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<span class="pagenum"><a name="pageii" id="pageii"></a>[page&nbsp;ii]</span>
<h3>UNIVERSITY MANUALS</h3>
<h4>EDITED BY PROFESSOR KNIGHT</h4>

<h2 style="margin-top: 2em;">LOGIC</h2>

<h3 style="margin-bottom: 2em;">INDUCTIVE AND DEDUCTIVE</h3>

<hr class="full" />

<span class="pagenum"><a name="pageiii" id="pageiii"></a>[page&nbsp;iii]</span>
<div class="center" style="margin-top: 2em; margin-bottom: 2em;"><div class="content1">
<span class="sc">Published May</span>, 1893<br />
<i>Reprinted December, 1893</i><br />
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>November, 1894</i><br />
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>January, 1899</i><br />
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>August, 1904</i><br />
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>June, 1909</i><br />
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>September, 1912</i><br />
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>July, 1913</i><br />
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>January, 1915</i>
  </div>  </div>
<span class="pagenum"><a name="pageiv" id="pageiv"></a>[page&nbsp;iv]</span>

<hr class="full" />

<h1 style="margin-top: 3em;">LOGIC</h1>

<h2 style="margin-bottom: 3em;">INDUCTIVE AND DEDUCTIVE</h2>

<h4>BY WILLIAM MINTO, M.A.</h4>
<p class="center">HON. LL.D. ST. ANDREWS<br />
<span class="sc">Late Professor of Logic in the University of Aberdeen</span></p>

<h4 style="margin-top: 8em; margin-bottom: 2em;">LONDON<br />
JOHN MURRAY, ALBEMARLE STREET, W.<br />
1915</h4>

<hr class="full" />

<span class="pagenum"><a name="pagev" id="pagev"></a>[page&nbsp;v]</span>

<h2 style="margin-top: 2em;">PREFACE.</h2>

<p>In this little treatise two things are attempted
that at first might appear incompatible. One
of them is to put the study of logical formul&aelig;
on a historical basis. Strangely enough, the
scientific evolution of logical forms, is a bit of
history that still awaits the zeal and genius of
some great scholar. I have neither ambition
nor qualification for such a <i>magnum opus</i>, and
my life is already more than half spent; but the
gap in evolutionary research is so obvious that
doubtless some younger man is now at work in
the field unknown to me. All that I can hope to
do is to act as a humble pioneer according to
my imperfect lights. Even the little I have done
represents work begun more than twenty years
ago, and continuously pursued for the last twelve
years during a considerable portion of my time.</p>

<p>The other aim, which might at first appear
inconsistent with this, is to increase the power
of Logic as a practical discipline. The main
purpose of this practical science, or scientific
art, is conceived to be the organisation of reason
against error, and error in its various kinds is
made the basis of the division of the subject. To
carry out this practical aim along with the historical
one is not hopeless, because throughout its
<span class="pagenum"><a name="pagevi" id="pagevi"></a>[page&nbsp;vi]</span>
long history Logic has been a practical science;
and, as I have tried to show at some length in
introductory chapters, has concerned itself at
different periods with the risks of error peculiar
to each.</p>

<p>To enumerate the various books, ancient and
modern, to which I have been indebted, would be
a vain parade. Where I have consciously adopted
any distinctive recent contribution to the long line
of tradition, I have made particular acknowledgment.
My greatest obligation is to my old professor,
Alexander Bain, to whom I owe my first
interest in the subject, and more details than I
can possibly separate from the general body of my
knowledge.</p>

<p class="author">W. M.</p>

<p class="authorleft"><span class="sc">Aberdeen</span>, <i>January, 1893</i>.</p>

<span class="pagenum"><a name="pagevii" id="pagevii"></a>[page&nbsp;vii]</span>

<p>Since these sentences were written, the author of
this book has died; and Professor Minto's <i>Logic</i>
is his last contribution to the literature of his
country. It embodies a large part of his teaching
in the philosophical class-room of his University,
and doubtless reflects the spirit of the whole of it.</p>

<p>Scottish Philosophy has lost in him one of its
typical representatives, and the University of the
North one of its most stimulating teachers. There
have been few more distinguished men than
William Minto in the professoriate of Aberdeen;
and the memory of what he was, of his wide and
varied learning, his brilliant conversation, his
urbanity, and his rare power of sympathy with
men with whose opinions he did not agree, will
remain a possession to many who mourn his loss.</p>

<p>It will be something if this little book keeps his
memory alive, both amongst the students who
owed so much to him, and in the large circle of
friends who used to feel the charm of his
personality.</p>

<p class="author">WILLIAM KNIGHT.</p>

<span class="pagenum"><a name="pageviii" id="pageviii"></a>[page&nbsp;viii]</span>

<h2 style="margin-top: 4em;"><i>GENERAL PLAN OF THE SERIES.</i></h2>

<div class="figcenter"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-007.png" width="112" height="16" alt="fancy rule" border="0" /></div>

<p><i>This Series is primarily designed to aid the University Extension
Movement throughout Great Britain and America, and to supply
the need so widely felt by students, of Text-books for study and
reference, in connexion with the authorised Courses of Lectures.</i></p>

<p><i>The Manuals differ from those already in existence in that they
are not intended for School use, or for Examination purposes; and
that their aim is to educate, rather than to inform. The statement
of details is meant to illustrate the working of general laws, and the
development of principles; while the historical evolution of the
subject dealt with is kept in view, along with its philosophical
significance.</i></p>

<p><i>The remarkable success which has attended University Extension
in Britain has been partly due to the combination of scientific treatment
with popularity, and to the union of simplicity with thoroughness.
This movement, however, can only reach those resident in the
larger centres of population, while all over the country there are
thoughtful persons who desire the same kind of teaching. It is for
them also that this Series is designed. Its aim is to supply the
general reader with the same kind of teaching as is given in the
Lectures, and to reflect the spirit which has characterised the movement,
viz., the combination of principles with facts, and of methods
with results.</i></p>

<p><i>The Manuals are also intended to be contributions to the Literature
of the Subjects with which they respectively deal, quite apart from
University Extension; and some of them will be found to meet a
general rather than a special want.</i></p>

<p><i>They will be issued simultaneously in England and America.
Volumes dealing with separate sections of Literature, Science,
Philosophy, History, and Art have been assigned to representative
literary men, to University Professors, or to Extension Lecturers
connected with Oxford, Cambridge, London, and the Universities of
Scotland and Ireland.</i></p>

<p><i>A list of the works in this Series will be found at the end of the
volume.</i></p>

<hr class="full" />
<span class="pagenum"><a name="pageix" id="pageix"></a>[page&nbsp;ix]</span>

<h2 style="margin-top: 2em;">CONTENTS.</h2>

<h3>INTRODUCTION.</h3>

<h3><a class="contents" href="#page1">I.</a></h3>
<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>&nbsp;</td>
       <td class="right">PAGE</td>
</tr>
<tr>
       <td>The Origin and Scope of Logic,</td>
       <td class="right"><a href="#page1">1</a></td>
</tr>
</table>

<h3><a class="contents" href="#page17">II.</a></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Logic as a Preventive of Error or Fallacy&mdash;The Inner
Sophist,</td>
       <td class="right"><a href="#page17">17</a></td>
</tr>
</table>

<h3><a class="contents" href="#page29">III.</a></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>The Axioms of Dialectic and of Syllogism,</td>
       <td class="right"><a href="#page29">29</a></td>
</tr>
</table>

<h2 style="margin-top: 3em;"><a class="contents" href="#page40">BOOK I.</a></h2>

<h3>THE LOGIC OF CONSISTENCY&mdash;SYLLOGISM AND DEFINITION.</h3>

<h3 style="margin-top: 3em;"><a class="contents" href="#page43">PART I.</a></h3>

<h3>THE ELEMENTS OF PROPOSITIONS.</h3>

<h3><span class="sc"><a class="contents" href="#page43">Chapter I.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>General Names and Allied Distinctions,</td>
       <td class="right"><a href="#page43">43</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page62">Chapter II.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>The Syllogistic Analysis of Proposition, into Terms. <br />
	   (1) The Bare Analytic Forms. <br />
	   (2) The Practice of Syllogistic Analysis. <br />
       (3) Some Technical Difficulties,</td>
       <td class="right" valign="top"><a href="#page62">62</a></td>
</tr>
</table>

<span class="pagenum"><a name="pagex" id="pagex"></a>[page&nbsp;x]</span>

<h2 style="margin-top: 3em;"><a class="contents" href="#page82">PART II.</a></h2>

<h3>DEFINITION.</h3>

<h3><span class="sc"><a class="contents" href="#page82">Chapter I.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>(1) Imperfect Understanding of Words. <br />
	       (2) Verification of the Meaning&mdash;Dialectic. <br />
		   (3) Fixation of the Meaning&mdash;Division or Classification, Definition, Naming,</td>
       <td class="right" valign="top"><a href="#page82">82</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page105">Chapter II.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>The Five Predicables&mdash;Verbal and Real Predication,</td>
       <td class="right" valign="top"><a href="#page105">105</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page112">Chapter III.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Aristotle's Categories,</td>
       <td class="right" valign="top"><a href="#page112">112</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page120">Chapter IV.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>The Controversy about Universals&mdash;Difficulties concerning
the <br />Relation of General Names to Thought and to Reality,</td>
       <td class="right" valign="top"><a href="#page120">120</a></td>
</tr>
</table>

<h3 style="margin-top: 3em;"><a class="contents" href="#page131">PART III.</a></h3>

<h3>THE INTERPRETATION OF PROPOSITIONS.</h3>

<h3><span class="sc"><a class="contents" href="#page131">Chapter I.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Theories of Predication&mdash;Theories of Judgment,</td>
       <td class="right" valign="top"><a href="#page131">131</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page139">Chapter II.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>The "Opposition" of Propositions&mdash;The Interpretation of
"No,"</td>
       <td class="right" valign="top"><a href="#page139">139</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page146">Chapter III.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>The Implication of Propositions&mdash;Immediate Formal Inference&mdash;Eduction,</td>
       <td class="right" valign="top"><a href="#page146">146</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page156">Chapter IV.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>The Counter-Implication of Propositions,</td>
       <td class="right" valign="top"><a href="#page156">156</a></td>
</tr>
</table>

<h3 style="margin-top: 3em;"><a class="contents" href="#page167">PART IV.</a></h3>

<h3>THE INTERDEPENDENCE OF PROPOSITIONS.</h3>

<h3><span class="sc"><a class="contents" href="#page167">Chapter I.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>The Syllogism,</td>
       <td class="right" valign="top"><a href="#page167">167</a></td>
</tr>
</table>
<span class="pagenum"><a name="pagexi" id="pagexi"></a>[page&nbsp;xi]</span>

<h3><span class="sc"><a class="contents" href="#page173">Chapter II.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>The Figures and Moods of the Syllogism. <br />
	       (1) The First Figure. <br />
		   (2) The Minor Figures and their Reduction to the First. <br />
		   (3) Sorites,</td>
       <td class="right" valign="top"><a href="#page173">173</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page185">Chapter III.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>The Demonstration of the Syllogistic Moods&mdash;The Canons
of the Syllogism,</td>
       <td class="right" valign="top"><a href="#page185">185</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page196">Chapter IV.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>The Analysis of Arguments into Syllogistic Forms,</td>
       <td class="right" valign="top"><a href="#page196">196</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page205">Chapter V.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Enthymemes,</td>
       <td class="right" valign="top"><a href="#page205">205</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page209">Chapter VI.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>The Utility of the Syllogism,</td>
       <td class="right" valign="top"><a href="#page209">209</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page215">Chapter VII.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Conditional Arguments&mdash;Hypothetical Syllogism, Disjunctive
Syllogism and Dilemma,</td>
       <td class="right" valign="top"><a href="#page215">215</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page226">Chapter VIII.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Fallacies in Deductive Argument&mdash;<i>Petitio Principii</i> and
<i>Ignoratio Elenchi</i>,</td>
       <td class="right" valign="top"><a href="#page226">226</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page235">Chapter IX.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Formal or Aristotelian Induction&mdash;Inductive Argument&mdash;The
Inductive Syllogism,</td>
       <td class="right" valign="top"><a href="#page235">235</a></td>
</tr>
</table>

<h2 style="margin-top: 3em;"><a class="contents" href="#page241">BOOK II.</a></h2>

<h3>INDUCTIVE LOGIC, OR THE LOGIC OF SCIENCE.</h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Introduction,</td>
       <td class="right" valign="top"><a href="#page243">243</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page273">Chapter I.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>The Data of Experience as Grounds of Inference or Rational
Belief,</td>
       <td class="right" valign="top"><a href="#page273">273</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page285">Chapter II.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Ascertainment of Simple Facts in their Order&mdash;Personal
Observation&mdash;<br />Hearsay Evidence&mdash;Method of Testing
Traditional Evidence,</td>
       <td class="right" valign="top"><a href="#page285">285</a></td>
</tr>
</table>

<span class="pagenum"><a name="pagexii" id="pagexii"></a>[page&nbsp;xii]</span>

<h3><span class="sc"><a class="contents" href="#page295">Chapter III.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Ascertainment of Facts of Causation. <br />(1) <i>Post Hoc Ergo
Propter Hoc.</i> <br />(2) Meaning of Cause&mdash;Methods of Observation&mdash;Mill's
Experimental Methods,</td>
       <td class="right" valign="top"><a href="#page295">295</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page308">Chapter IV.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Method of Observation&mdash;Single Difference. <br />(1) The Principle
of Single Difference. <br />(2) Application of the
Principle,</td>
       <td class="right" valign="top"><a href="#page308">308</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page318">Chapter V.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Methods of Observation&mdash;Elimination&mdash;Single Agreement.<br />
          (1) The Principle of Elimination. <br />
          (2) The Principle of Single Agreement. <br />
		  (3) Mill's "Joint Method of Agreement and Difference,"</td>
       <td class="right" valign="top"><a href="#page318">318</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page329">Chapter VI.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Methods of Observation&mdash;Minor Methods. <br />
	      (1) Concomitant Variations. <br />
		  (2) Single Residue,</td>
       <td class="right" valign="top"><a href="#page329">329</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page334">Chapter VII.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>The Method of Explanation. <br />
	      (1) The Four Stages of Orderly Procedure. <br />
		  (2) Obstacles to Explanation&mdash;Plurality of Causes and Intermixture of Effects. <br />
		  (3) The Proof of a Hypothesis,</td>
       <td class="right" valign="top"><a href="#page334">334</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page351">Chapter VIII.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Supplementary Methods of Investigation. <br />
	      (1) The Maintenance of Averages&mdash;Supplement to the Method of Difference. <br />
		  (2) The Presumption from Extra-Casual Coincidence,</td>
       <td class="right" valign="top"><a href="#page351">351</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page362">Chapter IX.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Probable Inference to Particulars&mdash;The Measurement of
Probability,</td>
       <td class="right" valign="top"><a href="#page362">362</a></td>
</tr>
</table>

<h3><span class="sc"><a class="contents" href="#page367">Chapter X.</a></span></h3>

<table width="70%" align="center" summary="contents" border="0">
<tr>
       <td>Inference from Analogy,</td>
       <td class="right" valign="top"><a href="#page367">367</a></td>
</tr>
</table>
    <br />
<span class="pagenum"><a name="page1" id="page1"></a>[page&nbsp;1]</span>

<hr class="full" />

<h2 style="margin-top: 3em;">INTRODUCTION.</h2>

<h3>I.&mdash;THE ORIGIN AND SCOPE OF LOGIC.</h3>

<p>The question has sometimes been asked, Where should
we begin in Logic? Particularly within the present
century has this difficulty been felt, when the study
of Logic has been revived and made intricate by the
different purposes of its cultivators.</p>

<p>Where did the founder of Logic begin? Where did
Aristotle begin? This seems to be the simplest way
of settling where we should begin, for the system
shaped by Aristotle is still the trunk of the tree,
though there have been so many offshoots from the
old stump and so many parasitic plants have wound
themselves round it that Logic is now almost as
tangled a growth as the Yews of Borrowdale&mdash;</p>

<div class="poem">  <div class="stanza">
<p>An intertwisted mass of fibres serpentine</p>
<p>Upcoiling and inveterately convolved.</p>
  </div>  </div>

<p>It used to be said that Logic had remained for two
thousand years precisely as Aristotle left it. It was
an example of a science or art perfected at one stroke
by the genius of its first inventor. The bewildered
student must often wish that this were so: it is only
superficially true. Much of Aristotle's nomenclature
and his central formul&aelig; have been retained, but they
<span class="pagenum"><a name="page2" id="page2"></a>[page&nbsp;2]</span>
have been very variously supplemented and interpreted
to very different purposes&mdash;often to no purpose at all.</p>

<p>The Cambridge mathematician's boast about his
new theorem&mdash;"The best of it all is that it can
never by any possibility be made of the slightest use
to anybody for anything"&mdash;might be made with truth
about many of the later developments of Logic. We
may say the same, indeed, about the later developments
of any subject that has been a playground for
generation after generation of acute intellects, happy in
their own disinterested exercise. Educational subjects&mdash;subjects
appropriated for the general schooling of
young minds&mdash;are particularly apt to be developed
out of the lines of their original intention. So many
influences conspire to pervert the original aim. The
convenience of the teacher, the convenience of the
learner, the love of novelty, the love of symmetry,
the love of subtlety; easy-going indolence on the one
hand and intellectual restlessness on the other&mdash;all
these motives act from within on traditional matter
without regard to any external purpose whatever.
Thus in Logic difficulties have been glossed over and
simplified for the dull understanding, while acute minds
have revelled in variations and new and ingenious
manipulations of the old formul&aelig;, and in multiplication
and more exact and symmetrical definition of the old
distinctions.</p>

<p>To trace the evolution of the forms and theories of
Logic under these various influences during its periods
of active development is a task more easily conceived
than executed, and one far above the ambition of an
introductory treatise. But it is well that even he who
writes for beginners should recognise that the forms
now commonly used have been evolved out of a
<span class="pagenum"><a name="page3" id="page3"></a>[page&nbsp;3]</span>
simpler tradition. Without entering into the details
of the process, it is possible to indicate its main stages,
and thus furnish a clue out of the modern labyrinthine
confusion of purposes.</p>

<p>How did the Aristotelian Logic originate? Its
central feature is the syllogistic forms. In what
circumstances did Aristotle invent these? For what
purpose? What use did he contemplate for them?
In rightly understanding this, we shall understand
the original scope or province of Logic, and thus be
in a position to understand more clearly how it has
been modified, contracted, expanded, and supplemented.</p>

<p>Logic has always made high claims as the <i>scientia
scientiarum</i>, the science of sciences. The builders of
this Tower of Babel are threatened in these latter days
with confusion of tongues. We may escape this
danger if we can recover the designs of the founder,
and of the master-builders who succeeded him.</p>

<p>Aristotle's Logic has been so long before the world
in abstract isolation that we can hardly believe that its
form was in any way determined by local accident. A
horror as of sacrilege is excited by the bare suggestion
that the author of this grand and venerable work,
one of the most august monuments of transcendent
intellect, was in his day and generation only a pre-eminent
tutor or schoolmaster, and that his logical
writings were designed for the accomplishment of his
pupils in a special art in which every intellectually
ambitious young Athenian of the period aspired to
excel. Yet such is the plain fact, baldly stated.
Aristotle's Logic in its primary aim was as practical
as a treatise on Navigation, or "Cavendish on
Whist". The latter is the more exact of the two
<span class="pagenum"><a name="page4" id="page4"></a>[page&nbsp;4]</span>
comparisons. It was in effect in its various parts a
series of handbooks for a temporarily fashionable intellectual
game, a peculiar mode of disputation or dialectic,<a id="footnotetagIntI1" name="footnotetagIntI1"></a><a href="#footnoteIntI1"><sup>1</sup></a>
the game of Question and Answer, the game so fully
illustrated in the Dialogues of Plato, the game identified
with the name of Socrates.</p>

<p>We may lay stress, if we like, on the intellectuality
of the game, and the high topics on which it was
exercised. It was a game that could flourish only
among a peculiarly intellectual people; a people less
acute would find little sport in it. The Athenians
still take a singular delight in disputation. You
<span class="pagenum"><a name="page5" id="page5"></a>[page&nbsp;5]</span>
cannot visit Athens without being struck by it. You
may still see groups formed round two protagonists
in the caf&eacute;s or the squares, or among the ruins of
the Acropolis, in a way to remind you of Socrates
and his friends. They do not argue as Gil Blas and
his Hibernians did with heat and temper, ending
in blows. They argue for the pure love of arguing,
the audience sitting or standing by to see fair play
with the keenest enjoyment of intellectual thrust
and parry. No other people could argue like the
Greeks without coming to blows. It is one of their
characteristics now, and so it was in old times two
thousand years ago. And about a century before
Aristotle reached manhood, they had invented this
peculiarly difficult and trying species of disputative
pastime, in which we find the genesis of Aristotle's
logical treatises.</p>

<p>To get a proper idea of this debate by Question and
Answer, which we may call Socratic disputation after
its most renowned master, one must read some of the
dialogues of Plato. I will indicate merely the skeleton
of the game, to show how happily it lent itself to
Aristotle's analysis of arguments and propositions.</p>

<p>A thesis or proposition is put up for debate, <i>e.g.</i>, that
knowledge is nothing else than sensible perception,<a id="footnotetagIntI2" name="footnotetagIntI2"></a><a href="#footnoteIntI2"><sup>2</sup></a> that
it is a greater evil to do wrong than to suffer wrong,<a id="footnotetagIntI3" name="footnotetagIntI3"></a><a href="#footnoteIntI3"><sup>3</sup></a>
that the love of gain is not reprehensible.<a id="footnotetagIntI4" name="footnotetagIntI4"></a><a href="#footnoteIntI4"><sup>4</sup></a> There are
two disputants, but they do not speak on the question
by turns, so many minutes being allowed to each as
in a modern encounter of wits. One of the two, who
may be called the Questioner, is limited to asking
<span class="pagenum"><a name="page6" id="page6"></a>[page&nbsp;6]</span>
questions, the other, the Respondent, is limited to
answering. Further, the Respondent can answer only
"Yes" or "No," with perhaps a little explanation:
on his side the Questioner must ask only questions
that admit of the simple answer "Yes" or "No".
The Questioner's business is to extract from the
Respondent admissions involving the opposite of what
he has undertaken to maintain. The Questioner tries
in short to make him contradict himself. Only a
very stupid Respondent would do this at once: the
Questioner plies him with general principles, analogies,
plain cases; leads him on from admission to admission,
and then putting the admissions together convicts him
out of his own mouth of inconsistency.<a id="footnotetagIntI5" name="footnotetagIntI5"></a><a href="#footnoteIntI5"><sup>5</sup></a></p>

<p>Now mark precisely where Aristotle struck in with
his invention of the Syllogism, the invention on which
he prided himself as specially his own, and the forms
of which have clung to Logic ever since, even in the
usage of those who deride Aristotle's Moods and Figures
as antiquated superstitions. Suppose yourself the
Questioner, where did he profess to help you with his
mechanism? In effect, as the word Syllogism indicates,
it was when you had obtained a number of admissions,
<span class="pagenum"><a name="page7" id="page7"></a>[page&nbsp;7]</span>
and wished to reason them together, to demonstrate
how they bore upon the thesis in dispute, how they
hung together, how they necessarily involved what
you were contending for. And the essence of his
mechanism was the reduction of the admitted propositions
to common terms, and to certain types or forms
which are manifestly equivalent or inter-dependent.
Aristotle advised his pupils also in the tactics of the
game, but his grand invention was the form or type of
admissions that you should strive to obtain, and the
effective manipulation of them when you had got
them.</p>

