera.</p> + +<p>The main principle of division must of course be natural affinity; the +classes formed must be natural groups: and the formation of these has +already been sufficiently treated of. But the principles of natural +grouping must be applied in subordination to the principle of a natural +series. The groups must not be so constituted as to place in the same +group things which ought to occupy different points of the general +scale. The precaution necessary to be observed for this purpose is, that +the <i>primary</i> divisions must be grounded not on all distinctions +indiscriminately, but on those which correspond to variations in the +degree of the main phenomenon. The series of Animated Nature should be +broken into parts at the points where the variation in the degree of +intensity of the main phenomenon (as marked by its principal characters, +Sensation, Thought, Voluntary Motion, &c.) begins to be attended by +conspicuous changes in the miscellaneous properties of the animal. Such +well-marked changes take place, for example, where the class Mammalia +ends; at the points where Fishes are separated from Insects, Insects +from Mollusca, &c. When so formed, the primary natural groups will +compose the series by mere juxtaposition, without redistribution; <span class="pagenum"><a name="Page_289" id="Page_289">[Pg 289]</a></span>each +of them corresponding to a definite portion of the scale. In like manner +each family should, if possible, be so subdivided, that one portion of +it shall stand higher and the other lower, though of course contiguous, +in the general scale; and only when this is impossible is it allowable +to ground the remaining subdivisions on characters having no +determinable connexion with the main phenomenon.</p> + +<p>Where the principal phenomenon so far transcends in importance all other +properties on which a classification could be grounded, as it does in +the case of animated existence, any considerable deviation from the rule +last laid down is in general sufficiently guarded against by the first +principle of a natural arrangement, that of forming the groups according +to the most important characters. All attempts at a scientific +classification of animals, since first their anatomy and physiology were +successfully studied, have been framed with a certain degree of +instinctive reference to a natural series, and have accorded in many +more points than they have differed, with the classification which would +most naturally have been grounded on such a series. But the accordance +has not always been complete; and it still is often a matter of +discussion, which of several classifications best accords with the true +scale of intensity of the main phenomenon. Cuvier, for example, has been +justly criticized for having formed his natural groups with an undue +degree of reference to the mode of alimentation, a circumstance directly +connected only with organic life, and not lending to the arrangement +most appropriate for the purposes of an investigation of the laws of +animal life, since both carnivorous and herbivorous or frugivorous +animals are found at almost every degree in the scale of animal +perfection. Blainville's classification has been considered by high +authorities to be free from this defect; as representing correctly, by +the mere order of the principal groups, the successive degeneracy of +animal nature from its highest to its most imperfect exemplification.</p> + + +<p class="newsection"><a name="BOOK_IV_CHAPTER_VIII_5">§ 5.</a> A classification of any large portion of the field of nature in +conformity to the foregoing principles, has hitherto <span class="pagenum"><a name="Page_290" id="Page_290">[Pg 290]</a></span>been found +practicable only in one great instance, that of animals. In the case +even of vegetables, the natural arrangement has not been carried beyond +the formation of natural groups. Naturalists have found, and probably +will continue to find it impossible to form those groups into any +series, the terms of which correspond to real gradations in the +phenomenon of vegetative or organic life. Such a difference of degree +may be traced between the class of Vascular Plants and that of Cellular, +which includes lichens, algæ, and other substances whose organization is +simpler and more rudimentary than that of the higher order of +vegetables, and which therefore approach nearer to mere inorganic +nature. But when we rise much above this point, we do not find any +sufficient difference in the degree in which different plants possess +the properties of organization and life. The dicotyledons are of more +complex structure, and somewhat more perfect organization, than the +monocotyledons: and some dicotyledonous families, such as the Compositæ, +are rather more complex in their organization than the rest. But the +differences are not of a marked character, and do not promise to throw +any particular light upon the conditions and laws of vegetable life and +development. If they did, the classification of vegetables would have to +be made, like that of animals, with reference to the scale or series +indicated.</p> + +<p>Although the scientific arrangements of organic nature afford as yet the +only complete example of the true principles of rational classification, +whether as to the formation of groups or of series, those principles are +applicable to all cases in which mankind are called upon to bring the +various parts of any extensive subject into mental co-ordination. They +are as much to the point when objects are to be classed for purposes of +art or business, as for those of science. The proper arrangement, for +example, of a code of laws, depends on the same scientific conditions as +the classifications in natural history; nor could there be a better +preparatory discipline for that important function, than the study of +the principles of a natural arrangement, not only in the abstract, but +in their actual application to the class of phenomena for which they +were first elaborated, <span class="pagenum"><a name="Page_291" id="Page_291">[Pg 291]</a></span>and which are still the best school for learning +their use. Of this the great authority on codification, Bentham, was +perfectly aware: and his early <i>Fragment on Government</i>, the admirable +introduction to a series of writings unequalled in their department, +contains clear and just views (as far as they go) on the meaning of a +natural arrangement, such as could scarcely have occurred to any one who +lived anterior to the age of Linnæus and Bernard de Jussieu.</p> + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"><p><a name="Footnote_1_45" id="Footnote_1_45"></a><a href="#FNanchor_1_45"><span class="label">[1]</span></a> Supra, <span title="See Vol. I.">book iii. ch. ii. § 3, 4, 5</span>.</p></div> + +<div class="footnote"><p><a name="Footnote_2_46" id="Footnote_2_46"></a><a href="#FNanchor_2_46"><span class="label">[2]</span></a> Mr. Bailey has given by far the best statement of this +theory. "The general name," he says, "raises up the image sometimes of +one individual of the class formerly seen, sometimes of another, not +unfrequently of many individuals in succession; and it sometimes +suggests an image made up of elements from several different objects, by +a latent process of which I am not conscious." (Letters on the +Philosophy of the Human Mind, 1st series, letter 22.) But Mr. Bailey +must allow that we carry on inductions and ratiocinations respecting the +class, by means of this idea or conception of some one individual in it. +This is all I require. The name of a class calls up some idea, through +which we can, to all intents and purposes, think of the class as such, +and not solely of an individual member of it.</p></div> + +<div class="footnote"><p><a name="Footnote_3_47" id="Footnote_3_47"></a><a href="#FNanchor_3_47"><span class="label">[3]</span></a> I have entered rather fully into this question in chap. +xvii. of <i>An Examination of Sir William Hamilton's Philosophy</i>, headed +"The Doctrine of Concepts or General Notions," which contains my last +views on the subject.</p></div> + +<div class="footnote"><p><a name="Footnote_4_48" id="Footnote_4_48"></a><a href="#FNanchor_4_48"><span class="label">[4]</span></a> Other examples of inappropriate conceptions are given by +Dr. Whewell (<i>Phil. Ind. Sc.</i> ii. 185) as follows:—"Aristotle and his +followers endeavoured in vain to account for the mechanical relation of +forces in the lever, by applying the <i>inappropriate</i> geometrical +conceptions of the properties of the circle: they failed in explaining +the <i>form</i> of the luminous spot made by the sun shining through a hole, +because they applied the <i>inappropriate</i> conception of a circular +<i>quality</i> in the sun's light: they speculated to no purpose about the +elementary composition of bodies, because they assumed the +<i>inappropriate</i> conception of <i>likeness</i> between the elements and the +compound, instead of the genuine notion of elements merely <i>determining</i> +the qualities of the compound." But in these cases there is more than an +inappropriate conception; there is a false conception; one which has no +prototype in nature, nothing corresponding to it in facts. This is +evident in the last two examples, and is equally true in the first; the +"properties of the circle" which were referred to, being purely +fantastical. There is, therefore, an error beyond the wrong choice of a +principle of generalization; there is a false assumption of matters of +fact. The attempt is made to resolve certain laws of nature into a more +general law, that law not being one which, though real, is +inappropriate, but one wholly imaginary.</p></div> + +<div class="footnote"><p><a name="Footnote_5_49" id="Footnote_5_49"></a><a href="#FNanchor_5_49"><span class="label">[5]</span></a> Professor Bain.</p></div> + +<div class="footnote"><p><a name="Footnote_6_50" id="Footnote_6_50"></a><a href="#FNanchor_6_50"><span class="label">[6]</span></a> This sentence having been erroneously understood as if I +had meant to assert that belief is nothing but an irresistible +association, I think it necessary to observe that I express no theory +respecting the ultimate analysis either of reasoning or of belief, two +of the most obscure points in analytical psychology. I am speaking not +of the powers themselves, but of the previous conditions necessary to +enable those powers to exert themselves: of which conditions I am +contending that language is not one, senses and association being +sufficient without it.</p></div> + +<div class="footnote"><p><a name="Footnote_7_51" id="Footnote_7_51"></a><a href="#FNanchor_7_51"><span class="label">[7]</span></a> Mr. Bailey agrees with me in thinking that whenever "from +something actually present to my senses conjoined with past experience, +I feel satisfied that something has happened, or will happen, or is +happening, beyond the sphere of my personal observation," I may with +strict propriety be said to reason: and of course to reason inductively, +for demonstrative reasoning is excluded by the circumstances of the +case. (<i>The Theory of Reasoning</i>, 2nd ed. p. 27.)</p></div> + +<div class="footnote"><p><a name="Footnote_8_52" id="Footnote_8_52"></a><a href="#FNanchor_8_52"><span class="label">[8]</span></a> <i>Novum Organum Renovatum</i>, pp. 35-37.</p></div> + +<div class="footnote"><p><a name="Footnote_9_53" id="Footnote_9_53"></a><a href="#FNanchor_9_53"><span class="label">[9]</span></a> <i>Nov. Org. Renov.</i>, pp. 39, 40.</p></div> + +<div class="footnote"><p><a name="Footnote_10_54" id="Footnote_10_54"></a><a href="#FNanchor_10_54"><span class="label">[10]</span></a> P. 217, 4to edition.</p></div> + +<div class="footnote"><p><a name="Footnote_11_55" id="Footnote_11_55"></a><a href="#FNanchor_11_55"><span class="label">[11]</span></a> "E, ex, extra, extraneus, étranger, stranger." +</p><p> +Another etymological example sometimes cited is the derivation of the +English <i>uncle</i> from the Latin <i>avus</i>. It is scarcely possible for two +words to bear fewer outward marks of relationship, yet there is but one +step between them; <i>avus</i>, <i>avunculus</i>, <i>uncle</i>. +</p><p> +So <i>pilgrim</i>, from <i>ager</i>: <i>per agrum</i>, <i>peragrinus</i>, <i>peregrinus</i>, +<i>pellegrino</i>, <i>pilgrim</i>.</p></div> + +<div class="footnote"><p><a name="Footnote_12_56" id="Footnote_12_56"></a><a href="#FNanchor_12_56"><span class="label">[12]</span></a> P. 226-7.</p></div> + +<div class="footnote"><p><a name="Footnote_13_57" id="Footnote_13_57"></a><a href="#FNanchor_13_57"><span class="label">[13]</span></a> <i>Essays</i>, p. 214.</p></div> + +<div class="footnote"><p><a name="Footnote_14_58" id="Footnote_14_58"></a><a href="#FNanchor_14_58"><span class="label">[14]</span></a> Ibid. 215.</p></div> + +<div class="footnote"><p><a name="Footnote_15_59" id="Footnote_15_59"></a><a href="#FNanchor_15_59"><span class="label">[15]</span></a> Such cases give a clear insight into the process of the +degeneration of languages in periods of history when literary culture +was suspended; and we are now in danger of experiencing a similar evil +through the superficial extension of the same culture. So many persons +without anything deserving the name of education have become writers by +profession, that written language may almost be said to be principally +wielded by persons ignorant of the proper use of the instrument, and who +are spoiling it more and more for those who understand it. Vulgarisms, +which creep in nobody knows how, are daily depriving the English +language of valuable modes of expressing thought. To take a present +instance: the verb <i>transpire</i> formerly conveyed very expressively its +correct meaning, viz. to <i>become known</i> through unnoticed channels—to +exhale, as it were, into publicity through invisible pores, like a +vapour or gas disengaging itself. But of late a practice has commenced +of employing this word, for the sake of finery, as a mere synonym of <i>to +happen</i>: "the events which have <i>transpired</i> in the Crimea," meaning the +incidents of the war. This vile specimen of bad English is already seen +in the despatches of noblemen and viceroys: and the time is apparently +not far distant when nobody will understand the word if used in its +proper sense. It is a great error to think that these corruptions of +language do no harm. Those who are struggling with the difficulty (and +who know by experience how great it already is) of expressing oneself +clearly with precision, find their resources continually narrowed by +illiterate writers, who seize and twist from its purpose some form of +speech which once served to convey briefly and compactly an unambiguous +meaning. It would hardly be believed how often a writer is compelled to +a circumlocution by the single vulgarism, introduced during the last few +years, of using the word <i>alone</i> as an adverb, <i>only</i> not being fine +enough for the rhetoric of ambitious ignorance. A man will say "to which +I am not alone bound by honour but also by law," unaware that what he +has unintentionally said is, that he is <i>not alone</i> bound, some other +person being bound with him. Formerly if any one said, "I am not alone +responsible for this," he was understood to mean, (what alone his words +mean in correct English,) that he is not the sole person responsible; +but if he now used such an expression, the reader would be confused +between that and two other meanings; that he is not <i>only responsible</i> +but something more; or that he is responsible <i>not only for this</i> but +for something besides. The time is coming when Tennyson's Œnone could +not say "I will not die alone," lest she should be supposed to mean that +she would not only die but do something else. +</p><p> +The blunder of writing <i>predicate</i> for <i>predict</i> has become so widely +diffused that it bids fair to render one of the most useful terms in the +scientific vocabulary of Logic unintelligible. The mathematical and +logical term "to eliminate" is undergoing a similar destruction. All who +are acquainted either with the proper use of the word or with its +etymology, know that to eliminate a thing is to thrust it out; but those +who know nothing about it, except that it is a fine-looking phrase, use +it in a sense precisely the reverse, to denote, not turning anything +out, but bringing it in. They talk of <i>eliminating</i> some truth, or other +useful result, from a mass of details. I suspect that this error must at +first have arisen from some confusion between <i>to eliminate</i> and <i>to +enucleate</i>. +</p><p> +Though no such evil consequences as take place in these instances, are +likely to arise from the modern freak of writing <i>sanatory</i> instead of +sanitary, it deserves notice as a charming specimen of pedantry +engrafted upon ignorance. Those who thus undertake to correct the +spelling of the classical English writers, are not aware that the +meaning of <i>sanatory</i>, if there were such a word in the language, would +have reference not to the preservation of health, but to the cure of +disease.</p></div> + +<div class="footnote"><p><a name="Footnote_16_60" id="Footnote_16_60"></a><a href="#FNanchor_16_60"><span class="label">[16]</span></a> <i>Historical Introduction</i>, vol. i. pp. 66-8.</p></div> + +<div class="footnote"><p><a name="Footnote_17_61" id="Footnote_17_61"></a><a href="#FNanchor_17_61"><span class="label">[17]</span></a> <i>History of Scientific Ideas</i>, ii. 110, 111.</p></div> + +<div class="footnote"><p><a name="Footnote_18_62" id="Footnote_18_62"></a><a href="#FNanchor_18_62"><span class="label">[18]</span></a> <i>Hist. Sc. Id.</i> ii. 111-113.</p></div> + +<div class="footnote"><p><a name="Footnote_19_63" id="Footnote_19_63"></a><a href="#FNanchor_19_63"><span class="label">[19]</span></a> <i>Nov. Org. Renov.</i> pp. 286, 287.</p></div> + +<div class="footnote"><p><a name="Footnote_20_64" id="Footnote_20_64"></a><a href="#FNanchor_20_64"><span class="label">[20]</span></a> <i>Hist. Sc. Id.</i> ii. 120-122.</p></div> + +<div class="footnote"><p><a name="Footnote_21_65" id="Footnote_21_65"></a><a href="#FNanchor_21_65"><span class="label">[21]</span></a> I say probably, not certainly, because this is not the +consideration by which a botanist determines what shall or shall not be +admitted as a species. In natural history those objects belong to the +same species, which are, or consistently with experience might have +been, produced from the same stock. But this distinction, in most, and +probably in all cases, happily accords with the other. It seems to be a +law of physiology, that animals and plants do really, in the +philosophical as well as the popular sense, propagate their kind; +transmitting to their descendants all the distinctions of Kind (down to +the most special or lowest Kind) which they themselves possess.</p></div> + +<div class="footnote"><p><a name="Footnote_22_66" id="Footnote_22_66"></a><a href="#FNanchor_22_66"><span class="label">[22]</span></a> <i>Nov. Org. Renov.</i> p. 274.</p></div> + +<div class="footnote"><p><a name="Footnote_23_67" id="Footnote_23_67"></a><a href="#FNanchor_23_67"><span class="label">[23]</span></a> <i>Hist. Sc. Id.</i> i. 133.</p></div> + +<div class="footnote"><p><a name="Footnote_24_68" id="Footnote_24_68"></a><a href="#FNanchor_24_68"><span class="label">[24]</span></a> Dr. Whewell, in his reply (<i>Philosophy of Discovery</i>, p. +270) says that he "stopped short of, or rather passed by, the doctrine +of a series of organized beings," because he "thought it bad and narrow +philosophy." If he did, it was evidently without understanding this form +of the doctrine; for he proceeds to quote a passage from his "History," +in which the doctrine he condemns is designated as that of "a mere +linear progression in nature, which would place each genus in contact +only with the preceding and succeeding ones." Now the series treated of +in the text agrees with this linear progression in nothing whatever but +in being a progression. +</p><p> +It would surely be possible to arrange all <i>places</i> (for example) in the +order of their distance from the North Pole, though there would be not +merely a plurality, but a whole circle of places at every single +gradation in the scale.</p></div> +</div> + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_293" id="Page_293">[Pg 293]</a></span></p> +<h2><a name="BOOK_V" id="BOOK_V"></a>BOOK V.<br /> +ON FALLACIES.</h2> + + +<blockquote><p><span class="pagenum"><a name="Page_294" id="Page_294">[Pg 294]</a></span></p><p>"Errare non modo affirmando et negando, sed etiam sentiendo, et in +tacitâ hominum cogitatione contingit."—<span class="smcap">Hobbes</span>, <i>Computatio sive +Logica</i>, ch. v.</p></blockquote> + +<blockquote><p>"Il leur semble qu'il n'y a qu'à douter par fantaisie, et qu'il n'y a +qu'à dire en général que notre nature est infirme; que notre esprit est +plein d'aveuglement; qu'il faut avoir un grand soin de se défaire de ses +préjugés, et autres choses semblables. Ils pensent que cela suffit pour +ne plus se laisser séduire à ses sens, et pour ne plus se tromper du +tout. Il ne suffit pas de dire que l'esprit est foible, il faut lui +faire sentir ses foiblesses. Ce n'est pas assez de dire qu'il est sujet +à l'erreur, il faut lui découvrir en quoi consistent ses +erreurs."—<span class="smcap">Malebranche</span>, <i>Recherche de la Vérité</i>.</p></blockquote> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_295" id="Page_295">[Pg 295]</a></span></p> +<h3><a name="BOOK_V_CHAPTER_I" id="BOOK_V_CHAPTER_I"></a>CHAPTER I.<br /> +OF FALLACIES IN GENERAL.</h3> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_I_1">§ 1.</a> It is a maxim of the schoolmen, that "contrariorum eadem est +scientia:" we never really know what a thing is, unless we are also able +to give a sufficient account of its opposite. Conformably to this maxim, +one considerable section, in most treatises on Logic, is devoted to the +subject of Fallacies; and the practice is too well worthy of observance, +to allow of our departing from it. The philosophy of reasoning, to be +complete, ought to comprise the theory of bad as well as of good +reasoning.</p> + +<p>We have endeavoured to ascertain the principles by which the sufficiency +of any proof can be tested, and by which the nature and amount of +evidence needful to prove any given conclusion can be determined +beforehand. If these principles were adhered to, then although the +number and value of the truths ascertained would be limited by the +opportunities, or by the industry, ingenuity, and patience, of the +individual inquirer, at least error would not be embraced instead of +truth. But the general consent of mankind, founded on their experience, +vouches for their being far indeed from even this negative kind of +perfection in the employment of their reasoning powers.</p> + +<p>In the conduct of life—in the practical business of mankind—wrong +inferences, incorrect interpretations of experience, unless after much +culture of the thinking faculty, are absolutely inevitable: and with +most people, after the highest degree of culture they ever attain, such +erroneous inferences, producing corresponding errors in conduct, are +lamentably frequent. Even in the speculations to which eminent +intellects have systematically devoted themselves, and in reference to +which the collective mind of the scientific world is always <span class="pagenum"><a name="Page_296" id="Page_296">[Pg 296]</a></span>at hand to +aid the efforts and correct the aberrations of individuals, it is only +from the more perfect sciences, from those of which the subject-matter +is the least complicated, that opinions not resting on a correct +induction have at length, generally speaking, been expelled. In the +departments of inquiry relating to the more complex phenomena of nature, +and especially those of which the subject is man, whether as a moral and +intellectual, a social, or even as a physical being; the diversity of +opinions still prevalent among instructed persons, and the equal +confidence with which those of the most contrary ways of thinking cling +to their respective tenets, are proof not only that right modes of +philosophizing are not yet generally adopted on those subjects, but that +wrong ones are: that inquirers have not only in general missed the +truth, but have often embraced error; that even the most cultivated +portion of our species have not yet learned to abstain from drawing +conclusions which the evidence does not warrant.</p> + +<p>The only complete safeguard against reasoning ill, is the habit of +reasoning well; familiarity with the principles of correct reasoning, +and practice in applying those principles. It is, however, not +unimportant to consider what are the most common modes of bad reasoning; +by what appearances the mind is most likely to be seduced from the +observance of true principles of induction; what, in short, are the most +common and most dangerous varieties of Apparent Evidence, whereby +persons are misled into opinions for which there does not exist evidence +really conclusive.</p> + +<p>A catalogue of the varieties of apparent evidence which are not real +evidence, is an enumeration of Fallacies. Without such an enumeration, +therefore, the present work would be wanting in an essential point. And +while writers who included in their theory of reasoning nothing more +than ratiocination, have, in consistency with this limitation, confined +their remarks to the fallacies which have their seat in that portion of +the process of investigation; we, who profess to treat of the whole +process, must add to our directions for performing it rightly, warnings +against performing it wrongly in any of its <span class="pagenum"><a name="Page_297" id="Page_297">[Pg 297]</a></span>parts: whether the +ratiocinative or the experimental portion of it be in fault, or the +fault lie in dispensing with ratiocination and induction altogether.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_I_2">§ 2.</a> In considering the sources of unfounded inference, it is +unnecessary to reckon the errors which arise, not from a wrong method, +nor even from ignorance of the right one, but from a casual lapse, +through hurry or inattention, in the application of the true principles +of induction. Such errors, like the accidental mistakes in casting up a +sum, do not call for philosophical analysis or classification; +theoretical considerations can throw no light upon the means of avoiding +them. In the present treatise our attention is required, not to mere +inexpertness in performing the operation in the right way, (the only +remedies for which are increased attention and more sedulous practice,) +but to the modes of performing it in a way fundamentally wrong; the +conditions under which the human mind persuades itself that it has +sufficient grounds for a conclusion which it has not arrived at by any +of the legitimate methods of induction—which it has not even carelessly +or overhastily, endeavoured to test by those legitimate methods.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_I_3">§ 3.</a> There is another branch of what may be called the Philosophy of +Error, which must be mentioned here, though only to be excluded from our +subject. The sources of erroneous opinions are twofold, moral and +intellectual. Of these, the moral do not fall within the compass of this +work. They may be classed under two general heads; Indifference to the +attainment of truth, and Bias: of which last the most common case is +that in which we are biassed by our wishes; but the liability is almost +as great to the undue adoption of a conclusion which is disagreeable to +us, as of one which is agreeable, if it be of a nature to bring into +action any of the stronger passions. Persons of timid character are the +more predisposed to believe any statement, the more it is calculated to +alarm them. Indeed it is a psychological law, deducible from the most +general laws of the mental constitution of man, that <span class="pagenum"><a name="Page_298" id="Page_298">[Pg 298]</a></span>any strong passion +renders us credulous as to the existence of objects suitable to excite +it.</p> + +<p>But the moral causes of opinions, though with most persons the most +powerful of all, are but remote causes: they do not act directly, but by +means of the intellectual causes; to which they bear the same relation +that the circumstances called, in the theory of medicine, <i>predisposing</i> +causes, bear to <i>exciting</i> causes. Indifference to truth cannot, in and +by itself, produce erroneous belief; it operates by preventing the mind +from collecting the proper evidences, or from applying to them the test +of a legitimate and rigid induction; by which omission it is exposed +unprotected to the influence of any species of apparent evidence which +offers itself spontaneously, or which is elicited by that smaller +quantity of trouble which the mind may be willing to take. As little is +Bias a direct source of wrong conclusions. We cannot believe a +proposition only by wishing, or only by dreading, to believe it. The +most violent inclination to find a set of propositions true, will not +enable the weakest of mankind to believe them without a vestige of +intellectual grounds—without any, even apparent, evidence. It acts +indirectly, by placing the intellectual grounds of belief in an +incomplete or distorted shape before his eyes. It makes him shrink from +the irksome labour of a rigorous induction, when he has a misgiving that +its result may be disagreeable; and in such examination as he does +institute, it makes him exert that which is in a certain measure +voluntary, his attention, unfairly, giving a larger share of it to the +evidence which seems favourable to the desired conclusion, a smaller to +that which seems unfavourable. It operates, too, by making him look out +eagerly for reasons, or apparent reasons, to support opinions which are +conformable, or resist those which are repugnant, to his interests or +feelings; and when the interests or feelings are common to great numbers +of persons, reasons are accepted and pass current, which would not for a +moment be listened to in that character, if the conclusion had nothing +more powerful than its reasons to speak in its behalf. The natural or +acquired partialities of mankind are continually throwing up +philosophical <span class="pagenum"><a name="Page_299" id="Page_299">[Pg 299]</a></span>theories, the sole recommendation of which consists in +the premises they afford for proving cherished doctrines, or justifying +favourite feelings: and when any one of these theories has been so +thoroughly discredited as no longer to serve the purpose, another is +always ready to take its place. This propensity, when exercised in +favour of any widely-spread persuasion or sentiment, is often decorated +with complimentary epithets; and the contrary habit of keeping the +judgment in complete subordination to evidence, is stigmatized by +various hard names, as scepticism, immorality, coldness, +hard-heartedness, and similar expressions according to the nature of the +case. But though the opinions of the generality of mankind, when not +dependent on mere habit and inculcation, have their root much more in +the inclinations than in the intellect, it is a necessary condition to +the triumph of the moral bias that it should first pervert the +understanding. Every erroneous inference, though originating in moral +causes, involves the intellectual operation of admitting insufficient +evidence as sufficient; and whoever was on his guard against all kinds +of inconclusive evidence which can be mistaken for conclusive, would be +in no danger of being led into error even by the strongest bias. There +are minds so strongly fortified on the intellectual side, that they +could not blind themselves to the light of truth, however really +desirous of doing so; they could not, with all the inclination in the +world, pass off upon themselves bad arguments for good ones. If the +sophistry of the intellect could be rendered impossible, that of the +feelings, having no instrument to work with, would be powerless. A +comprehensive classification of all those things which, not being +evidence, are liable to appear such to the understanding, will, +therefore, of itself include all errors of judgment arising from moral +causes, to the exclusion only of errors of practice committed against +better knowledge.</p> + +<p>To examine, then, the various kinds of apparent evidence which are not +evidence at all, and of apparently conclusive evidence which do not +really amount to conclusiveness, is the object of that part of our +inquiry into which we are about to enter.</p> + +<p><span class="pagenum"><a name="Page_300" id="Page_300">[Pg 300]</a></span></p><p>The subject is not beyond the compass of classification and +comprehensive survey. The things, indeed, which are not evidence of any +given conclusion, are manifestly endless, and this negative property, +having no dependence on any positive ones, cannot be made the groundwork +of a real classification. But the things which, not being evidence, are +susceptible of being mistaken for it, are capable of a classification +having reference to the positive property which they possess, of +appearing to be evidence. We may arrange them, at our choice, on either +of two principles; according to the cause which makes them appear to be +evidence, not being so; or according to the particular kind of evidence +which they simulate. The Classification of Fallacies which will be +attempted in the ensuing chapter, is founded on these considerations +jointly.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_301" id="Page_301">[Pg 301]</a></span></p> +<h3><a name="BOOK_V_CHAPTER_II" id="BOOK_V_CHAPTER_II"></a>CHAPTER II.<br /> +CLASSIFICATION OF FALLACIES.</h3> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_II_1">§ 1.</a> In attempting to establish certain general distinctions which shall +mark out from one another the various kinds of Fallacious Evidence, we +propose to ourselves an altogether different aim from that of several +eminent thinkers, who have given, under the name of Political or other +Fallacies, a mere enumeration of a certain number of erroneous opinions; +false general propositions which happen to be often met with; <i>loci +communes</i> of bad arguments on some particular subject. Logic is not +concerned with the false opinions which people happen to entertain, but +with the manner in which they come to entertain them. The question is +not, what facts have at any time been erroneously supposed to be proof +of certain other facts, but what property in the facts it was which led +any one to this mistaken supposition.</p> + +<p>When a fact is supposed, though incorrectly, to be evidentiary of, or a +mark of, some other fact, there must be a cause of the error; the +supposed evidentiary fact must be connected in some particular manner +with the fact of which it is deemed evidentiary,—must stand in some +particular relation to it, without which relation it would not be +regarded in that light. The relation may either be one resulting from +the simple contemplation of the two facts side by side with one another, +or it may depend on some process of mind, by which a previous +association has been established between them. Some peculiarity of +relation, however, there must be; the fact which can, even by the +wildest aberration, be supposed to prove another fact, must stand in +some special position with regard to it; and if we could ascertain and +define that special position, we should perceive the origin of the +error.</p> + +<p><span class="pagenum"><a name="Page_302" id="Page_302">[Pg 302]</a></span></p><p>We cannot regard one fact as evidentiary of another, unless we believe +that the two are always, or in the majority of cases, conjoined. If we +believe A to be evidentiary of B, if when we see A we are inclined to +infer B from it, the reason is because we believe that wherever A is, B +also either always or for the most part exists, either as an antecedent, +a consequent, or a concomitant. If when we see A we are inclined not to +expect B—if we believe A to be evidentiary of the absence of B—it is +because we believe that where A is, B either is never, or at least +seldom, found. Erroneous conclusions, in short, no less than correct +conclusions, have an invariable relation to a general formula, either +expressed or tacitly implied. When we infer some fact from some other +fact which does not really prove it, we either have admitted, or, if we +maintained consistency, ought to admit, some groundless general +proposition respecting the conjunction of the two phenomena.</p> + +<p>For every property, therefore, in facts, or in our mode of considering +facts, which leads us to believe that they are habitually conjoined when +they are not, or that they are not when in reality they are, there is a +corresponding kind of Fallacy; and an enumeration of fallacies would +consist in a specification of those properties in facts, and those +peculiarities in our mode of considering them, which give rise to this +erroneous opinion.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_II_2">§ 2.</a> To begin, then; the supposed connexion, or repugnance, between the +two facts, may either be a conclusion from evidence (that is, from some +other proposition or propositions) or may be admitted without any such +ground; admitted, as the phrase is, on its own evidence; embraced as +self-evident, as an axiomatic truth. This gives rise to the first great +distinction, that between Fallacies of Inference, and Fallacies of +Simple Inspection. In the latter division must be included not only all +cases in which a proposition is believed and held for true, literally +without any extrinsic evidence, either of specific experience or general +reasoning; but those more frequent cases in which simple inspection +<span class="pagenum"><a name="Page_303" id="Page_303">[Pg 303]</a></span>creates a <i>presumption</i> in favour of a proposition; not sufficient for +belief, but sufficient to cause the strict principles of a regular +induction to be dispensed with, and creating a predisposition to believe +it on evidence which would be seen to be insufficient if no such +presumption existed. This class, comprehending the whole of what may be +termed Natural Prejudices, and which I shall call indiscriminately +Fallacies of Simple Inspection or Fallacies <i>à priori</i>, shall be placed +at the head of our list.</p> + +<p>Fallacies of Inference, or erroneous conclusions from supposed evidence, +must be subdivided according to the nature of the apparent evidence from +which the conclusions are drawn; or (what is the same thing) according +to the particular kind of sound argument which the fallacy in question +simulates. But there is a distinction to be first drawn, which does not +answer to any of the divisions of sound arguments, but arises out of the +nature of bad ones. We may know exactly what our evidence is, and yet +draw a false conclusion from it; we may conceive precisely what our +premises are, what alleged matters of fact, or general principles, are +the foundation of our inference; and yet, because the premises are +false, or because we have inferred from them what they will not support, +our conclusion may be erroneous. But a case, perhaps even more frequent, +is that in which the error arises from not conceiving our premises with +due clearness, that is, (as shown in the preceding Book,<a name="FNanchor_1_69" id="FNanchor_1_69"></a><a href="#Footnote_1_69" class="fnanchor">[1]</a>) with due +fixity: forming one conception of our evidence when we collect or +receive it, and another when we make use of it; or unadvisedly, and in +general unconsciously, substituting, as we proceed, different premises +in the place of those with which we set out, or a different conclusion +for that which we undertook to prove. This gives existence to a class of +fallacies which may be justly termed (in a phrase borrowed from Bentham) +Fallacies of Confusion; comprehending, among others, all those which +have their source in language, whether arising from the vagueness or +ambiguity of our terms, or from casual associations with them.</p> + +<p><span class="pagenum"><a name="Page_304" id="Page_304">[Pg 304]</a></span></p><p>When the fallacy is not one of Confusion, that is, when the proposition +believed, and the evidence on which it is believed, are steadily +apprehended and unambiguously expressed, there remain to be made two +cross divisions. The Apparent Evidence may be either particular facts, +or foregone generalizations; that is, the process may simulate either +simple Induction, or Deduction; and again, the evidence, whether +consisting of supposed facts or of general propositions, may be false in +itself, or, being true, may fail to bear out the conclusion attempted to +be founded on it. This gives us first, Fallacies of Induction and +Fallacies of Deduction, and then a subdivision of each of these, +according as the supposed evidence is false, or true but inconclusive.</p> + +<p>Fallacies of Induction, where the facts on which the induction proceeds +are erroneous, may be termed Fallacies of Observation. The term is not +strictly accurate, or rather, not accurately coextensive with the class +of fallacies which I propose to designate by it. Induction is not always +grounded on facts immediately observed, but sometimes on facts inferred: +and when these last are erroneous, the error may not be, in the literal +sense of the term, an instance of bad observation, but of bad inference. +It will be convenient, however, to make only one class of all the +inductions of which the error lies in not sufficiently ascertaining the +facts on which the theory is grounded; whether the cause of failure be +mal-observation, or simple non-observation, and whether the +mal-observation be direct, or by means of intermediate marks which do +not prove what they are supposed to prove. And in the absence of any +comprehensive term to denote the ascertainment, by whatever means, of +the facts on which an induction is grounded, I will venture to retain +for this class of fallacies, under the explanation now given, the title +of Fallacies of Observation.</p> + +<p>The other class of inductive fallacies, in which the facts are correct, +but the conclusion not warranted by them, are properly denominated +Fallacies of Generalization: and these, again, fall into various +subordinate classes or natural groups, some of which will be enumerated +in their proper place.</p> + +<p><span class="pagenum"><a name="Page_305" id="Page_305">[Pg 305]</a></span></p><p>When we now turn to Fallacies of Deduction, namely those modes of +incorrect argumentation in which the premises, or some of them, are +general propositions, and the argument a ratiocination; we may of course +subdivide these also into two species similar to the two preceding, +namely, those which proceed on false premises, and those of which the +premises, though true, do not support the conclusion. But of these +species, the first must necessarily fall under some one of the heads +already enumerated. For the error must be either in those premises which +are general propositions, or in those which assert individual facts. In +the former case it is an Inductive Fallacy, of one or the other class; +in the latter it is a Fallacy of Observation: unless, in either case, +the erroneous premise has been assumed on simple inspection, in which +case the fallacy is <i>à priori</i>. Or finally, the premises, of whichever +kind they are, may never have been conceived in so distinct a manner as +to produce any clear consciousness by what means they were arrived at; +as in the case of what is called reasoning in a circle: and then the +fallacy is one of Confusion.</p> + +<p>There remain, therefore, as the only class of fallacies having properly +their seat in deduction, those in which the premises of the +ratiocination do not bear out its conclusion; the various cases, in +short, of vicious argumentation, provided against by the rules of the +syllogism. We shall call these, Fallacies of Ratiocination.</p> + +<p>We have thus five distinguishable classes of fallacy, which may be +expressed in the following synoptic table:—</p> + + +<div class="center"> +<table class="wider" border="0" cellpadding="1" cellspacing="0" summary=""> +<tr><td align="left" valign="top" colspan="4" style="border-top:1px black solid;border-left:1px black solid;">Fallacies</td><td style="border-top:1px black solid;border-right:1px black solid;"></td></tr> +<tr><td style="width:5%;border-left:1px black solid;"></td><td align="left" valign="top" colspan="3" style="border-top:1px black solid;border-left:1px black solid;">of Simple Inspection</td><td align="left" valign="top" style="width:40%;border-top:1px black solid;border-right:1px black solid;">1. Fallacies <i>à priori</i>.</td></tr> +<tr><td style="border-left:1px black solid;"></td><td align="left" valign="top" colspan="3" style="border-top:1px black solid;border-left:1px black solid;">of Inference</td><td style="border-top:1px black solid;border-right:1px black solid;"></td></tr> +<tr><td style="border-left:1px black solid;"></td><td style="width:5%;border-left:1px black solid;"></td><td align="left" valign="top" colspan="2" style="border-top:1px black solid;border-left:1px black solid;">from evidence distinctly conceived</td><td style="border-top:1px black solid;border-right:1px black solid;"></td></tr> +<tr><td style="border-left:1px black solid;"></td><td style="border-left:1px black solid;"></td><td style="width:5%;border-left:1px black solid;"></td><td align="left" valign="top" style="width:45%;border-top:1px black solid;border-left:1px black solid;">Inductive Fallacies</td><td align="left" valign="top" style="border-top:1px black solid;border-right:1px black solid;">2. Fallacies of Observation.</td></tr> +<tr><td style="border-left:1px black solid;"></td><td style="border-left:1px black solid;"></td><td style="border-left:1px black solid;"></td><td style="border-left:1px black solid;"></td><td align="left" valign="top" style="border-right:1px black solid;">3. Fallacies of Generalization.</td></tr> +<tr><td style="border-left:1px black solid;"></td><td style="border-left:1px black solid;"></td><td style="border-left:1px black solid;"></td><td align="left" valign="top" style="border-top:1px black solid;border-left:1px black solid;">Deductive Fallacies</td><td align="left" valign="top" style="border-top:1px black solid;border-right:1px black solid;">4. Fallacies of Ratiocination.</td></tr> +<tr><td style="border-bottom:1px black solid;border-left:1px black solid;"></td><td style="border-bottom:1px black solid;border-left:1px black solid;"></td><td align="left" valign="top" colspan="2" style="border-top:1px black solid;border-left:1px black solid;border-bottom:1px black solid;">from evidence indistinctly conceived</td><td align="left" valign="top" style="border-top:1px black solid;border-right:1px black solid;border-bottom:1px black solid;">5. Fallacies of Confusion.</td></tr> +</table> +</div> + +<p class="newsection"><a name="BOOK_V_CHAPTER_II_3">§ 3.</a> We must not, however, expect to find that men's actual errors +always, or even commonly, fall so unmistakeably <span class="pagenum"><a name="Page_306" id="Page_306">[Pg 306]</a></span>under some one of these +classes, as to be incapable of being referred to any other. Erroneous +arguments do not admit of such a sharply cut division as valid arguments +do. An argument fully stated, with all its steps distinctly set out, in +language not susceptible of misunderstanding, must, if it be erroneous, +be so in some one of these five modes unequivocally: or indeed of the +first four, since the fifth, on such a supposition, would vanish. But it +is not in the nature of bad reasoning to express itself thus +unambiguously. When a sophist, whether he is imposing on himself or +attempting to impose on others, can be constrained to throw his +sophistry into so distinct a form, it needs, in a large proportion of +cases, no further exposure.</p> + +<p>In all arguments, everywhere but in the schools, some of the links are +suppressed; <i>à fortiori</i> when the arguer either intends to deceive, or +is a lame and inexpert thinker, little accustomed to bring his reasoning +processes to any test: and it is in those steps of the reasoning which +are made in this tacit and half-conscious, or even wholly unconscious +manner, that the error oftenest lurks. In order to detect the fallacy, +the proposition thus silently assumed must be supplied; but the +reasoner, most likely, has never really asked himself what he was +assuming: his confuter, unless permitted to extort it from him by the +Socratic mode of interrogation, must himself judge what the suppressed +premise ought to be in order to support the conclusion. And hence, in +the words of Archbishop Whately, "it must be often a matter of doubt, or +rather, of arbitrary choice, not only to which genus each <i>kind</i> of +fallacy should be referred, but even to which kind to refer any one +<i>individual</i> fallacy; for since, in any course of argument, <i>one</i> +premise is usually suppressed, it frequently happens in the case of a +fallacy, that the hearers are left to the alternative of supplying +<i>either</i> a premise which is <i>not true</i>, or <i>else</i>, one which <i>does not +prove</i> the conclusion: <i>e. g.</i> if a man expatiates on the distress of +the country, and thence argues that the government is tyrannical, we +must suppose him to assume <i>either</i> that 'every distressed country is +under a tyranny,' which is a manifest falsehood, <i>or</i> merely that 'every +country under a <span class="pagenum"><a name="Page_307" id="Page_307">[Pg 307]</a></span>tyranny is distressed,' which, however true, proves +nothing, the middle term being undistributed." The former would be +ranked, in our distribution, among fallacies of generalization, the +latter among those of ratiocination. "Which are we to suppose the +speaker meant us to understand? Surely" (if he understood himself) "just +whichever each of his hearers might happen to prefer: some might assent +to the false premise; others allow the unsound syllogism."</p> + +<p>Almost all fallacies, therefore, might in strictness be brought under +our fifth class, Fallacies of Confusion. A fallacy can seldom be +absolutely referred to any of the other classes; we can only say, that +if all the links were filled up which should be capable of being +supplied in a valid argument, it would either stand thus (forming a +fallacy of one class), or thus (a fallacy of another); or at furthest we +may say, that the conclusion is most <i>likely</i> to have originated in a +fallacy of such and such a class. Thus in the illustration just quoted, +the error committed may be traced with most probability to a fallacy of +generalization; that of mistaking an uncertain mark, or piece of +evidence, for a certain one; concluding from an effect to some one of +its possible causes, when there are others which would have been equally +capable of producing it.</p> + +<p>Yet, though the five classes run into each other, and a particular error +often seems to be arbitrarily assigned to one of them rather than to any +of the rest, there is considerable use in so distinguishing them. We +shall find it convenient to set apart, as Fallacies of Confusion, those +of which confusion is the most obvious characteristic; in which no other +cause can be assigned for the mistake committed, than neglect or +inability to state the question properly, and to apprehend the evidence +with definiteness and precision. In the remaining four classes I shall +place not only the cases in which the evidence is clearly seen to be +what it is, and yet a wrong conclusion drawn from it, but also those in +which, although there be confusion, the confusion is not the sole cause +of the error, but there is some shadow of a ground for it in the nature +of the evidence itself. And in distributing these cases of partial +<span class="pagenum"><a name="Page_308" id="Page_308">[Pg 308]</a></span>confusion among the four classes, I shall, when there can be any +hesitation as to the precise seat of the fallacy, suppose it to be in +that part of the process in which, from the nature of the case, and the +tendencies of the human mind, an error would in the particular +circumstances be the most probable.</p> + +<p>After these observations we shall proceed, without further preamble, to +consider the five classes in their order.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_309" id="Page_309">[Pg 309]</a></span></p> +<h3><a name="BOOK_V_CHAPTER_III" id="BOOK_V_CHAPTER_III"></a>CHAPTER III.<br /> +FALLACIES OF SIMPLE INSPECTION; OR <i>À PRIORI</i> FALLACIES.</h3> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_III_1">§ 1.</a> The tribe of errors of which we are to treat in the first instance, +are those in which no actual inference takes place at all: the +proposition (it cannot in such cases be called a conclusion) being +embraced, not as proved, but as requiring no proof; as a self-evident +truth; or else as having such intrinsic verisimilitude, that external +evidence not in itself amounting to proof, is sufficient in aid of the +antecedent presumption.</p> + +<p>An attempt to treat this subject comprehensively would be a +transgression of the bounds prescribed to this work, since it would +necessitate the inquiry which, more than any other, is the grand +question of what is called metaphysics, viz. What are the propositions +which may reasonably be received without proof? That there must be some +such propositions all are agreed, since there cannot be an infinite +series of proof, a chain suspended from nothing. But to determine what +these propositions are, is the <i>opus magnum</i> of the more recondite +mental philosophy. Two principal divisions of opinion on the subject +have divided the schools of philosophy from its first dawn. The one +recognises no ultimate premises but the facts of our subjective +consciousness; our sensations, emotions, intellectual states of mind, +and volitions. These, and whatever by strict rules of induction can be +derived from these, it is possible, according to this theory, for us to +know; of all else we must remain in ignorance. The opposite school hold +that there are other existences, suggested indeed to our minds by these +subjective phenomena, but not inferrible from them, by any process +either of deduction or of induction; which, however, we must, by the +constitution of our mental nature <span class="pagenum"><a name="Page_310" id="Page_310">[Pg 310]</a></span>recognise as realities; and +realities, too, of a higher order than the phenomena of our +consciousness, being the efficient causes and necessary substrata of all +Phenomena. Among these entities they reckon Substances, whether matter +or spirit; from the dust under our feet to the soul, and from that to +Deity. All these, according to them, are preternatural or supernatural +beings, having no likeness in experience, though experience is entirely +a manifestation of their agency. Their existence, together with more or +less of the laws to which they conform in their operations, are, on this +theory, apprehended and recognised as real by the mind itself +intuitively: experience (whether in the form of sensation or of mental +feeling) having no other part in the matter than as affording facts +which are consistent with these necessary postulates of reason, and +which are explained and accounted for by them.</p> + +<p>As it is foreign to the purpose of the present treatise to decide +between these conflicting theories, we are precluded from inquiring into +the existence, or defining the extent and limits, of knowledge <i>à +priori</i>, and from characterizing the kind of correct assumption which +the fallacy of incorrect assumption, now under consideration, simulates. +Yet since it is allowed on both sides that such assumptions are often +made improperly, we may find it practicable, without entering into the +ultimate metaphysical grounds of the discussion, to state some +speculative propositions, and suggest some practical cautions, +respecting the forms in which such unwarranted assumptions are most +likely to be made.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_III_2">§ 2.</a> In the cases in which, according to the thinkers of the ontological +school, the mind apprehends, by intuition, things, and the laws of +things, not cognizable by our sensitive faculty; those intuitive, or +supposed intuitive, perceptions are undistinguishable from what the +opposite school are accustomed to call ideas of the mind. When they +themselves say that they perceive the things by an immediate act of a +faculty given for that purpose by their Creator, it would be said of +them by their opponents that they find an idea or conception <span class="pagenum"><a name="Page_311" id="Page_311">[Pg 311]</a></span>in their +own minds, and from the idea or conception, infer the existence of a +corresponding objective reality. Nor would this be an unfair statement, +but a mere version into other words of the account given by many of +themselves; and one to which the more clear-sighted of them might, and +generally do, without hesitation, subscribe. Since, therefore, in the +cases which lay the strongest claims to be examples of knowledge <i>à +priori</i>, the mind proceeds from the idea of a thing to the reality of +the thing itself, we cannot be surprised by finding that illicit +assumptions <i>à priori</i> consist in doing the same thing erroneously: in +mistaking subjective facts for objective, laws of the percipient mind +for laws of the perceived object, properties of the ideas or conceptions +for properties of the things conceived.</p> + +<p>Accordingly, a large proportion of the erroneous thinking which exists +in the world proceeds on a tacit assumption, that the same order must +obtain among the objects in nature which obtains among our ideas of +them. That if we always think of two things together, the two things +must always exist together. That if one thing makes us think of another +as preceding or following it, that other must precede it or follow it in +actual fact. And conversely, that when we cannot conceive two things +together they cannot exist together, and that their combination may, +without further evidence, be rejected from the list of possible +occurrences.</p> + +<p>Few persons, I am inclined to think, have reflected on the great extent +to which this fallacy has prevailed, and prevails, in the actual beliefs +and actions of mankind. For a first illustration of it, we may refer to +a large class of popular superstitions. If any one will examine in what +circumstances most of those things agree, which in different ages and by +different portions of the human race have been considered as omens or +prognostics of some interesting event, whether calamitous or fortunate; +they will be found very generally characterized by this peculiarity, +that they cause the mind to <i>think</i> of that, of which they are therefore +supposed to forebode the actual occurrence. "Talk of the devil, and he +will appear," has passed into a proverb. Talk of the devil, that is, +raise the <span class="pagenum"><a name="Page_312" id="Page_312">[Pg 312]</a></span>idea, and the reality will follow. In times when the +appearance of that personage in a visible form was thought to be no +unfrequent occurrence, it has doubtless often happened to persons of +vivid imagination and susceptible nerves, that talking of the devil has +caused them to fancy they saw him; as, even in our more incredulous +days, listening to ghost stories predisposes us to see ghosts; and thus, +as a prop to the <i>à priori</i> fallacy, there might come to be added an +auxiliary fallacy of mal-observation, with one of false generalization +grounded on it. Fallacies of different orders often herd or cluster +together in this fashion, one smoothing the way for another. But the +origin of the superstition is evidently that which we have assigned. In +like manner it has been universally considered unlucky to speak of +misfortune. The day on which any calamity happened has been considered +an unfortunate day, and there has been a feeling everywhere, and in some +nations a religious obligation, against transacting any important +business on that day. For on such a day our thoughts are likely to be of +misfortune. For a similar reason, any untoward occurrence in commencing +an undertaking has been considered ominous of failure; and often, +doubtless, has really contributed to it, by putting the persons engaged +in the enterprise more or less out of spirits: but the belief has +equally prevailed where the disagreeable circumstance was, independently +of superstition, too insignificant to depress the spirits by any +influence of its own. All know the story of Cæsar's accidentally +stumbling in the act of landing on the African coast; and the presence +of mind with which he converted the direful presage into a favourable +one by exclaiming, "Africa, I embrace thee." Such omens, it is true, +were often conceived as warnings of the future, given by a friendly or a +hostile deity; but this very superstition grew out of a pre-existing +tendency; the god was supposed to send, as an indication of what was to +come, something which people were already disposed to consider in that +light. So in the case of lucky or unlucky names. Herodotus tells us how +the Greeks, on the way to Mycale, were encouraged in their enterprise by +the arrival of a deputation <span class="pagenum"><a name="Page_313" id="Page_313">[Pg 313]</a></span>from Samos, one of the members of which was +named Hegesistratus, the leader of armies.</p> + +<p>Cases may be pointed out in which something which could have no real +effect but to make persons <i>think</i> of misfortune, was regarded not +merely as a prognostic, but as something approaching to an actual cause +of it. The <i>εὐφήμει</i> of the Greeks, and <i>favete linguis</i>, or +<i>bona verba quæso</i>, of the Romans, evince the care with which they +endeavoured to repress the utterance of any word expressive or +suggestive of ill fortune; not from notions of delicate politeness, to +which their general mode of conduct and feeling had very little +reference, but from <i>bonâ fide</i> alarm lest the event so suggested to the +imagination should in fact occur. Some vestige of a similar superstition +has been known to exist among uneducated persons even in our own day: it +is thought an unchristian thing to talk of, or suppose, the death of any +person while he is alive. It is known how careful the Romans were to +avoid, by an indirect mode of speech, the utterance of any word directly +expressive of death or other calamity: how instead of <i>mortuus est</i> they +said <i>vixit</i>; and "be the event fortunate or <i>otherwise</i>" instead of +<i>adverse</i>. The name Maleventum, of which Salmasius so sagaciously +detected the Thessalian origin (<i>Μαλόεις</i>, <i>Μαλοέντος</i>), +they changed into the highly propitious denomination, Beneventum; Egesta +into Segesta; and Epidamnus, a name so interesting in its associations +to the reader of Thucydides, they exchanged for Dyrrhachium, to escape +the perils of a word suggestive of <i>damnum</i> or detriment.</p> + +<p>"If an hare cross the highway," says Sir Thomas Browne,<a name="FNanchor_2_70" id="FNanchor_2_70"></a><a href="#Footnote_2_70" class="fnanchor">[2]</a> "there are +few above threescore that are not perplexed thereat; which +notwithstanding is but an augurial terror, according to that received +expression, <i>Inauspicatum dat iter oblatus lepus</i>. And the ground of the +conceit was probably no greater than this, that a fearful animal passing +by us portended unto us something to be feared; as upon the like +consideration the meeting of a fox presaged some future imposture." Such +<span class="pagenum"><a name="Page_314" id="Page_314">[Pg 314]</a></span>superstitions as these last must be the result of study; they are too +recondite for natural or spontaneous growth. But when the attempt was +once made to construct a science of predictions, any association, though +ever so faint or remote, by which an object could be connected in +however far-fetched a manner with ideas either of prosperity or of +danger and misfortune, was enough to determine its being classed among +good or evil omens.</p> + +<p>An example of rather a different kind from any of these, but falling +under the same principle, is the famous attempt on which so much labour +and ingenuity were expended by the alchemists, to make gold potable. The +motive to this was a conceit that potable gold could be no other than +the universal medicine: and why gold? Because it was so precious. It +must have all marvellous properties as a physical substance, because the +mind was already accustomed to marvel at it.</p> + +<p>From a similar feeling, "every substance," says Dr. Paris,<a name="FNanchor_3_71" id="FNanchor_3_71"></a><a href="#Footnote_3_71" class="fnanchor">[3]</a> "whose +origin is involved in mystery, has at different times been eagerly +applied to the purposes of medicine. Not long since, one of those +showers which are now known to consist of the excrements of insects, +fell in the north of Italy; the inhabitants regarded it as manna, or +some supernatural panacea, and they swallowed it with such avidity, that +it was only by extreme address that a small quantity was obtained for a +chemical examination." The superstition, in this instance, though +doubtless partly of a religious character, probably in part also arose +from the prejudice that a wonderful thing must of course have wonderful +properties.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_III_3">§ 3.</a> The instances of <i>à priori</i> fallacy which we have hitherto cited +belong to the class of vulgar errors, and do not now, nor in any but a +rude age ever could, impose upon minds of any considerable attainments. +But those to which we are about to proceed, have been, and still are, +all but universally prevalent among thinkers. The same disposition <span class="pagenum"><a name="Page_315" id="Page_315">[Pg 315]</a></span>to +give objectivity to a law of the mind—to suppose that what is true of +our ideas of things must be true of the things themselves—exhibits +itself in many of the most accredited modes of philosophical +investigation, both on physical and on metaphysical subjects. In one of +its most undisguised manifestations, it embodies itself in two maxims, +which lay claim to axiomatic truth: Things which we cannot think of +together, cannot coexist; and Things which we cannot help thinking of +together, must coexist. I am not sure that the maxims were ever +expressed in these precise words, but the history both of philosophy and +of popular opinions abounds with exemplifications of both forms of the +doctrine.</p> + +<p>To begin with the latter of them: Things which we cannot think of except +together, must exist together. This is assumed in the generally received +and accredited mode of reasoning which concludes that A must accompany B +in point of fact, because "it is involved in the idea." Such thinkers do +not reflect that the idea, being a result of abstraction, ought to +conform to the facts, and cannot make the facts conform to it. The +argument is at most admissible as an appeal to authority; a surmise, +that what is now part of the idea, must, before it became so, have been +found by previous inquirers in the facts. Nevertheless, the philosopher +who more than all others made professions of rejecting authority, +Descartes, constructed his system on this very basis. His favourite +device for arriving at truth, even in regard to outward things, was by +looking into his own mind for it. "Credidi me," says his celebrated +maxim, "pro regulâ generali sumere posse, omne id quod valdè dilucidè et +distinctè concipiebam, verum esse;" whatever can be very clearly +conceived, must certainly exist; that is, as he afterwards explains it, +if the idea includes existence. And on this ground he infers that +geometrical figures really exist, because they can be distinctly +conceived. Whenever existence is "involved in an idea," a thing +conformable to the idea must really exist; which is as much as to say, +whatever the idea contains must have its equivalent in the thing; and +what we <span class="pagenum"><a name="Page_316" id="Page_316">[Pg 316]</a></span>are not able to leave out of the idea cannot be absent from the +reality.<a name="FNanchor_4_72" id="FNanchor_4_72"></a><a href="#Footnote_4_72" class="fnanchor">[4]</a> This assumption pervades the philosophy not only of +Descartes, but of all the thinkers who received their impulse mainly +from him, in particular the two most remarkable among them, Spinoza and +Leibnitz, from whom the modern German metaphysical philosophy is +essentially an emanation. I am indeed disposed to think that the fallacy +now under consideration has been the cause of two-thirds of the bad +philosophy, and especially of the bad metaphysics, which the human mind +has never ceased to produce. Our general ideas contain nothing but what +has been put into them, either by our passive experience, or by our +active habits of thought; and the metaphysicians in all ages, who have +attempted to construct the laws of the universe by reasoning from our +supposed necessities of thought, have always proceeded, and only could +proceed, by laboriously finding in their own minds what they themselves +had formerly put there, and evolving from their ideas of things what +they had first <i>involved</i> in those ideas. In this way all deeply-rooted +opinions and feelings are enabled to create apparent demonstrations of +their truth and reasonableness, as it were out of their own substance.</p> + +<p>The other form of the fallacy; Things which we cannot think of together +cannot exist together,—including as one of its branches, that what we +cannot think of as existing cannot exist at all,—may thus be briefly +expressed: Whatever is inconceivable must be false.</p> + +<p>Against this prevalent doctrine I have sufficiently argued in a former +Book,<a name="FNanchor_5_73" id="FNanchor_5_73"></a><a href="#Footnote_5_73" class="fnanchor">[5]</a> and nothing is required in this place but <span class="pagenum"><a name="Page_317" id="Page_317">[Pg 317]</a></span>examples. It was +long held that Antipodes were impossible because of the difficulty which +was found in conceiving persons with their heads in the same direction +as our feet. And it was one of the received arguments against the +Copernican system, that we cannot conceive so great a void space as that +system supposes to exist in the celestial regions. When men's +imaginations had always been used to conceive the stars as firmly set in +solid spheres, they naturally found much difficulty in imagining them in +so different, and, as it doubtless appeared to them, so precarious a +situation. But they had no right to mistake the limitation (whether +natural, or, as it in fact proved, only artificial) of their own +faculties, for an inherent limitation of the possible modes of existence +in the universe.</p> + +<p>It may be said in objection, that the error in these cases was in the +minor premise, not the major; an error of fact, not of principle; that +it did not consist in supposing that what is inconceivable cannot be +true, but in supposing antipodes to be inconceivable, when present +experience proves that they can be conceived. Even if this objection +were allowed, and the proposition that what is inconceivable cannot be +true were suffered to remain unquestioned as a speculative truth, it +would be a truth on which no practical consequence could ever be +founded, since, on this showing, it is impossible to affirm of any +proposition, not being a contradiction in terms, that it is +inconceivable. Antipodes were really, not fictitiously, inconceivable to +our ancestors: they are indeed conceivable to us; and as the limits of +our power of conception have been so largely extended, by the extension +of our experience and the more varied exercise of our imagination, so +may posterity find many combinations perfectly conceivable to them which +are inconceivable to us. But, as beings of limited experience, we must +always and necessarily have limited conceptive powers; while it does not +by any means follow that the same limitation obtains in the +possibilities of nature, nor even in her actual manifestations.</p> + +<p>Rather more than a century and a half ago it was a scientific maxim, +disputed by no one, and which no one deemed to <span class="pagenum"><a name="Page_318" id="Page_318">[Pg 318]</a></span>require any proof, that +"a thing cannot act where it is not." With this weapon the Cartesians +waged a formidable war against the theory of gravitation, which, +according to them, involving so obvious an absurdity, must be rejected +<i>in limine</i>: the sun could not possibly act upon the earth, not being +there. It was not surprising that the adherents of the old systems of +astronomy should urge this objection against the new; but the false +assumption imposed equally on Newton himself, who in order to turn the +edge of the objection, imagined a subtle ether which filled up the space +between the sun and the earth, and by its intermediate agency was the +proximate cause of the phenomena of gravitation. "It is inconceivable," +said Newton, in one of his letters to Dr. Bentley,<a name="FNanchor_6_74" id="FNanchor_6_74"></a><a href="#Footnote_6_74" class="fnanchor">[6]</a> "that inanimate +brute matter should, without the mediation of something else, which is +not material, operate upon and affect other matter <i>without mutual +contact</i>.... That gravity should be innate, inherent, and essential to +matter, so that one body may act on another, at a distance, through a +vacuum, without the mediation of anything else, by and through which +their action and force may be conveyed from one to another, is to me so +great an absurdity, that I believe no man, who in philosophical matters +has a competent faculty of thinking, can ever fall into it." This +passage should be hung up in the cabinet of every cultivator of science +who is ever tempted to pronounce a fact impossible because it appears to +him inconceivable. In our own day one would be more tempted, though with +equal injustice, to reverse the concluding observation, and consider the +seeing any absurdity at all in a thing so simple and natural, to be what +really marks the absence of "a competent faculty of thinking." No one +now feels any difficulty in conceiving gravity to be, as much as any +other property is, "inherent, and essential to matter," nor finds the +comprehension of it facilitated in the smallest degree by the +supposition of an ether (though some recent inquirers do give this as an +explanation of it); nor thinks it at all incredible that the celestial +bodies can and do act where they, in actual bodily presence, <span class="pagenum"><a name="Page_319" id="Page_319">[Pg 319]</a></span>are not. +To us it is not more wonderful that bodies should act upon one another +"without mutual contact," than that they should do so when in contact; +we are familiar with both these facts, and we find them equally +inexplicable, but equally easy to believe. To Newton, the one, because +his imagination was familiar with it, appeared natural and a matter of +course, while the other, for the contrary reason, seemed too absurd to +be credited.</p> + +<p>It is strange that any one, after such a warning, should rely implicitly +on the evidence <i>à priori</i> of such propositions as these, that matter +cannot think; that space, or extension, is infinite; that nothing can be +made out of nothing (<i>ex nihilo nihil fit</i>). Whether these propositions +are true or not this is not the place to determine, nor even whether the +questions are soluble by the human faculties. But such doctrines are no +more self-evident truths, than the ancient maxim that a thing cannot act +where it is not, which probably is not now believed by any educated +person in Europe.<a name="FNanchor_7_75" id="FNanchor_7_75"></a><a href="#Footnote_7_75" class="fnanchor">[7]</a> Matter cannot think; why? because we <i>cannot +conceive</i> thought to be annexed to any arrangement of material +particles. Space is infinite, because having never known any part of it +which had not other parts beyond it, we <i>cannot conceive</i> an absolute +termination. <i>Ex nihilo nihil fit</i>, because having never known any +physical product without a pre-existing physical material, we <i>cannot</i>, +or think we cannot, <i>imagine</i> a creation out of nothing. But these +things may in themselves be as conceivable as gravitation without an +intervening medium, which Newton thought too great an absurdity for any +person of a competent faculty of philosophical thinking to admit: and +even supposing them not conceivable, this, for aught we know, may be +merely one of the limitations of our very limited minds, and not in +nature at all.