<p>An example will show the nature of this help, and
what it was worth. To bring the thing nearer home,
let us, instead of an example from Plato, whose topics
often seem artificial to us now, take a thesis from last
century, a paradox still arguable, Mandeville's famous&mdash;some
would say infamous&mdash;paradox that Private
Vices are Public Benefits. Undertake to maintain this,
and you will have no difficulty in getting a respondent
prepared to maintain the negative. The plain men,
such as Socrates cross-questioned, would have declared
at once that a vice is a vice, and can never do any good
to anybody. Your Respondent denies your proposition
simply: he upholds that private vices never are
public benefits, and defies you to extract from him any
admission inconsistent with this. Your task then is to
lure him somehow into admitting that in some cases
what is vicious in the individual may be of service to
the State. This is enough: you are not concerned to
establish that this holds of all private vices. A single
instance to the contrary is enough to break down his
universal negative. You cannot, of course, expect
him to make the necessary admission in direct terms:
<span class="pagenum"><a name="page8" id="page8"></a>[page&nbsp;8]</span>
you must go round about. You know, perhaps, that
he has confidence in Bishop Butler as a moralist. You
try him with the saying: "To aim at public and
private good are so far from being inconsistent that
they mutually promote each other". Does he admit
this?</p>

<p>Perhaps he wants some little explanation or exemplification
to enable him to grasp your meaning. This
was within the rules of the game. You put cases to
him, asking for his "Yes" or "No" to each. Suppose
a man goes into Parliament, not out of any zeal for
the public good, but in pure vainglory, or to serve his
private ends, is it possible for him to render the State
good service? Or suppose a milk-seller takes great
pains to keep his milk pure, not because he cares for
the public health, but because it pays, is this a benefit
to the public?</p>

<p>Let these questions be answered in the affirmative,
putting you in possession of the admission that some
actions undertaken for private ends are of public
advantage, what must you extract besides to make good
your position as against the Respondent? To see
clearly at this stage what now is required, though you
have to reach it circuitously, masking your approach
under difference of language, would clearly be an
advantage. This was the advantage that Aristotle's
method offered to supply. A disputant familiar with
his analysis would foresee at once that if he could get
the Respondent to admit that all actions undertaken
for private ends are vicious, the victory was his, while
nothing short of this would serve.</p>

<p>Here my reader may interject that he could have
seen this without any help from Aristotle, and that
anybody may see it without knowing that what he has
<span class="pagenum"><a name="page9" id="page9"></a>[page&nbsp;9]</span>
to do is, in Aristotelian language, to construct a syllogism
in Bokardo. I pass this over. I am not concerned
at this point to defend the utility of Aristotle's
method. All that I want is to illustrate the kind of
use that it was intended for. Perhaps if Aristotle had
not habituated men's minds to his analysis, we should
none of us have been able to discern coherence and
detect incoherence as quickly and clearly as we do now.</p>

<p>But to return to our example. As Aristotle's pupil,
you would have seen at the stage we are speaking of
that the establishment of your thesis must turn upon
the definition of virtue and vice. You must proceed,
therefore, to cross-examine your Respondent about
this. You are not allowed to ask him what he means
by virtue, or what he means by vice. In accordance
with the rules of the dialectic, it is your business to
propound definitions, and demand his Yes or No to
them. You ask him, say, whether he agrees with
Shaftesbury's definition of a virtuous action as an
action undertaken purely for the good of others. If
he assents, it follows that an action undertaken with
any suspicion of a self-interested motive cannot be
numbered among the virtues. If he agrees, further,
that every action must be either vicious or virtuous,
you have admissions sufficient to prove your original
thesis. All that you have now to do to make your
triumph manifest, is to display the admissions you
have obtained in common terms.</p>

<blockquote><p>
Some actions done with a self-interested motive are public
benefits.</p>
<p style="margin-top: -1em">
All actions done with a self-interested motive are private
vices.
</p></blockquote>

<p>From these premisses it follows irresistibly that</p>

<blockquote><p>
Some private vices are public benefits.
</p></blockquote>
<span class="pagenum"><a name="page10" id="page10"></a>[page&nbsp;10]</span>

<p>This illustration may serve to show the kind of
disputation for which Aristotle's logic was designed,
and thus to make clear its primary uses and its
limitations.</p>

<p>To realise its uses, and judge whether there is
anything analogous to them in modern needs, conceive
the chief things that it behoved Questioner
and Respondent in this game to know. All that a
proposition necessarily implies; all that two propositions
put together imply; on what conditions and
to what extent one admission is inconsistent with
another; when one admission necessarily involves
another; when two necessarily involve a third. And
to these ends it was obviously necessary to have an
exact understanding of the terms used, so as to avoid
the snares of ambiguous language.</p>

<p>That a Syllogistic or Logic of Consistency should
emerge out of Yes-and-No Dialectic was natural.
Things in this world come when they are wanted:
inventions are made on the spur of necessity. It was
above all necessary in this kind of debate to avoid
contradicting yourself: to maintain your consistency.
A clever interrogator spread out proposition after proposition
before you and invited your assent, choosing
forms of words likely to catch your prejudices and lure
you into self-contradiction. An organon, instrument,
or discipline calculated to protect you as Respondent
and guide you as Questioner by making clear what an
admission led to, was urgently called for, and when
the game had been in high fashion for more than a
century Aristotle's genius devised what was wanted,
meeting at the same time, no doubt, collateral needs
that had arisen from the application of Dialectic to
various kinds of subject-matter.</p>
<span class="pagenum"><a name="page11" id="page11"></a>[page&nbsp;11]</span>

<p>The thoroughness of Aristotle's system was doubtless
due partly to the searching character of the
dialectic in which it had its birth. No other mode of
disputation makes such demands upon the disputant's
intellectual agility and precision, or is so well adapted
to lay bare the skeleton of an argument.</p>

<p>The uses of Aristotle's logical treatises remained
when the fashion that had called them forth had
passed.<a id="footnotetagIntI6" name="footnotetagIntI6"></a><a href="#footnoteIntI6"><sup>6</sup></a> Clear and consistent thinking, a mastery of
the perplexities and ambiguities of language, power to
detect identity of meaning under difference of expression,
a ready apprehension of all that a proposition
implies, all that may be educed or deduced from it&mdash;whatever
helps to these ends must be of perpetual use.
"To purge the understanding of those errors which
lie in the confusion and perplexities of an inconsequent
thinking," is a modern description of the main scope
of Logic.<a id="footnotetagIntI7" name="footnotetagIntI7"></a><a href="#footnoteIntI7"><sup>7</sup></a> It is a good description of the branch of
Logic that keeps closest to the Aristotelian tradition.</p>
<span class="pagenum"><a name="page12" id="page12"></a>[page&nbsp;12]</span>

<p>The limitations as well as the uses of Aristotle's logic
may be traced to the circumstances of its origin. Both
parties to the disputation, Questioner and Respondent
alike, were mainly concerned with the inter-dependence
of the propositions put forward. Once the Respondent
had given his assent to a question, he was bound in
consistency to all that it implied. He must take all
the consequences of his admission. It might be true
or it might be false as a matter of fact: all the same
he was bound by it: its truth or falsehood was
immaterial to his position as a disputant. On the
other hand, the Questioner could not go beyond the
admissions of the Respondent. It has often been
alleged as a defect in the Syllogism that the conclusion
does not go beyond the premisses, and ingenious
attempts have been made to show that it is really an
advance upon the premisses. But having regard to the
primary use of the syllogism, this was no defect, but a
necessary character of the relation. The Questioner
could not in fairness assume more than had been
granted by implication. His advance could only be an
argumentative advance: if his conclusion contained a
grain more than was contained in the premisses, it was
a sophistical trick, and the Respondent could draw
back and withhold his assent. He was bound in consistency
to stand by his admissions; he was not
bound to go a fraction of an inch beyond them.</p>

<p>We thus see how vain it is to look to the Aristotelian
tradition for an organon of truth or a criterion of
falsehood. Directly and primarily, at least, it was not
so; the circumstances of its origin gave it a different
bent. Indirectly and secondarily, no doubt, it served
this purpose, inasmuch as truth was the aim of all
serious thinkers who sought to clear their minds and
<span class="pagenum"><a name="page13" id="page13"></a>[page&nbsp;13]</span>
the minds of others by Dialectic. But in actual debate
truth was represented merely by the common-sense of
the audience. A dialectician who gained a triumph by
outraging this, however cleverly he might outwit his
antagonist, succeeded only in amusing his audience,
and dialecticians of the graver sort aimed at more
serious uses and a more respectful homage, and did
their best to discountenance merely eristic disputation.
Further, it would be a mistake to conclude because
Aristotle's Logic, as an instrument of Dialectic, concerned
itself with the syllogism of propositions rather
than their truth, that it was merely an art of quibbling.
On the contrary, it was essentially the art of preventing
and exposing quibbling. It had its origin in quibbling,
no doubt, inasmuch as what we should call verbal
quibbling was of the essence of Yes-and-No Dialectic,
and the main secret of its charm for an intellectual
and disputatious people; but it came into being as
a safeguard against quibbling, not a serviceable
adjunct.</p>

<p style="margin-top: 2.5em">The medi&aelig;val developments of Logic retained and
even exaggerated the syllogistic character of the
original treatises. Interrogative dialectic had disappeared
in the Middle Ages whether as a diversion
or as a discipline: but errors of inconsistency still
remained the errors against which principally educated
men needed a safeguard. Men had to keep their
utterances in harmony with the dogmas of the Church.
A clear hold of the exact implications of a proposition,
whether singly or in combination with other propositions,
was still an important practical need. The
Inductive Syllogism was not required, and its treatment
dwindled to insignificance in medi&aelig;val text-books, but
<span class="pagenum"><a name="page14" id="page14"></a>[page&nbsp;14]</span>
the Deductive Syllogism and the formal apparatus
for the definition of terms held the field.</p>

<p>It was when observation of Nature and its laws
became a paramount pursuit that the defects of
Syllogistic Logic began to be felt. Errors against
which this Logic offered no protection then called for
a safeguard&mdash;especially the errors to which men are
liable in the investigation of cause and effect. "Bring
your thoughts into harmony one with another," was
the demand of Aristotle's age. "Bring your thoughts
into harmony with authority," was the demand of the
Middle Ages. "Bring them into harmony with fact,"
was the requirement most keenly felt in more recent
times. It is in response to this demand that what
is commonly but not very happily known as Inductive
Logic has been formulated.</p>

<p>In obedience to custom, I shall follow the now
ordinary division of Logic into Deductive and Inductive.
The titles are misleading in many ways, but
they are fixed by a weight of usage which it would
be vain to try to unsettle. Both come charging down
the stream of time each with its cohort of doctrines
behind it, borne forward with irresistible momentum.</p>

<p>The best way of preventing confusion now is to
retain the established titles, recognise that the doctrines
behind each have a radically different aim or end, and
supply the interpretation of this end from history.
What they have in common may be described as the
prevention of error, the organisation of reason against
error. I have shown that owing to the bent impressed
upon it by the circumstances of its origin, the errors
chiefly safeguarded by the Aristotelian logic were the
errors of inconsistency. The other branch of Logic,
commonly called Induction, was really a separate
<span class="pagenum"><a name="page15" id="page15"></a>[page&nbsp;15]</span>
evolution, having its origin in a different practical
need. The history of this I will trace separately
after we have seen our way through the Aristotelian
tradition and its accretions. The Experimental
Methods are no less manifestly the germ, the evolutionary
centre or starting-point, of the new Logic
than the Syllogism is of the old, and the main errors
safeguarded are errors of fact and inference from
fact.</p>

<p>At this stage it will be enough to indicate briefly
the broad relations between Deductive Logic and
Inductive Logic.</p>

<p>Inductive Logic, as we now understand it&mdash;the Logic
of Observation and Explanation&mdash;was first formulated
and articulated to a System of Logic by J. S. Mill. It
was he that added this wing to the old building. But
the need of it was clearly expressed as early as the
thirteenth century. Roger Bacon, the Franciscan friar
(1214-1292), and not his more illustrious namesake
Francis, Lord Verulam, was the real founder of
Inductive Logic. It is remarkable that the same
century saw Syllogistic Logic advanced to its most
complete development in the system of Petrus
Hispanus, a Portuguese scholar who under the title
of John XXI. filled the Papal Chair for eight months
in 1276-7.</p>

<p>A casual remark of Roger Bacon's in the course of
his advocacy of Experimental Science in the <i>Opus
Majus</i> draws a clear line between the two branches
of Logic. "There are," he says, "two ways of
knowing, by Argument and by Experience. Argument
concludes a question, but it does not make us feel
certain, unless the truth be also found in experience."</p>
<span class="pagenum"><a name="page16" id="page16"></a>[page&nbsp;16]</span>

<p>On this basis the old Logic may be clearly distinguished
from the new, taking as the general aim of Logic the
protection of the mind against the errors to which it
is liable in the acquisition of knowledge.</p>

<p>All knowledge, broadly speaking, comes either from
Authority, <i>i.e.</i>, by argument from accepted premisses,
or from Experience. If it comes from Authority it
comes through the medium of words: if it comes from
Experience it comes through the senses. In taking
in knowledge through words we are liable to certain
errors; and in taking in knowledge through the senses
we are liable to certain errors. To protect against the
one is the main end of "Deductive" Logic: to protect
against the other is the main end of "Inductive"
Logic. As a matter of fact the pith of treatises on
Deduction and Induction is directed to those ends
respectively, the old meanings of Deduction and
Induction as formal processes (to be explained afterwards)
being virtually ignored.</p>

<p>There is thus no antagonism whatever between the
two branches of Logic. They are directed to different
ends. The one is supplementary to the other. The
one cannot supersede the other.</p>

<p>Aristotelian Logic can never become superfluous as
long as men are apt to be led astray by words. Its
ultimate business is to safeguard in the interpretation
of the tradition of language. The mere syllogistic, the
bare forms of equivalent or consistent expression, have
a very limited utility, as we shall see. But by cogent
sequence syllogism leads to proposition, and proposition
to term, and term to a close study of the relations
between words and thoughts and things.</p>

<p class="note1"><a id="footnoteIntI1" name="footnoteIntI1"></a><a class="footnote" href="#footnotetagIntI1">Footnote 1:</a>
We know for certain&mdash;and it is one of the evidences of the
importance attached to this trivial-looking pastime&mdash;that two of
the great teacher's logical treatises, the Topics and the Sophistical
Refutations, were written especially for the guidance of Questioners
and Respondents. The one instructs the disputant how to
qualify himself methodically for discussion before an ordinary
audience, when the admissions extracted from the respondent are
matters of common belief, the questioner's skill being directed to
make it appear that the respondent's position is inconsistent with
these. The other is a systematic exposure of sophistical tricks,
mostly verbal quibbles, whereby a delusive appearance of victory
in debate may be obtained. But in the concluding chapter of the
<i>Elenchi</i>, where Aristotle claims not only that his method is
superior to the empirical methods of rival teachers, but that
it is entirely original, it is the Syllogism upon which he lays
stress as his peculiar and chief invention. The Syllogism, the
pure forms of which are expounded in his Prior Analytics, is really
the centre of Aristotle's logical system, whether the propositions
to which it is applied are matters of scientific truth as in the Posterior
Analytics, or matters of common opinion as in the Topics.
The treatise on Interpretation, <i>i.e.</i>, the interpretation of the
Respondent's "Yes" and "No," is preliminary to the Syllogism,
the reasoning of the admissions together. Even in the half-grammatical
half-logical treatise on the Categories, the author
always keeps an eye on the Syllogistic analysis.</p>

<p class="note1"><a id="footnoteIntI2" name="footnoteIntI2"></a><a class="footnote" href="#footnotetagIntI2">Footnote 2:</a> The&aelig;tetus, 151 E.</p>

<p class="note1"><a id="footnoteIntI3" name="footnoteIntI3"></a><a class="footnote" href="#footnotetagIntI3">Footnote 3:</a> Gorgias, 473 D.</p>

<p class="note1"><a id="footnoteIntI4" name="footnoteIntI4"></a><a class="footnote" href="#footnotetagIntI4">Footnote 4:</a> Hipparchus, 225 A.</p>

<p class="note1"><a id="footnoteIntI5" name="footnoteIntI5"></a><a class="footnote" href="#footnotetagIntI5">Footnote 5:</a>
In its leading and primary use, this was a mode of debate, a
duel of wits, in which two men engaged before an audience. But
the same form could be used, and was used, notably by Socrates,
not in an eristic spirit but as a means of awakening people to the
consequences of certain admissions or first principles, and thus
making vague knowledge explicit and clear. The mind being
detained on proposition after proposition as assent was given to
it, dialectic was a valuable instrument of instruction and exposition.
But whatever the purpose of the exercise, controversial triumph,
or solid grounding in the first principles&mdash;"the evolution of in-dwelling
conceptions"&mdash;the central interest lay in the syllogising or reasoning
together of the separately assumed or admitted propositions.</p>

<p class="note1"><a id="footnoteIntI6" name="footnoteIntI6"></a><a class="footnote" href="#footnotetagIntI6">Footnote 6:</a>
Like every other fashion, Yes-and-No Dialectic had its period,
its rise and fall. The invention of it is ascribed to Zeno the
Eleatic, the answering and questioning Zeno, who flourished
about the middle of the fifth century B.C. Socrates (469-399) was
in his prime at the beginning of the great Peloponnesian War
when Pericles died in 429. In that year Plato was born, and
lived to 347, "the olive groves of Academe" being established
centre of his teaching from about 386 onwards. Aristotle (384-322),
who was the tutor of Alexander the Great, established his
school at the Lyceum when Alexander became king in 336 and
set out on his career of conquest. That Yes-and-No Dialectic was
then a prominent exercise, his logical treatises everywhere bear
witness. The subsequent history of the game is obscure. It is
probable that Aristotle's thorough exposition of its legitimate
arts and illegitimate tricks helped to destroy its interest as an
amusement.</p>

<p class="note1"><a id="footnoteIntI7" name="footnoteIntI7"></a><a class="footnote" href="#footnotetagIntI7">Footnote 7:</a>
Hamilton's <i>Lectures</i>, iii. p. 37.</p>

<span class="pagenum"><a name="page17" id="page17"></a>[page&nbsp;17]</span>

<h3 style="margin-top: 2em;">II.&mdash;LOGIC AS A PREVENTIVE OF ERROR OR FALLACY.&mdash;THE INNER SOPHIST.</h3>

<p>Why describe Logic as a system of defence against
error? Why say that its main end and aim is the
organisation of reason against confusion and falsehood?
Why not rather say, as is now usual, that its
end is the attainment of truth? Does this not come
to the same thing?</p>

<p>Substantially, the meaning is the same, but the
latter expression is more misleading. To speak of
Logic as a body of rules for the investigation of truth
has misled people into supposing that Logic claims to
be an art of Discovery, that it claims to lay down rules
by simply observing which investigators may infallibly
arrive at new truths. Now, this does not hold even of
the Logic of Induction, still less of the older Logic, the
precise relation of which to truth will become apparent
as we proceed. It is only by keeping men from going
astray and by disabusing them when they think they
have reached their destination that Logic helps men
on the road to truth. Truth often lies hid in the centre
of a maze, and logical rules only help the searcher
onwards by giving him warning when he is on the
wrong track and must try another. It is the searcher's
own impulse that carries him forward: Logic does not
so much beckon him on to the right path as beckon
him back from the wrong. In laying down the conditions
of correct interpretation, of valid argument, of
trustworthy evidence, of satisfactory explanation,
Logic shows the inquirer how to test and purge his
conclusions, not how to reach them.</p>

<p>To discuss, as is sometimes done, whether Fallacies
lie within the proper sphere of Logic, is to obscure the
<span class="pagenum"><a name="page18" id="page18"></a>[page&nbsp;18]</span>
real connexion between Fallacies and Logic. It is the
existence of Fallacies that calls Logic into existence;
as a practical science Logic is needed as a protection
against Fallacies. Such historically is its origin. We
may, if we like, lay down an arbitrary rule that a
treatise on Logic should be content to expound the
correct forms of interpretation and reasoning and
should not concern itself with the wrong. If we take
this view we are bound to pronounce Fallacies extra-logical.
But to do so is simply to cripple the usefulness
of Logic as a practical science. The manipulation
of the bare logical forms, without reference to fallacious
departures from them, is no better than a nursery
exercise. Every correct form in Logic is laid down as
a safeguard against some erroneous form to which
men are prone, whether in the interpretation of argument
or the interpretation of experience, and the
statement and illustration of the typical forms of
wrong procedure should accompany <i>pari passu</i> the
exposition of the right procedure.</p>

<p style="margin-top: 2.5em">In accordance with this principle, I shall deal with
special fallacies, special snares or pitfalls&mdash;misapprehension
of words, misinterpretation of propositions,
misunderstanding of arguments, misconstruction of
facts, evidences, or signs&mdash;each in connexion with its
appropriate safeguard. This seems to me the most
profitable method. But at this stage, it may be worth
while, by way of emphasising the need for Logic as a
science of rational belief, to take a survey of the most
general tendencies to irrational belief, the chief kinds
of illusion or bias that are rooted in the human constitution.
We shall then better appreciate the magnitude
of the task that Logic attempts in seeking to protect
<span class="pagenum"><a name="page19" id="page19"></a>[page&nbsp;19]</span>
reason against its own fallibility and the pressure of
the various forces that would usurp its place.</p>

<p>It is a common notion that we need Logic to protect
us against the arts of the Sophist, the dishonest
juggler with words and specious facts. But in truth
the Inner Sophist, whose instruments are our own
inborn propensities to error, is a much more dangerous
enemy. For once that we are the victims of designing
Sophists, we are nine times the victims of our own
irrational impulses and prejudices. Men generally
deceive themselves before they deceive others.</p>

<p>Francis Bacon drew attention to these inner perverting
influences, these universal sources of erroneous
belief, in his <i>De Augmentis</i> and again in his <i>Novum
Organum</i>, under the designation of <i>Idola</i>, <ins title="eidôla">(&#949;&#7988;&#948;&#969;&#955;&#945;)</ins>
deceptive appearances of truth, illusions. His classification
of <i>Idola&mdash;Idola Tribus</i>, illusions common to
all men, illusions of the race; <i>Idola Specus</i>, personal
illusions, illusions peculiar to the "den" in which
each man lives; <i>Idola Fori</i>, illusions of conversation,
vulgar prejudices embodied in words; <i>Idola Theatri</i>,
illusions of illustrious doctrine, illusions imposed by
the dazzling authority of great names&mdash;is defective as
a classification inasmuch as the first class includes all
the others, but like all his writings it is full of sagacious
remarks and happy examples. Not for the sake of
novelty, but because it is well that matters so important
should be presented from more than one point of view,
I shall follow a division adapted from the more scientific,
if less picturesque, arrangement of Professor
Bain, in his chapter on the Fallacious Tendencies of
the Human Mind.<a id="footnotetagIntII1" name="footnotetagIntII1"></a><a href="#footnoteIntII1"><sup>1</sup></a></p>
<span class="pagenum"><a name="page20" id="page20"></a>[page&nbsp;20]</span>