</p> + +<p>No writer has more directly identified himself with the fallacy now +under consideration, or has embodied it in more distinct terms, than +Leibnitz. In his view, unless a thing was <span class="pagenum"><a name="Page_320" id="Page_320">[Pg 320]</a></span>not merely conceivable, but +even explainable, it could not exist in nature. All <i>natural</i> phenomena, +according to him, must be susceptible of being accounted for <i>à priori</i>. +The only facts of which no explanation could be given but the will of +God, were miracles properly so called. "Je reconnais," says he,<a name="FNanchor_8_76" id="FNanchor_8_76"></a><a href="#Footnote_8_76" class="fnanchor">[8]</a> +"qu'il n'est pas permis de nier ce qu'on n'entend pas; mais j'ajoute +qu'on a droit de nier (au moins dans l'ordre naturel) ce qui absolument +n'est point intelligible ni explicable. Je soutiens aussi ... qu'enfin +la conception des créatures n'est pas la mesure du pouvoir de Dieu, mais +que leur conceptivité, ou force de concevoir, est la mesure du pouvoir +de la nature, tout ce qui est conforme à l'ordre naturel pouvant être +conçu ou entendu par quelque créature."</p> + +<p>Not content with assuming that nothing can be true which we are unable +to conceive, scientific inquirers have frequently given a still further +extension to the doctrine, and held that, even of things not altogether +inconceivable, that which we can conceive with the greatest ease is +likeliest to be true. It was long an admitted axiom, and is not yet +entirely discredited, that "nature always acts by the simplest means," +<i>i.e.</i> by those which are most easily conceivable.<a name="FNanchor_9_77" id="FNanchor_9_77"></a><a href="#Footnote_9_77" class="fnanchor">[9]</a> A large proportion +of all the errors ever committed in the investigation of the laws of +nature, have arisen from the assumption that the most familiar +explanation or hypothesis must be the truest. One of the most +instructive facts in scientific history is the pertinacity with which +the human mind clung to the belief that the heavenly bodies must move in +circles, or be carried round by the revolution of spheres; merely +because those were in themselves the simplest suppositions: though, to +make them accord with the facts which were ever contradicting them more +and more, it became necessary to add sphere to sphere and circle to +circle, until the original simplicity was converted into almost +inextricable complication.</p> + + +<p><span class="pagenum"><a name="Page_321" id="Page_321">[Pg 321]</a></span></p><p class="newsection"><a name="BOOK_V_CHAPTER_III_4">§ 4.</a> We pass to another <i>à priori</i> fallacy or natural prejudice, allied +to the former, and originating as that does, in the tendency to presume +an exact correspondence between the laws of the mind and those of things +external to it. The fallacy may be enunciated in this general +form—Whatever can be thought of apart exists apart: and its most +remarkable manifestation consists in the personification of +abstractions. Mankind in all ages have had a strong propensity to +conclude that wherever there is a name, there must be a distinguishable +separate entity corresponding to the name; and every complex idea which +the mind has formed for itself by operating upon its conceptions of +individual things, was considered to have an outward objective reality +answering to it. Fate, Chance, Nature, Time, Space, were real beings, +nay, even gods. If the analysis of qualities in the earlier part of this +work be correct, names of qualities and names of substances stand for +the very same sets of facts or phenomena; <i>whiteness</i> and <i>a white +thing</i> are only different phrases, required by convenience for speaking +of the same external fact under different relations. Not such, however, +was the notion which this verbal distinction suggested of old, either to +the vulgar or to the scientific. Whiteness was an entity, inhering or +sticking in the white substance: and so of all other qualities. So far +was this carried, that even concrete general terms were supposed to be, +not names of indefinite numbers of individual substances, but names of a +peculiar kind of entities termed Universal Substances. Because we can +think and speak of man in general, that is, of all persons in so far as +possessing the common attributes of the species, without fastening our +thoughts permanently on some one individual person; therefore man in +general was supposed to be, not an aggregate of individual persons, but +an abstract or universal man, distinct from these.</p> + +<p>It may be imagined what havoc metaphysicians trained in these habits +made with philosophy, when they came to the largest generalizations of +all. <i>Substantiæ Secundæ</i> of any kind were bad enough, but such +Substantiæ Secundæ as <i>τὸ ὄν</i>, for example, and <i>τὸ ἕν</i>, +standing for peculiar entities supposed to <span class="pagenum"><a name="Page_322" id="Page_322">[Pg 322]</a></span>be inherent in all things +which <i>exist</i>, or which are said to be <i>one</i>, were enough to put an end +to all intelligible discussion; especially since, with a just perception +that the truths which philosophy pursues are <i>general</i> truths, it was +soon laid down that these general substances were the only subjects of +science, being immutable, while individual substances cognizable by the +senses, being in a perpetual flux, could not be the subject of real +knowledge. This misapprehension of the import of general language +constitutes Mysticism, a word so much oftener written and spoken than +understood. Whether in the Vedas, in the Platonists, or in the +Hegelians, mysticism is neither more nor less than ascribing objective +existence to the subjective creations of our own faculties, to ideas or +feelings of the mind; and believing that by watching and contemplating +these ideas of its own making, it can read in them what takes place in +the world without.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_III_5">§ 5.</a> Proceeding with the enumeration of <i>à priori</i> fallacies, and +endeavouring to arrange them with as much reference as possible to their +natural affinities, we come to another, which is also nearly allied to +the fallacy preceding the last, standing in the same relation to one +variety of it as the fallacy last mentioned does to the other. This, +too, represents nature as under incapacities corresponding to those of +our intellect; but instead of only asserting that nature cannot do a +thing because we cannot conceive it done, goes the still greater length +of averring that nature does a particular thing, on the sole ground that +we can see no reason why she should not. Absurd as this seems when so +plainly stated, it is a received principle among scientific authorities +for demonstrating <i>à priori</i> the laws of physical phenomena. A +phenomenon must follow a certain law, because we see no reason why it +should deviate from that law in one way rather than in another. This is +called the Principle of the Sufficient Reason;<a name="FNanchor_10_78" id="FNanchor_10_78"></a><a href="#Footnote_10_78" class="fnanchor">[10]</a> and by means of it +philosophers often flatter themselves that they are able <span class="pagenum"><a name="Page_323" id="Page_323">[Pg 323]</a></span>to establish, +without any appeal to experience, the most general truths of +experimental physics.</p> + +<p>Take, for example, two of the most elementary of all laws, the law of +inertia and the first law of motion. A body at rest cannot, it is +affirmed, begin to move unless acted upon by some external force: +because, if it did, it must either move up or down, forward or backward, +and so forth; but if no outward force acts upon it, there can be <i>no +reason</i> for its moving up rather than down, or down rather than up, &c., +<i>ergo</i>, it will not move at all.</p> + +<p>This reasoning I conceive to be entirely fallacious, as indeed Dr. +Brown, in his treatise on Cause and Effect, has shown with great +acuteness and justness of thought. We have before remarked, that almost +every fallacy may be referred to different genera by different modes of +filling up the suppressed steps; and this particular one may, at our +option, be brought under <i>petitio principii</i>. It supposes that nothing +can be a "sufficient reason" for a body's moving in one particular +direction, except some external force. But this is the very thing to be +proved. Why not some <i>internal</i> force? Why not the law of the thing's +own nature? Since these philosophers think it necessary to prove the law +of inertia, they of course do not suppose <i>it</i> to be self-evident; they +must, therefore, be of opinion that, previously to all proof, the +supposition of a body's moving by internal impulse is an admissible +hypothesis; but if so, why is not the hypothesis also admissible, that +the internal impulse acts naturally in some one particular direction, +not in another? If spontaneous motion might have been the law of matter, +why not spontaneous motion towards the sun, towards the earth, or +towards the zenith? Why not, as the ancients supposed, towards a +particular place in the universe, appropriated to each particular kind +of substance? Surely it is not allowable to say that spontaneity of +motion is credible in itself, but not credible if supposed to take place +in any determinate direction.</p> + +<p>Indeed, if any one chose to assert that all bodies when uncontrolled set +out in a direct line towards the north pole, he might equally prove his +point by the principle of the <span class="pagenum"><a name="Page_324" id="Page_324">[Pg 324]</a></span>Sufficient Reason. By what right is it +assumed that a state of rest is the particular state which cannot be +deviated from without special cause? Why not a state of motion, and of +some particular sort of motion? Why may we not say that the natural +state of a horse left to himself is to amble, because otherwise he must +either trot, gallop, or stand still, and because we know no reason why +he should do one of these rather than another? If this is to be called +an unfair use of the "sufficient reason," and the other a fair one, +there must be a tacit assumption that a state of rest is more natural to +a horse than a state of ambling. If this means that it is the state +which the animal will assume when left to himself, that is the very +point to be proved; and if it does not mean this, it can only mean that +a state of rest is the simplest state, and therefore the most likely to +prevail in nature, which is one of the fallacies or natural prejudices +we have already examined.</p> + +<p>So again of the First Law of Motion; that a body once moving will, if +left to itself, continue to move uniformly in a straight line. An +attempt is made to prove this law by saying, that if not, the body must +deviate either to the right or to the left, and that there is no reason +why it should do one more than the other. But who could know, +antecedently to experience, whether there was a reason or not? Might it +not be the nature of bodies, or of some particular bodies, to deviate +towards the right? or if the supposition is preferred, towards the east, +or south? It was long thought that bodies, terrestrial ones at least, +had a natural tendency to deflect downwards; and there is no shadow of +anything objectionable in the supposition, except that it is not true. +The pretended proof of the law of motion is even more manifestly +untenable than that of the law of inertia, for it is flagrantly +inconsistent; it assumes that the continuance of motion in the direction +first taken is more natural than deviation either to the right or to the +left, but denies that one of these can possibly be more natural than the +other. All these fancies of the possibility of knowing what is natural +or not natural by any other means than experience, are, in truth, +entirely futile. The real and only proof of the laws of motion, or of +<span class="pagenum"><a name="Page_325" id="Page_325">[Pg 325]</a></span>any other law of the universe, is experience; it is simply that no +other suppositions explain or are consistent with the facts of universal +nature.</p> + +<p>Geometers have, in all ages, been open to the imputation of endeavouring +to prove the most general facts of the outward world by sophistical +reasoning, in order to avoid appeals to the senses. Archimedes, says +Professor Playfair,<a name="FNanchor_11_79" id="FNanchor_11_79"></a><a href="#Footnote_11_79" class="fnanchor">[11]</a> established some of the elementary propositions +of statics by a process in which he "borrows no principle from +experiment, but establishes his conclusion entirely by reasoning <i>à +priori</i>. He assumes, indeed, that equal bodies, at the ends of the equal +arms of a lever, will balance one another; and also that a cylinder or +parallelopiped of homogeneous matter, will be balanced about its centre +of magnitude. These, however, are not inferences from experience; they +are, properly speaking, conclusions deduced from the principle of the +Sufficient Reason." And to this day there are few geometers who would +not think it far more scientific to establish these or any other +premises in this way, than to rest their evidence on that familiar +experience which in the case in question might have been so safely +appealed to.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_III_6">§ 6.</a> Another natural prejudice, of most extensive prevalence, and which +had a great share in producing the errors fallen into by the ancients in +their physical inquiries, was this: That the differences in nature must +correspond to our received distinctions; that effects which we are +accustomed, in popular language, to call by different names, and arrange +in different classes, must be of different natures, and have different +causes. This prejudice, so evidently of the same origin with those +already treated of, marks more especially the earliest stage of science, +when it has not yet broken loose from the trammels of every-day +phraseology. The extraordinary prevalence of the fallacy among the Greek +philosophers may be accounted for by their generally knowing no other +language than their own; from which it was a consequence <span class="pagenum"><a name="Page_326" id="Page_326">[Pg 326]</a></span>that their +ideas followed the accidental or arbitrary combinations of that +language, more completely than can happen among the moderns to any but +illiterate persons. They had great difficulty in distinguishing between +things which their language confounded, or in putting mentally together +things which it distinguished; and could hardly combine the objects in +nature, into any classes but those which were made for them by the +popular phrases of their own country: or at least could not help +fancying those classes to be natural, and all others arbitrary and +artificial. Accordingly, scientific investigation among the Greek +schools of speculation and their followers in the middle ages, was +little more than a mere sifting and analysing of the notions attached to +common language. They thought that by determining the meaning of words, +they could become acquainted with facts. "They took for granted," says +Dr. Whewell,<a name="FNanchor_12_80" id="FNanchor_12_80"></a><a href="#Footnote_12_80" class="fnanchor">[12]</a> "that philosophy must result from the relations of +those notions which are involved in the common use of language, and they +proceeded to seek it by studying such notions." In his next chapter, Dr. +Whewell has so well illustrated and exemplified this error, that I shall +take the liberty of quoting him at some length.</p> + +<p>"The propensity to seek for principles in the common usages of language +may be discerned at a very early period. Thus we have an example of it +in a saying which is reported of Thales, the founder of Greek +philosophy. When he was asked, 'What is the <i>greatest</i> thing?' he +replied '<i>Place</i>; for all other things are <i>in</i> the world, but the world +is <i>in</i> it.' In Aristotle we have the consummation of this mode of +speculation. The usual point from which he starts in his inquiries is, +that <i>we say</i> thus or thus in common language. Thus, when he has to +discuss the question whether there be, in any part of the universe, a +void, or space in which there is nothing, he inquires first in how many +senses we say that one thing is <i>in</i> another. He enumerates many of +these; we say the part is in the whole, as the finger is <i>in</i> the hand; +again we say, the species is in the genus, as man is included <i>in</i> +animal; again, <span class="pagenum"><a name="Page_327" id="Page_327">[Pg 327]</a></span>the government of Greece is <i>in</i> the king; and various +other senses are described and exemplified, but of all these <i>the most +proper</i> is when we say a thing is <i>in</i> a vessel, and generally <i>in +place</i>. He next examines what <i>place</i> is, and comes to this conclusion, +that 'if about a body there be another body including it, it is in +place, and if not, not.' A body moves when it changes its place; but he +adds, that if water be in a vessel, the vessel being at rest, the parts +of the water may still move, for they are included by each other; so +that while the whole does not change its place, the parts may change +their place in a circular order. Proceeding then to the question of a +<i>void</i>, he as usual examines the different senses in which the term is +used, and adopts as the most proper, <i>place without matter</i>: with no +useful result.</p> + +<p>"Again, in a question concerning mechanical action, he says, 'When a man +moves a stone by pushing it with a stick, <i>we say</i> both that the man +moves the stone, and that the stick moves the stone, but the latter +<i>more properly</i>.'</p> + +<p>"Again, we find the Greek philosophers applying themselves to extract +their dogmas from the most general and abstract notions which they could +detect; for example, from the conception of the Universe as One or as +Many things. They tried to determine how far we may, or must, combine +with these conceptions that of a whole, of parts, of number, of limits, +of place, of beginning or end, of full or void, of rest, or motion, of +cause and effect, and the like. The analysis of such conceptions with +such a view, occupies, for instance, almost the whole of Aristotle's +Treatise on the Heavens."</p> + +<p>The following paragraph merits particular attention:—"Another mode of +reasoning, very widely applied in these attempts, was the <i>doctrine of +contrarieties</i>, in which it was assumed, that adjectives or substances +which are in common language, or in some abstract mode of conception, +opposed to each other, must point at some fundamental antithesis in +nature, which it is important to study. Thus Aristotle says that the +Pythagoreans, from the contrasts which number suggests, collected ten +principles—Limited and Unlimited, Odd and Even, One and Many, Right and +Left, Male and <span class="pagenum"><a name="Page_328" id="Page_328">[Pg 328]</a></span>Female, Rest and Motion, Straight and Curved, Light and +Darkness, Good and Evil, Square and Oblong.... Aristotle himself deduced +the doctrine of four elements and other dogmas by oppositions of the +same kind."</p> + +<p>Of the manner in which, from premises obtained in this way, the ancients +attempted to deduce laws of nature, an example is given in the same work +a few pages further on. "Aristotle decides that there is no void, on +such arguments as this. In a void there could be no difference of up and +down; for as in nothing there are no differences, so there are none in a +privation or negation; but a void is merely a privation or negation of +matter; therefore, in a void, bodies could not move up and down, which +it is in their nature to do. It is easily seen" (Dr. Whewell very justly +adds) "that such a mode of reasoning elevates the familiar forms of +language, and the intellectual connexions of terms, to a supremacy over +facts; making truth depend upon whether terms are or are not privative, +and whether we say that bodies fall <i>naturally</i>."</p> + +<p>The propensity to assume that the same relations obtain between objects +themselves, which obtain between our ideas of them, is here seen in the +extreme stage of its development. For the mode of philosophizing, +exemplified in the foregoing instances, assumes no less than that the +proper way of arriving at knowledge of nature, is to study nature itself +subjectively; to apply our observation and analysis not to the facts, +but to the common notions entertained of the facts.</p> + +<p>Many other equally striking examples may be given of the tendency to +assume that things which for the convenience of common life are placed +in different classes, must differ in every respect. Of this nature was +the universal and deeply-rooted prejudice of antiquity and the middle +ages, that celestial and terrestrial phenomena must be essentially +different, and could in no manner or degree depend on the same laws. Of +the same kind, also, was the prejudice against which Bacon contended, +that nothing produced by nature could be successfully imitated by man: +"Calorem solis et ignis toto genere differre; <span class="pagenum"><a name="Page_329" id="Page_329">[Pg 329]</a></span>ne scilicet homines +putent se per opera ignis, aliquid simile iis quæ in Natura fiunt, +educere et formare posse:" and again, "Compositionem tantum opus +Hominis, Mistionem vero opus solius Naturæ esse: ne scilicet homines +sperent aliquam ex arte Corporum naturalium generationem aut +transformationem."<a name="FNanchor_13_81" id="FNanchor_13_81"></a><a href="#Footnote_13_81" class="fnanchor">[13]</a> The grand distinction in the ancient scientific +speculations, between natural and violent motions, though not without a +plausible foundation in the appearances themselves, was doubtless +greatly recommended to adoption by its conformity to this prejudice.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_III_7">§ 7.</a> From the fundamental error of the scientific inquirers of +antiquity, we pass, by a natural association, to a scarcely less +fundamental one of their great rival and successor, Bacon. It has +excited the surprise of philosophers that the detailed system of +inductive logic, which this extraordinary man laboured to construct, has +been turned to so little direct use by subsequent inquirers, having +neither continued, except in a few of its generalities, to be recognised +as a theory, nor having conducted in practice to any great scientific +results. But this, though not unfrequently remarked, has scarcely +received any plausible explanation; and some, indeed, have preferred to +assert that all rules of induction are useless, rather than suppose that +Bacon's rules are grounded on an insufficient analysis of the inductive +process. Such, however, will be seen to be the fact, as soon as it is +considered, that Bacon entirely overlooked Plurality of Causes. All his +rules tacitly imply the assumption, so contrary to all we now know of +nature, that a phenomenon cannot have more than one cause.</p> + +<p>When he is inquiring into what he terms the <i>forma calidi aut frigidi</i>, +<i>gravis aut levis</i>, <i>sicci aut humidi</i>, and the like, he never for an +instant doubts that there is some one thing, some invariable condition +or set of conditions, which is present in all cases of heat, or cold, or +whatever other phenomenon he is considering; the only difficulty being +to find what it is; which accordingly he tries to do by a process of +elimination, <span class="pagenum"><a name="Page_330" id="Page_330">[Pg 330]</a></span>rejecting or excluding, by negative instances, whatever is +not the <i>forma</i> or cause, in order to arrive at what is. But, that this +<i>forma</i> or cause is <i>one</i> thing, and that it is the same in all hot +objects, he has no more doubt of, than another person has that there is +always some cause <i>or other</i>. In the present state of knowledge it could +not be necessary, even if we had not already treated so fully of the +question, to point out how widely this supposition is at variance with +the truth. It is particularly unfortunate for Bacon that, falling into +this error, he should have fixed almost exclusively upon a class of +inquiries in which it was especially fatal; namely, inquiries into the +causes of the sensible qualities of objects. For his assumption, +groundless in every case, is false in a peculiar degree with respect to +those sensible qualities. In regard to scarcely any of them has it been +found possible to trace any unity of cause, any set of conditions +invariably accompanying the quality. The conjunctions of such qualities +with one another constitute the variety of Kinds, in which, as already +remarked, it has not been found possible to trace any law. Bacon was +seeking for what did not exist. The phenomenon of which he sought for +the one cause has oftenest no cause at all, and when it has, depends (as +far as hitherto ascertained) on an unassignable variety of distinct +causes.</p> + +<p>And on this rock every one must split, who represents to himself as the +first and fundamental problem of science to ascertain what is the cause +of a given effect, rather than what are the effects of a given cause. It +was shown, in an early stage of our inquiry into the nature of +Induction,<a name="FNanchor_14_82" id="FNanchor_14_82"></a><a href="#Footnote_14_82" class="fnanchor">[14]</a> how much more ample are the resources which science +commands for the latter than for the former inquiry, since it is upon +the latter only that we can throw any direct light by means of +experiment; the power of artificially producing an effect, implying a +previous knowledge of at least one of its causes. If we discover the +causes of effects, it is generally by having previously discovered the +effects of causes: the greatest skill in devising crucial instances for +the former purpose may only <span class="pagenum"><a name="Page_331" id="Page_331">[Pg 331]</a></span>end, as Bacon's physical inquiries did, in +no result at all. Was it that his eagerness to acquire the power of +producing for man's benefit effects of practical importance to human +life, rendering him impatient of pursuing that end by a circuitous +route, made even him, the champion of experiment, prefer the direct +mode, though one of mere observation, to the indirect, in which alone +experiment was possible? Or had even Bacon not entirely cleared his mind +from the notion of the ancients, that "rerum cognoscere <i>causas</i>" was +the sole object of philosophy, and that to inquire into the <i>effects</i> of +things belonged to servile and mechanical arts?</p> + +<p>It is worth remarking that, while the only efficient mode of cultivating +speculative science was missed from an undue contempt of manual +operations, the false speculative views thus engendered gave in their +turn a false direction to such practical and mechanical aims as were +suffered to exist. The assumption universal among the ancients and in +the middle ages, that there were <i>principles</i> of heat and cold, dryness +and moisture, &c., led directly to a belief in alchemy; in a +transmutation of substances, a change from one Kind into another. Why +should it not be possible to make gold? Each of the characteristic +properties of gold has its <i>forma</i>, its essence, its set of conditions, +which if we could discover, and learn how to realize, we could +superinduce that particular property upon any other substance, upon +wood, or iron, or lime, or clay. If, then, we could effect this with +respect to every one of the essential properties of the precious metal, +we should have converted the other substance into gold. Nor did this, if +once the premises were granted, appear to transcend the real powers of +mankind. For daily experience showed that almost every one of the +distinctive sensible properties of any object, its consistence, its +colour, its taste, its smell, its shape, admitted of being totally +changed by fire, or water, or some other chemical agent. The <i>formæ</i> of +all those qualities seeming, therefore, to be within human power either +to produce or to annihilate, not only did the transmutation of +substances appear abstractedly possible, but the employment of <span class="pagenum"><a name="Page_332" id="Page_332">[Pg 332]</a></span>the +power, at our choice, for practical ends, seemed by no means +hopeless.<a name="FNanchor_15_83" id="FNanchor_15_83"></a><a href="#Footnote_15_83" class="fnanchor">[15]</a></p> + +<p>A prejudice, universal in the ancient world, and from which Bacon was so +far from being free, that it pervaded and vitiated the whole practical +part of his system of logic, may with good reason be ranked high in the +order of Fallacies of which we are now treating.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_III_8">§ 8.</a> There remains one <i>à priori</i> fallacy or natural prejudice, the most +deeply-rooted, perhaps, of all which we have enumerated: one which not +only reigned supreme in the ancient world, but still possesses almost +undisputed dominion over many of the most cultivated minds; and some of +the most remarkable of the numerous instances by which I shall think it +necessary to exemplify it, will be taken from recent thinkers. This is, +that the conditions of a phenomenon must, or at least probably will, +resemble the phenomenon itself.</p> + +<p>Conformably to what we have before remarked to be of frequent +occurrence, this fallacy might without much impropriety have been placed +in a different class, among Fallacies of Generalization: for experience +does afford a certain degree of countenance to the assumption. The cause +does, in very many cases, resemble its effect; like produces like. Many +phenomena have a direct tendency to perpetuate their own existence, or +to give rise to other phenomena similar to themselves. Not to mention +forms actually moulded on one another, as impressions on wax and the +like, in which the closest resemblance between the effect and its cause +is the very law of the phenomenon; all motion tends to continue itself, +with its own velocity, and in its own original direction; and the motion +of one body tends to set others in motion, which is indeed the most +common of the modes in which the <span class="pagenum"><a name="Page_333" id="Page_333">[Pg 333]</a></span>motions of bodies originate. We need +scarcely refer to contagion, fermentation, and the like; or to the +production of effects by the growth or expansion of a germ or rudiment +resembling on a smaller scale the completed phenomenon, as in the growth +of a plant or animal from an embryo, that embryo itself deriving its +origin from another plant or animal of the same kind. Again, the +thoughts, or reminiscences, which are effects of our past sensations, +resemble those sensations; feelings produce similar feelings by way of +sympathy; acts produce similar acts by involuntary or voluntary +imitation. With so many appearances in its favour, no wonder if a +presumption naturally grew up, that causes must <i>necessarily</i> resemble +their effects, and that like could <i>only</i> be produced by like.</p> + +<p>This principle of fallacy has usually presided over the fantastical +attempts to influence the course of nature by conjectural means, the +choice of which was not directed by previous observation and experiment. +The guess almost always fixed upon some means which possessed features +of real or apparent resemblance to the end in view. If a charm was +wanted, as by Ovid's Medea, to prolong life, all long-lived animals, or +what were esteemed such, were collected and brewed into a broth:—</p> + +<p> +<span style="margin-left: 6.5em;">... nec defuit illic</span><br /> +<span style="margin-left: 2.5em;">Squamea Cinyphii tenuis membrana chelydri</span><br /> +<span style="margin-left: 2.5em;">Vivacisque jecur cervi: quibus insuper addit</span><br /> +<span style="margin-left: 2.5em;">Ora caputque novem cornicis sæcula passæ.</span><br /> +</p> + +<p>A similar notion was embodied in the celebrated medical theory called +the "Doctrine of Signatures," "which is no less," says Dr. Paris,<a name="FNanchor_16_84" id="FNanchor_16_84"></a><a href="#Footnote_16_84" class="fnanchor">[16]</a> +"than a belief that every natural substance which possesses any +medicinal virtue indicates by an obvious and well-marked external +character the disease for which it is a remedy, or the object for which +it should be employed." This outward character was generally some +feature of resemblance, real or fantastical, either to the effect <span class="pagenum"><a name="Page_334" id="Page_334">[Pg 334]</a></span>it +was supposed to produce, or to the phenomenon over which its power was +thought to be exercised. "Thus the lungs of a fox must be a specific for +asthma, because that animal is remarkable for its strong powers of +respiration. Turmeric has a brilliant yellow colour, which indicates +that it has the power of curing the jaundice; for the same reason, +poppies must relieve diseases of the head; Agaricus those of the +bladder; <i>Cassia fistula</i> the affections of the intestines, and +Aristolochia the disorders of the uterus: the polished surface and stony +hardness which so eminently characterize the seeds of the Lithospermum +officinale (common gromwell) were deemed a certain indication of their +efficacy in calculous and gravelly disorders; for a similar reason, the +roots of the Saxifraga granulata (white saxifrage) gained reputation in +the cure of the same disease; and the Euphrasia (eye-bright) acquired +fame, as an application in complaints of the eye, because it exhibits a +black spot in its corolla resembling the pupil. The blood-stone, the +Heliotropium of the ancients, from the occasional small specks or points +of a blood-red colour exhibited on its green surface, is even at this +very day employed in many parts of England and Scotland, to stop a +bleeding from the nose; and nettle tea continues a popular remedy for +the cure of <i>Urticaria</i>. It is also asserted that some substances bear +the <i>signatures</i> of the humours, as the petals of the red rose that of +the blood, and the roots of rhubarb and the flowers of saffron that of +the bile."</p> + +<p>The early speculations respecting the chemical composition of bodies +were rendered abortive by no circumstance more, than by their invariably +taking for granted that the properties of the elements must resemble +those of the compounds which were formed from them.</p> + +<p>To descend to more modern instances; it was long thought, and was +stoutly maintained by the Cartesians and even by Leibnitz against the +Newtonian system, (nor did Newton himself, as we have seen, contest the +assumption, but eluded it by an arbitrary hypothesis), that nothing (of +a physical nature at least) could account for motion, except previous +motion; the impulse or impact of some other body. It was <span class="pagenum"><a name="Page_335" id="Page_335">[Pg 335]</a></span>very long +before the scientific world could prevail upon itself to admit +attraction and repulsion (<i>i. e.</i> spontaneous tendencies of particles to +approach or recede from one another) as ultimate laws, no more requiring +to be accounted for than impulse itself, if indeed the latter were not, +in truth, resolvable into the former. From the same source arose the +innumerable hypotheses devised to explain those classes of motions which +appeared more mysterious than others because there was no obvious mode +of attributing them to impulse, as for example the voluntary motions of +the human body. Such were the interminable systems of vibrations +propagated along the nerves, or animal spirits rushing up and down +between the muscles and the brain; which, if the facts could have been +proved, would have been an important addition to our knowledge of +physiological laws; but the mere invention, or arbitrary supposition of +them, could not unless by the strongest delusion be supposed to render +the phenomena of animal life more comprehensible, or less mysterious. +Nothing, however, seemed satisfactory, but to make out that motion was +caused by motion; by something like itself. If it was not one kind of +motion, it must be another. In like manner it was supposed that the +physical qualities of objects must arise from some similar quality, or +perhaps only some quality bearing the same name, in the particles or +atoms of which the objects were composed; that a sharp taste, for +example, must arise from sharp particles. And reversing the inference, +the effects produced by a phenomenon must, it was supposed, resemble in +their physical attributes the phenomenon itself. The influences of the +planets were supposed to be analogous to their visible peculiarities: +Mars, being of a red colour, portended fire and slaughter; and the like.</p> + +<p>Passing from physics to metaphysics, we may notice among the most +remarkable fruits of this <i>à priori</i> fallacy, two closely analogous +theories, employed in ancient and modern times to bridge over the chasm +between the world of mind and that of matter: the <i>species sensibiles</i> +of the Epicureans, and the modern doctrine of perception by means of +ideas. These theories are indeed, probably, indebted for their existence +<span class="pagenum"><a name="Page_336" id="Page_336">[Pg 336]</a></span>not solely to the fallacy in question, but to that fallacy combined +with another natural prejudice already adverted to, that a thing cannot +act where it is not. In both doctrines it is assumed that the phenomenon +which takes place <i>in us</i> when we see or touch an object, and which we +regard as an effect of that object, or rather as its presence to our +organs, must of necessity resemble very closely the outward object +itself. To fulfil this condition, the Epicureans supposed that objects +were constantly projecting in all directions impalpable images of +themselves, which entered at the eyes and penetrated to the mind; while +modern metaphysicians, though they rejected this hypothesis, agreed in +deeming it necessary to suppose that not the thing itself, but a mental +image or representation of it, was the direct object of perception. Dr. +Reid had to employ a world of argument and illustration to familiarize +people with the truth, that the sensations or impressions on our minds +need not necessarily be copies of, or bear any resemblance to, the +causes which produce them; in opposition to the natural prejudice which +led people to assimilate the action of bodies upon our senses, and +through them upon our minds, to the transfer of a given form from one +object to another by actual moulding. The works of Dr. Reid are even now +the most effectual course of study for detaching the mind from the +prejudice of which this was an example. And the value of the service +which he thus rendered to popular philosophy, is not much diminished +although we may hold, with Brown, that he went too far in imputing the +"ideal theory" as an actual tenet, to the generality of the philosophers +who preceded him, and especially to Locke and Hume: for if they did not +themselves consciously fall into the error, unquestionably they often +led their readers into it.</p> + +<p>The prejudice, that the conditions of a phenomenon must resemble the +phenomenon, is occasionally exaggerated, at least verbally, into a still +more palpable absurdity; the conditions of the thing are spoken of as if +they <i>were</i> the very thing itself. In Bacon's model-inquiry, which +occupies so great a space in the <i>Novum Organum</i>, the <i>inquisitio in +formam calidi</i>, the conclusion which he favours is that heat is a kind +of <span class="pagenum"><a name="Page_337" id="Page_337">[Pg 337]</a></span>motion; meaning of course not the feeling of heat, but the +conditions of the feeling; meaning, therefore, only that wherever there +is heat, there must first be a particular kind of motion; but he makes +no distinction in his language between these two ideas, expressing +himself as if heat, and the conditions of heat, were one and the same +thing. So Darwin, in the beginning of his <i>Zoonomia</i>, says, "The word +<i>idea</i> has various meanings in the writers of metaphysic: it is here +used simply for those notions of external things which our organs of +sense bring us acquainted with originally," (thus far the proposition, +though vague, is unexceptionable in meaning,) "and is defined a +contraction, a motion, or configuration, of the fibres which constitute +the immediate organ of sense." Our <i>notions</i>, a configuration of the +fibres! What kind of logician must he be who thinks that a phenomenon is +<i>defined</i> to <i>be</i> the condition on which he supposes it to depend? +Accordingly he says soon after, not that our ideas are caused by, or +consequent on, certain organic phenomena, but "our ideas <i>are</i> animal +motions of the organs of sense." And this confusion runs through the +four volumes of the <i>Zoonomia</i>; the reader never knows whether the +writer is speaking of the effect, or of its supposed cause; of the idea, +a state of mental consciousness, or of the state of the nerves and brain +which he considers it to presuppose.</p> + +<p>I have given a variety of instances in which the natural prejudice, that +causes and their effects must resemble one another, has operated in +practice so as to give rise to serious errors. I shall now go further, +and produce from writings even of the present or very recent times, +instances in which this prejudice is laid down as an established +principle. M. Victor Cousin, in the last of his celebrated lectures on +Locke, enunciates the maxim in the following unqualified terms. "Tout ce +qui est vrai de l'effet est vrai de la cause." A doctrine to which, +unless in some peculiar and technical meaning of the words cause and +effect, it is not to be imagined that any person would literally adhere: +but he who could so write must be far enough from seeing, that the very +reverse might be the fact; that there is nothing impossible in the +<span class="pagenum"><a name="Page_338" id="Page_338">[Pg 338]</a></span>supposition that no one property which is true of the effect might be +true of the cause. Without going quite so far in point of expression, +Coleridge, in his <i>Biographia Literaria</i>,<a name="FNanchor_17_85" id="FNanchor_17_85"></a><a href="#Footnote_17_85" class="fnanchor">[17]</a> affirms as an "evident +truth," that "the law of causality holds only between homogeneous +things, <i>i. e.</i> things having some common property," and therefore +"cannot extend from one world into another, its opposite:" hence, as +mind and matter have no common property, mind cannot act upon matter, +nor matter upon mind. What is this but the <i>à priori</i> fallacy of which +we are speaking? The doctrine, like many others of Coleridge, is taken +from Spinoza, in the first book of whose <i>Ethica (De Deo)</i> it stands as +the Third Proposition, "Quæ res nihil commune inter se habent, earum una +alterius causa esse non potest," and is there proved from two so-called +axioms, equally gratuitous with itself: but Spinoza, ever systematically +consistent, pursued the doctrine to its inevitable consequence, the +materiality of God.</p> + +<p>The same conception of impossibility led the ingenious and subtle mind +of Leibnitz to his celebrated doctrine of a pre-established harmony. He, +too, thought that mind could not act upon matter, nor matter upon mind, +and that the two, therefore, must have been arranged by their Maker like +two clocks, which, though unconnected with one another, strike +simultaneously, and always point to the same hour. Malebranche's equally +famous theory of Occasional Causes was another form of the same +conception: instead of supposing the clocks originally arranged to +strike together, he held that when the one strikes, God interposes, and +makes the other strike in correspondence with it.</p> + +<p>Descartes, in like manner, whose works are a rich mine of almost every +description of <i>à priori</i> fallacy, says that the Efficient Cause must at +least have all the perfections of the effect, and for this singular +reason: "Si enim ponamus aliquid in ideâ reperiri quod non fuerit in +ejus causâ, hoc igitur habet a nihilo;" of which it is scarcely a parody +to say, that if there <span class="pagenum"><a name="Page_339" id="Page_339">[Pg 339]</a></span>be pepper in the soup there must be pepper in the +cook who made it, since otherwise the pepper would be without a cause. A +similar fallacy is committed by Cicero in his second book <i>De Finibus</i>, +where, speaking in his own person against the Epicureans, he charges +them with inconsistency in saying that the pleasures of the mind had +their origin from those of the body, and yet that the former were more +valuable, as if the effect could surpass the cause. "Animi voluptas +oritur propter voluptatem corporis, et major est animi voluptas quam +corporis? ita fit ut gratulator lætior sit quam is cui gratulatur." Even +that, surely, is not an impossibility: a person's good fortune has often +given more pleasure to others than it gave to the person himself.</p> + +<p>Descartes, with no less readiness, applies the same principle the +converse way, and infers the nature of the effects from the assumption +that they must, in this or that property or in all their properties, +resemble their cause. To this class belong his speculations, and those +of so many others after him, tending to infer the order of the universe, +not from observation, but by <i>à priori</i> reasoning from supposed +qualities of the Godhead. This sort of inference was probably never +carried to a greater length than it was in one particular instance by +Descartes, when, as a proof of one of his physical principles, that the +quantity of motion in the universe is invariable, he had recourse to the +immutability of the Divine Nature. Reasoning of a very similar character +is however nearly as common now as it was in his time, and does duty +largely as a means of fencing off disagreeable conclusions. Writers have +not yet ceased to oppose the theory of divine benevolence to the +evidence of physical facts, to the principle of population for example. +And people seem in general to think that they have used a very powerful +argument, when they have said, that to suppose some proposition true, +would be a reflection on the goodness or wisdom of the Deity. Put into +the simplest possible terms, their argument is, "If it had depended on +me, I would not have made the proposition true, therefore it is not +true." Put into other words it stands thus: "God is perfect, therefore +(what I think) perfection must <span class="pagenum"><a name="Page_340" id="Page_340">[Pg 340]</a></span>obtain in nature." But since in reality +every one feels that nature is very far from perfect, the doctrine is +never applied consistently. It furnishes an argument which (like many +others of a similar character) people like to appeal to when it makes +for their own side. Nobody is convinced by it, but each appears to think +that it puts religion on his side of the question, and that it is a +useful weapon of offence for wounding an adversary.</p> + +<p>Although several other varieties of <i>à priori</i> fallacy might probably be +added to those here specified, these are all against which it seems +necessary to give any special caution. Our object is to open, without +attempting or affecting to exhaust, the subject. Having illustrated, +therefore, this first class of Fallacies at sufficient length, I shall +proceed to the second.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_341" id="Page_341">[Pg 341]</a></span></p> +<h3><a name="BOOK_V_CHAPTER_IV" id="BOOK_V_CHAPTER_IV"></a>CHAPTER IV.<br /> +FALLACIES OF OBSERVATION.</h3> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_IV_1">§ 1.</a> From the fallacies which are properly Prejudices, or presumptions +antecedent to, and superseding, proof, we pass to those which lie in the +incorrect performance of the proving process. And as Proof, in its +widest extent, embraces one or more, or all, of three processes, +Observation, Generalization, and Deduction; we shall consider in their +order the errors capable of being committed in these three operations. +And first, of the first mentioned.</p> + +<p>A fallacy of misobservation may be either negative or positive; either +Non-observation or Mal-observation. It is non-observation, when all the +error consists in overlooking, or neglecting, facts or particulars which +ought to have been observed. It is mal-observation, when something is +not simply unseen, but seen wrong; when the fact or phenomenon, instead +of being recognised for what it is in reality, is mistaken for something +else.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_IV_2">§ 2.</a> Non-observation may either take place by overlooking instances, or +by overlooking some of the circumstances of a given instance. If we were +to conclude that a fortune-teller was a true prophet, from not adverting +to the cases in which his predictions had been falsified by the event, +this would be non-observation of instances; but if we overlooked or +remained ignorant of the fact that in cases where the predictions had +been fulfilled, he had been in collusion with some one who had given him +the information on which they were grounded, this would be +non-observation of circumstances.</p> + +<p><span class="pagenum"><a name="Page_342" id="Page_342">[Pg 342]</a></span></p><p>The former case, in so far as the act of induction from insufficient +evidence is concerned, does not fall under this second class of +Fallacies, but under the third, Fallacies of Generalization. In every +such case, however, there are two defects or errors instead of one: +there is the error of treating the insufficient evidence as if it were +sufficient, which is a Fallacy of the third class; and there is the +insufficiency itself; the not having better evidence; which, when such +evidence, or in other words, when other instances, were to be had, is +Non-observation: and the erroneous inference, so far as it is to be +attributed to this cause, is a Fallacy of the second class.</p> + +<p>It belongs not to our purpose to treat of non-observation as arising +from casual inattention, from general slovenliness of mental habits, +want of due practice in the use of the observing faculties, or +insufficient interest in the subject. The question pertinent to logic +is—Granting the want of complete competency in the observer, on what +points is that insufficiency on his part likely to lead him wrong? or +rather, what sorts of instances, or of circumstances in any given +instance, are most likely to escape the notice of observers generally; +of mankind at large.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_IV_3">§ 3.</a> First, then, it is evident that when the instances on one side of a +question are more likely to be remembered and recorded than those on the +other; especially if there be any strong motive to preserve the memory +of the first, but not of the latter; these last are likely to be +overlooked, and escape the observation of the mass of mankind. This is +the recognised explanation of the credit given, in spite of reason and +evidence, to many classes of impostors: to quack doctors, and +fortune-tellers in all ages; to the "cunning man" of modern times and +the oracles of old. Few have considered the extent to which this fallacy +operates in practice, even in the teeth of the most palpable negative +evidence. A striking example of it is the faith which the uneducated +portion of the agricultural classes, in this and other countries, +continue to repose in the prophecies as to weather supplied by almanac +makers: <span class="pagenum"><a name="Page_343" id="Page_343">[Pg 343]</a></span>though every season affords to them numerous cases of +completely erroneous prediction; but as every season also furnishes some +cases in which the prediction is fulfilled, this is enough to keep up +the credit of the prophet, with people who do not reflect on the number +of instances requisite for what we have called, in our inductive +terminology, the Elimination of Chance; since a certain number of casual +coincidences not only may but will happen, between any two unconnected +events.</p> + +<p>Coleridge, in one of the essays in the <i>Friend</i>, has illustrated the +matter we are now considering, in discussing the origin of a proverb, +"which, differently worded, is to be found in all the languages of +Europe," viz. "Fortune favours fools." He ascribes it partly to the +"tendency to exaggerate all effects that seem disproportionate to their +visible cause, and all circumstances that are in any way strongly +contrasted with our notions of the persons under them." Omitting some +explanations which would refer the error to mal-observation, or to the +other species of non-observation (that of circumstances), I take up the +quotation farther on. "Unforeseen coincidences may have greatly helped a +man, yet if they have done for him only what possibly from his own +abilities he might have effected for himself, his good luck will excite +less attention, and the instances be less remembered. That clever men +should attain their objects seems natural, and we neglect the +circumstances that perhaps produced that success of themselves, without +the intervention of skill or foresight; but we dwell on the fact and +remember it, as something strange, when the same happens to a weak or +ignorant man. So too, though the latter should fail in his undertakings +from concurrences that might have happened to the wisest man, yet his +failure being no more than might have been expected and accounted for +from his folly, it lays no hold on our attention, but fleets away among +the other undistinguished waves in which the stream of ordinary life +murmurs by us, and is forgotten. Had it been as true as it was +notoriously false, that those all-embracing discoveries, which have shed +a dawn of <i>science</i> on the <i>art</i> of chemistry, and give no obscure +promise of some <span class="pagenum"><a name="Page_344" id="Page_344">[Pg 344]</a></span>one great constitutive law, in the light of which dwell +dominion and the power of prophecy; if these discoveries, instead of +having been, as they really were, preconcerted by meditation, and +evolved out of his own intellect, had occurred by a set of lucky +<i>accidents</i> to the illustrious father and founder of philosophic +alchemy; if they had presented themselves to Professor Davy exclusively +in consequence of his <i>luck</i> in possessing a particular galvanic +battery; if this battery, as far as Davy was concerned, had itself been +an <i>accident</i>, and not (as in point of fact it was) desired and obtained +by him for the purpose of ensuring the testimony of experience to his +principles, and in order to bind down material nature under the +inquisition of reason, and force from her, as by torture, unequivocal +answers to <i>prepared</i> and <i>preconceived</i> questions,—yet still they +would not have been talked of or described as instances of <i>luck</i>, but +as the natural results of his admitted genius and known skill. But +should an accident have disclosed similar discoveries to a mechanic at +Birmingham or Sheffield, and if the man should grow rich in consequence, +and partly by the envy of his neighbours and partly with good reason, be +considered by them as a man <i>below par</i> in the general powers of his +understanding; then, 'O what a lucky fellow! Well, Fortune <i>does</i> favour +fools—that's for certain!—It is always so!' And forthwith the +exclaimer relates half a dozen similar instances. Thus accumulating the +one sort of facts and never collecting the other, we do, as poets in +their diction, and quacks of all denominations do in their reasoning, +put a part for the whole."</p> + +<p>This passage very happily sets forth the manner in which, under the +loose mode of induction which proceeds <i>per enumerati onem simplicem</i>, +not seeking for instances of such a kind as to be decisive of the +question, but generalizing from any which occur, or rather which are +remembered, opinions grow up with the apparent sanction of experience, +which have no foundation in the laws of nature at all. "Itaque recte +respondit ille," (we may say with Bacon,<a name="FNanchor_18_86" id="FNanchor_18_86"></a><a href="#Footnote_18_86" class="fnanchor">[18]</a>) "qui cum suspensa <span class="pagenum"><a name="Page_345" id="Page_345">[Pg 345]</a></span>tabula +in templo ei monstraretur eorum, qui vota solverant, quod naufragii +periculo elapsi sint, atque interrogando premeretur, anne tum quidem +Deorum numen agnosceret, quæsivit denuo, <i>At ubi sunt illi depicti qui +post vota nuncupata perierunt?</i> Eadem ratio est fere omnis +superstitionis, ut in Astrologicis, in Somniis, Ominibus, Nemesibus, et +hujusmodi; in quibus, homines delectati hujusmodi vanitatibus, advertunt +eventus, ubi implentur; ast ubi fallunt, licet multo frequentius, tamen +negligunt, et prætereunt." And he proceeds to say, that independently of +the love of the marvellous, or any other bias in the inclinations, there +is a natural tendency in the intellect itself to this kind of fallacy; +since the mind is more moved by affirmative instances, though negative +ones are of most use in philosophy; "Is tamen humano intellectui error +est proprius et perpetuus, ut magis moveatur et excitetur Affirmativis +quam Negativis; cum rite et ordine æquum se utrique præbere debeat; quin +contra, in omni Axiomate vero constituendo, major vis est instantiæ +negativæ."</p> + +<p>But the greatest of all causes of non-observation is a preconceived +opinion. This it is which, in all ages, has made the whole race of +mankind, and every separate section of it, for the most part unobservant +of all facts, however abundant, even when passing under their own eyes, +which are contradictory to any first appearance, or any received tenet. +It is worth while to recal occasionally to the oblivious memory of +mankind some of the striking instances in which opinions that the +simplest experiment would have shown to be erroneous, continued to be +entertained because nobody ever thought of trying that experiment. One +of the most remarkable of these was exhibited in the Copernican +controversy. The opponents of Copernicus argued that the earth did not +move, because if it did, a stone let fall from the top of a high tower +would not reach the ground at the foot of the tower, but at a little +distance from it, in a contrary direction to the earth's course; in the +same manner (said they) as, if a ball is let drop from the mast-head +while the ship is in full sail, it does not fall exactly at the foot of +the mast, but nearer to the stern of the vessel. The Copernicans would +have silenced these objectors at once if they had <span class="pagenum"><a name="Page_346" id="Page_346">[Pg 346]</a></span><i>tried</i> dropping a +ball from the mast-head, since they would have found that it does fall +exactly at the foot, as the theory requires: but no; they admitted the +spurious fact, and struggled vainly to make out a difference between the +two cases. "The ball was no <i>part</i> of the ship—and the motion forward +was not <i>natural</i>, either to the ship or to the ball. The stone, on the +other hand, let fall from the top of the tower, was a <i>part</i> of the +earth; and therefore, the diurnal and annular revolutions which were +<i>natural</i> to the earth, were also <i>natural</i> to the stone: the stone +would, therefore, retain the same motion with the tower, and strike the +ground precisely at the bottom of it."<a name="FNanchor_19_87" id="FNanchor_19_87"></a><a href="#Footnote_19_87" class="fnanchor">[19]</a></p> + +<p>Other examples, scarcely less striking, are recorded by Dr. Whewell,<a name="FNanchor_20_88" id="FNanchor_20_88"></a><a href="#Footnote_20_88" class="fnanchor">[20]</a> +where imaginary laws of nature have continued to be received as real, +merely because no person had steadily looked at facts which almost every +one had the opportunity of observing. "A vague and loose mode of looking +at facts very easily observable, left men for a long time under the +belief that a body ten times as heavy as another falls ten times as +fast; that objects immersed in water are always magnified, without +regard to the form of the surface; that the magnet exerts an +irresistible force; that crystal is always found associated with ice; +and the like. These and many others are examples how blind and careless +man can be even in observation of the plainest and commonest +appearances; and they show us that the mere faculties of perception, +although constantly exercised upon innumerable objects, may long fail in +leading to any exact knowledge."</p> + +<p>If even on physical facts, and these of the most obvious character, the +observing faculties of mankind can be to this degree the passive slaves +of their preconceived impressions, we need not be surprised that this +should be so lamentably true as all experience attests it to be, on +things more nearly connected with their stronger feelings—on moral, +social, and religious subjects. The information which an ordinary +traveller brings back from a foreign country, as the result of the +evidence of <span class="pagenum"><a name="Page_347" id="Page_347">[Pg 347]</a></span>his senses, is almost always such as exactly confirms the +opinions with which he set out. He has had eyes and ears for such things +only as he expected to see. Men read the sacred books of their religion, +and pass unobserved therein, multitudes of things utterly +irreconcileable with even their own notions of moral excellence. With +the same authorities before them, different historians, alike innocent +of intentional misrepresentation, see only what is favourable to +Protestants or Catholics, royalists or republicans, Charles I. or +Cromwell; while others, having set out with the preconception that +extremes must be in the wrong, are incapable of seeing truth and justice +when these are wholly on one side.</p> + +<p>The influence of a preconceived theory is well exemplified in the +superstitions of barbarians respecting the virtues of medicaments and +charms. The negroes, among whom coral, as of old among ourselves, is +worn as an amulet, affirm, according to Dr. Paris,<a name="FNanchor_21_89" id="FNanchor_21_89"></a><a href="#Footnote_21_89" class="fnanchor">[21]</a> that its colour +"is always affected by the state of health of the wearer, it becoming +paler in disease." On a matter open to universal observation, a general +proposition which has not the smallest vestige of truth is received as a +result of experience; the preconceived opinion preventing, it would +seem, any observation whatever on the subject.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_IV_4">§ 4.</a> For illustration of the first species of non-observation, that of +Instances, what has now been stated may suffice. But there may also be +non-observation of some material circumstances, in instances which have +not been altogether overlooked—nay, which may be the very instances on +which the whole superstructure of a theory has been founded. As, in the +cases hitherto examined, a general proposition was too rashly adopted, +on the evidence of particulars, true indeed, but insufficient to support +it; so in the cases to which we now turn, the particulars themselves +have been imperfectly observed, and the singular propositions on which +the generalization is grounded, or some at least of those singular +propositions, are false.</p> + +<p><span class="pagenum"><a name="Page_348" id="Page_348">[Pg 348]</a></span></p><p>Such, for instance, was one of the mistakes committed in the celebrated +phlogistic theory; a doctrine which accounted for combustion by the +extrication of a substance called phlogiston, supposed to be contained +in all combustible matter. The hypothesis accorded tolerably well with +superficial appearances: the ascent of flame naturally suggests the +escape of a substance; and the visible residuum of ashes, in bulk and +weight, generally falls extremely short of the combustible material. The +error was, non-observation of an important portion of the actual +residue, namely, the gaseous products of combustion. When these were at +last noticed and brought into account, it appeared to be an universal +law, that all substances gain instead of losing weight by undergoing +combustion; and, after the usual attempt to accommodate the old theory +to the new fact by means of an arbitrary hypothesis (that phlogiston had +the quality of positive levity instead of gravity), chemists were +conducted to the true explanation, namely, that instead of a substance +separated, there was on the contrary a substance absorbed.</p> + +<p>Many of the absurd practices which have been deemed to possess medicinal +efficacy, have been indebted for their reputation to non-observance of +some accompanying circumstance which was the real agent in the cures +ascribed to them. Thus, of the sympathetic powder of Sir Kenelm Digby: +"Whenever any wound had been inflicted, this powder was applied to the +weapon that had inflicted it, which was, moreover, covered with +ointment, and dressed two or three times a day. The wound itself, in the +meantime, was directed to be brought together, and carefully bound up +with clean linen rags, but <i>above all, to be let alone</i> for seven days, +at the end of which period the bandages were removed, when the wound was +generally found perfectly united. The triumph of the cure was decreed to +the mysterious agency of the sympathetic powder which had been so +assiduously applied to the weapon, whereas it is hardly necessary to +observe that the promptness of the cure depended on the total exclusion +of air from the wound, and upon the sanative operations of nature not +having received any disturbance from the officious <span class="pagenum"><a name="Page_349" id="Page_349">[Pg 349]</a></span>interference of art. +The result, beyond all doubt, furnished the first hint which led +surgeons to the improved practice of healing wounds by what is +technically called the <i>first intention</i>."<a name="FNanchor_22_90" id="FNanchor_22_90"></a><a href="#Footnote_22_90" class="fnanchor">[22]</a> "In all records," adds +Dr. Paris, "of extraordinary cures performed by mysterious agents, there +is a great desire to conceal the remedies and other curative means which +were simultaneously administered with them; thus Oribasius commends in +high terms a necklace of Pæony root for the cure of epilepsy; but we +learn that he always took care to accompany its use with copious +evacuations, although he assigns to them no share of credit in the cure. +In later times we have a good specimen of this species of deception, +presented to us in a work on Scrofula by Mr. Morley, written, as we are +informed, for the sole purpose of restoring the much injured character +and use of the Vervain; in which the author directs the root of this +plant to be tied with a yard of white satin riband around the neck, +where it is to remain until the patient is cured; but mark—during this +interval he calls to his aid the most active medicines in the materia +medica."<a name="FNanchor_23_91" id="FNanchor_23_91"></a><a href="#Footnote_23_91" class="fnanchor">[23]</a></p> + +<p>In other cases the cures really produced by rest, regimen, and +amusement, have been ascribed to the medicinal, or occasionally to the +supernatural, means which were put in requisition. "The celebrated John +Wesley, while he commemorates the triumph of sulphur and supplication +over his bodily infirmity, forgets to appreciate the resuscitating +influence of four months' repose from his apostolic labours; and such is +the disposition of the human mind to place confidence in the operation +of mysterious agents, that we find him more disposed to attribute his +cure to a brown paper plaister of egg and brimstone, than to Dr. +Fothergill's salutary prescription of country air, rest, asses' milk, +and horse exercise."<a name="FNanchor_24_92" id="FNanchor_24_92"></a><a href="#Footnote_24_92" class="fnanchor">[24]</a></p> + +<p>In the following example, the circumstance overlooked was of a somewhat +different character. "When the yellow fever raged in America, the +practitioners trusted exclusively to the copious use of mercury; at +first this plan was deemed so universally efficacious, that, in the +enthusiasm of the <span class="pagenum"><a name="Page_350" id="Page_350">[Pg 350]</a></span>moment, it was triumphantly proclaimed that death +never took place after the mercury had evinced its effect upon the +system: all this was very true, but it furnished no proof of the +efficacy of that metal, since the disease in its aggravated form was so +rapid in its career, that it swept away its victims long before the +system could be brought under mercurial influence, while in its milder +shape it passed off equally well without any assistance from art."<a name="FNanchor_25_93" id="FNanchor_25_93"></a><a href="#Footnote_25_93" class="fnanchor">[25]</a></p> + +<p>In these examples the circumstance overlooked was cognizable by the +senses. In other cases, it is one the knowledge of which could only be +arrived at by reasoning; but the fallacy may still be classed under the +head to which, for want of a more appropriate name, we have given the +appellation Fallacies of Non-observation. It is not the nature of the +faculties which ought to have been employed, but the non-employment of +them, which constitutes this Natural Order of Fallacies. Wherever the +error is negative, not positive; wherever it consists especially in +<i>overlooking</i>, in being ignorant or unmindful of some fact which, if +known and attended to, would have made a difference in the conclusion +arrived at; the error is properly placed in the Class which we are +considering. In this Class, there is not, as in all other fallacies +there is, a positive mis-estimate of evidence actually had. The +conclusion would be just, if the portion which is seen of the case were +the whole of it; but there is another portion overlooked, which vitiates +the result.</p> + +<p>For instance, there is a remarkable doctrine which has occasionally +found a vent in the public speeches of unwise legislators, but which +only in one instance that I am aware of has received the sanction of a +philosophical writer, namely M. Cousin, who, in his preface to the +<i>Gorgias</i> of Plato, contending that punishment must have some other and +higher justification than the prevention of crime, makes use of this +argument—that if punishment were only for the sake of example, it would +be indifferent whether we punished the innocent or the guilty, since the +punishment, considered as an <span class="pagenum"><a name="Page_351" id="Page_351">[Pg 351]</a></span>example, is equally efficacious in either +case. Now we must, in order to go along with this reasoning, suppose, +that the person who feels himself under temptation, observing somebody +punished, concludes himself to be in danger of being punished likewise, +and is terrified accordingly. But it is forgotten that if the person +punished is supposed to be innocent, or even if there be any doubt of +his guilt, the spectator will reflect that his own danger, whatever it +may be, is not contingent on his guiltiness, but threatens him equally +if he remains innocent, and how therefore is he deterred from guilt by +the apprehension of such punishment? M. Cousin supposes that people will +be dissuaded from guilt by whatever renders the condition of the guilty +more perilous, forgetting that the condition of the innocent (also one +of the elements in the calculation) is, in the case supposed, made +perilous in precisely an equal degree. This is a fallacy of overlooking; +or of non-observation, within the intent of our classification.</p> + +<p>Fallacies of this description are the great stumbling-block to correct +thinking in political economy. The economical workings of society afford +numerous cases in which the effects of a cause consist of two sets of +phenomena: the one immediate, concentrated, obvious to all eyes, and +passing, in common apprehension, for the whole effect; the other widely +diffused, or lying deeper under the surface, and which is exactly +contrary to the former. Take, for instance, the common notion so +plausible at the first glance, of the encouragement given to industry by +lavish expenditure. A, who spends his whole income, and even his +capital, in expensive living, is supposed to give great employment to +labour. B, who lives on a small portion, and invests the remainder in +the funds, is thought to give little or no employment. For everybody +sees the gains which are made by A's tradesmen, servants, and others, +while his money is spending. B's savings, on the contrary, pass into the +hands of the person whose stock he purchased, who with it pays a debt he +owed to some banker, who lends it again to some merchant or +manufacturer; and the capital being laid out in hiring spinners and +weavers, or carriers and the crews of merchant vessels, not only gives +immediate employment to <span class="pagenum"><a name="Page_352" id="Page_352">[Pg 352]</a></span>at least as much industry as A employs during +the whole of his career, but coming back with increase by the sale of +the goods which have been manufactured or imported, forms a fund for the +employment of the same and perhaps a greater quantity of labour in +perpetuity. But the observer does not see, and therefore does not +consider, what becomes of B's money; he does see what is done with A's: +he observes the amount of industry which A's profusion feeds; he +observes not the far greater quantity which it prevents from being fed; +and thence the prejudice, universal to the time of Adam Smith, that +prodigality encourages industry, and parsimony is a discouragement to +it.</p> + +<p>The common argument against free trade was a fallacy of the same nature. +The purchaser of British silk encourages British industry; the purchaser +of Lyons silk encourages only French; the former conduct is patriotic, +the latter ought to be interdicted by law. The circumstance is +overlooked, that the purchaser of any foreign commodity necessarily +causes, directly or indirectly, the export of an equivalent value of +some article of home production (beyond what would otherwise be +exported), either to the same foreign country or to some other; which +fact, though from the complication of the circumstances it cannot always +be verified by specific observation, no observation can possibly be +brought to contradict, while the evidence of reasoning on which it rests +is irrefragable. The fallacy is, therefore, the same as in the preceding +case, that of seeing a part only of the phenomena, and imagining that +part to be the whole: and may be ranked among Fallacies of +Non-observation.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_IV_5">§ 5.</a> To complete the examination of the second of our five classes, we +have now to speak of Mal-observation; in which the error does not lie in +the fact that something is unseen, but that something seen is seen +wrong.</p> + +<p>Perception being infallible evidence of whatever is really perceived, +the error now under consideration can be committed no otherwise than by +mistaking for conception what is in fact inference. We have formerly +shown how intimately the two <span class="pagenum"><a name="Page_353" id="Page_353">[Pg 353]</a></span>are blended in almost everything which is +called observation, and still more in every Description.<a name="FNanchor_26_94" id="FNanchor_26_94"></a><a href="#Footnote_26_94" class="fnanchor">[26]</a> What is +actually on any occasion perceived by our senses being so minute in +amount, and generally so unimportant a portion of the state of facts +which we wish to ascertain or to communicate; it would be absurd to say +that either in our observations, or in conveying their result to others, +we ought not to mingle inference with fact; all that can be said is, +that when we do so we ought to be aware of what we are doing, and to +know what part of the assertion rests on consciousness, and is therefore +indisputable, what part on inference, and is therefore questionable.</p> + +<p>One of the most celebrated examples of an universal error produced by +mistaking an inference for the direct evidence of the senses, was the +resistance made, on the ground of common sense, to the Copernican +system. People fancied they <i>saw</i> the sun rise and set, the stars +revolve in circles round the pole. We now know that they saw no such +thing; what they really saw was a set of appearances, equally +reconcileable with the theory they held and with a totally different +one. It seems strange that such an instance as this, of the testimony of +the senses pleaded with the most entire conviction in favour of +something which was a mere inference of the judgment, and, as it turned +out, a false inference, should not have opened the eyes of the bigots of +common sense, and inspired them with a more modest distrust of the +competency of mere ignorance to judge the conclusions of cultivated +thought.</p> + +<p>In proportion to any person's deficiency of knowledge and mental +cultivation, is generally his inability to discriminate between his +inferences and the perceptions on which they were grounded. Many a +marvellous tale, many a scandalous anecdote, owes its origin to this +incapacity. The narrator relates, not what he saw or heard, but the +impression which he derived from what he saw or heard, and of which +perhaps the greater part consisted of inference, though the whole is +related not as inference but as matter-of-fact. The difficulty of +inducing <span class="pagenum"><a name="Page_354" id="Page_354">[Pg 354]</a></span>witnesses to restrain within any moderate limits the +intermixture of their inferences with the narrative of their +perceptions, is well known to experienced cross-examiners; and still +more is this the case when ignorant persons attempt to describe any +natural phenomenon. "The simplest narrative," says Dugald Stewart,<a name="FNanchor_27_95" id="FNanchor_27_95"></a><a href="#Footnote_27_95" class="fnanchor">[27]</a> +"of the most illiterate observer involves more or less of hypothesis; +nay, in general, it will be found that, in proportion to his ignorance, +the greater is the number of conjectural principles involved in his +statements. A village apothecary (and, if possible, in a still greater +degree, an experienced nurse) is seldom able to describe the plainest +case, without employing a phraseology of which every word is a theory: +whereas a simple and genuine specification of the phenomena which mark a +particular disease; a specification unsophisticated by fancy, or by +preconceived opinions, may be regarded as unequivocal evidence of a mind +trained by long and successful study to the most difficult of all arts, +that of the faithful <i>interpretation</i> of nature."</p> + +<p>The universality of the confusion between perceptions and the inferences +drawn from them, and the rarity of the power to discriminate the one +from the other, ceases to surprise us when we consider that in the far +greater number of instances the actual perceptions of our senses are of +no importance or interest to us except as marks from which we infer +something beyond them. It is not the colour and superficial extension +perceived by the eye that are important to us, but the object, of which +those visible appearances testify the presence; and where the sensation +itself is indifferent, as it generally is, we have no motive to attend +particularly to it, but acquire a habit of passing it over without +distinct consciousness, and going on at once to the inference. So that +to know what the sensation actually was, is a study in itself, to which +painters, for example, have to train themselves by special and +long-continued discipline and application. In things further removed +from the dominion of the outward senses, no one who has not great +experience in psychological analysis is competent to <span class="pagenum"><a name="Page_355" id="Page_355">[Pg 355]</a></span>break this intense +association; and when such analytic habits do not exist in the requisite +degree, it is hardly possible to mention any of the habitual judgments +of mankind on subjects of a high degree of abstraction, from the being +of a God and the immortality of the soul down to the multiplication +table, which are not, or have not been, considered as matter of direct +intuition. So strong is the tendency to ascribe an intuitive character +to judgments which are mere inferences, and often false ones. No one can +doubt that many a deluded visionary has actually believed that he was +directly inspired from Heaven, and that the Almighty had conversed with +him face to face; which yet was only, on his part, a conclusion drawn +from appearances to his senses, or feelings in his internal +consciousness, which afforded no warrant for any such belief. A caution, +therefore, against this class of errors, is not only needful but +indispensable; though to determine whether, on any of the great +questions of metaphysics, such errors are actually committed, belongs +not to this place, but, as I have so often said, to a different science.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_356" id="Page_356">[Pg 356]</a></span></p> +<h3><a name="BOOK_V_CHAPTER_V" id="BOOK_V_CHAPTER_V"></a>CHAPTER V.<br /> +FALLACIES OF GENERALIZATION.</h3> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_V_1">§ 1.</a> The class of Fallacies of which we are now to speak, is the most +extensive of all; embracing a greater number and variety of unfounded +inferences than any of the other classes, and which it is even more +difficult to reduce to sub-classes or species. If the attempt made in +the preceding books to define the principles of well-grounded +generalization has been successful, all generalizations not conformable +to those principles might, in a certain sense, be brought under the +present class: when however the rules are known and kept in view, but a +casual lapse committed in the application of them, this is a blunder, +not a fallacy. To entitle an error of generalization to the latter +epithet, it must be committed on principle; there must lie in it some +erroneous general conception of the inductive process; the legitimate +mode of drawing conclusions from observation and experiment must be +fundamentally misconceived.</p> + +<p>Without attempting anything so chimerical as an exhaustive +classification of all the misconceptions which can exist on the subject, +let us content ourselves with noting, among the cautions which might be +suggested, a few of the most useful and needful.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_V_2">§ 2.</a> In the first place, there are certain kinds of generalization +which, if the principles already laid down be correct, <i>must</i> be +groundless: experience cannot afford the necessary conditions for +establishing them by a correct induction. Such, for instance, are all +inferences from the order of nature existing on the earth, or in the +solar system, to that which may exist in remote parts of the universe; +where the phenomena, <span class="pagenum"><a name="Page_357" id="Page_357">[Pg 357]</a></span>for aught we know, may be entirely different, or +may succeed one another according to different laws, or even according +to no fixed law at all. Such, again, in matters dependent on causation, +are all universal negatives, all propositions that assert impossibility. +The non-existence of any given phenomenon, however uniformly experience +may as yet have testified to the fact, proves at most that no cause, +adequate to its production, has yet manifested itself; but that no such +causes exist in nature can only be inferred if we are so foolish as to +suppose that we know all the forces in nature. The supposition would at +least be premature while our acquaintance with some even of those which +we do know is so extremely recent. And however much our knowledge of +nature may hereafter be extended, it is not easy to see how that +knowledge could ever be complete, or how, if it were, we could ever be +assured of its being so.</p> + +<p>The only laws of nature which afford sufficient warrant for attributing +impossibility (even with reference to the existing order of nature, and +to our own region of the universe), are first, those of number and +extension, which are paramount to the laws of the succession of +phenomena, and not exposed to the agency of counteracting causes; and +secondly, the universal law of causality itself. That no variation in +any effect or consequent will take place while the whole of the +antecedents remain the same, may be affirmed with full assurance. But, +that the addition of some new antecedent might not entirely alter and +subvert the accustomed consequent, or that antecedents competent to do +this do not exist in nature, we are in no case empowered positively to +conclude.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_V_3">§ 3.</a> It is next to be remarked that all generalizations which profess, +like the theories of Thales, Democritus, and others of the early Greek +speculators, to resolve all things into some one element, or like many +modern theories, to resolve phenomena radically different into the same, +are necessarily false. By radically different phenomena I mean +impressions on our senses which differ in quality, and not merely <span class="pagenum"><a name="Page_358" id="Page_358">[Pg 358]</a></span>in +degree. On this subject what appeared necessary was said in the chapter +on the Limits to the Explanation of Laws of Nature; but as the fallacy +is even in our own times a common one, I shall touch on it somewhat +further in this place.</p> + +<p>When we say that the force which retains the planets in their orbits is +resolved into gravity, or that the force which makes substances combine +chemically is resolved into electricity, we assert in the one case what +is, and in the other case what might, and probably will ultimately, be a +legitimate result of induction. In both these cases, motion is resolved +into motion. The assertion is, that a case of motion, which was supposed +to be special, and to follow a distinct law of its own, conforms to and +is included in the general law which regulates another class of motions. +But, from these and similar generalizations, countenance and currency +have been given to attempts to resolve, not motion into motion, but heat +into motion, light into motion, sensation itself into motion; states of +consciousness into states of the nervous system, as in the ruder forms +of the materialist philosophy; vital phenomena into mechanical or +chemical processes, as in some schools of physiology.</p> + +<p>Now I am far from pretending that it may not be capable of proof, or +that it will not be an important addition to our knowledge if proved, +that certain motions in the particles of bodies are among the +<i>conditions</i> of the production of heat or light; that certain assignable +physical modifications of the nerves may be the <i>conditions</i> not only of +our sensations or emotions, but even of our thoughts; that certain +mechanical and chemical conditions may, in the order of nature, be +sufficient to determine to action the physiological laws of life. All I +insist upon, in common with every thinker who entertains any clear idea +of the logic of science, is, that it shall not be supposed that by +proving these things one step would be made towards a real explanation +of heat, light, or sensation; or that the generic peculiarity of those +phenomena can be in the least degree evaded by any such discoveries, +however <span class="pagenum"><a name="Page_359" id="Page_359">[Pg 359]</a></span>well established. Let it be shown, for instance, that the most +complex series of physical causes and effects succeed one another in the +eye and in the brain to produce a sensation of colour; rays falling on +the eye, refracted, converging, crossing one another, making an inverted +image on the retina, and after this a motion—let it be a vibration, or +a rush of nervous fluid, or whatever else you are pleased to suppose, +along the optic nerve—a propagation of this motion to the brain itself, +and as many more different motions as you choose; still, at the end of +these motions, there is something which is not motion, there is a +feeling or sensation of colour. Whatever number of motions we may be +able to interpolate, and whether they be real or imaginary, we shall +still find, at the end of the series, a motion antecedent and a colour +consequent. The mode in which any one of the motions produces the next, +might possibly be susceptible of explanation by some general law of +motion; but the mode in which the last motion produces the sensation of +colour, cannot be explained by any law of motion; it is the law of +colour: which is, and must always remain, a peculiar thing. Where our +consciousness recognises between two phenomena an inherent distinction; +where we are sensible of a difference which is not merely of degree, and +feel that no adding one of the phenomena to itself would produce the +other; any theory which attempts to bring either under the laws of the +other must be false; though a theory which merely treats the one as a +cause or condition of the other, may possibly be true.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_V_4">§ 4.</a> Among the remaining forms of erroneous generalization, several of +those most worthy of and most requiring notice have fallen under our +examination in former places, where, in investigating the rules of +correct induction, we have had occasion to advert to the distinction +between it and some common mode of the incorrect. In this number is what +I have formerly called the natural Induction of uninquiring minds, the +Induction of the ancients, which proceeds <i>per <span class="pagenum"><a name="Page_360" id="Page_360">[Pg 360]</a></span>enumerationem +simplicem</i>: "This, that, and the other A are B, I cannot think of any A +which is not B, therefore every A is B." As a final condemnation of this +rude and slovenly mode of generalization, I will quote Bacon's emphatic +denunciation of it; the most important part, as I have more than once +ventured to assert, of the permanent service rendered by him to +philosophy. "Inductio quæ procedit per enumerationem simplicem, res +puerilis est, et precario concludit" (concludes only <i>by your leave</i>, or +provisionally,) "et periculo exponitur ab instantiâ contradictoriâ, et +plerumque secundum pauciora quam par est, et <i>ex his tantummodo quæ +præsto sunt pronunciat</i>. At Inductio quæ ad inventionem et +demonstrationem Scientiarum et Artium erit utilis, Naturam separare +debet, per rejectiones et exclusiones debitas; ac deinde post negativas +tot quot sufficiunt, super affirmativas concludere."</p> + +<p>I have already said that the mode of Simple Enumeration is still the +common and received method of Induction in whatever relates to man and +society. Of this a very few instances, more by way of memento than of +instruction, may suffice. What, for example, is to be thought of all the +"common-sense" maxims for which the following may serve as the universal +formula, "Whatsoever has never been, will never be." As for example: +negroes have never been as civilized as whites sometimes are, therefore +it is impossible they should be so. Women, as a class, are supposed not +to have hitherto been equal in intellect to men, therefore they are +necessarily inferior. Society cannot prosper without this or the other +institution; <i>e.g.</i> in Aristotle's time, without slavery; in later +times, without an established priesthood, without artificial +distinctions of rank, &c. One poor person in a thousand, educated, while +the nine hundred and ninety-nine remain uneducated, has usually aimed at +raising himself out of his class, therefore education makes people +dissatisfied with the condition of a labourer. Bookish men, taken from +speculative pursuits and set to work on something they know nothing +about, have generally been found or thought to do it ill; therefore +philosophers are unfit for business, &c. &c. All these are inductions by +simple enumeration. Reasons having some <span class="pagenum"><a name="Page_361" id="Page_361">[Pg 361]</a></span>reference to the canons of +scientific investigation have been attempted to be given, however +unsuccessfully, for some of these propositions; but to the multitude of +those who parrot them, the <i>enumeratio simplex, ex his tantummodo quæ +præsto sunt pronuncians</i>, is the sole evidence. Their fallacy consists +in this, that they are inductions without elimination: there has been no +real comparison of instances, nor even ascertainment of the material +facts in any given instance. There is also the further error, of +forgetting that such generalizations, even if well established, could +not be ultimate truths, but must be results of laws much more +elementary; and therefore, until deduced from such, could at most be +admitted as empirical laws, holding good within the limits of space and +time by which the particular observations that suggested the +generalization were bounded.</p> + +<p>This error, of placing more empirical laws, and laws in which there is +no direct evidence of causation, on the same footing of certainty as +laws of cause and effect, an error which is at the root of perhaps the +greater number of bad inductions, is exemplified only in its grossest +form in the kind of generalizations to which we have now referred. +These, indeed, do not possess even the degree of evidence which pertains +to a well-ascertained empirical law; but admit of refutation on the +empirical ground itself, without ascending to causal laws. A little +reflection, indeed, will show that mere negations can only form the +ground of the lowest and least valuable kind of empirical law. A +phenomenon has never been noticed; this only proves that the conditions +of that phenomenon have not yet occurred in experience, but does not +prove that they may not occur hereafter. There is a better kind of +empirical law than this, namely, when a phenomenon which is observed +presents within the limits of observation a series of gradations, in +which a regularity, or something like a mathematical law, is +perceptible: from which, therefore, something may be rationally presumed +as to those terms of the series which are beyond the limits of +observation. But in negation there are no gradations, and no series: the +generalizations, therefore, which deny the possibility of any given +condition of man and <span class="pagenum"><a name="Page_362" id="Page_362">[Pg 362]</a></span>society merely because it has never yet been +witnessed, cannot possess this higher degree of validity even as +empirical laws. What is more, the minuter examination which that higher +order of empirical laws presupposes, being applied to the subject-matter +of these, not only does not confirm but actually refutes them. For in +reality the past history of Man and Society, instead of exhibiting them +as immovable, unchangeable, incapable of ever presenting new phenomena, +shows them on the contrary to be, in many most important particulars, +not only changeable, but actually undergoing a progressive change. The +empirical law, therefore, best expressive, in most cases, of the genuine +result of observation, would be, not that such and such a phenomenon +will continue unchanged, but that it will continue to change in some +particular manner.</p> + +<p>Accordingly, while almost all generalizations relating to Man and +Society, antecedent to the last fifty years, have erred in the gross way +which we have attempted to characterize, namely, by implicitly assuming +that human nature and society will for ever revolve in the same orbit, +and exhibit essentially the same phenomena; which is also the vulgar +error of the ostentatiously practical, the votaries of so-called common +sense, in our day, especially in Great Britain; the more thinking minds +of the present age, having applied a more minute analysis to the past +records of our race, have for the most part adopted a contrary opinion, +that the human species is in a state of necessary progression, and that +from the terms of the series which are past we may infer positively +those which are yet to come. Of this doctrine, considered as a +philosophical tenet, we shall have occasion to speak more fully in the +concluding Book. If not, in all its forms, free from error, it is at +least free from the gross and stupid error which we previously +exemplified. But, in all except the most eminently philosophical minds, +it is infected with precisely the same <i>kind</i> of fallacy as that is. For +we must remember that even this other and better generalization, the +progressive change in the condition of the human species, is, after all, +but an empirical law: to which, too, it is not difficult to point out +exceedingly <span class="pagenum"><a name="Page_363" id="Page_363">[Pg 363]</a></span>large exceptions; and even if these could be got rid of, +either by disputing the facts or by explaining and limiting the theory, +the general objection remains valid against the supposed law, as +applicable to any other than what, in our third book, were termed +Adjacent Cases. For not only is it no ultimate, but not even a causal +law. Changes do indeed take place in human affairs, but every one of +those changes depends on determinate causes; the "progressiveness of the +species" is not a cause, but a summary expression for the general result +of all the causes. So soon as, by a quite different sort of induction, +it shall be ascertained what causes have produced these successive +changes, from the beginning of history, in so far as they have really +taken place, and by what causes of a contrary tendency they have been +occasionally checked or entirely counteracted, we may then be prepared +to predict the future with reasonable foresight; we may be in possession +of the real <i>law</i> of the future; and may be able to declare on what +circumstances the continuance of the same onward movement will +eventually depend. But this it is the error of many of the more advanced +thinkers, in the present age, to overlook; and to imagine that the +empirical law collected from a mere comparison of the condition of our +species at different past times, is a real law, is <i>the</i> law of its +changes, not only past but also to come. The truth is, that the causes +on which the phenomena of the moral world depend, are in every age, and +almost in every country, combined in some different proportion; so that +it is scarcely to be expected that the general result of them all should +conform very closely, in its details at least, to any uniformly +progressive series. And all generalizations which affirm that mankind +have a tendency to grow better or worse, richer or poorer, more +cultivated or more barbarous, that population increases faster than +subsistence, or subsistence than population, that inequality of fortune +has a tendency to increase or to break down, and the like, propositions +of considerable value as empirical laws within certain (but generally +rather narrow) limits, are in reality true or false according to times +and circumstances.</p> + +<p>What we have said of empirical generalizations from times <span class="pagenum"><a name="Page_364" id="Page_364">[Pg 364]</a></span>past to times +still to come, holds equally true of similar generalizations from +present times to times past; when persons whose acquaintance with moral +and social facts is confined to their own age, take the men and the +things of that age for the type of men and things in general, and apply +without scruple to the interpretation of the events of history, the +empirical laws which represent sufficiently for daily guidance the +common phenomena of human nature at that time and in that particular +state of society. If examples are wanted, almost every historical work, +until a very recent period, abounded in them. The same may be said of +those who generalize empirically from the people of their own country to +the people of other countries, as if human beings felt, judged, and +acted, everywhere in the same manner.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_V_5">§ 5.</a> In the foregoing instances, the distinction is confounded between +empirical laws, which express merely the customary order of the +succession of effects, and the laws of causation on which the effects +depend. There may, however, be incorrect generalization when this +mistake is not committed; when the investigation takes its proper +direction, that of causes, and the result erroneously obtained purports +to be a really causal law.</p> + +<p>The most vulgar form of this fallacy is that which is commonly called +<i>post hoc, ergo propter hoc</i>, or, <i>cum hoc, ergo propter hoc</i>. As when +it was inferred that England owed her industrial pre-eminence to her +restrictions on commerce: as when the old school of financiers, and some +speculative writers, maintained that the national debt was one of the +causes of national prosperity: as when the excellence of the Church, of +the Houses of Lords and Commons, of the procedure of the law courts, +&c., were inferred from the mere fact that the country had prospered +under them. In such cases as these, if it can be rendered probable by +other evidence that the supposed causes have some tendency to produce +the effect ascribed to them, the fact of its having been produced, +though only in one instance, is of some value as a verification by +specific experience: but in itself it goes scarcely any way at all +<span class="pagenum"><a name="Page_365" id="Page_365">[Pg 365]</a></span>towards establishing such a tendency, since, admitting the effect, a +hundred other antecedents could show an equally strong title of <i>that</i> +kind to be considered as the cause.</p> + +<p>In these examples we see bad generalization <i>à posteriori</i>, or +empiricism properly so called: causation inferred from casual +conjunction, without either due elimination, or any presumption arising +from known properties of the supposed agent. But bad generalization <i>à +priori</i> is fully as common: which is properly called false theory; +conclusions drawn, by way of deduction, from properties of some one +agent which is known or supposed to be present, all other coexisting +agents being overlooked. As the former is the error of sheer ignorance, +so the latter is especially that of semi-instructed minds; and is mainly +committed in attempting to explain complicated phenomena by a simpler +theory than their nature admits of. As when one school of physicians +sought for the universal principle of all disease in "lentor and morbid +viscidity of the blood," and imputing most bodily derangements to +mechanical obstructions, thought to cure them by mechanical +remedies;<a name="FNanchor_28_96" id="FNanchor_28_96"></a><a href="#Footnote_28_96" class="fnanchor">[28]</a> while another, the chemical school, "acknowledged no +source of disease but the presence of some hostile acid or alkali, or +some deranged condition in the chemical composition of the fluid or +solid parts," and conceived, therefore, that "all remedies must act by +producing chemical changes in the body. We find Tournefort busily +engaged in testing every vegetable juice, in order to discover in it +some traces of an acid or alkaline ingredient, which might confer upon +it medicinal activity. The fatal errors into <span class="pagenum"><a name="Page_366" id="Page_366">[Pg 366]</a></span>which such an hypothesis +was liable to betray the practitioner, received an awful illustration in +the history of the memorable fever that raged at Leyden in the year +1699, and which consigned two-thirds of the population of that city to +an untimely grave; an event which in a great measure depended upon the +Professor Sylvius de la Boe, who having just embraced the chemical +doctrines of Van Helmont, assigned the origin of the distemper to a +prevailing acid, and declared that its cure could alone [only] be +effected by the copious administration of absorbent and testaceous +medicines."<a name="FNanchor_29_97" id="FNanchor_29_97"></a><a href="#Footnote_29_97" class="fnanchor">[29]</a></p> + +<p>These aberrations in medical theory have their exact parallels in +politics. All the doctrines which ascribe absolute goodness to +particular forms of government, particular social arrangements, and even +to particular modes of education, without reference to the state of +civilization and the various distinguishing characters of the society +for which they are intended, are open to the same objection—that of +assuming one class of influencing circumstances to be the paramount +rulers of phenomena which depend in an equal or greater degree on many +others. But on these considerations it is the less necessary that we +should now dwell, as they will occupy our attention more largely in the +concluding Book.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_V_6">§ 6.</a> The last of the modes of erroneous generalization to which I shall +advert, is that to which we may give the name of False Analogies. This +Fallacy stands distinguished from those already treated of by the +peculiarity, that it does not even simulate a complete and conclusive +induction, but consists in the misapplication of an argument which is at +best only admissible as an inconclusive presumption, where real proof is +unattainable.</p> + +<p>An argument from analogy, is an inference that what is true in a certain +case, is true in a case known to be somewhat similar, but not known to +be exactly parallel, that is, to be similar in all the material +circumstances. An object has the property B: another object is not known +to have that property, <span class="pagenum"><a name="Page_367" id="Page_367">[Pg 367]</a></span>but resembles the first in a property A, not +known to be connected with B; and the conclusion to which the analogy +points, is that this object has the property B also. As, for example, +that the planets are inhabited, because the earth is so. The planets +resemble the earth in describing elliptical orbits round the sun, in +being attracted by it and by one another, in being nearly spherical, +revolving on their axes, &c.; but it is not known that any of these +properties, or all of them together, are the conditions on which the +possession of inhabitants is dependent, or are marks of those +conditions. Nevertheless, so long as we do not know what the conditions +are, they <i>may</i> be connected by some law of nature with those common +properties; and to the extent of that possibility the planets are more +likely to be inhabited, than if they did not resemble the earth at all. +This non-assignable and generally small increase of probability, beyond +what would otherwise exist, is all the evidence which a conclusion can +derive from analogy. For if we have the slightest reason to suppose any +real connexion between the two properties A and B, the argument is no +longer one of analogy. If it had been ascertained (I purposely put an +absurd supposition) that there was a connexion by causation between the +fact of revolving on an axis and the existence of animated beings, or if +there were any reasonable ground for even suspecting such a connexion, a +probability would arise of the existence of inhabitants in the planets, +which might be of any degree of strength, up to a complete induction; +but we should then infer the fact from the ascertained or presumed law +of causation, and not from the analogy of the earth.</p> + +<p>The name analogy, however, is sometimes employed by extension to denote +those arguments of an inductive character but not amounting to a real +induction, which are employed to strengthen the argument drawn from a +simple resemblance. Though A, the property common to the two cases, +cannot be shown to be the cause or effect of B, the analogical reasoner +will endeavour to show that there is some less close degree of connexion +between them; that A is one of a set of conditions from which, when all +united, B would result; or is an occasional <span class="pagenum"><a name="Page_368" id="Page_368">[Pg 368]</a></span>effect of some cause which +has been known also to produce B; and the like. Any of which things, if +shown, would render the existence of B by so much more probable, than if +there had not been even that amount of known connexion between B and A.</p> + +<p>Now an error or fallacy of analogy may occur in two ways. Sometimes it +consists in employing an argument of either of the above kinds with +correctness indeed, but overrating its probative force. This very common +aberration is sometimes supposed to be particularly incident to persons +distinguished for their imagination; but in reality it is the +characteristic intellectual vice of those whose imaginations are barren, +either from want of exercise, natural defect, or the narrowness of their +range of ideas. To such minds objects present themselves clothed in but +few properties; and as, therefore, few analogies between one object and +another occur to them, they almost invariably overrate the degree of +importance of those few: while one whose fancy takes a wider range, +perceives and remembers so many analogies tending to conflicting +conclusions, that he is much less likely to lay undue stress on any of +them. We always find that those are the greatest slaves to metaphorical +language, who have but one set of metaphors.</p> + +<p>But this is only one of the modes of error in the employment of +arguments of analogy. There is another, more properly deserving the name +of fallacy; namely, when resemblance in one point is inferred from +resemblance in another point, though there is not only no evidence to +connect the two circumstances by way of causation, but the evidence +tends positively to disconnect them. This is properly the Fallacy of +False Analogies.</p> + +<p>As a first instance, we may cite that favourite argument in defence of +absolute power, drawn from the analogy of paternal government in a +family, which government, however much in need of control, is not and +cannot be controlled by the children themselves, while they remain +children. Paternal government, says the argument, works well; therefore, +despotic government in a state will work well. I wave, as not <span class="pagenum"><a name="Page_369" id="Page_369">[Pg 369]</a></span>pertinent +in this place, all that could be said in qualification of the alleged +excellence of paternal government. However this might be, the argument +from the family to the state would not the less proceed on a false +analogy; implying that the beneficial working of parental government +depends, in the family, on the only point which it has in common with +political despotism, namely, irresponsibility. Whereas it depends, when +real, not on that but on two other circumstances of the case, the +affection of the parent for the children, and the superiority of the +parent in wisdom and experience; neither of which properties can be +reckoned on, or are at all likely to exist, between a political despot +and his subjects; and when either of these circumstances fails even in +the family, and the influence of the irresponsibility is allowed to work +uncorrected, the result is anything but good government. This, +therefore, is a false analogy.</p> + +<p>Another example is the not uncommon <i>dictum</i>, that bodies politic have +youth, maturity, old age, and death, like bodies natural: that after a +certain duration of prosperity, they tend spontaneously to decay. This +also is a false analogy, because the decay of the vital powers in an +animated body can be distinctly traced to the natural progress of those +very changes of structure which, in their earlier stages, constitute its +growth to maturity: while in the body politic the progress of those +changes cannot, generally speaking, have any effect but the still +further continuance of growth: it is the stoppage of that progress, and +the commencement of retrogression, that alone would constitute decay. +Bodies politic die, but it is of disease, or violent death: they have no +old age.</p> + +<p>The following sentence from Hooker's <i>Ecclesiastical Polity</i> is an +instance of a false analogy from physical bodies to what are called +bodies politic. "As there could be in natural bodies no motion of +anything unless there were some which moveth all things, and continueth +immovable: even so in politic societies there must be some unpunishable, +or else no man shall suffer punishment." There is a double fallacy here, +for not only the analogy, but the premise from which it is drawn, is +untenable. The notion that there must be something immovable <span class="pagenum"><a name="Page_370" id="Page_370">[Pg 370]</a></span>which +moves all other things, is the old scholastic error of a <i>primum +mobile</i>.</p> + +<p>The following instance I quote from Archbishop Whately's <i>Rhetoric</i>: "It +would be admitted that a great and permanent diminution in the quantity +of some useful commodity, such as corn, or coal, or iron, throughout the +world, would be a serious and lasting loss; and again, that if the +fields and coal mines yielded regularly double quantities, with the same +labour, we should be so much the richer; hence it might be inferred, +that if the quantity of gold and silver in the world were diminished +one-half, or were doubled, like results would follow; the utility of +these metals, for the purposes of coin, being very great. Now there are +many points of resemblance and many of difference, between the precious +metals on the one hand, and corn, coal, &c., on the other; but the +important circumstance to the supposed argument is, that the <i>utility</i> +of gold and silver (as coin, which is far the chief) <i>depends on their +value</i>, which is regulated by their scarcity; or rather, to speak +strictly, by the difficulty of obtaining them; whereas, if corn and coal +were ten times as abundant (<i>i.e.</i> more easily obtained), a bushel of +either would still be as useful as now. But if it were twice as easy to +procure gold as it is, a sovereign would be twice as large; if only half +as easy it would be of the size of a half-sovereign, and this (besides +the trifling circumstance of the cheapness or dearness of gold +ornaments) would be all the difference. The analogy, therefore, fails in +the point essential to the argument."</p> + +<p>The same author notices, after Bishop Copleston, the case of False +Analogy which consists in inferring from the similarity in many respects +between the metropolis of a country and the heart of the animal body, +that the increased size of the metropolis is a disease.</p> + +<p>Some of the false analogies on which systems of physics were confidently +grounded in the time of the Greek philosophers, are such as we now call +fanciful, not that the resemblances are not often real, but that it is +long since any one has been inclined to draw from them the inferences +which were then drawn. Such, for instance, are the curious speculations +<span class="pagenum"><a name="Page_371" id="Page_371">[Pg 371]</a></span>of the Pythagoreans on the subject of numbers. Finding that the +distances of the planets bore or seemed to bear to one another a +proportion not varying much from that of the divisions of the monochord, +they inferred from it the existence of an inaudible music, that of the +spheres: as if the music of a harp had depended solely on the numerical +proportions, and not on the material, nor even on the existence of any +material, any strings at all. It has been similarly imagined that +certain combinations of numbers, which were found to prevail in some +natural phenomena, must run through the whole of nature: as that there +must be four elements, because there are four possible combinations of +hot and cold, wet and dry; that there must be seven planets, because +there were seven metals, and even because there were seven days of the +week. Kepler himself thought that there could be only six planets +because there were only five regular solids. With these we may class the +reasonings, so common in the speculations of the ancients, founded on a +supposed <i>perfection</i> in nature: meaning by nature the customary order +of events as they take place of themselves without human interference. +This also is a rude guess at an analogy supposed to pervade all +phenomena, however dissimilar. Since what was thought to be perfection +appeared to obtain in some phenomena, it was inferred (in opposition to +the plainest evidence) to obtain in all. "We always suppose that which +is better to take place in nature, if it be possible," says Aristotle: +and the vaguest and most heterogeneous qualities being confounded +together under the notion of being <i>better</i>, there was no limit to the +wildness of the inferences. Thus, because the heavenly bodies were +"perfect," they must move in circles and uniformly. For "they" (the +Pythagoreans) "would not allow," says Geminus,<a name="FNanchor_30_98" id="FNanchor_30_98"></a><a href="#Footnote_30_98" class="fnanchor">[30]</a> "of any such disorder +among divine and eternal things, as that they should sometimes move +quicker and sometimes slower, and sometimes stand still; for no one +would tolerate such anomaly in the movements even of a man, who was +decent and orderly. The occasions of life, however, are often reasons +for men going <span class="pagenum"><a name="Page_372" id="Page_372">[Pg 372]</a></span>quicker or slower; but in the incorruptible nature of the +stars, it is not possible that any cause can be alleged of quickness or +slowness." It is seeking an argument of analogy very far, to suppose +that the stars must observe the rules of decorum in gait and carriage, +prescribed for themselves by the long-bearded philosophers satirized by +Lucian.</p> + +<p>As late as the Copernican controversy it was urged as an argument in +favour of the true theory of the solar system, that it placed the fire, +the noblest element, in the centre of the universe. This was a remnant +of the notion that the order of nature must be perfect, and that +perfection consisted in conformity to rules of precedency in dignity, +either real or conventional. Again, reverting to numbers: certain +numbers were <i>perfect</i>, therefore those numbers must obtain in the great +phenomena of nature. Six was a perfect number, that is, equal to the sum +of all its factors; an additional reason why there must be exactly six +planets. The Pythagoreans, on the other hand, attributed perfection to +the number ten; but agreed in thinking that the perfect number must be +somehow realized in the heavens; and knowing only of nine heavenly +bodies, to make up the enumeration, they asserted "that there was an +<i>antichthon</i> or counter-earth, on the other side of the sun, invisible +to us."<a name="FNanchor_31_99" id="FNanchor_31_99"></a><a href="#Footnote_31_99" class="fnanchor">[31]</a> Even Huygens was persuaded that when the number of the +heavenly bodies had reached twelve, it could not admit of any further +increase. Creative power could not go beyond that sacred number.</p> + +<p>Some curious instances of false analogy are to be found in the arguments +of the Stoics to prove the equality of all crimes, and the equal +wretchedness of all who had not realized their idea of perfect virtue. +Cicero, towards the end of his Fourth Book <i>De Finibus</i>, states some of +these as follows. "Ut, inquit, in fidibus plurimis, si nulla earum ita +contenta numeris sit, ut concentum servare possit, omnes æque incontentæ +sunt; sic peccata, quia discrepant, æque discrepant; paria sunt igitur." +To which Cicero himself aptly answers, "æque contingit omnibus fidibus, +ut incontentæ sint; <span class="pagenum"><a name="Page_373" id="Page_373">[Pg 373]</a></span>illud non continuo, ut æque incontentæ." The Stoic +resumes: "Ut enim, inquit, gubernator æque peccat, si palcarum navem +evertit, et si auri; item æque peccat qui parentem, et qui servum, +injuriâ verberat;" assuming, that because the magnitude of the interest +at stake makes no difference in the mere defect of skill, it can make +none in the moral defect: a false analogy. Again, "Quis ignorat, si +plures ex alto emergere velint, propius fore eos quidem ad respirandum, +qui ad summam jam aquam appropinquant, sed nihilo magis respirare posse, +quam eos, qui sunt in profundo? Nihil ergo adjuvat procedere, et +progredi in virtute, quominus miserrimus sit, antequam ad eam +pervenerit, quoniam in aquâ nihil adjuvat: et quoniam catuli, qui jam +despecturi sunt, cæci æque, et ii qui modo nati; Platonem quoque necesse +est, quoniam nondum videbat sapientiam, æque cæcum animo, ac Phalarim +fuisse." Cicero, in his own person, combats these false analogies by +other analogies tending to an opposite conclusion. "Ista similia non +sunt, Cato.... Illa sunt similia; hebes acies est cuipiam oculorum: +corpore alius languescit: hi curatione adhibitâ levantur in dies: alter +valet plus quotidie: alter videt. Hi similes sunt omnibus, qui virtuti +student; levantur vitiis, levantur erroribus."</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_V_7">§ 7.</a> In these and all other arguments drawn from remote analogies, and +from metaphors, which are cases of analogy, it is apparent (especially +when we consider the extreme facility of raising up contrary analogies +and conflicting metaphors) that so far from the metaphor or analogy +proving anything, the applicability of the metaphor is the very thing to +be made out. It has to be shown that in the two cases asserted to be +analogous, the same law is really operating; that between the known +resemblance and the inferred one there is some connexion by means of +causation. Cicero and Cato might have bandied opposite analogies for +ever; it rested with each of them to prove by just induction, or at +least to render probable, that the case resembled the one set of +analogous cases and not the other, in the circumstances on which the +disputed question really hinged. Metaphors, for the most part, +therefore, <span class="pagenum"><a name="Page_374" id="Page_374">[Pg 374]</a></span>assume the proposition which they are brought to prove: +their use is, to aid the apprehension of it; to make clearly and vividly +comprehended what it is that the person who employs the metaphor is +proposing to make out; and sometimes also, by what media he proposes to +do so. For an apt metaphor, though it cannot prove, often suggests the +proof.</p> + +<p>For instance, when D'Alembert (I believe) remarked that in certain +governments, only two creatures find their way to the highest places, +the eagle and the serpent; the metaphor not only conveys with great +vividness the assertion intended, but contributes towards substantiating +it, by suggesting, in a lively manner, the means by which the two +opposite characters thus typified effect their rise. When it is said +that a certain person misunderstands another because the lesser of two +objects cannot comprehend the greater, the application of what is true +in the literal sense of the word <i>comprehend</i>, to its metaphorical +sense, points to the fact which is the ground and justification of the +assertion, viz. that one mind cannot thoroughly understand another +unless it can contain it in itself, that is, unless it possesses all +that is contained in the other. When it is urged as an argument for +education, that if the soil is left uncultivated, weeds will spring up, +the metaphor, though no proof, but a statement of the thing to be +proved, states it in terms which, by suggesting a parallel case, put the +mind upon the track of the real proof. For, the reason why weeds grow in +an uncultivated soil, is that the seeds of worthless products exist +everywhere, and can germinate and grow in almost all circumstances, +while the reverse is the case with those which are valuable; and this +being equally true of mental products, this mode of conveying an +argument, independently of its rhetorical advantages, has a logical +value; since it not only suggests the grounds of the conclusion, but +points to another case in which those grounds have been found, or at +least deemed to be, sufficient.</p> + +<p>On the other hand, when Bacon, who is equally conspicuous in the use and +abuse of figurative illustration, says that the stream of time has +brought down to us only the least valuable part of the writings of the +ancients, as a river carries <span class="pagenum"><a name="Page_375" id="Page_375">[Pg 375]</a></span>froth and straws floating on its surface, +while more weighty objects sink to the bottom; this, even if the +assertion illustrated by it were true, would be no good illustration, +there being no parity of cause. The levity by which substances float on +a stream, and the levity which is synonymous with worthlessness, have +nothing in common except the name; and (to show how little value there +is in the metaphor) we need only change the word into <i>buoyancy</i>, to +turn the semblance of argument involved in Bacon's illustration against +himself.</p> + +<p>A metaphor, then, is not to be considered as an argument, but as an +assertion that an argument exists; that a parity subsists between the +case from which the metaphor is drawn and that to which it is applied. +This parity may exist though the two cases be apparently very remote +from one another; the only resemblance existing between them may be a +resemblance of relations, an analogy in Ferguson's and Archbishop +Whately's sense: as in the preceding instance, in which an illustration +from agriculture was applied to mental cultivation.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_V_8">§ 8.</a> To terminate the subject of Fallacies of Generalization, it remains +to be said, that the most fertile source of them is bad classification: +bringing together in one group, and under one name, things which have no +common properties, or none but such as are too unimportant to allow +general propositions of any considerable value to be made respecting the +class. The misleading effect is greatest, when a word which in common +use expresses some definite fact, is extended by slight links of +connexion to cases in which that fact does not exist, but some other or +others, only slightly resembling it. Thus Bacon,<a name="FNanchor_32_100" id="FNanchor_32_100"></a><a href="#Footnote_32_100" class="fnanchor">[32]</a> in speaking of the +<i>Idola</i> or Fallacies arising from notions <i>temere et inæqualiter à rebus +abstractæ</i>, exemplifies them by the notion of Humidum or Wet, so +familiar in the physics of antiquity and of the middle ages. "Invenietur +verbum istud, Humidum, nihil aliud quam nota confusa diversarum +<span class="pagenum"><a name="Page_376" id="Page_376">[Pg 376]</a></span>actionum, quæ nullam constantiam aut reductionem patiuntur. Significat +enim, et quod circa aliud corpus facile se circumfundit; et quod in se +est indeterminabile, nec consistere potest; et quod facile cedit +undique; et quod facile se dividit et dispergit; et quod facile se unit +et colligit; et quod facile fluit, et in motu ponitur; et quod alteri +corpori facile adhæret, idque madefacit; et quod facile reducitur in +liquidum, sive colliquatur, cum antea consisteret. Itaque quum ad hujus +nominis prædicationem et impositionem ventum sit; si alia accipias, +flamma humida est; si alia accipias, aer humidus non est; si alia, +pulvis minutus humidus est; si alia, vitrum humidum est: ut facile +appareat, istam notionem ex aquâ tantum, et communibus et vulgaribus +liquoribus, absque ullâ debitâ verificatione, temere abstractam esse."</p> + +<p>Bacon himself is not exempt from a similar accusation when inquiring +into the nature of heat: where he occasionally proceeds like one who +seeking for the cause of hardness, after examining that quality in iron, +flint, and diamond, should expect to find that it is something which can +be traced also in hard water, a hard knot, and a hard heart.</p> + +<p>The word <i>κίνησις</i> in the Greek philosophy, and the words +Generation and Corruption both then and long afterwards, denoted such a +multitude of heterogeneous phenomena, that any attempt at philosophizing +in which those words were used was almost as necessarily abortive as if +the word <i>hard</i> had been taken to denote a class including all the +things mentioned above. <i>Κίνησις</i>, for instance, which properly +signified motion, was taken to denote not only all motion but even all +change: <i>ἀλλοίωσις</i> being recognised as one of the modes of +<i>κίνησις</i>. The effect was, to connect with every form of +<i>ἀλλοίωσις</i> or change, ideas drawn from motion in the proper and literal +sense, and which had no real connexion with any other kind of <i>κίνησις</i> than that. Aristotle and Plato laboured under a continual +embarrassment from this misuse of terms. But if we proceed further in +this direction we shall encroach upon the Fallacy of Ambiguity, which +belongs to a different class, the last in order of our classification, +Fallacies of Confusion.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_377" id="Page_377">[Pg 377]</a></span></p> +<h3><a name="BOOK_V_CHAPTER_VI" id="BOOK_V_CHAPTER_VI"></a>CHAPTER VI.<br /> +FALLACIES OF RATIOCINATION.</h3> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_VI_1">§ 1.</a> We have now, in our progress through the classes of Fallacies, +arrived at those to which, in the common books of logic, the appellation +is in general exclusively appropriated; those which have their seat in +the ratiocinative or deductive part of the investigation of truth. On +these fallacies it is the less necessary for us to insist at any length, +as they have been most satisfactorily treated in a work familiar to +almost all, in this country at least, who feel any interest in these +speculations, Archbishop Whately's <i>Logic</i>. Against the more obvious +forms of this class of fallacies, the rules of the syllogism are a +complete protection. Not (as we have so often said) that the +ratiocination cannot be good unless it be in the form of a syllogism; +but that, by showing it in that form, we are sure to discover if it be +bad, or at least if it contain any fallacy of this class.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_VI_2">§ 2.</a> Among Fallacies of Ratiocination, we ought perhaps to include the +errors committed in processes which have the appearance only, not the +reality, of an inference from premises; the fallacies connected with the +conversion and æquipollency of propositions. I believe errors of this +description to be far more frequently committed than is generally +supposed, or than their extreme obviousness might seem to admit of. For +example, the simple conversion of an universal affirmative proposition, +All A are B, therefore all B are A, I take to be a very common form of +error: though committed, like many other fallacies, oftener in the +silence of thought than in express words, for it can scarcely be clearly +enunciated without being detected. And so with another form of fallacy, +not <span class="pagenum"><a name="Page_378" id="Page_378">[Pg 378]</a></span>substantially different from the preceding: the erroneous +conversion of an hypothetical proposition. The proper converse of an +hypothetical proposition is this: If the consequent be false, the +antecedent is false; but this, If the consequent be true, the antecedent +is true, by no means holds good, but is an error corresponding to the +simple conversion of an universal affirmative. Yet hardly anything is +more common than for people, in their private thoughts, to draw this +inference. As when the conclusion is accepted, which it so often is, for +proof of the premises. That the premises cannot be true if the +conclusion is false, is the unexceptionable foundation of the legitimate +mode of reasoning called a <i>reductio ad absurdum</i>. But people +continually think and express themselves, as if they also believed that +the premises cannot be false if the conclusion is true. The truth, or +supposed truth, of the inferences which follow from a doctrine, often +enables it to find acceptance in spite of gross absurdities in it. How +many philosophical systems which had scarcely any intrinsic +recommendation, have been received by thoughtful men because they were +supposed to lend additional support to religion, morality, some +favourite view of politics, or some other cherished persuasion: not +merely because their wishes were thereby enlisted on its side, but +because its leading to what they deemed sound conclusions appeared to +them a strong presumption in favour of its truth: though the +presumption, when viewed in its true light, amounted only to the absence +of that particular evidence of falsehood, which would have resulted from +its leading by correct inference to something already known to be false.</p> + +<p>Again, the very frequent error in conduct, of mistaking reverse of wrong +for right, is the practical form of a logical error with respect to the +Opposition of Propositions. It is committed for want of the habit of +distinguishing the <i>contrary</i> of a proposition from the <i>contradictory</i> +of it, and of attending to the logical canon, that contrary +propositions, though they cannot both be true, may both be false. If the +error were to express itself in words, it would run distinctly counter +to this canon. It generally, however, does not so express itself, and +<span class="pagenum"><a name="Page_379" id="Page_379">[Pg 379]</a></span>to compel it to do so is the most effectual method of detecting and +exposing it.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_VI_3">§ 3.</a> Among Fallacies of Ratiocination are to be ranked in the first +place, all the cases of vicious syllogism laid down in the books. These +generally resolve themselves into having more than three terms to the +syllogism, either avowedly, or in the covert mode of an undistributed +middleterm, or an <i>illicit process</i> of one of the two extremes. It is +not, indeed, very easy fully to convict an argument of falling under any +one of these vicious cases in particular; for the reason already more +than once referred to, that the premises are seldom formally set out: if +they were, the fallacy would impose upon nobody; and while they are not, +it is almost always to a certain degree optional in what manner the +suppressed link shall be filled up. The rules of the syllogism are rules +for compelling a person to be aware of the whole of what he must +undertake to defend if he persists in maintaining his conclusion. He has +it almost always in his power to make his syllogism good by introducing +a false premise; and hence it is scarcely ever possible decidedly to +affirm that any argument involves a bad syllogism: but this detracts +nothing from the value of the syllogistic rules, since it is by them +that a reasoner is compelled distinctly to make his election what +premises he is prepared to maintain. The election made, there is +generally so little difficulty in seeing whether the conclusion follows +from the premises set out, that we might without much logical +impropriety have merged this fourth class of fallacies in the fifth, or +Fallacies of Confusion.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_VI_4">§ 4.</a> Perhaps, however, the commonest, and certainly the most dangerous +fallacies of this class, are those which do not lie in a single +syllogism, but slip in between one syllogism and another in a chain of +argument, and are committed by <i>changing the premises</i>. A proposition is +proved, or an acknowledged truth laid down, in the first part of an +argumentation, and in the second a further argument is founded not on +the same proposition, but on some other, resembling it sufficiently <span class="pagenum"><a name="Page_380" id="Page_380">[Pg 380]</a></span>to +be mistaken for it. Instances of this fallacy will be found in almost +all the argumentative discourses of unprecise thinkers; and we need only +here advert to one of the obscurer forms of it, recognised by the +schoolmen as the fallacy <i>à dicto secundum quid ad dictum simpliciter</i>. +This is committed when, in the premises, a proposition is asserted with +a qualification, and the qualification lost sight of in the conclusion; +or oftener, when a limitation or condition, though not asserted, is +necessary to the truth of the proposition, but is forgotten when that +proposition comes to be employed as a premise. Many of the bad arguments +in vogue belong to this class of error. The premise is some admitted +truth, some common maxim, the reasons or evidence for which have been +forgotten, or are not thought of at the time, but if they had been +thought of would have shown the necessity of so limiting the premise +that it would no longer have supported the conclusion drawn from it.</p> + +<p>Of this nature is the fallacy in what is called, by Adam Smith and +others, the Mercantile Theory in Political Economy. That theory sets out +from the common maxim, that whatever brings in money enriches; or that +every one is rich in proportion to the quantity of money he obtains. +From this it is concluded that the value of any branch of trade, or of +the trade of the country altogether, consists in the balance of money it +brings in; that any trade which carries more money out of the country +than it draws into it is a losing trade; that therefore money should be +attracted into the country and kept there, by prohibitions and bounties: +and a train of similar corollaries. All for want of reflecting that if +the riches of an individual are in proportion to the quantity of money +he can command, it is because that is the measure of his power of +purchasing money's worth; and is therefore subject to the proviso that +he is not debarred from employing his money in such purchases. The +premise, therefore, is only true <i>secundum quid</i>; but the theory assumes +it to be true absolutely, and infers that increase of money is increase +of riches, even when produced by means subversive of the condition under +which alone money can be riches.</p> + +<p><span class="pagenum"><a name="Page_381" id="Page_381">[Pg 381]</a></span></p><p>A second instance is, the argument by which it used to be contended, +before the commutation of tithe, that tithes fell on the landlord, and +were a deduction from rent; because the rent of tithe-free land was +always higher than that of land of the same quality, and the same +advantages of situation, subject to tithe. Whether it be true or not +that a tithe falls on rent, a treatise on Logic is not the place to +examine; but it is certain that this is no proof of it. Whether the +proposition be true or false, tithe-free land must, by the necessity of +the case, pay a higher rent. For if tithes do not fall on rent, it must +be because they fall on the consumer; because they raise the price of +agricultural produce. But if the produce be raised in price, the farmer +of tithe-free as well as the farmer of tithed land gets the benefit. To +the latter the rise is but a compensation for the tithe he pays; to the +first, who pays none, it is clear gain, and therefore enables him, and +if there be freedom of competition forces him, to pay so much more rent +to his landlord. The question remains, to what class of fallacies this +belongs. The premise is, that the owner of tithed land receives less +rent than the owner of tithe-free land; the conclusion is, that +therefore he receives less than he himself would receive if tithe were +abolished. But the premise is only true conditionally; the owner of +tithed land receives less than what the owner of tithe-free land is +enabled to receive <i>when other lands are tithed</i>; while the conclusion +is applied to a state of circumstances in which that condition fails, +and in which, by consequence, the premise would not be true. The +fallacy, therefore, is <i>à dicto secundum quid ad dictum simpliciter</i>.</p> + +<p>A third example is the opposition sometimes made to legitimate +interferences of government in the economical affairs of society, +grounded on a misapplication of the maxim, that an individual is a +better judge than the government, of what is for his own pecuniary +interest. This objection was urged to Mr. Wakefield's principle of +colonization; the concentration of the settlers, by fixing such a price +on unoccupied land as may preserve the most desirable proportion between +the quantity of land in culture, and the labouring population. Against +this it was argued, that if individuals <span class="pagenum"><a name="Page_382" id="Page_382">[Pg 382]</a></span>found it for their advantage to +occupy extensive tracts of land, they, being better judges of their own +interest than the legislature (which can only proceed on general rules) +ought not to be restrained from doing so. But in this argument it was +forgotten that the fact of a person's taking a large tract of land is +evidence only that it is his interest to take as much as other people, +but not that it might not be for his interest to content himself with +less, if he could be assured that other people would do so too; an +assurance which nothing but a government regulation can give. If all +other people took much, and he only a little, he would reap none of the +advantages derived from the concentration of the population and the +consequent possibility of procuring labour for hire, but would have +placed himself, without equivalent, in a situation of voluntary +inferiority. The proposition, therefore, that the quantity of land which +people will take when left to themselves is that which is most for their +interest to take, is true only <i>secundum quid</i>: it is only their +interest while they have no guarantee for the conduct of one another. +But the arrangement disregards the limitation, and takes the proposition +for true <i>simpliciter</i>.</p> + +<p>One of the conditions oftenest dropped, when what would otherwise be a +true proposition is employed as a premise for proving others, is the +condition of <i>time</i>. It is a principle of political economy that prices, +profits, wages, &c. "always find their level;" but this is often +interpreted as if it meant that they are always, or generally, <i>at</i> +their level; while the truth is, as Coleridge epigrammatically expresses +it, that they are always <i>finding</i> their level, "which might be taken as +a paraphrase or ironical definition of a storm."</p> + +<p>Under the same head of fallacy (<i>à dicto secundum quid ad dictum +simpliciter</i>) might be placed all the errors which are vulgarly called +misapplications of abstract truths: that is, where a principle, true (as +the common expression is) <i>in the abstract</i>, that is, all modifying +causes being supposed absent, is reasoned on as if it were true +absolutely, and no modifying circumstance could ever by possibility +exist. This very common <span class="pagenum"><a name="Page_383" id="Page_383">[Pg 383]</a></span>form of error it is not requisite that we +should exemplify here, as it will be particularly treated of hereafter +in its application to the subjects on which it is most frequent and most +fatal, those of politics and society.<a name="FNanchor_33_101" id="FNanchor_33_101"></a><a href="#Footnote_33_101" class="fnanchor">[33]</a></p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_384" id="Page_384">[Pg 384]</a></span></p> +<h3><a name="BOOK_V_CHAPTER_VII" id="BOOK_V_CHAPTER_VII"></a>CHAPTER VII.<br /> +FALLACIES OF CONFUSION.</h3> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_VII_1">§ 1.</a> Under this fifth and last class it is convenient to arrange all +those fallacies, in which the source of error is not so much a false +estimate of the probative force of known evidence, as an indistinct, +indefinite, and fluctuating conception of what the evidence is.</p> + +<p>At the head of these stands that multitudinous body of fallacious +reasonings, in which the source of error is the ambiguity of terms: when +something which is true if a word be used in a particular sense, is +reasoned on as if it were true in another sense. In such a case there is +not a mal-estimation of evidence, because there is not properly any +evidence to the point at all; there is evidence, but to a different +point, which from a confused apprehension of the meaning of the terms +used, is supposed to be the same. This error will naturally be oftener +committed in our ratiocinations than in our direct inductions, because +in the former we are deciphering our own or other people's notes, while +in the latter we have the things themselves present, either to the +senses or to the memory. Except, indeed, when the induction is not from +individual cases to a generality, but from generalities to a still +higher generalization; in that case the fallacy of ambiguity may affect +the inductive process as well as the ratiocinative. It occurs in +ratiocination in two ways: when the middleterm is ambiguous, or when one +of the terms of the syllogism is taken in one sense in the premises, and +in another sense in the conclusion.</p> + +<p>Some good exemplifications of this fallacy are given by Archbishop +Whately. "One case," says he, "which may be regarded as coming under the +head of Ambiguous Middle, is (what I believe logical writers mean by +'<i>Fallacia Figuræ <span class="pagenum"><a name="Page_385" id="Page_385">[Pg 385]</a></span>Dictionis</i>,') the fallacy built on the grammatical +structure of language, from men's usually taking for granted that +<i>paronymous</i> (or <i>conjugate</i>) words, <i>i.e.</i> those belonging to each +other, as the substantive, adjective, verb, &c. of the same root, have a +precisely corresponding meaning; which is by no means universally the +case. Such a fallacy could not indeed be even exhibited in strict +logical form, which would preclude even the attempt at it, since it has +two middleterms in sound as well as sense. But nothing is more common in +practice than to vary continually the terms employed, with a view to +grammatical convenience; nor is there anything unfair in such a +practice, as long as the <i>meaning</i> is preserved unaltered; <i>e.g.</i> +'murder should be punished with death; this man is a murderer, therefore +he deserves to die,' &c. Here we proceed on the assumption (in this case +just) that to commit murder, and to be a murderer,—to deserve death, +and to be one who ought to die, are, respectively, equivalent +expressions; and it would frequently prove a heavy inconvenience to be +debarred this kind of liberty; but the abuse of it gives rise to the +Fallacy in question: <i>e.g.</i> <i>projectors</i> are unfit to be trusted; this +man has formed a <i>project</i>, therefore he is unfit to be trusted: here +the sophist proceeds on the hypothesis that he who forms a <i>project</i> +must be a <i>projector</i>: whereas the bad sense that commonly attaches to +the latter word, is not at all implied in the former. This fallacy may +often be considered as lying not in the Middle, but in one of the terms +of the Conclusion; so that the conclusion drawn shall not be, in +reality, at all warranted by the premises, though it will appear to be +so, by means of the grammatical affinity of the words: <i>e.g.</i> to be +acquainted with the guilty is a <i>presumption</i> of guilt; this man is so +acquainted, therefore we may <i>presume</i> that he is guilty: this argument +proceeds on the supposition of an exact correspondence between <i>presume</i> +and <i>presumption</i>, which, however, does not really exist; for +'presumption' is commonly used to express a kind of <i>slight suspicion</i>; +whereas, 'to presume' amounts to actual belief. There are innumerable +instances of a non-correspondence in paronymous words, similar to that +above instanced; as between <i>art</i> and <i>artful</i>, <i>design</i> and +<i>designing</i>, <span class="pagenum"><a name="Page_386" id="Page_386">[Pg 386]</a></span><i>faith</i> and <i>faithful</i>, &c.; and the more slight the +variation of the meaning, the more likely is the fallacy to be +successful; for when the words have become so widely removed in sense as +'pity' and 'pitiful,' every one would perceive such a fallacy, nor could +it be employed but in jest.<a name="FNanchor_34_102" id="FNanchor_34_102"></a><a href="#Footnote_34_102" class="fnanchor">[34]</a></p> + +<p>"The present Fallacy is nearly allied to, or rather, perhaps, may be +regarded as a branch of, that founded on <i>etymology</i>; viz. when a term +is used, at one time in its customary, and at another in its +etymological sense. Perhaps no example of this can be found that is more +extensively and mischievously employed than in the case of the word +<i>representative</i>: assuming that its right meaning must correspond +exactly with the strict and original sense of the verb 'represent,' the +sophist persuades the multitude, that a member of the House of Commons +is bound to be guided in all points by the opinion of his constituents; +and, in short, to be merely their <i>spokesman</i>; whereas law and custom, +which in this case may be considered as fixing the meaning of the term, +require no such thing, but enjoin the representative to act according to +the best of his <i>own</i> judgment, and on his own responsibility."</p> + +<p>The following are instances of great practical importance, in which +arguments are habitually founded on a verbal ambiguity.</p> + +<p>The mercantile public are frequently led into this fallacy by the +phrase, "scarcity of money." In the language of commerce "money" has two +meanings: <i>currency</i>, or the circulating medium; and <i>capital seeking +investment</i>, especially investment on loan. In this last sense the word +is used when the "money market" is spoken of, and when the "value of +money" is said to be high or low, the rate of interest being <span class="pagenum"><a name="Page_387" id="Page_387">[Pg 387]</a></span>meant. The +consequence of this ambiguity is, that as soon as scarcity of money in +the latter of these senses begins to be felt,—as soon as there is +difficulty of obtaining loans, and the rate of interest is high,—it is +concluded that this must arise from causes acting upon the quantity of +money in the other and more popular sense; that the circulating medium +must have diminished in quantity, or ought to be increased. I am aware +that, independently of the double meaning of the term, there are in +facts themselves some peculiarities, giving an apparent support to this +error; but the ambiguity of the language stands on the very threshold of +the subject, and intercepts all attempts to throw light upon it.</p> + +<p>Another ambiguous expression which continually meets us in the political +controversies of the present time, especially in those which relate to +organic changes, is the phrase "influence of property:" which is +sometimes used for the influence of respect for superior intelligence, +or gratitude for the kind offices which persons of large property have +it so much in their power to bestow; at other times for the influence of +fear; fear of the worst sort of power, which large property also gives +to its possessor, the power of doing mischief to dependents. To confound +these two, is the standing fallacy of ambiguity brought against those +who seek to purify the electoral system from corruption and +intimidation. Persuasive influence, acting through the conscience of the +voter, and carrying his heart and mind with it, is beneficial—therefore +(it is pretended) coercive influence, which compels him to forget that +he is a moral agent, or to act in opposition to his moral convictions, +ought not to be placed under restraint.</p> + +<p>Another word which is often turned into an instrument of the fallacy of +ambiguity, is Theory. In its most proper acceptation, theory means the +completed result of philosophical induction from experience. In that +sense, there are erroneous as well as true theories, for induction may +be incorrectly performed, but theory of some sort is the necessary +result of knowing anything of a subject, and having put one's knowledge +into the form of general propositions for the guidance of practice. In +this, the proper sense of the word, Theory is the <span class="pagenum"><a name="Page_388" id="Page_388">[Pg 388]</a></span>explanation of +practice. In another and a more vulgar sense, theory means any mere +fiction of the imagination, endeavouring to conceive how a thing may +possibly have been produced, instead of examining how it was produced. +In this sense only are theory, and theorists, unsafe guides; but because +of this, ridicule or discredit is attempted to be attached to theory in +its proper sense, that is, to legitimate generalization, the end and aim +of all philosophy; and a conclusion is represented as worthless, just +because that has been done, which if done correctly, constitutes the +highest worth that a principle for the guidance of practice can possess, +namely, to comprehend in a few words the real law on which a phenomenon +depends, or some property or relation which is universally true of it.</p> + +<p>"The Church" is sometimes understood to mean the clergy alone, sometimes +the whole body of believers, or at least of communicants. The +declamations respecting the inviolability of church property are +indebted for the greater part of their apparent force to this ambiguity. +The clergy, being called the church, are supposed to be the real owners +of what is called church property; whereas they are in truth only the +managing members of a much larger body of proprietors, and enjoy on +their own part a mere usufruct, not extending beyond a life interest.