<p>The illusions to which we are all subject may best
be classified according to their origin in the depths of
our nature. Let us try to realise how illusory beliefs
arise.</p>

<p>What is a belief? One of the uses of Logic is
to set us thinking about such simple terms. An
exhaustive analysis and definition of belief is one
of the most difficult of psychological problems. We
cannot enter upon that: let us be content with a few
simple characters of belief.</p>

<p>First, then, belief is a state of mind. Second, this
state of mind is outward-pointing: it has a reference
beyond itself, a reference to the order of things outside
us. In believing, we hold that the world as it is, has
been, or will be, corresponds to our conceptions of
it. Third, belief is the guide of action: it is in accordance
with what we believe that we direct our activities.
If we want to know what a man really believes, we
look at his action. This at least is the clue to what
he believes at the moment. "I cannot," a great
orator once said, "read the minds of men." This was
received with ironical cheers. "No," he retorted, "but
I can construe their acts." Promoters of companies
are expected to invest their own money as a guarantee
of good faith. If a man says he believes the world is
coming to an end in a year, and takes a lease of a
house for fifteen years, we conclude that his belief is
not of the highest degree of strength.</p>
<span class="pagenum"><a name="page21" id="page21"></a>[page&nbsp;21]</span>

<p>The close connexion of belief with our activities,
enables us to understand how illusions, false conceptions
of reality, arise. The illusions of Feeling and
the illusions of Custom are well understood, but other
sources of illusion, which may be designated Impatient
Impulse and Happy Exercise, are less generally
recognised. An example or two will show what is
meant. We cannot understand the strength of these
perverting influences till we realise them in our own
case. We detect them quickly enough in others.
Seeing that in common speech the word illusion
implies a degree of error amounting almost to insanity,
and the illusions we speak of are such as no man is
ever quite free from, it is perhaps less startling to use
the word <i>bias</i>.</p>

<h3 style="margin-top: 2em;"><i>The Bias of Impatient Impulse.</i></h3>

<p>As a being formed for action, not only does healthy
man take a pleasure in action, physical and mental, for
its own sake, irrespective of consequences, but he is so
charged with energy that he cannot be comfortable
unless it finds a free vent. In proportion to the amount
and excitability of his energy, restraint, obstruction,
delay is irksome, and soon becomes a positive and
intolerable pain. Any bar or impediment that gives us
pause is hateful even to think of: the mere prospect
annoys and worries.</p>

<p>Hence it arises that belief, a feeling of being prepared
for action, a conviction that the way is clear
before us for the free exercise of our activities, is a very
powerful and exhilarating feeling, as much a necessity
of happy existence as action itself. We see this when
we consider how depressing and uncomfortable a
<span class="pagenum"><a name="page22" id="page22"></a>[page&nbsp;22]</span>
condition is the opposite state to belief, namely, doubt,
perplexity, hesitation, uncertainty as to our course.
And realising this, we see how strong a bias we
have in this fact of our nature, this imperious inward
necessity for action; how it urges us to act without
regard to consequences, and to jump at beliefs without
inquiry. For, unless inquiry itself is our business, a
self-sufficient occupation, it means delay and obstruction.</p>

<p>This ultimate fact of our nature, this natural inbred
constitutional impatience, explains more than half of
the wrong beliefs that we form and persist in. We
must have a belief of some kind: we cannot be happy
till we get it, and we take up with the first that seems
to show the way clear. It may be right or it may be
wrong: it is not, of course, necessarily always wrong:
but that, so far as we are concerned, is a matter of
accident. The pressing need for a belief of some sort,
upon which our energies may proceed in anticipation
at least, will not allow us to stop and inquire. Any
course that offers a relief from doubt and hesitation,
any conviction that lets the will go free, is eagerly
embraced.</p>

<p>It may be thought that this can apply only to beliefs
concerning the consequences of our own personal
actions, affairs in which we individually play a part.
It is from them, no doubt, that our nature takes this
set: but the habit once formed is extended to all sorts
of matters in which we have no personal interest. Tell
an ordinary Englishman, it has been wittily said, that
it is a question whether the planets are inhabited, and
he feels bound at once to have a confident opinion on
the point. The strength of the conviction bears no
proportion to the amount of reason spent in reaching
<span class="pagenum"><a name="page23" id="page23"></a>[page&nbsp;23]</span>
it, unless it may be said that as a general rule the less
a belief is reasoned the more confidently it is held.</p>

<p>"A grocer," writes Mr. Bagehot in an acute essay
on "The Emotion of Conviction,"<a id="footnotetagIntII2" name="footnotetagIntII2"></a><a href="#footnoteIntII2"><sup>2</sup></a>
"has a full creed as to foreign policy, a young lady a complete theory
of the Sacraments, as to which neither has any doubt.
A girl in a country parsonage will be sure that Paris
never can be taken, or that Bismarck is a wretch." An
attitude of philosophic doubt, of suspended judgment,
is repugnant to the natural man. Belief is an independent
joy to him.</p>

<p>This bias works in all men. While there is life,
there is pressure from within on belief, tending to push
reason aside. The force of the pressure, of course,
varies with individual temperament, age, and other
circumstances. The young are more credulous than
the old, as having greater energy: they are apt, as
Bacon puts it, to be "carried away by the sanguine
element in their temperament". Shakespeare's Laertes
is a study of the impulsive temperament, boldly contrasted
with Hamlet, who has more discourse of reason.
When Laertes hears that his father has been killed, he
hurries home, collects a body of armed sympathisers,
bursts into the presence of the king, and threatens with
his vengeance&mdash;the wrong man. He never pauses to
make inquiry: like Hotspur he is "a wasp-stung and
impatient fool"; he must wreak his revenge on
somebody, and at once. Hamlet's father also has
been murdered, but his reason must be satisfied before
he proceeds to his revenge, and when doubtful proof is
offered, he waits for proof more relative.</p>

<p>Bacon's <i>Idola Tribus</i> and Dr. Bain's illustrations of
<span class="pagenum"><a name="page24" id="page24"></a>[page&nbsp;24]</span>
incontinent energy, are mostly examples of unreasoning
intellectual activity, hurried generalisations, unsound
and superficial analogies, rash hypotheses. Bacon
quotes the case of the sceptic in the temple of
Poseidon, who, when shown the offerings of those
who had made vows in danger and been delivered,
and asked whether he did not now acknowledge the
power of the god, replied: "But where are they who
made vows and yet perished?" This man answered
rightly, says Bacon. In dreams, omens, retributions,
and such like, we are apt to remember when they
come true and to forget the cases when they fail.
If we have seen but one man of a nation, we are
apt to conclude that all his countrymen are like him;
we cannot suspend our judgment till we have seen
more. Confident belief, as Dr. Bain remarks, is the
primitive attitude of the human mind: it is only by
slow degrees that this is corrected by experience.
The old adage, "Experience teaches fools," has a
meaning of its own, but in one sense it is the reverse
of the truth. The mark of a fool is that he is not
taught by experience, and we are all more or less
intractable pupils, till our energies begin to fail.</p>

<h3 style="margin-top: 2em;"><i>The Bias of Happy Exercise.</i></h3>

<p>If an occupation is pleasant in itself, if it fully
satisfies our inner craving for action, we are liable
to be blinded thereby to its consequences. Happy
exercise is the fool's Paradise. The fallacy lies not
in being content with what provides a field for the
full activity of our powers: to be content in such a
case may be the height of wisdom: but the fallacy
lies in claiming for our occupation results, benefits,
<span class="pagenum"><a name="page25" id="page25"></a>[page&nbsp;25]</span>
utilities that do not really attend upon it. Thus we
see subjects of study, originally taken up for some
purpose, practical, artistic, or religious, pursued into
elaborate detail far beyond their original purpose,
and the highest value, intellectual, spiritual, moral,
claimed for them by their votaries, when in truth they
merely serve to consume so much vacant energy, and
may be a sheer waste of time that ought to be otherwise
employed.</p>

<p>But as I am in danger of myself furnishing an
illustration of this bias&mdash;it is nowhere more prevalent
than in philosophy&mdash;I will pass to our next head.</p>

<h3 style="margin-top: 2em;"><i>The Bias of the Feelings.</i></h3>

<p>This source of illusion is much more generally
understood. The blinding and perverting influence
of passion on reason has been a favourite theme with
moralists ever since man began to moralise, and is
acknowledged in many a popular proverb. "Love is
blind;" "The wish is father to the thought;" "Some
people's geese are all swans;" and so forth.</p>

<p>We need not dwell upon the illustration of it. Fear
and Sloth magnify dangers and difficulties; Affection
can see no imperfection in its object: in the eyes of
Jealousy a rival is a wretch. From the nature of the
case we are much more apt to see examples in others
than in ourselves. If the strength of this bias were
properly understood by everybody, the mistake would
not so often be committed of suspecting bad faith,
conscious hypocrisy, when people are found practising
the grossest inconsistencies, and shutting their eyes
apparently in deliberate wilfulness to facts held under
their very noses. Men are inclined to ascribe this
<span class="pagenum"><a name="page26" id="page26"></a>[page&nbsp;26]</span>
human weakness to women. Reasoning from feeling
is said to be feminine logic. But it is a human
weakness.</p>

<p>To take one very powerful feeling, the feeling of
self-love or self-interest&mdash;this operates in much more
subtle ways than most people imagine, in ways so
subtle that the self-deceiver, however honest, would
fail to be conscious of the influence if it were pointed
out to him. When the slothful man saith, There is a
lion in the path, we can all detect the bias to his
belief, and so we can when the slothful student says
that he will work hard to-morrow, or next week, or
next month; or when the disappointed man shows an
exaggerated sense of the advantages of a successful
rival or of his own disadvantages. But self-interest
works to bias belief in much less palpable ways than
those. It is this bias that accounts for the difficulty
that men of antagonistic interests have in seeing the
arguments or believing in the honesty of their
opponents. You shall find conferences held between
capitalists and workmen in which the two sides, both
represented by men incapable of consciously dishonest
action, fail altogether to see the force of each other's
arguments, and are mutually astonished each at the
other's blindness.</p>

<h3 style="margin-top: 2em;"><i>The Bias of Custom.</i></h3>

<p>That custom, habits of thought and practice, affect
belief, is also generally acknowledged, though the
strength and wide reach of the bias is seldom realised.
Very simple cases of unreasoning prejudice were
adduced by Locke, who was the first to suggest a
general explanation of them in the "Association of
<span class="pagenum"><a name="page27" id="page27"></a>[page&nbsp;27]</span>
Ideas" (<i>Human Understanding</i>, bk. ii. ch. xxxiii.). There
is, for instance, the fear that overcomes many people
when alone in the dark. In vain reason tells them that
there is no real danger; they have a certain tremor of
apprehension that they cannot get rid of, because
darkness is inseparably connected in their minds with
images of horror. Similarly we contract unreasonable
dislikes to places where painful things have happened
to us. Equally unreasoning, if not unreasonable, is
our attachment to customary doctrines or practices,
and our invincible antipathy to those who do not
observe them.</p>

<p>Words are very common vehicles for the currency
of this kind of prejudice, good or bad meanings being
attached to them by custom. The power of words in
this way is recognised in the proverb: "Give a dog
a bad name, and then hang him". These verbal
prejudices are Bacon's <i>Idola Fori</i>, illusions of conversation.
Each of us is brought up in a certain sect or
party, and accustomed to respect or dishonour certain
sectarian or party names, Whig, Tory, Radical,
Socialist, Evolutionist, Broad, Low, or High Church.
We may meet a man without knowing under what
label he walks and be charmed with his company:
meet him again when his name is known, and all is
changed.</p>

<p>Such errors are called Fallacies of Association to
point to the psychological explanation. This is that
by force of association certain ideas are brought into
the mind, and that once they are there, we cannot help
giving them objective reality. For example, a doctor
comes to examine a patient, and finds certain
symptoms. He has lately seen or heard of many cases
of influenza, we shall say; influenza is running in his
<span class="pagenum"><a name="page28" id="page28"></a>[page&nbsp;28]</span>
head. The idea once suggested has all the advantage
of possession.</p>

<p>But why is it that a man cannot get rid of an idea?
Why does it force itself upon him as a belief? Association,
custom, explains how it got there, but not why it
persists in staying.</p>

<p>To explain this we must call in our first fallacious
principle, the Impatience of Doubt or Delay, the
imperative inward need for a belief of some sort.</p>

<p>And this leads to another remark, that though for
convenience of exposition, we separate these various
influences, they are not separated in practice. They
may and often do act all together, the Inner Sophist
concentrating his forces.</p>

<p>Finally, it may be asked whether, seeing that
illusions are the offspring of such highly respectable
qualities as excess of energy, excess of feeling, excess
of docility, it is a good thing for man to be disillusioned.
The rose-colour that lies over the world for
youth is projected from the abundant energy and
feeling within: disillusion comes with failing energies,
when hope is "unwilling to be fed". Is it good then
to be disillusioned? The foregoing exposition would
be egregiously wrong if the majority of mankind did
not resent the intrusion of Reason and its organising
lieutenant Logic. But really there is no danger that
this intrusion succeeds to the extent of paralysing
action and destroying feeling, and uprooting custom.
The utmost that Logic can do is to modify the excess
of these good qualities by setting forth the conditions
of rational belief. The student who masters those
conditions will soon see the practical wisdom of
applying his knowledge only in cases where the
grounds of rational belief are within his reach. To
<span class="pagenum"><a name="page29" id="page29"></a>[page&nbsp;29]</span>
apply it to the consequences of every action would be
to yield to that bias of incontinent activity which is,
perhaps, our most fruitful source of error.</p>

<p class="note1"><a id="footnoteIntII1" name="footnoteIntII1"></a><a class="footnote" href="#footnotetagIntII1">Footnote 1:</a>
Bain's <i>Logic</i>, bk. vi. chap. iii. Bacon intended his <i>Idola</i> to
bear the same relation to his <i>Novum Organum</i> that Aristotle's
Fallacies or Sophistical Tricks bore to the old Organum. But in
truth, as I have already indicated, what Bacon classifies is our
inbred tendencies to form <i>idola</i> or false images, and it is these
same tendencies that make us liable to the fallacies named by
Aristotle. Some of Aristotle's, as we shall see, are fallacies of
Induction.</p>

<p class="note1"><a id="footnoteIntII2" name="footnoteIntII2"></a><a class="footnote" href="#footnotetagIntII2">Footnote 2:</a>
Bagehot's <i>Literary Studies</i>, ii. 427.</p>

<h3 style="margin-top: 2em;">III.&mdash;THE AXIOMS OF DIALECTIC AND OF SYLLOGISM.</h3>

<p>There are certain principles known as the Laws of
Thought or the Maxims of Consistency. They are
variously expressed, variously demonstrated, and
variously interpreted, but in one form or another they
are often said to be the foundation of all Logic. It
is even said that all the doctrines of Deductive or
Syllogistic Logic may be educed from them. Let us
take the most abstract expression of them, and see
how they originated. Three laws are commonly
given, named respectively the Law of Identity, the
Law of Contradiction and the Law of Excluded
Middle.</p>

<p>1. <i>The Law of Identity.</i> A is A. Socrates is
Socrates. Guilt is guilt.</p>

<p>2. <i>The Law of Contradiction.</i> A is not not-A.
Socrates is not other than Socrates. Guilt is not
other than guilt. Or A is not at once <i>b</i> and not-<i>b</i>.
Socrates is not at once good and not-good. Guilt is
not at once punishable and not-punishable.</p>

<p>3. <i>The Law of Excluded Middle.</i> Everything is
either A or not-A; or, A is either <i>b</i> or not-<i>b</i>. A given
thing is either Socrates or not-Socrates, either guilty
or not-guilty. It must be one or the other: no middle
is possible.</p>

<p>Why lay down principles so obvious, in some interpretations,
and so manifestly sophistical in others?
The bare forms of modern Logic have been reached
<span class="pagenum"><a name="page30" id="page30"></a>[page&nbsp;30]</span>
by a process of attenuation from a passage in Aristotle's
<i>Metaphysics</i><a id="footnotetagIntIII1" name="footnotetagIntIII1"></a><a href="#footnoteIntIII1"><sup>1</sup></a>
(iii. 3, 4, 1005<i>b</i> &ndash; 1008). He is there
laying down the first principle of demonstration, which
he takes to be that "it is impossible that the same
predicate can both belong, and not belong, to the same
subject, at the same time, and in the same sense".<a id="footnotetagIntIII2" name="footnotetagIntIII2"></a><a href="#footnoteIntIII2"><sup>2</sup></a>
That Socrates knows grammar, and does not know
grammar&mdash;these two propositions cannot both be
true at the same time, and in the same sense. Two
contraries cannot exist together in the same subject.
The double answer Yes and No cannot be given to one
and the same question understood in the same sense.</p>

<p>But why did Aristotle consider it necessary to lay
down a principle so obvious? Simply because among
the subtle dialecticians who preceded him the principle
had been challenged. The Platonic dialogue Euthydemus
shows the farcical lengths to which such
quibbling was carried. The two brothers vanquish
all opponents, but it is by claiming that the answer
No does not preclude the answer Yes. "Is not the
honourable honourable, and the base base?" asks
Socrates. "That is as I please," replies Dionysodorus.
Socrates concludes that there is no arguing
with such men: they repudiate the first principles of
dialectic.</p>

<p>There were, however, more respectable practitioners
<span class="pagenum"><a name="page31" id="page31"></a>[page&nbsp;31]</span>
who canvassed on more plausible grounds any form
into which ultimate doctrines about contraries and
contradictions, truth and falsehood, could be put, and
therefore Aristotle considered it necessary to put forth
and defend at elaborate length a statement of a first
principle of demonstration. "Contradictions cannot
both be true of the same subject at the same time
and in the same sense." This is the original form of
the Law of Contradiction.</p>

<p>The words "of the same subject," "at the same
time," and "in the same sense," are carefully chosen
to guard against possible quibbles. "<i>Socrates knows
grammar.</i>" By Socrates we must mean the same
individual man. And even of the same man the
assertion may be true at one time and not at another.
There was a time when Socrates did not know
grammar, though he knows it now. And the assertion
may be true in one sense and not in another. It may
be true that Socrates knows grammar, yet not that he
knows everything that is to be known about grammar,
or that he knows as much as Aristarchus.</p>

<p>Aristotle acknowledges that this first principle
cannot itself be demonstrated, that is, deduced from
any other. If it is denied, you can only reduce the
denier to an absurdity. And in showing how to
proceed in so doing, he says you must begin by
coming to an agreement about the words used, that
they signify the same for one and the other disputant.<a id="footnotetagIntIII3" name="footnotetagIntIII3"></a><a href="#footnoteIntIII3"><sup>3</sup></a>
<span class="pagenum"><a name="page32" id="page32"></a>[page&nbsp;32]</span>
No dialectic is possible without this understanding.
This first principle of Dialectic is the original of the
Law of Identity. While any question as to the
truth or falsehood of a question is pending, from the
beginning to the end of any logical process, the words
must continue to be accepted in the same sense.
Words must have an identical reference to things.</p>

<p>Incidentally in discussing the Axiom of Contradiction
<ins title="axiôma tês antiphaseôs">(<span style="font-size: 0.9em;">&#7936;</span>&xi;&#943;&omega;&mu;&alpha;
&tau;<span style="font-size: 0.9em;">&#7970;</span>&sigmaf;
<span style="font-size: 0.9em;">&#7936;</span>&nu;&tau;&iota;&phi;&#940;&sigma;&epsilon;&omega;&sigmaf;</ins>),<a id="footnotetagIntIII4"
name="footnotetagIntIII4"></a><a href="#footnoteIntIII4"><sup>4</sup></a>
Aristotle lays down what is now
known as the Law of Excluded Middle. Of two contradictories
one or other must be true: we must either
affirm or deny any one thing of any other: no mean
or middle is possible.</p>

<p style="margin-top: 2.5em">In their origin, then, these so-called Laws of Thought
were simply the first principles of Dialectic and
Demonstration. Consecutive argument, coherent
ratiocination, is impossible unless they are taken for
granted.</p>

<p>If we divorce or abstract them from their original
application, and consider them merely as laws of
thinking or of being, any abstract expression, or
illustration, or designation of them may easily be
pushed into antagonism with other plain truths or
first principles equally rudimentary. Without entering
into the perplexing and voluminous discussion to
which these laws have been subjected by logicians
within the last hundred years, a little casuistry is
necessary to enable the student to understand within
what limits they hold good.</p>

<p><i>Socrates is Socrates.</i> The name Socrates is a name
<span class="pagenum"><a name="page33" id="page33"></a>[page&nbsp;33]</span>
for something to which you and I refer when we
use the name. Unless we have the same reference,
we cannot hold any argument about the thing, or
make any communication one to another about it.</p>

<p>But if we take <i>Socrates is Socrates</i> to mean that, "An
object of thought or thing is identical with itself," "An
object of thought or thing cannot be other than itself,"
and call this a law of thought, we are met at once by
a difficulty. Thought, properly speaking, does not
begin till we pass beyond the identity of an object
with itself. Thought begins only when we recognise
the likeness between one object and others. To keep
within the self-identity of the object is to suspend
thought. "Socrates was a native of Attica,"
"Socrates was a wise man," "Socrates was put to
death as a troubler of the commonweal"&mdash;whenever
we begin to think or say anything about Socrates, to
ascribe any attributes to him, we pass out of his self-identity
into his relations of likeness with other men,
into what he has in common with other men.</p>

<p>Hegelians express this plain truth with paradoxical
point when they say: "Of any definite existence
or thought, therefore, it may be said with quite
as much truth that it <i>is not</i>, as that it <i>is</i>, its own
bare self".<a id="footnotetagIntIII5" name="footnotetagIntIII5"></a><a href="#footnoteIntIII5"><sup>5</sup></a>
Or, "A thing must other itself in order
to be itself". Controversialists treat this as a subversion
of the laws of Identity and Contradiction.
But it is only Hegel's fun&mdash;his paradoxical way of
putting the plain truth that any object has more in
common with other objects than it has peculiar to
itself. Till we enter into those aspects of agreement
with other objects, we cannot truly be said to think at
<span class="pagenum"><a name="page34" id="page34"></a>[page&nbsp;34]</span>
all. If we say merely that a thing is itself, we may
as well say nothing about it. To lay down this is not
to subvert the Law of Identity, but to keep it from
being pushed to the extreme of appearing to deny the
Law of Likeness, which is the foundation of all the
characters, attributes, or qualities of things in our
thoughts.</p>

<p>That self-same objects are like other self-same
objects, is an assumption distinct from the Law of
Identity, and any interpretation of it that excludes
this assumption is to be repudiated. But does not
the law of Identity as well as the law of the likeness
of mutually exclusive identities presuppose that there
are objects self-same, like others, and different from
others? Certainly: this is one of the presuppositions
of Logic.<a id="footnotetagIntIII6" name="footnotetagIntIII6"></a><a href="#footnoteIntIII6"><sup>6</sup></a>
We assume that the world of which we
talk and reason is separated into such objects in our
thoughts. We assume that such words as <i>Socrates</i>
represent individual objects with a self-same being or
substance; that such words as <i>wisdom</i>, <i>humour</i>, <i>ugliness</i>,
<i>running</i>, <i>sitting</i>, <i>here</i>, <i>there</i>, represent attributes,
qualities,
characters or predicates of individuals; that
such words as <i>man</i> represent groups or classes of
individuals.</p>