</p> + +<p>The following is a Stoical argument taken from Cicero <i>De Finibus</i>, book +the third: "Quod est bonum, omne laudabile est. Quod autem laudabile +est, omne honestum est. Bonum igitur quod est, honestum est." Here the +ambiguous word is <i>laudabile</i>, which in the minor premise means anything +which mankind are accustomed, on good grounds, to admire or value; as +beauty, for instance, or good fortune: but in the major, it denotes +exclusively moral qualities. In much the same manner the Stoics +endeavoured logically to justify as philosophical truths, their +figurative and rhetorical expressions of ethical sentiment: as that the +virtuous man is alone free, alone beautiful, alone a king, &c. Whoever +has virtue has Good (because it has been previously determined not to +call anything else good); but, again, Good necessarily includes +<span class="pagenum"><a name="Page_389" id="Page_389">[Pg 389]</a></span>freedom, beauty, and even kingship, all these being good things; +therefore whoever has virtue has all these.</p> + +<p>The following is an argument of Descartes to prove, in his <i>à priori</i> +manner, the being of a God. The conception, says he, of an infinite +Being proves the real existence of such a being. For if there is not +really any such being, <i>I</i> must have made the conception; but if I could +make it, I can also unmake it; which evidently is not true; therefore +there must be, externally to myself, an archetype, from which the +conception was derived. In this argument (which, it may be observed, +would equally prove the real existence of ghosts and of witches) the +ambiguity is in the pronoun <i>I</i>, by which, in one place, is to be +understood my <i>will</i>, in another the <i>laws of my nature</i>. If the +conception, existing as it does in my mind, had no original without, the +conclusion would unquestionably follow that <i>I</i> made it; that is, the +laws of my nature must have somehow evolved it: but that my <i>will</i> made +it, would not follow. Now when Descartes afterwards adds that I cannot +unmake the conception, he means that I cannot get rid of it by an act of +my will: which is true, but is not the proposition required. I can as +much unmake this conception as I can any other: no conception which I +have once had, can I ever dismiss by mere volition: but what some of the +laws of my nature have produced, other laws, or those same laws in other +circumstances, may, and often do, subsequently efface.</p> + +<p>Analogous to this are some of the ambiguities in the free-will +controversy; which, as they will come under special consideration in the +concluding Book, I only mention <i>memoriæ causâ</i>. In that discussion, +too, the word <i>I</i> is often shifted from one meaning to another, at one +time standing for my volitions, at another time for the actions which +are the consequences of them, or the mental dispositions from which they +proceed. The latter ambiguity is exemplified in an argument of Coleridge +(in his <i>Aids to Reflection</i>), in support of the freedom of the will. It +is not true, he says, that a man is governed by motives; "the man makes +the motive, not the motive the <span class="pagenum"><a name="Page_390" id="Page_390">[Pg 390]</a></span>man;" the proof being that "what is a +strong motive to one man is no motive at all to another." The premise is +true, but only amounts to this, that different persons have different +degrees of susceptibility to the same motive; as they have also to the +same intoxicating liquid, which however does not prove that they are +free to be drunk or not drunk, whatever quantity of the fluid they may +drink. What is proved is, that certain mental conditions in the person +himself, must co-operate, in the production of the act, with the +external inducement: but those mental conditions also are the effect of +causes; and there is nothing in the argument to prove that they can +arise without a cause—that a spontaneous determination of the will, +without any cause at all, ever takes place, as the free-will doctrine +supposes.</p> + +<p>The double use, in the free-will controversy, of the word Necessity, +which sometimes stands only for Certainty, at other times for +Compulsion; sometimes for what <i>cannot</i> be prevented, at other times +only for what we have reason to be assured <i>will</i> not; we shall have +occasion hereafter to pursue to some of its ulterior consequences.</p> + +<p>A most important ambiguity, both in common and in metaphysical language, +is thus pointed out by Archbishop Whately in the Appendix to his Logic: +"<i>Same</i> (as well as <i>One</i>, <i>Identical</i>, and other words derived from +them,) is used frequently in a sense very different from its primary +one, as applicable to a <i>single</i> object; being employed to denote great +<i>similarity</i>. When several objects are undistinguishably alike, <i>one +single description</i> will apply equally to any of them; and thence they +are said to be all of <i>one and the same</i> nature, appearance, &c. As, +<i>e.g.</i> when we say 'this house is built of the <i>same</i> stone with such +another,' we only mean that the stones are undistinguishable in their +qualities; not that the one building was pulled down, and the other +constructed with the materials. Whereas <i>sameness</i>, in the primary +sense, does not even necessarily imply similarity; for if we say of any +man that he is greatly altered since such a time, we understand, and +indeed imply by the very expression, that he is <i>one person</i>, though +different in several qualities. It is worth <span class="pagenum"><a name="Page_391" id="Page_391">[Pg 391]</a></span>observing also, that Same, +in the secondary sense, admits, according to popular usage, of degrees: +we speak of two things being <i>nearly</i> the same, but not entirely: +personal identity does not admit of degrees. Nothing, perhaps, has +contributed more to the error of Realism than inattention to this +ambiguity. When several persons are said to have <i>one and the same</i> +opinion, thought, or idea, many men, overlooking the true simple +statement of the case, which is, that they are <i>all thinking alike</i>, +look for something more abstruse and mystical, and imagine there must be +some <i>One Thing</i>, in the primary sense, though not an individual, which +is present at once in the mind of each of these persons; and thence +readily sprung Plato's theory of Ideas, each of which was, according to +him, one real, eternal object, existing entire and complete in each of +the individual objects that are known by one name."</p> + +<p>It is, indeed, not a matter of inference but of authentic history, that +Plato's doctrine of Ideas, and the Aristotelian doctrine (in this +respect similar to the Platonic) of substantial forms and second +substances, grew up in the precise way here pointed out; from the +supposed necessity of finding, in things which were said to have the +<i>same</i> nature, or the <i>same</i> qualities, something which was the <i>same</i> +in the very sense in which a man is the same as himself. All the idle +speculations respecting <i>τὸ ὄν</i>, <i>τὸ ἕν</i>, <i>τὸ ὅμοίον</i>, and similar +abstractions, so common in the ancient and in some modern schools of +thought, sprang from the same source. The Aristotelian logicians saw, +however, one case of the ambiguity, and provided against it with their +peculiar felicity in the invention of technical language, when they +distinguished things which differed both <i>specie</i> and <i>numero</i>, from +those which differed <i>numero tantum</i>, that is, which were exactly alike +(in some particular respect at least) but were distinct individuals. An +extension of this distinction to the two meanings of the word Same, +namely, things which are the same <i>specie tantum</i>, and a thing which is +the same <i>numero</i> as well as <i>specie</i>, would have prevented the +confusion which has been a source of so much darkness and such an +abundance of positive error in metaphysical philosophy.</p> + +<p><span class="pagenum"><a name="Page_392" id="Page_392">[Pg 392]</a></span></p><p>One of the most singular examples of the length to which a thinker of +eminence may be led away by an ambiguity of language, is afforded by +this very case. I refer to the famous argument by which Bishop Berkeley +flattered himself that he had for ever put an end to "scepticism, +atheism, and irreligion." It is briefly as follows. I thought of a thing +yesterday; I ceased to think of it; I think of it again to-day. I had, +therefore, in my mind yesterday an <i>idea</i> of the object; I have also an +idea of it to-day; this idea is evidently not another, but the very same +idea. Yet an intervening time elapsed in which I had it not. Where was +the idea during this interval? It must have been somewhere; it did not +cease to exist; otherwise the idea I had yesterday could not be the +<i>same</i> idea; no more than the man I see alive to-day can be the same +whom I saw yesterday, if the man has died in the meanwhile. Now an idea +cannot be conceived to exist anywhere except in a mind; and hence there +must exist an Universal Mind, in which all ideas have their permanent +residence, during the intervals of their conscious presence in our own +minds.</p> + +<p>It is evident that Berkeley here confounded sameness <i>numero</i> with +sameness <i>specie</i>, that is, with exact resemblance, and assumed the +former where there was only the latter; not perceiving that when we say +we have the same thought to-day which we had yesterday, we do not mean +the same individual thought, but a thought exactly similar: as we say +that we have the same illness which we had last year, meaning only the +same sort of illness.</p> + +<p>In one remarkable instance the scientific world was divided into two +furiously hostile parties by an ambiguity of language affecting a branch +of science which, more completely than most others, enjoys the advantage +of a precise and well-defined terminology. I refer to the famous dispute +respecting the <i>vis viva</i>, the history of which is given at large in +Professor Playfair's Dissertation. The question was, whether the <i>force</i> +of a moving body was proportional (its mass being given) to its velocity +simply, or to the square of its velocity: and the ambiguity was in the +word Force. "One of the effects," says <span class="pagenum"><a name="Page_393" id="Page_393">[Pg 393]</a></span>Playfair, "produced by a moving +body is proportional to the square of the velocity, while another is +proportional to the velocity simply:" from whence clearer thinkers were +subsequently led to establish a double measure of the efficiency of a +moving power, one being called <i>vis viva</i>, and the other <i>momentum</i>. +About the facts, both parties were from the first agreed: the only +question was, with which of the two effects the term <i>force</i> should be, +or could most conveniently be, associated. But the disputants were by no +means aware that this was all; they thought that force was one thing, +the production of effects another; and the question, by which set of +effects the force which produced both the one and the other should be +measured, was supposed to be a question not of terminology but of fact.</p> + +<p>The ambiguity of the word Infinite is the real fallacy in the amusing +logical puzzle of Achilles and the Tortoise, a puzzle which has been too +hard for the ingenuity or patience of many philosophers, and which no +less a thinker than Sir William Hamilton considered as insoluble; as a +sound argument, though leading to a palpable falsehood. The fallacy, as +Hobbes hinted, lies in the tacit assumption that whatever is infinitely +divisible is infinite; but the following solution, (to the invention of +which I have no claim,) is more precise and satisfactory.</p> + +<p>The argument is, let Achilles run ten times as fast as the tortoise, yet +if the tortoise has the start, Achilles will never overtake him. For +suppose them to be at first separated by an interval of a thousand feet: +when Achilles has run these thousand feet, the tortoise will have got on +a hundred; when Achilles has run those hundred, the tortoise will have +run ten, and so on for ever: therefore Achilles may run for ever without +overtaking the tortoise.</p> + +<p>Now, the "for ever," in the conclusion, means, for any length of time +that can be supposed; but in the premises "ever" does not mean any +<i>length</i> of time: it means any <i>number of subdivisions</i> of time. It +means that we may divide a thousand feet by ten, and that quotient again +by ten, and so on as often as we please; that there never needs be an +end <span class="pagenum"><a name="Page_394" id="Page_394">[Pg 394]</a></span>to the subdivisions of the distance, nor consequently to those of +the time in which it is performed. But an unlimited number of +subdivisions may be made of that which is itself limited. The argument +proves no other infinity of duration than may be embraced within five +minutes. As long as the five minutes are not expired, what remains of +them may be divided by ten, and again by ten, as often as we like, which +is perfectly compatible with their being only five minutes altogether. +It proves, in short, that to pass through this finite space requires a +time which is infinitely divisible, but not an infinite time: the +confounding of which distinction Hobbes had already seen to be the gist +of the fallacy.</p> + +<p>The following ambiguities of the word <i>right</i> (in addition to the +obvious and familiar one of <i>a</i> right and the <i>adjective</i> right) are +extracted from a forgotten paper of my own, in a periodical:—</p> + +<p>"Speaking morally, you are said to have a right to do a thing, if all +persons are morally bound not to hinder you from doing it. But, in +another sense, to have a right to do a thing is the opposite of having +<i>no</i> right to do it, <i>i.e.</i> of being under a moral obligation to forbear +doing it. In this sense, to say that you have a right to do a thing, +means that you may do it without any breach of duty on your part; that +other persons not only ought not to hinder you, but have no cause to +think worse of you for doing it. This is a perfectly distinct +proposition from the preceding. The right which you have by virtue of a +duty incumbent upon other persons, is obviously quite a different thing +from a right consisting in the absence of any duty incumbent upon +yourself. Yet the two things are perpetually confounded. Thus a man will +say he has a right to publish his opinions; which may be true in this +sense, that it would be a breach of duty in any other person to +interfere and prevent the publication: but he assumes thereupon, that in +publishing his opinions, he himself violates no duty; which may either +be true or false, depending, as it does, on his having taken due pains +to satisfy himself, first, that the opinions are true, and next, that +their publication in this manner, and at <span class="pagenum"><a name="Page_395" id="Page_395">[Pg 395]</a></span>this particular juncture, will +probably be beneficial to the interests of truth on the whole.</p> + +<p>"The second ambiguity is that of confounding a right of any kind, with a +right to enforce that right by resisting or punishing a violation of it. +People will say, for example, that they have a right to good government, +which is undeniably true, it being the moral duty of their governors to +govern them well. But in granting this, you are supposed to have +admitted their right or liberty to turn out their governors, and perhaps +to punish them, for having failed in the performance of this duty; +which, far from being the same thing, is by no means universally true, +but depends on an immense number of varying circumstances," requiring to +be conscientiously weighed before adopting or acting on such a +resolution. This last example is (like others which have been cited) a +case of fallacy within fallacy; it involves not only the second of the +two ambiguities pointed out, but the first likewise.</p> + +<p>One not unusual form of the Fallacy of Ambiguous Terms, is known +technically as the Fallacy of Composition and Division: when the same +term is collective in the premises, distributive in the conclusion, or +<i>vice versâ</i>: or when the middle term is collective in one premise, +distributive in the other. As if one were to say (I quote from +Archbishop Whately) "All the angles of a triangle are equal to two right +angles: ABC is an angle of a triangle; therefore ABC is equal to two +right angles.... There is no fallacy more common, or more likely to +deceive, than the one now before us. The form in which it is most +usually employed is to establish some truth, separately, concerning +<i>each single</i> member of a certain class, and thence to infer the same of +the <i>whole collectively</i>." As in the argument one sometimes hears, to +prove that the world could do without great men. If Columbus (it is +said) had never lived, America would still have been discovered, at most +only a few years later; if Newton had never lived, some other person +would have discovered the law of gravitation; and so forth. Most true: +these things would have been <span class="pagenum"><a name="Page_396" id="Page_396">[Pg 396]</a></span>done, but in all probability not until +some one had again been found with the qualities of Columbus or Newton. +Because any one great man might have had his place supplied by other +great men, the argument concludes that all great men could have been +dispensed with. The term "great men" is distributive in the premises and +collective in the conclusion.</p> + +<p>"Such also is the fallacy which probably operates on most adventurers in +lotteries; <i>e.g.</i> 'the gaining of a high prize is no uncommon +occurrence; and what is no uncommon occurrence may reasonably be +expected; therefore the gaining of a high prize may reasonably be +expected:' the conclusion when applied to the individual (as in practice +it is) must be understood in the sense of 'reasonably expected <i>by a +certain individual</i>;' therefore for the major premise to be true, the +middle term must be understood to mean, 'no uncommon occurrence to some +one <i>particular</i> person;' whereas for the minor (which has been placed +first) to be true, you must understand it of 'no uncommon occurrence to +<i>some one or other</i>;' and thus you will have the Fallacy of Composition.</p> + +<p>"This is a Fallacy with which men are extremely apt to deceive +<i>themselves</i>; for when a multitude of particulars are presented to the +mind, many are too weak or too indolent to take a comprehensive view of +them, but confine their attention to each single point, by turns; and +then decide, infer, and act, accordingly: <i>e.g.</i> the imprudent +spendthrift, finding that he is able to afford this, <i>or</i> that, <i>or</i> the +other expense, forgets that <i>all of them together</i> will ruin him." The +debauchee destroys his health by successive acts of intemperance, +because no <i>one</i> of those acts would be of itself sufficient to do him +any serious harm. A sick person reasons with himself, "one, and another, +and another, of my symptoms, do not prove that I have a fatal disease;" +and practically concludes that all taken together do not prove it.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_VII_2">§ 2.</a> We have now sufficiently exemplified one of the principal Genera in +this Order of Fallacies; where, the source of error being the ambiguity +of terms, the premises are verbally <span class="pagenum"><a name="Page_397" id="Page_397">[Pg 397]</a></span>what is required to support the +conclusion, but not really so. In the second great Fallacy of Confusion +they are neither verbally nor really sufficient, though, from their +multiplicity and confused arrangement, and still oftener from defect of +memory, they are not seen to be what they are. The fallacy I mean is +that of Petitio Principii, or begging the question; including the more +complex and not uncommon variety of it, which is termed Reasoning in a +Circle.</p> + +<p><i>Petitio Principii</i>, as defined by Archbishop Whately, is the fallacy +"in which the premise either appears manifestly to be the same as the +conclusion, or is actually proved from the conclusion, or is such as +would naturally and properly so be proved." By the last clause I presume +is meant, that it is not susceptible of any other proof; for otherwise, +there would be no fallacy. To deduce from a proposition, propositions +from which it would itself more naturally be deduced, is often an +allowable deviation from the usual didactic order; or at most, what, by +an adaptation of a phrase familiar to mathematicians, may be called a +logical <i>inelegance</i>.<a name="FNanchor_35_103" id="FNanchor_35_103"></a><a href="#Footnote_35_103" class="fnanchor">[35]</a></p> + +<p>The employment of a proposition to prove that on which it is itself +dependent for proof, by no means implies the degree of mental imbecility +which might at first be supposed. The difficulty of comprehending how +this fallacy could possibly be committed, disappears when we reflect +that all persons, even the instructed, hold a great number of opinions +without exactly recollecting how they came by them. Believing that they +have at some former time verified them by sufficient evidence, but +having forgotten what the evidence was, they may easily be betrayed into +deducing from them the very propositions which are alone capable of +serving as premises for <span class="pagenum"><a name="Page_398" id="Page_398">[Pg 398]</a></span>their establishment. "As if," says Archbishop +Whately, "one should attempt to prove the being of a God from the +authority of Holy Writ;" which might easily happen to one with whom both +doctrines, as fundamental tenets of his religious creed, stand on the +same ground of familiar and traditional belief.</p> + +<p>Arguing in a circle, however, is a stronger case of the fallacy, and +implies more than the mere passive reception of a premise by one who +does not remember how it is to be proved. It implies an actual attempt +to prove two propositions reciprocally from one another; and is seldom +resorted to, at least in express terms, by any person in his own +speculations, but is committed by those who, being hard pressed by an +adversary, are forced into giving reasons for an opinion of which, when +they began to argue, they had not sufficiently considered the grounds. +As in the following example from Archbishop Whately: "Some mechanicians +attempt to prove (what they ought to lay down as a probable but doubtful +hypothesis<a name="FNanchor_36_104" id="FNanchor_36_104"></a><a href="#Footnote_36_104" class="fnanchor">[36]</a>) that every particle of matter gravitates equally: 'why?' +'because those bodies which contain more particles ever gravitate more +strongly, <i>i.e.</i> are heavier:' 'but, (it may be urged,) those which are +heaviest are not always more bulky;' 'no, but they contain more +particles, though more closely condensed:' 'how do you know that?' +'because they are heavier:' 'how does that prove it?' 'because all +particles of matter gravitating equally, that mass which is specifically +the heavier must needs have the more of them in the same space.'" It +appears to me that the fallacious reasoner, in his private thoughts, +would not be likely to proceed beyond the first step. He would acquiesce +in the sufficiency of the reason first given, "bodies which contain more +particles are heavier." It is when he finds this questioned, and is +called upon to <span class="pagenum"><a name="Page_399" id="Page_399">[Pg 399]</a></span>prove it, without knowing how, that he tries to +establish his premise by supposing proved what he is attempting to prove +by it. The most effectual way, in fact, of exposing a Petitio Principii, +when circumstances allow of it, is by challenging the reasoner to prove +his premises; which if he attempts to do, he is necessarily driven into +arguing in a circle.</p> + +<p>It is not uncommon, however, for thinkers, and those not of the lowest +description, to be led, even in their own thoughts, not indeed into +formally proving each of two propositions from the other, but into +admitting propositions which can only be so proved. In the preceding +example the two together form a complete and consistent, though +hypothetical, explanation of the facts concerned. And the tendency to +mistake mutual coherency for truth; to trust one's safety to a strong +chain though it has no point of support; is at the bottom of much which, +when reduced to the strict forms of argumentation, can exhibit itself no +otherwise than as reasoning in a circle. All experience bears testimony +to the enthralling effect of neat concatenation in a system of +doctrines, and the difficulty with which people admit the persuasion +that anything which holds so well together can possibly fall.</p> + +<p>Since every case where a conclusion which can only be proved from +certain premises is used for the proof of those premises, is a case of +<i>petitio principii</i>, that fallacy includes a very great proportion of +all incorrect reasoning. It is necessary, for completing our view of the +fallacy, to exemplify some of the disguises under which it is accustomed +to mask itself, and to escape exposure.</p> + +<p>A proposition would not be admitted by any person in his senses as a +corollary from itself, unless it were expressed in language which made +it seem different. One of the commonest modes of so expressing it, is to +present the proposition itself in abstract terms, as a proof of the same +proposition expressed in concrete language. This is a very frequent +mode, not only of pretended proof, but of pretended explanation; and is +parodied when Molière makes <span class="pagenum"><a name="Page_400" id="Page_400">[Pg 400]</a></span>one of his absurd physicians say, "l'opium +endormit parcequ'il a une vertu soporifique," or, in the equivalent +doggrel,</p> + +<p> +<span style="margin-left: 3.5em;">Mihi à docto doctore,</span><br /> +<span style="margin-left: 3.5em;">Domandatur causam et rationem quare</span><br /> +<span style="margin-left: 2.5em;">Opium facit dormire.</span><br /> +<span style="margin-left: 3.5em;">A quoi respondeo,</span><br /> +<span style="margin-left: 3.5em;">Quia est in eo</span><br /> +<span style="margin-left: 3.5em;">Virtus dormitiva,</span><br /> +<span style="margin-left: 2.5em;">Cujus est natura</span><br /> +<span style="margin-left: 3.5em;">Sensus assoupire.</span><br /> +</p> + +<p>The words Nature and Essence are grand instruments of this mode of +begging the question. As in the well-known argument of the scholastic +theologians, that the mind thinks always, because the <i>essence</i> of the +mind is to think. Locke had to point out, that if by essence is here +meant some property which must manifest itself by actual exercise at all +times, the premise is a direct assumption of the conclusion; while if it +only means that to think is the distinctive property of a mind, there is +no connexion between the premise and the conclusion, since it is not +necessary that a distinctive property should be perpetually in action.</p> + +<p>The following is one of the modes in which these abstract terms, Nature +and Essence, are used as instruments of this fallacy. Some particular +properties of a thing are selected, more or less arbitrarily, to be +termed its nature or essence; and when this has been done, these +properties are supposed to be invested with a kind of indefeasibleness; +to have become paramount to all the other properties of the thing, and +incapable of being prevailed over or counteracted by them. As when +Aristotle, in a passage already cited, "decides that there is no void on +such arguments as this: in a void there could be no difference of up and +down; for as in nothing there are no differences, so there are none in a +privation or negation; but a void is merely a privation or negation of +matter; therefore, in a void, bodies could not move up and down, which +it is in their <i>nature</i> to do."<a name="FNanchor_37_105" id="FNanchor_37_105"></a><a href="#Footnote_37_105" class="fnanchor">[37]</a> In other words; it is in the +<i>nature</i> of bodies to move up and down, <i>ergo</i> any <span class="pagenum"><a name="Page_401" id="Page_401">[Pg 401]</a></span>physical fact which +supposes them not so to move, cannot be authentic. This mode of +reasoning, by which a bad generalization is made to overrule all facts +which contradict it, is <i>petitio principii</i> in one of its most palpable +forms.</p> + +<p>None of the modes of assuming what should be proved are in more frequent +use than what are termed by Bentham "question-begging appellatives;" +names which beg the question under the disguise of stating it. The most +potent of these are such as have a laudatory or vituperative character. +For instance, in politics, the word Innovation. The dictionary meaning +of this term being merely "a change to something new," it is difficult +for the defenders even of the most salutary improvement to deny that it +is an innovation; yet the word having acquired in common usage a +vituperative connotation in addition to its dictionary meaning, the +admission is always construed as a large concession to the disadvantage +of the thing proposed.</p> + +<p>The following passage from the argument in refutation of the Epicureans, +in the second book of Cicero <i>de Finibus</i>, affords a fine example of +this sort of fallacy. "Et quidem illud ipsum non nimium probo (et tantum +patior) philosophum loqui de cupiditatibus finiendis. An potest +cupiditas finiri? tollenda est, atque extrahenda radicitus. Quis est +enim, in quo sit cupiditas, quin recte cupidus dici possit? Ergo et +avarus erit, sed finite: adulter, verum habebit modum: et luxuriosus +eodem modo. Qualis ista philosophia est, quæ non interitum afferat +pravitatis, sed sit contenta mediocritate vitiorum?" The question was, +whether certain desires, when kept within bounds, are vices or not; and +the argument decides the point by applying to them a word (<i>cupiditas</i>) +which <i>implies</i> vice. It is shown, however, in the remarks which follow, +that Cicero did not intend this as a serious argument, but as a +criticism on what he deemed an inappropriate expression. "Rem ipsam +prorsus probo: elegantiam desidero. Appellet hæc <i>desideria naturæ</i>; +cupiditatis nomen servet alio," &c. But many persons, both ancient and +modern, have employed this, or something equivalent to it, as a real and +conclusive argument. We may remark that the <span class="pagenum"><a name="Page_402" id="Page_402">[Pg 402]</a></span>passage respecting +<i>cupiditas</i> and <i>cupidus</i> is also an example of another fallacy already +noticed, that of Paronymous Terms.</p> + +<p>Many more of the arguments of the ancient moralists, and especially of +the Stoics, fall within the definition of Petitio Principii. In the <i>De +Finibus</i>, for example, which I continue to quote as being probably the +best extant exemplification at once of the doctrines and the methods of +the schools of philosophy existing at that time; of what value as +arguments are such pleas as those of Cato in the third book: That if +virtue were not happiness, it could not be a thing to <i>boast</i> of: That +if death or pain were evils, it would be impossible not to fear them, +and it could not, therefore, be laudable to despise them, &c. In one way +of viewing these arguments, they may be regarded as appeals to the +authority of the general sentiment of mankind, which had stamped its +approval upon certain actions and characters by the phrases referred to; +but that such could have been the meaning intended is very unlikely, +considering the contempt of the ancient philosophers for vulgar opinion. +In any other sense they are clear cases of Petitio Principii, since the +word laudable, and the idea of boasting, imply principles of conduct; +and practical maxims can only be proved from speculative truths, namely +from the properties of the subject matter, and cannot, therefore, be +employed to prove those properties. As well might it be argued that a +government is good because we ought to support it, or that there is a +God because it is our duty to pray to him.</p> + +<p>It is assumed by all the disputants in the <i>De Finibus</i> as the +foundation of the inquiry into the <i>summum bonum</i>, that "sapiens semper +beatus est." Not simply that wisdom gives the best chance of happiness, +or that wisdom consists in knowing what happiness is, and by what things +it is promoted; these propositions would not have been enough for +them:—but that the sage always is, and must of necessity be, happy. The +idea that wisdom could be consistent with unhappiness, was always +rejected as inadmissible: the reason assigned by one of the +interlocutors, near the beginning of the <span class="pagenum"><a name="Page_403" id="Page_403">[Pg 403]</a></span>third book, being, that if the +wise could be unhappy, there was little use in pursuing wisdom. But by +unhappiness they did not mean pain or suffering; to that, it was granted +that the wisest person was liable in common with others: he was happy, +because in possessing wisdom he had the most valuable of all +possessions, the most to be sought and prized of all things, and to +possess the most valuable thing was to be the most happy. By laying it +down, therefore, at the commencement of the inquiry, that the sage must +be happy, the disputed question respecting the <i>summum bonum</i> was in +fact begged; with the further assumption, that pain and suffering, so +far as they can coexist with wisdom, are not unhappiness, and are no +evil.</p> + +<p>The following are additional instances of Petitio Principii, under more +or less of disguise.</p> + +<p>Plato, in the <i>Sophistes</i>, attempts to prove that things may exist which +are incorporeal, by the argument that justice and wisdom are +incorporeal, and justice and wisdom must be something. Here, if by +<i>something</i> be meant, as Plato did in fact mean, a thing capable of +existing in and by itself, and not as a quality of some other thing, he +begs the question in asserting that justice and wisdom must be +something: if he means anything else, his conclusion is not proved. This +fallacy might also be classed under ambiguous middleterm: <i>something</i>, +in the one premise, meaning some substance, in the other merely some +object of thought, whether substance or attribute.</p> + +<p>It was formerly an argument employed in proof of what is now no longer a +popular doctrine, the infinite divisibility of matter, that every +portion of matter, however small, must at least have an upper and an +under surface. Those who used this argument did not see that it assumed +the very point in dispute, the impossibility of arriving at a minimum of +thickness; for if there be a minimum, its upper and under surface will +of course be one: it will be itself a surface, and no more. The argument +owes its very considerable plausibility to this, that the premise does +actually seem more obvious than the conclusion, though really identical +with it. As expressed in <span class="pagenum"><a name="Page_404" id="Page_404">[Pg 404]</a></span>the premise, the proposition appeals directly +and in concrete language to the incapacity of the human imagination for +conceiving a minimum. Viewed in this light, it becomes a case of the <i>à +priori</i> fallacy or natural prejudice, that whatever cannot be conceived +cannot exist. Every fallacy of Confusion (it is almost unnecessary to +repeat) will, if cleared up, become a fallacy of some other sort; and it +will be found of deductive or ratiocinative fallacies generally, that +when they mislead, there is mostly, as in this case, a fallacy of some +other description lurking under them, by virtue of which chiefly it is +that the verbal juggle, which is the outside or body of this kind of +fallacy, passes undetected.</p> + +<p>Euler's Algebra, a book otherwise of great merit, but full, to +overflowing, of logical errors in respect to the foundation of the +science, contains the following argument to prove that <i>minus</i> +multiplied by <i>minus</i> gives <i>plus</i>, a doctrine the opprobrium of all +mere mathematicians, and which Euler had not a glimpse of the true +method of proving. He says, <i>minus</i> multiplied by <i>minus</i> cannot give +<i>minus</i>; for <i>minus</i> multiplied by <i>plus</i> gives <i>minus</i>, and <i>minus</i> +multiplied by <i>minus</i> cannot give the same product as <i>minus</i> multiplied +by <i>plus</i>. Now one is obliged to ask, why minus multiplied by minus must +give any product at all? and if it does, why its product cannot be the +same as that of minus multiplied by plus? for this would seem, at the +first glance, not more absurd than that minus by minus should give the +same as plus by plus, the proposition which Euler prefers to it. The +premise requires proof, as much as the conclusion: nor can it be proved, +except by that more comprehensive view of the nature of multiplication, +and of algebraic processes in general, which would also supply a far +better proof of the mysterious doctrine which Euler is here endeavouring +to demonstrate.</p> + +<p>A striking instance of reasoning in a circle is that of some ethical +writers, who first take for their standard of moral truth what, being +the general, they deem to be the natural or instinctive sentiments and +perceptions of mankind, and then explain away the numerous instances of +divergence from their assumed standard, by representing them as cases in +which the <span class="pagenum"><a name="Page_405" id="Page_405">[Pg 405]</a></span>perceptions are unhealthy. Some particular mode of conduct or +feeling is affirmed to be <i>unnatural</i>; why? because it is abhorrent to +the universal and natural sentiments of mankind. Finding no such +sentiment in yourself, you question the fact; and the answer is (if your +antagonist is polite), that you are an exception, a peculiar case. But +neither (say you) do I find in the people of some other country, or of +some former age, any such feeling of abhorrence; "ay, but their feelings +were sophisticated and unhealthy."</p> + +<p>One of the most notable specimens of reasoning in a circle is the +doctrine of Hobbes, Rousseau, and others, which rests the obligations by +which human beings are bound as members of society, on a supposed social +compact. I wave the consideration of the fictitious nature of the +compact itself; but when Hobbes, through the whole Leviathan, +elaborately deduces the obligation of obeying the sovereign, not from +the necessity or utility of doing so, but from a promise supposed to +have been made by our ancestors, on renouncing savage life and agreeing +to establish political society, it is impossible not to retort by the +question, why are we bound to keep a promise made for us by others? or +why bound to keep a promise at all? No satisfactory ground can be +assigned for the obligation, except the mischievous consequences of the +absence of faith and mutual confidence among mankind. We are, therefore, +brought round to the interests of society, as the ultimate ground of the +obligation of a promise; and yet those interests are not admitted to be +a sufficient justification for the existence of government and law. +Without a promise it is thought that we should not be bound to that +which is implied in all modes of living in society, namely, to yield a +general obedience to the laws therein established; and so necessary is +the promise deemed, that if none has actually been made, some additional +safety is supposed to be given to the foundations of society by feigning +one.</p> + + +<p class="newsection"><a name="BOOK_V_CHAPTER_VII_3">§ 3.</a> Two principal subdivisions of the class of Fallacies of Confusion +having been disposed of; there remains a third, in which the confusion +is not, as in the Fallacy of Ambiguity, <span class="pagenum"><a name="Page_406" id="Page_406">[Pg 406]</a></span>in misconceiving the import of +the premises, nor, as in <i>Petitio Principii</i>, in forgetting what the +premises are, but in mistaking the conclusion which is to be proved. +This is the fallacy of <i>Ignoratio Elenchi</i>, in the widest sense of the +phrase; also called by Archbishop Whately the Fallacy of Irrelevant +Conclusion. His examples and remarks are highly worthy of citation.</p> + +<p>"Various kinds of propositions are, according to the occasion, +substituted for the one of which proof is required: sometimes the +particular for the universal; sometimes a proposition with different +terms; and various are the contrivances employed to effect and to +conceal this substitution, and to make the conclusion which the sophist +has drawn, answer practically the same purpose as the one he ought to +have established. We say, 'practically the same purpose,' because it +will very often happen that some <i>emotion</i> will be excited, some +sentiment impressed on the mind, (by a dexterous employment of this +fallacy), such as shall bring men into the <i>disposition</i> requisite for +your purpose; though they may not have assented to, or even stated +distinctly in their own minds, the <i>proposition</i> which it was your +business to establish. Thus if a sophist has to defend one who has been +guilty of some <i>serious</i> offence, which he wishes to extenuate, though +he is unable distinctly to prove that it is not such, yet if he can +succeed in <i>making the audience laugh</i> at some casual matter, he has +gained practically the same point. So also if any one has pointed out +the extenuating circumstances in some particular case of offence, so as +to show that it differs widely from the generality of the same class, +the sophist if he find himself unable to disprove these circumstances, +may do away the force of them, by simply <i>referring the action to that +very class</i>, which no one can deny that it belongs to, and the very name +of which will excite a feeling of disgust sufficient to counteract the +extenuation; <i>e.g.</i> let it be a case of peculation, and that many +<i>mitigating</i> circumstances have been brought forward which cannot be +denied; the sophistical opponent will reply, 'Well, but after all, the +man is a <i>rogue</i>, and there is an end of it;' now in reality this was +(by hypothesis) never the question; and the <span class="pagenum"><a name="Page_407" id="Page_407">[Pg 407]</a></span>mere assertion of what was +never denied, <i>ought</i> not, in fairness, to be regarded as decisive: but, +practically, the odiousness of the word, arising in great measure from +the association of those very circumstances which belong to most of the +class, but which we have supposed to be <i>absent</i> in <i>this particular</i> +instance, excites precisely that feeling of disgust, which in effect +destroys the force of the defence. In like manner we may refer to this +head all cases of improper appeal to the passions, and everything else +which is mentioned by Aristotle as extraneous to the matter in hand +(<i>ἔξω τοῦ πράγματος</i>)."</p> + +<p>Again, "instead of proving that 'this prisoner has committed an +atrocious fraud,' you prove that the fraud he is accused of is +atrocious: instead of proving (as in the well-known tale of Cyrus and +the two coats) that the taller boy had a right to force the other boy to +exchange coats with him, you prove that the exchange would have been +advantageous to both: instead of proving that the poor ought to be +relieved in this way rather than in that, you prove that the poor ought +to be relieved: instead of proving that the irrational agent—whether a +brute or a madman—can never be deterred from any act by apprehension of +punishment (as for instance a dog from sheep-biting, by fear of being +beaten), you prove that the beating of one dog does not operate as an +<i>example</i> to <i>other</i> dogs, &c.</p> + +<p>"It is evident that <i>ignoratio elenchi</i> may be employed as well for the +apparent refutation of your opponent's proposition, as for the apparent +establishment of your own; for it is substantially the same thing, to +prove what was not denied or to disprove what was not asserted. The +latter practice is not less common, and it is more offensive, because it +frequently amounts to a personal affront, in attributing to a person, +opinions, &c., which he perhaps holds in abhorrence. Thus, when in a +discussion one party vindicates, on the ground of general expediency, a +particular instance of resistance to government in a case of intolerable +oppression, the opponent may gravely maintain, 'that we ought not to do +evil that good may come;' a proposition which of course had never been +denied, the point in dispute being, 'whether <span class="pagenum"><a name="Page_408" id="Page_408">[Pg 408]</a></span>resistance in this +particular case <i>were</i> doing evil or not.' Or again, by way of +disproving the assertion of the right of private judgment in religion, +one may hear a grave argument to prove that 'it is impossible every one +can be <i>right in his judgment</i>.'"</p> + +<p>The works of controversial writers are seldom free from this fallacy. +The attempts, for instance, to disprove the population doctrines of +Malthus, have been mostly cases of <i>ignoratio elenchi</i>. Malthus has been +supposed to be refuted if it could be shown that in some countries or +ages population has been nearly stationary; as if he had asserted that +population always increases in a given ratio, or had not expressly +declared that it increases only in so far as it is not restrained by +prudence, or kept down by poverty and disease. Or, perhaps, a collection +of facts is produced to prove that in some one country the people are +better off with a dense population than they are in another country with +a thin one; or that the people have become more numerous and better off +at the same time. As if the assertion were that a dense population could +not possibly be well off: as if it were not part of the very doctrine, +and essential to it, that where there is a more abundant capital there +may be a greater population without any increase of poverty, or even +with a diminution of it.</p> + +<p>The favourite argument against Berkeley's theory of the non-existence of +matter, and the most popularly effective, next to a "grin"<a name="FNanchor_38_106" id="FNanchor_38_106"></a><a href="#Footnote_38_106" class="fnanchor">[38]</a>—an +argument, moreover, which is not confined to "coxcombs," nor to men like +Samuel Johnson, whose greatly overrated ability certainly did not lie in +the direction of metaphysical speculation, but is the stock argument of +the Scotch school of metaphysicians—is a palpable <i>ignoratio elenchi</i>. +The argument is perhaps as frequently expressed by gesture as by words, +and one of its commonest forms consists in knocking a stick against the +ground. This short and easy confutation overlooks the fact, that in +denying matter, Berkeley did not deny anything to which our senses <span class="pagenum"><a name="Page_409" id="Page_409">[Pg 409]</a></span>bear +witness, and therefore cannot be answered by any appeal to them. His +scepticism related to the supposed substratum, or hidden cause of the +appearances perceived by our senses: the evidence of which, whatever may +be thought of its conclusiveness, is certainly not the evidence of +sense. And it will always remain a signal proof of the want of +metaphysical profundity of Reid, Stewart, and, I am sorry to add, of +Brown, that they should have persisted in asserting that Berkeley, if he +believed his own doctrine, was bound to walk into the kennel, or run his +head against a post. As if persons who do not recognise an occult cause +of their sensations, could not possibly believe that a fixed order +subsists among the sensations themselves. Such a want of comprehension +of the distinction between a thing and its sensible manifestation, or, +in metaphysical language, between the noumenon and the phenomenon, would +be impossible to even the dullest disciple of Kant or Coleridge.</p> + +<p>It would be easy to add a greater number of examples of this fallacy, as +well as of the others which I have attempted to characterize. But a more +copious exemplification does not seem to be necessary; and the +intelligent reader will have little difficulty in adding to the +catalogue from his own reading and experience. We shall therefore here +close our exposition of the general principles of logic, and proceed to +the supplementary inquiry which is necessary to complete our design.</p> + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"><p><a name="Footnote_1_69" id="Footnote_1_69"></a><a href="#FNanchor_1_69"><span class="label">[1]</span></a> Supra, p. <a href="#Page_204">204</a>.</p></div> + +<div class="footnote"><p><a name="Footnote_2_70" id="Footnote_2_70"></a><a href="#FNanchor_2_70"><span class="label">[2]</span></a> <i>Vulgar Errors</i>, book v. chap. 21.</p></div> + +<div class="footnote"><p><a name="Footnote_3_71" id="Footnote_3_71"></a><a href="#FNanchor_3_71"><span class="label">[3]</span></a> <i>Pharmacologia</i>, Historical Introduction, p. 16.</p></div> + +<div class="footnote"><p><a name="Footnote_4_72" id="Footnote_4_72"></a><a href="#FNanchor_4_72"><span class="label">[4]</span></a> The author of one of the Bridgewater Treatises has fallen, +as it seems to me, into a similar fallacy when, after arguing in rather +a curious way to prove that matter may exist without any of the known +properties of matter, and may therefore be changeable, he concludes that +it cannot be eternal, because "eternal (passive) existence necessarily +involves incapability of change." I believe it would be difficult to +point out any other connexion between the facts of eternity and +unchangeableness, than a strong association between the two ideas. Most +of the <i>à priori</i> arguments, both religious and anti-religious, on the +origin of things, are fallacies drawn from the same source.</p></div> + +<div class="footnote"><p><a name="Footnote_5_73" id="Footnote_5_73"></a><a href="#FNanchor_5_73"><span class="label">[5]</span></a> Supra, <span title="See Vol. I.">book ii. chap. v. § 6</span>, and <span title="See Vol. I.">ch. vii. § 1, 2, 3</span>. See +also <i>Examination of Sir William Hamilton's Philosophy</i>, chap. vi. and +elsewhere.</p></div> + +<div class="footnote"><p><a name="Footnote_6_74" id="Footnote_6_74"></a><a href="#FNanchor_6_74"><span class="label">[6]</span></a> I quote this passage from Playfair's celebrated +<i>Dissertations on the Progress of Mathematical and Physical Science</i>.</p></div> + +<div class="footnote"><p><a name="Footnote_7_75" id="Footnote_7_75"></a><a href="#FNanchor_7_75"><span class="label">[7]</span></a> This statement I must now correct, as too unqualified. The +maxim in question was maintained with full conviction by no less an +authority than Sir William Hamilton. See my <i>Examination</i>, chap. xxiv.</p></div> + +<div class="footnote"><p><a name="Footnote_8_76" id="Footnote_8_76"></a><a href="#FNanchor_8_76"><span class="label">[8]</span></a> <i>Nouveaux Essais sur l'Entendement Humain—Avant-propos</i>. +(Œuvres, Paris ed. 1842, vol. i. p. 19.)</p></div> + +<div class="footnote"><p><a name="Footnote_9_77" id="Footnote_9_77"></a><a href="#FNanchor_9_77"><span class="label">[9]</span></a> This doctrine also was accepted as true, and conclusions +were grounded on it, by Sir William Hamilton. See <i>Examination</i>, chap. +xxiv.</p></div> + +<div class="footnote"><p><a name="Footnote_10_78" id="Footnote_10_78"></a><a href="#FNanchor_10_78"><span class="label">[10]</span></a> Not that of Leibnitz, but the principle commonly appealed +to under that name by mathematicians.</p></div> + +<div class="footnote"><p><a name="Footnote_11_79" id="Footnote_11_79"></a><a href="#FNanchor_11_79"><span class="label">[11]</span></a> <i>Dissertation</i>, ut supra, p. 27.</p></div> + +<div class="footnote"><p><a name="Footnote_12_80" id="Footnote_12_80"></a><a href="#FNanchor_12_80"><span class="label">[12]</span></a> <i>Hist. Ind. Sc.</i> Book i. chap. i.</p></div> + +<div class="footnote"><p><a name="Footnote_13_81" id="Footnote_13_81"></a><a href="#FNanchor_13_81"><span class="label">[13]</span></a> <i>Novum Organum</i>, Aph. 75.</p></div> + +<div class="footnote"><p><a name="Footnote_14_82" id="Footnote_14_82"></a><a href="#FNanchor_14_82"><span class="label">[14]</span></a> Supra, <span title="See Vol. I.">book iii. ch. vii. § 4</span>.</p></div> + +<div class="footnote"><p><a name="Footnote_15_83" id="Footnote_15_83"></a><a href="#FNanchor_15_83"><span class="label">[15]</span></a> It is hardly needful to remark that nothing is here +intended to be said against the possibility at some future period of +making gold; by first discovering it to be a compound, and putting +together its different elements or ingredients. But this is a totally +different idea from that of the seekers of the grand arcanum.</p></div> + +<div class="footnote"><p><a name="Footnote_16_84" id="Footnote_16_84"></a><a href="#FNanchor_16_84"><span class="label">[16]</span></a> <i>Pharmacologia</i>, pp. 43-5.</p></div> + +<div class="footnote"><p><a name="Footnote_17_85" id="Footnote_17_85"></a><a href="#FNanchor_17_85"><span class="label">[17]</span></a> Vol. i. chap. 8.</p></div> + +<div class="footnote"><p><a name="Footnote_18_86" id="Footnote_18_86"></a><a href="#FNanchor_18_86"><span class="label">[18]</span></a> <i>Nov. Org.</i>, Aph. 46.</p></div> + +<div class="footnote"><p><a name="Footnote_19_87" id="Footnote_19_87"></a><a href="#FNanchor_19_87"><span class="label">[19]</span></a> Playfair's <i>Dissertation</i>, sect. 4.</p></div> + +<div class="footnote"><p><a name="Footnote_20_88" id="Footnote_20_88"></a><a href="#FNanchor_20_88"><span class="label">[20]</span></a> <i>Nov. Org. Renov.</i>, p. 61.</p></div> + +<div class="footnote"><p><a name="Footnote_21_89" id="Footnote_21_89"></a><a href="#FNanchor_21_89"><span class="label">[21]</span></a> <i>Pharmacologia</i>, p. 21.</p></div> + +<div class="footnote"><p><a name="Footnote_22_90" id="Footnote_22_90"></a><a href="#FNanchor_22_90"><span class="label">[22]</span></a> <i>Pharmacologia</i>, pp. 23-4.</p></div> + +<div class="footnote"><p><a name="Footnote_23_91" id="Footnote_23_91"></a><a href="#FNanchor_23_91"><span class="label">[23]</span></a> Ibid. p. 28.</p></div> + +<div class="footnote"><p><a name="Footnote_24_92" id="Footnote_24_92"></a><a href="#FNanchor_24_92"><span class="label">[24]</span></a> Ibid. p. 62.</p></div> + +<div class="footnote"><p><a name="Footnote_25_93" id="Footnote_25_93"></a><a href="#FNanchor_25_93"><span class="label">[25]</span></a> <i>Pharmacologia</i>, pp. 61-2.</p></div> + +<div class="footnote"><p><a name="Footnote_26_94" id="Footnote_26_94"></a><a href="#FNanchor_26_94"><span class="label">[26]</span></a> Supra, p. <a href="#Page_182">182</a>.</p></div> + +<div class="footnote"><p><a name="Footnote_27_95" id="Footnote_27_95"></a><a href="#FNanchor_27_95"><span class="label">[27]</span></a> <i>Elements of the Philosophy of the Mind</i>, vol. ii. ch. 4, +sect. 5.</p></div> + +<div class="footnote"><p><a name="Footnote_28_96" id="Footnote_28_96"></a><a href="#FNanchor_28_96"><span class="label">[28]</span></a> "Thus Fourcroy," says Dr. Paris, "explained the operation +of mercury by its specific gravity, and the advocates of this doctrine +favoured the general introduction of the preparations of iron, +especially in scirrhus of the spleen or liver, upon the same +hypothetical principle; for, say they, whatever is most forcible in +removing the obstruction must be the most proper instrument of cure; +such is steel, which, besides the attenuating power with which it is +furnished, has still a greater force in this case from the gravity of +its particles, which, being seven times specifically heavier than any +vegetable, acts in proportion with a stronger impulse, and therefore is +a more powerful deobstruent. This may be taken as a specimen of the +style in which these mechanical physicians reasoned and +practised."—<i>Pharmacologia</i>, pp. 38-9.</p></div> + +<div class="footnote"><p><a name="Footnote_29_97" id="Footnote_29_97"></a><a href="#FNanchor_29_97"><span class="label">[29]</span></a> <i>Pharmacologia</i>, pp. 39, 40.</p></div> + +<div class="footnote"><p><a name="Footnote_30_98" id="Footnote_30_98"></a><a href="#FNanchor_30_98"><span class="label">[30]</span></a> I quote from Dr. Whewell's <i>Hist. Ind. Sc.</i> 3rd ed. i. +129.</p></div> + +<div class="footnote"><p><a name="Footnote_31_99" id="Footnote_31_99"></a><a href="#FNanchor_31_99"><span class="label">[31]</span></a> <i>Hist. Ind. Sc.</i> i. 52.</p></div> + +<div class="footnote"><p><a name="Footnote_32_100" id="Footnote_32_100"></a><a href="#FNanchor_32_100"><span class="label">[32]</span></a> <i>Nov. Org.</i> Aph. 60.</p></div> + +<div class="footnote"><p><a name="Footnote_33_101" id="Footnote_33_101"></a><a href="#FNanchor_33_101"><span class="label">[33]</span></a> "An advocate," says Mr. De Morgan (<i>Formal Logic</i>, p. +270), "is sometimes guilty of the argument <i>à dicto secundum quid ad +dictum simpliciter</i>: it is his business to do for his client all that +his client might <i>honestly</i> do for himself. Is not the word in italics +frequently omitted? <i>Might</i> any man honestly try to do for himself all +that counsel frequently try to do for him? We are often reminded of the +two men who stole the leg of mutton; one could swear he had not got it, +the other that he had not taken it. The counsel is doing his duty by his +client, the client has left the matter to his counsel. Between the +unexecuted intention of the client, and the unintended execution of the +counsel, there may be a wrong done, and, if we are to believe the usual +maxims, no wrong-doer." +</p><p> +The same writer justly remarks (p. 251) that there is a converse +fallacy, <i>à dicto simpliciter ad dictum secundum quid</i>, called by the +scholastic logicians, <i>fallacia accidentis</i>; and another which may be +called <i>à dicto secundum quid ad dictum secundum alterum quid</i> (p. 265). +For apt instances of both, I must refer the reader to Mr. De Morgan's +able chapter on Fallacies.</p></div> + +<div class="footnote"><p><a name="Footnote_34_102" id="Footnote_34_102"></a><a href="#FNanchor_34_102"><span class="label">[34]</span></a> An example of this fallacy is the popular error that +<i>strong</i> drink must be a cause of <i>strength</i>. There is here fallacy +within fallacy; for granting that the words "strong" and "strength" were +not (as they are) applied in a totally different sense to fermented +liquors and to the human body, there would still be involved the error +of supposing that an effect must be like its cause; that the conditions +of a phenomenon are likely to resemble the phenomenon itself; which we +have already treated of as an <i>à priori</i> fallacy of the first rank. As +well might it be supposed that a strong poison will make the person who +takes it, strong.</p></div> + +<div class="footnote"><p><a name="Footnote_35_103" id="Footnote_35_103"></a><a href="#FNanchor_35_103"><span class="label">[35]</span></a> In his later editions, Archbishop Whately confines the +name of Petitio Principii "to those cases in which one of the premises +either is manifestly the same in sense with the conclusion, or is +actually proved from it, or is such as the persons you are addressing +are not likely to know, or to admit, except as an inference from the +conclusion: as, <i>e.g.</i> if any one should infer the authenticity of a +certain history, from its recording such and such facts, the reality of +which rests on the evidence of that history."</p></div> + +<div class="footnote"><p><a name="Footnote_36_104" id="Footnote_36_104"></a><a href="#FNanchor_36_104"><span class="label">[36]</span></a> No longer even a probable hypothesis, since the +establishment of the atomic theory; it being now certain that the +integral particles of different substances gravitate unequally. It is +true that these particles, though real <i>minima</i> for the purposes of +chemical combination, may not be the ultimate particles of the +substance; and this doubt alone renders the hypothesis admissible, even +as an hypothesis.</p></div> + +<div class="footnote"><p><a name="Footnote_37_105" id="Footnote_37_105"></a><a href="#FNanchor_37_105"><span class="label">[37]</span></a> <i>Hist. Ind. Sc.</i> i. 34.</p></div> + +<div class="footnote"><p><a name="Footnote_38_106" id="Footnote_38_106"></a><a href="#FNanchor_38_106"><span class="label">[38]</span></a> "And coxcombs vanquish Berkeley with a grin."</p></div> +</div> + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_411" id="Page_411">[Pg 411]</a></span></p> +<h3><a name="BOOK_VI" id="BOOK_VI"></a>BOOK VI.<br /> +ON THE LOGIC OF THE MORAL SCIENCES.</h3> + + +<blockquote><p><span class="pagenum"><a name="Page_412" id="Page_412">[Pg 412]</a></span></p><p>"Si l'homme peut prédire, avec une assurance presque entière, les +phénomènes dont il connaît les lois; si lors même qu'elles lui sont +inconnues, il peut, d'après l'expérience, prévoir avec une grande +probabilité les événemens de l'avenir; pourquoi regarderait-on comme une +entreprise chimérique, celle de tracer avec quelque vraisemblance le +tableau des destinées futures de l'espèce humaine, d'après les résultats +de son histoire? Le seul fondement de croyance dans les sciences +naturelles, est cette idée, que les lois générales, connues ou ignorées, +qui règlent les phénomènes de l'univers, sont nécessaires et constantes; +et par quelle raison ce principe serait-il moins vrai pour le +développement des facultés intellectuelles et morales de l'homme, que +pour les autres opérations de la nature? Enfin, puisque des opinions +formées d'après l'expérience ... sont la seule règle de la conduite des +hommes les plus sages, pourquoi interdirait-on au philosophe d'appuyer +ses conjectures sur cette même base, pourvu qu'il ne leur attribue pas +une certitude supérieure à celle qui peut naître du nombre, de la +constance, de l'exactitude des observations?"—<span class="smcap">Condorcet</span>, <i>Esquisse d'un +Tableau Historique des Progrès de l'Esprit Humain</i>.</p></blockquote> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_413" id="Page_413">[Pg 413]</a></span></p> +<h3><a name="BOOK_VI_CHAPTER_I" id="BOOK_VI_CHAPTER_I"></a>CHAPTER I.<br /> +INTRODUCTORY REMARKS.</h3> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_I_1">§ 1.</a> Principles of Evidence and Theories of Method are not to be +constructed <i>à priori</i>. The laws of our rational faculty, like those of +every other natural agency, are only learnt by seeing the agent at work. +The earlier achievements of science were made without the conscious +observance of any Scientific Method; and we should never have known by +what process truth is to be ascertained, if we had not previously +ascertained many truths. But it was only the easier problems which could +be thus resolved: natural sagacity, when it tried its strength against +the more difficult ones, either failed altogether, or if it succeeded +here and there in obtaining a solution, had no sure means of convincing +others that its solution was correct. In scientific investigation, as in +all other works of human skill, the way of obtaining the end is seen as +it were instinctively by superior minds in some comparatively simple +case, and is then, by judicious generalization, adapted to the variety +of complex cases. We learn to do a thing in difficult circumstances, by +attending to the manner in which we have spontaneously done the same +thing in easier ones.</p> + +<p>This truth is exemplified by the history of the various branches of +knowledge which have successively, in the ascending order of their +complication, assumed the character of sciences; and will doubtless +receive fresh confirmation from those, of which the final scientific +constitution is yet to come, and which are still abandoned to the +uncertainties of vague and popular discussion. Although several other +sciences have emerged from this state at a comparatively recent date, +none now remain in it except those which relate to man himself, <span class="pagenum"><a name="Page_414" id="Page_414">[Pg 414]</a></span>the +most complex and most difficult subject of study on which the human mind +can be engaged.</p> + +<p>Concerning the physical nature of man, as an organized being,—though +there is still much uncertainty and much controversy, which can only be +terminated by the general acknowledgment and employment of stricter +rules of induction than are commonly recognised,—there is, however, a +considerable body of truths which all who have attended to the subject +consider to be fully established; nor is there now any radical +imperfection in the method observed in this department of science by its +most distinguished modern teachers. But the laws of Mind, and, in even a +greater degree, those of Society, are so far from having attained a +similar state of even partial recognition, that it is still a +controversy whether they are capable of becoming subjects of science in +the strict sense of the term: and among those who are agreed on this +point, there reigns the most irreconcileable diversity on almost every +other. Here, therefore, if anywhere, the principles laid down in the +preceding Books may be expected to be useful.</p> + +<p>If, on matters so much the most important with which human intellect can +occupy itself, a more general agreement is ever to exist among thinkers; +if what has been pronounced "the proper study of mankind" is not +destined to remain the only subject which Philosophy cannot succeed in +rescuing from Empiricism; the same process through which the laws of +many simpler phenomena have by general acknowledgment been placed beyond +dispute, must be consciously and deliberately applied to those more +difficult inquiries. If there are some subjects on which the results +obtained have finally received the unanimous assent of all who have +attended to the proof, and others on which mankind have not yet been +equally successful; on which the most sagacious minds have occupied +themselves from the earliest date, and have never succeeded in +establishing any considerable body of truths, so as to be beyond denial +or doubt; it is by generalizing the methods successfully followed in the +former inquiries, and adapting them to the latter, that we may hope to +remove this blot on the face of <span class="pagenum"><a name="Page_415" id="Page_415">[Pg 415]</a></span>science. The remaining chapters are an +endeavour to facilitate this most desirable object.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_I_2">§ 2.</a> In attempting this, I am not unmindful how little can be done +towards it in a mere treatise on Logic, or how vague and unsatisfactory +all precepts of Method must necessarily appear, when not practically +exemplified in the establishment of a body of doctrine. Doubtless, the +most effectual mode of showing how the sciences of Ethics and Politics +may be constructed, would be to construct them: a task which, it needs +scarcely be said, I am not about to undertake. But even if there were no +other examples, the memorable one of Bacon would be sufficient to +demonstrate, that it is sometimes both possible and useful to point out +the way, though without being oneself prepared to adventure far into it. +And if more were to be attempted, this at least is not a proper place +for the attempt.</p> + +<p>In substance, whatever can be done in a work like this for the Logic of +the Moral Sciences, has been or ought to have been accomplished in the +five preceding Books; to which the present can be only a kind of +supplement or appendix, since the methods of investigation applicable to +moral and social science must have been already described, if I have +succeeded in enumerating and characterizing those of science in general. +It remains, however, to examine which of those methods are more +especially suited to the various branches of moral inquiry; under what +peculiar facilities or difficulties they are there employed; how far the +unsatisfactory state of those inquiries is owing to a wrong choice of +methods, how far to want of skill in the application of right ones; and +what degree of ultimate success may be attained or hoped for, by a +better choice or more careful employment of logical processes +appropriate to the case. In other words, whether moral sciences exist, +or can exist; to what degree of perfection they are susceptible of being +carried; and by what selection or adaptation of the methods brought to +view in the previous part of this work, that degree of perfection is +attainable.</p> + +<p><span class="pagenum"><a name="Page_416" id="Page_416">[Pg 416]</a></span></p><p>At the threshold of this inquiry we are met by an objection, which, if +not removed, would be fatal to the attempt to treat human conduct as a +subject of science. Are the actions of human beings, like all other +natural events, subject to invariable laws? Does that constancy of +causation, which is the foundation of every scientific theory of +successive phenomena, really obtain among them? This is often denied; +and for the sake of systematic completeness, if not from any very urgent +practical necessity, the question should receive a deliberate answer in +this place. We shall devote to the subject a chapter apart.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_417" id="Page_417">[Pg 417]</a></span></p> +<h3><a name="BOOK_VI_CHAPTER_II" id="BOOK_VI_CHAPTER_II"></a>CHAPTER II.<br /> +OF LIBERTY AND NECESSITY.</h3> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_II_1">§ 1.</a> The question, whether the law of causality applies in the same +strict sense to human actions as to other phenomena, is the celebrated +controversy concerning the freedom of the will: which, from at least as +far back as the time of Pelagius, has divided both the philosophical and +the religious world. The affirmative opinion is commonly called the +doctrine of Necessity, as asserting human volitions and actions to be +necessary and inevitable. The negative maintains that the will is not +determined, like other phenomena, by antecedents, but determines itself; +that our volitions are not, properly speaking, the effects of causes, or +at least have no causes which they uniformly and implicitly obey.</p> + +<p>I have already made it sufficiently apparent that the former of these +opinions is that which I consider the true one; but the misleading terms +in which it is often expressed, and the indistinct manner in which it is +usually apprehended, have both obstructed its reception, and perverted +its influence when received. The metaphysical theory of free will, as +held by philosophers, (for the practical feeling of it, common in a +greater or less degree to all mankind, is in no way inconsistent with +the contrary theory,) was invented because the supposed alternative of +admitting human actions to be <i>necessary</i>, was deemed inconsistent with +every one's instinctive consciousness, as well as humiliating to the +pride and even degrading to the moral nature of man. Nor do I deny that +the doctrine, as sometimes held, is open to these imputations; for the +misapprehension in which I shall be able to show that they originate, +unfortunately is not confined to the opponents of the doctrine, but +participated in by many, perhaps we might say by most, of its +supporters.</p> + + +<p><span class="pagenum"><a name="Page_418" id="Page_418">[Pg 418]</a></span></p><p class="newsection"><a name="BOOK_VI_CHAPTER_II_2">§ 2.</a> Correctly conceived, the doctrine called Philosophical Necessity +is simply this: that, given the motives which are present to an +individual's mind, and given likewise the character and disposition of +the individual, the manner in which he will act might be unerringly +inferred: that if we knew the person thoroughly, and knew all the +inducements which are acting upon him, we could foretell his conduct +with as much certainty as we can predict any physical event. This +proposition I take to be a mere interpretation of universal experience, +a statement in words of what every one is internally convinced of. No +one who believed that he knew thoroughly the circumstances of any case, +and the characters of the different persons concerned, would hesitate to +foretell how all of them would act. Whatever degree of doubt he may in +fact feel, arises from the uncertainty whether he really knows the +circumstances, or the character of some one or other of the persons, +with the degree of accuracy required: but by no means from thinking that +if he did know these things, there could be any uncertainty what the +conduct would be. Nor does this full assurance conflict in the smallest +degree with what is called our feeling of freedom. We do not feel +ourselves the less free, because those to whom we are intimately known +are well assured how we shall will to act in a particular case. We +often, on the contrary, regard the doubt what our conduct will be, as a +mark of ignorance of our character, and sometimes even resent it as an +imputation. The religious metaphysicians who have asserted the freedom +of the will, have always maintained it to be consistent with divine +foreknowledge of our actions: and if with divine, then with any other +foreknowledge. We may be free, and yet another may have reason to be +perfectly certain what use we shall make of our freedom. It is not, +therefore, the doctrine that our volitions and actions are invariable +consequents of our antecedent states of mind, that is either +contradicted by our consciousness, or felt to be degrading.</p> + +<p>But the doctrine of causation, when considered as obtaining between our +volitions and their antecedents, is almost universally conceived as +involving more than this. Many do not <span class="pagenum"><a name="Page_419" id="Page_419">[Pg 419]</a></span>believe, and very few practically +feel, that there is nothing in causation but invariable, certain, and +unconditional sequence. There are few to whom mere constancy of +succession appears a sufficiently stringent bond of union for so +peculiar a relation as that of cause and effect. Even if the reason +repudiates, the imagination retains, the feeling of some more intimate +connexion, of some peculiar tie, or mysterious constraint exercised by +the antecedent over the consequent. Now this it is which, considered as +applying to the human will, conflicts with our consciousness, and +revolts our feelings. We are certain that, in the case of our volitions, +there is not this mysterious constraint. We know that we are not +compelled, as by a magical spell, to obey any particular motive. We +feel, that if we wished to prove that we have the power of resisting the +motive, we could do so, (that wish being, it needs scarcely be observed, +a <i>new antecedent</i>;) and it would be humiliating to our pride, and (what +is of more importance) paralysing to our desire of excellence if we +thought otherwise. But neither is any such mysterious compulsion now +supposed, by the best philosophical authorities, to be exercised by any +other cause over its effect. Those who think that causes draw their +effects after them by a mystical tie, are right in believing that the +relation between volitions and their antecedents is of another nature. +But they should go farther, and admit that this is also true of all +other effects and their antecedents. If such a tie is considered to be +involved in the word necessity, the doctrine is not true of human +actions; but neither is it then true of inanimate objects. It would be +more correct to say that matter is not bound by necessity than that mind +is so.</p> + +<p>That the free-will metaphysicians, being mostly of the school which +rejects Hume's and Brown's analysis of Cause and Effect, should miss +their way for want of the light which that analysis affords, cannot +surprise us. The wonder is, that the necessarians, who usually admit +that philosophical theory, should in practice equally lose sight of it. +The very same misconception of the doctrine called Philosophical +Necessity, which prevents the opposite party from recognising its truth, +I believe to exist more or less obscurely in the minds of most +<span class="pagenum"><a name="Page_420" id="Page_420">[Pg 420]</a></span>necessarians, however they may in words disavow it. I am much mistaken +if they habitually feel that the necessity which they recognise in +actions is but uniformity of order, and capability of being predicted. +They have a feeling as if there were at bottom a stronger tie between +the volitions and their causes: as if, when they asserted that the will +is governed by the balance of motives, they meant something more cogent +than if they had only said, that whoever knew the motives, and our +habitual susceptibilities to them, could predict how we should will to +act. They commit, in opposition to their own scientific system, the very +same mistake which their adversaries commit in obedience to theirs; and +in consequence do really in some instances suffer those depressing +consequences, which their opponents erroneously impute to the doctrine +itself.