<p>Some logicians in expressing the Law of Identity
have their eye specially upon the objects signified
by general names or abstract names, <i>man</i>, <i>education</i>.<a id="footnotetagIntIII7" name="footnotetagIntIII7"></a><a href="#footnoteIntIII7"><sup>7</sup></a>
"A concept is identical with the sum of its characters,"
or, "Classes are identical with the sum of the individuals
composing them". The assumptions thus
expressed in technical language which will hereafter
<span class="pagenum"><a name="page35" id="page35"></a>[page&nbsp;35]</span>
be explained are undoubtedly assumptions that Logic
makes: but since they are statements of the internal
constitution of some of the identities that words represent,
to call them the Law of Identity is to depart
confusingly from traditional usage.<a id="footnotetagIntIII8" name="footnotetagIntIII8"></a><a href="#footnoteIntIII8"><sup>8</sup></a></p>

<p>That throughout any logical process a word must
signify the same object, is one proposition: that the
object signified by a general name is identical with
the sum of the individuals to each of whom it is
applicable, or with the sum of the characters that
they bear in common, is another proposition. Logic
assumes both: Aristotle assumed both: but it is the
first that is historically the original of all expressions
of the Law of Identity in modern text-books.</p>

<p>Yet another expression of a Law of Identity which
is really distinct from and an addition to Aristotle's
original. <i>Socrates was an Athenian, a philosopher, an
ugly man, an acute dialectician, etc.</i> Let it be granted
that the word Socrates bears the same signification
throughout all these and any number more of predicates,
we may still ask: "But what is it that Socrates
signifies?" The title Law of Identity is sometimes
given<a id="footnotetagIntIII9" name="footnotetagIntIII9"></a><a href="#footnoteIntIII9"><sup>9</sup></a>
to a theory on this point. <i>Socrates is Socrates.</i>
"An individual is the identity running through the
totality of its attributes." Is this not, it may be
<span class="pagenum"><a name="page36" id="page36"></a>[page&nbsp;36]</span>
asked, to confuse thought and being, to resolve
Socrates into a string of words? No: real existence
is one of the admissible predicates of Socrates: one
of the attributes under which we conceive him. But
whether we accept or reject this "Law of Identity,"
it is an addition to Aristotle's dialectical "law of
identity"; it is a theory of the metaphysical nature
of the identity signified by a Singular name. And
the same may be said of yet another theory of Identity,
that, "An individual is identical with the totality of its
predicates," or (another way of putting the same theory),
"An individual is a conflux of generalities".</p>

<p style="margin-top: 2.5em">To turn next to the Laws of Contradiction and
Excluded Middle. These also may be subjected to
Casuistry, making clearer what they assert by showing
what they do not deny.</p>

<p>They do not deny that things change, and that successive
states of the same thing may pass into one
another by imperceptible degrees. A thing may be
neither here nor there: it may be on the passage
from here to there: and, while it is in motion, we
may say, with equal truth, that it is neither here nor
there, or that it is both here and there. Youth passes
gradually into age, day into night: a given man or a
given moment may be on the borderland between the
two.</p>

<p>Logic does not deny the existence of indeterminate
margins: it merely lays down that for purposes of
clear communication and coherent reasoning the line
must be drawn somewhere between <i>b</i>, and not-<i>b</i>.</p>

<p>A difference, however, must be recognised between
logical negation and the negations of common thought
and common speech. The latter are definite to a
<span class="pagenum"><a name="page37" id="page37"></a>[page&nbsp;37]</span>
degree with which the mere Logic of Consistency does
not concern itself. To realise this is to understand
more clearly the limitations of Formal Logic.</p>

<p>In common speech, to deny a quality of anything is
by implication to attribute to it some other quality of
the same kind. Let any man tell me that "the streets
of such and such a town are not paved with wood," I
at once conclude that they are paved with some other
material. It is the legitimate effect of his negative
proposition to convey this impression to my mind. If,
proceeding on this, I go on to ask: "Then they are
paved with granite or asphalt, or this or that?" and
he turns round and says: "I did not say they were
paved at all," I should be justified in accusing him of
a quibble. In ordinary speech, to deny one kind of
pavement is to assert pavement of some kind. Similarly,
to deny that So-and-so is not in the Twenty-first
Regiment, is to imply that he is in another
regiment, that he is in the army in some regiment.
To retort upon this inference: "He is not in the
army at all," is a quibble: as much so as it would be
to retort: "There is no such person in existence".</p>

<p>Now Logic does not take account of this implication,
and nothing has contributed more to bring upon it the
reproach of quibbling. In Logic, to deny a quality is
simply to declare a repugnance between it and the
subject; negation is mere sublation, taking away, and
implies nothing more. Not-<i>b</i> is entirely indefinite:
it may cover anything except <i>b</i>.</p>

<p>Is Logic then really useless, or even misleading,
inasmuch as it ignores the definite implication of
negatives in ordinary thought and speech? In ignoring
this implication, does Logic oppose this implication
as erroneous? Does Logic shelter the quibbler who
<span class="pagenum"><a name="page38" id="page38"></a>[page&nbsp;38]</span>
trades upon it? By no means: to jump to this conclusion
were a misunderstanding. The fact only is
that nothing beyond the logical Law of Contradiction
needs to be assumed for any of the processes of Formal
Logic. Aristotle required to assume nothing more for
his syllogistic formul&aelig;, and Logic has not yet included
in its scope any process that requires any further
assumption. "If not-<i>b</i> represent everything except <i>b</i>,
everything outside <i>b</i>, then that A is <i>b</i>, and that A is
not-<i>b</i>, cannot both be true, and one or other of them
must be true."</p>

<p>Whether the scope of Logic ought to be extended is
another question. It seems to me that the scope of
Logic may legitimately be extended so as to take
account both of the positive implication of negatives
and the negative implication of positives. I therefore
deal with this subject in a separate chapter following
on the ordinary doctrines of Immediate Inference,
where I try to explain the simple Law of Thought
involved. When I say that the extension is legitimate,
I mean that it may be made without departing from
the traditional view of Logic as a practical science,
conversant with the nature of thought and its expression
only in so far as it can provide practical guidance
against erroneous interpretations and inferences. The
extension that I propose is in effect an attempt to bring
within the fold of Practical Logic some of the results
of the dialectic of Hegel and his followers, such as Mr.
Bradley and Mr. Bosanquet, Professor Caird and Professor
Wallace.<a id="footnotetagIntIII10" name="footnotetagIntIII10"></a><a href="#footnoteIntIII10"><sup>10</sup></a></p>

<p>The logical processes formulated by Aristotle are
<span class="pagenum"><a name="page39" id="page39"></a>[page&nbsp;39]</span>
merely stages in the movement of thought towards
attaining definite conceptions of reality. To treat
their conclusions as positions in which thought may
dwell and rest, is an error, against which Logic itself
as a practical science may fairly be called upon to
guard. It may even be conceded that the Aristotelian
processes are artificial stages, courses that thought
does not take naturally, but into which it has to be
forced for a purpose. To concede this is not to concede
that the Aristotelian logic is useless, as long as
we have reason on our side in holding that thought is
benefited and strengthened against certain errors by
passing through those artificial stages.</p>

<p class="note1"><a id="footnoteIntIII1" name="footnoteIntIII1"></a><a class="footnote" href="#footnotetagIntIII1">Footnote 1:</a>
The first statement of the Law of Identity in the form <i>Ens
est ens</i> is ascribed by Hamilton (<i>Lectures</i>, iii. 91) to Antonius
Andreas, a fourteenth century commentator on the <i>Metaphysics</i>.
But Andreas is merely expounding what Aristotle sets forth in
iii. 4, 1006 <i>a, b</i>. <i>Ens est ens</i> does not mean in Andreas what
A is A means in Hamilton.</p>

<p class="note1"><a id="footnoteIntIII2" name="footnoteIntIII2"></a><a class="footnote" href="#footnotetagIntIII2">Footnote 2:</a>
<ins title="to gar auto hama huparchein te kai mê huparchein adynaton tô autô kai kata to auto, . . . ahutê dê pasôn esti bebaiotatê tôn archôn.">&tau;&#8056;
&gamma;&#8048;&rho; &alpha;&#8016;&tau;&#8056; &#7941;&mu;&alpha; &#8017;&pi;&#940;&rho;&chi;&epsilon;&iota;&nu;
&tau;&epsilon; &kappa;&alpha;&#8054; &mu;&#x1F74; &#8017;&pi;&#940;&rho;&chi;&epsilon;&iota;&nu; &#7936;&delta;&#973;&nu;&alpha;&tau;&omicron;&nu;
&tau;&#8183; &alpha;&#8016;&tau;&#8183; &kappa;&alpha;&#8054; &kappa;&alpha;&tau;&#8048; &tau;&#8056; &alpha;&#8016;&tau;&#8056;, . . .
&alpha;&#8021;&tau;&eta; &delta;&#8052; &pi;&alpha;&sigma;&#8182;&nu; &#7952;&sigma;&tau;&#8054;
&beta;&epsilon;&beta;&alpha;&iota;&omicron;&tau;&#940;&tau;&eta; &tau;&#8182;&nu; &#7936;&rho;&chi;&#8182;&nu;.</ins> &nbsp;iii. 3, 1005<i>b</i>, 19-23.</p>

<p class="note1"><a id="footnoteIntIII3" name="footnoteIntIII3"></a><a class="footnote" href="#footnotetagIntIII3">Footnote 3:</a>
Hamilton credits Andreas with maintaining, "against Aristotle,"
that "the principle of Identity, and not the principle of
Contradiction, is the one absolutely first". Which comes first, is
a scholastic question on which ingenuity may be exercised. But
in fact Aristotle put the principle of Identity first in the above
plain sense, and Andreas only expounded more formally what
Aristotle had said.</p>

<p class="note1"><a id="footnoteIntIII4" name="footnoteIntIII4"></a><a class="footnote" href="#footnotetagIntIII4">Footnote 4:</a>
<ins title="Metaxu antiphaseôs edechetai einai outhen, all' anankê ê phanai ê apophanai en kath' henos hotioun.">&Mu;&epsilon;&tau;&alpha;&xi;&#8017;
&#8048;&nu;&tau;&iota;&phi;&#8049;&sigma;&epsilon;&omega;&sigmaf;
&#7952;&nu;&delta;&#8051;&chi;&epsilon;&tau;&alpha;&iota; &epsilon;&#7990;&nu;&alpha;&iota; &omicron;&#x1F50;&theta;&#8051;&nu;,
&#7936;&lambda;&lambda;&#8127; &#7936;&nu;&#940;&gamma;&kappa;&eta; &#7970; &phi;&#8049;&nu;&alpha;&iota; &#7970;
&#8048;&pi;&omicron;&phi;&#8049;&nu;&alpha;&iota; &#7954;&nu; &kappa;&alpha;&theta;&#8127;
&#7953;&nu;&#8056;&sigmaf; &#8001;&tau;&iota;&omicron;&#8166;&nu;.</ins>
&nbsp;<i>Metaph.</i> iii. 7, 1011<i>b</i>, 23-4.</p>

<p class="note1"><a id="footnoteIntIII5" name="footnoteIntIII5"></a><a class="footnote" href="#footnotetagIntIII5">Footnote 5:</a>
Prof. Caird's <i>Hegel</i>, p. 138.</p>

<p class="note1"><a id="footnoteIntIII6" name="footnoteIntIII6"></a><a class="footnote" href="#footnotetagIntIII6">Footnote 6:</a>
See Venn, <i>Empirical Logic</i>, 1-8.</p>

<p class="note1"><a id="footnoteIntIII7" name="footnoteIntIII7"></a><a class="footnote" href="#footnotetagIntIII7">Footnote 7:</a>
<i>E.g.</i>, Hamilton, lect. v.; Veitch's <i>Institutes of
Logic</i>, chaps, xii., xiii.</p>

<p class="note1"><a id="footnoteIntIII8" name="footnoteIntIII8"></a><a class="footnote" href="#footnotetagIntIII8">Footnote 8:</a>
The confusion probably arises in this way. First, these
"laws" are formulated as laws of thought that Logic assumes.
Second, a notion arises that these laws are the only postulates of
Logic: that all logical doctrines can be "evolved" from them.
Third, when it is felt that more than the identical reference of
words or the identity of a thing with itself must be assumed in
Logic, the Law of Identity is extended to cover this further
assumption.</p>

<p class="note1"><a id="footnoteIntIII9" name="footnoteIntIII9"></a><a class="footnote" href="#footnotetagIntIII9">Footnote 9:</a>
<i>E.g.</i>, Bosanquet's <i>Logic</i>, ii. 207.</p>

<p class="note1"><a id="footnoteIntIII10" name="footnoteIntIII10"></a><a class="footnote" href="#footnotetagIntIII10">Footnote 10:</a>
Bradley, <i>Principles of Logic</i>; Bosanquet, <i>Logic or The
Morphology of Knowledge</i>; Caird, <i>Hegel</i> (in Blackwood's
Philosophical Classics); Wallace, <i>The Logic of Hegel</i>.</p>
<span class="pagenum"><a name="page40" id="page40"></a>[page&nbsp;40]</span>

<h1 style="margin-top: 3em;">BOOK I.</h1>

<h2>THE LOGIC OF CONSISTENCY. SYLLOGISM AND DEFINITION.</h2>
<span class="pagenum"><a name="page43" id="page43"></a>[page&nbsp;43]</span>

<h2 style="margin-top: 3em;">PART I.</h2>

<h3>THE ELEMENTS OF PROPOSITIONS.</h3>

<div class="figcenter"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-140.png" width="304" height="35" alt="fancy rule" border="0" /></div>

<h3><span class="sc">Chapter I</span>.</h3>

<h3>GENERAL NAMES AND ALLIED DISTINCTIONS.</h3>

<p>To discipline us against the errors we are liable to
in receiving knowledge through the medium of
words&mdash;such is one of the objects of Logic, the
main object of what may be called the Logic of
Consistency.</p>

<p>Strictly speaking, we may receive knowledge about
things through signs or single words, as a nod, a wink,
a cry, a call, a command. But an assertory sentence,
proposition, or predication, is the unit with which Logic
concerns itself&mdash;a sentence in which a subject is named
and something is said or predicated about it. Let a
man once understand the errors incident to this regular
mode of communication, and he may safely be left to
protect himself against the errors incident to more
rudimentary modes.</p>

<p>A proposition, whether long or short, is a unit, but
it is an analysable unit. And the key to syllogistic
<span class="pagenum"><a name="page44" id="page44"></a>[page&nbsp;44]</span>
analysis is the General Name. Every proposition,
every sentence in which we convey knowledge to
another, contains a general name or its equivalent.
That is to say, every proposition may be resolved
into a form in which the predicate is a general name.
A knowledge of the function of this element of speech
is the basis of all logical discipline. Therefore, though
we must always remember that the proposition is
the real unit of speech, and the general name
only an analytic element, we take the general name
and its allied distinctions in thought and reality
first.</p>

<p>How propositions are analysed for syllogistic
purposes will be shown by-and-by, but we must
first explain various technical terms that logicians
have devised to define the features of this cardinal
element. The technical terms <span class="sc">Class, Concept,
Notion, Attribute, Extension</span> or <span class="sc">Denotation,
Intension</span> or <span class="sc">Connotation, Genus, Species, Differentia,
Singular Name, Collective Name, Abstract
Name</span>, all centre round it.</p>

<p>A general name is a name applicable to a number
of different things on the ground of some likeness
among them, as <i>man</i>, <i>ratepayer</i>, <i>man of courage</i>,
<i>man who fought at Waterloo</i>.</p>

<p>From the examples it will be seen that a general
name logically is not necessarily a single word. Any
word or combination of words that serves a certain
function is technically a general name. The different
ways of making in common speech the equivalent of
a general name logically are for the grammarian to
consider.</p>

<p>In the definition of a general name attention is called
to two distinct considerations, the individual objects to
<span class="pagenum"><a name="page45" id="page45"></a>[page&nbsp;45]</span>
each of which the name is applicable, and the points of
resemblance among them, in virtue of which they have
a common name. For those distinctions there are
technical terms.</p>

<p><b>Class</b> is the technical term for the objects, different
yet agreeing, to each of which a general name may be
applied.</p>

<p>The points of resemblance are called the common
<b>attributes</b> of the class.</p>

<p>A class may be constituted on one attribute or on
several. <i>Ratepayer</i>, <i>woman ratepayer</i>, <i>unmarried woman
ratepayer</i>; <i>soldier</i>, <i>British soldier</i>, <i>British soldier on
foreign service</i>. But every individual to which the
general name can be applied must possess the common
attribute or attributes.</p>

<p>These common attributes are also called the <b>Notion</b>
of the class, inasmuch as it is these that the mind
notes or should note when the general name is applied.
<b>Concept</b> is a synonym perhaps in more common use
than notion; the rationale of this term (derived from
<i>con</i> and <i>capere</i>, to take or grasp together) being that it
is by means of the points of resemblance that the
individuals are grasped or held together by the mind.
These common points are the one in the many, the
same amidst the different, the identity signified by the
common name. The name of an attribute as thought
of by itself without reference to any individual or class
possessing it, is called an <b>Abstract</b> name. By contradistinction,
the name of an individual or a class is
<b>Concrete</b>.</p>

<p>Technical terms are wanted also to express the
relation of the individuals and the attributes to the
general name. The individuals jointly are spoken of
as the <b>Denotation</b>, or <b>Extension</b> or <b>Scope</b> of the
<span class="pagenum"><a name="page46" id="page46"></a>[page&nbsp;46]</span>
name; the common attributes as its <b>Connotation</b>,
<b>Intension</b>, <b>Comprehension</b>, or <b>Ground</b>. The whole
denotation, etc., is the class; the whole connotation,
etc., is the concept.<a id="footnotetagPI-ChI1" name="footnotetagPI-ChI1"></a><a href="#footnotePI-ChI1"><sup>1</sup></a>
<span class="pagenum"><a name="page47" id="page47"></a>[page&nbsp;47]</span>
The limits of a "class" in Logic are fixed by the
common attributes. Any individual object that
<span class="pagenum"><a name="page48" id="page48"></a>[page&nbsp;48]</span>
possesses these is a member. The statement of them
is the <b>Definition</b>.</p>

<p>To predicate a general name of any object, as,
"This is a cat," "This is a very sad affair," is to
refer that object to a class, which is equivalent to
saying that it has certain features of resemblance with
other objects, that it reminds us of them by its likeness
to them. Thus to say that the predicate of every
proposition is a general name, expressed or implied, is
the same as to say that every predication may be
taken as a reference to a class.</p>

<p>Ordinarily our notion or concept of the common
features signified by general names is vague and hazy.
The business of Logic is to make them clear. It is to
this end that the individual objects of the class are
<span class="pagenum"><a name="page49" id="page49"></a>[page&nbsp;49]</span>
summoned before the mind. In ordinary thinking
there is no definite array or muster of objects: when
we think of "dog" or "cat," "accident," "book,"
"beggar," "ratepayer," we do not stop to call before
the mind a host of representatives of the class, nor do
we take precise account of their common attributes.
The concept of "house" is what all houses have in
common. To make this explicit would be no easy
matter, and yet we are constantly referring objects to
the class "house". We shall see presently that if
we wish to make the connotation or concept clear we
must run over the denotation or class, that is to say,
the objects to which the general name is applied in
common usage. Try, for example, to conceive clearly
what is meant by house, tree, dog, walking-stick.
You think of individual objects, so-called, and of what
they have in common.</p>

<p>A class may be constituted on one property or on
many. There are several points common to all
houses, enclosing walls, a roof, a means of exit and
entrance. For the full concept of the natural kinds,
<i>men</i>, <i>dogs</i>, <i>mice</i>, etc., we should have to go to the
natural historian.</p>

<p><b>Degrees of generality.</b> One class is said to be of
higher generality than another when it includes that
other and more. Thus animal includes man, dog,
horse, etc.; man includes Aryan, Semite, etc.; Aryan
includes Hindoo, Teuton, Celt, etc.</p>

<p>The technical names for higher and lower classes
are <b>Genus</b> and <b>Species</b>. These terms are not fixed as
in Natural History to certain grades, but are purely
relative one to another, and movable up and down a
scale of generality. A class may be a species
relatively to one class, which is above it, and a genus
<span class="pagenum"><a name="page50" id="page50"></a>[page&nbsp;50]</span>
relatively to one below it. Thus Aryan is a species
of the genus man, Teuton a species of the genus
Aryan.</p>

<p>In the graded divisions of Natural History genus
and species are fixed names for certain grades. Thus:
Vertebrates form a "division"; the next subdivision,
<i>e.g.</i>, Mammals, Birds, Reptiles, etc., is called a "class";
the next, <i>e.g.</i>, Rodents, Carnivora, Ruminants, an
"order"; the next, <i>e.g.</i>, Rats, Squirrels, Beavers, a
"genus"; the next, <i>e.g.</i>, Brown rats, Mice, a
"species".</p>

<div class="center">
<div class="content" style="margin-left: 15em;">
              Vertebrates (division).</div>
<div class="content" style="margin-left: 17em;">
<b>|</b></div>
<div class="content" style="margin-left: 13em;">
           Mammals, Birds, Reptiles, etc. (class).</div>
<div class="content" style="margin-left: 15em;">
<b>|</b></div>
<div class="content" style="margin-left: 11em;">
       Rodents, Ruminants, Carnivors, etc. (order).</div>
<div class="content" style="margin-left: 13em;">
<b>|</b></div>
<div class="content" style="margin-left: 9em;">
   Rats, Squirrels, Beavers, etc. (genus).</div>
<div class="content" style="margin-left: 10em;">
<b>|</b></div>
<div class="content" style="margin-left: 7em;">
Brown rats, Mice, etc. (species).</div>
</div>

<p style="margin-top: 3em">If we subdivide a large class into smaller classes,
and, again, subdivide these subdivisions, we come at
last to single objects.</p><br />

<div class="center">
<div class="content" style="margin-left: 16em;">
            Men</div>
<div class="content" style="margin-left: 17em;">
<b>|</b></div>
<div class="content" style="margin-left: 13em;">
           &mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;<br />
        Europeans, Asiatics, etc.</div>
<div class="content" style="margin-left: 15em;">
<b>|</b></div>
<div class="content" style="margin-left: 11em;">
        &mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;<br />
    Englishmen, Frenchmen, etc.</div>
	<div class="content" style="margin-left: 13em;">
<b>|</b></div>
<div class="content" style="margin-left: 9em;">
    &mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;<br />
John Doe, Richard Roe, etc.</div>
</div>
<span class="pagenum"><a name="page51" id="page51"></a>[page&nbsp;51]</span>

<p>A table of higher and lower classes arranged in order
has been known from of old as a <i>tree</i> of division or
classification. The following is Porphyry's "tree":&mdash;</p>

<div class="figcenter"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-060-296.png" width="296" height="500" alt="Porphyry's 'tree'" border="0" /></div>
<span class="pagenum"><a name="page52" id="page52"></a>[page&nbsp;52]</span>

<p>The single objects are called <b>Individuals</b>, because
the division cannot be carried farther. The highest
class is technically the <b>Summum Genus</b>, or <i>Genus
generalissimum</i>; the next highest class to any species
is the <b>Proximum Genus</b>; the lowest group before you
descend to individuals is the <b>Infima Species</b>, or <i>Species
specialissima</i>.</p>

<p>The attribute or attributes whereby a species is
distinguished from other species of the same genus, is
called its <b>differentia</b> or <b>differenti&aelig;</b>. The various
species of houses are differentiated by their several
uses, dwelling-house, town-house, ware-house, public-house.
Poetry is a species of Fine Art, its differentia
being the use of metrical language as its instrument.</p>

<p>A lower class, indicated by the name of its higher
class qualified by adjectives or adjective phrases
expressing its differential property or properties, is said
to be described <b>per genus et differentiam</b>. Examples:
"Black-bird," "note-book," "clever man," "man of
Kent," "eminent British painter of marine subjects".
By giving a combination of attributes common to him
with nobody else, we may narrow down the application
of a name to an individual: "The Commander-in-Chief
of the British forces at the battle of Waterloo".</p>

<p>Other attributes of classes as divided and defined,
have received technical names.</p>

<p>An attribute common to all the individuals of a
class, found in that class only, and following from the
essential or defining attributes, though not included
among them, is called a <b>Proprium</b>.</p>

<p>An attribute that belongs to some, but not to all, or
that belongs to all, but is not a necessary consequence
of the essential attributes, is called an <b>Accident</b>.</p>

<p>The clearest examples of Propria are found in
<span class="pagenum"><a name="page53" id="page53"></a>[page&nbsp;53]</span>
mathematical figures. Thus, the defining property of
an equilateral triangle is the equality of the sides: the
equality of the angles is a proprium. That the three
angles of a triangle are together equal to two right
angles is a proprium, true of all triangles, and deducible
from the essential properties of a triangle.</p>

<p>Outside Mathematics, it is not easy to find <i>propria</i>
that satisfy the three conditions of the definition. It
is a useful exercise of the wits to try for such. Educability&mdash;an
example of the proprium in medi&aelig;val
text-books&mdash;is common to men, and results from man's
essential constitution; but it is not peculiar; other
animals are educable. That man cooks his food is
probably a genuine proprium.</p>

<p>That horses run wild in Thibet: that gold is found
in California: that clergymen wear white ties, are
examples of Accidents. Learning is an accident in
man, though educability is a proprium.</p>

<p>What is known technically as an <b>Inseparable
Accident</b>, such as the black colour of the crow or the
Ethiopian, is not easy to distinguish from the Proprium.
It is distinguished only by the third character,
deducibility from the essence.<a id="footnotetagPI-ChI2" name="footnotetagPI-ChI2"></a><a href="#footnotePI-ChI2"><sup>2</sup></a></p>
<span class="pagenum"><a name="page54" id="page54"></a>[page&nbsp;54]</span>

<p>Accidents that are both common and peculiar are often
useful for distinguishing members of a class. Distinctive
dresses or badges, such as the gown of a student,
the hood of a D.D., are accidents, but mark the class of
the individual wearer. So with the colours of flowers.</p>

<p><i>Genus</i>, <i>Species</i>, <i>Differentia</i>, <i>Proprium</i>, and
<i>Accidens</i>
have been known since the time of Porphyry as the
<span class="sc">Five Predicables</span>. They are really only terms used
in dividing and defining. We shall return to them
and endeavour to show that they have no significance
except with reference to fixed schemes, scientific or
popular, of Division or Classification.</p>

<p>Given such a fixed scheme, very nice questions
may be raised as to whether a particular attribute is
a defining attribute, or a proprium, or an accident, or
an inseparable accident. Such questions afford great
scope for the exercise of the analytic intellect.</p>

<p style="margin-top: 2.5em">We shall deal more particularly with degrees of
generality when we come to Definition. This much
has been necessary to explain an unimportant but
much discussed point in Logic, what is known as
the inverse variation of Connotation and Denotation.</p>

<p>Connotation and Denotation are often said to vary
inversely in quantity. The larger the connotation the
smaller the denotation, and <i>vice versâ</i>. With certain
qualifications the statement is correct enough, but it
is a rough compendious way of expressing the facts
and it needs qualification.</p>

<p>The main fact to be expressed is that the more
<span class="pagenum"><a name="page55" id="page55"></a>[page&nbsp;55]</span>
general a name is, the thinner is its meaning. The
wider the scope, the shallower the ground. As you
rise in the scale of generality, your classes are wider
but the number of common attributes is less. Inversely,
the name of a species has a smaller denotation than
the name of its genus, but a richer connotation. <i>Fruit-tree</i>
applies to fewer objects than <i>tree</i>, but the objects
denoted have more in common: so with <i>apple</i> and
<i>fruit-tree</i>, <i>Ribston Pippin</i> and <i>apple</i>.</p>

<p>Again, as a rule, if you increase the connotation you
contract the area within which the name is applicable.
Take any group of things having certain attributes in
common, say, <i>men of ability</i>: add <i>courage</i>, <i>beauty</i>, <i>height
of six feet</i>, <i>chest measurement of 40 inches</i>, and with each
addition fewer individuals are to be found possessing
all the common attributes.</p>

<p>This is obvious enough, and yet the expression inverse
variation is open to objection. For the denotation may
be increased in a sense without affecting the connotation.
The birth of an animal may be said to increase the
denotation: every year thousands of new houses are
built: there are swarms of flies in a hot summer and
few in a cold. But all the time the connotation of
<i>animal</i>, <i>house</i>, or <i>fly</i> remains the same: the word does
not change its meaning.</p>

<p>It is obviously wrong to say that they vary in inverse
proportion. Double or treble the number of attributes,
and you do not necessarily reduce the denotation by
one-half or one-third.</p>

<p>It is, in short, the meaning or connotation that is
the main thing. This determines the application of a
word. As a rule if you increase meaning, you restrict
scope. Let your idea, notion, or concept of <i>culture</i>
be a knowledge of Mathematics, Latin and Greek:
<span class="pagenum"><a name="page56" id="page56"></a>[page&nbsp;56]</span>
your <i>men of culture</i> will be more numerous than if you
require from each of them these qualifications <i>plus</i> a
modern language, an acquaintance with the Fine Arts,
urbanity of manners, etc.</p>

<p>It is just possible to increase the connotation without
decreasing the denotation, to thicken or deepen the
concept without diminishing the class. This is possible
only when two properties are exactly co-extensive, as
equilaterality and equiangularity in triangles.</p>

<p><b>Singular</b> and <b>Proper Names.</b> A Proper or Singular
name is a name used to designate an individual. Its
function, as distinguished from that of the general
name, is to be used purely for the purpose of distinctive
reference.</p>

<p>A man is not called Tom or Dick because he is like
in certain respects to other Toms or other Dicks. The
Toms or the Dicks do not form a logical class. The
names are given purely for purposes of distinction, to
single out an individual subject. The Arabic equivalent
for a Proper name, <i>alam</i>, "a mark," "a sign-post," is
a recognition of this.</p>

<p>In the expressions "a Napoleon," "a Hotspur," "a
Harry," the names are not singular names logically,
but general names logically, used to signify the possession
of certain attributes.</p>

<p>A man may be nicknamed on a ground, but if the
name sticks and is often used, the original meaning is
forgotten. If it suggests the individual in any one of
his qualities, any point in which he resembles other
individuals, it is no longer a Proper or Singular name
logically, that is, in logical function. That function
is fulfilled when it has called to mind the individual
intended.</p>

<p>To ask, as is sometimes done, whether Proper names
<span class="pagenum"><a name="page57" id="page57"></a>[page&nbsp;57]</span>
are connotative or denotative, is merely a confusion of
language. The distinction between connotation and
denotation, extension and intension, applies only
to general names. Unless a name is general, it
has neither extension nor intension:<a id="footnotetagPI-ChI3" name="footnotetagPI-ChI3"></a><a href="#footnotePI-ChI3"><sup>3</sup></a>
a Proper or Singular name is essentially the opposite of a general
name and has neither the one nor the other.</p>

<p>A nice distinction may be drawn between Proper
and Singular names, though they are strict synonyms
for the same logical function. It is not essential to
the discharge of that function that the name should be
strictly appropriated to one object. There are many
Toms and many Dicks. It is enough that the word
indicates the individual without confusion in the
particular circumstances.</p>

<p>This function may be discharged by words and
combinations of words that are not Proper in the
grammatical sense. "This man," "the cover of this
book," "the Prime Minister of England," "the seer of
<span class="pagenum"><a name="page58" id="page58"></a>[page&nbsp;58]</span>
Chelsea," may be Singular names as much as Honolulu
or Lord Tennyson.</p>

<p>In common speech Singular names are often
manufactured <i>ad hoc</i> by taking a general name and
narrowing it down by successive qualifications till it
applies only to one individual, as "The leading subject
of the Sovereign of England at the present time". If
it so happens that an individual has some attribute or
combination peculiar to himself, he may be suggested
by the mention of that attribute or combination:&mdash;"the
inventor of the steam-engine," "the author of
Hudibras".</p>

<p>Have such names a connotation? The student may
exercise his wits on the question. It is a nice one, an
excellent subject of debate. Briefly, if we keep rigid
hold of the meaning of connotation, this Singular name
has none. The combination is a singular name only
when it is the subject of a predication or an attribution,
as in the sentences, "The position of the leading subject
of etc., is a difficult one," or "The leading subject of
etc., wears an eyeglass". In such a sentence as
"So-and-so is the leading subject of etc.," the
combined name has a connotation, but then it is a
general and not a singular name.</p>

<p><b>Collective Names</b>, as distinguished from General
Names. A collective name is a name for a number of
similar units taken as a whole&mdash;a name for a totality
of similar units, as army, regiment, mob, mankind,
patrimony, personal estate.</p>

<p>A group or collection designated by a collective name
is so far like a class that the individual objects have
something in common: they are not heterogeneous
but homogeneous. A mob is a collection of human
beings; a regiment of soldiers; a library of books.</p>
<span class="pagenum"><a name="page59" id="page59"></a>[page&nbsp;59]</span>

<p>The distinction lies in this, that whatever is said
of a collective name is said about the collection as a
whole, and does not apply to each individual; whatever
is said of a general name applies to each
individual. Further, the collective name can be
predicated only of the whole group, as a whole; the
general name is predicable of each, distributively.
"Mankind has been in existence for thousands of
years;" "The mob passed through the streets."
In such expressions as "An honest man's the noblest
work of God," the subject is functionally a collective
name.</p>

<p>A collective name may be used as a general name
when it is extended on the ground of what is common
to all such totalities as it designates. "An excited
mob is dangerous;" "An army without discipline is
useless." The collective name is then "connotative"
of the common characters of the collection.</p>

<p><b>Material or Substantial Names.</b> The question
has been raised whether names of material, gold,
water, snow, coal, are general or collective singular.
In the case of pieces or bits of a material, it is true that
any predicate made concerning the material, such as
"Sugar is sweet," or "Water quenches thirst," applies
to any and every portion. But the separate portions
are not individuals in the whole signified by a material
name as individuals are in a class. Further, the name
of material cannot be predicated of a portion as a class
name can be of an individual. We cannot say, "This
is a sugar". When we say, "This is a piece of sugar,"
sugar is a collective name for the whole material.
There are probably words on the borderland between
general names and collective names. In such expressions
as "This is a <i>coal</i>," "The bonnie <i>water</i> o' Urie,"
<span class="pagenum"><a name="page60" id="page60"></a>[page&nbsp;60]</span>
the material name is used as a general name. The
real distinction is between the distributive use and the
collective use of a name; as a matter of grammatical
usage, the same word may be used either way, but
logically in any actual proposition it must be either
one or the other.</p>

<p><b>Abstract Names</b> are names for the common attributes
or concepts on which classes are constituted. A
concrete name is a name directly applicable to an
individual in all his attributes, that is, as he exists in
the concrete. It may be written on a ticket and pinned
to him. When we have occasion to speak of the point
or points in which a number of individuals resemble
one another, we use what is called an abstract name.
"Generous man," "clever man," "timid man," are
concrete names; "generosity," "cleverness," "timidity,"
are abstract names.</p>

<p>It is disputed whether abstract names are connotative.
The question is a confused one: it is like asking
whether the name of a town is municipal. An abstract
name is the name of a connotation as a separate
object of thought or reference, conceived or spoken of
in abstraction from individual accidents. Strictly
speaking it is notative rather than <i>con</i>notative: it cannot
be said to have a connotation because it is itself
the symbol of what is called the connotation of a
general name.<a id="footnotetagPI-ChI4" name="footnotetagPI-ChI4"></a><a href="#footnotePI-ChI4"><sup>4</sup></a></p>
<span class="pagenum"><a name="page61" id="page61"></a>[page&nbsp;61]</span>

<p>The distinction between abstract names and concrete
names is virtually a grammatical distinction, that is,
a distinction in mode of predication. We may use
concrete names or abstract names at our pleasure to
express the same meaning. To say that "John
is a timid man" is the same thing as saying that
"Timidity is one of the properties or characteristics
or attributes of John". "Pride and cruelty generally
go together;" "Proud men are generally cruel men."</p>

<p>General names are predicable of individuals because
they possess certain attributes: to predicate the
possession of those attributes is the same thing as to
predicate the general name.</p>

<p>Abstract forms of predication are employed in
common speech quite as frequently as concrete, and
are, as we shall see, a great source of ambiguity and
confusion.</p>

<p class="note1"><a id="footnotePI-ChI1" name="footnotePI-ChI1"></a><a class="footnote" href="#footnotetagPI-ChI1">Footnote 1:</a>
It has been somewhat too hastily assumed on the authority
of Mansel (Note to Aldrich, pp. 16, 17) that Mill inverted the
scholastic tradition in his use of the word <i>Connotative</i>. Mansel
puts his statement doubtfully, and admits that there was some
licence in the use of the word Connotative, but holds that in
Scholastic Logic an adjective was said to "signify <i>primarily</i> the
attribute, and to <i>connote</i> or <i>signify secondarily</i>
(<ins title="prossêmainein">&pi;&rho;&omicron;&sigma;&sigma;&eta;&mu;&alpha;&#x1F77;&nu;&epsilon;&iota;&nu;
</ins>)
the subject of inhesion". The truth is that Mansel's view
was a theory of usage not a statement of actual usage, and he had good
reason for putting it doubtfully.</p>

<p class="note1">As a matter of fact, the history of the distinction follows the
simple type of increasing precision and complexity, and Mill was
in strict accord with standard tradition. By the Nominalist
commentators on the <i>Summul&aelig;</i> of Petrus Hispanus certain names,
adjectives grammatically, are called <i>Connotativa</i> as opposed to
<i>Absoluta</i>, simply because they have a double function. White is
connotative as signifying both a subject, such as Socrates, of
whom "whiteness" is an attribute, and an attribute "whiteness":
the names "Socrates" and "whiteness" are Absolute, as having
but a single signification. Occam himself speaks of the subject
as the primary signification, and the attribute as the secondary,
because the answer to "What is white?" is "Something informed
with whiteness," and the subject is in the nominative case while
the attribute is in an oblique case (<i>Logic</i>, part I. chap. x.). Later
on we find that Tataretus (<i>Expositio in Summulas</i>, A.D. 1501),
while mentioning (Tract. Sept. <i>De Appellationibus</i>) that it is a
matter of dispute among Doctores whether a connotative name
<i>connotat</i> the subject or the attribute, is perfectly explicit in his
own definition, "Terminus connotativus est qui pr&aelig;ter illud pro
quo supponit connotat aliquid adjacere vel non adjacere rei pro
qua supponit" (Tract. Sept. <i>De Suppositionibus</i>). And this
remained the standard usage as long as the distinction remained
in logical text-books. We find it very clearly expressed by
Clichtoveus, a Nominalist, quoted as an authority by Guthutius
in his <i>Gymnasium Speculativum</i>, Paris, 1607 (<i>De Terminorum
Cognitione</i>, pp. 78-9). "Terminus absolutus est, qui solum illud
pro quo in propositione supponit, significat. Connotativus autem,
qui ultra idipsum, aliud importat." Thus <i>man</i> and <i>animal</i> are
absolute terms, which simply stand for (supponunt pro) the things
they signify. <i>White</i> is a connotative name, because "it stands
for (supponit pro) a subject in which it is an accident: and beyond
this, still signifies an accident, which is in that subject, and is
expressed by an abstract name". Only Clichtoveus drops the
verb <i>connotat</i>, perhaps as a disputable term, and says simply <i>ultra
importat</i>.</p>

<p class="note1">So in the Port Royal Logic (1662), from which possibly Mill
took the distinction: "Les noms qui signifient les choses comme
modifi&eacute;es, marquant premi&egrave;rement et directement la chose, quoique
plus confus&eacute;ment, et indirectement le mode, quoique plus
distinctement, sont appel&eacute;s <i>adjectifs</i> ou <i>connotatifs</i>; comme rond,
dur, juste, prudent" (part i. chap ii.).</p>

<p class="note1">What Mill did was not to invert Scholastic usage but to revive
the distinction, and extend the word connotative to general names
on the ground that they also imported the possession of attributes.
The word has been as fruitful of meticulous discussion as it was
in the Renaissance of Logic, though the ground has changed.
The point of Mill's innovation was, premising that general names
are not absolute but are applied in virtue of a meaning, to put
emphasis on this meaning as the cardinal consideration. What
he called the connotation had dropped out of sight as not being
required in the Syllogistic Forms. This was as it were the point
at which he put in his horn to toss the prevalent conception of
Logic as Syllogistic.</p>

<p class="note1">The real drift of Mill's innovation has been obscured by the
fact that it was introduced among the preliminaries of Syllogism,
whereas its real usefulness and significance belongs not to
Syllogism in the strict sense but to Definition. He added to
the confusion by trying to devise forms of Syllogism based on
connotation, and by discussing the Axiom of the Syllogism from
this point of view. For syllogistic purposes, as we shall see,
Aristotle's forms are perfect, and his conception of the proposition
in extension the only correct conception. Whether the centre
of gravity in Consistency Logic should not be shifted back
from Syllogism to Definition, the latter being the true centre
of consistency, is another question. The tendency of Mill's
polemic was to make this change. And possibly the secret of
the support it has recently received from Mr. Bradley and Mr.
Bosanquet is that they, following Hegel, are moving in the
same direction.</p>

<p class="note1">In effect, Mill's doctrine of Connotation helped to fix a conception
of the general name first dimly suggested by Aristotle
when he recognised that names of genera and species signify
Quality, in showing what sort a thing is. Occam carried this a
step farther towards clear light by including among Connotative
Terms such general names as "monk," name of classes that at
once suggest a definite attribute. The third step was made by
Mill in extending the term Connotation to such words as "man,"
"horse," the <i>Infim&aelig; Species</i> of the Schoolmen, the Species of
modern science.</p>

<p class="note1">Whether connotation was the best term to use for this purpose,
rather than extension, may be questioned: but at least it was in
the line of tradition through Occam.</p>

<p class="note1"><a id="footnotePI-ChI2" name="footnotePI-ChI2"></a><a class="footnote" href="#footnotetagPI-ChI2">Footnote 2:</a>
The history of the definition of the <i>Proprium</i> is an example
of the tendency of distinctions to become more minute and at the
same time more purposeless. Aristotle's <ins title="idion">&#x1FD0;&delta;&iota;&omicron;&nu;</ins> was an attribute,
such as the laugh of the man or the bark of the dog, common to
all of a class and peculiar to the class (<i>quod convenit omni soli et
semper</i>) yet not comprised in the definition of the class. Porphyry
recognised three varieties of <ins title="idia">&#x1FD0;&delta;&iota;&alpha;</ins> besides this, four in all, as
follows:&mdash;(1) an attribute peculiar to a species but not possessed
by all, as knowledge of medicine or geometry; (2) possessed by a
whole species but not peculiar to it, as being a biped in man; (3)
peculiar to a species, and possessed by all at a certain time, as
turning grey in old age; (4) Aristotle's "proprium," peculiar and
possessed by all, as risibility. The idea of the Proprium as
deducible from or consequent on the essence would seem to
have originated in the desire to find something common to all
Poryphyry's four varieties.</p>

<p class="note1"><a id="footnotePI-ChI3" name="footnotePI-ChI3"></a><a class="footnote" href="#footnotetagPI-ChI3">Footnote 3:</a>
It is a plausible contention that in the case of the Singular
name the extension is at a minimum and the intension at a
maximum, the extension being one individual, and the intension
the totality of his attributes. But this is an inexact and confused
use of words. A name does not <i>extend</i> beyond the individual
except when it is used to signify one or more of his prominent
qualities, that is, is used with the function of a general name.
The <i>ex</i>tension of a Singular name is zero: it has no extension.
On the other hand, it suggests, in its function as a Singular name,
no properties or qualities; it suggests only a subject; <i>i.e.</i>, it has
no intension. The ambiguity of the term Denotation helps the
confusion in the case of Singular names. "Denote" in common
speech means to indicate, to distinguish. But when in Logic we
say that a general name denotes individuals, we have no thought
of indicating or distinguishing: we mean only that it is applicable
to any one, without respect of individuals, either in predication or
epithetic description.</p>

<p class="note1"><a id="footnotePI-ChI4" name="footnotePI-ChI4"></a><a class="footnote" href="#footnotetagPI-ChI4">Footnote 4:</a>
Strictly speaking, as I have tried to indicate all along, the
words Connotation and Denotation, or Extension and Intension,
apply only to general names. Outside general names, they have
no significance. An adjective with its noun is a general name, of
which the adjective gives part of the Connotation. If we apply
the word connotation to signify merely the suggestion of an
attribute in whatever grammatical connexion, then an abstract
name is undoubtedly as much connotative as an adjective. The
word <i>Sweetness</i> has the same meaning as <i>Sweet</i>: it indicates or
signifies, conveys to the mind of the reader the same attribute:
the only difference is that it does not at the same time indicate a
subject in which the attribute is found, as <i>sweet apple</i>. The
meaning is not <i>con</i>noted.</p>
<span class="pagenum"><a name="page62" id="page62"></a>[page&nbsp;62]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter II</span>.</h3>

<h3>THE SYLLOGISTIC ANALYSIS OF PROPOSITIONS INTO TERMS.</h3>

<h3 style="margin-top: 2em;">I.&mdash;<span class="sc">The Bare Analytic Forms.</span></h3>

<p>The word "term" is loosely used as a mere synonym
for a name: strictly speaking, a term (<ins title="horos"><span style="font-size: 0.9em;">&#8005;</span>&rho;&omicron;&sigmaf;</ins>, a boundary)
is one of the parts of a proposition as analysed into
Subject and Predicate. In Logic, a term is a technical
word in an analysis made for a special purpose, that
purpose being to test the mutual consistency of
propositions.</p>

<p>For this purpose, the propositions of common
speech may be viewed as consisting of two <b>Terms</b>, a
linkword called the copula (positive or negative)
expressing a relation between them, and certain
symbols of quantity used to express that relation
more precisely.</p>

<p>Let us indicate the Subject term by S, and the
Predicate term by P.</p>

<p>All propositions may be analysed into one or other
of four forms:&mdash;</p>

<div class="poem">  <div class="stanza">
<p>All S is P,</p>
<p>No S is P,</p>
<p>Some S is P,</p>
<p>Some S is not P.</p>
  </div>  </div>
<span class="pagenum"><a name="page63" id="page63"></a>[page&nbsp;63]</span>

<p>All S is P is called the <b>Universal Affirmative</b>,
and is indicated by the symbol A (the first vowel of
Affirmo).</p>

<p>No S is P is called the <b>Universal Negative</b>, symbol
E (the first vowel of Nego).</p>

<p>Some S is P is called the <b>Particular Affirmative</b>,
symbol I (the second vowel of <i>aff</i>Irmo).</p>