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_II_3">§ 3.</a> I am inclined to think that this error is almost wholly an effect +of the associations with a word; and that it would be prevented, by +forbearing to employ, for the expression of the simple fact of +causation, so extremely inappropriate a term as Necessity. That word, in +its other acceptations, involves much more than mere uniformity of +sequence: it implies irresistibleness. Applied to the will, it only +means that the given cause will be followed by the effect, subject to +all possibilities of counteraction by other causes: but in common use it +stands for the operation of those causes exclusively, which are supposed +too powerful to be counteracted at all. When we say that all human +actions take place of necessity, we only mean that they will certainly +happen if nothing prevents:—when we say that dying of want, to those +who cannot get food, is a necessity, we mean that it will certainly +happen whatever may be done to prevent it. The application of the same +term to the agencies on which human actions depend, as is used to +express those agencies of nature which are really uncontrollable, cannot +fail, when habitual, to create a feeling of uncontrollableness in the +former also. This however is a mere illusion. There are physical +sequences which we call necessary, as death for want of food or air; +there are others which, though as much cases of causation as the +<span class="pagenum"><a name="Page_421" id="Page_421">[Pg 421]</a></span>former, are not said to be necessary, as death from poison, which an +antidote, or the use of the stomach-pump, will sometimes avert. It is +apt to be forgotten by people's feelings, even if remembered by their +understandings, that human actions are in this last predicament: they +are never (except in some cases of mania) ruled by any one motive with +such absolute sway, that there is no room for the influence of any +other. The causes, therefore, on which action depends, are never +uncontrollable; and any given effect is only necessary provided that the +causes tending to produce it are not controlled. That whatever happens, +could not have happened otherwise unless something had taken place which +was capable of preventing it, no one surely needs hesitate to admit. But +to call this by the name necessity is to use the term in a sense so +different from its primitive and familiar meaning, from that which it +bears in the common occasions of life, as to amount almost to a play +upon words. The associations derived from the ordinary sense of the term +will adhere to it in spite of all we can do: and though the doctrine of +Necessity, as stated by most who hold it, is very remote from fatalism, +it is probable that most necessarians are fatalists, more or less, in +their feelings.</p> + +<p>A fatalist believes, or half believes (for nobody is a consistent +fatalist), not only that whatever is about to happen, will be the +infallible result of the causes which produce it, (which is the true +necessarian doctrine,) but moreover that there is no use in struggling +against it; that it will happen however we may strive to prevent it. +Now, a necessarian, believing that our actions follow from our +characters, and that our characters follow from our organization, our +education, and our circumstances, is apt to be, with more or less of +consciousness on his part, a fatalist as to his own actions, and to +believe that his nature is such, or that his education and circumstances +have so moulded his character, that nothing can now prevent him from +feeling and acting in a particular way, or at least that no effort of +his own can hinder it. In the words of the sect which in our own day has +most perseveringly inculcated and most perversely misunderstood this +great doctrine, his character <span class="pagenum"><a name="Page_422" id="Page_422">[Pg 422]</a></span>is formed <i>for</i> him, and not <i>by</i> him; +therefore his wishing that it had been formed differently is of no use; +he has no power to alter it. But this is a grand error. He has, to a +certain extent, a power to alter his character. Its being, in the +ultimate resort, formed for him, is not inconsistent with its being, in +part, formed <i>by</i> him as one of the intermediate agents. His character +is formed by his circumstances (including among these his particular +organization); but his own desire to mould it in a particular way, is +one of those circumstances, and by no means one of the least +influential. We cannot, indeed, directly will to be different from what +we are. But neither did those who are supposed to have formed our +characters, directly will that we should be what we are. Their will had +no direct power except over their own actions. They made us what they +did make us, by willing, not the end, but the requisite means; and we, +when our habits are not too inveterate, can, by similarly willing the +requisite means, make ourselves different. If they could place us under +the influence of certain circumstances, we, in like manner, can place +ourselves under the influence of other circumstances. We are exactly as +capable of making our own character, <i>if we will</i>, as others are of +making it for us.</p> + +<p>Yes (answers the Owenite), but these words, "if we will," surrender the +whole point: since the will to alter our own character is given us, not +by any efforts of ours, but by circumstances which we cannot help; it +comes to us either from external causes, or not at all. Most true: if +the Owenite stops here, he is in a position from which nothing can expel +him. Our character is formed by us as well as for us; but the wish which +induces us to attempt to form it is formed for us; and how? Not, in +general, by our organization, nor wholly by our education, but by our +experience; experience of the painful consequences of the character we +previously had: or by some strong feeling of admiration or aspiration, +accidentally aroused. But to think that we have no power of altering our +character, and to think that we shall not use our power unless we desire +to use it, are very different things, and have a very different effect +on the mind. A person who does <span class="pagenum"><a name="Page_423" id="Page_423">[Pg 423]</a></span>not wish to alter his character, cannot +be the person who is supposed to feel discouraged or paralysed by +thinking himself unable to do it. The depressing effect of the fatalist +doctrine can only be felt where there <i>is</i> a wish to do what that +doctrine represents as impossible. It is of no consequence what we think +forms our character, when we have no desire of our own about forming it; +but it is of great consequence that we should not be prevented from +forming such a desire by thinking the attainment impracticable, and that +if we have the desire, we should know that the work is not so +irrevocably done as to be incapable of being altered.</p> + +<p>And indeed, if we examine closely, we shall find that this feeling, of +our being able to modify our own character <i>if we wish</i>, is itself the +feeling of moral freedom which we are conscious of. A person feels +morally free who feels that his habits or his temptations are not his +masters, but he theirs: who even in yielding to them knows that he could +resist; that were he desirous of altogether throwing them off, there +would not be required for that purpose a stronger desire than he knows +himself to be capable of feeling. It is of course necessary, to render +our consciousness of freedom complete, that we should have succeeded in +making our character all we have hitherto attempted to make it; for if +we have wished and not attained, we have, to that extent, not power over +our own character, we are not free. Or at least, we must feel that our +wish, if not strong enough to alter our character, is strong enough to +conquer our character when the two are brought into conflict in any +particular case of conduct. And hence it is said with truth, that none +but a person of confirmed virtue is completely free.</p> + +<p>The application of so improper a term as Necessity to the doctrine of +cause and effect in the matter of human character, seems to me one of +the most signal instances in philosophy of the abuse of terms, and its +practical consequences one of the most striking examples of the power of +language over our associations. The subject will never be generally +understood, until that objectionable term is dropped. The free-will +doctrine, by keeping in view precisely that portion of the truth <span class="pagenum"><a name="Page_424" id="Page_424">[Pg 424]</a></span>which +the word Necessity puts out of sight, namely the power of the mind to +co-operate in the formation of its own character, has given to its +adherents a practical feeling much nearer to the truth than has +generally (I believe) existed in the minds of necessarians. The latter +may have had a stronger sense of the importance of what human beings can +do to shape the characters of one another; but the free-will doctrine +has, I believe, fostered in its supporters a much stronger spirit of +self-culture.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_II_4">§ 4.</a> There is still one fact which requires to be noticed (in addition +to the existence of a power of self-formation) before the doctrine of +the causation of human actions can be freed from the confusion and +misapprehensions which surround it in many minds. When the will is said +to be determined by motives, a motive does not mean always, or solely, +the anticipation of a pleasure or of a pain. I shall not here inquire +whether it be true that, in the commencement, all our voluntary actions +are mere means consciously employed to obtain some pleasure, or avoid +some pain. It is at least certain that we gradually, through the +influence of association, come to desire the means without thinking of +the end: the action itself becomes an object of desire, and is performed +without reference to any motive beyond itself. Thus far, it may still be +objected, that, the action having through association become +pleasurable, we are, as much as before, moved to act by the anticipation +of a pleasure, namely the pleasure of the action itself. But granting +this, the matter does not end here. As we proceed in the formation of +habits, and become accustomed to will a particular act or a particular +course of conduct because it is pleasurable, we at last continue to will +it without any reference to its being pleasurable. Although, from some +change in us or in our circumstances, we have ceased to find any +pleasure in the action, or perhaps to anticipate any pleasure as the +consequence of it, we still continue to desire the action, and +consequently to do it. In this manner it is that habits of hurtful +excess continue to be practised although they have ceased to be +pleasurable; and in this manner also it is that the habit of willing to +persevere in the <span class="pagenum"><a name="Page_425" id="Page_425">[Pg 425]</a></span>course which he has chosen, does not desert the moral +hero, even when the reward, however real, which he doubtless receives +from the consciousness of well-doing, is anything but an equivalent for +the sufferings he undergoes, or the wishes which he may have to +renounce.</p> + +<p>A habit of willing is commonly called a purpose; and among the causes of +our volitions, and of the actions which flow from them, must be reckoned +not only likings and aversions, but also purposes. It is only when our +purposes have become independent of the feelings of pain or pleasure +from which they originally took their rise, that we are said to have a +confirmed character. "A character," says Novalis, "is a completely +fashioned will:" and the will, once so fashioned, may be steady and +constant, when the passive susceptibilities of pleasure and pain are +greatly weakened, or materially changed.</p> + +<p>With the corrections and explanations now given, the doctrine of the +causation of our volitions by motives, and of motives by the desirable +objects offered to us, combined with our particular susceptibilities of +desire, may be considered, I hope, as sufficiently established for the +purposes of this treatise.<a name="FNanchor_1_107" id="FNanchor_1_107"></a><a href="#Footnote_1_107" class="fnanchor">[1]</a></p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_426" id="Page_426">[Pg 426]</a></span></p> +<h3><a name="BOOK_VI_CHAPTER_III" id="BOOK_VI_CHAPTER_III"></a>CHAPTER III.<br /> +THAT THERE IS, OR MAY BE, A SCIENCE OF HUMAN NATURE.</h3> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_III_1">§ 1.</a> It is a common notion, or at least it is implied in many common +modes of speech, that the thoughts, feelings, and actions of sentient +beings are not a subject of science, in the same strict sense in which +this is true of the objects of outward nature. This notion seems to +involve some confusion of ideas, which it is necessary to begin by +clearing up.</p> + +<p>Any facts are fitted, in themselves, to be a subject of science, which +follow one another according to constant laws; although those laws may +not have been discovered, nor even be discoverable by our existing +resources. Take, for instance, the most familiar class of meteorological +phenomena, those of rain and sunshine. Scientific inquiry has not yet +succeeded in ascertaining the order of antecedence and consequence among +these phenomena, so as to be able, at least in our regions of the earth, +to predict them with certainty, or even with any high degree of +probability. Yet no one doubts that the phenomena depend on laws, and +that these must be derivative laws resulting from known ultimate laws, +those of heat, electricity, vaporization, and elastic fluids. Nor can it +be doubted that if we were acquainted with all the antecedent +circumstances, we could, even from those more general laws, predict +(saving difficulties of calculation) the state of the weather at any +future time. Meteorology, therefore, not only has in itself every +natural requisite for being, but actually is, a science; though, from +the difficulty of observing the facts on which the phenomena depend (a +difficulty inherent in the peculiar nature of those phenomena) the +science is extremely imperfect; and were it perfect, might probably be +of little avail <span class="pagenum"><a name="Page_427" id="Page_427">[Pg 427]</a></span>in practice, since the data requisite for applying its +principles to particular instances would rarely be procurable.</p> + +<p>A case may be conceived, of an intermediate character between the +perfection of science, and this its extreme imperfection. It may happen +that the greater causes, those on which the principal part of the +phenomena depends, are within the reach of observation and measurement; +so that if no other causes intervened, a complete explanation could be +given not only of the phenomenon in general, but of all the variations +and modifications which it admits of. But inasmuch as other, perhaps +many other causes, separately insignificant in their effects, co-operate +or conflict in many or in all cases with those greater causes; the +effect, accordingly, presents more or less of aberration from what would +be produced by the greater causes alone. Now if these minor causes are +not so constantly accessible, or not accessible at all, to accurate +observation; the principal mass of the effect may still, as before, be +accounted for, and even predicted; but there will be variations and +modifications which we shall not be competent to explain thoroughly, and +our predictions will not be fulfilled accurately, but only +approximately.</p> + +<p>It is thus, for example, with the theory of the tides. No one doubts +that Tidology (as Dr. Whewell proposes to call it) is really a science. +As much of the phenomena as depends on the attraction of the sun and +moon is completely understood, and may in any, even unknown, part of the +earth's surface, be foretold with certainty; and the far greater part of +the phenomena depends on those causes. But circumstances of a local or +casual nature, such as the configuration of the bottom of the ocean, the +degree of confinement from shores, the direction of the wind, &c., +influence, in many or in all places, the height and time of the tide; +and a portion of these circumstances being either not accurately +knowable, not precisely measurable, or not capable of being certainly +foreseen, the tide in known places commonly varies from the calculated +result of general principles by some difference that we cannot explain, +and in unknown ones may vary from it by a difference that we are not +able to foresee or conjecture. Nevertheless, <span class="pagenum"><a name="Page_428" id="Page_428">[Pg 428]</a></span>not only is it certain +that these variations depend on causes, and follow their causes by laws +of unerring uniformity; not only, therefore, is tidology a science, like +meteorology, but it is, what hitherto at least meteorology is not, a +science largely available in practice. General laws may be laid down +respecting the tides, predictions may be founded on those laws, and the +result will in the main, though often not with complete accuracy, +correspond to the predictions.</p> + +<p>And this is what is or ought to be meant by those who speak of sciences +which are not <i>exact</i> sciences. Astronomy was once a science, without +being an exact science. It could not become exact until not only the +general course of the planetary motions, but the perturbations also, +were accounted for, and referred to their causes. It has become an exact +science, because its phenomena have been brought under laws +comprehending the whole of the causes by which the phenomena are +influenced, whether in a great or only in a trifling degree, whether in +all or only in some cases, and assigning to each of those causes the +share of effect which really belongs to it. But in the theory of the +tides the only laws as yet accurately ascertained, are those of the +causes which affect the phenomenon in all cases, and in a considerable +degree; while others which affect it in some cases only, or, if in all, +only in a slight degree, have not been sufficiently ascertained and +studied to enable us to lay down their laws; still less to deduce the +completed law of the phenomenon, by compounding the effects of the +greater with those of the minor causes. Tidology, therefore, is not yet +an exact science; not from any inherent incapacity of being so, but from +the difficulty of ascertaining with complete precision the real +derivative uniformities. By combining, however, the exact laws of the +greater causes, and of such of the minor ones as are sufficiently known, +with such empirical laws or such approximate generalizations respecting +the miscellaneous variations as can be obtained by specific observation, +we can lay down general propositions which will be true in the main, and +on which, with allowance for the degree of their probable inaccuracy, we +may safely ground our expectations and our conduct.</p> + + +<p><span class="pagenum"><a name="Page_429" id="Page_429">[Pg 429]</a></span></p><p class="newsection"><a name="BOOK_VI_CHAPTER_III_2">§ 2.</a> The science of human nature is of this description. It falls far +short of the standard of exactness now realized in Astronomy; but there +is no reason that it should not be as much a science as Tidology is, or +as Astronomy was when its calculations had only mastered the main +phenomena, but not the perturbations.</p> + +<p>The phenomena with which this science is conversant being the thoughts, +feelings, and actions of human beings, it would have attained the ideal +perfection of a science if it enabled us to foretell how an individual +would think, feel, or act, throughout life, with the same certainty with +which astronomy enables us to predict the places and the occultations of +the heavenly bodies. It needs scarcely be stated that nothing +approaching to this can be done. The actions of individuals could not be +predicted with scientific accuracy, were it only because we cannot +foresee the whole of the circumstances in which those individuals will +be placed. But further, even in any given combination of (present) +circumstances, no assertion, which is both precise and universally true, +can be made respecting the manner in which human beings will think, +feel, or act. This is not, however, because every person's modes of +thinking, feeling, and acting, do not depend on causes; nor can we doubt +that if, in the case of any individual, our data could be complete, we +even now know enough of the ultimate laws by which mental phenomena are +determined, to enable us in many cases to predict, with tolerable +certainty, what, in the greater number of supposable combinations of +circumstances, his conduct or sentiments would be. But the impressions +and actions of human beings are not solely the result of their present +circumstances, but the joint result of those circumstances and of the +characters of the individuals: and the agencies which determine human +character are so numerous and diversified, (nothing which has happened +to the person throughout life being without its portion of influence,) +that in the aggregate they are never in any two cases exactly similar. +Hence, even if our science of human nature were theoretically perfect, +that is, if we could calculate any character as we can calculate the +orbit of <span class="pagenum"><a name="Page_430" id="Page_430">[Pg 430]</a></span>any planet, <i>from given data</i>; still, as the data are never +all given, nor ever precisely alike in different cases, we could neither +make positive predictions, nor lay down universal propositions.</p> + +<p>Inasmuch, however, as many of those effects which it is of most +importance to render amenable to human foresight and control are +determined, like the tides, in an incomparably greater degree by general +causes, than by all partial causes taken together; depending in the main +on those circumstances and qualities which are common to all mankind, or +at least to large bodies of them, and only in a small degree on the +idiosyncrasies of organization or the peculiar history of individuals; +it is evidently possible with regard to all such effects, to make +predictions which will <i>almost</i> always be verified, and general +propositions which are almost always true. And whenever it is sufficient +to know how the great majority of the human race, or of some nation or +class of persons, will think, feel, and act, these propositions are +equivalent to universal ones. For the purposes of political and social +science this <i>is</i> sufficient. As we formerly remarked,<a name="FNanchor_2_108" id="FNanchor_2_108"></a><a href="#Footnote_2_108" class="fnanchor">[2]</a> an approximate +generalization is, in social inquiries, for most practical purposes +equivalent to an exact one; that which is only probable when asserted of +individual human beings indiscriminately selected, being certain when +affirmed of the character and collective conduct of masses.</p> + +<p>It is no disparagement, therefore, to the science of Human Nature, that +those of its general propositions which descend sufficiently into detail +to serve as a foundation for predicting phenomena in the concrete, are +for the most part only approximately true. But in order to give a +genuinely scientific character to the study, it is indispensable that +these approximate generalizations, which in themselves would amount only +to the lowest kind of empirical laws, should be connected deductively +with the laws of nature from which they result; should be resolved into +the properties of the causes on which the phenomena depend. In other +words, the <span class="pagenum"><a name="Page_431" id="Page_431">[Pg 431]</a></span>science of Human Nature may be said to exist, in proportion +as the approximate truths, which compose a practical knowledge of +mankind, can be exhibited as corollaries from the universal laws of +human nature on which they rest; whereby the proper limits of those +approximate truths would be shown, and we should be enabled to deduce +others for any new state of circumstances, in anticipation of specific +experience.</p> + +<p>The proposition now stated is the text on which the two succeeding +chapters will furnish the comment.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_432" id="Page_432">[Pg 432]</a></span></p> +<h3><a name="BOOK_VI_CHAPTER_IV" id="BOOK_VI_CHAPTER_IV"></a>CHAPTER IV.<br /> +OF THE LAWS OF MIND.</h3> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_IV_1">§ 1.</a> What the Mind is, as well as what Matter is, or any other question +respecting Things in themselves, as distinguished from their sensible +manifestations, it would be foreign to the purposes of this treatise to +consider. Here, as throughout our inquiry, we shall keep clear of all +speculations respecting the mind's own nature, and shall understand by +the laws of mind, those of mental Phenomena; of the various feelings or +states of consciousness of sentient beings. These, according to the +classification we have uniformly followed, consist of Thoughts, +Emotions, Volitions, and Sensations; the last being as truly states of +Mind as the three former. It is usual indeed to speak of sensations as +states of body, not of mind. But this is the common confusion, of giving +one and the same name to a phenomenon and to the proximate cause or +conditions of the phenomenon. The immediate antecedent of a sensation is +a state of body, but the sensation itself is a state of mind. If the +word mind means anything, it means that which feels. Whatever opinion we +hold respecting the fundamental identity or diversity of matter and +mind, in any case the distinction between mental and physical facts, +between the internal and the external world, will always remain, as a +matter of classification: and in that classification, sensations, like +all other feelings, must be ranked as mental phenomena. The mechanism of +their production, both in the body itself and in what is called outward +nature, is all that can with any propriety be classed as physical.</p> + +<p>The phenomena of mind, then, are the various feelings of our nature, +both those improperly called physical, and those <span class="pagenum"><a name="Page_433" id="Page_433">[Pg 433]</a></span>peculiarly designated +as mental: and by the laws of mind, I mean the laws according to which +those feelings generate one another.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_IV_2">§ 2.</a> All states of mind are immediately caused either by other states of +mind, or by states of body. When a state of mind is produced by a state +of mind, I call the law concerned in the case, a law of Mind. When a +state of mind is produced directly by a state of body, the law is a law +of Body, and belongs to physical science.</p> + +<p>With regard to those states of mind which are called sensations, all are +agreed that these have for their immediate antecedents, states of body. +Every sensation has for its proximate cause some affection of the +portion of our frame called the nervous system; whether this affection +originate in the action of some external object, or in some pathological +condition of the nervous organization itself. The laws of this portion +of our nature—the varieties of our sensations, and the physical +conditions on which they proximately depend—manifestly belong to the +province of Physiology.</p> + +<p>Whether the remainder of our mental states are similarly dependent on +physical conditions, is one of the <i>vexatæ questiones</i> in the science of +human nature. It is still disputed whether our thoughts, emotions, and +volitions are generated through the intervention of material mechanism; +whether we have organs of thought and of emotion, in the same sense in +which we have organs of sensation. Many eminent physiologists hold the +affirmative. These contend, that a thought (for example) is as much the +result of nervous agency, as a sensation: that some particular state of +our nervous system, in particular of that central portion of it called +the brain, invariably precedes, and is presupposed by, every state of +our consciousness. According to this theory, one state of mind is never +really produced by another: all are produced by states of body. When one +thought seems to call up another by association, it is not really a +thought which recals a thought; the association did not exist between +the two thoughts, but between the two states of the brain or nerves +<span class="pagenum"><a name="Page_434" id="Page_434">[Pg 434]</a></span>which preceded the thoughts: one of those states recals the other, each +being attended, in its passage, by the particular state of consciousness +which is consequent on it. On this theory the uniformities of succession +among states of mind would be mere derivative uniformities, resulting +from the laws of succession of the bodily states which cause them. There +would be no original mental laws, no Laws of Mind in the sense in which +I use the term, at all: and mental science would be a mere branch, +though the highest and most recondite branch, of the science of +physiology. M. Comte, accordingly, claims the scientific cognizance of +moral and intellectual phenomena exclusively for physiologists; and not +only denies to Psychology, or Mental Philosophy properly so called, the +character of a science, but places it, in the chimerical nature of its +objects and pretensions, almost on a par with astrology.</p> + +<p>But, after all has been said which can be said, it remains incontestible +that there exist uniformities of succession among states of mind, and +that these can be ascertained by observation and experiment. Further, +that every mental state has a nervous state for its immediate antecedent +and proximate cause, though extremely probable, cannot hitherto be said +to be proved, in the conclusive manner in which this can be proved of +sensations; and even were it certain, yet every one must admit that we +are wholly ignorant of the characteristics of these nervous states; we +know not, and at present have no means of knowing, in what respect one +of them differs from another; and our only mode of studying their +successions or coexistences must be by observing the successions and +coexistences of the mental states, of which they are supposed to be the +generators or causes. The successions, therefore, which obtain among +mental phenomena, do not admit of being deduced from the physiological +laws of our nervous organization: and all real knowledge of them must +continue, for a long time at least, if not always, to be sought in the +direct study, by observation and experiment, of the mental successions +themselves. Since therefore the order of our mental phenomena must be +studied in those phenomena, and not inferred from the laws of <span class="pagenum"><a name="Page_435" id="Page_435">[Pg 435]</a></span>any +phenomena more general, there is a distinct and separate Science of +Mind.</p> + +<p>The relations, indeed, of that science to the science of physiology must +never be overlooked or undervalued. It must by no means be forgotten +that the laws of mind may be derivative laws resulting from laws of +animal life, and that their truth therefore may ultimately depend on +physical conditions; and the influence of physiological states or +physiological changes in altering or counteracting the mental +successions, is one of the most important departments of psychological +study. But, on the other hand, to reject the resource of psychological +analysis, and construct the theory of the mind solely on such data as +physiology at present affords, seems to me as great an error in +principle, and an even more serious one in practice. Imperfect as is the +science of mind, I do not scruple to affirm, that it is in a +considerably more advanced state than the portion of physiology which +corresponds to it; and to discard the former for the latter appears to +me an infringement of the true canons of inductive philosophy, which +must produce, and which does produce, erroneous conclusions in some very +important departments of the science of human nature.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_IV_3">§ 3.</a> The subject, then, of Psychology, is the uniformities of +succession, the laws, whether ultimate or derivative, according to which +one mental state succeeds another; is caused by, or at least, is caused +to follow, another. Of these laws, some are general, others more +special. The following are examples of the most general laws.</p> + +<p>First: Whenever any state of consciousness has once been excited in us, +no matter by what cause; an inferior degree of the same state of +consciousness, a state of consciousness resembling the former, but +inferior in intensity, is capable of being reproduced in us, without the +presence of any such cause as excited it at first. Thus, if we have once +seen or touched an object, we can afterwards think of the object though +it be absent from our sight or from our touch. If we have been joyful or +grieved at some event, we can think of, or <span class="pagenum"><a name="Page_436" id="Page_436">[Pg 436]</a></span>remember our past joy or +grief, though no new event of a happy or painful nature has taken place. +When a poet has put together a mental picture of an imaginary object, a +Castle of Indolence, a Una, or a Hamlet, he can afterwards think of the +ideal object he has created, without any fresh act of intellectual +combination. This law is expressed by saying, in the language of Hume, +that every mental <i>impression</i> has its <i>idea</i>.</p> + +<p>Secondly: These ideas, or secondary mental states, are excited by our +impressions, or by other ideas, according to certain laws which are +called Laws of Association. Of these laws the first is, that similar +ideas tend to excite one another. The second is, that when two +impressions have been frequently experienced (or even thought of) either +simultaneously or in immediate succession, then whenever one of these +impressions, or the idea of it, recurs, it tends to excite the idea of +the other. The third law is, that greater intensity in either or both of +the impressions, is equivalent, in rendering them excitable by one +another, to a greater frequency of conjunction. These are the laws of +ideas: on which I shall not enlarge in this place, but refer the reader +to works professedly psychological, in particular to Mr. James Mill's +<i>Analysis of the Phenomena of the Human Mind</i>, where the principal laws +of association, along with many of their applications, are copiously +exemplified, and with a masterly hand.<a name="FNanchor_3_109" id="FNanchor_3_109"></a><a href="#Footnote_3_109" class="fnanchor">[3]</a></p> + +<p>These simple or elementary Laws of Mind have been ascertained by the +ordinary methods of experimental inquiry; nor could they have been +ascertained in any other manner. But <span class="pagenum"><a name="Page_437" id="Page_437">[Pg 437]</a></span>a certain number of elementary +laws having thus been obtained, it is a fair subject of scientific +inquiry how far those laws can be made to go in explaining the actual +phenomena. It is obvious that complex laws of thought and feeling not +only may, but must, be generated from these simple laws. And it is to be +remarked, that the case is not always one of Composition of Causes: the +effect of concurring causes is not always precisely the sum of the +effects of those causes when separate, nor even always an effect of the +same kind with them. Reverting to the distinction which occupies so +prominent a place in the theory of induction; the laws of the phenomena +of mind are sometimes analogous to mechanical, but sometimes also to +chemical laws. When many impressions or ideas are operating in the mind +together, there sometimes takes place a process, of a similar kind to +chemical combination. When impressions have been so often experienced in +conjunction, that each of them calls up readily and instantaneously the +ideas of the whole group, those ideas sometimes melt and coalesce into +one another, and appear not several ideas, but one; in the same manner +as, when the seven prismatic colours are presented to the eye in rapid +succession, the sensation produced is that of white. But as in this last +case it is correct to say that the seven colours when they rapidly +follow one another <i>generate</i> white, but not that they actually <i>are</i> +white; so it appears to me that the Complex Idea, formed by the blending +together of several simpler ones, should, when it really appears simple, +(that is, when the separate elements are not consciously distinguishable +in it,) be said to <i>result from</i>, or <i>be generated by</i>, the simple +ideas, not to <i>consist</i> of them. Our idea of an orange really <i>consists</i> +of the simple ideas of a certain colour, a certain form, a certain taste +and smell, &c., because we can, by interrogating our consciousness, +perceive all these elements in the idea. But we cannot perceive, in so +apparently simple a feeling as our perception of the shape of an object +by the eye, all that multitude of ideas derived from other senses, +without which it is well ascertained that no such visual perception +would ever have had existence; nor, in our idea of Extension, can we +discover those elementary <span class="pagenum"><a name="Page_438" id="Page_438">[Pg 438]</a></span>ideas of resistance, derived from our +muscular frame, in which it has been conclusively shown that the idea +originates. These therefore are cases of mental chemistry: in which it +is proper to say that the simple ideas generate, rather than that they +compose, the complex ones.</p> + +<p>With respect to all the other constituents of the mind, its beliefs, its +abstruser conceptions, its sentiments, emotions, and volitions; there +are some (among whom are Hartley, and the author of the <i>Analysis</i>) who +think that the whole of these are generated from simple ideas of +sensation, by a chemistry similar to that which we have just +exemplified. These philosophers have made out a great part of their +case, but I am not satisfied that they have established the whole of it. +They have shown that there is such a thing as mental chemistry; that the +heterogeneous nature of a feeling A, considered in relation to B and C, +is no conclusive argument against its being generated from B and C. +Having proved this, they proceed to show, that where A is found, B and C +were or may have been present, and why therefore, they ask, should not A +have been generated from B and C? But even if this evidence were carried +to the highest degree of completeness which it admits of; if it were +shown (which hitherto it has not, in all cases, been) that certain +groups of associated ideas not only might have been, but actually were, +present whenever the more recondite mental feeling was experienced; this +would amount only to the Method of Agreement, and could not prove +causation until confirmed by the more conclusive evidence of the Method +of Difference. If the question be whether Belief is a mere case of close +association of ideas, it would be necessary to examine experimentally if +it be true that any ideas whatever, provided they are associated with +the required degree of closeness, give rise to belief. If the inquiry be +into the origin of moral feelings, the feeling for example of moral +reprobation, it is necessary to compare all the varieties of actions or +states of mind which are ever morally disapproved, and see whether in +all these cases it can be shown, or reasonably surmised, that the action +or state of mind had become connected by association, in the +disapproving mind, with some particular class of hateful or disgusting +<span class="pagenum"><a name="Page_439" id="Page_439">[Pg 439]</a></span>ideas; and the method employed is, thus far, that of Agreement. But +this is not enough. Supposing this proved, we must try further by the +Method of Difference, whether this particular kind of hateful or +disgusting ideas, when it becomes associated with an action previously +indifferent, will render that action a subject of moral disapproval. If +this question can be answered in the affirmative, it is shown to be a +law of the human mind, that an association of that particular +description is the generating cause of moral reprobation. That all this +is the case has been rendered extremely probable, but the experiments +have not been tried with the degree of precision necessary for a +complete and absolutely conclusive induction.<a name="FNanchor_4_110" id="FNanchor_4_110"></a><a href="#Footnote_4_110" class="fnanchor">[4]</a></p> + +<p>It is further to be remembered, that even if all which this theory of +mental phenomena contends for could be proved, we should not be the more +enabled to resolve the laws of the more complex feelings into those of +the simpler ones. The generation of one class of mental phenomena from +another, whenever it can be made out, is a highly interesting fact in +psychological chemistry; but it no more supersedes the necessity of an +experimental study of the generated phenomenon, than a knowledge of the +properties of oxygen and sulphur enables us to deduce those of sulphuric +acid without specific observation and experiment. Whatever, therefore, +may be the final issue of the attempt to account for the origin of our +judgments, our desires, or our volitions, from simpler mental phenomena, +it is not the less imperative to ascertain the sequences of the complex +phenomena themselves, by special study in conformity to the canons of +Induction. Thus, in respect to Belief, psychologists will always have to +inquire, what beliefs we have by direct consciousness, and according to +what laws one belief produces another; what are the laws, <span class="pagenum"><a name="Page_440" id="Page_440">[Pg 440]</a></span>in virtue of +which one thing is recognised by the mind, either rightly or +erroneously, as evidence of another thing. In regard to Desire, they +will have to examine what objects we desire naturally, and by what +causes we are made to desire things originally indifferent, or even +disagreeable to us; and so forth. It may be remarked, that the general +laws of association prevail among these more intricate states of mind, +in the same manner as among the simpler ones. A desire, an emotion, an +idea of the higher order of abstraction, even our judgments and +volitions when they have become habitual, are called up by association, +according to precisely the same laws as our simple ideas.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_IV_4">§ 4.</a> In the course of these inquiries it will be natural and necessary +to examine, how far the production of one state of mind by another is +influenced by any assignable state of body. The commonest observation +shows that different minds are susceptible in very different degrees, to +the action of the same psychological causes. The idea, for example, of a +given desirable object, will excite in different minds very different +degrees of intensity of desire. The same subject of meditation, +presented to different minds, will excite in them very unequal degrees +of intellectual action. These differences of mental susceptibility in +different individuals may be, first, original and ultimate facts, or, +secondly, they may be consequences of the previous mental history of +those individuals, or thirdly and lastly, they may depend on varieties +of physical organization. That the previous mental history of the +individuals must have some share in producing or in modifying the whole +of their mental character, is an inevitable consequence of the laws of +mind; but that differences of bodily structure also co-operate, is the +opinion of all physiologists, confirmed by common experience. It is to +be regretted that hitherto this experience, being accepted in the gross, +without due analysis, has been made the groundwork of empirical +generalizations most detrimental to the progress of real knowledge.</p> + +<p><span class="pagenum"><a name="Page_441" id="Page_441">[Pg 441]</a></span></p><p>It is certain that the natural differences which really exist in the +mental predispositions or susceptibilities of different persons, are +often not unconnected with diversities in their organic constitution. +But it does not therefore follow that these organic differences must in +all cases influence the mental phenomena directly and immediately. They +often affect them through the medium of their psychological causes. For +example, the idea of some particular pleasure may excite in different +persons, even independently of habit or education, very different +strengths of desire, and this may be the effect of their different +degrees or kinds of nervous susceptibility; but these organic +differences, we must remember, will render the pleasurable sensation +itself more intense in one of these persons than in the other; so that +the idea of the pleasure will also be an intenser feeling, and will, by +the operation of mere mental laws, excite an intenser desire, without +its being necessary to suppose that the desire itself is directly +influenced by the physical peculiarity. As in this, so in many cases, +such differences in the kind or in the intensity of the physical +sensations as must necessarily result from differences of bodily +organization, will of themselves account for many differences not only +in the degree, but even in the kind, of the other mental phenomena. So +true is this, that even different <i>qualities</i> of mind, different types +of mental character, will naturally be produced by mere differences of +intensity in the sensations generally: as is well pointed out in an able +essay on Dr. Priestley, mentioned in a former chapter:—</p> + +<p>"The sensations which form the elements of all knowledge are received +either simultaneously or successively; when several are received +simultaneously, as the smell, the taste, the colour, the form, &c. of a +fruit, their association together constitutes our idea of an <i>object</i>; +when received successively, their association makes up the idea of an +<i>event</i>. Anything, then, which favours the associations of synchronous +ideas, will tend to produce a knowledge of objects, a perception of +qualities; while anything which favours association in the successive +order, will tend to produce a knowledge of events, of the <span class="pagenum"><a name="Page_442" id="Page_442">[Pg 442]</a></span>order of +occurrences, and of the connexion of cause and effect: in other words, +in the one case a perceptive mind, with a discriminate feeling of the +pleasurable and painful properties of things, a sense of the grand and +the beautiful, will be the result: in the other, a mind attentive to the +movements and phenomena, a ratiocinative and philosophic intellect. Now +it is an acknowledged principle, that all sensations experienced during +the presence of any vivid impression, become strongly associated with +it, and with each other; and does it not follow, that the synchronous +feelings of a sensitive constitution, (<i>i.e.</i> the one which has vivid +impressions,) will be more intimately blended than in a differently +formed mind? If this suggestion has any foundation in truth, it leads to +an inference not unimportant; that where nature has endowed an +individual with great original susceptibility, he will probably be +distinguished by fondness for natural history, a relish for the +beautiful and great, and moral enthusiasm; where there is but a +mediocrity of sensibility, a love of science, of abstract truth, with a +deficiency of taste and of fervour, is likely to be the result."</p> + +<p>We see from this example, that when the general laws of mind are more +accurately known, and above all, more skilfully applied to the detailed +explanation of mental peculiarities, they will account for many more of +those peculiarities than is ordinarily supposed. Unfortunately the +reaction of the last and present generation against the philosophy of +the eighteenth century has produced a very general neglect of this great +department of analytical inquiry; of which, consequently, the recent +progress has been by no means proportional to its early promise. The +majority of those who speculate on human nature, prefer dogmatically to +assume that the mental differences which they perceive, or think they +perceive, among human beings, are ultimate facts, incapable of being +either explained or altered, rather than take the trouble of fitting +themselves, by the requisite processes of thought, for referring those +mental differences to the outward causes by which they are for the most +part produced, and on <span class="pagenum"><a name="Page_443" id="Page_443">[Pg 443]</a></span>the removal of which they would cease to exist. +The German school of metaphysical speculation, which has not yet lost +its temporary predominance in European thought, has had this among many +other injurious influences: and at the opposite extreme of the +psychological scale, no writer, either of early or of recent date, is +chargeable in a higher degree with this aberration from the true +scientific spirit, than M. Comte.</p> + +<p>It is certain that, in human beings at least, differences in education +and in outward circumstances are capable of affording an adequate +explanation of by far the greatest portion of character; and that the +remainder may be in great part accounted for by physical differences in +the sensations produced in different individuals by the same external or +internal cause. There are, however, some mental facts which do not seem +to admit of these modes of explanation. Such, to take the strongest +case, are the various instincts of animals, and the portion of human +nature which corresponds to those instincts. No mode has been suggested, +even by way of hypothesis, in which these can receive any satisfactory, +or even plausible, explanation from psychological causes alone; and +there is great reason to think that they have as positive, and even as +direct and immediate, a connexion with physical conditions of the brain +and nerves, as any of our mere sensations have. A supposition which (it +is perhaps not superfluous to add) in no way conflicts with the +indisputable fact, that these instincts may be modified to any extent, +or entirely conquered, in human beings at least, by other mental +influences, and by education.</p> + +<p>Whether organic causes exercise a direct influence over any other +classes of mental phenomena, is hitherto as far from being ascertained, +as is the precise nature of the organic conditions even in the case of +instincts. The physiology, however, of the brain and nervous system is +in a state of such rapid advance, and is continually bringing forth such +new and interesting results, that if there be really a connexion between +mental peculiarities and any varieties cognizable by our senses in the +structure of the cerebral and nervous apparatus, the <span class="pagenum"><a name="Page_444" id="Page_444">[Pg 444]</a></span>nature of that +connexion is now in a fair way of being found out. The latest +discoveries in cerebral physiology appear to have proved, that any such +connexion which may exist is of a radically different character from +that contended for by Gall and his followers, and that whatever may +hereafter be found to be the true theory of the subject, phrenology at +least is untenable.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_445" id="Page_445">[Pg 445]</a></span></p> +<h3><a name="BOOK_VI_CHAPTER_V" id="BOOK_VI_CHAPTER_V"></a>CHAPTER V.<br /> +OF ETHOLOGY, OR THE SCIENCE OF THE FORMATION OF CHARACTER.</h3> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_V_1">§ 1.</a> The laws of mind as characterized in the preceding chapter, compose +the universal or abstract portion of the philosophy of human nature; and +all the truths of common experience, constituting a practical knowledge +of mankind, must, to the extent to which they are truths, be results or +consequences of these. Such familiar maxims, when collected <i>à +posteriori</i> from observation of life, occupy among the truths of the +science the place of what, in our analysis of Induction, have so often +been spoken of under the title of Empirical Laws.</p> + +<p>An Empirical Law (it will be remembered) is an uniformity, whether of +succession or of coexistence, which holds true in all instances within +our limits of observation, but is not of a nature to afford any +assurance that it would hold beyond those limits; either because the +consequent is not really the effect of the antecedent, but forms part +along with it of a chain of effects, flowing from prior causes not yet +ascertained; or because there is ground to believe that the sequence +(though a case of causation) is resolvable into simpler sequences, and, +depending therefore on a concurrence of several natural agencies, is +exposed to an unknown multitude of possibilities of counteraction. In +other words, an empirical law is a generalization, of which, not content +with finding it true, we are obliged to ask, why is it true? knowing +that its truth is not absolute, but dependent on some more general +conditions, and that it can only be relied on in so far as there is +ground of assurance that those conditions are realized.</p> + +<p><span class="pagenum"><a name="Page_446" id="Page_446">[Pg 446]</a></span></p><p>Now, the observations concerning human affairs collected from common +experience, are precisely of this nature. Even if they were universally +and exactly true within the bounds of experience, which they never are, +still they are not the ultimate laws of human action; they are not the +principles of human nature, but results of those principles under the +circumstances in which mankind have happened to be placed. When the +Psalmist said in his haste that "all men are liars," he enunciated what +in some ages and countries is borne out by ample experience; but it is +not a law of man's nature to lie; though it is one of the consequences +of the laws of human nature, that lying is nearly universal when certain +external circumstances exist universally, especially circumstances +productive of habitual distrust and fear. When the character of the old +is asserted to be cautious, and of the young impetuous, this, again, is +but an empirical law; for it is not because of their youth that the +young are impetuous, nor because of their age that the old are cautious. +It is chiefly, if not wholly, because the old, during their many years +of life, have generally had much experience of its various evils, and +having suffered or seen others suffer much from incautious exposure to +them, have acquired associations favourable to circumspection: while the +young, as well from the absence of similar experience as from the +greater strength of the inclinations which urge them to enterprise, +engage themselves in it more readily. Here, then, is the <i>explanation</i> +of the empirical law; here are the conditions which ultimately determine +whether the law holds good or not. If an old man has not been oftener +than most young men in contact with danger and difficulty, he will be +equally incautious: if a youth has not stronger inclinations than an old +man, he probably will be as little enterprising. The empirical law +derives whatever truth it has, from the causal laws of which it is a +consequence. If we know those laws, we know what are the limits to the +derivative law: while, if we have not yet accounted for the empirical +law—if it rest only on observation—there is no safety in applying it +far beyond the limits of time, place, and circumstance, in which the +observations were made.</p> + +<p><span class="pagenum"><a name="Page_447" id="Page_447">[Pg 447]</a></span></p><p>The really scientific truths, then, are not these empirical laws, but +the causal laws which explain them. The empirical laws of those +phenomena which depend on known causes, and of which a general theory +can therefore be constructed, have, whatever may be their value in +practice, no other function in science than that of verifying the +conclusions of theory. Still more must this be the case when most of the +empirical laws amount, even within the limits of observation, only to +approximate generalizations.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_V_2">§ 2.</a> This however is not, so much as is sometimes supposed, a +peculiarity of the sciences called moral. It is only in the simplest +branches of science that empirical laws are ever exactly true; and not +always in those. Astronomy, for example, is the simplest of all the +sciences which explain, in the concrete, the actual course of natural +events. The causes or forces, on which astronomical phenomena depend, +are fewer in number than those which determine any other of the great +phenomena of nature. Accordingly, as each effect results from the +conflict of but few causes, a great degree of regularity and uniformity +might be expected to exist among the effects; and such is really the +case: they have a fixed order, and return in cycles. But propositions +which should express, with absolute correctness, all the successive +positions of a planet until the cycle is completed, would be of almost +unmanageable complexity, and could be obtained from theory alone. The +generalizations which can be collected on the subject from direct +observation, even such as Kepler's law, are mere approximations: the +planets, owing to their perturbations by one another, do not move in +exact ellipses. Thus even in astronomy, perfect exactness in the mere +empirical laws is not to be looked for; much less, then, in more complex +subjects of inquiry.</p> + +<p>The same example shows how little can be inferred against the +universality or even the simplicity of the ultimate laws, from the +impossibility of establishing any but approximate empirical laws of the +effects. The laws of causation according to which a class of phenomena +are produced may be very few <span class="pagenum"><a name="Page_448" id="Page_448">[Pg 448]</a></span>and simple, and yet the effects themselves +may be so various and complicated that it shall be impossible to trace +any regularity whatever completely through them. For the phenomena in +question may be of an eminently modifiable character; insomuch that +innumerable circumstances are capable of influencing the effect, +although they may all do it according to a very small number of laws. +Suppose that all which passes in the mind of man is determined by a few +simple laws: still, if those laws be such that there is not one of the +facts surrounding a human being, or of the events which happen to him, +that does not influence in some mode or degree his subsequent mental +history, and if the circumstances of different human beings are +extremely different, it will be no wonder if very few propositions can +be made respecting the details of their conduct or feelings, which will +be true of all mankind.</p> + +<p>Now, without deciding whether the ultimate laws of our mental nature are +few or many, it is at least certain that they are of the above +description. It is certain that our mental states, and our mental +capacities and susceptibilities, are modified, either for a time or +permanently, by everything which happens to us in life. Considering +therefore how much these modifying causes differ in the case of any two +individuals, it would be unreasonable to expect that the empirical laws +of the human mind, the generalizations which can be made respecting the +feelings or actions of mankind without reference to the causes that +determine them, should be anything but approximate generalizations. They +are the common wisdom of common life, and as such are invaluable; +especially as they are mostly to be applied to cases not very dissimilar +to those from which they were collected. But when maxims of this sort, +collected from Englishmen, come to be applied to Frenchmen, or when +those collected from the present day are applied to past or future +generations, they are apt to be very much at fault. Unless we have +resolved the empirical law into the laws of the causes on which it +depends, and ascertained that those causes extend to the case which we +have in view, there can be no reliance placed in our inferences. <span class="pagenum"><a name="Page_449" id="Page_449">[Pg 449]</a></span>For +every individual is surrounded by circumstances different from those of +every other individual; every nation or generation of mankind from every +other nation or generation: and none of these differences are without +their influence in forming a different type of character. There is, +indeed, also a certain general resemblance; but peculiarities of +circumstances are continually constituting exceptions even to the +propositions which are true in the great majority of cases.</p> + +<p>Although, however, there is scarcely any mode of feeling or conduct +which is, in the absolute sense, common to all mankind; and though the +generalizations which assert that any given variety of conduct or +feeling will be found universally, (however nearly they may approximate +to truth within given limits of observation,) will be considered as +scientific propositions by no one who is at all familiar with scientific +investigation; yet all modes of feeling and conduct met with among +mankind have causes which produce them; and in the propositions which +assign those causes, will be found the explanation of the empirical +laws, and the limiting principle of our reliance on them. Human beings +do not all feel and act alike in the same circumstances; but it is +possible to determine what makes one person, in a given position, feel +or act in one way, another in another; how any given mode of feeling and +conduct, compatible with the general laws (physical and mental) of human +nature, has been, or may be, formed. In other words, mankind have not +one universal character, but there exist universal laws of the Formation +of Character. And since it is by these laws, combined with the facts of +each particular case, that the whole of the phenomena of human action +and feeling are produced, it is on these that every rational attempt to +construct the science of human nature in the concrete, and for practical +purposes, must proceed.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_V_3">§ 3.</a> The laws, then, of the formation of character being the principal +object of scientific inquiry into human nature; it remains to determine +the method of investigation best fitted for ascertaining them. And the +logical principles <span class="pagenum"><a name="Page_450" id="Page_450">[Pg 450]</a></span>according to which this question is to be decided, +must be those which preside over every other attempt to investigate the +laws of very complex phenomena. For it is evident that both the +character of any human being, and the aggregate of the circumstances by +which that character has been formed, are facts of a high order of +complexity. Now to such cases we have seen that the Deductive Method, +setting out from general laws, and verifying their consequences by +specific experience, is alone applicable. The grounds of this great +logical doctrine have formerly been stated: and its truth will derive +additional support from a brief examination of the specialities of the +present case.</p> + +<p>There are only two modes in which laws of nature can be ascertained: +deductively, and experimentally: including under the denomination of +experimental inquiry, observation as well as artificial experiment. Are +the laws of the formation of character susceptible of a satisfactory +investigation by the method of experimentation? Evidently not; because, +even if we suppose unlimited power of varying the experiment, (which is +abstractedly possible, though no one but an oriental despot has that +power, or if he had, would probably be disposed to exercise it,) a still +more essential condition is wanting; the power of performing any of the +experiments with scientific accuracy.</p> + +<p>The instances requisite for the prosecution of a directly experimental +inquiry into the formation of character, would be a number of human +beings to bring up and educate, from infancy to mature age. And to +perform any one of these experiments with scientific propriety, it would +be necessary to know and record every sensation or impression received +by the young pupil from a period long before it could speak; including +its own notions respecting the sources of all those sensations and +impressions. It is not only impossible to do this completely, but even +to do so much of it as should constitute a tolerable approximation. One +apparently trivial circumstance which eluded our vigilance, might let in +a train of impressions and associations sufficient to vitiate the +experiment as an authentic exhibition of the effects flowing from given +causes. No one who has sufficiently reflected on education <span class="pagenum"><a name="Page_451" id="Page_451">[Pg 451]</a></span>is ignorant +of this truth: and whoever has not, will find it most instructively +illustrated in the writings of Rousseau and Helvetius on that great +subject.</p> + +<p>Under this impossibility of studying the laws of the formation of +character by experiments purposely contrived to elucidate them, there +remains the resource of simple observation. But if it be impossible to +ascertain the influencing circumstances with any approach to +completeness even when we have the shaping of them ourselves, much more +impossible is it when the cases are further removed from our +observation, and altogether out of our control. Consider the difficulty +of the very first step—of ascertaining what actually is the character +of the individual, in each particular case that we examine. There is +hardly any person living, concerning some essential part of whose +character there are not differences of opinion even among his intimate +acquaintances: and a single action, or conduct continued only for a +short time, goes a very little way towards ascertaining it. We can only +make our observations in a rough way, and <i>en masse</i>; not attempting to +ascertain completely in any given instance, what character has been +formed, and still less by what causes; but only observing in what state +of previous circumstances it is found that certain marked mental +qualities or deficiencies <i>oftenest</i> exist. These conclusions, besides +that they are mere approximate generalizations, deserve no reliance even +as such, unless the instances are sufficiently numerous to eliminate not +only chance, but every assignable circumstance in which a number of the +cases examined may happen to have resembled one another. So numerous and +various, too, are the circumstances which form individual character, +that the consequence of any particular combination is hardly ever some +definite and strongly marked character, always found where that +combination exists, and not otherwise. What is obtained, even after the +most extensive and accurate observation, is merely a comparative result; +as for example, that in a given number of Frenchmen, taken +indiscriminately, there will be found more persons of a particular +mental tendency, and fewer of the contrary tendency, <span class="pagenum"><a name="Page_452" id="Page_452">[Pg 452]</a></span>than among an +equal number of Italians or English, similarly taken; or thus: of a +hundred Frenchmen and an equal number of Englishmen, fairly selected, +and arranged according to the degree in which they possess a particular +mental characteristic, each number, 1, 2, 3, &c., of the one series, +will be found to possess more of that characteristic than the +corresponding number of the other. Since, therefore, the comparison is +not one of kinds, but of ratios and degrees; and since in proportion as +the differences are slight, it requires a greater number of instances to +eliminate chance; it cannot often happen to any one to know a sufficient +number of cases with the accuracy requisite for making the sort of +comparison last mentioned; less than which, however, would not +constitute a real induction. Accordingly there is hardly one current +opinion respecting the characters of nations, classes, or descriptions +of persons, which is universally acknowledged as indisputable.<a name="FNanchor_5_111" id="FNanchor_5_111"></a><a href="#Footnote_5_111" class="fnanchor">[5]</a></p> + +<p>And finally, if we could even obtain by way of experiment a much more +satisfactory assurance of these generalizations than is really possible, +they would still be only empirical <span class="pagenum"><a name="Page_453" id="Page_453">[Pg 453]</a></span>laws. They would show, indeed, that +there was some connexion between the type of character formed, and the +circumstances existing in the case; but not what the precise connexion +was, nor to which of the peculiarities of those circumstances the effect +was really owing. They could only, therefore, be received as results of +causation, requiring to be resolved into the general laws of the causes: +until the determination of which, we could not judge within what limits +the derivative laws might serve as presumptions in cases yet unknown, or +even be depended on as permanent in the very cases from which they were +collected. The French people had, or were supposed to have, a certain +national character: but they drive out their royal family and +aristocracy, alter their institutions, pass through a series of +extraordinary events for half a century, and at the end of that time are +found to be, in many respects, greatly altered. A long list of mental +and moral differences are observed, or supposed, to exist between men +and women: but at some future, and, it may be hoped, not distant period, +equal freedom and an equally independent social position come to be +possessed by both, and their differences of character are either removed +or totally altered.</p> + +<p>But if the differences which we think we observe between French and +English, or between men and women, can be connected with more general +laws; if they be such as might be expected to be produced by the +differences of government, former customs, and physical peculiarities in +the two nations, and by the diversities of education, occupations, +personal independence, and social privileges, and whatever original +differences there may be in bodily strength and nervous sensibility, +between the two sexes; then, indeed, the coincidence of the two kinds of +evidence justifies us in believing that we have both reasoned rightly +and observed rightly. Our observation, though not sufficient as proof, +is ample as verification. And having ascertained not only the empirical +laws, but the causes, of the peculiarities, we need be under no +difficulty in judging how far they may be expected to be permanent, or +by what circumstances they would be modified or destroyed.</p> + + +<p><span class="pagenum"><a name="Page_454" id="Page_454">[Pg 454]</a></span></p><p class="newsection"><a name="BOOK_VI_CHAPTER_V_4">§ 4.</a> Since, then, it is impossible to obtain really accurate +propositions respecting the formation of character from observation and +experiment alone, we are driven perforce to that which, even if it had +not been the indispensable, would have been the most perfect, mode of +investigation, and which it is one of the principal aims of philosophy +to extend; namely, that which tries its experiments not on the complex +facts, but on the simple ones of which they are compounded; and after +ascertaining the laws of the causes, the composition of which gives rise +to the complex phenomena, then considers whether these will not explain +and account for the approximate generalizations which have been framed +empirically respecting the sequences of those complex phenomena. The +laws of the formation of character are, in short, derivative laws, +resulting from the general laws of mind; and are to be obtained by +deducing them from those general laws; by supposing any given set of +circumstances, and then considering what, according to the laws of mind, +will be the influence of those circumstances on the formation of +character.</p> + +<p>A science is thus formed, to which I would propose to give the name of +Ethology, or the Science of Character; from <i>ἦθος</i>, a word more +nearly corresponding to the term "character" as I here use it, than any +other word in the same language. The name is perhaps etymologically +applicable to the entire science of our mental and moral nature; but if, +as is usual and convenient, we employ the name Psychology for the +science of the elementary laws of mind, Ethology will serve for the +ulterior science which determines the kind of character produced, in +conformity to those general laws, by any set of circumstances, physical +and moral. According to this definition, Ethology is the science which +corresponds to the art of education; in the widest sense of the term, +including the formation of national or collective character as well as +individual. It would indeed be vain to expect (however completely the +laws of the formation of character might be ascertained) that we could +know so accurately the circumstances of any given case as to be able +positively to predict the character that would be <span class="pagenum"><a name="Page_455" id="Page_455">[Pg 455]</a></span>produced in that +case. But we must remember that a degree of knowledge far short of the +power of actual prediction, is often of much practical value. There may +be great power of influencing phenomena, with a very imperfect knowledge +of the causes by which they are in any given instance determined. It is +enough that we know that certain means have a <i>tendency</i> to produce a +given effect, and that others have a tendency to frustrate it. When the +circumstances of an individual or of a nation are in any considerable +degree under our control, we may, by our knowledge of tendencies, be +enabled to shape those circumstances in a manner much more favourable to +the ends we desire, than the shape which they would of themselves +assume. This is the limit of our power; but within this limit the power +is a most important one.</p> + +<p>This science of Ethology may be called the Exact Science of Human +Nature; for its truths are not, like the empirical laws which depend on +them, approximate generalizations, but real laws. It is, however, (as in +all cases of complex phenomena) necessary to the exactness of the +propositions, that they should be hypothetical only, and affirm +tendencies, not facts. They must not assert that something will always, +or certainly, happen; but only that such and such will be the effect of +a given cause, so far as it operates uncounteracted. It is a scientific +proposition, that bodily strength tends to make men courageous; not that +it always makes them so: that an interest on one side of a question +tends to bias the judgment; not that it invariably does so: that +experience tends to give wisdom; not that such is always its effect. +These propositions, being assertive only of tendencies, are not the less +universally true because the tendencies may be frustrated.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_V_5">§ 5.</a> While on the one hand Psychology is altogether, or principally, a +science of observation and experiment, Ethology, as I have conceived it, +is, as I have already remarked, altogether deductive. The one ascertains +the simple laws of Mind in general, the other traces their operation in +complex combinations of circumstances. Ethology stands to <span class="pagenum"><a name="Page_456" id="Page_456">[Pg 456]</a></span>Psychology in +a relation very similar to that in which the various branches of natural +philosophy stand to mechanics. The principles of Ethology are properly +the middle principles, the <i>axiomata media</i> (as Bacon would have said) +of the science of mind: as distinguished, on the one hand from the +empirical laws resulting from simple observation, and on the other from +the highest generalizations.