<p>Some S is not P is called the <b>Particular Negative</b>,
symbol O (the second vowel of <i>neg</i>O).</p>

<p>The distinction between Universal and Particular
is called a distinction in <b>Quantity</b>; between Affirmative
and Negative, a distinction in <b>Quality</b>. A and E,
I and O, are of the same quantity, but of different
quality: A and I, E and O, same in quality, different
in quantity.</p>

<p>In this symbolism, no provision is made for expressing
degrees of particular quantity. <i>Some</i> stands for
any number short of all: it may be one, few, most,
or all but one. The debates in which Aristotle's
pupils were interested turned mainly on the proof or
disproof of general propositions; if only a proposition
could be shown to be not universal, it did not matter
how far or how little short it came. In the Logic of
Probability, the degree becomes of importance.</p>

<p>Distinguish, in this Analysis, to avoid subsequent
confusion, between the Subject and the Subject Term,
the Predicate and the Predicate Term. The Subject
is the Subject Term quantified: in A and E,<a id="footnotetagPI-ChII1" name="footnotetagPI-ChII1"></a><a href="#footnotePI-ChII1"><sup>1</sup></a>
"All S";
<span class="pagenum"><a name="page64" id="page64"></a>[page&nbsp;64]</span>
in I and O, "Some S". The Predicate is the Predicate
Term with the Copula, positive or negative: in
A and I, "is P"; in E and O, "is not P".</p>

<p>It is important also, in the interest of exactness, to
note that S and P, with one exception, represent
general names. They are symbols for classes. P is
so always: S also except when the Subject is an
individual object. In the machinery of the Syllogism,
predications about a Singular term are treated as
Universal Affirmatives. "Socrates is a wise man"
is of the form All S is P.</p>

<p>S and P being general names, the signification of
the symbol "is" is not the same as the "is" of
common speech, whether the substantive verb or the
verb of incomplete predication. In the syllogistic
form, "is" means <i>is contained in</i>, "is not," <i>is not
contained in</i>.</p>

<p>The relations between the terms in the four forms
are represented by simple diagrams known as Euler's
circles.</p>

<div class="figcenter"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-073-600.png" width="600" height="185" alt="Euler's circles - 1  concentric circles of P and S, S in centre - A, 2  S and P in the same circle - A, 3  S and P each in a circle, overlapping circle. - I and O, 4  S in one circle and P in another circle.-  E , 5  concentric circles of S and P; P in centre - I?" border="0" /></div>

<p>Diagram 5 is a purely artificial form, having no
representative in common speech. In the affirmations
of common speech, P is always a term of greater
extent than S.</p>

<p>No. 2 represents the special case where S and P
<span class="pagenum"><a name="page65" id="page65"></a>[page&nbsp;65]</span>
are coextensive, as in All equiangular triangles are
equilateral.</p>

<p>S and P being general names, they are said to be
<b>distributed</b> when the proposition applies to them in
their whole extent, that is, when the assertion covers
every individual in the class.</p>

<p>In E, the Universal Negative, both terms are
distributed: "No S is P" wholly excludes the two
classes one from the other, imports that not one
individual of either is in the other.</p>

<p>In A, S is distributed, but not P. S is wholly in
P, but nothing is said about the extent of P beyond S.</p>

<p>In O, S is undistributed, P is distributed. A part of
S is declared to be wholly excluded from P.</p>

<p>In I, neither S nor P is distributed.</p>

<p>It will be seen that the Predicate term of a Negative
proposition is always distributed, of an Affirmative,
always undistributed.</p>

<p>A little indistinctness in the signification of P crept
into medi&aelig;val text-books, and has tended to confuse
modern disputation about the import of Predication.
Unless P is a class name, the ordinary doctrine of
distribution is nonsense; and Euler's diagrams are
meaningless. Yet many writers who adopt both
follow medi&aelig;val usage in treating P as the equivalent
of an adjective, and consequently "is" as identical
with the verb of incomplete predication in common
speech.</p>

<p style="margin-top: 2.5em">It should be recognised that these syllogistic forms
are purely artificial, invented for a purpose, namely,
the simplification of syllogising. Aristotle indicated
the precise usage on which his syllogism is based
<span class="pagenum"><a name="page66" id="page66"></a>[page&nbsp;66]</span>
(<i>Prior Analytics</i>, i. 1 and 4). His form<a id="footnotetagPI-ChII2" name="footnotetagPI-ChII2"></a><a href="#footnotePI-ChII2"><sup>2</sup></a>
for All S is
P, is S is wholly in P; for No S is P, S is wholly not
in P. His copula is not "is," but "is in," and it is
a pity that this usage was not kept. "All S is in P"
would have saved much confusion. But, doubtless
for the sake of simplicity, the besetting sin of tutorial
handbooks, All S is P crept in instead, illustrated by
such examples as "All men are mortal".</p>

<p>Thus the "is" of the syllogistic form became confused
with the "is" of common speech, and the syllogistic
view of predication as being equivalent to inclusion in,
or exclusion from a class, was misunderstood. The
true Aristotelian doctrine is not that predication
consists in referring subjects to classes, but only that
for certain logical purposes it may be so regarded.
The syllogistic forms are artificial forms. They
were not originally intended to represent the actual
processes of thought expressed in common speech.
To argue that when I say "All crows are black," I
do not form a class of black things, and contemplate
crows within it as one circle is within another, is to
contradict no intelligent logical doctrine.</p>

<p>The root of the confusion lies in quoting sentences
from common speech as examples of the logical forms,
forgetting that those forms are purely artificial.
"Omnis homo est mortalis," "All men are mortal,"
is not an example formally of All S is P. P is a
symbol for a substantive word or combination of
words, and mortal is an adjective. Strictly speaking,
there is no formal equivalent in common speech, that
is, in the forms of ordinary use&mdash;no strict grammatical
<span class="pagenum"><a name="page67" id="page67"></a>[page&nbsp;67]</span>
formal equivalent&mdash;for the syllogistic propositional
symbols. We can make an equivalent, but it is not
a form that men would use in ordinary intercourse.
"All man is in mortal being" would be a strict
equivalent, but it is not English grammar.</p>

<p>Instead of disputing confusedly whether All S is P
should be interpreted in extension or in comprehension,
it would be better to recognise the original and traditional
use of the symbols S and P as class names, and
employ other symbols for the expression in comprehension
or connotation. Thus, let <i>s</i> and <i>p</i> stand for
the connotation. Then the equivalent for All S is
P would be All S has <i>p</i>, or <i>p</i> always accompanies <i>s</i>, or
<i>p</i> belongs to all S.</p>

<p>It may be said that if predication is treated in this
way, Logic is simplified to the extent of childishness.
And indeed, the manipulation of the bare forms with
the help of diagrams and mnemonics is a very humble
exercise. The real discipline of Syllogistic Logic lies
in the reduction of common speech to these forms.</p>

<p>This exercise is valuable because it promotes clear
ideas about the use of general names in predication,
their ground in thought and reality, and the liabilities
to error that lurk in this fundamental instrument of
speech.</p>

<p class="note1"><a id="footnotePI-ChII1" name="footnotePI-ChII1"></a><a class="footnote" href="#footnotetagPI-ChII1">Footnote 1:</a>
For perfect symmetry, the form of E should be All S is not P.
"No S is P" is adopted for E to avoid conflict with a form of
common speech, in which All S is not P conveys the meaning of
the Particular Negative. "All advices are not safe" does not
mean that safeness is denied of all advices, but that safeness
cannot be affirmed of all, <i>i.e.</i>, Not all advices are safe, <i>i.e.</i>,
some
are not.</p>

<p class="note1"><a id="footnotePI-ChII2" name="footnotePI-ChII2"></a><a class="footnote" href="#footnotetagPI-ChII2">Footnote 2:</a>
His most precise form, I should say, for in "P is predicated
of every S" he virtually follows common speech.</p>

<h3 style="margin-top: 2em;">II.&mdash;<span class="sc">The Practice of Syllogistic Analysis.</span></h3>

<p>The basis of the analysis is the use of general names
in predication. To say that in predication a subject is
referred to a class, is only another way of saying that
in every categorical sentence the predicate is a general
name express or implied: that it is by means of
general names that we convey our thoughts about
things to others.</p>
<span class="pagenum"><a name="page68" id="page68"></a>[page&nbsp;68]</span>

<p>"Milton is a great poet." "Quoth Hudibras,
<i>I smell a rat</i>." <i>Great poet</i> is a general name: it means
certain qualities, and applies to anybody possessing
them. <i>Quoth</i> implies a general name, a name for
persons <i>speaking</i>, connoting or meaning a certain act
and applicable to anybody in the performance of it.
<i>Quoth</i> expresses also past time: thus it implies another
general name, a name for persons <i>in past time</i>, connoting
a quality which differentiates a species in the genus
persons speaking, and making the predicate term
"persons speaking in past time". Thus the proposition
<i>Quoth Hudibras</i>, analysed into the syllogistic
form S is in P, becomes S (Hudibras) is in P (persons
speaking in past time). The Predicate term P is a
class constituted on those properties. <i>Smell a rat</i> also
implies a general name, meaning an act or state
predicable of many individuals.</p>

<p>Even if we add the grammatical object of <i>Quoth</i> to
the analysis, the Predicate term is still a general name.
Hudibras is only one of the persons speaking in past
time who have spoken of themselves as being in a
certain mood of suspicion.<a id="footnotetagPI-ChII3" name="footnotetagPI-ChII3"></a><a href="#footnotePI-ChII3"><sup>1</sup></a></p>

<p>The learner may well ask what is the use of twisting
<span class="pagenum"><a name="page69" id="page69"></a>[page&nbsp;69]</span>
plain speech into these uncouth forms. The use is
certainly not obvious. The analysis may be directly
useful, as Aristotle claimed for it, when we wish
to ascertain exactly whether one proposition contradicts
another, or forms with another or others a valid
link in an argument. This is to admit that it is
only in perplexing cases that the analysis is of direct
use. The indirect use is to familiarise us with
what the forms of common speech imply, and thus
strengthen the intellect for interpreting the condensed
and elliptical expression in which common speech
abounds.</p>

<p>There are certain technical names applied to the
components of many-worded general names, <b>Categorematic</b>
and <b>Syncategorematic</b>, <b>Subject</b> and
<b>Attributive</b>. The distinctions are really grammatical
rather than logical, and of little practical value.</p>

<p>A word that can stand by itself as a term is said to
be Categorematic. <i>Man</i>, <i>poet</i>, or any other common
noun.</p>

<p>A word that can only form part of a term is
Syncategorematic. Under this definition come all
adjectives and adverbs.</p>

<p>The student's ingenuity may be exercised in applying
the distinction to the various parts of speech. A verb
may be said to be <i>Hypercategorematic</i>, implying, as it
does, not only a term, but also a copula.</p>

<p>A nice point is whether the Adjective is categorematic
or syncategorematic. The question depends
on the definition of "term" in Logic. In common
speech an adjective may stand by itself as a predicate,
and so might be said to be Categorematic. "This
heart is merry." But if a term is a class, or the name
of a class, it is not Categorematic in the above
<span class="pagenum"><a name="page70" id="page70"></a>[page&nbsp;70]</span>
definition. It can only help to specify a class when
attached to the name of a higher genus.</p>

<p>Mr. Fowler's words <b>Subject</b> and <b>Attributive</b>
express practically the same distinction, except that
Attributive is of narrower extent than syncategorematic.
An Attributive is a word that connotes an attribute or
property, as <i>hot</i>, <i>valorous</i>, and is always grammatically
an adjective.</p>

<p>The <b>expression of Quantity</b>, that is, of Universality
or non-universality, is all-important in syllogistic
formul&aelig;. In them universality is expressed by <i>All</i>
or <i>None</i>. In ordinary speech universality is expressed
in various forms, concrete and abstract, plain and
figurative, without the use of "all" or "none".</p>

<div class="poem">  <div class="stanza">
<p>Uneasy lies the head that wears a crown.</p>
<p>He can't be wrong whose life is in the right.</p>
<p>What cat's averse to fish?</p>
<p>Can the leopard change his spots?</p>
<p>The longest road has an end.</p>
<p>Suspicion ever haunts the guilty mind.</p>
<p>Irresolution is always a sign of weakness.</p>
<p>Treason never prospers.</p>
  </div>  </div>

<p>A proposition in which the quantity is not expressed
is called by Aristotle <b>Indefinite</b> (<ins title="adioristos"><span style="font-size: 0.9em;">&#7936;</span>&delta;&iota;&#972;&rho;&iota;&sigma;&tau;&omicron;&sigmaf;</ins>). For
"indefinite"<a id="footnotetagPI-ChII4" name="footnotetagPI-ChII4"></a><a href="#footnotePI-ChII4"><sup>2</sup></a> Hamilton suggests <b>Preindesignate</b>,
<span class="pagenum"><a name="page71" id="page71"></a>[page&nbsp;71]</span>
undesignated, that is, before being received from common
speech for the syllogistic mill. A proposition is
<b>Predesignate</b> when the quantity is definitely indicated.
All the above propositions are "Predesignate" universals,
and reducible to the form All S is P, or No
S is P.</p>

<p>The following propositions are no less definitely
particular, reducible to the form I or O. In them as
in the preceding quantity is formally expressed, though
the forms used are not the artificial syllogistic forms:&mdash;</p>

<div class="poem">  <div class="stanza">
<p>Afflictions are often salutary.</p>
<p>Not every advice is a safe one.</p>
<p>All that glitters is not gold.</p>
<p>Rivers generally<a id="footnotetagPI-ChII5" name="footnotetagPI-ChII5"></a><a href="#footnotePI-ChII5"><sup>3</sup></a> run into the sea.</p>
  </div>  </div>

<p>Often, however, it is really uncertain from the form
of common speech whether it is intended to express a
universal or a particular. The quantity is not formally
expressed. This is especially the case with proverbs
and loose floating sayings of a general tendency. For
example:&mdash;</p>

<div class="poem">  <div class="stanza">
<p>Haste makes waste.</p>
<p>Knowledge is power.</p>
<p>Light come, light go.</p>
<p>Left-handed men are awkward antagonists.</p>
<p>Veteran soldiers are the steadiest in fight.</p>
  </div>  </div>
<span class="pagenum"><a name="page72" id="page72"></a>[page&nbsp;72]</span>

<p>Such sayings are in actual speech for the most part
delivered as universals.<a id="footnotetagPI-ChII6" name="footnotetagPI-ChII6"></a><a href="#footnotePI-ChII6"><sup>4</sup></a> It is a useful exercise of the
Socratic kind to decide whether they are really so.
This can only be determined by a survey of facts. The
best method of conducting such a survey is probably
(1) to pick out the concrete subject, "hasty actions,"
"men possessed of knowledge," "things lightly
acquired"; (2) to fix the attribute or attributes predicated;
(3) to run over the individuals of the subject
class and settle whether the attribute is as a matter of
fact meant to be predicated of each and every one.</p>

<p>This is the operation of <b>Induction</b>. If one individual
can be found of whom the attribute is not meant to be
predicated, the proposition is not intended as Universal.</p>

<p>Mark the difference between settling what is intended
and settling what is true. The conditions of truth and
the errors incident to the attempt to determine it, are
the business of the Logic of Rational Belief, commonly
entitled Inductive Logic. The kind of "induction"
here contemplated has for its aim merely to determine
the quantity of a proposition in common acceptation,
which can be done by considering in what cases the
proposition would generally be alleged. This corresponds
nearly as we shall see to Aristotelian Induction,
the acceptance of a universal statement when no
instance to the contrary is alleged.</p>

<p>It is to be observed that for this operation we do not
<span class="pagenum"><a name="page73" id="page73"></a>[page&nbsp;73]</span>
practically use the syllogistic form All S is P. We do
not raise the question Is All S, P? That is, we do not
constitute in thought a class P: the class in our minds
is S, and what we ask is whether an attribute predicated
of this class is truly predicated of every individual
of it.</p>

<p>Suppose we indicate by <i>p</i> the attribute, knot of
attributes, or concept on which the class P is constituted,
then All S is P is equivalent to "All S has <i>p</i>":
and Has All S <i>p</i>? is the form of a question that we
have in our minds when we make an inductive survey
on the above method. I point this out to emphasise
the fact that there is no prerogative in the form All S
is P except for syllogistic purposes.</p>

<p>This inductive survey may be made a useful
<b>Collateral Discipline</b>. The bare forms of Syllogistic
are a useless item of knowledge unless they are
applied to concrete thought. And determining the
quantity of a common aphorism or saw, the limits
within which it is meant to hold good, is a valuable
discipline in exactness of understanding. In trying
to penetrate to the inner intention of a loose general
maxim, we discover that what it is really intended
to assert is a general connexion of attributes, and a
survey of concrete cases leads to a more exact apprehension
of those attributes. Thus in considering
whether <i>Knowledge is power</i> is meant to be asserted
of all knowledge, we encounter along with such
examples as the sailor's knowledge that wetting a
rope shortens it, which enabled some masons to raise
a stone to its desired position, or the knowledge of
French roads possessed by the German invaders,&mdash;along
with such examples as these we encounter cases
where a knowledge of difficulties without a knowledge
<span class="pagenum"><a name="page74" id="page74"></a>[page&nbsp;74]</span>
of the means of overcoming them is paralysing to
action. Samuel Daniel says:&mdash;</p>

<div class="poem">  <div class="stanza">
<p>Where timid knowledge stands considering</p>
<p>Audacious ignorance has done the deed.</p>
  </div>  </div>

<p>Studying numerous cases where "Knowledge is
power" is alleged or denied, we find that what is
meant is that a knowledge of the right means of
doing anything is power&mdash;in short, that the predicate
is not made of all knowledge, but only of a species
of knowledge.</p>

<p>Take, again, <i>Custom blunts sensibility</i>. Putting this
in the concrete, and inquiring what predicate is made
about "men accustomed to anything" (S), we have
no difficulty in finding examples where such men are
said to become indifferent to it. We find such illustrations
as Lovelace's famous "Paradox":&mdash;</p>

<div class="poem">  <div class="stanza">
<p>Through foul we follow fair</p>
<p class="i2">For had the world one face</p>
<p>And earth been bright as air</p>
<p class="i2">We had known neither place.</p>
<p>Indians smell not their nest</p>
<p>The Swiss and Finn taste best</p>
<p class="i2">The spices of the East.</p>
  </div>  </div>

<p>So men accustomed to riches are not acutely sensible
of their advantages: dwellers in noisy streets cease to
be distracted by the din: the watchmaker ceases to
hear the multitudinous ticking in his shop: the
neighbours of chemical works are not annoyed by the
smells like the casual passenger. But we find also
that wine-tasters acquire by practice an unusual
delicacy of sense; that the eyes once accustomed to
a dim light begin to distinguish objects that were at
<span class="pagenum"><a name="page75" id="page75"></a>[page&nbsp;75]</span>
first indistinguishable; and so on. What meanings
of "custom" and of "sensibility" will reconcile these
apparently conflicting examples? What are the exact
attributes signified by the names? We should probably
find that by sensibility is meant emotional sensibility
as distinguished from intellectual discrimination, and
that by custom is meant familiarity with impressions
whose variations are not attended to, or subjection to
one unvarying impression.</p>

<p>To verify the meaning of abstract proverbs in this
way is to travel over the road by which the Greek
dialecticians were led to feel the importance of
definition. Of this more will be said presently. If
it is contended that such excursions are beyond the
bounds of Formal Logic, the answer is that the
exercise is a useful one and that it starts naturally
and conveniently from the formul&aelig; of Logic. It is the
practice and discipline that historically preceded the
Aristotelian Logic, and in the absence of which the
Aristotelian formul&aelig; would have a narrowing and
cramping effect.</p>

<p><b>Can all propositions be reduced to the syllogistic
form?</b> Probably: but this is a purely scientific inquiry,
collateral to Practical Logic. The concern of Practical
Logic is chiefly with forms of proposition that favour
inaccuracy or inexactness of thought. When there is
no room for ambiguity or other error, there is no virtue
in artificial syllogistic form. The attempt so to reduce
any and every proposition may lead, however, to the
study of what Mr. Bosanquet happily calls the
"Morphology" of Judgment, Judgment being the
technical name for the mental act that accompanies
the utterance of a proposition. Even in such sentences
as "How hot it is!" or "It rains," the rudiment of
<span class="pagenum"><a name="page76" id="page76"></a>[page&nbsp;76]</span>
subject and predicate may be detected. When a man
says "How hot it is," he conveys the meaning, though
there is no definitely formed subject in his mind, that
the outer world at the moment of his speaking has a
certain quality or attribute. So with "It rains". The
study of such examples in their context, however, reveals
the fact that the same form of Common speech may
cover different subjects and predicates in different
connexions. Thus in the argument:&mdash;</p>

<div class="poem">  <div class="stanza">
<p>"Whatever is, is best.</p>
<p class="i2">It rains!"&mdash;</p>
  </div>  </div>

<p>the Subject is <i>Rain</i> and the Predicate <i>is now</i>, "is at
the present time," "is in the class of present events".</p>

<p class="note1"><a id="footnotePI-ChII3" name="footnotePI-ChII3"></a><a class="footnote" href="#footnotetagPI-ChII3">Footnote 1:</a>
Remember that when we speak of a general name, we do not
necessarily mean a single word. A general name, logically
viewed, is simply the name of a <i>genus</i>, kind, or class: and
whether this is single-worded or many-worded is, strictly
speaking, a grammatical question. "Man," "man-of-ability,"
"man-of-ability-and-courage," "man-of-ability-and-courage-and-gigantic-stature,"
"man-who-fought-at-Marathon"&mdash;these are
all general names in their logical function. No matter how the
constitutive properties of the class are indicated, by one word or
in combination, that word or combination is a general name.
In actual speech we can seldom indicate by a single word the
meaning predicated.</p>

<p class="note1"><a id="footnotePI-ChII4" name="footnotePI-ChII4"></a><a class="footnote" href="#footnotetagPI-ChII4">Footnote 2:</a>
The objection taken to the word "indefinite," that the
quantity of particular propositions is indefinite, <i>some</i> meaning
any quantity less than all, is an example of the misplaced and
frivolous subtlety that has done so much to disorder the tradition
of Logic. By "indefinite" is simply meant not definitely
expressed as either Universal or Particular, Total or Partial.
The same objection might be taken to any word used to express
the distinction: the degree of quantity in Some S is not
"designate" any more than it is "definite" or "dioristic".</p>

<p class="note1"><a id="footnotePI-ChII5" name="footnotePI-ChII5"></a><a class="footnote" href="#footnotetagPI-ChII5">Footnote 3:</a>
<i>Generally.</i> In this word we have an instance of the frequent
conflict
between the words of common speech and logical terminology.
How it arises shall be explained in next chapter. A General proposition
is a synonym for a Universal proposition (if the forms A
and E are so termed): but "generally" in common speech means
"for the most part," and is represented by the symbol of particular
quantity, <i>Some</i>.</p>

<p class="note1"><a id="footnotePI-ChII6" name="footnotePI-ChII6"></a><a class="footnote" href="#footnotetagPI-ChII6">Footnote 4:</a>
With some logicians it is a mechanical rule in reducing to
syllogistic form to treat as I or O all sentences in which there is
no formal expression of quantity. This is to err on the safe side,
but common speakers are not so guarded, and it is to be presumed
rather that they have a universal application in their minds when
they do not expressly qualify.</p>

<h3 style="margin-top: 2em;">III.&mdash;<span class="sc">Some Technical Difficulties.</span></h3>

<p><i>The formula for</i> <b>Exclusive Propositions</b>. "None
but the brave deserve the fair": "No admittance
except on business": "Only Protestants can sit on the
throne of England".</p>

<p>These propositions exemplify different ways in
common speech of naming a subject <i>exclusively</i>, the
predication being made of all outside a certain term.
"None that are not brave, etc.;" "none that are not
on business, etc.;" "none that are not Protestants,
etc.". No not-S is P. It is only about all outside the
given term that the universal assertion is made: we
say nothing universally about the individuals within
the term: we do not say that all Protestants are
eligible, nor that all persons on business are admitted,
nor that every one of the brave deserves the fair. All
that we say is that the possession of the attribute
named is an indispensable condition: a person may
<span class="pagenum"><a name="page77" id="page77"></a>[page&nbsp;77]</span>
possess the attribute, and yet on other grounds may
not be entitled to the predicate.</p>

<p>The justification for taking special note of this form
in Logic is that we are apt by inadvertence to make an
inclusive inference from it. Let it be said that None
but those who work hard can reasonably expect to
pass, and we are apt to take this as meaning that all
who work hard may reasonably expect to pass. But
what is denied of every Not-S is not necessarily
affirmed of every S.</p>

<p><i>The expression of</i> <b>Tense</b> or <b>Time</b> <i>in the Syllogistic
Forms</i>. Seeing that the Copula in S is P or S is in P
does not express time, but only a certain relation
between S and P, the question arises Where are we to
put time in the analytic formula? "Wheat is dear;"
"All had fled;" time is expressed in these propositions,
and our formula should render the whole content of
what is given. Are we to include it in the Predicate
term or in the Subject term? If it must not be left
out altogether, and we cannot put it with the copula,
we have a choice between the two terms.</p>

<p>It is a purely scholastic question. The common
technical treatment is to view the tense as part of the
predicate. "All had fled," All S is P, <i>i.e.</i>, the whole
subject is included in a class constituted on the
attributes of flight at a given time. It may be that the
Predicate is solely a predicate of time. "The Board
met yesterday at noon." S is P, <i>i.e.</i>, the meeting of
the Board is one of the events characterised by having
happened at a certain time, agreeing with other events
in that respect.</p>

<p>But in some cases the time is more properly regarded
as part of the subject. <i>E.g.</i>, "Wheat is dear". S
does not here stand for wheat collectively, but for the
<span class="pagenum"><a name="page78" id="page78"></a>[page&nbsp;78]</span>
wheat now in the market, the wheat of the present
time: it is concerning this that the attribute of dearness
is predicated; it is this that is in the class of dear
things.</p>

<p><i>The expression of</i> <b>Modality</b> <i>in the Syllogistic Forms</i>.
Propositions in which the predicate is qualified by an
expression of necessity, contingency, possibility or
impossibility [<i>i.e.</i>, in English by <i>must</i>, <i>may</i>, <i>can</i>,
or
<i>cannot</i>], were called in Medi&aelig;val Logic <i>Modal</i> Propositions.
"Two and two <i>must</i> make four." "Grubs
<i>may</i> become butterflies." "Z <i>can</i> paint." "Y <i>cannot</i>
fly."</p>

<p>There are two recognised ways of reducing such
propositions to the form S is P. One is to distinguish
between the <i>Dictum</i> and the <i>Mode</i>, the proposition and
the qualification of its certainty, and to treat the <i>Dictum</i>
as the Subject and the <i>Mode</i> as the Predicate. Thus:
"That two and two make four is necessary"; "That
Y can fly is impossible".</p>

<p>The other way is to treat the Mode as part of the
predicate. The propriety of this is not obvious in the
case of Necessary propositions, but it is unobjectionable
in the case of the other three modes. Thus: "Grubs
are things that have the potentiality of becoming
butterflies"; "Z has the faculty of painting"; "Y
has not the faculty of flying".</p>

<p>The chief risk of error is in determining the quantity
of the subject about which the Contingent or Possible
predicate is made. When it is said that "Victories
may be gained by accident," is the predicate made
concerning All victories or Some only? Here we are
apt to confuse the meaning of the contingent assertion
with the matter of fact on which in common belief it
rests. It is true only that some victories have been
<span class="pagenum"><a name="page79" id="page79"></a>[page&nbsp;79]</span>
gained by accident, and it is on this ground that we
assert in the absence of certain knowledge concerning
any victory that it may have been so gained. The
latter is the effect of the contingent assertion: it is
made about any victory in the absence of certain
knowledge, that is to say, formally about all.</p>

<p>The history of Modals in Logic is a good illustration
of intricate confusion arising from disregard of a
clear traditional definition. The treatment of them by
Aristotle was simple, and had direct reference to tricks
of disputation practised in his time. He specified four
"modes," the four that descended to medi&aelig;val logic,
and he concerned himself chiefly with the import
of contradicting these modals. What is the true
contradictory of such propositions as, "It is possible
to be" (<ins title="dynaton einai">&delta;&upsilon;&nu;&alpha;&tau;<span style="font-size: 0.9em;">&#8056;</span>&nu; &epsilon;<span style="font-size: 0.9em;">&#7990;</span>&nu;&alpha;&iota;</ins>),
"It admits of being" (<ins title="endechetai einai"><span style="font-size: 0.9em;">&#7952;</span>&nu;&delta;&#941;&chi;&epsilon;&tau;&alpha;&iota; &epsilon;<span style="font-size: 0.9em;">&#7990;</span>&nu;&alpha;&iota;</ins>),
"It must be" (<ins title="anankaion einai"><span style="font-size: 0.9em;">&#7936;</span>&nu;&alpha;&gamma;&kappa;&alpha;<span style="font-size: 0.9em;">&#8150;</span>&omicron;&nu; &epsilon;&#7990;&nu;&alpha;&iota;</ins>),
"It is impossible to be" (<ins title="adynaton einai"><span style="font-size: 0.9em;">&#7936;</span>&delta;&#973;&nu;&alpha;&tau;&omicron;&nu; &epsilon;<span style="font-size: 0.9em;">&#7990;</span>&nu;&alpha;&iota;</ins>)?
What is implied in saying
"No" to such propositions put interrogatively? "Is
it possible for Socrates to fly?" "No." Does this
mean that it is not possible for Socrates to fly, or that
it is possible for Socrates not to fly?</p>

<p>A disputant who had trapped a respondent into
admitting that it is possible for Socrates not to fly,
might have pushed the concession farther in some
such way as this: "Is it possible for Socrates not
to walk?" "Certainly." "Is it possible for him to
walk?" "Yes." "When you say that it is possible
for a man to do anything do you not believe that it is
possible for him to do it?" "Yes." "But you have
admitted that it is possible for Socrates not to fly?"</p>

<p>It was in view of such perplexities as these that
Aristotle set forth the true contradictories of his four
Modals. We may laugh at such quibbles now and
<span class="pagenum"><a name="page80" id="page80"></a>[page&nbsp;80]</span>
wonder that a grave logician should have thought
them worth guarding against. But historically this
is the origin of the Modals of Formal Logic, and to
divert the names of them to signify other distinctions
than those between modes of qualifying the certainty
of a statement is to introduce confusion.</p>

<p>Thus we find "Alexander was a great general," given
as an example of a Contingent Modal, on the ground
that though as a matter of fact Alexander was so he
might have been otherwise. It was not <i>necessary</i> that
Alexander should be a great general: therefore the
proposition is <i>contingent</i>. Now the distinction between
Necessary truth and Contingent truth may be important
philosophically: but it is merely confusing to call the
character of propositions as one or the other by the
name of Modality. The original Modality is a mode
of expression: to apply the name to this character is
to shift its meaning.</p>

<p>A more simple and obviously unwarrantable departure
from tradition is to extend the name Modality to
any grammatical qualification of a single verb in
common speech. On this understanding "Alexander
conquered Darius" is given by Hamilton as a <i>Pure</i>
proposition, and "Alexander conquered Darius honourably"
as a <i>Modal</i>. This is a merely grammatical
distinction, a distinction in the mode of composing the
predicate term in common speech. In logical tradition
Modality is a mode of qualifying the certainty of an
affirmation. "The conquest of Darius by Alexander
was honourable," or "Alexander in conquering Darius
was an honourable conqueror," is the syllogistic form
of the proposition: it is simply assertory, not qualified
in any "mode".</p>

<p>There is a similar misunderstanding in Mr. Shedden's
<span class="pagenum"><a name="page81" id="page81"></a>[page&nbsp;81]</span>
treatment of "generally" as constituting a Modal in
such sentences, as "Rivers <i>generally</i> flow into the sea".
He argues that as <i>generally</i> is not part either of the
Subject term or of the Predicate term, it must belong
to the Copula, and is therefore a <i>modal</i> qualification of
the whole assertion. He overlooked the fact that the
word "generally" is an expression of Quantity: it
determines the quantity of the Subject term.</p>

<p>Finally it is sometimes held (<i>e.g.</i>, by Mr. Venn) that
the question of Modality belongs properly to Scientific
or Inductive Logic, and is out of place in Formal
Logic. This is so far accurate that it is for Inductive
Logic to expound the conditions of various degrees of
certainty. The consideration of Modality is pertinent
to Formal Logic only in so far as concerns special
perplexities in the expression of it. The treatment of
it by Logicians has been rendered intricate by torturing
the old tradition to suit different conceptions of the end
and aim of Logic.</p>
<span class="pagenum"><a name="page82" id="page82"></a>[page&nbsp;82]</span>

<h2 style="margin-top: 3em;">PART II.</h2>

<h3>DEFINITION.</h3>

<div class="figcenter"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-140.png" width="304" height="35" alt="fancy rule" border="0" /></div>

<h3><span class="sc">Chapter I.</span></h3>

<h3>IMPERFECT UNDERSTANDING OF WORDS AND THE REMEDIES THEREFOR.&mdash;DIALECTIC.&mdash;DEFINITION.</h3>

<p>We cannot inquire far into the meaning of proverbs or
traditional sayings without discovering that the common
understanding of general and abstract names is
loose and uncertain. Common speech is a quicksand.</p>

<p>Consider how we acquire our vocabulary, how we
pick up the words that we use from our neighbours and
from books, and why this is so soon becomes apparent.
Theoretically we know the full meaning of a name
when we know all the attributes that it connotes, and
we are not justified in extending it except to objects
that possess all the attributes. This is the logical ideal,
but between the <i>ought to be</i> of Logic and the <i>is</i> of
practical life, there is a vast difference. How seldom
do we conceive words in their full meaning! And who
is to instruct us in the full meaning? It is not as in
the exact sciences, where we start with a knowledge of
<span class="pagenum"><a name="page83" id="page83"></a>[page&nbsp;83]</span>
the full meaning. In Geometry, for example, we learn
the definitions of the words used, <i>point</i>, <i>line</i>, <i>parallel</i>,
etc., before we proceed to use them. But in common
speech, we learn words first in their application to
individual cases. Nobody ever defined <i>good</i> to us, or
<i>fair</i>, or <i>kind</i>, or <i>highly educated</i>. We hear the words
applied to individual objects: we utter them in the
same connexion: we extend them to other objects that
strike us as like without knowing the precise points
of likeness that the convention of common speech
includes. The more exact meaning we learn by
gradual induction from individual cases. <i>Ugly</i>, <i>beautiful</i>,
<i>good</i>, <i>bad</i>&mdash;we learn the words first as applicable to
things and persons: gradually there arises a more or
less definite sense of what the objects so designated
have in common. The individual's extension of the
name proceeds upon what in the objects has most
impressed him when he caught the word: this may
differ in different individuals; the usage of neighbours
corrects individual eccentricities. The child in arms
shouts <i>Da</i> at the passing stranger who reminds him
of his father: for him at first it is a general name
applicable to every man: by degrees he learns that
for him it is a singular name.</p>

<p>The mode in which words are learnt and extended
may be studied most simply in the nursery. A child,
say, has learnt to say <i>mambro</i> when it sees its nurse.
The nurse works a hand-turned sewing machine, and
sings to it as she works. In the street the child sees
an organ-grinder singing as he turns his handle: it
calls <i>mambro</i>: the nurse catches the meaning and the
child is overjoyed. The organ-grinder has a monkey:
the child has an india-rubber monkey toy: it calls this
also <i>mambro</i>. The name is extended to a monkey in
<span class="pagenum"><a name="page84" id="page84"></a>[page&nbsp;84]</span>
a picture-book. It has a toy musical box with a
handle: this also becomes <i>mambro</i>, the word being
extended along another line of resemblance. A stroller
with a French fiddle comes within the denotation of
the word: a towel-rail is also called <i>mambro</i> from some
fancied resemblance to the fiddle. A very swarthy
hunch-back <i>mambro</i> frightens the child: this leads to
the transference of the word to a terrific coalman with
a bag of coals on his back. In a short time the word
has become a name for a great variety of objects that
have nothing whatever common to all of them, though
each is strikingly like in some point to a predecessor
in the series. When the application becomes too
heterogeneous, the word ceases to be of use as a
sign and is gradually abandoned, the most impressive
meaning being the last to go. In a child's vocabulary
where the word <i>mambro</i> had a run of nearly two years,
its last use was as an adjective signifying ugly or
horrible.</p>

<p>The history of such a word in a child's language is
a type of what goes on in the language of men. In
the larger history we see similar extensions under
similar motives, checked and controlled in the same
way by surrounding usage.</p>

<p>It is obvious that to avoid error and confusion, the
meaning or connotation of names, the concepts, should
somehow be fixed: names cannot otherwise have an
identical reference in human intercourse. We may
call this ideal fixed concept the <b>Logical Concept</b>: or
we may call it the <b>Scientific Concept</b>, inasmuch as
one of the main objects of the sciences is to attain
such ideals in different departments of study. But in
actual speech we have also the <b>Personal Concept</b>,
which varies more or less with the individual user,
<span class="pagenum"><a name="page85" id="page85"></a>[page&nbsp;85]</span>
and the <b>Popular</b> or <b>Vernacular Concept</b>, which,
though roughly fixed, varies from social sect to social
sect and from generation to generation.</p>

<p>The variations in Popular Concepts may be traced
in linguistic history. Words change with things and
with the aspects of things, as these change in public
interest and importance. As long as the attributes
that govern the application of words are simple,
sensible attributes, little confusion need arise: the
variations are matters of curious research for the
philologist, but are logically insignificant. Murray's
Dictionary, or such books as Trench's <i>English Past
and Present</i>, supply endless examples, as many, indeed
as there are words in the language. <i>Clerk</i> has almost
as many connotations as our typical <i>mambro</i>: clerk
in holy orders, church clerk, town clerk, clerk of
assize, grocer's clerk. In Early English, the word
meant "man in a religious order, cleric, clergyman";
ability to read, write, and keep accounts being a
prominent attribute of the class, the word was
extended on this simple ground till it has ceased
altogether to cover its original field except as a
formal designation. But no confusion is caused by
the variation, because the property connoted is
simple.<a id="footnotetagPII-ChI1" name="footnotetagPII-ChI1"></a><a href="#footnotePII-ChI1"><sup>1</sup></a>
So with any common noun: street, carriage,
ship, house, merchant, lawyer, professor. We might
be puzzled to give an exact definition of such words,
<span class="pagenum"><a name="page86" id="page86"></a>[page&nbsp;86]</span>
to say precisely what they connote in common usage;
but the risk of error in the use of them is small.</p>

<p>When we come to words of which the logical concept
is a complex relation, an obscure or intangible
attribute, the defects of the popular conception and its
tendencies to change and confusion, are of the greatest
practical importance. Take such words as <i>Monarchy</i>,
<i>tyranny</i>, <i>civil freedom</i>, <i>freedom of contract</i>,
<i>landlord</i>,
<i>gentleman</i>, <i>prig</i>, <i>culture</i>, <i>education</i>,
<i>temperance</i>, <i>generosity</i>.
Not merely should we find it difficult to give an
analytic definition of such words: we might be unable
to do so, and yet flatter ourselves that we had a clear
understanding of their meaning. But let two men
begin to discuss any proposition in which any such
word is involved, and it will often be found that they
take the word in different senses. If the relation
expressed is complex, they have different sides or lines
of it in their minds; if the meaning is an obscure
quality, they are guided in their application of it by
different outward signs.</p>

<p>Monarchy, in its original meaning, is applied to a
form of government in which the will of one man is
supreme, to make laws or break them, to appoint or
dismiss officers of state and justice, to determine peace
or war, without control of statute or custom. But
supreme power is never thus uncontrolled in reality;
and the word has been extended to cover governments
in which the power of the titular head is controlled in
many different modes and degrees. The existence of
a head, with the title of King or Emperor, is the
simplest and most salient fact: and wherever this
exists, the popular concept of a monarchy is realised.
The President of the United States has more real
power than the Sovereign of Great Britain; but the
<span class="pagenum"><a name="page87" id="page87"></a>[page&nbsp;87]</span>
one government is called a Republic and the other
a Monarchy. People discuss the advantages and
disadvantages of monarchy without first deciding
whether they take the word in its etymological sense
of unlimited power, or its popular sense of titular
kingship, or its logical sense of power definitely
limited in certain ways. And often in debate,
monarchy is really a singular term for the government
of Great Britain.</p>

<p><i>Culture</i>, <i>religious</i>, <i>generous</i>, are names for inward
states or qualities: with most individuals some simple
outward sign directs the application of the word&mdash;it
may be manner, or bearing, or routine observances, or
even nothing more significant than the cut of the
clothes or of the hair. Small things undoubtedly are
significant, and we must judge by small things when
we have nothing else to go by: but instead of trying
to get definite conceptions for our moral epithets, and
suspending judgment till we know that the use of the
epithet is justified, the trifling superficial sign becomes
for us practically the whole meaning of the word. We
feel that we must have a judgment of some sort at
once: only simple signs are suited to our impatience.</p>

<p>It was with reference to this state of things that
Hegel formulated his paradox that the true abstract
thinker is the plain man who laughs at philosophy as
what he calls abstract and unpractical. He holds
decided opinions for or against this or the other
abstraction, <i>freedom</i>, <i>tyranny</i>, <i>revolution</i>, <i>reform</i>,
<i>socialism</i>,
but what these words mean and within what limits the
things signified are desirable or undesirable, he is in
too great a hurry to pause and consider.</p>

<p>The disadvantages of this kind of "abstract" thinking
are obvious. The accumulated wisdom of mankind
<span class="pagenum"><a name="page88" id="page88"></a>[page&nbsp;88]</span>
is stored in language. Until we have cleared our
conceptions, and penetrated to the full meaning of
words, that wisdom is a sealed book to us. Wise
maxims are interpreted by us hastily in accordance
with our own narrow conceptions. All the vocables of a
language may be more or less familiar to us, and yet
we may not have learnt it as an instrument of thought.
Outside the very limited range of names for what we
see and use in the daily routine of life, food and clothes
and the common occupations of men, words have little
meaning for us, and are the vehicles merely of thin
preconceptions and raw prejudices.</p>

<p>The remedy for "abstract" thinking is more thinking,
and in pursuing this two aims may be specified for the
sake of clearness, though they are closely allied, and
progress towards both may often be made by one and
the same operation. (1) We want to reach a clear and
full conception of the meaning of names as used now
or at a given time. Let us call this the <i>Verification of
the Meaning</i>. (2) We want to fix such conceptions,
and if necessary readjust their boundaries. This is the
province of <i>Definition</i>, which cannot be effectually performed
without <i>Scientific Classification</i> or <i>Division</i>.</p>

<h3 style="margin-top: 2em;">I.&mdash;<span class="sc">Verification of the Meaning&mdash;Dialectic.</span></h3>

<p>This can only be done by assembling the objects
to which the words are applied, and considering what
they have in common. To ascertain the actual
connotation we must run over the actual denotation.
And since in such an operation two or more minds are
better than one, discussion or dialectic is both more
fruitful and more stimulating than solitary reflection
or reading.</p>
<span class="pagenum"><a name="page89" id="page89"></a>[page&nbsp;89]</span>

<p>The first to practise this process on a memorable
scale, and with a distinct method and purpose, was
Socrates. To insist upon the necessity of clear
conceptions, and to assist by his dialectic procedure
in forming them, was his contribution to philosophy.</p>

<p>His plan was to take a common name, profess
ignorance of its meaning, and ask his interlocutor
whether he would apply it in such and such an
instance, producing one after another. According to
Xenophon's <i>Memorabilia</i> he habitually chose the
commonest names, <i>good</i>, <i>unjust</i>, <i>fitting</i>, and so forth,
and tried to set men thinking about them, and
helped them by his questions to form an intelligent
conception of the meaning.</p>

<p>For example, what is the meaning of injustice?
Would you say that the man who cheats or deceives
is unjust? Suppose a man deceives his enemies, is
there any injustice in that? Can the definition be
that a man who deceives his friends is unjust? But
there are cases where friends are deceived for their
own good: are these cases of injustice? A general
may inspirit his soldiers by a falsehood. A man
may cajole a weapon out of his friend's hand when
he sees him about to commit suicide. A father may
deceive his son into taking medicine. Would you
call these men unjust? By some such process of
interrogation we are brought to the definition that
a man is unjust who deceives his friends to their
hurt.</p>

<p>Observe that in much of his dialectic the aim of
Socrates was merely to bring out the meaning lying
vague and latent, as it were, in the common mind.
His object was simply what we have called the
verification of the meaning. And a dialectic that
<span class="pagenum"><a name="page90" id="page90"></a>[page&nbsp;90]</span>
confines itself to the consideration of what is ordinarily
meant as distinct from what ought to be meant
may often serve a useful purpose. Disputes about
words are not always as idle as is sometimes
supposed. Mr. H. Sidgwick truly remarks (<i>à propos</i>
of the terms of Political Economy) that there is
often more profit in seeking a definition than in
finding it. Conceptions are not merely cleared but
deepened by the process. Mr. Sidgwick's remarks
are so happy that I must take leave to quote them:
they apply not merely to the verification of ordinary
meaning but also to the study of special uses by
authorities, and the reasons for those special uses.</p>

<blockquote><p>
"The truth is&mdash;as most readers of Plato know, only it is
a truth difficult to retain and apply&mdash;that what we gain by
discussing a definition is often but slightly represented in
the superior fitness of the formula that we ultimately adopt;
it consists chiefly in the greater clearness and fulness in
which the characteristics of the matter to which the
formula refers have been brought before the mind in the
process of seeking for it. While we are apparently aiming
at definitions of terms, our attention should be really fixed
on distinctions and relations of fact. These latter are what
we are concerned to know, contemplate, and as far as
possible arrange and systematise; and in subjects where
we cannot present them to the mind in ordinary fulness by
the exercise of the organs of sense, there is no way of
surveying them so convenient as that of reflecting on our
use of common terms.... In comparing different definitions
our aim should be far less to decide which we ought to
adopt, than to apprehend and duly consider the grounds on
which each has commended itself to reflective minds. We
shall generally find that each writer has noted some
relation, some resemblance or difference, which others have
overlooked; and we shall gain in completeness, and often
<span class="pagenum"><a name="page91" id="page91"></a>[page&nbsp;91]</span>
in precision, of view by following him in his observations,
whether or not we follow him in his conclusions."<a id="footnotetagPII-ChI2" name="footnotetagPII-ChI2"></a><a href="#footnotePII-ChI2"><sup>2</sup></a>
</p></blockquote>