</p> + +<p>And this seems a suitable place for a logical remark, which, though of +general application, is of peculiar importance in reference to the +present subject. Bacon has judiciously observed that the <i>axiomata +media</i> of every science principally constitute its value. The lowest +generalizations, until explained by and resolved into the middle +principles of which they are the consequences, have only the imperfect +accuracy of empirical laws; while the most general laws are <i>too</i> +general, and include too few circumstances, to give sufficient +indication of what happens in individual cases, where the circumstances +are almost always immensely numerous. In the importance, therefore, +which Bacon assigns, in every science, to the middle principles, it is +impossible not to agree with him. But I conceive him to have been +radically wrong in his doctrine respecting the mode in which these +<i>axiomata media</i> should be arrived at; though there is no one +proposition laid down in his works for which he has been more +extravagantly eulogized. He enunciates as an universal rule, that +induction should proceed from the lowest to the middle principles, and +from those to the highest, never reversing that order, and consequently +leaving no room for the discovery of new principles by way of deduction +at all. It is not to be conceived that a man of his sagacity could have +fallen into this mistake, if there had existed in his time, among the +sciences which treat of successive phenomena, one single instance of a +deductive science, such as mechanics, astronomy, optics, acoustics, &c. +now are. In those sciences it is evident that the higher and middle +principles are by no means derived from the lowest, but the reverse. In +some of them the very highest generalizations were those earliest +ascertained with any scientific exactness; as, for example (in +mechanics), the laws of motion. Those <span class="pagenum"><a name="Page_457" id="Page_457">[Pg 457]</a></span>general laws had not indeed at +first the acknowledged universality which they acquired after having +been successfully employed to explain many classes of phenomena to which +they were not originally seen to be applicable; as when the laws of +motion were employed, in conjunction with other laws, to explain +deductively the celestial phenomena. Still, the fact remains, that the +propositions which were afterwards recognised as the most general truths +of the science, were, of all its accurate generalizations, those +earliest arrived at. Bacon's greatest merit cannot therefore consist, as +we are so often told that it did, in exploding the vicious method +pursued by the ancients of flying to the highest generalizations first, +and deducing the middle principles from them; since this is neither a +vicious nor an exploded, but the universally accredited method of modern +science, and that to which it owes its greatest triumphs. The error of +ancient speculation did not consist in making the largest +generalizations first, but in making them without the aid or warrant of +rigorous inductive methods, and applying them deductively without the +needful use of that important part of the Deductive Method termed +Verification.</p> + +<p>The order in which truths of the various degrees of generality should be +ascertained, cannot, I apprehend, be prescribed by any unbending rule. I +know of no maxim which can be laid down on the subject, but to obtain +those first, in respect to which the conditions of a real induction can +be first and most completely realized. Now, wherever our means of +investigation can reach causes, without stopping at the empirical laws +of the effects, the simplest cases, being those in which fewest causes +are simultaneously concerned, will be most amenable to the inductive +process; and these are the cases which elicit laws of the greatest +comprehensiveness. In every science, therefore, which has reached the +stage at which it becomes a science of causes, it will be usual as well +as desirable first to obtain the highest generalizations, and then +deduce the more special ones from them. Nor can I discover any +foundation for the Baconian maxim, so much extolled by subsequent +writers, except this: That before we attempt to <span class="pagenum"><a name="Page_458" id="Page_458">[Pg 458]</a></span>explain deductively +from more general laws any new class of phenomena, it is desirable to +have gone as far as is practicable in ascertaining the empirical laws of +those phenomena; so as to compare the results of deduction, not with one +individual instance after another, but with general propositions +expressive of the points of agreement which have been found among many +instances. For if Newton had been obliged to verify the theory of +gravitation, not by deducing from it Kepler's laws, but by deducing all +the observed planetary positions which had served Kepler to establish +those laws, the Newtonian theory would probably never have emerged from +the state of an hypothesis.<a name="FNanchor_6_112" id="FNanchor_6_112"></a><a href="#Footnote_6_112" class="fnanchor">[6]</a></p> + +<p>The applicability of these remarks to the special case under +consideration, cannot admit of question. The science of the formation of +character is a science of causes. The subject is one to which those +among the canons of induction, by which laws of causation are +ascertained, can be rigorously applied. It is, therefore, both natural +and advisable to ascertain the simplest, which are necessarily the most +general, laws of causation first, and to deduce the middle principles +from them. In other words, Ethology, the deductive science, is a system +of corollaries from Psychology, the experimental science.</p> + + +<p><span class="pagenum"><a name="Page_459" id="Page_459">[Pg 459]</a></span></p><p class="newsection"><a name="BOOK_VI_CHAPTER_V_6">§ 6.</a> Of these, the earlier alone has been, as yet, really conceived or +studied as a science; the other, Ethology, is still to be created. But +its creation has at length become practicable. The empirical laws, +destined to verify its deductions, have been formed in abundance by +every successive age of humanity; and the premises for the deductions +are now sufficiently complete. Excepting the degree of uncertainty which +still exists as to the extent of the natural differences of individual +minds, and the physical circumstances on which these may be dependent, +(considerations which are of secondary importance when we are +considering mankind in the average, or <i>en masse</i>,) I believe most +competent judges will agree that the general laws of the different +constituent elements of human nature are even now sufficiently +understood, to render it possible for a competent thinker to deduce from +those laws with a considerable approach to certainty, the particular +type of character which would be formed, in mankind generally, by any +assumed set of circumstances. A science of Ethology, founded on the laws +of Psychology, is therefore possible; though little has yet been done, +and that little not at all systematically, towards forming it. The +progress of this important but most imperfect science will depend on a +double process: first, that of deducing theoretically the ethological +consequences of particular circumstances of position, and comparing them +with the recognised results of common experience; and secondly, the +reverse operation; increased study of the various types of human nature +that are to be found in the world; conducted by persons not only capable +of analysing and recording the circumstances in which these types +severally prevail, but also sufficiently acquainted with psychological +laws, to be able to explain and account for the characteristics of the +type, by the peculiarities of the circumstances: the residuum alone, +when there proves to be any, being set down to the account of congenital +predispositions.</p> + +<p>For the experimental or <i>à posteriori</i> part of this process, the +materials are continually accumulating by the observation of mankind. So +far as thought is concerned, the great problem of Ethology is to deduce +the requisite middle principles <span class="pagenum"><a name="Page_460" id="Page_460">[Pg 460]</a></span>from the general laws of Psychology. +The subject to be studied is, the origin and sources of all those +qualities in human beings which are interesting to us, either as facts +to be produced, to be avoided, or merely to be understood: and the +object is, to determine, from the general laws of mind, combined with +the general position of our species in the universe, what actual or +possible combinations of circumstances are capable of promoting or of +preventing the production of those qualities. A science which possesses +middle principles of this kind, arranged in the order, not of causes, +but of the effects which it is desirable to produce or to prevent, is +duly prepared to be the foundation of the corresponding Art. And when +Ethology shall be thus prepared, practical education will be the mere +transformation of those principles into a parallel system of precepts, +and the adaptation of these to the sum total of the individual +circumstances which exist in each particular case.</p> + +<p>It is hardly necessary again to repeat, that, as in every other +deductive science, verification <i>à posteriori</i> must proceed <i>pari passu</i> +with deduction <i>à priori</i>. The inference given by theory as to the type +of character which would be formed by any given circumstances, must be +tested by specific experience of those circumstances whenever +obtainable; and the conclusions of the science as a whole, must undergo +a perpetual verification and correction from the general remarks +afforded by common experience respecting human nature in our own age, +and by history respecting times gone by. The conclusions of theory +cannot be trusted, unless confirmed by observation; nor those of +observation, unless they can be affiliated to theory, by deducing them +from the laws of human nature, and from a close analysis of the +circumstances of the particular situation. It is the accordance of these +two kinds of evidence separately taken—the consilience of <i>à priori</i> +reasoning and specific experience—which forms the only sufficient +ground for the principles of any science so "immersed in matter," +dealing with such complex and concrete phenomena, as Ethology.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_461" id="Page_461">[Pg 461]</a></span></p> +<h3><a name="BOOK_VI_CHAPTER_VI" id="BOOK_VI_CHAPTER_VI"></a>CHAPTER VI.<br /> +GENERAL CONSIDERATIONS ON THE SOCIAL SCIENCE.</h3> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_VI_1">§ 1.</a> Next after the science of individual man, comes the science of man +in society: of the actions of collective masses of mankind, and the +various phenomena which constitute social life.</p> + +<p>If the formation of individual character is already a complex subject of +study, this subject must be, in appearance at least, still more complex; +because the number of concurrent causes, all exercising more or less +influence on the total effect, is greater, in the proportion in which a +nation, or the species at large, exposes a larger surface to the +operation of agents, psychological and physical, than any single +individual. If it was necessary to prove, in opposition to an existing +prejudice, that the simpler of the two is capable of being a subject of +science; the prejudice is likely to be yet stronger against the +possibility of giving a scientific character to the study of Politics, +and of the phenomena of Society. It is, accordingly, but of yesterday +that the conception of a political or social science has existed, +anywhere but in the mind of here and there an insulated thinker, +generally very ill prepared for its realization: though the subject +itself has of all others engaged the most general attention, and been a +theme of interested and earnest discussions, almost from the beginning +of recorded time.</p> + +<p>The condition indeed of politics, as a branch of knowledge, was until +very lately, and has scarcely even yet ceased to be, that which Bacon +animadverted on, as the natural state of the sciences while their +cultivation is abandoned to practitioners; not being carried on as a +branch of speculative inquiry, but only with a view to the exigencies of +daily practice, <span class="pagenum"><a name="Page_462" id="Page_462">[Pg 462]</a></span>and the <i>fructifera experimenta</i>, therefore, being +aimed at, almost to the exclusion of the <i>lucifera</i>. Such was medical +investigation, before physiology and natural history began to be +cultivated as branches of general knowledge. The only questions examined +were, what diet is wholesome, or what medicine will cure some given +disease; without any previous systematic inquiry into the laws of +nutrition, and of the healthy and morbid action of the different organs, +on which laws the effect of any diet or medicine must evidently depend. +And in politics, the questions which engaged general attention were +similar:—Is such an enactment, or such a form of government, beneficial +or the reverse—either universally, or to some particular community? +without any previous inquiry into the general conditions by which the +operation of legislative measures, or the effects produced by forms of +government, are determined. Students in politics thus attempted to study +the pathology and therapeutics of the social body, before they had laid +the necessary foundation in its physiology; to cure disease, without +understanding the laws of health. And the result was such as it must +always be when persons, even of ability, attempt to deal with the +complex questions of a science before its simpler and more elementary +truths have been established.</p> + +<p>No wonder that when the phenomena of society have so rarely been +contemplated in the point of view characteristic of science, the +philosophy of society should have made little progress; should contain +few general propositions sufficiently precise and certain, for common +inquirers to recognise in them a scientific character. The vulgar notion +accordingly is, that all pretension to lay down general truths on +politics and society is quackery; that no universality and no certainty +are attainable in such matters. What partly excuses this common notion +is, that it is really not without foundation in one particular sense. A +large proportion of those who have laid claim to the character of +philosophic politicians, have attempted, not to ascertain universal +sequences, but to frame universal precepts. They have imagined some one +form of government, or system of laws, to fit all cases; a pretension +<span class="pagenum"><a name="Page_463" id="Page_463">[Pg 463]</a></span>well meriting the ridicule with which it is treated by practitioners, +and wholly unsupported by the analogy of the art to which, from the +nature of its subject, that of politics must be the most nearly allied. +No one now supposes it possible that one remedy can cure all diseases, +or even the same disease in all constitutions and habits of body.</p> + +<p>It is not necessary even to the perfection of a science, that the +corresponding art should possess universal, or even general, rules. The +phenomena of society might not only be completely dependent on known +causes, but the mode of action of all those causes might be reducible to +laws of considerable simplicity, and yet no two cases might admit of +being treated in precisely the same manner. So great might be the +variety of circumstances on which the results in different cases depend, +that the art might not have a single general precept to give, except +that of watching the circumstances of the particular case, and adapting +our measures to the effects which, according to the principles of the +science, result from those circumstances. But although, in so +complicated a class of subjects, it is impossible to lay down practical +maxims of universal application, it does not follow that the phenomena +do not conform to universal laws.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_VI_2">§ 2.</a> All phenomena of society are phenomena of human nature, generated +by the action of outward circumstances upon masses of human beings: and +if, therefore, the phenomena of human thought, feeling, and action, are +subject to fixed laws, the phenomena of society cannot but conform to +fixed laws, the consequence of the preceding. There is, indeed, no hope +that these laws, though our knowledge of them were as certain and as +complete as it is in astronomy, would enable us to predict the history +of society, like that of the celestial appearances, for thousands of +years to come. But the difference of certainty is not in the laws +themselves, it is in the data to which these laws are to be applied. In +astronomy the causes influencing the result are few, and change little, +and that little according to known laws; we can ascertain what they are +now, and thence determine what they will <span class="pagenum"><a name="Page_464" id="Page_464">[Pg 464]</a></span>be at any epoch of a distant +future. The data, therefore, in astronomy, are as certain as the laws +themselves. The circumstances, on the contrary, which influence the +condition and progress of society, are innumerable, and perpetually +changing; and though they all change in obedience to causes, and +therefore to laws, the multitude of the causes is so great as to defy +our limited powers of calculation. Not to say that the impossibility of +applying precise numbers to facts of such a description, would set an +impassable limit to the possibility of calculating them beforehand, even +if the powers of the human intellect were otherwise adequate to the +task.</p> + +<p>But, as before remarked, an amount of knowledge quite insufficient for +prediction, may be most valuable for guidance. The science of society +would have attained a very high point of perfection, if it enabled us, +in any given condition of social affairs, in the condition for instance +of Europe or any European country at the present time, to understand by +what causes it had, in any and every particular, been made what it was; +whether it was tending to any, and to what, changes; what effects each +feature of its existing state was likely to produce in the future; and +by what means any of those effects might be prevented, modified, or +accelerated, or a different class of effects superinduced. There is +nothing chimerical in the hope that general laws, sufficient to enable +us to answer these various questions for any country or time with the +individual circumstances of which we are well acquainted, do really +admit of being ascertained; and that the other branches of human +knowledge, which this undertaking presupposes, are so far advanced that +the time is ripe for its commencement. Such is the object of the Social +Science.</p> + +<p>That the nature of what I consider the true method of the science may be +made more palpable, by first showing what that method is not; it will be +expedient to characterize briefly two radical misconceptions of the +proper mode of philosophizing on society and government, one or other of +which is, either explicitly or more often unconsciously, entertained by +almost all who have meditated or argued respecting <span class="pagenum"><a name="Page_465" id="Page_465">[Pg 465]</a></span>the logic of +politics since the notion of treating it by strict rules, and on +Baconian principles, has been current among the more advanced thinkers. +These erroneous methods, if the word method can be applied to erroneous +tendencies arising from the absence of any sufficiently distinct +conception of method, may be termed the Experimental, or Chemical, mode +of investigation, and the Abstract, or Geometrical, mode. We shall begin +with the former.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_466" id="Page_466">[Pg 466]</a></span></p> +<h3><a name="BOOK_VI_CHAPTER_VII" id="BOOK_VI_CHAPTER_VII"></a>CHAPTER VII.<br /> +OF THE CHEMICAL, OR EXPERIMENTAL, METHOD IN THE SOCIAL SCIENCE.</h3> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_VII_1">§ 1.</a> The laws of the phenomena of society are, and can be, nothing but +the laws of the actions and passions of human beings united together in +the social state. Men, however, in a state of society, are still men; +their actions and passions are obedient to the laws of individual human +nature. Men are not, when brought together, converted into another kind +of substance, with different properties; as hydrogen and oxygen are +different from water, or as hydrogen, oxygen, carbon, and azote, are +different from nerves, muscles, and tendons. Human beings in society +have no properties but those which are derived from, and may be resolved +into, the laws of the nature of individual man. In social phenomena the +Composition of Causes is the universal law.</p> + +<p>Now, the method of philosophizing which may be termed chemical overlooks +this fact, and proceeds as if the nature of man as an individual were +not concerned at all, or were concerned in a very inferior degree, in +the operations of human beings in society. All reasoning in political or +social affairs, grounded on principles of human nature, is objected to +by reasoners of this sort, under such names as "abstract theory." For +the direction of their opinions and conduct, they profess to demand, in +all cases without exception, specific experience.</p> + +<p>This mode of thinking is not only general with practitioners in +politics, and with that very numerous class who (on a subject which no +one, however ignorant, thinks himself incompetent to discuss) profess to +guide themselves by common sense rather than by science; but is often +countenanced by persons with greater pretensions to instruction; persons +who, having sufficient acquaintance with books and with the current +<span class="pagenum"><a name="Page_467" id="Page_467">[Pg 467]</a></span>ideas to have heard that Bacon taught mankind to follow experience, and +to ground their conclusions on facts instead of metaphysical +dogmas—think that, by treating political facts in as directly +experimental a method as chemical facts, they are showing themselves +true Baconians, and proving their adversaries to be mere syllogizers and +schoolmen. As, however, the notion of the applicability of experimental +methods to political philosophy cannot coexist with any just conception +of these methods themselves, the kind of arguments from experience which +the chemical theory brings forth as its fruits (and which form the +staple, in this country especially, of parliamentary and hustings +oratory,) are such as, at no time since Bacon, would have been admitted +to be valid in chemistry itself, or in any other branch of experimental +science. They are such as these; that the prohibition of foreign +commodities must conduce to national wealth, because England has +flourished under it, or because countries in general which have adopted +it have flourished; that our laws, or our internal administration, or +our constitution, are excellent for a similar reason: and the eternal +arguments from historical examples, from Athens or Rome, from the fires +in Smithfield or the French Revolution.</p> + +<p>I will not waste time in contending against modes of argumentation which +no person, with the smallest practice in estimating evidence, could +possibly be betrayed into; which draw conclusions of general application +from a single unanalysed instance, or arbitrarily refer an effect to +some one among its antecedents, without any process of elimination or +comparison of instances. It is a rule both of justice and of good sense +to grapple not with the absurdest, but with, the most reasonable form of +a wrong opinion. We shall suppose our inquirer acquainted with the true +conditions of experimental investigation, and competent in point of +acquirements for realizing them, so far as they can be realized. He +shall know as much of the facts of history as mere erudition can +teach—as much as can be proved by testimony, without the assistance of +any theory; and if those mere facts, properly collated, can fulfil the +conditions of a real induction, he shall be qualified for the task.</p> + +<p><span class="pagenum"><a name="Page_468" id="Page_468">[Pg 468]</a></span></p><p>But, that no such attempt can have the smallest chance of success, has +been abundantly shown in the tenth chapter of the Third Book.<a name="FNanchor_7_113" id="FNanchor_7_113"></a><a href="#Footnote_7_113" class="fnanchor">[7]</a> We +there examined whether effects which depend on a complication of causes +can be made the subject of a true induction by observation and +experiment; and concluded, on the most convincing grounds, that they +cannot. Since, of all effects, none depend on so great a complication of +causes as social phenomena, we might leave our case to rest in safety on +that previous showing. But a logical principle as yet so little familiar +to the ordinary run of thinkers, requires to be insisted on more than +once, in order to make the due impression; and the present being the +case which of all others exemplifies it the most strongly, there will be +advantage in re-stating the grounds of the general maxim, as applied to +the specialities of the class of inquiries now under consideration.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_VII_2">§ 2.</a> The first difficulty which meets us in the attempt to apply +experimental methods for ascertaining the laws of social phenomena, is +that we are without the means of making artificial experiments. Even if +we could contrive experiments at leisure, and try them without limit, we +should do so under immense disadvantage; both from the impossibility of +ascertaining and taking note of all the facts of each case, and because +(those facts being in a perpetual state of change) before sufficient +time had elapsed to ascertain the result of the experiment, some +material circumstances would always have ceased to be the same. But it +is unnecessary to consider the logical objections which would exist to +the conclusiveness of our experiments, since we palpably never have the +power of trying any. We can only watch those which nature produces, or +which are produced for other reasons. We cannot adapt our logical means +to our wants, by varying the circumstances as the exigencies of +elimination may require. If the spontaneous instances, formed by +cotemporary events and by the successions of phenomena recorded in +history, afford a sufficient <span class="pagenum"><a name="Page_469" id="Page_469">[Pg 469]</a></span>variation of circumstances, an induction +from specific experience is attainable; otherwise not. The question to +be resolved is, therefore, whether the requisites for induction +respecting the causes of political effects or the properties of +political agents, are to be met with in history? including under the +term, cotemporary history. And in order to give fixity to our +conceptions, it will be advisable to suppose this question asked in +reference to some special subject of political inquiry or controversy; +such as that frequent topic of debate in the present century, the +operation of restrictive and prohibitory commercial legislation upon +national wealth. Let this, then, be the scientific question to be +investigated by specific experience.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_VII_3">§ 3.</a> In order to apply to the case the most perfect of the methods of +experimental inquiry, the Method of Difference, we require to find two +instances, which tally in every particular except the one which is the +subject of inquiry. If two nations can be found which are alike in all +natural advantages and disadvantages; whose people resemble each other +in every quality, physical and moral, spontaneous and acquired; whose +habits, usages, opinions, laws and institutions are the same in all +respects, except that one of them has a more protective tariff, or in +other respects interferes more with the freedom of industry; if one of +these nations is found to be rich, and the other poor, or one richer +than the other, this will be an <i>experimentum crucis</i>: a real proof by +experience, which of the two systems is most favourable to national +riches. But the supposition that two such instances can be met with is +manifestly absurd. Nor is such a concurrence even abstractly possible. +Two nations which agreed in everything except their commercial policy, +would agree also in that. Differences of legislation are not inherent +and ultimate diversities; are not properties of Kinds. They are effects +of pre-existing causes. If the two nations differ in this portion of +their institutions, it is from some difference in their position, and +thence in their apparent interests, or in some portion or other of their +opinions, habits, and tendencies; which opens a view <span class="pagenum"><a name="Page_470" id="Page_470">[Pg 470]</a></span>of further +differences without any assignable limit, capable of operating on their +industrial prosperity, as well as on every other feature of their +condition, in more ways than can be enumerated or imagined. There is +thus a demonstrated impossibility of obtaining, in the investigations of +the social science, the conditions required for the most conclusive form +of inquiry by specific experience.</p> + +<p>In the absence of the direct, we may next try, as in other cases, the +supplementary resource, called in a former place the Indirect Method of +Difference: which, instead of two instances differing in nothing but the +presence or absence of a given circumstance, compares two <i>classes</i> of +instances respectively agreeing in nothing but the presence of a +circumstance on the one side and its absence on the other. To choose the +most advantageous case conceivable, (a case far too advantageous to be +ever obtained,) suppose that we compare one nation which has a +restrictive policy, with two or more nations agreeing in nothing but in +permitting free trade. We need not now suppose that either of these +nations agrees with the first in all its circumstances; one may agree +with it in some of its circumstances, and another in the remainder. And +it may be argued, that if these nations remain poorer than the +restrictive nation, it cannot be for want either of the first or of the +second set of circumstances, but it must be for want of the protective +system. If (we might say) the restrictive nation had prospered from the +one set of causes, the first of the free-trade nations would have +prospered equally; if by reason of the other, the second would: but +neither has: therefore the prosperity was owing to the restrictions. +This will be allowed to be a very favourable specimen of an argument +from specific experience in politics, and if this be inconclusive, it +would not be easy to find another preferable to it.</p> + +<p>Yet, that it is inconclusive, scarcely requires to be pointed out. Why +must the prosperous nation have prospered from one cause exclusively? +National prosperity is always the collective result of a multitude of +favourable circumstances; and of these, the restrictive nation may unite +a greater number <span class="pagenum"><a name="Page_471" id="Page_471">[Pg 471]</a></span>than either of the others, though it may have all of +those circumstances in common with either one or the other of them. Its +prosperity may be partly owing to circumstances common to it with one of +those nations, and partly with the other, while they, having each of +them only half the number of favourable circumstances, have remained +inferior. So that the closest imitation which can be made, in the social +science, of a legitimate induction from direct experience, gives but a +specious semblance of conclusiveness, without any real value.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_VII_4">§ 4.</a> The Method of Difference in either of its forms being thus +completely out of the question, there remains the Method of Agreement. +But we are already aware of how little value this method is, in cases +admitting Plurality of Causes: and social phenomena are those in which +the plurality prevails in the utmost possible extent.</p> + +<p>Suppose that the observer makes the luckiest hit which could be given by +any conceivable combination of chances: that he finds two nations which +agree in no circumstance whatever, except in having a restrictive +system, and in being prosperous; or a number of nations, all prosperous, +which have no antecedent circumstances common to them all but that of +having a restrictive policy. It is unnecessary to go into the +consideration of the impossibility of ascertaining from history, or even +from cotemporary observation, that such is really the fact: that the +nations agree in no other circumstance capable of influencing the case. +Let us suppose this impossibility vanquished, and the fact ascertained +that they agree only in a restrictive system as an antecedent, and +industrial prosperity as a consequent. What degree of presumption does +this raise, that the restrictive system caused the prosperity? One so +trifling as to be equivalent to none at all. That some one antecedent is +the cause of a given effect, because all other antecedents have been +found capable of being eliminated, is a just inference, only if the +effect can have but one cause. If it admits of several, nothing is more +natural than that each of these should separately admit of being +<span class="pagenum"><a name="Page_472" id="Page_472">[Pg 472]</a></span>eliminated. Now, in the case of political phenomena, the supposition of +unity of cause is not only wide of the truth, but at an immeasurable +distance from it. The causes of every social phenomenon which we are +particularly interested about, security, wealth, freedom, good +government, public virtue, general intelligence, or their opposites, are +infinitely numerous: especially the external or remote causes, which +alone are, for the most part, accessible to direct observation. No one +cause suffices of itself to produce any of these phenomena; while there +are countless causes which have some influence over them, and may +co-operate either in their production or in their prevention. From the +mere fact, therefore, of our having been able to eliminate some +circumstance, we can by no means infer that this circumstance was not +instrumental to the effect in some of the very instances from which we +have eliminated it. We can conclude that the effect is sometimes +produced without it; but not that, when present, it does not contribute +its share.</p> + +<p>Similar objections will be found to apply to the Method of Concomitant +Variations. If the causes which act upon the state of any society +produced effects differing from one another in kind; if wealth depended +on one cause, peace on another, a third made people virtuous, a fourth +intelligent; we might, though unable to sever the causes from one +another, refer to each of them that property of the effect which waxed +as it waxed, and which waned as it waned. But every attribute of the +social body is influenced by innumerable causes; and such is the mutual +action of the coexisting elements of society, that whatever affects any +one of the more important of them, will by that alone, if it does not +affect the others directly, affect them indirectly. The effects, +therefore, of different agents not being different in quality, while the +quantity of each is the mixed result of all the agents, the variations +of the aggregate cannot bear an uniform proportion to those of any one +of its component parts.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_VII_5">§ 5.</a> There remains the Method of Residues; which appears, on the first +view, less foreign to this kind of inquiry <span class="pagenum"><a name="Page_473" id="Page_473">[Pg 473]</a></span>than the three other +methods, because it only requires that we should accurately note the +circumstances of some one country, or state of society. Making +allowance, thereupon, for the effect of all causes whose tendencies are +known, the residue which those causes are inadequate to explain may +plausibly be imputed to the remainder of the circumstances which are +known to have existed in the case. Something similar to this is the +method which Coleridge<a name="FNanchor_8_114" id="FNanchor_8_114"></a><a href="#Footnote_8_114" class="fnanchor">[8]</a> describes himself as having followed in his +political essays in the <i>Morning Post</i>. "On every great occurrence I +endeavoured to discover in past history the event that most nearly +resembled it. I procured, whenever it was possible, the contemporary +historians, memorialists, and pamphleteers. Then fairly subtracting the +points of difference from those of likeness, as the balance favoured the +former or the latter, I conjectured that the result would be the same or +different. As, for instance, in the series of essays entitled 'A +comparison of France under Napoleon with Rome under the first Cæsars,' +and in those which followed, 'on the probable final restoration of the +Bourbons.' The same plan I pursued at the commencement of the Spanish +Revolution, and with the same success, taking the war of the United +Provinces with Philip II. as the groundwork of the comparison." In this +inquiry he no doubt employed the Method of Residues; for, in +"subtracting the points of difference from those of likeness," he +doubtless weighed, and did not content himself with numbering, them: he +doubtless took those points of agreement only, which he presumed from +their own nature to be capable of influencing the effect, and, allowing +for that influence, concluded that the remainder of the result would be +referable to the points of difference.</p> + +<p>Whatever may be the efficacy of this method, it is, as we long ago +remarked, not a method of pure observation and experiment; it concludes, +not from a comparison of instances, but from the comparison of an +instance with the result of a previous deduction. Applied to social +phenomena, it presupposes <span class="pagenum"><a name="Page_474" id="Page_474">[Pg 474]</a></span>that the causes from which part of the effect +proceeded are already known; and as we have shown that these cannot have +been known by specific experience, they must have been learnt by +deduction from principles of human nature; experience being called in +only as a supplementary resource, to determine the causes which produced +an unexplained residue. But if the principles of human nature may be had +recourse to for the establishment of some political truths, they may for +all. If it be admissible to say, England must have prospered by reason +of the prohibitory system, because after allowing for all the other +tendencies which have been operating, there is a portion of prosperity +still to be accounted for; it must be admissible to go to the same +source for the effect of the prohibitory system, and examine what +account the laws of human motives and actions will enable us to give of +<i>its</i> tendencies. Nor, in fact, will the experimental argument amount to +anything, except in verification of a conclusion drawn from those +general laws. For we may subtract the effect of one, two, three, or four +causes, but we shall never succeed in subtracting the effect of all +causes except one: while it would be a curious instance of the dangers +of too much caution, if, to avoid depending on <i>à priori</i> reasoning +concerning the effect of a single cause, we should oblige ourselves to +depend on as many separate <i>à priori</i> reasonings as there are causes +operating concurrently with that particular cause in some given +instance.</p> + +<p>We have now sufficiently characterized the gross misconception of the +mode of investigation proper to political phenomena, which I have termed +the Chemical Method. So lengthened a discussion would not have been +necessary, if the claim to decide authoritatively on political doctrines +were confined to persons who had competently studied any one of the +higher departments of physical science. But since the generality of +those who reason on political subjects, satisfactorily to themselves and +to a more or less numerous body of admirers, know nothing whatever of +the methods of physical investigation beyond a few precepts which they +continue to parrot after Bacon, being entirely unaware that Bacon's +conception <span class="pagenum"><a name="Page_475" id="Page_475">[Pg 475]</a></span>of scientific inquiry has done its work, and that science +has now advanced into a higher stage; there are probably many to whom +such remarks as the foregoing may still be useful. In an age in which +chemistry itself, when attempting to deal with the more complex chemical +sequences, those of the animal or even the vegetable organism, has found +it necessary to become, and has succeeded in becoming, a Deductive +Science—it is not to be apprehended that any person of scientific +habits, who has kept pace with the general progress of the knowledge of +nature, can be in danger of applying the methods of elementary chemistry +to explore the sequences of the most complex order of phenomena in +existence.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_476" id="Page_476">[Pg 476]</a></span></p> +<h3><a name="BOOK_VI_CHAPTER_VIII" id="BOOK_VI_CHAPTER_VIII"></a>CHAPTER VIII.<br /> +OF THE GEOMETRICAL, OR ABSTRACT METHOD.</h3> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_VIII_1">§ 1.</a> The misconception discussed in the preceding chapter is, as we +said, chiefly committed by persons not much accustomed to scientific +investigation: practitioners in politics, who rather employ the +commonplaces of philosophy to justify their practice, than seek to guide +their practice by philosophic principles: or imperfectly educated +persons, who, in ignorance of the careful selection and elaborate +comparison of instances required for the formation of a sound theory, +attempt to found one upon a few coincidences which they have casually +noticed.</p> + +<p>The erroneous method of which we are now to treat, is, on the contrary, +peculiar to thinking and studious minds. It never could have suggested +itself but to persons of some familiarity with the nature of scientific +research; who,—being aware of the impossibility of establishing, by +casual observation or direct experimentation, a true theory of sequences +so complex as are those of the social phenomena,—have recourse to the +simpler laws which are immediately operative in those phenomena, and +which are no other than the laws of the nature of the human beings +therein concerned. These thinkers perceive (what the partisans of the +chemical or experimental theory do not) that the science of society must +necessarily be deductive. But, from an insufficient consideration of the +specific nature of the subject matter,—and often because (their own +scientific education having stopped short in too early a stage) geometry +stands in their minds as the type of all deductive science, it is to +geometry rather than to astronomy and natural philosophy, that they +unconsciously assimilate the deductive science of society.</p> + +<p><span class="pagenum"><a name="Page_477" id="Page_477">[Pg 477]</a></span></p><p>Among the differences between geometry (a science of coexistent facts, +altogether independent of the laws of the succession of phenomena), and +those physical Sciences of Causation which have been rendered deductive, +the following is one of the most conspicuous: That geometry affords no +room for what so constantly occurs in mechanics and its applications, +the case of conflicting forces; of causes which counteract or modify one +another. In mechanics we continually find two or more moving forces +producing, not motion, but rest; or motion in a different direction from +that which would have been produced by either of the generating forces. +It is true that the effect of the joint forces is the same when they act +simultaneously, as if they had acted one after another, or by turns; and +it is in this that the difference between mechanical and chemical laws +consists. But still the effects, whether produced by successive or by +simultaneous action, do, wholly or in part, cancel one another: what the +one force does, the other, partly or altogether, undoes. There is no +similar state of things in geometry. The result which follows from one +geometrical principle has nothing that conflicts with the result which +follows from another. What is proved true from one geometrical theorem, +what would be true if no other geometrical principles existed, cannot be +altered and made no longer true by reason of some other geometrical +principle. What is once proved true is true in all cases, whatever +supposition may be made in regard to any other matter.</p> + +<p>Now a conception, similar to this last, would appear to have been formed +of the social science, in the minds of the earlier of those who have +attempted to cultivate it by a deductive method. Mechanics would be a +science very similar to geometry, if every motion resulted from one +force alone, and not from a conflict of forces. In the geometrical +theory of society, it seems to be supposed that this is really the case +with the social phenomena; that each of them results always from only +one force, one single property of human nature.</p> + +<p>At the point which we have now reached, it cannot be <span class="pagenum"><a name="Page_478" id="Page_478">[Pg 478]</a></span>necessary to say +anything either in proof or in illustration of the assertion that such +is not the true character of the social phenomena. There is not, among +these most complex and (for that reason) most modifiable of all +phenomena, any one over which innumerable forces do not exercise +influence; which does not depend on a conjunction of very many causes. +We have not, therefore, to prove the notion in question to be an error, +but to prove that the error has been committed; that so mistaken a +conception of the mode in which the phenomena of society are produced, +has actually been ascertained.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_VIII_2">§ 2.</a> One numerous division of the reasoners who have treated social +facts according to geometrical methods, not admitting any modification +of one law by another, must for the present be left out of +consideration; because in them this error is complicated with, and is +the effect of, another fundamental misconception, of which we have +already taken some notice, and which will be further treated of before +we conclude. I speak of those who deduce political conclusions not from +laws of nature, not from sequences of phenomena, real or imaginary, but +from unbending practical maxims. Such, for example, are all who found +their theory of politics on what is called abstract right, that is to +say, on universal precepts; a pretension of which we have already +noticed the chimerical nature. Such, in like manner, are those who make +the assumption of a social contract, or any other kind of original +obligation, and apply it to particular cases by mere interpretation. But +in this the fundamental error is the attempt to treat an art like a +science, and to have a deductive art; the irrationality of which will be +shown in a future chapter. It will be proper to take our exemplification +of the geometrical theory from those thinkers who have avoided this +additional error, and who entertain, so far, a juster idea of the nature +of political inquiry.</p> + +<p>We may cite, in the first instance, those who assume as the principle of +their political philosophy that government is <span class="pagenum"><a name="Page_479" id="Page_479">[Pg 479]</a></span>founded on fear; that the +dread of each other is the one motive by which human beings were +originally brought into a state of society, and are still held in it. +Some of the earlier scientific inquirers into politics, in particular +Hobbes, assumed this proposition, not by implication, but avowedly, as +the foundation of their doctrine, and attempted to build a complete +philosophy of politics thereupon. It is true that Hobbes did not find +this one maxim sufficient to carry him through the whole of his subject, +but was obliged to eke it out by the double sophism of an original +contract. I call this a double sophism; first, as passing off a fiction +for a fact, and, secondly, assuming a practical principle, or precept, +as the basis of a theory; which is a <i>petitio principii</i>, since (as we +noticed in treating of that Fallacy) every rule of conduct, even though +it be so binding a one as the observance of a promise, must rest its own +foundations on the theory of the subject, and the theory, therefore, +cannot rest upon it.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_VIII_3">§ 3.</a> Passing over less important instances, I shall come at once to the +most remarkable example afforded by our own times of the geometrical +method in politics; emanating from persons who were well aware of the +distinction between science and art; who knew that rules of conduct must +follow, not precede, the ascertainment of laws of nature, and that the +latter, not the former, is the legitimate field for the application of +the deductive method. I allude to the interest-philosophy of the Bentham +school.</p> + +<p>The profound and original thinkers who are commonly known under this +description, founded their general theory of government on one +comprehensive premise, namely, that men's actions are always determined +by their interests. There is an ambiguity in this last expression; for, +as the same philosophers, especially Bentham, gave the name of an +interest to anything which a person likes, the proposition may be +understood to mean only this, that men's actions are always determined +by their wishes. In this sense, however, it would not bear out any of +the consequences which these writers drew <span class="pagenum"><a name="Page_480" id="Page_480">[Pg 480]</a></span>from it; and the word, +therefore, in their political reasonings, must be understood to mean +(which is also the explanation they themselves, on such occasions, gave +of it) what is commonly termed private, or worldly, interest.</p> + +<p>Taking the doctrine, then, in this sense, an objection presents itself +<i>in limine</i> which might be deemed a fatal one, namely, that so sweeping +a proposition is far from being universally true. Human beings are not +governed in all their actions by their worldly interests. This, however, +is by no means so conclusive an objection as it at first appears; +because in politics we are for the most part concerned with the conduct +not of individual persons, but either of a series of persons (as a +succession of kings) or a body or mass of persons, as a nation, an +aristocracy, or a representative assembly. And whatever is true of a +large majority of mankind, may without much error be taken for true of +any succession of persons, considered as a whole, or of any collection +of persons in which the act of the majority becomes the act of the whole +body. Although, therefore, the maxim is sometimes expressed in a manner +unnecessarily paradoxical, the consequences drawn from it will hold +equally good if the assertion be limited as follows—Any succession of +persons, or the majority of any body of persons, will be governed in the +bulk of their conduct by their personal interests. We are bound to allow +to this school of thinkers the benefit of this more rational statement +of their fundamental maxim, which is also in strict conformity to the +explanations which, when considered to be called for, have been given by +themselves.</p> + +<p>The theory goes on to infer, quite correctly, that if the actions of +mankind are determined in the main by their selfish interests, the only +rulers who will govern according to the interest of the governed, are +those whose selfish interests are in accordance with it. And to this is +added a third proposition, namely, that no rulers have their selfish +interest identical with that of the governed, unless it be rendered so +by accountability, that is, by dependence on the will of the governed. +In other words (and as the result of the whole), that the desire of +retaining or the fear of losing their power, and whatever is <span class="pagenum"><a name="Page_481" id="Page_481">[Pg 481]</a></span>thereon +consequent, is the sole motive which can be relied on for producing on +the part of rulers a course of conduct in accordance with the general +interest.</p> + +<p>We have thus a fundamental theorem of political science, consisting of +three syllogisms, and depending chiefly on two general premises, in each +of which a certain effect is considered as determined only by one cause, +not by a concurrence of causes. In the one, it is assumed that the +actions of average rulers are determined solely by self-interest; in the +other, that the sense of identity of interest with the governed, is +produced and producible by no other cause than responsibility.</p> + +<p>Neither of these propositions is by any means true; the last is +extremely wide of the truth.</p> + +<p>It is not true that the actions even of average rulers are wholly, or +anything approaching to wholly, determined by their personal interest, +or even by their own opinion of their personal interest. I do not speak +of the influence of a sense of duty, or feelings of philanthropy, +motives never to be mainly relied on, though (except in countries or +during periods of great moral debasement) they influence almost all +rulers in some degree, and some rulers in a very great degree. But I +insist only on what is true of all rulers, viz. that the character and +course of their actions is largely influenced (independently of personal +calculation) by the habitual sentiments and feelings, the general modes +of thinking and acting, which prevail throughout the community of which +they are members; as well as by the feelings, habits, and modes of +thought which characterize the particular class in that community to +which they themselves belong. And no one will understand or be able to +decypher their system of conduct, who does not take all these things +into account. They are also much influenced by the maxims and traditions +which have descended to them from other rulers, their predecessors; +which maxims and traditions have been known to retain an ascendancy +during long periods, even in opposition to the private interests of the +rulers for the time being. I put aside the influence of other less +general causes. Although, therefore, <span class="pagenum"><a name="Page_482" id="Page_482">[Pg 482]</a></span>the private interest of the rulers +or of the ruling class is a very powerful force, constantly in action, +and exercising the most important influence upon their conduct; there is +also, in what they do, a large portion which that private interest by no +means affords a sufficient explanation of: and even the particulars +which constitute the goodness or badness of their government, are in +some, and no small degree, influenced by those among the circumstances +acting upon them, which cannot, with any propriety, be included in the +term self-interest.</p> + +<p>Turning now to the other proposition, that responsibility to the +governed is the only cause capable of producing in the rulers a sense of +identity of interest with the community; this is still less admissible +as an universal truth, than even the former. I am not speaking of +perfect identity of interest, which is an impracticable chimera; which, +most assuredly, responsibility to the people does not give. I speak of +identity in essentials; and the essentials are different at different +places and times. There are a large number of cases in which those +things which it is most for the general interest that the rulers should +do, are also those which they are prompted to do by their strongest +personal interest, the consolidation of their power. The suppression, +for instance, of anarchy and resistance to law,—the complete +establishment of the authority of the central government, in a state of +society like that of Europe in the middle ages,—is one of the strongest +interests of the people, and also of the rulers simply because they are +the rulers: and responsibility on their part could not strengthen, +though in many conceivable ways it might weaken, the motives prompting +them to pursue this object. During the greater part of the reign of +Queen Elizabeth, and of many other monarchs who might be named, the +sense of identity of interest between the sovereign and the majority of +the people was probably stronger than it usually is in responsible +governments: everything that the people had most at heart, the monarch +had at heart too. Had Peter the Great, or the rugged savages whom he +began to civilize, the truest inclination <span class="pagenum"><a name="Page_483" id="Page_483">[Pg 483]</a></span>towards the things which were +for the real interest of those savages?</p> + +<p>I am not here attempting to establish a theory of government, and am not +called upon to determine the proportional weight which ought to be given +to the circumstances which this school of geometrical politicians left +out of their system, and those which they took into it. I am only +concerned to show that their method was unscientific; not to measure the +amount of error which may have affected their practical conclusions.</p> + +<p>It is but justice to them, however, to remark, that their mistake was +not so much one of substance as of form; and consisted in presenting in +a systematic shape, and as the scientific treatment of a great +philosophical question, what should have passed for that which it really +was, the mere polemics of the day. Although the actions of rulers are by +no means wholly determined by their selfish interests, it is chiefly as +a security against those selfish interests that constitutional checks +are required; and for that purpose such checks, in England, and the +other nations of modern Europe, can in no manner be dispensed with. It +is likewise true, that in these same nations, and in the present age, +responsibility to the governed is the only means practically available +to create a feeling of identity of interest, in the cases, and on the +points, where that feeling does not sufficiently exist. To all this, and +to the arguments which may be founded on it in favour of measures for +the correction of our representative system, I have nothing to object; +but I confess my regret, that the small though highly important portion +of the philosophy of government, which was wanted for the immediate +purpose of serving the cause of parliamentary reform, should have been +held forth by thinkers of such eminence as a complete theory.</p> + +<p>It is not to be imagined possible, nor is it true in point of fact, that +these philosophers regarded the few premises of their theory as +including all that is required for explaining social phenomena, or for +determining the choice of forms of government <span class="pagenum"><a name="Page_484" id="Page_484">[Pg 484]</a></span>and measures of +legislation and administration. They were too highly instructed, of too +comprehensive intellect, and some of them of too sober and practical a +character, for such an error. They would have applied and did apply +their principles with innumerable allowances. But it is not allowances +that are wanted. There is little chance of making due amends in the +superstructure of a theory for the want of sufficient breadth in its +foundations. It is unphilosophical to construct a science out of a few +of the agencies by which the phenomena are determined, and leave the +rest to the routine of practice or the sagacity of conjecture. We either +ought not to pretend to scientific forms, or we ought to study all the +determining agencies equally, and endeavour, so far as it can be done, +to include all of them within the pale of the science; else we shall +infallibly bestow a disproportionate attention upon those which our +theory takes into account, while we misestimate the rest, and probably +underrate their importance. That the deductions should be from the whole +and not from a part only of the laws of nature that are concerned, would +be desirable even if those omitted were so insignificant in comparison +with the others, that they might, for most purposes and on most +occasions, be left out of the account. But this is far indeed from being +true in the social science. The phenomena of society do not depend, in +essentials, on some one agency or law of human nature, with only +inconsiderable modifications from others. The whole of the qualities of +human nature influence those phenomena, and there is not one which +influences them in a small degree. There is not one, the removal or any +great alteration of which would not materially affect the whole aspect +of society, and change more or less the sequences of social phenomena +generally.</p> + +<p>The theory which has been the subject of these remarks is in this +country at least, the principal cotemporary example of what I have +styled the geometrical method of philosophizing in the social science; +and our examination of it has, for this reason, been more detailed than +would otherwise have been suitable to a work like the present. Having +now sufficiently <span class="pagenum"><a name="Page_485" id="Page_485">[Pg 485]</a></span>illustrated the two erroneous methods, we shall pass +without further preliminary to the true method; that which proceeds +(conformably to the practice of the more complex physical sciences) +deductively indeed, but by deduction from many, not from one or a very +few, original premises; considering each effect as (what it really is) +an aggregate result of many causes, operating sometimes through the +same, sometimes through different mental agencies, or laws of human +nature.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_486" id="Page_486">[Pg 486]</a></span></p> +<h3><a name="BOOK_VI_CHAPTER_IX" id="BOOK_VI_CHAPTER_IX"></a>CHAPTER IX.<br /> +OF THE PHYSICAL, OR CONCRETE DEDUCTIVE METHOD.</h3> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_IX_1">§ 1.</a> After what has been said to illustrate the nature of the inquiry +into social phenomena, the general character of the method proper to +that inquiry is sufficiently evident, and needs only to be +recapitulated, not proved. However complex the phenomena, all their +sequences and coexistences result from the laws of the separate +elements. The effect produced, in social phenomena, by any complex set +of circumstances, amounts precisely to the sum of the effects of the +circumstances taken singly: and the complexity does not arise from the +number of the laws themselves, which is not remarkably great; but from +the extraordinary number and variety of the data or elements—of the +agents which, in obedience to that small number of laws, co-operate +towards the effect. The Social Science, therefore (which, by a +convenient barbarism, has been termed Sociology,) is a deductive +science; not, indeed, after the model of geometry, but after that of the +more complex physical sciences. It infers the law of each effect from +the laws of causation on which that effect depends; not, however, from +the law merely of one cause, as in the geometrical method; but by +considering all the causes which conjunctly influence the effect, and +compounding their laws with one another. Its method, in short, is the +Concrete Deductive Method; that of which astronomy furnishes the most +perfect, natural philosophy a somewhat less perfect example, and the +employment of which, with the adaptations and precautions required by +the subject, is beginning to regenerate physiology.</p> + +<p>Nor does it admit of doubt, that similar adaptations and precautions are +indispensable in sociology. In applying, to that most complex of all +studies, what is demonstrably the sole method capable of throwing the +light of science even upon <span class="pagenum"><a name="Page_487" id="Page_487">[Pg 487]</a></span>phenomena of a far inferior degree of +complication, we ought to be aware that the same superior complexity +which renders the instrument of Deduction more necessary, renders it +also more precarious; and we must be prepared to meet, by appropriate +contrivances, this increase of difficulty.</p> + +<p>The actions and feelings of human beings in the social state, are, no +doubt, entirely governed by psychological and ethological laws: whatever +influence any cause exercises upon the social phenomena, it exercises +through those laws. Supposing therefore the laws of human actions and +feelings to be sufficiently known, there is no extraordinary difficulty +in determining from those laws, the nature of the social effects which +any given cause tends to produce. But when the question is that of +compounding several tendencies together, and computing the aggregate +result of many coexistent causes; and especially when, by attempting to +predict what will actually occur in a given case, we incur the +obligation of estimating and compounding the influences of all the +causes which happen to exist in that case; we attempt a task, to proceed +far in which, surpasses the compass of the human faculties.</p> + +<p>If all the resources of science are not sufficient to enable us to +calculate <i>à priori</i>, with complete precision, the mutual action of +three bodies gravitating towards one another; it may be judged with what +prospect of success we should endeavour to calculate the result of the +conflicting tendencies which are acting in a thousand different +directions and promoting a thousand different changes at a given instant +in a given society: although we might and ought to be able, from the +laws of human nature, to distinguish correctly enough the tendencies +themselves, so far as they depend on causes accessible to our +observation; and to determine the direction which each of them, if +acting alone, would impress upon society, as well as, in a general way +at least, to pronounce that some of these tendencies are more powerful +than others.</p> + +<p>But, without dissembling the necessary imperfections of the <i>à priori</i> +method when applied to such a subject, neither <span class="pagenum"><a name="Page_488" id="Page_488">[Pg 488]</a></span>ought we, on the other +hand, to exaggerate them. The same objections, which apply to the Method +of Deduction in this its most difficult employment, apply to it, as we +formerly showed,<a name="FNanchor_9_115" id="FNanchor_9_115"></a><a href="#Footnote_9_115" class="fnanchor">[9]</a> in its easiest; and would even there have been +insuperable, if there had not existed, as was then fully explained, an +appropriate remedy. This remedy consists in the process which, under the +name of Verification, we have characterized as the third essential +constituent part of the Deductive Method; that of collating the +conclusions of the ratiocination either with the concrete phenomena +themselves, or, when such are obtainable, with their empirical laws. The +ground of confidence in any concrete deductive science is not the <i>à +priori</i> reasoning itself, but the accordance between its results and +those of observation <i>à posteriori</i>. Either of these processes, apart +from the other, diminishes in value as the subject increases in +complication, and this in so rapid a ratio as soon to become entirely +worthless; but the reliance to be placed in the concurrence of the two +sorts of evidence, not only does not diminish in anything like the same +proportion, but is not necessarily much diminished at all. Nothing more +results than a disturbance in the order of precedency of the two +processes, sometimes amounting to its actual inversion: insomuch that +instead of deducing our conclusions by reasoning, and verifying them by +observation, we in some cases begin by obtaining them conjecturally from +specific experience, and afterwards connect them with the principles of +human nature by <i>à priori</i> reasonings, which reasonings are thus a real +Verification.</p> + +<p>The only thinker who, with a competent knowledge of scientific methods +in general, has attempted to characterize the Method of Sociology, M. +Comte, considers this inverse order as inseparably inherent in the +nature of sociological speculation. He looks upon the social science as +essentially consisting of generalizations from history, verified, not +originally suggested, by deduction from the laws of human nature. Though +there is a truth contained in this opinion, of which I <span class="pagenum"><a name="Page_489" id="Page_489">[Pg 489]</a></span>shall presently +endeavour to show the importance, I cannot but think that this truth is +enunciated in too unlimited a manner, and that there is considerable +scope in sociological inquiry for the direct, as well as for the +inverse, Deductive Method.</p> + +<p>It will, in fact, be shown in the next chapter, that there is a kind of +sociological inquiries to which, from their prodigious complication, the +method of direct deduction is altogether inapplicable, while by a happy +compensation it is precisely in these cases that we are able to obtain +the best empirical laws: to these inquiries, therefore, the Inverse +Method is exclusively adapted. But there are also, as will presently +appear, other cases in which it is impossible to obtain from direct +observation anything worthy the name of an empirical law; and it +fortunately happens that these are the very cases in which the Direct +Method is least affected by the objection which undoubtedly must always +affect it in a certain degree.</p> + +<p>We shall begin, then, by looking at the Social Science as a science of +direct Deduction, and considering what can be accomplished in it, and +under what limitations, by that mode of investigation. We shall, then, +in a separate chapter, examine and endeavour to characterize the inverse +process.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_IX_2">§ 2.</a> It is evident, in the first place, that Sociology, considered as a +system of deductions <i>à priori</i>, cannot be a science of positive +predictions, but only of tendencies. We may be able to conclude, from +the laws of human nature applied to the circumstances of a given state +of society, that a particular cause will operate in a certain manner +unless counteracted; but we can never be assured to what extent or +amount it will so operate, or affirm with certainty that it will not be +counteracted; because we can seldom know, even approximately, all the +agencies which may coexist with it, and still less calculate the +collective result of so many combined elements. The remark, however, +must here be once more repeated, that knowledge insufficient for +prediction may be most valuable for guidance. It is not necessary for +the <span class="pagenum"><a name="Page_490" id="Page_490">[Pg 490]</a></span>wise conduct of the affairs of society, no more than of any one's +private concerns, that we should be able to foresee infallibly the +results of what we do. We must seek our objects by means which may +perhaps be defeated, and take precautions against dangers which possibly +may never be realized. The aim of practical politics is to surround any +given society with the greatest possible number of circumstances of +which the tendencies are beneficial, and to remove or counteract, as far +as practicable, those of which the tendencies are injurious. A knowledge +of the tendencies only, though without the power of accurately +predicting their conjunct result, gives us to a certain extent this +power.</p> + +<p>It would, however, be an error to suppose that even with respect to +tendencies, we could arrive in this manner at any great number of +propositions which will be true in all societies without exception. Such +a supposition would be inconsistent with the eminently modifiable nature +of the social phenomena, and the multitude and variety of the +circumstances by which they are modified; circumstances never the same, +or even nearly the same, in two different societies, or in two different +periods of the same society. This would not be so serious an obstacle +if, though the causes acting upon society in general are numerous, those +which influence any one feature of society were limited in number; for +we might then insulate any particular social phenomenon, and investigate +its laws without disturbance from the rest. But the truth is the very +opposite of this. Whatever affects, in an appreciable degree, any one +element of the social state, affects through it all the other elements. +The mode of production of all social phenomena is one great case of +Intermixture of Laws. We can never either understand in theory or +command in practice the condition of a society in any one respect, +without taking into consideration its condition in all other respects. +There is no social phenomenon which is not more or less influenced by +every other part of the condition of the same society, and therefore by +every cause which is influencing any other of the contemporaneous social +phenomena. There is, in short, what physiologists term a <i>consensus</i>, +similar to that existing among the <span class="pagenum"><a name="Page_491" id="Page_491">[Pg 491]</a></span>various organs and functions of the +physical frame of man and the more perfect animals; and constituting one +of the many analogies which have rendered universal such expressions as +the "body politic" and "body natural." It follows from this <i>consensus</i>, +that unless two societies could be alike in all the circumstances which +surround and influence them, (which would imply their being alike in +their previous history,) no portion whatever of the phenomena will, +unless by accident, precisely correspond; no one cause will produce +exactly the same effects in both. Every cause, as its effect spreads +through society, comes somewhere in contact with different sets of +agencies, and thus has its effects on some of the social phenomena +differently modified; and these differences, by their reaction, produce +a difference even in those of the effects which would otherwise have +been the same. We can never, therefore, affirm with certainty that a +cause which has a particular tendency in one people or in one age will +have exactly the same tendency in another, without referring back to our +premises, and performing over again for the second age or nation, that +analysis of the whole of its influencing circumstances which we had +already performed for the first. The deductive science of society will +not lay down a theorem, asserting in an universal manner the effect of +any cause; but will rather teach us how to frame the proper theorem for +the circumstances of any given case. It will not give the laws of +society in general, but the means of determining the phenomena of any +given society from the particular elements or data of that society.</p> + +<p>All the general propositions which can be framed by the deductive +science, are therefore, in the strictest sense of the word, +hypothetical. They are grounded on some supposititious set of +circumstances, and declare how some given cause would operate in those +circumstances, supposing that no others were combined with them. If the +set of circumstances supposed have been copied from those of any +existing society, the conclusions will be true of that society, +provided, and in as far as, the effect of those circumstances shall not +be modified by others which have not been taken into the account. <span class="pagenum"><a name="Page_492" id="Page_492">[Pg 492]</a></span>If we +desire a nearer approach to concrete truth, we can only aim at it by +taking, or endeavouring to take, a greater number of individualizing +circumstances into the computation.</p> + +<p>Considering, however, in how accelerating a ratio the uncertainty of our +conclusions increases, as we attempt to take the effect of a greater +number of concurrent causes into our calculations; the hypothetical +combinations of circumstances on which we construct the general theorems +of the science, cannot be made very complex, without so +rapidly-accumulating a liability to error as must soon deprive our +conclusions of all value. This mode of inquiry, considered as a means of +obtaining general propositions, must, therefore, on pain of frivolity, +be limited to those classes of social facts which, though influenced +like the rest by all sociological agents, are under the <i>immediate</i> +influence, principally at least, of a few only.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_IX_3">§ 3.</a> Notwithstanding the universal <i>consensus</i> of the social phenomena, +whereby nothing which takes place in any part of the operations of +society is without its share of influence on every other part; and +notwithstanding the paramount ascendancy which the general state of +civilization and social progress in any given society must hence +exercise over all the partial and subordinate phenomena; it is not the +less true that different species of social facts are in the main +dependent, immediately and in the first resort, on different kinds of +causes; and therefore not only may with advantage, but must, be studied +apart: just as in the natural body we study separately the physiology +and pathology of each of the principal organs and tissues, though every +one is acted upon by the state of all the others: and though the +peculiar constitution and general state of health of the organism +co-operates with, and often preponderates over, the local causes, in +determining the state of any particular organ.</p> + +<p>On these considerations is grounded the existence of distinct and +separate, though not independent, branches or departments of +sociological speculation.</p> + +<p>There is, for example, one large class of social phenomena, <span class="pagenum"><a name="Page_493" id="Page_493">[Pg 493]</a></span>in which +the immediately determining causes are principally those which act +through the desire of wealth; and in which the psychological law mainly +concerned is the familiar one, that a greater gain is preferred to a +smaller. I mean, of course, that portion of the phenomena of society +which emanate from the industrial, or productive, operations of mankind; +and from those of their acts through which the distribution of the +products of those industrial operations takes place, in so far as not +effected by force, or modified by voluntary gift. By reasoning from that +one law of human nature, and from the principal outward circumstances +(whether universal or confined to particular states of society) which +operate upon the human mind through that law, we may be enabled to +explain and predict this portion of the phenomena of society, so far as +they depend on that class of circumstances only; overlooking the +influence of any other of the circumstances of society; and therefore +neither tracing back the circumstances which we do take into account, to +their possible origin in some other facts in the social state, nor +making allowance for the manner in which any of those other +circumstances may interfere with, and counteract or modify, the effect +of the former. A science may thus be constructed, which has received the +name of Political Economy.</p> + +<p>The motive which suggests the separation of this portion of the social +phenomena from the rest, and the creation of a distinct science relating +to them is,—that they do <i>mainly</i> depend, at least in the first resort, +on one class of circumstances only; and that even when other +circumstances interfere, the ascertainment of the effect due to the one +class of circumstances alone, is a sufficiently intricate and difficult +business to make it expedient to perform it once for all, and then allow +for the effect of the modifying circumstances; especially as certain +fixed combinations of the former are apt to recur often, in conjunction +with ever-varying circumstances of the latter class.</p> + +<p>Political Economy, as I have said on another occasion, concerns itself +only with "such of the phenomena of the social state as take place in +consequence of the pursuit of wealth. <span class="pagenum"><a name="Page_494" id="Page_494">[Pg 494]</a></span>It makes entire abstraction of +every other human passion or motive; except those which may be regarded +as perpetually antagonizing principles to the desire of wealth, namely, +aversion to labour, and desire of the present enjoyment of costly +indulgences. These it takes, to a certain extent, into its calculations, +because these do not merely, like our other desires, occasionally +conflict with the pursuit of wealth, but accompany it always as a drag +or impediment, and are therefore inseparably mixed up in the +consideration of it. Political Economy considers mankind as occupied +solely in acquiring and consuming wealth; and aims at showing what is +the course of action into which mankind, living in a state of society, +would be impelled, if that motive, except in the degree in which it is +checked by the two perpetual counter-motives above adverted to, were +absolute ruler of all their actions. Under the influence of this desire, +it shows mankind accumulating wealth, and employing that wealth in the +production of other wealth; sanctioning by mutual agreement the +institution of property; establishing laws to prevent individuals from +encroaching upon the property of others by force or fraud; adopting +various contrivances for increasing the productiveness of their labour; +settling the division of the produce by agreement, under the influence +of competition (competition itself being governed by certain laws, which +laws are therefore the ultimate regulators of the division of the +produce); and employing certain expedients (as money, credit, &c.) to +facilitate the distribution. All these operations, though many of them +are really the result of a plurality of motives, are considered by +political economy as flowing solely from the desire of wealth. The +science then proceeds to investigate the laws which govern these several +operations, under the supposition that man is a being who is determined, +by the necessity of his nature, to prefer a greater portion of wealth to +a smaller, in all cases, without any other exception than that +constituted by the two counter-motives already specified. Not that any +political economist was ever so absurd as to suppose that mankind are +really thus constituted, but because this is the mode in which science +must necessarily proceed. When an effect <span class="pagenum"><a name="Page_495" id="Page_495">[Pg 495]</a></span>depends on a concurrence of +causes, these causes must be studied one at a time, and their laws +separately investigated, if we wish, through the causes, to obtain the +power of either predicting or controlling the effect; since the law of +the effect is compounded of the laws of all the causes which determine +it. The law of the centripetal and that of the projectile force must +have been known, before the motions of the earth and planets could be +explained, or many of them predicted. The same is the case with the +conduct of man in society. In order to judge how he will act under the +variety of desires and aversions which are concurrently operating upon +him, we must know how he would act under the exclusive influence of each +one in particular. There is, perhaps, no action of a man's life in which +he is neither under the immediate nor under the remote influence of any +impulse but the mere desire of wealth. With respect to those parts of +human conduct of which wealth is not even the principal object, to these +political economy does not pretend that its conclusions are applicable. +But there are also certain departments of human affairs, in which the +acquisition of wealth is the main and acknowledged end. It is only of +these that political economy takes notice. The manner in which it +necessarily proceeds is that of treating the main and acknowledged end +as if it were the sole end; which, of all hypotheses equally simple, is +the nearest to the truth. The political economist inquires, what are the +actions which would be produced by this desire, if within the +departments in question it were unimpeded by any other. In this way a +nearer approximation is obtained than would otherwise be practicable to +the real order of human affairs in those departments. This approximation +has then to be corrected by making proper allowance for the effects of +any impulses of a different description, which can be shown to interfere +with the result in any particular case. Only in a few of the most +striking cases (such as the important one of the principle of +population) are these corrections interpolated into the expositions of +political economy itself; the strictness of purely scientific +arrangement being thereby somewhat departed from, for the sake of +practical utility. So far as it is known or may be <span class="pagenum"><a name="Page_496" id="Page_496">[Pg 496]</a></span>presumed, that the +conduct of mankind in the pursuit of wealth is under the collateral +influence of any other of the properties of our nature, than the desire +of obtaining the greatest quantity of wealth with the least labour and +self-denial, the conclusions of political economy will so far fail of +being applicable to the explanation or prediction of real events, until +they are modified by a correct allowance for the degree of influence +exercised by the other cause."<a name="FNanchor_10_116" id="FNanchor_10_116"></a><a href="#Footnote_10_116" class="fnanchor">[10]</a></p> + +<p>Extensive and important practical guidance may be derived, in any given +state of society, from general propositions such as those above +indicated; even though the modifying influence of the miscellaneous +causes which the theory does not take into account, as well as the +effect of the general social changes in progress, be provisionally +overlooked. And though it has been a very common error of political +economists to draw conclusions from the elements of one state of +society, and apply them to other states in which many of the elements +are not the same; it is even then not difficult, by tracing back the +demonstrations, and introducing the new premises in their proper places, +to make the same general course of argument which served for the one +case, serve for the others too.</p> + +<p>For example, it has been greatly the custom of English political +economists to discuss the laws of the distribution of the produce of +industry, on a supposition which is scarcely realized anywhere out of +England and Scotland, namely, that the produce is "shared among three +classes, altogether distinct from one another, labourers, capitalists, +and landlords; and that all these are free agents, permitted in law and +in fact to set upon their labour, their capital, and their land, +whatever price they are able to get for it. The conclusions of the +science, being all adapted to a society thus constituted, require to be +revised whenever they are applied to any other. They are inapplicable +where the only capitalists are the landlords, and the labourers are +their property, as in slave countries. They are inapplicable where the +almost universal landlord is the <span class="pagenum"><a name="Page_497" id="Page_497">[Pg 497]</a></span>state as in India. They are +inapplicable where the agricultural labourer is generally the owner both +of the land itself and of the capital, as frequently in France, or of +the capital only, as in Ireland." But though it may often be very justly +objected to the existing race of political economists "that they attempt +to construct a permanent fabric out of transitory materials; that they +take for granted the immutability of arrangements of society, many of +which are in their nature fluctuating or progressive, and enunciate with +as little qualification as if they were universal and absolute truths, +propositions which are perhaps applicable to no state of society except +the particular one in which the writer happened to live;" this does not +take away the value of the propositions, considered with reference to +the state of society from which they were drawn. And even as applicable +to other states of society, "it must not be supposed that the science is +so incomplete and unsatisfactory as this might seem to prove. Though +many of its conclusions are only locally true, its method of +investigation is applicable universally; and as whoever has solved a +certain number of algebraic equations, can without difficulty solve all +others of the same kind, so whoever knows the political economy of +England, or even of Yorkshire, knows that of all nations, actual or +possible, provided he have good sense enough not to expect the same +conclusion to issue from varying premises." Whoever is thoroughly master +of the laws which, under free competition, determine the rent, profits, +and wages, received by landlords, capitalists, and labourers, in a state +of society in which the three classes are completely separate, will have +no difficulty in determining the very different laws which regulate the +distribution of the produce among the classes interested in it, in any +of the states of cultivation and landed property set forth in the +foregoing extract.<a name="FNanchor_11_117" id="FNanchor_11_117"></a><a href="#Footnote_11_117" class="fnanchor">[11]</a></p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_IX_4">§ 4.</a> I would not here undertake to decide what other hypothetical or +abstract sciences similar to Political Economy, <span class="pagenum"><a name="Page_498" id="Page_498">[Pg 498]</a></span>may admit of being +carved out of the general body of the social science; what other +portions of the social phenomena are in a sufficiently close and +complete dependence, in the first resort, on a peculiar class of causes, +to make it convenient to create a preliminary science of those causes; +postponing the consideration of the causes which act through them, or in +concurrence with them, to a later period of the inquiry. There is +however among these separate departments one which cannot be passed over +in silence, being of a more comprehensive and commanding character than +any of the other branches into which the social science may admit of +being divided. Like them, it is directly conversant with the causes of +only one class of social facts, but a class which exercises, immediately +or remotely, a paramount influence over the rest. I allude to what may +be termed Political Ethology, or the theory of the causes which +determine the type of character belonging to a people or to an age. Of +all the subordinate branches of the social science, this is the most +completely in its infancy. The causes of national character are scarcely +at all understood, and the effect of institutions or social arrangements +upon the character of the people is generally that portion of their +effects which is least attended to, and least comprehended. Nor is this +wonderful, when we consider the infant state of the Science of Ethology +itself, from whence the laws must be drawn, of which the truths of +political ethology can be but results and exemplifications.</p> + +<p>Yet to whoever well considers the matter, it must appear that the laws +of national (or collective) character are by far the most important +class of sociological laws. In the first place, the character which is +formed by any state of social circumstances is in itself the most +interesting phenomenon which that state of society can possibly present. +Secondly, it is also a fact which enters largely into the production of +all the other phenomena. And above all, the character, that is, the +opinions, feelings, and habits, of the people, though greatly the +results of the state of society which precedes them, are also greatly +the causes of the state of society which follows them; and are the power +by which all those of the circumstances of <span class="pagenum"><a name="Page_499" id="Page_499">[Pg 499]</a></span>society which are +artificial, laws and customs for instance, are altogether moulded: +customs evidently, laws no less really, either by the direct influence +of public sentiment upon the ruling powers, or by the effect which the +state of national opinion and feeling has in determining the form of +government and shaping the character of the governors.</p> + +<p>As might be expected, the most imperfect part of those branches of +social inquiry which have been cultivated as separate sciences, is the +theory of the manner in which their conclusions are affected by +ethological considerations. The omission is no defect in them as +abstract or hypothetical sciences, but it vitiates them in their +practical application as branches of a comprehensive social science. In +political economy for instance, empirical laws of human nature are +tacitly assumed by English thinkers, which are calculated only for Great +Britain and the United States. Among other things, an intensity of +competition is constantly supposed, which, as a general mercantile fact, +exists in no country in the world except those two. An English political +economist, like his countrymen in general, has seldom learned that it is +possible that men, in conducting the business of selling their goods +over a counter, should care more about their ease or their vanity than +about their pecuniary gain. Yet those who know the habits of the +Continent of Europe are aware how apparently small a motive often +outweighs the desire of money-getting, even in the operations which have +money-getting for their direct object. The more highly the science of +ethology is cultivated, and the better the diversities of individual and +national character are understood, the smaller, probably, will the +number of propositions become, which it will be considered safe to build +on as universal principles of human nature.</p> + +<p>These considerations show that the process of dividing off the social +science into compartments, in order that each may be studied separately, +and its conclusions afterwards corrected for practice by the +modifications supplied by the others, must be subject to at least one +important limitation. Those portions alone of the social phenomena can +with advantage be made the subjects, even provisionally, of distinct +branches of science, <span class="pagenum"><a name="Page_500" id="Page_500">[Pg 500]</a></span>into which the diversities of character between +different nations or different times enter as influencing causes only in +a secondary degree. Those phenomena, on the contrary, with which the +influences of the ethological state of the people are mixed up at every +step (so that the connexion of effects and causes cannot be even rudely +marked out without taking those influences into consideration) could not +with any advantage, nor without great disadvantage, be treated +independently of political ethology, nor, therefore, of all the +circumstances by which the qualities of a people are influenced. For +this reason (as well as for others which will hereafter appear) there +can be no separate Science of Government; that being the fact which, of +all others, is most mixed up, both as cause and effect, with the +qualities of the particular people or of the particular age. All +questions respecting the tendencies of forms of government must stand +part of the general science of society, not of any separate branch of +it.</p> + +<p>This general Science of Society, as distinguished from the separate +departments of the science (each of which asserts its conclusions only +conditionally, subject to the paramount control of the laws of the +general science) now remains to be characterized. And as will be shown +presently, nothing of a really scientific character is here possible, +except by the inverse deductive method. But before we quit the subject +of those sociological speculations which proceed by way of direct +deduction, we must examine in what relation they stand to that +indispensable element in all deductive sciences, Verification by +Specific Experience—comparison between the conclusions of reasoning and +the results of observation.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_IX_5">§ 5.</a> We have seen that, in most deductive sciences, and among the rest +in Ethology itself, which is the immediate foundation of the Social +Science, a preliminary work of preparation is performed on the observed +facts, to fit them for being rapidly and accurately collated (sometimes +even for being collated at all) with the conclusions of theory. This +preparatory treatment consists in finding general propositions which +express concisely what is common to large classes of <span class="pagenum"><a name="Page_501" id="Page_501">[Pg 501]</a></span>observed facts: +and these are called the empirical laws of the phenomena. We have, +therefore, to inquire, whether any similar preparatory process can be +performed on the facts of the social science; whether there are any +empirical laws in history or statistics.</p> + +<p>In statistics, it is evident that empirical laws may sometimes be +traced; and the tracing them forms an important part of that system of +indirect observation on which we must often rely for the data of the +Deductive Science. The process of the science consists in inferring +effects from their causes; but we have often no means of observing the +causes, except through the medium of their effects. In such cases the +deductive science is unable to predict the effects, for want of the +necessary data; it can determine what causes are capable of producing +any given effect, but not with what frequency and in what quantities +those causes exist. An instance in point is afforded by a newspaper now +lying before me. A statement was furnished by one of the official +assignees in bankruptcy, showing among the various bankruptcies which it +had been his duty to investigate, in how many cases the losses had been +caused by misconduct of different kinds, and in how many by unavoidable +misfortunes. The result was, that the number of failures caused by +misconduct greatly preponderated over those arising from all other +causes whatever. Nothing but specific experience could have given +sufficient ground for a conclusion to this purport. To collect, +therefore, such empirical laws (which are never more than approximate +generalizations) from direct observation, is an important part of the +process of sociological inquiry.</p> + +<p>The experimental process is not here to be regarded as a distinct road +to the truth, but as a means (happening accidentally to be the only, or +the best, available) for obtaining the necessary data for the deductive +science. When the immediate causes of social facts are not open to +direct observation, the empirical law of the effects gives us the +empirical law (which in that case is all that we can obtain) of the +causes likewise. But those immediate causes depend on remote causes; and +the empirical law, obtained by this indirect mode <span class="pagenum"><a name="Page_502" id="Page_502">[Pg 502]</a></span>of observation, can +only be relied on as applicable to unobserved cases, so long as there is +reason to think that no change has taken place in any of the remote +causes on which the immediate causes depend. In making use, therefore, +of even the best statistical generalizations for the purpose of +inferring (though it be only conjecturally) that the same empirical laws +will hold in any new case, it is necessary that we be well acquainted +with the remoter causes, in order that we may avoid applying the +empirical law to cases which differ in any of the circumstances on which +the truth of the law ultimately depends. And thus, even where +conclusions derived from specific observation are available for +practical inferences in new cases, it is necessary that the deductive +science should stand sentinel over the whole process; that it should be +constantly referred to, and its sanction obtained to every inference.</p> + +<p>The same thing holds true of all generalizations which can be grounded +on history. Not only there are such generalizations, but it will +presently be shown that the general science of society, which inquires +into the laws of succession and coexistence of the great facts +constituting the state of society and civilization at any time, can +proceed in no other manner than by making such +generalizations—afterwards to be confirmed by connecting them with the +psychological and ethological laws on which they must really depend.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_IX_6">§ 6.</a> But (reserving this question for its proper place) in those more +special inquiries which form the subject of the separate branches of the +social science, this twofold logical process and reciprocal verification +is not possible: specific experience affords nothing amounting to +empirical laws. This is particularly the case where the object is to +determine the effect of any one social cause among a great number acting +simultaneously; the effect, for example, of corn laws, or of a +prohibitive commercial system generally. Though it may be perfectly +certain, from theory, what <i>kind</i> of effects corn laws must produce, and +in what general direction their influence must tell upon industrial +prosperity; their effect is <span class="pagenum"><a name="Page_503" id="Page_503">[Pg 503]</a></span>yet of necessity so much disguised by the +similar or contrary effects of other influencing agents, that specific +experience can at most only show that on the average of some great +number of instances, the cases where there were corn laws exhibited the +effect in a greater degree than those where there were not. Now the +number of instances necessary to exhaust the whole round of combinations +of the various influential circumstances, and thus afford a fair +average, never can be obtained. Not only we can never learn with +sufficient authenticity the facts of so many instances, but the world +itself does not afford them in sufficient numbers, within the limits of +the given state of society and civilization which such inquiries always +presuppose. Having thus no previous empirical generalizations with which +to collate the conclusions of theory, the only mode of direct +verification which remains is to compare those conclusions with the +result of an individual experiment or instance. But here the difficulty +is equally great. For in order to verify a theory by an experiment, the +circumstances of the experiment must be exactly the same with those +contemplated in the theory. But in social phenomena the circumstances of +no two cases are exactly alike. A trial of corn laws in another country +or in a former generation, would go a very little way towards verifying +a conclusion drawn respecting their effect in this generation and in +this country. It thus happens, in most cases, that the only individual +instance really fitted to verify the predictions of theory is the very +instance for which the predictions were made; and the verification comes +too late to be of any avail for practical guidance.</p> + +<p>Although, however, direct verification is impossible, there is an +indirect verification, which is scarcely of less value, and which is +always practicable. The conclusion drawn as to the individual case, can +only be directly verified in that case; but it is verified indirectly, +by the verification of other conclusions, drawn in other individual +cases from the same laws. The experience which comes too late to verify +the particular proposition to which it refers, is not too late to help +towards verifying <span class="pagenum"><a name="Page_504" id="Page_504">[Pg 504]</a></span>the general sufficiency of the theory. The test of +the degree in which the science affords safe ground for predicting (and +consequently for practically dealing with) what has not yet happened, is +the degree in which it would have enabled us to predict what has +actually occurred. Before our theory of the influence of a particular +cause, in a given state of circumstances, can be entirely trusted, we +must be able to explain and account for the existing state of all that +portion of the social phenomena which that cause has a tendency to +influence. If, for instance, we would apply our speculations in +political economy to the prediction or guidance of the phenomena of any +country, we must be able to explain all the mercantile or industrial +facts of a general character, appertaining to the present state of that +country: to point out causes sufficient to account for all of them, and +prove, or show good ground for supposing, that these causes have really +existed. If we cannot do this, it is a proof either that the facts which +ought to be taken into account are not yet completely known to us, or +that although we know the facts, we are not masters of a sufficiently +perfect theory to enable us to assign their consequences. In either case +we are not, in the present state of our knowledge, fully competent to +draw conclusions, speculative or practical, for that country. In like +manner if we would attempt to judge of the effect which any political +institution would have, supposing that it could be introduced into any +given country; we must be able to show that the existing state of the +practical government of that country, and of whatever else depends +thereon, together with the particular character and tendencies of the +people, and their state in respect to the various elements of social +well-being, are such as the institutions they have lived under, in +conjunction with the other circumstances of their nature or of their +position, were calculated to produce.</p> + +<p>To prove (in short) that our science, and our knowledge of the +particular case, render us competent to predict the future, we must show +that they would have enabled us to predict the present and the past. If +there be anything which we could <span class="pagenum"><a name="Page_505" id="Page_505">[Pg 505]</a></span>not have predicted, this constitutes a +residual phenomenon, requiring further study for the purpose of +explanation; and we must either search among the circumstances of the +particular case until we find one which, on the principles of our +existing theory, accounts for the unexplained phenomenon, or we must +turn back, and seek the explanation by an extension and improvement of +the theory itself.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_506" id="Page_506">[Pg 506]</a></span></p> +<h3><a name="BOOK_VI_CHAPTER_X" id="BOOK_VI_CHAPTER_X"></a>CHAPTER X.<br /> +OF THE INVERSE DEDUCTIVE, OR HISTORICAL METHOD.</h3> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_X_1">§ 1.</a> There are two kinds of sociological inquiry. In the first kind, the +question proposed is, what effect will follow from a given cause, a +certain general condition of social circumstances being presupposed. As, +for example, what would be the effect of imposing or of repealing corn +laws, of abolishing monarchy or introducing universal suffrage, in the +present condition of society and civilization in any European country, +or under any other given supposition with regard to the circumstances of +society in general: without reference to the changes which might take +place, or which may already be in progress, in those circumstances. But +there is also a second inquiry, namely, what are the laws which +determine those general circumstances themselves. In this last the +question is, not what will be the effect of a given cause in a certain +state of society, but what are the causes which produce, and the +phenomena which characterize, States of Society generally. In the +solution of this question consists the general Science of Society; by +which the conclusions of the other and more special kind of inquiry must +be limited and controlled.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_X_2">§ 2.</a> In order to conceive correctly the scope of this general science, +and distinguish it from the subordinate departments of sociological +speculation, it is necessary to fix the ideas attached to the phrase, "a +State of Society." What is called a state of society, is the +simultaneous state of all the greater social facts or phenomena. Such +are, the degree of knowledge, and of intellectual and moral culture, +existing in the community, and in every class of it; the state of +industry, <span class="pagenum"><a name="Page_507" id="Page_507">[Pg 507]</a></span>of wealth and its distribution; the habitual occupations of +the community; their division into classes, and the relations of those +classes to one another; the common beliefs which they entertain on all +the subjects most important to mankind, and the degree of assurance with +which those beliefs are held; their tastes, and the character and degree +of their æsthetic development; their form of government, and the more +important of their laws and customs. The condition of all these things, +and of many more which will readily suggest themselves, constitute the +state of society or the state of civilization at any given time.</p> + +<p>When states of society, and the causes which produce them, are spoken of +as a subject of science, it is implied that there exists a natural +correlation among these different elements; that not every variety of +combination of these general social facts is possible, but only certain +combinations; that, in short, there exist Uniformities of Coexistence +between the states of the various social phenomena. And such is the +truth; as is indeed a necessary consequence of the influence exercised +by every one of those phenomena over every other. It is a fact implied +in the <i>consensus</i> of the various parts of the social body.</p> + +<p>States of society are like different constitutions or different ages in +the physical frame; they are conditions not of one or a few organs or +functions, but of the whole organism. Accordingly, the information which +we possess respecting past ages, and respecting the various states of +society now existing in different regions of the earth, does, when duly +analysed, exhibit uniformities. It is found that when one of the +features of society is in a particular state, a state of many other +features, more or less precisely determinate, always or usually coexists +with it.</p> + +<p>But the uniformities of coexistence obtaining among phenomena which are +effects of causes, must (as we have so often observed) be corollaries +from the laws of causation by which these phenomena are really +determined. The mutual correlation between the different elements of +each state of society, is therefore a derivative law, resulting from the +laws which regulate <span class="pagenum"><a name="Page_508" id="Page_508">[Pg 508]</a></span>the succession between one state of society and +another: for the proximate cause of every state of society is the state +of society immediately preceding it. The fundamental problem, therefore, +of the social science, is to find the laws according to which any state +of society produces the state which succeeds it and takes its place. +This opens the great and vexed question of the progressiveness of man +and society; an idea involved in every just conception of social +phenomena as the subject of a science.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_X_3">§ 3.</a> It is one of the characters, not absolutely peculiar to the +sciences of human nature and society, but belonging to them in a +peculiar degree, to be conversant with a subject-matter whose properties +are changeable. I do not mean changeable from day to day, but from age +to age; so that not only the qualities of individuals vary, but those of +the majority are not the same in one age as in another.</p> + +<p>The principal cause of this peculiarity is the extensive and constant +reaction of the effects upon their causes. The circumstances in which +mankind are placed, operating according to their own laws and to the +laws of human nature, form the characters of the human beings; but the +human beings, in their turn, mould and shape the circumstances, for +themselves and for those who come after them. From this reciprocal +action there must necessarily result either a cycle or a progress. In +astronomy also, every fact is at once effect and cause; the successive +positions of the various heavenly bodies produce changes both in the +direction and in the intensity of the forces by which those positions +are determined. But in the case of the solar system, these mutual +actions bring round again, after a certain number of changes, the former +state of circumstances; which of course leads to the perpetual +recurrence of the same series in an unvarying order. Those bodies, in +short, revolve in orbits: but there are (or, conformably to the laws of +astronomy, there might be) others which, instead of an orbit, describe a +trajectory—a course not returning into itself. One or other of these +must be the type to which human affairs must conform.</p> + +<p><span class="pagenum"><a name="Page_509" id="Page_509">[Pg 509]</a></span></p><p>One of the thinkers who earliest conceived the succession of historical +events as subject to fixed laws, and endeavoured to discover these laws +by an analytical survey of history, Vico, the celebrated author of the +<i>Scienza Nuova</i>, adopted the former of these opinions. He conceived the +phenomena of human society as revolving in an orbit; as going through +periodically the same series of changes. Though there were not wanting +circumstances tending to give some plausibility to this view, it would +not bear a close scrutiny: and those who have succeeded Vico in this +kind of speculations have universally adopted the idea of a trajectory +or progress, in lieu of an orbit or cycle.</p> + +<p>The words Progress and Progressiveness are not here to be understood as +synonymous with improvement and tendency to improvement. It is +conceivable that the laws of human nature might determine, and even +necessitate, a certain series of changes in man and society, which might +not in every case, or which might not on the whole, be improvements. It +is my belief indeed that the general tendency is, and will continue to +be, saving occasional and temporary exceptions, one of improvement; a +tendency towards a better and happier state. This, however, is not a +question of the method of the social science, but a theorem of the +science itself. For our purpose it is sufficient, that there is a +progressive change both in the character of the human race, and in their +outward circumstances so far as moulded by themselves: that in each +successive age the principal phenomena of society are different from +what they were in the age preceding, and still more different from any +previous age: the periods which most distinctly mark these successive +changes being intervals of one generation, during which a new set of +human beings have been educated, have grown up from childhood, and taken +possession of society.</p> + +<p>The progressiveness of the human race is the foundation on which a +method of philosophizing in the social science has been of late years +erected, far superior to either of the two modes which had previously +been prevalent, the chemical or experimental, and the geometrical modes. +This method, <span class="pagenum"><a name="Page_510" id="Page_510">[Pg 510]</a></span>which is now generally adopted by the most advanced +thinkers on the Continent, consists in attempting, by a study and +analysis of the general facts of history, to discover (what these +philosophers term) the law of progress: which law, once ascertained, +must according to them enable us to predict future events, just as after +a few terms of an infinite series in algebra we are able to detect the +principle of regularity in their formation, and to predict the rest of +the series to any number of terms we please. The principal aim of +historical speculation in France, of late years, has been to ascertain +this law. But while I gladly acknowledge the great services which have +been rendered to historical knowledge by this school, I cannot but deem +them to be mostly chargeable with a fundamental misconception of the +true method of social philosophy. The misconception consists in +supposing that the order of succession which we may be able to trace +among the different states of society and civilization which history +presents to us, even if that order were more rigidly uniform than it has +yet been proved to be, could ever amount to a law of nature. It can only +be an empirical law. The succession of states of the human mind and of +human society cannot have an independent law of its own; it must depend +on the psychological and ethological laws which govern the action of +circumstances on men and of men on circumstances. It is conceivable that +those laws might be such, and the general circumstances of the human +race such, as to determine the successive transformations of man and +society to one given and unvarying order. But even if the case were so, +it cannot be the ultimate aim of science to discover an empirical law. +Until that law could be connected with the psychological and ethological +laws on which it must depend, and, by the consilience of deduction <i>à +priori</i> with historical evidence, could be converted from an empirical +law into a scientific one, it could not be relied on for the prediction +of future events, beyond, at most, strictly adjacent cases. M. Comte +alone, among the new historical school, has seen the necessity of thus +connecting all our generalizations from history with the laws of human +nature.</p> + + +<p><span class="pagenum"><a name="Page_511" id="Page_511">[Pg 511]</a></span></p><p class="newsection"><a name="BOOK_VI_CHAPTER_X_4">§ 4.</a> But, while it is an imperative rule never to introduce any +generalization from history into the social science unless sufficient +grounds can be pointed out for it in human nature, I do not think any +one will contend that it would have been possible, setting out from the +principles of human nature and from the general circumstances of the +position of our species, to determine <i>à priori</i> the order in which +human development must take place, and to predict, consequently, the +general facts of history up to the present time. After the first few +terms of the series, the influence exercised over each generation by the +generations which preceded it, becomes (as is well observed by the +writer last referred to) more and more preponderant over all other +influences; until at length what we now are and do, is in a very small +degree the result of the universal circumstances of the human race, or +even of our own circumstances acting through the original qualities of +our species, but mainly of the qualities produced in us by the whole +previous history of humanity. So long a series of actions and reactions +between Circumstances and Man, each successive term being composed of an +ever greater number and variety of parts, could not possibly be computed +by human faculties from the elementary laws which produce it. The mere +length of the series would be a sufficient obstacle, since a slight +error in any one of the terms would augment in rapid progression at +every subsequent step.</p> + +<p>If, therefore, the series of the effects themselves did not, when +examined as a whole, manifest any regularity, we should in vain attempt +to construct a general science of society. We must in that case have +contented ourselves with that subordinate order of sociological +speculation formerly noticed, namely, with endeavouring to ascertain +what would be the effect of the introduction of any new cause, in a +state of society supposed to be fixed; a knowledge sufficient for the +more common exigencies of daily political practice, but liable to fail +in all cases in which the progressive movement of society is one of the +influencing elements; and therefore more precarious in proportion as the +case is more important. But since both the natural varieties of mankind, +and the original diversities of <span class="pagenum"><a name="Page_512" id="Page_512">[Pg 512]</a></span>local circumstances, are much less +considerable than the points of agreement, there will naturally be a +certain degree of uniformity in the progressive development of the +species and of its works. And this uniformity tends to become greater, +not less, as society advances; since the evolution of each people, which +is at first determined exclusively by the nature and circumstances of +that people, is gradually brought under the influence (which becomes +stronger as civilization advances) of the other nations of the earth, +and of the circumstances by which they have been influenced. History +accordingly does, when judiciously examined, afford Empirical Laws of +Society. And the problem of general sociology is to ascertain these, and +connect them with the laws of human nature, by deductions showing that +such were the derivative laws naturally to be expected as the +consequences of those ultimate ones.</p> + +<p>It is, indeed, hardly ever possible, even after history has suggested +the derivative law, to demonstrate <i>à priori</i> that such was the only +order of succession or of coexistence in which the effects could, +consistently with the laws of human nature, have been produced. We can +at most make out that there were strong <i>à priori</i> reasons for expecting +it, and that no other order of succession or coexistence would have been +so likely to result from the nature of man and the general circumstances +of his position. Often we cannot do even this; we cannot even show that +what did take place was probable <i>à priori</i>, but only that it was +possible. This, however,—which, in the Inverse Deductive Method that we +are now characterizing, is a real process of verification,—is as +indispensable, as verification by specific experience has been shown to +be, where the conclusion is originally obtained by the direct way of +deduction. The empirical laws must be the result of but a few instances, +since few nations have ever attained at all, and still fewer by their +own independent development, a high stage of social progress. If, +therefore, even one or two of these few instances be insufficiently +known, or imperfectly analysed into their elements, and therefore not +adequately compared with other instances, nothing is more probable than +<span class="pagenum"><a name="Page_513" id="Page_513">[Pg 513]</a></span>that a wrong empirical law will emerge instead of the right one. +Accordingly, the most erroneous generalizations are continually made +from the course of history: not only in this country, where history +cannot yet be said to be at all cultivated as a science, but in other +countries, where it is so cultivated, and by persons well versed in it. +The only check or corrective is, constant verification by psychological +and ethological laws. We may add to this, that no one but a person +competently skilled in those laws is capable of preparing the materials +for historical generalization, by analysing the facts of history, or +even by observing the social phenomena of his own time. No other will be +aware of the comparative importance of different facts, nor consequently +know what facts to look for, or to observe; still less will he be +capable of estimating the evidence of facts which, as is the case with +most, cannot be ascertained by direct observation or learnt from +testimony, but must be inferred from marks.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_X_5">§ 5.</a> The Empirical Laws of Society are of two kinds; some are +uniformities of coexistence, some of succession. According as the +science is occupied in ascertaining and verifying the former sort of +uniformities or the latter, M. Comte gives it the title of Social +Statics, or of Social Dynamics; conformably to the distinction in +mechanics between the conditions of equilibrium and those of movement; +or in biology, between the laws of organization and those of life. The +first branch of the science ascertains the conditions of stability in +the social union: the second, the laws of progress. Social Dynamics is +the theory of Society considered in a state of progressive movement; +while Social Statics is the theory of the <i>consensus</i> already spoken of +as existing among the different parts of the social organism; in other +words, the theory of the mutual actions and reactions of contemporaneous +social phenomena; "making<a name="FNanchor_12_118" id="FNanchor_12_118"></a><a href="#Footnote_12_118" class="fnanchor">[12]</a> provisionally, as far as possible, +abstraction, for scientific purposes, of the fundamental movement <span class="pagenum"><a name="Page_514" id="Page_514">[Pg 514]</a></span>which +is at all times gradually modifying the whole of them.</p> + +<p>"In this first point of view, the provisions of sociology will enable us +to infer one from another (subject to ulterior verification by direct +observation) the various characteristic marks of each distinct mode of +social existence; in a manner essentially analogous to what is now +habitually practised in the anatomy of the physical body. This +preliminary aspect, therefore, of political science, of necessity +supposes that (contrary to the existing habits of philosophers) each of +the numerous elements of the social state, ceasing to be looked at +independently and absolutely, shall be always and exclusively considered +relatively to all the other elements, with the whole of which it is +united by mutual interdependence. It would be superfluous to insist here +upon the great and constant utility of this branch of sociological +speculation. It is, in the first place, the indispensable basis of the +theory of social progress. It may, moreover, be employed, immediately, +and of itself, to supply the place, provisionally at least, of direct +observation, which in many cases is not always practicable for some of +the elements of society, the real condition of which may however be +sufficiently judged of by means of the relations which connect them with +others previously known. The history of the sciences may give us some +notion of the habitual importance of this auxiliary resource, by +reminding us, for example, how the vulgar errors of mere erudition +concerning the pretended acquirements of the ancient Egyptians in the +higher astronomy, were irrevocably dissipated (even before sentence had +been passed on them by a sounder erudition) from the single +consideration of the inevitable connexion between the general state of +astronomy and that of abstract geometry, then evidently in its infancy. +It would be easy to cite a multitude of analogous cases, the character +of which could admit of no dispute. In order to avoid exaggeration, +however, it should be remarked, that these necessary relations among the +different aspects of society cannot, from their very nature, be so +simple and precise that the results observed could only have arisen from +some one mode of mutual co-ordination. <span class="pagenum"><a name="Page_515" id="Page_515">[Pg 515]</a></span>Such a notion, already too +narrow in the science of life, would be completely at variance with the +still more complex nature of sociological speculations. But the exact +estimation of these limits of variation, both in the healthy and in the +morbid state, constitutes, at least as much as in the anatomy of the +natural body, an indispensable complement to every theory of +Sociological Statics; without which the indirect exploration above +spoken of would often lead into error.</p> + +<p>"This is not the place for methodically demonstrating the existence of a +necessary relation among all the possible aspects of the same social +organism; a point on which, in principle at least, there is now little +difference of opinion among sound thinkers. From whichever of the social +elements we choose to set out, we may easily recognise that it has +always a connexion, more or less immediate, with all the other elements, +even with those which at first sight appear the most independent of it. +The dynamical consideration of the progressive development of civilized +humanity, affords, no doubt, a still more efficacious means of effecting +this interesting verification of the <i>consensus</i> of the social +phenomena, by displaying the manner in which every change in any one +part, operates immediately, or very speedily, upon all the rest. But +this indication may be preceded, or at all events followed, by a +confirmation of a purely statical kind; for, in politics as in +mechanics, the communication of motion from one object to another proves +a connexion between them. Without descending to the minute +interdependence of the different branches of any one science or art, is +it not evident that among the different sciences, as well as among most +of the arts, there exists such a connexion, that if the state of any one +well marked division of them is sufficiently known to us, we can with +real scientific assurance infer, from their necessary correlation, the +contemporaneous state of every one of the others? By a further extension +of this consideration, we may conceive the necessary relation which +exists between the condition of the sciences in general and that of the +arts in general, except that the mutual dependence is less intense in +proportion as it is more indirect. The same is the <span class="pagenum"><a name="Page_516" id="Page_516">[Pg 516]</a></span>case when, instead +of considering the aggregate of the social phenomena in some one people, +we examine it simultaneously in different contemporaneous nations; +between which the perpetual reciprocity of influence, especially in +modern times, cannot be contested, though the <i>consensus</i> must in this +case be ordinarily of a less decided character, and must decrease +gradually with the affinity of the cases and the multiplicity of the +points of contact, so as at last, in some cases, to disappear almost +entirely; as for example between Western Europe and Eastern Asia, of +which the various general states of society appear to have been hitherto +almost independent of one another."</p> + +<p>These remarks are followed by illustrations of one of the most +important, and until lately, most neglected, of the general principles +which, in this division of the social science, may be considered as +established; namely, the necessary correlation between the form of +government existing in any society and the contemporaneous state of +civilization: a natural law, which stamps the endless discussions and +innumerable theories respecting forms of government in the abstract, as +fruitless and worthless, for any other purpose than as a preparatory +treatment of materials to be afterwards used for the construction of a +better philosophy.</p> + +<p>As already remarked, one of the main results of the science of social +statics would be to ascertain the requisites of stable political union. +There are some circumstances which, being found in all societies without +exception, and in the greatest degree where the social union is most +complete, may be considered (when psychological and ethological laws +confirm the indication) as conditions of the existence of the complex +phenomenon called a State. For example, no numerous society has ever +been held together without laws, or usages equivalent to them; without +tribunals, and an organized force of some sort to execute their +decisions. There have always been public authorities whom, with more or +less strictness and in cases more or less accurately defined, the rest +of the community obeyed, or according to general opinion were bound to +obey. By following out this course of inquiry we shall find <span class="pagenum"><a name="Page_517" id="Page_517">[Pg 517]</a></span>a number of +requisites, which have been present in every society that has maintained +a collective existence, and on the cessation of which it has either +merged in some other society, or reconstructed itself on some new basis, +in which the conditions were conformed to. Although these results, +obtained by comparing different forms and states of society, amount in +themselves only to empirical laws; some of them, when once suggested, +are found to follow with so much probability from general laws of human +nature, that the consilience of the two processes raises the evidence to +proof, and the generalizations to the rank of scientific truths.</p> + +<p>This seems to be affirmable (for instance) of the conclusions arrived at +in the following passage; extracted, with some alterations, from a +criticism on the negative philosophy of the eighteenth century,<a name="FNanchor_13_119" id="FNanchor_13_119"></a><a href="#Footnote_13_119" class="fnanchor">[13]</a> and +which I quote, though (as in some former instances) from myself, because +I have no better way of illustrating the conception I have formed of the +kind of theorems of which sociological statics would consist.</p> + +<p>"The very first element of the social union, obedience to a government +of some sort, has not been found so easy a thing to establish in the +world. Among a timid and spiritless race like the inhabitants of the +vast plains of tropical countries, passive obedience may be of natural +growth; though even there we doubt whether it has ever been found among +any people with whom fatalism, or in other words, submission to the +pressure of circumstances as a divine decree, did not prevail as a +religious doctrine. But the difficulty of inducing a brave and warlike +race to submit their individual <i>arbitrium</i> to any common umpire, has +always been felt to be so great, that nothing short of supernatural +power has been deemed adequate to overcome it; and such tribes have +always assigned to the first institution of civil society a divine +origin. So differently did those judge who knew savage men by actual +experience, from those who had no acquaintance with them except in the +civilized state. In modern Europe itself, after the fall of <span class="pagenum"><a name="Page_518" id="Page_518">[Pg 518]</a></span>the Roman +empire, to subdue the feudal anarchy and bring the whole people of any +European nation into subjection to government (though Christianity in +the most concentrated form of its influence was co-operating in the +work) required thrice as many centuries as have elapsed since that time.</p> + +<p>"Now if these philosophers had known human nature under any other type +than that of their own age, and of the particular classes of society +among whom they lived, it would have occurred to them, that wherever +this habitual submission to law and government has been firmly and +durably established, and yet the vigour and manliness of character which +resisted its establishment have been in any degree preserved, certain +requisites have existed, certain conditions have been fulfilled, of +which the following may be regarded as the principal.</p> + +<p>"First: there has existed, for all who were accounted citizens,—for all +who were not slaves, kept down by brute force,—a system of <i>education</i>, +beginning with infancy and continued through life, of which whatever +else it might include, one main and incessant ingredient was +<i>restraining discipline</i>. To train the human being in the habit, and +thence the power, of subordinating his personal impulses and aims, to +what were considered the ends of society; of adhering, against all +temptation, to the course of conduct which those ends prescribed; of +controlling in himself all feelings which were liable to militate +against those ends, and encouraging all such as tended towards them; +this was the purpose, to which every outward motive that the authority +directing the system could command, and every inward power or principle +which its knowledge of human nature enabled it to evoke, were +endeavoured to be rendered instrumental. The entire civil and military +policy of the ancient commonwealths was such a system of training; in +modern nations its place has been attempted to be supplied, principally, +by religious teaching. And whenever and in proportion as the strictness +of the restraining discipline was relaxed, the natural tendency of +mankind to anarchy re-asserted itself; the state <span class="pagenum"><a name="Page_519" id="Page_519">[Pg 519]</a></span>became disorganized +from within; mutual conflict for selfish ends, neutralized the energies +which were required to keep up the contest against natural causes of +evil; and the nation, after a longer or briefer interval of progressive +decline, became either the slave of a despotism, or the prey of a +foreign invader.</p> + +<p>"The second condition of permanent political society has been found to +be, the existence, in some form or other, of the feeling of allegiance +or loyalty. This feeling may vary in its objects, and is not confined to +any particular form of government; but whether in a democracy or in a +monarchy, its essence is always the same; viz. that there be in the +constitution of the state <i>something</i> which is settled, something +permanent, and not to be called in question; something which, by general +agreement, has a right to be where it is, and to be secure against +disturbance, whatever else may change. This feeling may attach itself, +as among the Jews (and in most of the commonwealths of antiquity), to a +common God or gods, the protectors and guardians of their state. Or it +may attach itself to certain persons, who are deemed to be, whether by +divine appointment, by long prescription, or by the general recognition +of their superior capacity and worthiness, the rightful guides and +guardians of the rest. Or it may connect itself with laws; with ancient +liberties or ordinances. Or, finally, (and this is the only shape in +which the feeling is likely to exist hereafter,) it may attach itself to +the principles of individual freedom and political and social equality, +as realized in institutions which as yet exist nowhere, or exist only in +a rudimentary state. But in all political societies which have had a +durable existence, there has been some fixed point: something which +people agreed in holding sacred; which, wherever freedom of discussion +was a recognised principle, it was of course lawful to contest in +theory, but which no one could either fear or hope to see shaken in +practice; which, in short (except perhaps during some temporary crisis) +was in the common estimation placed beyond discussion. And the necessity +of this may easily be made evident. A state never is, nor until mankind +are vastly improved, can <span class="pagenum"><a name="Page_520" id="Page_520">[Pg 520]</a></span>hope to be, for any long time exempt from +internal dissension; for there neither is nor has ever been any state of +society in which collisions did not occur between the immediate +interests and passions of powerful sections of the people. What, then, +enables nations to weather these storms, and pass through turbulent +times without any permanent weakening of the securities for peaceable +existence? Precisely this—that however important the interests about +which men fell out, the conflict did not affect the fundamental +principle of the system of social union which happened to exist; nor +threaten large portions of the community with the subversion of that on +which they had built their calculations, and with which their hopes and +aims had become identified. But when the questioning of these +fundamental principles is (not the occasional disease, or salutary +medicine, but) the habitual condition of the body politic; and when all +the violent animosities are called forth, which spring naturally from +such a situation, the state is virtually in a position of civil war; and +can never long remain free from it in act and fact.</p> + +<p>"The third essential condition of stability in political society, is a +strong and active principle of cohesion among the members of the same +community or state. We need scarcely say that we do not mean +nationality, in the vulgar sense of the term; a senseless antipathy to +foreigners; indifference to the general welfare of the human race, or an +unjust preference of the supposed interests of our own country; a +cherishing of bad peculiarities because they are national, or a refusal +to adopt what has been found good by other countries. We mean a +principle of sympathy, not of hostility; of union, not of separation. We +mean a feeling of common interest among those who live under the same +government, and are contained within the same natural or historical +boundaries. We mean, that one part of the community do not consider +themselves as foreigners with regard to another part; that they set a +value on their connexion—feel that they are one people, that their lot +is cast together, that evil to any of their fellow-countrymen is evil to +themselves, and do not desire selfishly to free themselves from their +share of any <span class="pagenum"><a name="Page_521" id="Page_521">[Pg 521]</a></span>common inconvenience by severing the connexion. How strong +this feeling was in those ancient commonwealths which attained any +durable greatness, every one knows. How happily Rome, in spite of all +her tyranny, succeeded in establishing the feeling of a common country +among the provinces of her vast and divided empire, will appear when any +one who has given due attention to the subject shall take the trouble to +point it out. In modern times the countries which have had that feeling +in the strongest degree have been the most powerful countries; England, +France, and, in proportion to their territory and resources, Holland and +Switzerland; while England in her connexion with Ireland, is one of the +most signal examples of the consequences of its absence. Every Italian +knows why Italy is under a foreign yoke; every German knows what +maintains despotism in the Austrian empire; the evils of Spain flow as +much from the absence of nationality among the Spaniards themselves, as +from the presence of it in their relations with foreigners: while the +completest illustration of all is afforded by the republics of South +America, where the parts of one and the same state adhere so slightly +together, that no sooner does any province think itself aggrieved by the +general government than it proclaims itself a separate nation."</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_X_6">§ 6.</a> While the derivative laws of social statics are ascertained by +analysing different states of society, and comparing them with one +another, without regard to the order of their succession; the +consideration of the successive order is, on the contrary, predominant +in the study of social dynamics, of which the aim is to observe and +explain the sequences of social conditions. This branch of the social +science would be as complete as it can be made, if every one of the +leading general circumstances of each generation were traced to its +causes in the generation immediately preceding. But the <i>consensus</i> is +so complete, (especially in modern history,) that in the filiation of +one generation and another, it is the whole which produces the whole, +rather than any part a part. Little progress, therefore, can be made in +establishing <span class="pagenum"><a name="Page_522" id="Page_522">[Pg 522]</a></span>the filiation, directly from laws of human nature, without +having first ascertained the immediate or derivative laws according to +which social states generate one another as society advances; the +<i>axiomata media</i> of General Sociology.</p> + +<p>The empirical laws which are most readily obtained by generalization +from history do not amount to this. They are not the "middle principles" +themselves, but only evidence towards the establishment of such +principles. They consist of certain general tendencies which may be +perceived in society; a progressive increase of some social elements and +diminution of others, or a gradual change in the general character of +certain elements. It is easily seen, for instance, that as society +advances, mental tend more and more to prevail over bodily qualities, +and masses over individuals: that the occupation of all that portion of +mankind who are not under external restraint is at first chiefly +military, but society becomes progressively more and more engrossed with +productive pursuits, and the military spirit gradually gives way to the +industrial; to which many similar truths might be added. And with +generalizations of this description, ordinary inquirers, even of the +historical school now predominant on the Continent, are satisfied. But +these and all such results are still at too great a distance from the +elementary laws of human nature on which they depend,—too many links +intervene, and the concurrence of causes at each link is far too +complicated,—to enable these propositions to be presented as direct +corollaries from those elementary principles. They have, therefore, in +the minds of most inquirers, remained in the state of empirical laws, +applicable only within the bounds of actual observation; without any +means of determining their real limits, and of judging whether the +changes which have hitherto been in progress are destined to continue +indefinitely, or to terminate, or even to be reversed.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_X_7">§ 7.</a> In order to obtain better empirical laws, we must not rest +satisfied with noting the progressive changes which manifest themselves +in the separate elements of society, and <span class="pagenum"><a name="Page_523" id="Page_523">[Pg 523]</a></span>in which nothing is indicated +but the relation of fragments of the effect to corresponding fragments +of the cause. It is necessary to combine the statical view of social +phenomena with the dynamical, considering not only the progressive +changes of the different elements, but the contemporaneous condition of +each; and thus obtain empirically the law of correspondence not only +between the simultaneous states, but between the simultaneous changes, +of those elements. This law of correspondence it is, which, duly +verified <i>à priori</i>, would become the real scientific derivative law of +the development of humanity and human affairs.</p> + +<p>In the difficult process of observation and comparison which is here +required, it would evidently be a great assistance if it should happen +to be the fact, that some one element in the complex existence of social +man is pre-eminent over all others as the prime agent of the social +movement. For we could then take the progress of that one element as the +central chain, to each successive link of which, the corresponding links +of all the other progressions being appended, the succession of the +facts would by this alone be presented in a kind of spontaneous order, +far more nearly approaching to the real order of their filiation than +could be obtained by any other merely empirical process.</p> + +<p>Now, the evidence of history and that of human nature combine, by a +striking instance of consilience, to show that there really is one +social element which is thus predominant, and almost paramount, among +the agents of the social progression. This is, the state of the +speculative faculties of mankind; including the nature of the beliefs +which by any means they have arrived at, concerning themselves and the +world by which they are surrounded.</p> + +<p>It would be a great error, and one very little likely to be committed, +to assert that speculation, intellectual activity, the pursuit of truth, +is among the more powerful propensities of human nature, or holds a +predominating place in the lives of any, save decidedly exceptional, +individuals. But, notwithstanding the relative weakness of this +principle among other sociological agents, its influence is the main +determining cause <span class="pagenum"><a name="Page_524" id="Page_524">[Pg 524]</a></span>of the social progress; all the other dispositions of +our nature which contribute to that progress, being dependent on it for +the means of accomplishing their share of the work. Thus (to take the +most obvious case first,) the impelling force to most of the +improvements effected in the arts of life, is the desire of increased +material comfort; but as we can only act upon external objects in +proportion to our knowledge of them, the state of knowledge at any time +is the limit of the industrial improvements possible at that time; and +the progress of industry must follow, and depend on, the progress of +knowledge. The same thing may be shown to be true, though it is not +quite so obvious, of the progress of the fine arts. Further, as the +strongest propensities of uncultivated or half-cultivated human nature +(being the purely selfish ones, and those of a sympathetic character +which partake most of the nature of selfishness) evidently tend in +themselves to disunite mankind, not to unite them,—to make them rivals, +not confederates; social existence is only possible by a disciplining of +those more powerful propensities, which consists in subordinating them +to a common system of opinions. The degree of this subordination is the +measure of the completeness of the social union, and the nature of the +common opinions determines its kind. But in order that mankind should +conform their actions to any set of opinions, these opinions must exist, +must be believed by them. And thus, the state of the speculative +faculties, the character of the propositions assented to by the +intellect, essentially determines the moral and political state of the +community, as we have already seen that it determines the physical.</p> + +<p>These conclusions, deduced from the laws of human nature, are in entire +accordance with the general facts of history. Every considerable change +historically known to us in the condition of any portion of mankind, +when not brought about by external force, has been preceded by a change, +of proportional extent, in the state of their knowledge, or in their +prevalent beliefs. As between any given state of speculation, and the +correlative state of everything else, it was almost always the former +which first showed itself; though the effects, no <span class="pagenum"><a name="Page_525" id="Page_525">[Pg 525]</a></span>doubt, reacted +potently upon the cause. Every considerable advance in material +civilization has been preceded by an advance in knowledge: and when any +great social change has come to pass, either in the way of gradual +development or of sudden conflict, it has had for its precursor a great +change in the opinions and modes of thinking of society. Polytheism, +Judaism, Christianity, Protestantism, the critical philosophy of modern +Europe, and its positive science—each of these has been a primary agent +in making society what it was at each successive period, while society +was but secondarily instrumental in making <i>them</i>, each of them (so far +as causes can be assigned for its existence) being mainly an emanation +not from the practical life of the period, but from the previous state +of belief and thought. The weakness of the speculative propensity in +mankind generally, has not, therefore, prevented the progress of +speculation from governing that of society at large; it has only, and +too often, prevented progress altogether, where the intellectual +progression has come to an early stand for want of sufficiently +favourable circumstances.</p> + +<p>From this accumulated evidence, we are justified in concluding, that the +order of human progression in all respects will mainly depend on the +order of progression in the intellectual convictions of mankind, that +is, on the law of the successive transformations of human opinions. The +question remains, whether this law can be determined; at first from +history as an empirical law, then converted into a scientific theorem by +deducing it <i>à priori</i> from the principles of human nature. As the +progress of knowledge and the changes in the opinions of mankind are +very slow, and manifest themselves in a well-defined manner only at long +intervals; it cannot be expected that the general order of sequence +should be discoverable from the examination of less than a very +considerable part of the duration of the social progress. It is +necessary to take into consideration the whole of past time, from the +first recorded condition of the human race, to the memorable phenomena +of the last and present generations.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_X_8">§ 8.</a> The investigation which I have thus endeavoured to <span class="pagenum"><a name="Page_526" id="Page_526">[Pg 526]</a></span>characterize, +has been systematically attempted, up to the present time, by M. Comte +alone. His work is hitherto the only known example of the study of +social phenomena according to this conception of the Historical Method. +Without discussing here the worth of his conclusions, and especially of +his predictions and recommendations with respect to the Future of +society, which appear to me greatly inferior in value to his +appreciation of the Past, I shall confine myself to mentioning one +important generalization, which M. Comte regards as the fundamental law +of the progress of human knowledge. Speculation he conceives to have, on +every subject of human inquiry, three successive stages; in the first of +which it tends to explain the phenomena by supernatural agencies, in the +second by metaphysical abstractions, and in the third or final state +confines itself to ascertaining their laws of succession and similitude. +This generalization appears to me to have that high degree of scientific +evidence, which is derived from the concurrence of the indications of +history with the probabilities derived from the constitution of the +human mind. Nor could it be easily conceived, from the mere enunciation +of such a proposition, what a flood of light it lets in upon the whole +course of history; when its consequences are traced, by connecting with +each of the three states of human intellect which it distinguishes, and +with each successive modification of those three states, the correlative +condition of other social phenomena.<a name="FNanchor_14_120" id="FNanchor_14_120"></a><a href="#Footnote_14_120" class="fnanchor">[14]</a></p> + +<p><span class="pagenum"><a name="Page_527" id="Page_527">[Pg 527]</a></span></p><p>But whatever decision competent judges may pronounce on the results +arrived at by any individual inquirer, the method now characterized is +that by which the derivative laws of social order and of social progress +must be sought. By its aid we may hereafter succeed not only in looking +far forward into the future history of the human race, but in +determining what artificial means may be used, and to what extent, to +accelerate the natural progress in so far as it is beneficial; to +compensate for whatever may be its inherent inconveniences or +disadvantages; and to guard against the dangers or accidents to which +our species is exposed from the necessary incidents of its progression. +Such practical instructions, founded on the highest branch of +speculative sociology, will form the noblest and most beneficial portion +of the Political Art.</p> + +<p>That of this science and art even the foundations are but beginning to +be laid, is sufficiently evident. But the superior <span class="pagenum"><a name="Page_528" id="Page_528">[Pg 528]</a></span>minds are fairly +turning themselves towards that object. It has become the aim of really +scientific thinkers to connect by theories the facts of universal +history: it is acknowledged to be one of the requisites of a general +system of social doctrine, that it should explain, so far as the data +exist, the main facts of history; and a Philosophy of History is +generally admitted to be at once the verification, and the initial form, +of the Philosophy of the Progress of Society.</p> + +<p>If the endeavours now making in all the more cultivated nations, and +beginning to be made even in England (usually the last to enter into the +general movement of the European mind) for the construction of a +Philosophy of History, shall be directed and controlled by those views +of the nature of sociological evidence which I have (very briefly and +imperfectly) attempted to characterize; they cannot fail to give birth +to a sociological system widely removed from the vague and conjectural +character of all former attempts, and worthy to take its place, at last, +among the sciences. When this time shall come, no important branch of +human affairs will be any longer abandoned to empiricism and +unscientific surmise: the circle of human knowledge will be complete, +and it can only thereafter receive further enlargement by perpetual +expansion from within.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_529" id="Page_529">[Pg 529]</a></span></p> +<h3><a name="BOOK_VI_CHAPTER_XI" id="BOOK_VI_CHAPTER_XI"></a>CHAPTER XI.<br /> +ADDITIONAL ELUCIDATIONS OF THE SCIENCE OF HISTORY.</h3> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_XI_1">§ 1.</a> The doctrine which the preceding chapters were intended to enforce +and elucidate—that the collective series of social phenomena, in other +words the course of history, is subject to general laws, which +philosophy may possibly detect—has been familiar for generations to the +scientific thinkers of the Continent, and has for the last quarter of a +century passed out of their peculiar domain, into that of newspapers and +ordinary political discussion. In our own country, however, at the time +of the first publication of this Treatise, it was almost a novelty, and +the prevailing habits of thought on historical subjects were the very +reverse of a preparation for it. Since then a great change has taken +place, and has been eminently promoted by the important work of Mr. +Buckle; who, with characteristic energy, flung down this great +principle, together with many striking exemplifications of it, into the +arena of popular discussion, to be fought over by a sort of combatants, +in the presence of a sort of spectators, who would never even have been +aware that there existed such a principle if they had been left to learn +its existence from the speculations of pure science. And hence has +arisen a considerable amount of controversy, tending not only to make +the principle rapidly familiar to the majority of cultivated minds, but +also to clear it from the confusions and misunderstandings by which it +was but natural that it should for a time be clouded, and which impair +the worth of the doctrine to those who accept it, and are the +stumbling-block of many who do not.</p> + +<p>Among the impediments to the general acknowledgment, by thoughtful +minds, of the subjection of historical facts to scientific laws, the +most fundamental continues to be that <span class="pagenum"><a name="Page_530" id="Page_530">[Pg 530]</a></span>which is grounded on the doctrine +of Free Will, or in other words, on the denial that the law of +invariable Causation holds true of human volitions: for if it does not, +the course of history, being the result of human volitions, cannot be a +subject of scientific laws, since the volitions on which it depends can +neither be foreseen, nor reduced to any canon of regularity even after +they have occurred. I have discussed this question, as far as seemed +suitable to the occasion, in a former chapter: and I only think it +necessary to repeat, that the doctrine of the Causation of human +actions, improperly called the doctrine of Necessity, affirms no +mysterious <i>nexus</i>, or overruling fatality: it asserts only that men's +actions are the joint result of the general laws and circumstances of +human nature, and of their own particular characters; those characters +again being the consequence of the natural and artificial circumstances +that constituted their education, among which circumstances must be +reckoned their own conscious efforts. Any one who is willing to take (if +the expression may be permitted) the trouble of thinking himself into +the doctrine as thus stated, will find it, I believe, not only a +faithful interpretation of the universal experience of human conduct, +but a correct representation of the mode in which he himself, in every +particular case, spontaneously interprets his own experience of that +conduct.</p> + +<p>But if this principle is true of individual man, it must be true of +collective man. If it is the law of human life, the law must be realized +in history. The experience of human affairs when looked at <i>en masse</i>, +must be in accordance with it if true, or repugnant to it if false. The +support which this <i>à posteriori</i> verification affords to the law, is +the part of the case which has been most clearly and triumphantly +brought out by Mr. Buckle.</p> + +<p>The facts of statistics, since they have been made a subject of careful +recordation and study, have yielded conclusions, some of which have been +very startling to persons not accustomed to regard moral actions as +subject to uniform laws. The very events which in their own nature +appear most capricious and uncertain, and which in any individual case +no <span class="pagenum"><a name="Page_531" id="Page_531">[Pg 531]</a></span>attainable degree of knowledge would enable us to foresee, occur, +when considerable numbers are taken into the account, with a degree of +regularity approaching to mathematical. What act is there which all +would consider as more completely dependent on individual character, and +on the exercise of individual free will, than that of slaying a fellow +creature? Yet in any large country, the number of murders, in proportion +to the population, varies (it has been found) very little from one year +to another, and in its variations never deviates widely from a certain +average. What is still more remarkable, there is a similar approach to +constancy in the proportion of these murders annually committed with +every particular kind of instrument. There is a like approximation to +identity, as between one year and another, in the comparative number of +legitimate and of illegitimate births. The same thing is found true of +suicides, accidents, and all other social phenomena of which the +registration is sufficiently perfect; one of the most curiously +illustrative examples being the fact, ascertained by the registers of +the London and Paris post-offices, that the number of letters posted +which the writers have forgotten to direct, is nearly the same, in +proportion to the whole number of letters posted, in one year as in +another. "Year after year," says Mr. Buckle, "the same proportion of +letter-writers forget this simple act; so that for each successive +period we can actually foretell the number of persons whose memory will +fail them in regard to this trifling, and as it might appear, accidental +occurrence."<a name="FNanchor_15_121" id="FNanchor_15_121"></a><a href="#Footnote_15_121" class="fnanchor">[15]</a></p> + +<p>This singular degree of regularity <i>en masse</i>, combined with the extreme +of irregularity in the cases composing the mass, is a felicitous +verification <i>à posteriori</i> of the law of causation in its application +to human conduct. Assuming the truth of that law, every human action, +every murder for instance, is the concurrent result of two sets of +causes. On the one part, the general circumstances of the country and +its inhabitants; the moral, educational, economical, and other +influences operating on the whole people, and constituting what we term +the state <span class="pagenum"><a name="Page_532" id="Page_532">[Pg 532]</a></span>of civilization. On the other part, the great variety of +influences special to the individual: his temperament, and other +peculiarities of organization, his parentage, habitual associates, +temptations, and so forth. If we now take the whole of the instances +which occur within a sufficiently large field to exhaust all the +combinations of these special influences, or in other words, to +eliminate chance; and if all these instances have occurred within such +narrow limits of time, that no material change can have taken place in +the general influences constituting the state of civilization of the +country; we may be certain, that if human actions are governed by +invariable laws, the aggregate result will be something like a constant +quantity. The number of murders committed within that space and time, +being the effect partly of general causes which have not varied, and +partly of partial causes the whole round of whose variations has been +included, will be, practically speaking, invariable.</p> + +<p>Literally and mathematically invariable it is not, and could not be +expected to be: because the period of a year is too short to include +<i>all</i> the possible combinations of partial causes, while it is, at the +same time, sufficiently long to make it probable that in some years at +least, of every series, there will have been introduced new influences +of a more or less general character; such as a more vigorous or a more +relaxed police; some temporary excitement from political or religious +causes; or some incident generally notorious, of a nature to act +morbidly on the imagination. That in spite of these unavoidable +imperfections in the data, there should be so very trifling a margin of +variation in the annual results, is a brilliant confirmation of the +general theory.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_XI_2">§ 2.</a> The same considerations which thus strikingly corroborate the +evidence of the doctrine, that historical facts are the invariable +effects of causes, tend equally to clear that doctrine from various +misapprehensions, the existence of which has been put in evidence by the +recent discussions. Some persons, for instance, seemingly imagine the +doctrine to imply, not merely that the total number of murders committed +in a <span class="pagenum"><a name="Page_533" id="Page_533">[Pg 533]</a></span>given space and time, is entirely the effect of the general +circumstances of society, but that every particular murder is so too: +that the individual murderer is, so to speak, a mere instrument in the +hands of general causes; that he himself has no option, or if he has, +and chose to exercise it, some one else would be necessitated to take +his place: that if any one of the actual murderers had abstained from +the crime, some person who would otherwise have remained innocent, would +have committed an extra murder to make up the average. Such a corollary +would certainly convict any theory which necessarily led to it of +absurdity. It is obvious, however, that each particular murder depends, +not on the general state of society only, but on that combined with +causes special to the case, which are generally much more powerful: and +if these special causes, which have greater influence than the general +ones in causing every particular murder, have no influence on the number +of murders in a given period, it is because the field of observation is +so extensive as to include all possible combinations of the special +causes—all varieties of individual character and individual temptation +compatible with the general state of society. The collective experiment, +as it may be termed, exactly separates the effect of the general from +that of the special causes, and shows the net result of the former: but +it declares nothing at all respecting the amount of influence of the +special causes, be it greater or smaller, since the scale of the +experiment extends to the number of cases within which the effects of +the special causes balance one another, and disappear in that of the +general causes.</p> + +<p>I will not pretend that all the defenders of the theory have always kept +their language free from this same confusion, and have shown no tendency +to exalt the influence of general causes at the expense of special. I am +of opinion, on the contrary, that they have done so in a very great +degree, and by so doing have encumbered their theory with difficulties, +and laid it open to objections, which do not necessarily affect it. +Some, for example (among whom is Mr. Buckle himself), have inferred, or +allowed it to be supposed that they inferred, from the regularity in +the recurrence <span class="pagenum"><a name="Page_534" id="Page_534">[Pg 534]</a></span>of events which depend on moral qualities, that the +moral qualities of mankind are little capable of being improved, or are +of little importance in the general progress of society, compared with +intellectual or economic causes. But to draw this inference is to forget +that the statistical tables, from which the invariable averages are +deduced, were compiled from facts occurring within narrow geographical +limits and in a small number of successive years; that is, from a field +the whole of which was under the operation of the same general causes, +and during too short a time to allow of much change therein. All moral +causes but those common to the country generally, have been eliminated +by the great number of instances taken; and those which are common to +the whole country have not varied considerably, in the short space of +time comprised in the observations. If we admit the supposition that +they have varied; if we compare one age with another, or one country +with another, or even one part of a country with another, differing in +position and character as to the moral elements, the crimes committed +within a year give no longer the same, but a widely different numerical +aggregate. And this cannot but be the case: for inasmuch as every single +crime committed by an individual mainly depends on his moral qualities, +the crimes committed by the entire population of the country must depend +in an equal degree on their collective moral qualities. To render this +element inoperative upon the large scale, it would be necessary to +suppose that the general moral average of mankind does not vary from +country to country or from age to age; which is not true, and even if it +were true, could not possibly be proved by any existing statistics. I do +not on this account the less agree in the opinion of Mr. Buckle, that +the intellectual element in mankind, including in that expression the +nature of their beliefs, the amount of their knowledge, and the +development of their intelligence, is the predominant circumstance in +determining their progress. But I am of this opinion, not because I +regard their moral or economical condition either as less powerful or +less variable agencies, but because these are in a great degree the +consequences of the intellectual condition, and are, in all cases, +limited by it; as was observed in the <span class="pagenum"><a name="Page_535" id="Page_535">[Pg 535]</a></span>preceding chapter. The +intellectual changes are the most conspicuous agents in history, not +from their superior force, considered in themselves, but because +practically they work with the united power belonging to all three.<a name="FNanchor_16_122" id="FNanchor_16_122"></a><a href="#Footnote_16_122" class="fnanchor">[16]</a></p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_XI_3">§ 3.</a> There is another distinction often neglected in the discussion of +this subject, which it is extremely important to observe. The theory of +the subjection of social progress to invariable laws, is often held in +conjunction with the doctrine, that social progress cannot be materially +influenced by the exertions of individual persons, or by the acts of +governments. But though these opinions are often held by the same +persons, they are two very different opinions, and the confusion between +them is the eternally recurring error of confounding Causation with +Fatalism. Because whatever happens will be the effect of causes, human +volitions among the rest, it does not follow that volitions, even those +of peculiar individuals, are not of great efficacy as causes. If any one +in a storm at sea, because about the same number of persons in every +year perish by shipwreck, should conclude that it was useless for him to +attempt to save <span class="pagenum"><a name="Page_536" id="Page_536">[Pg 536]</a></span>his own life, we should call him a Fatalist; and should +remind him that the efforts of shipwrecked persons to save their lives +are so far from being immaterial, that the average amount of those +efforts is one of the causes on which the ascertained annual number of +deaths by shipwreck depend. However universal the laws of social +development may be, they cannot be more universal or more rigorous than +those of the physical agencies of nature; yet human will can convert +these into instruments of its designs, and the extent to which it does +so makes the chief difference between savages and the most highly +civilized people. Human and social facts, from their more complicated +nature, are not less, but more, modifiable, than mechanical and chemical +facts; human agency, therefore, has still greater power over them. And +accordingly, those who maintain that the evolution of society depends +exclusively, or almost exclusively, on general causes, always include +among these the collective knowledge and intellectual development of the +race. But if of the race, why not also of some powerful monarch or +thinker, or of the ruling portion of some political society, acting +through its government? Though the varieties of character among ordinary +individuals neutralize one another on any large scale, exceptional +individuals in important positions do not in any given age neutralize +one another; there was not another Themistocles, or Luther, or Julius +Cæsar, of equal powers and contrary dispositions, who exactly balanced +the given Themistocles, Luther, and Cæsar, and prevented them from +having any permanent effect. Moreover, for aught that appears, the +volitions of exceptional persons, or the opinions and purposes of the +individuals who at some particular time compose a government, may be +indispensable links in the chain of causation by which even the general +causes produce their effects; and I believe this to be the only tenable +form of the theory.</p> + +<p>Lord Macaulay, in a celebrated passage of one of his early essays (let +me add that it was one which he did not himself choose to reprint), +gives expression to the doctrine of the absolute inoperativeness of +great men, more unqualified, I should think, than has been given to it +by any writer of equal abilities. <span class="pagenum"><a name="Page_537" id="Page_537">[Pg 537]</a></span>He compares them to persons who +merely stand on a loftier height, and thence receive the sun's rays a +little earlier, than the rest of the human race. "The sun illuminates +the hills while it is still below the horizon, and truth is discovered +by the highest minds a little before it becomes manifest to the +multitude. This is the extent of their superiority. They are the first +to catch and reflect a light which, without their assistance, must in a +short time be visible to those who lie far beneath them."<a name="FNanchor_17_123" id="FNanchor_17_123"></a><a href="#Footnote_17_123" class="fnanchor">[17]</a> If this +metaphor is to be carried out, it follows that if there had been no +Newton, the world would not only have had the Newtonian system, but +would have had it equally soon; as the sun would have risen just as +early to spectators in the plain if there had been no mountain at hand +to catch still earlier rays. And so it would be, if truths, like the +sun, rose by their own proper motion, without human effort; but not +otherwise. I believe that if Newton had not lived, the world must have +waited for the Newtonian philosophy until there had been another Newton, +or his equivalent. No ordinary man, and no succession of ordinary men, +could have achieved it. I will not go the length of saying that what +Newton did in a single life, might not have been done in successive +steps by some of those who followed him, each singly inferior to him in +genius. But even the least of those steps required a man of great +intellectual superiority. Eminent men do not merely see the coming light +from the hill-top, they mount on the hill-top and evoke it; and if no +one had ever ascended thither, the light, in many cases, might never +have risen upon the plain at all. Philosophy and religion are abundantly +amenable to general causes; yet few will doubt, that had there been no +Socrates, no Plato, and no Aristotle, there would have been no +philosophy for the next two thousand years, nor in all probability then; +and that if there had been no Christ, and no St. Paul, there would have +been no Christianity.</p> + +<p>The point in which, above all, the influence of remarkable individuals +is decisive, is in determining the celerity of the movement. In most +states of society it is the existence of <span class="pagenum"><a name="Page_538" id="Page_538">[Pg 538]</a></span>great men which decides even +whether there shall be any progress. It is conceivable that Greece, or +that Christian Europe, might have been progressive in certain periods of +their history through general causes only: but if there had been no +Mahomet, would Arabia have produced Avicenna or Averroes, or Caliphs of +Bagdad or of Cordova? In determining, however, in what manner and order +the progress of mankind shall take place if it take place at all, much +less depends on the character of individuals. There is a sort of +necessity established in this respect by the general laws of human +nature; by the constitution of the human mind. Certain truths cannot be +discovered, or inventions made, unless certain others have been made +first; certain social improvements, from the nature of the case, can +only follow, and not precede, others. The order of human progress, +therefore, may to a certain extent have definite laws assigned to it: +while as to its celerity, or even as to its taking place at all, no +generalization, extending to the human species generally, can possibly +be made; but only some very precarious approximate generalizations, +confined to the small portion of mankind in whom there has been anything +like consecutive progress within the historical period, and deduced from +their special position, or collected from their particular history. Even +looking to the <i>manner</i> of progress, the order of succession of social +states, there is need of great flexibility in our generalizations. The +limits of variation in the possible development of social, as of animal +life, are a subject of which little is yet understood, and are one of +the great problems in social science. It is, at all events, a fact, that +different portions of mankind, under the influence of different +circumstances, have developed themselves in a more or less different +manner and into different forms; and among these determining +circumstances, the individual character of their great speculative +thinkers or practical organizers may well have been one. Who can tell +how profoundly the whole subsequent history of China may have been +influenced by the individuality of Confucius? and of Sparta (and hence +of Greece and the world) by that of Lycurgus?</p> + +<p>Concerning the nature and extent of what a great man <span class="pagenum"><a name="Page_539" id="Page_539">[Pg 539]</a></span>under favourable +circumstances can do for mankind, as well as of what a government can do +for a nation, many different opinions are possible; and every shade of +opinion on these points is consistent with the fullest recognition that +there are invariable laws of historical phenomena. Of course the degree +of influence which has to be assigned to these more special agencies, +makes a great difference in the precision which can be given to the +general laws, and in the confidence with which predictions can be +grounded on them. Whatever depends on the peculiarities of individuals, +combined with the accident of the positions they hold, is necessarily +incapable of being foreseen. Undoubtedly these casual combinations might +be eliminated like any others, by taking a sufficiently large cycle: the +peculiarities of a great historical character make their influence felt +in history sometimes for several thousand years, but it is highly +probable that they may make no difference at all at the end of fifty +millions. Since, however, we cannot obtain an average of the vast length +of time necessary to exhaust all the possible combinations of great men +and circumstances, as much of the law of evolution of human affairs as +depends upon this average, is and remains inaccessible to us: and within +the next thousand years, which are of considerably more importance to us +than the whole remainder of the fifty millions, the favourable and +unfavourable combinations which will occur will be to us purely +accidental. We cannot foresee the advent of great men. Those who +introduce new speculative thoughts or great practical conceptions into +the world, cannot have their epoch fixed beforehand. What science can +do, is this. It can trace through past history the general causes which +had brought mankind into that preliminary state, which when the right +sort of great man appeared, rendered them accessible to his influence. +If this state continues, experience renders it tolerably certain that in +a longer or shorter period the great man will be produced; provided that +the general circumstances of the country and people are (which very +often they are not) compatible with his existence; of which point also, +science can in some measure judge. It is in this manner that the results +of progress, except as to the celerity of their production, <span class="pagenum"><a name="Page_540" id="Page_540">[Pg 540]</a></span>can be, to +a certain extent, reduced to regularity and law. And the belief that +they can be so, is equally consistent with assigning very great, or very +little efficacy, to the influence of exceptional men, or of the acts of +governments. And the same may be said of all other accidents and +disturbing causes.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_XI_4">§ 4.</a> It would nevertheless be a great error to assign only a trifling +importance to the agency of eminent individuals, or of governments. It +must not be concluded that the influence of either is small, because +they cannot bestow what the general circumstances of society, and the +course of its previous history, have not prepared it to receive. Neither +thinkers nor governments effect all that they intend, but in +compensation they often produce important results which they did not in +the least foresee. Great men, and great actions, are seldom wasted: they +send forth a thousand unseen influences, more effective than those which +are seen; and though nine out of every ten things done, with a good +purpose, by those who are in advance of their age, produce no material +effect, the tenth thing produces effects twenty times as great as any +one would have dreamed of predicting from it. Even the men who for want +of sufficiently favourable circumstances left no impress at all upon +their own age, have often been of the greatest value to posterity. Who +could appear to have lived more entirely in vain, than some of the early +heretics? They were burnt or massacred, their writings extirpated, their +memory anathematized, and their very names and existence left for seven +or eight centuries in the obscurity of musty manuscripts—their history +to be gathered, perhaps, only from the sentences by which they were +condemned. Yet the memory of these men—men who resisted certain +pretensions or certain dogmas of the Church in the very age in which the +unanimous assent of Christendom was afterwards claimed as having been +given to them, and asserted as the ground of their authority—broke the +chain of tradition, established a series of precedents for resistance, +inspired later Reformers with the courage, and armed them with the +weapons, which they needed when mankind <span class="pagenum"><a name="Page_541" id="Page_541">[Pg 541]</a></span>were better prepared to follow +their impulse. To this example from men, let us add another from +governments. The comparatively enlightened rule of which Spain had the +benefit during a considerable part of the eighteenth century, did not +correct the fundamental defects of the Spanish people; and in +consequence, though it did great temporary good, so much of that good +perished with it, that it may plausibly be affirmed to have had no +permanent effect. The case has been cited as a proof how little +governments can do, in opposition to the causes which have determined +the general character of the nation. It does show how much there is +which they cannot do; but not that they can do nothing. Compare what +Spain was at the beginning of that half century of liberal government, +with what she had become at its close. That period fairly let in the +light of European thought upon the more educated classes; and it never +afterwards ceased to go on spreading. Previous to that time the change +was in an inverse direction; culture, light, intellectual and even +material activity, were becoming extinguished. Was it nothing to arrest +this downward and convert it into an upward course? How much that +Charles the Third and Aranda could not do, has been the ultimate +consequence of what they did! To that half century Spain owes that she +has got rid of the Inquisition, that she has got rid of the monks, that +she now has parliaments and (save in exceptional intervals) a free +press, and the feelings of freedom and citizenship, and is acquiring +railroads and all the other constituents of material and economical +progress. In the Spain which preceded that era there was not a single +element at work, which could have led to these results in any length of +time, if the country had continued to be governed as it was by the last +princes of the Austrian dynasty, or if the Bourbon rulers had been from +the first what, both in Spain and in Naples, they afterwards became.</p> + +<p>And if a government can do much, even when it seems to have done little, +in causing positive improvement, still greater are the issues dependent +on it in the way of warding off evils, both internal and external, which +else would stop improvement altogether. A good or a bad counsellor, in a +single city at a <span class="pagenum"><a name="Page_542" id="Page_542">[Pg 542]</a></span>particular crisis, has affected the whole subsequent +fate of the world. It is as certain as any contingent judgment +respecting historical events can be, that if there had been no +Themistocles there would have been no victory of Salamis; and had there +not, where would have been all our civilization? How different again +would have been the issue if Epaminondas, or Timoleon, or even +Iphicrates, instead of Chares and Lysicles, had commanded at Chæroneia. +As is well said in the second of two Essays on the Study of History,<a name="FNanchor_18_124" id="FNanchor_18_124"></a><a href="#Footnote_18_124" class="fnanchor">[18]</a> +in my judgment the soundest and most philosophical productions which the +recent controversies on this subject have called forth; historical +science authorizes not absolute, but only conditional predictions. +General causes count for much, but individuals also "produce great +changes in history, and colour its whole complexion long after their +death.... No one can doubt that the Roman republic would have subsided +into a military despotism if Julius Cæsar had never lived;" (thus much +was rendered practically certain by general causes): "but is it at all +clear that in that case Gaul would ever have formed a province of the +empire? Might not Varus have lost his three legions on the banks of the +Rhone? and might not that river have become the frontier instead of the +Rhine? This might well have happened if Cæsar and Crassus had changed +provinces; and it is surely impossible to say that in such an event the +venue (as lawyers say) of European civilization might not have been +changed. The Norman Conquest in the same way was as much the act of a +single man, as the writing of a newspaper article; and knowing as we do +the history of that man and his family, we can retrospectively predict +with all but infallible certainty, that no other person" (no other in +that age, I presume, is meant), "could have accomplished the enterprise. +If it had not been accomplished, is there any ground to suppose that +either our history or our national character would have been what they +are?"</p> + +<p>As is most truly remarked by the same writer, the whole stream of +Grecian history, as cleared up by Mr. Grote, is one <span class="pagenum"><a name="Page_543" id="Page_543">[Pg 543]</a></span>series of examples +how often events on which the whole destiny of subsequent civilization +turned, were dependent on the personal character for good or evil of +some one individual. It must be said, however, that Greece furnishes the +most extreme example of this nature to be found in history, and is a +very exaggerated specimen of the general tendency. It has happened only +that once, and will probably never happen again, that the fortunes of +mankind depended upon keeping a certain order of things in existence in +a single town, or a country scarcely larger than Yorkshire; capable of +being ruined or saved by a hundred causes, of very slight magnitude in +comparison with the general tendencies of human affairs. Neither +ordinary accidents, nor the characters of individuals, can ever again be +so vitally important as they then were. The longer our species lasts, +and the more civilized it becomes, the more, as Comte remarks, does the +influence of past generations over the present, and of mankind <i>en +masse</i> over every individual in it, predominate over other forces: and +though the course of affairs never ceases to be susceptible of +alteration both by accidents and by personal qualities, the increasing +preponderance of the collective agency of the species over all minor +causes, is constantly bringing the general evolution of the race into +something which deviates less from a certain and preappointed track. +Historical science, therefore, is always becoming more possible: not +solely because it is better studied, but because, in every generation, +it becomes better adapted for study.</p> + + + +<hr class="chap" /><p><span class="pagenum"><a name="Page_544" id="Page_544">[Pg 544]</a></span></p> +<h3><a name="BOOK_VI_CHAPTER_XII" id="BOOK_VI_CHAPTER_XII"></a>CHAPTER XII.<br /> +OF THE LOGIC OF PRACTICE, OR ART; INCLUDING MORALITY AND POLICY.</h3> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_XII_1">§ 1.</a> In the preceding chapters we have endeavoured to characterize the +present state of those among the branches of knowledge called Moral, +which are sciences in the only proper sense of the term, that is, +inquiries into the course of nature. It is customary, however, to +include under the term moral knowledge, and even (though improperly) +under that of moral science, an inquiry the results of which do not +express themselves in the indicative, but in the imperative mood, or in +periphrases equivalent to it; what is called the knowledge of duties; +practical ethics, or morality.</p> + +<p>Now, the imperative mood is the characteristic of art, as distinguished +from science. Whatever speaks in rules, or precepts, not in assertions +respecting matters of fact, is art: and ethics, or morality, is properly +a portion of the art corresponding to the sciences of human nature and +society.<a name="FNanchor_19_125" id="FNanchor_19_125"></a><a href="#Footnote_19_125" class="fnanchor">[19]</a></p> + +<p>The Method, therefore, of Ethics, can be no other than that of Art, or +Practice, in general: and the portion yet uncompleted, of the task which +we proposed to ourselves in the concluding Book, is to characterize the +general Method of Art, as distinguished from Science.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_XII_2">§ 2.</a> In all branches of practical business, there are cases in which +individuals are bound to conform their practice to a pre-established +rule, while there are others in which it is part of their task to find +or construct the rule by which they are to <span class="pagenum"><a name="Page_545" id="Page_545">[Pg 545]</a></span>govern their conduct. The +first, for example, is the case of a judge, under a definite written +code. The judge is not called upon to determine what course would be +intrinsically the most advisable in the particular case in hand, but +only within what rule of law it falls; what the legislator has ordained +to be done in the kind of case, and must therefore be presumed to have +intended in the individual case. The method must here be wholly and +exclusively one of ratiocination, or syllogism; and the process is +obviously, what in our analysis of the syllogism we showed that all +ratiocination is, namely the interpretation of a formula.</p> + +<p>In order that our illustration of the opposite case may be taken from +the same class of subjects as the former, we will suppose, in contrast +with the situation of the judge, the position of a legislator. As the +judge has laws for his guidance, so the legislator has rules, and maxims +of policy; but it would be a manifest error to suppose that the +legislator is bound by these maxims in the same manner as the judge is +bound by the laws, and that all he has to do is to argue down from them +to the particular case, as the judge does from the laws. The legislator +is bound to take into consideration the reasons or grounds of the maxim; +the judge has nothing to do with those of the law, except so far as a +consideration of them may throw light upon the intention of the +law-maker, where his words have left it doubtful. To the judge, the +rule, once positively ascertained, is final; but the legislator, or +other practitioner, who goes by rules rather than by their reasons, like +the old-fashioned German tacticians who were vanquished by Napoleon, or +the physician who preferred that his patients should die by rule rather +than recover contrary to it, is rightly judged to be a mere pedant, and +the slave of his formulas.</p> + +<p>Now, the reasons of a maxim of policy, or of any other rule of art, can +be no other than the theorems of the corresponding science.</p> + +<p>The relation in which rules of art stand to doctrines of science may be +thus characterized. The art proposes to itself an end to be attained, +defines the end, and hands it over to the science. The science receives +it, considers it as a phenomenon <span class="pagenum"><a name="Page_546" id="Page_546">[Pg 546]</a></span>or effect to be studied, and having +investigated its causes and conditions, sends it back to art with a +theorem of the combination of circumstances by which it could be +produced. Art then examines these combinations of circumstances, and +according as any of them are or are not in human power, pronounces the +end attainable or not. The only one of the premises, therefore, which +Art supplies, is the original major premise, which asserts that the +attainment of the given end is desirable. Science then lends to Art the +proposition (obtained by a series of inductions or of deductions) that +the performance of certain actions will attain the end. From these +premises Art concludes that the performance of these actions is +desirable, and finding it also practicable, converts the theorem into a +rule or precept.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_XII_3">§ 3.</a> It deserves particular notice, that the theorem or speculative +truth is not ripe for being turned into a precept, until the whole, and +not a part merely, of the operation which belongs to science, has been +performed. Suppose that we have completed the scientific process only up +to a certain point; have discovered that a particular cause will produce +the desired effect, but have not ascertained all the negative conditions +which are necessary, that is, all the circumstances which, if present, +would prevent its production. If, in this imperfect state of the +scientific theory, we attempt to frame a rule of art, we perform that +operation prematurely. Whenever any counteracting cause, overlooked by +the theorem, takes place, the rule will be at fault: we shall employ the +means and the end will not follow. No arguing from or about the rule +itself will then help us through the difficulty: there is nothing for it +but to turn back and finish the scientific process which should have +preceded the formation of the rule. We must re-open the investigation, +to inquire into the remainder of the conditions on which the effect +depends; and only after we have ascertained the whole of these, are we +prepared to transform the completed law of the effect into a precept, in +which those circumstances or combinations of circumstances <span class="pagenum"><a name="Page_547" id="Page_547">[Pg 547]</a></span>which the +science exhibits as conditions, are prescribed as means.</p> + +<p>It is true that, for the sake of convenience, rules must be formed from +something less than this ideally perfect theory; in the first place, +because the theory can seldom be made ideally perfect; and next, +because, if all the counteracting contingencies, whether of frequent or +of rare occurrence, were included, the rules would be too cumbrous to be +apprehended and remembered by ordinary capacities, on the common +occasions of life. The rules of art do not attempt to comprise more +conditions than require to be attended to in ordinary cases; and are +therefore always imperfect. In the manual arts, where the requisite +conditions are not numerous, and where those which the rules do not +specify are generally either plain to common observation or speedily +learnt from practice, rules may often be safely acted on by persons who +know nothing more than the rule. But in the complicated affairs of life, +and still more in those of states and societies, rules cannot be relied +on, without constantly referring back to the scientific laws on which +they are founded. To know what are the practical contingencies which +require a modification of the rule, or which are altogether exceptions +to it, is to know what combinations of circumstances would interfere +with, or entirely counteract, the consequences of those laws: and this +can only be learnt by a reference to the theoretic grounds of the rule.</p> + +<p>By a wise practitioner, therefore, rules of conduct will only be +considered as provisional. Being made for the most numerous cases, or +for those of most ordinary occurrence, they point out the manner in +which it will be least perilous to act, where time or means do not exist +for analysing the actual circumstances of the case, or where we cannot +trust our judgment in estimating them. But they do not at all supersede +the propriety of going through (when circumstances permit) the +scientific process requisite for framing a rule from the data of the +particular case before us. At the same time, the common rule may very +properly serve as an admonition <span class="pagenum"><a name="Page_548" id="Page_548">[Pg 548]</a></span>that a certain mode of action has been +found by ourselves and others to be well adapted to the cases of most +common occurrence; so that if it be unsuitable to the case in hand, the +reason of its being so will be likely to arise from some unusual +circumstance.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_XII_4">§ 4.</a> The error is therefore apparent, of those who would deduce the line +of conduct proper to particular cases, from supposed universal practical +maxims; overlooking the necessity of constantly referring back to the +principles of the speculative science, in order to be sure of attaining +even the specific end which the rules have in view. How much greater +still, then, must the error be, of setting up such unbending principles, +not merely as universal rules for attaining a given end, but as rules of +conduct generally; without regard to the possibility, not only that some +modifying cause may prevent the attainment of the given end by the means +which the rule prescribes, but that success itself may conflict with +some other end, which may possibly chance to be more desirable.</p> + +<p>This is the habitual error of many of the political speculators whom I +have characterized as the geometrical school; especially in France, +where ratiocination from rules of practice forms the staple commodity of +journalism and political oratory; a misapprehension of the functions of +Deduction which has brought much discredit, in the estimation of other +countries, upon the spirit of generalization so honourably +characteristic of the French mind. The common-places of politics, in +France, are large and sweeping practical maxims, from which, as ultimate +premises, men reason downwards to particular applications, and this they +call being logical and consistent. For instance, they are perpetually +arguing that such and such a measure ought to be adopted, because it is +a consequence of the principle on which the form of government is +founded; of the principle of legitimacy, or the principle of the +sovereignty of the people. To which it may be answered, that if these be +really practical principles, they must rest on speculative grounds; the +sovereignty of the people (for example) <span class="pagenum"><a name="Page_549" id="Page_549">[Pg 549]</a></span>must be a right foundation for +government, because a government thus constituted tends to produce +certain beneficial effects. Inasmuch, however, as no government produces +all possible beneficial effects, but all are attended with more or fewer +inconveniences; and since these cannot usually be combated by means +drawn from the very causes which produce them; it would be often a much +stronger recommendation of some practical arrangement, that it does not +follow from what is called the general principle of the government, than +that it does. Under a government of legitimacy, the presumption is far +rather in favour of institutions of popular origin; and in a democracy, +in favour of arrangements tending to check the impetus of popular will. +The line of argumentation so commonly mistaken in France for political +philosophy, tends to the practical conclusion that we should exert our +utmost efforts to aggravate, instead of alleviating, whatever are the +characteristic imperfections of the system of institutions which we +prefer, or under which we happen to live.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_XII_5">§ 5.</a> The grounds, then, of every rule of art, are to be found in the +theorems of science. An art, or a body of art, consists of the rules, +together with as much of the speculative propositions as comprises the +justification of those rules. The complete art of any matter, includes a +selection of such a portion from the science, as is necessary to show on +what conditions the effects, which the art aims at producing, depend. +And Art in general, consists of the truths of Science, arranged in the +most convenient order for practice, instead of the order which is the +most convenient for thought. Science groups and arranges its truths, so +as to enable us to take in at one view as much as possible of the +general order of the universe. Art, though it must assume the same +general laws, follows them only into such of their detailed consequences +as have led to the formation of rules of conduct; and brings together +from parts of the field of science most remote from one another, the +truths relating to the production of the different and heterogeneous +conditions necessary to each effect which the exigencies of practical +life require to be produced.</p> + +<p><span class="pagenum"><a name="Page_550" id="Page_550">[Pg 550]</a></span></p><p>Science, therefore, following one cause to its various effects, while +art traces one effect to its multiplied and diversified causes and +conditions; there is need of a set of intermediate scientific truths, +derived from the higher generalities of science, and destined to serve +as the generalia or first principles of the various arts. The scientific +operation of framing these intermediate principles, M. Comte +characterizes as one of those results of philosophy which are reserved +for futurity. The only complete example which he points out as actually +realized, and which can be held up as a type to be imitated in more +important matters, is the general theory of the art of Descriptive +Geometry, as conceived by M. Monge. It is not, however, difficult to +understand what the nature of these intermediate principles must +generally be. After framing the most comprehensive possible conception +of the end to be aimed at, that is, of the effect to be produced, and +determining in the same comprehensive manner the set of conditions on +which that effect depends; there remains to be taken, a general survey +of the resources which can be commanded for realizing this set of +conditions; and when the result of this survey has been embodied in the +fewest and most extensive propositions possible, those propositions will +express the general relation between the available means and the end, +and will constitute the general scientific theory of the art; from which +its practical methods will follow as corollaries.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_XII_6">§ 6.</a> But though the reasonings which connect the end or purpose of every +art with its means, belong to the domain of Science, the definition of +the end itself belongs exclusively to Art, and forms its peculiar +province. Every art has one first principle, or general major premise, +not borrowed from science; that which enunciates the object aimed at, +and affirms it to be a desirable object. The builder's art assumes that +it is desirable to have buildings; architecture (as one of the fine +arts), that it is desirable to have them beautiful or imposing. The +hygienic and medical arts assume, the one that the preservation of +health, the other that the cure of disease, are fitting and desirable +ends. These are not propositions of science. <span class="pagenum"><a name="Page_551" id="Page_551">[Pg 551]</a></span>Propositions of science +assert a matter of fact: an existence, a coexistence, a succession, or a +resemblance. The propositions now spoken of do not assert that anything +is, but enjoin or recommend that something should be. They are a class +by themselves. A proposition of which the predicate is expressed, by the +words <i>ought</i> or <i>should be</i>, is generically different from one which is +expressed by <i>is</i>, or <i>will be</i>. It is true that, in the largest sense +of the words, even these propositions assert something as a matter of +fact. The fact affirmed in them is, that the conduct recommended excites +in the speaker's mind the feeling of approbation. This, however, does +not go to the bottom of the matter; for the speaker's approbation is no +sufficient reason why other people should approve; nor ought it to be a +conclusive reason even with himself. For the purposes of practice, every +one must be required to justify his approbation: and for this there is +need of general premises, determining what are the proper objects of +approbation, and what the proper order of precedence among those +objects.</p> + +<p>These general premises, together with the principal conclusions which +may be deduced from them, form (or rather might form) a body of +doctrine, which is properly the Art of Life, in its three departments, +Morality, Prudence or Policy, and Æsthetics; the Right, the Expedient, +and the Beautiful or Noble, in human conduct and works. To this art, +(which, in the main, is unfortunately still to be created,) all other +arts are subordinate; since its principles are those which must +determine whether the special aim of any particular art is worthy and +desirable, and what is its place in the scale of desirable things. Every +art is thus a joint result of laws of nature disclosed by science, and +of the general principles of what has been called Teleology, or the +Doctrine of Ends;<a name="FNanchor_20_126" id="FNanchor_20_126"></a><a href="#Footnote_20_126" class="fnanchor">[20]</a> which, borrowing the language of the German +metaphysicians, may also be termed, not improperly, the Principles of +Practical Reason.</p> + +<p>A scientific observer or reasoner, merely as such, is not <span class="pagenum"><a name="Page_552" id="Page_552">[Pg 552]</a></span>an adviser +for practice. His part is only to show that certain consequences follow +from certain causes, and that to obtain certain ends, certain means are +the most effectual. Whether the ends themselves are such as ought to be +pursued, and if so, in what cases and to how great a length, it is no +part of his business as a cultivator of science to decide, and science +alone will never qualify him for the decision. In purely physical +science, there is not much temptation to assume this ulterior office; +but those who treat of human nature and society invariably claim it; +they always undertake to say, not merely what is, but what ought to be. +To entitle them to do this, a complete doctrine of Teleology is +indispensable. A scientific theory, however perfect, of the subject +matter, considered merely as part of the order of nature, can in no +degree serve as a substitute. In this respect the various subordinate +arts afford a misleading analogy. In them there is seldom any visible +necessity for justifying the end, since in general its desirableness is +denied by nobody, and it is only when the question of precedence is to +be decided between that end and some other, that the general principles +of Teleology have to be called in: but a writer on Morals and Politics +requires those principles at every step. The most elaborate and +well-digested exposition of the laws of succession and coexistence among +mental or social phenomena, and of their relation to one another as +causes and effects, will be of no avail towards the art of Life or of +Society, if the ends to be aimed at by that art are left to the vague +suggestions of the <i>intellectus sibi permissus</i>, or are taken for +granted without analysis or questioning.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_XII_7">§ 7.</a> There is, then, a Philosophia Prima peculiar to Art, as there is +one which belongs to Science. There are not only first principles of +Knowledge, but first principles of Conduct. There must be some standard +by which to determine the goodness or badness, absolute and comparative, +of ends, or objects of desire. And whatever that standard is, there can +be but one: for if there were several ultimate principles of conduct, +the same conduct might be approved by <span class="pagenum"><a name="Page_553" id="Page_553">[Pg 553]</a></span>one of those principles and +condemned by another; and there would be needed some more general +principle, as umpire between them.</p> + +<p>Accordingly, writers on moral philosophy have mostly felt the necessity +not only of referring all rules of conduct, and all judgments of praise +and blame, to principles, but of referring them to some one principle; +some rule, or standard, with which all other rules of conduct were +required to be consistent, and from which by ultimate consequence they +could all be deduced. Those who have dispensed with the assumption of +such an universal standard, have only been enabled to do so by supposing +that a moral sense, or instinct, inherent in our constitution, informs +us, both what principles of conduct we are bound to observe, and also in +what order these should be subordinated to one another.</p> + +<p>The theory of the foundations of morality is a subject which it would be +out of place, in a work like this, to discuss at large, and which could +not to any useful purpose be treated incidentally. I shall content +myself therefore with saying, that the doctrine of intuitive moral +principles, even if true, would provide only for that portion of the +field of conduct which is properly called moral. For the remainder of +the practice of life some general principle, or standard, must still be +sought; and if that principle be rightly chosen, it will be found, I +apprehend, to serve quite as well for the ultimate principle of +Morality, as for that of Prudence, Policy, or Taste.</p> + +<p>Without attempting in this place to justify my opinion, or even to +define the kind of justification which it admits of, I merely declare my +conviction, that the general principle to which all rules of practice +ought to conform, and the test by which they should be tried, is that of +conduciveness to the happiness of mankind, or rather, of all sentient +beings: in other words, that the promotion of happiness is the ultimate +principle of Teleology.<a name="FNanchor_21_127" id="FNanchor_21_127"></a><a href="#Footnote_21_127" class="fnanchor">[21]</a></p> + +<p><span class="pagenum"><a name="Page_554" id="Page_554">[Pg 554]</a></span></p><p>I do not mean to assert that the promotion of happiness should be +itself the end of all actions, or even of all rules of action. It is the +justification, and ought to be the controller, of all ends, but is not +itself the sole end. There are many virtuous actions, and even virtuous +modes of action (though the cases are, I think, less frequent than is +often supposed) by which happiness in the particular instance is +sacrificed, more pain being produced than pleasure. But conduct of which +this can be truly asserted, admits of justification only because it can +be shown that on the whole more happiness will exist in the world, if +feelings are cultivated which will make people, in certain cases, +regardless of happiness. I fully admit that this is true: that the +cultivation of an ideal nobleness of will and conduct, should be to +individual human beings an end, to which the specific pursuit either of +their own happiness or of that of others (except so far as included in +that idea) should, in any case of conflict, give way. But I hold that +the very question, what constitutes this elevation of character, is +itself to be decided by a reference to happiness as the standard. The +character itself should be, to the individual, a paramount end, simply +because the existence of this ideal nobleness of character, or of a near +approach to it, in any abundance, would go further than all things else +towards making human life happy; both in the comparatively humble sense, +of pleasure and freedom from pain, and in the higher meaning, of +rendering life, not what it now is almost universally, puerile and +insignificant—but such as human beings with highly developed faculties +can care to have.</p> + + +<p class="newsection"><a name="BOOK_VI_CHAPTER_XII_8">§ 8.</a> With these remarks we must close this summary view of the +application of the general logic of scientific inquiry to the moral and +social departments of science. Notwithstanding the extreme generality of +the principles of method which I have laid down, (a generality which, I +trust, is not, in this instance, synonymous with vagueness) I have +indulged the hope that to some of those on whom the task will devolve of +bringing those most important of all sciences into a more <span class="pagenum"><a name="Page_555" id="Page_555">[Pg 555]</a></span>satisfactory +state, these observations may be useful; both in removing erroneous, and +in clearing up the true, conceptions of the means by which, on subjects +of so high a degree of complication, truth can be attained. Should this +hope be realized, what is probably destined to be the great intellectual +achievement of the next two or three generations of European thinkers +will have been in some degree forwarded.</p> + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"><p><a name="Footnote_1_107" id="Footnote_1_107"></a><a href="#FNanchor_1_107"><span class="label">[1]</span></a> Some arguments and explanations, supplementary to those in +the text, will be found in <i>An Examination of Sir William Hamilton's +Philosophy</i>, chap. xxvi.</p></div> + +<div class="footnote"><p><a name="Footnote_2_108" id="Footnote_2_108"></a><a href="#FNanchor_2_108"><span class="label">[2]</span></a> Supra, p. <a href="#Page_137">137</a>.</p></div> + +<div class="footnote"><p><a name="Footnote_3_109" id="Footnote_3_109"></a><a href="#FNanchor_3_109"><span class="label">[3]</span></a> When this chapter was written, Mr. Bain had not yet +published even the first part ("The Senses and the Intellect") of his +profound Treatise on the Mind. In this, the laws of association have +been more comprehensively stated and more largely exemplified than by +any previous writer; and the work, having been completed by the +publication of "The Emotions and the Will," may now be referred to as +incomparably the most complete analytical exposition of the mental +phenomena, on the basis of a legitimate Induction, which has yet been +produced. +</p><p> +Many striking applications of the laws of association to the explanation +of complex mental phenomena, are also to be found in Mr. Herbert +Spencer's "Principles of Psychology."</p></div> + +<div class="footnote"><p><a name="Footnote_4_110" id="Footnote_4_110"></a><a href="#FNanchor_4_110"><span class="label">[4]</span></a> In the case of the moral sentiments the place of direct +experiment is to a considerable extent supplied by historical +experience, and we are able to trace with a tolerable approach to +certainty the particular associations by which those sentiments are +engendered. This has been attempted, so far as respects the sentiment of +justice, in a little work by the present author, entitled +<i>Utilitarianism</i>.</p></div> + +<div class="footnote"><p><a name="Footnote_5_111" id="Footnote_5_111"></a><a href="#FNanchor_5_111"><span class="label">[5]</span></a> The most favourable cases for making such approximate +generalizations are what may be termed collective instances; where we +are fortunately enabled to see the whole class respecting which we are +inquiring, in action at once; and, from the qualities displayed by the +collective body, are able to judge what must be the qualities of the +majority of the individuals composing it. Thus the character of a nation +is shown in its acts as a nation; not so much in the acts of its +government, for those are much influenced by other causes; but in the +current popular maxims, and other marks of the general direction of +public opinion; in the character of the persons or writings that are +held in permanent esteem or admiration; in laws and institutions, so far +as they are the work of the nation itself, or are acknowledged and +supported by it; and so forth. But even here there is a large margin of +doubt and uncertainty. These things are liable to be influenced by many +circumstances: they are partly determined by the distinctive qualities +of that nation or body of persons, but partly also by external causes +which would influence any other body of persons in the same manner. In +order, therefore, to make the experiment really complete, we ought to be +able to try it without variation upon other nations: to try how +Englishmen would act or feel if placed in the same circumstances in +which we have supposed Frenchmen to be placed; to apply, in short, the +Method of Difference as well as that of Agreement. Now these experiments +we cannot try, nor even approximate to.</p></div> + +<div class="footnote"><p><a name="Footnote_6_112" id="Footnote_6_112"></a><a href="#FNanchor_6_112"><span class="label">[6]</span></a> "To which," says Dr. Whewell, "we may add, that it is +certain from the history of the subject, that in that case the +hypothesis would never have been framed at all." +</p><p> +Dr. Whewell (<i>Philosophy of Discovery</i>, pp. 277-282) defends Bacon's +rule against the preceding strictures. But his defence consists only in +asserting and exemplifying a proposition which I had myself stated, viz. +that though the largest generalizations may be the earliest made, they +are not at first seen in their entire generality, but acquire it by +degrees, as they are found to explain one class after another of +phenomena. The laws of motion, for example, were not known to extend to +the celestial regions, until the motions of the celestial bodies had +been deduced from them. This however does not in any way affect the +fact, that the middle principles of astronomy, the central force for +example, and the law of the inverse square, could not have been +discovered, if the laws of motion, which are so much more universal, had +not been known first. On Bacon's system of step-by-step generalization, +it would be impossible in any science to ascend higher than the +empirical laws; a remark which Dr. Whewell's own Inductive Tables, +referred to by him in support of his argument, amply bear out.</p></div> + +<div class="footnote"><p><a name="Footnote_7_113" id="Footnote_7_113"></a><a href="#FNanchor_7_113"><span class="label">[7]</span></a> <span title="See Vol. I.">Vol. i. p. 494 to the end of the chapter</span>.</p></div> + +<div class="footnote"><p><a name="Footnote_8_114" id="Footnote_8_114"></a><a href="#FNanchor_8_114"><span class="label">[8]</span></a> <i>Biographia Literaria</i>, i. 214.</p></div> + +<div class="footnote"><p><a name="Footnote_9_115" id="Footnote_9_115"></a><a href="#FNanchor_9_115"><span class="label">[9]</span></a> Supra, <span title="See Vol. I.">vol. i. p. 500</span>.</p></div> + +<div class="footnote"><p><a name="Footnote_10_116" id="Footnote_10_116"></a><a href="#FNanchor_10_116"><span class="label">[10]</span></a> <i>Essays on some Unsettled Questions of Political Economy</i>, +pp. 137-140.</p></div> + +<div class="footnote"><p><a name="Footnote_11_117" id="Footnote_11_117"></a><a href="#FNanchor_11_117"><span class="label">[11]</span></a> The quotations in this paragraph are from a paper written +by the author, and published in a periodical in 1834.</p></div> + +<div class="footnote"><p><a name="Footnote_12_118" id="Footnote_12_118"></a><a href="#FNanchor_12_118"><span class="label">[12]</span></a> <i>Cours de Philosophie Positive</i>, iv. 325-9.</p></div> + +<div class="footnote"><p><a name="Footnote_13_119" id="Footnote_13_119"></a><a href="#FNanchor_13_119"><span class="label">[13]</span></a> Since reprinted entire in <i>Dissertations and Discussions</i>, +as the concluding paper of the first volume.</p></div> + +<div class="footnote"><p><a name="Footnote_14_120" id="Footnote_14_120"></a><a href="#FNanchor_14_120"><span class="label">[14]</span></a> This great generalization is often unfavourably criticised +(as by Dr. Whewell for instance) under a misapprehension of its real +import. The doctrine, that the theological explanation of phenomena +belongs only to the infancy of our knowledge of them, ought not to be +construed as if it was equivalent to the assertion, that mankind, as +their knowledge advances, will necessarily cease to believe in any kind +of theology. This was M. Comte's opinion; but it is by no means implied +in his fundamental theorem. All that is implied is, that in an advanced +state of human knowledge, no other Ruler of the World will be +acknowledged than one who rules by universal laws, and does not at all, +or does not unless in very peculiar cases, produce events by special +interpositions. Originally all natural events were ascribed to such +interpositions. At present every educated person rejects this +explanation in regard to all classes of phenomena of which the laws have +been fully ascertained; though some have not yet reached the point of +referring all phenomena to the idea of Law, but believe that rain and +sunshine, famine and pestilence, victory and defeat, death and life, are +issues which the Creator does not leave to the operation of his general +laws, but reserves to be decided by express acts of volition. M. Comte's +theory is the negation of this doctrine. +</p><p> +Dr. Whewell equally misunderstands M. Comte's doctrine respecting the +second, or metaphysical stage of speculation. M. Comte did not mean that +"discussions concerning ideas" are limited to an early stage of inquiry, +and cease when science enters into the positive stage. (<i>Philosophy of +Discovery</i>, pp. 226 et seq.) In all M. Comte's speculations as much +stress is laid on the process of clearing up our conceptions, as on the +ascertainment of facts. When M. Comte speaks of the metaphysical stage +of speculation, he means the stage in which men speak of "Nature" and +other abstractions as if they were active forces, producing effects; +when Nature is said to do this, or forbid that; when Nature's horror of +a vacuum, Nature's non-admission of a break, Nature's <i>vis medicatrix</i>, +were offered as explanations of phenomena; when the qualities of things +were mistaken for real entities dwelling in the things; when the +phenomena of living bodies were thought to be accounted for by being +referred to a "vital force;" when, in short, the abstract names of +phenomena were mistaken for the causes of their existence. In this sense +of the word it cannot be reasonably denied that the metaphysical +explanation of phenomena, equally with the theological, gives way before +the advance of real science. +</p><p> +That the final, or positive stage, as conceived by M. Comte, has been +equally misunderstood, and that, notwithstanding some expressions open +to just criticism, M. Comte never dreamed of denying the legitimacy of +inquiry into all causes which are accessible to human investigation, I +have pointed out in a former place.</p></div> + +<div class="footnote"><p><a name="Footnote_15_121" id="Footnote_15_121"></a><a href="#FNanchor_15_121"><span class="label">[15]</span></a> Buckle's <i>History of Civilization</i>, i. 30.</p></div> + +<div class="footnote"><p><a name="Footnote_16_122" id="Footnote_16_122"></a><a href="#FNanchor_16_122"><span class="label">[16]</span></a> I have been assured by an intimate friend of Mr. Buckle +that he would not have withheld his assent from these remarks, and that +he never intended to affirm or imply that mankind are not progressive in +their moral as well as in their intellectual qualities. "In dealing with +his problem, he availed himself of the artifice resorted to by the +Political Economist, who leaves out of consideration the generous and +benevolent sentiments, and founds his science on the proposition that +mankind are actuated by acquisitive propensities alone," not because +such is the fact, but because it is necessary to begin by treating the +principal influence as if it was the sole one, and make the due +corrections afterwards. "He desired to make abstraction of the intellect +as the determining and dynamical element of the progression, eliminating +the more dependent set of conditions, and treating the more active one +as if it were an entirely independent variable." +</p><p> +The same friend of Mr. Buckle states that when he used expressions which +seemed to exaggerate the influence of general at the expense of special +causes, and especially at the expense of the influence of individual +minds, Mr. Buckle really intended no more than to affirm emphatically +that the greatest men cannot effect great changes in human affairs +unless the general mind has been in some considerable degree prepared +for them by the general circumstances of the age; a truth which, of +course, no one thinks of denying. And there certainly are passages in +Mr. Buckle's writings which speak of the influence exercised by great +individual intellects in as strong terms as could be desired.</p></div> + +<div class="footnote"><p><a name="Footnote_17_123" id="Footnote_17_123"></a><a href="#FNanchor_17_123"><span class="label">[17]</span></a> Essay on Dryden, in Miscellaneous Writings, i. 186.</p></div> + +<div class="footnote"><p><a name="Footnote_18_124" id="Footnote_18_124"></a><a href="#FNanchor_18_124"><span class="label">[18]</span></a> In the <i>Cornhill Magazine</i> for June and July 1861.</p></div> + +<div class="footnote"><p><a name="Footnote_19_125" id="Footnote_19_125"></a><a href="#FNanchor_19_125"><span class="label">[19]</span></a> It is almost superfluous to observe, that there is another +meaning of the word Art, in which it may be said to denote the poetical +department or aspect of things in general, in contradistinction to the +scientific. In the text, the word is used in its older, and I hope, not +yet obsolete sense.</p></div> + +<div class="footnote"><p><a name="Footnote_20_126" id="Footnote_20_126"></a><a href="#FNanchor_20_126"><span class="label">[20]</span></a> The word Teleology is also, but inconveniently and +improperly, employed by some writers as a name for the attempt to +explain the phenomena of the universe from final causes.</p></div> + +<div class="footnote"><p><a name="Footnote_21_127" id="Footnote_21_127"></a><a href="#FNanchor_21_127"><span class="label">[21]</span></a> For an express discussion and vindication of this +principle, see the little volume entitled "Utilitarianism."</p></div> + + +</div> +<p class="center">THE END.</p> + + +<hr class="chap" /> +<h2><a name="Transcribers_Notes" id="Transcribers_Notes"></a>Transcriber's Notes.</h2> + + +<p>Spelling irregularities where there was no obviously preferred version +were left as is. Variants include: "cotemporary" and "contemporary;" +"commonplaces" and "common-places;" "dependents" and "dependants;" +"dreamed" and "dreamt;" derivatives of "enclose" and "inclose;" "e. g." +and "e.g."; "i. e." and "i.e."; "misestimate" and "mis-estimate;" +"recal" and "recall" (and derivatives); derivatives of "paraphrase" and +"periphrase;" "subclass" and "sub-class" (and derivatives).</p> + +<p>Volume I. contains "το ὄν," while Volume II. spells it +"τὸ ὄν." The spellings were left as is, in each case.</p> + +<p>Changed "Phemomena" to "Phenomena" on page xv: "Successions of Social +Phenomena."</p> + +<p>Changed page reference for section 4 of Chapter XI on page xv of the +Table of Contents from "539" to "540."</p> + +<p>Changed "oberved" to "observed" on page 17: "the observed facts."</p> + +<p>A closing double quotation mark is missing on page 17. It was added +after the sentence that ends with "object of the inquiry."</p> + +<p>Changed "neverthless" to "nevertheless" on page 104: "phenomena would +nevertheless."</p> + +<p>For the mathematical formulas appearing on pages 152 and 153: +parentheses were added to make the linear form of the formula correct. +The equal sign was +preserved in "arc (sin = x)," although it makes more sense without it.</p> + +<p>Page 240 contains the word "'Squire." It intentionally begins with +an apostrophe, not an unmatched single quotation mark, and was left as +originally printed.</p> + +<p>Changed "eupiditatibus" to "cupiditatibus" on page 401: "de +cupiditatibus finiendis." And shortly thereafter, changed "eupiditas" to +"cupiditas:" "An potest cupiditas finiri." And then a bit further on, +changed "hæe" to "hæc:" "hæc desideria naturæ."</p> + + + + + + + + +<pre> + + + + + +End of the Project Gutenberg EBook of A System of Logic: Ratiocinative and +Inductive, by John Stuart Mill + +*** END OF THIS PROJECT GUTENBERG EBOOK A SYSTEM OF LOGIC, VOL II *** + +***** This file should be named 35421-h.htm or 35421-h.zip ***** +This and all associated files of various formats will be found in: + https://www.gutenberg.org/3/5/4/2/35421/ + +Produced by David Clarke, Stephen H. 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