<p>Mr. Sidgwick's own discussions of <i>Wealth</i>, <i>Value</i>,
and <i>Money</i> are models. A clue is often found to the
meaning in examining startlingly discrepant statements
connected with the same leading word. Thus
we find some authorities declaring that "style" cannot
be taught or learnt, while others declare that it can.
But on trying to ascertain what they mean by "style,"
we find that those who say it cannot be taught mean
either a certain marked individual character or manner
of writing&mdash;as in Buffon's saying, <i>Le style c'est l'homme
même</i>&mdash;or a certain felicity and dignity of expression,
while those who say style can be taught mean lucid
method in the structure of sentences or in the arrangement
of a discourse. Again in discussions on the
rank of poets, we find different conceptions of what
constitutes greatness in poetry lying at the root of
the inclusion of this or the other poet among great
poets. We find one poet excluded from the first rank
of greatness because his poetry was not serious;
another because his poetry was not widely popular;
another because he wrote comparatively little; another
because he wrote only songs or odes and never
attempted drama or epic. These various opinions
point to different conceptions of what constitutes
greatness in poets, different connotations of "great
poet". Comparing different opinions concerning
"education" we may be led to ask whether it means
more than instruction in the details of certain subjects,
whether it does not also import the formation of a
<span class="pagenum"><a name="page92" id="page92"></a>[page&nbsp;92]</span>
disposition to learn or an interest in learning or
instruction in a certain method of learning.</p>

<p style="margin-top: 2.5em">Historically, dialectic turning on the use of words
preceded the attempt to formulate principles of Definition,
and attempts at precise definition led to Division
and Classification, that is to systematic arrangement
of the objects to be defined. Attempt to define any
such word as "education," and you gradually become
sensible of the needs in respect of method that forced
themselves upon mankind in the history of thought.
You soon become aware that you cannot define it by
itself alone; that you are beset by a swarm of more or
less synonymous words, <i>instruction</i>, <i>discipline</i>, <i>culture</i>,
<i>training</i>, and so on; that these various words represent
distinctions and relations among things more or less
allied; and that, if each must be fixed to a definite
meaning, this must be done with reference to one
another and to the whole department of things that
they cover.</p>

<p>The first memorable attempts at scientific arrangement
were Aristotle's treatises on Ethics and Politics,
which had been the subjects of active dialectic
for at least a century before. That these the most
difficult of all departments to subject to scientific
treatment should have been the first chosen was due
simply to their preponderating interest: "The proper
study of mankind is man". The systems of what are
known as the Natural Sciences are of modern origin:
the first, that of Botany, dates from Cesalpinus in
the sixteenth century. But the principles on which
Aristotle proceeded in dividing and defining, principles
which have gradually themselves been more precisely
formulated, are principles applicable to all systematic
<span class="pagenum"><a name="page93" id="page93"></a>[page&nbsp;93]</span>
arrangements for purposes of orderly study. I give
them in the precise formul&aelig; which they have gradually
assumed in the tradition of Logic. The principles of
Division are often given in Formal Logic, and the
principles of Classification in Inductive Logic, but
there is no valid reason for the separation. The
classification of objects in the Natural Sciences, of
animals, plants, and stones, with a view to the thorough
study of them in form, structure, and function, is more
complex than classifications for more limited purposes,
and the tendency is to restrict the word classification to
these elaborate systems. But really they are only a
series of divisions and subdivisions, and the same
principles apply to each of the subordinate divisions
as well as to the division of the whole department
of study.</p>

<h3 style="margin-top: 2em;">II.&mdash;<span class="sc">Principles of Division or Classification and Definition.</span></h3>

<p>Confusion in the boundaries of names arises from
confused ideas regarding the resemblances and
differences of things. As a protective against this
confusion, things must be clearly distinguished in
their points of likeness and difference, and this
leads to their arrangement in systems, that is, to
division and classification. A name is not secure
against variation until it has a distinct place in
such a system as a symbol for clearly distinguished
attributes. Nor must we forget, further, that systems
have their day, that the best system attainable is
only temporary, and may have to be recast to
correspond with changes of things and of man's
way of looking at them.</p>
<span class="pagenum"><a name="page94" id="page94"></a>[page&nbsp;94]</span>

<p>The leading principles of <b>Division</b> may be stated
as follows:&mdash;</p>

<p class="ind">
I. Every division is made on the ground of differences
in some attribute common to all the members of
the whole to be divided.
</p>

<p>This is merely a way of stating what a logical
division is. It is a division of a generic whole or
<i>genus</i>, an indefinite number of objects thought of
together as possessing some common character or
attribute. All have this attribute, which is technically
called the <i>fundamentum divisionis</i>, or generic attribute.
But the whole is divisible into smaller groups (<i>species</i>),
each of which possesses the common character with
a difference (<i>differentia</i>). Thus, mankind may be
divided into White men, Black men, Yellow men, on
ground of the differences in the colour of their skins:
all have skins of some colour: this is the <i>fundamentum
divisionis</i>: but each subdivision or species has a
different colour: this is the <i>differentia</i>. Rectilineal
figures are divided into triangles, quadrangles,
pentagons, etc., on the ground of differences in the
number of angles.</p>

<p>Unless there is a <i>fund. div.</i>, <i>i.e.</i>, unless the differences
are differences in a common character, the division is
not a logical division. To divide men into Europeans,
opticians, tailors, blondes, brunettes, and dyspeptics
is not to make a logical division. This is seen more
clearly in connexion with the second condition of a
perfect division.</p>

<p class="ind">
II. In a perfect division, the subdivisions or species
are mutually exclusive.
</p>

<p>Every object possessing the common character
<span class="pagenum"><a name="page95" id="page95"></a>[page&nbsp;95]</span>
should be in one or other of the groups, and none
should be in more than one.</p>

<p>Confusion between classes, or overlapping, may
arise from two causes. It may be due (1) to faulty
division, to want of unity in the <i>fundamentum divisionis</i>;
(2) to the indistinct character of the objects to be
defined.</p>

<p>(1) Unless the division is based upon a single ground,
unless each species is based upon some mode of the
generic character, confusion is almost certain to arise.
Suppose the field to be divided, the objects to be
classified, are three-sided rectilineal plane figures,
each group must be based upon some modification of
the three sides. Divide them into equilateral, isosceles,
and scalene according as the three sides are all of
equal length, or two of equal length, or each of
different length, and you have a perfect division.
Similarly you can divide them perfectly according to
the character of the angles into acute-angled, right-angled
and obtuse-angled. But if you do not keep
to a single basis, as in dividing them into equilateral,
isosceles, scalene, and right-angled, you have a cross-division.
The same triangle might be both right-angled
and isosceles.</p>

<p>(2) Overlapping, however, may be unavoidable in
practice owing to the nature of the objects. There
may be objects in which the dividing characters
are not distinctly marked, objects that possess the
differenti&aelig; of more than one group in a greater or less
degree. Things are not always marked off from one
another by hard and fast lines. They shade into
one another by imperceptible gradations. A clear
separation of them may be impossible. In that case
you must allow a certain indeterminate margin between
<span class="pagenum"><a name="page96" id="page96"></a>[page&nbsp;96]</span>
your classes, and sometimes it may be necessary to
put an object into more than one class.</p>

<p>To insist that there is no essential difference unless
a clear demarcation can be made is a fallacy. A
sophistical trick called the <i>Sorites</i> or Heap from the
classical example of it was based upon this difficulty
of drawing sharp lines of definition. Assuming that
it is possible to say how many stones constitute a
heap, you begin by asking whether three stones form
a heap. If your respondent says No, you ask whether
four stones form a heap, then five, and so on and he
is puzzled to say when the addition of a single stone
makes that a heap which was not a heap before. Or
you may begin by asking whether twenty stones form
a heap, then nineteen, then eighteen, and so on, the
difficulty being to say when what was a heap ceases
to be so.</p>

<p>Where the objects classified are mixed states or
affections, the products of interacting factors, or
differently interlaced or interfused growths from
common roots, as in the case of virtues, or emotions,
or literary qualities, sharp demarcations are impossible.
To distinguish between wit and humour, or humour
and pathos, or pathos and sublimity is difficult because
the same composition may partake of more than one
character. The specific characters cannot be made
rigidly exclusive one of another.</p>

<p>Even in the natural sciences, where the individuals
are concrete objects of perception, it may be difficult
to decide in which of two opposed groups an object
should be included. Sydney Smith has commemorated
the perplexities of Naturalists over the newly discovered
animals and plants of Botany Bay, in especial
with the <i>Ornithorynchus</i>,&mdash;"a quadruped as big as a
<span class="pagenum"><a name="page97" id="page97"></a>[page&nbsp;97]</span>
large cat, with the eyes, colour, and skin of a mole,
and the bill and web-feet of a duck&mdash;puzzling Dr.
Shaw, and rendering the latter half of his life miserable,
from his utter inability to determine whether it
was a bird or a beast".</p>

<p class="ind">
III. The classes in any scheme of division should
be of co-ordinate rank.
</p>

<p>The classes may be mutually exclusive, and yet the
division imperfect, owing to their not being of equal
rank. Thus in the ordinary division of the Parts of
Speech, parts, that is, of a sentence, Prepositions and
Conjunctions are not co-ordinate in respect of function,
which is the basis of the division, with Nouns, Adjectives,
Verbs, and Adverbs. The preposition is a part
of a phrase which serves the same function as an
adjective, <i>e.g.</i>, <i>royal</i> army, army <i>of the king</i>; it is thus
functionally part of a part, or a particle. So with the
conjunction: it also is a part of a part, <i>i.e.</i>, part of a
clause serving the function of adjective or adverb.</p>

<p class="ind">
IV. The basis of division (<i>fundamentum divisionis</i>)
should be an attribute admitting of important
differences.
</p>

<p>The importance of the attribute chosen as basis may
vary with the purpose of the division. An attribute
that is of no importance in one division, may be
important enough to be the basis of another division.
Thus in a division of houses according to their architectural
attributes, the number of windows or the rent
is of little importance; but if houses are taxed or rated
according to the number of windows or the rent, these
attributes become important enough to be a basis of
division for purposes of taxation or rating. They then
admit of important differences.</p>
<span class="pagenum"><a name="page98" id="page98"></a>[page&nbsp;98]</span>

<p>That the importance is relative to the purpose of the
division should be borne in mind because there is a
tendency to regard attributes that are of importance
in any familiar or pre-eminent division as if they had
an absolute importance. In short, disregard of this
relativity is a fallacy to be guarded against.</p>

<p>In the sciences, the purpose being the attainment
and preservation of knowledge, the objects of study are
divided so as to serve that purpose. Groups must be
formed so as to bring together the objects that have
most in common. The question, Who are to be placed
together? in any arrangement for purposes of study,
receives the same answer for individuals and for classes
that have to be grouped into higher classes, namely,
Those that have most in common. This is what Dr.
Bain happily calls "the golden rule" of scientific
classification: "Of the various groupings of resembling
things, preference is given to such as have the greatest
number of attributes in common". I slightly modify
Dr. Bain's statement: he says "the most numerous
and the most important attributes in common". But
for scientific purposes number of attributes constitutes
importance, as is well recognised by Dr. Fowler when
he says that the test of importance in an attribute proposed
as a basis of classification is the number of
other attributes of which it is an index or invariable
accompaniment. Thus in Zoology the squirrel, the
rat, and the beaver are classed together as Rodents,
the difference between their teeth and the teeth of
other Mammalia being the basis of division, because
the difference in teeth is accompanied by differences in
many other properties. So the hedge-hog, the shrew-mouse,
and the mole, though very unlike in outward
appearance and habits, are classed together as Insectivora,
<span class="pagenum"><a name="page99" id="page99"></a>[page&nbsp;99]</span>
the difference in what they feed on being
accompanied by a number of other differences.</p>

<p style="margin-top: 2.5em"><i>The Principles of</i> <b>Definition</b>. The word "definition"
as used in Logic shows the usual tendency of words to
wander from a strict meaning and become ambiguous.
Throughout most of its uses it retains this much of a
common signification, the fixing or determining of the
boundaries of a class<a id="footnotetagPII-ChI3" name="footnotetagPII-ChI3"></a><a href="#footnotePII-ChI3"><sup>3</sup></a>
by making clear its constituent
attributes. Now in this making clear two processes
may be distinguished, a material process and a verbal
process. We have (1) the clearing up of the common
attributes by a careful examination of the objects
included in the class: and we have (2) the statement
of these common attributes in language. The rules
of definition given by Dr. Bain, who devotes a
separate Book in his Logic to the subject of
Definition, concern the first of these processes: the
rules more commonly given concern mainly the
second.</p>

<p>One eminent merit in Dr. Bain's treatment is that
it recognises the close connexion between Definition
and Classification. His cardinal rules are reduced to
two.</p>
<span class="pagenum"><a name="page100" id="page100"></a>[page&nbsp;100]</span>

<p class="ind">
I. <i>Assemble for comparison representative individuals
of the class.</i></p>

<p class="ind">II. <i>Assemble for comparison representative individuals
of the contrasted class or classes.</i>
</p>

<p>Seeing that the contrasted classes are contrasted on
some basis of division, this is in effect to recognise
that you cannot clearly define any class except in a
scheme of classification. You must have a wide <i>genus</i>
with its <i>fundamentum divisionis</i>, and, within this, <i>species</i>
distinguished by their several <i>differenti&aelig;</i>.</p>

<p>Next, as to the verbal process, rules are commonly
laid down mostly of a trifling and obvious character.
That "a definition should state neither more nor less
than the common attributes of the class," or than the
attributes signified by the class-name, is sometimes
given as a rule of definition. This is really an
explanation of what a definition is, a definition of a
definition. And as far as mere statement goes it is
not strictly accurate, for when the attributes of a
genus are known it is not necessary to give all the
attributes of the species, which include the generic
attributes as well, but it is sufficient to give the
generic name and the differentia. Thus Poetry may
be defined as "a Fine Art having metrical language
as its instrument". This is technically known as
definition <i>per genus et differentiam</i>. This mode of
statement is a recognition of the connexion between
Definition and Division.</p>

<p>The rule that "a definition should not be a synonymous
repetition of the name of the class to be defined,"
is too obvious to require formal statement. To describe
a Viceroy as a man who exercises viceregal functions,
may have point as an epigram in the case of a <i>faineant</i>
viceroy, but it is not a definition.</p>
<span class="pagenum"><a name="page101" id="page101"></a>[page&nbsp;101]</span>

<p>So with the rule that "a definition should not be
couched in ambiguous unfamiliar, or figurative
language". To call the camel "the ship of the
desert" is a suggestive and luminous description of
a property, but it is not a definition. So with the
noble description of Faith as "the substance of
things hoped for, the evidence of things not seen".
But if one wonders why so obvious a "rule" should
be laid down, the answer is that it has its historical
origin in the caprices of two classes of offenders,
mystical philosophers and pompous lexicographers.<a id="footnotetagPII-ChI4" name="footnotetagPII-ChI4"></a><a href="#footnotePII-ChI4"><sup>4</sup></a></p>

<p>That "the definition should be simply convertible
with the term for the class defined," so that we may
say, for example, either: "Wine is the juice of the
grape," or, "The juice of the grape is wine," is an
obvious corollary from the nature of definition, but
should hardly be dignified with the name of a "rule".</p>

<p style="margin-top: 2.5em"><i>The Principles of</i> <b>Naming</b>. Rules have been formulated
for the choice of names in scientific definition and
classification, but it may be doubted whether such choice
can be reduced to precise rule. It is enough to draw
attention to certain considerations obvious enough on
reflection.</p>

<p>We may take for granted that there should be
distinct names for every defining attribute (a <i>Terminology</i>)
and for every group or class (a <i>Nomenclature</i>).
What about the selection of the names? Suppose an
investigator is struck with likenesses and differences
that seem to him important enough to be the basis of
a new division, how should he be guided in his choice
of names for the new groups that he proposes? Should
<span class="pagenum"><a name="page102" id="page102"></a>[page&nbsp;102]</span>
he coin new names, or should he take old names and
try to fit them with new definitions?</p>

<p>The balance of advantages is probably in favour of
Dr. Whewell's dictum that "in framing scientific
terms, the appropriation of old words is preferable to
the invention of new ones". Only care must be taken
to keep as close as possible to the current meaning of
the old word, and not to run counter to strong associations.
This is an obvious precept with a view to
avoiding confusion. Suppose, for example, that in
dividing Governments you take the distribution of
political power as your basis of division and come to
the conclusion that the most important differences are
whether this power is vested in a few or in the
majority of the community. You want names to fix
this broad division. You decide instead of coining
the new word <i>Pollarchy</i> to express the opposite of
<i>Oligarchy</i> to use the old words <i>Republic</i> and <i>Oligarchy</i>.
You would find, as Sir George Cornewall Lewis
found, that however carefully you defined the word
Republic, a division under which the British Government
had to be ranked among Republics would not
be generally understood and accepted. Using the
word in the sense explained above, Mr. Bagehot
maintained that the constitution of Great Britain
was more Republican than that of the United
States, but his meaning was not taken except by
a few.</p>

<p>The difficulty in choosing between new words and
old words to express new meanings is hardly felt in
the exact sciences. It is at least at a minimum.
The innovator may encounter violent prejudice, but,
arguing with experts, he can at least make sure of
being understood, if his new division is based upon
<span class="pagenum"><a name="page103" id="page103"></a>[page&nbsp;103]</span>
real and important differences. But in other subjects
the difficulty of transmitting truth or of expressing it
in language suited for precise transmission, is almost
greater than the difficulty of arriving at truth. Between
new names and old names redefined, the possessor of
fresh knowledge, assuming it to be perfectly verified,
is in a quandary. The objects with which he deals
are already named in accordance with loose divisions
resting on strong prejudices. The names in current
use are absolutely incapable of conveying his meaning.
He must redefine them if he is to use them. But in
that case he runs the risk of being misunderstood
from people being too impatient to master his redefinition.
His right to redefine may even be challenged
without any reference to the facts to be expressed: he
may simply be accused of circulating false linguistic
coin, of debasing the verbal currency. The other
alternative open to him is to coin new words. In
that case he runs the risk of not being read at all.
His contribution to verified knowledge is passed by
as pedantic and unintelligible. There is no simple
rule of safety: between Scylla and Charybdis the
mariner must steer as best he may. Practically the
advantage lies with old words redefined, because
thereby discussion is provoked and discussion clears
the air.</p>

<p>Whether it is best to attempt a formal definition
or to use words in a private, peculiar, or esoteric
sense, and leave this to be gathered by the reader
from the general tenor of your utterances, is a question
of policy outside the limits of Logic. It is for the
logician to expound the method of Definition and the
conditions of its application: how far there are subjects
that do not admit of its application profitably must be
<span class="pagenum"><a name="page104" id="page104"></a>[page&nbsp;104]</span>
decided on other grounds. But it is probably true
that no man who declines to be bound by a formal
definition of his terms is capable of carrying them
in a clear unambiguous sense through a heated
controversy.</p>

<p class="note1"><a id="footnotePII-ChI1" name="footnotePII-ChI1"></a><a class="footnote" href="#footnotetagPII-ChI1">Footnote 1:</a>
Except, perhaps, in new offices to which the name is extended,
such as <i>Clerk</i> of School Board. The name, bearing its most
simple and common meaning, may cause popular misapprehension
of the nature of the duties. Any uncertainty in meaning may be
dangerous in practice: elections have been affected by the
ambiguity of this word.</p>

<p class="note1"><a id="footnotePII-ChI2" name="footnotePII-ChI2"></a><a class="footnote" href="#footnotetagPII-ChI2">Footnote 2:</a>
Sidgwick's <i>Political Economy</i>, pp. 52-3. Ed. 1883.</p>

<p class="note1"><a id="footnotePII-ChI3" name="footnotePII-ChI3"></a><a class="footnote" href="#footnotetagPII-ChI3">Footnote 3:</a>
Some logicians, however, speak of defining a thing, and
illustrate this as if by a thing they meant a concrete individual,
the realistic treatment of Universals lending itself to such
expressions. But though the authority of Aristotle might be
claimed for this, it is better to confine the name in strictness to
the main process of defining a class. Since, however, the method
is the same whether it is an individual or a class that we want to
make distinct, there is no harm in the extension of the word
definition to both varieties. See Davidson's <i>Logic of Definition</i>,
chap. ii.</p>

<p class="note1"><a id="footnotePII-ChI4" name="footnotePII-ChI4"></a><a class="footnote" href="#footnotetagPII-ChI4">Footnote 4:</a>
See Davidson's <i>Logic of Definition</i>, chap. iii.</p>
<span class="pagenum"><a name="page105" id="page105"></a>[page&nbsp;105]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter II</span>.</h3>

<h3>THE FIVE PREDICABLES.&mdash;VERBAL AND REAL PREDICATION.</h3>

<p>We give a separate chapter to this topic out of respect
for the space that it occupies in the history of Logic.
But except as an exercise in subtle distinction for its
own sake, all that falls to be said about the Predicables
might be given as a simple appendix to the chapter on
Definition.</p>

<p>Primarily, the Five Predicables or Heads of Predicables&mdash;Genus,
Species, Differentia, Proprium, and
Accidens&mdash;are not predicables at all, but merely a list
or enumeration of terms used in dividing and defining
on the basis of attributes. They have no meaning
except in connexion with a fixed scheme of division.
Given such a scheme, and we can distinguish in it
the whole to be divided (the <i>genus</i>), the subordinate
divisions (the <i>species</i>), the attribute or combination of
attributes on which each species is constituted (the
<i>differentia</i>), and other attributes, which belong to some
or all of the individuals but are not reckoned for
purposes of division and definition (<i>Propria</i> and <i>Accidentia</i>).
The list is not itself a logical division: it is heterogeneous,
not homogeneous; the two first are names
of classes, the three last of attributes. But corresponding
to it we might make a homogeneous division of
attributes, as follows:&mdash;</p>
<span class="pagenum"><a name="page106" id="page106"></a>[page&nbsp;106]</span>

<div class="figcenter"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-106-400.png" width="400" height="153" alt="Attributes chart" border="0" />
</div>

<p>The origin of the title Predicables as applied to these
five terms is curious, and may be worth noting as an
instance of the difficulty of keeping names precise, and
of the confusion arising from forgetting the purpose
of a name. Porphyry in his
<ins title="eisagôgê"> &epsilon;<span style="font-size: 0.9em;">&#7984;</span>&sigma;&alpha;&gamma;&omega;&gamma;<span style="font-size: 0.9em;">&#x1F74;</span></ins>
or Introduction
explains the five words (<ins title="phônai">&phi;&omega;&nu;&alpha;<span style="font-size: 0.9em;">&#8054;</span></ins>)
simply as terms that it is
useful for various purposes to know, expressly mentioning
definition and division. But he casually remarks
that Singular names, "This man," "Socrates," can
be predicated only of one individual, whereas <i>Genera</i>,
<i>Species</i>, <i>Differenti&aelig;</i>, etc., are predicables of many. That
is to say he describes them as Predicables simply by
contradistinction from Singular names. A name,
however, was wanted for the five terms taken all
together, and since they are not a logical division, but
merely a list of terms used in dividing and defining,
there was no apt general designation for them such
as would occur spontaneously. Thus it became the
custom to refer to them as the Predicables, a means of
reference to them collectively being desiderated, while
the meaning of this descriptive title was forgotten.</p>

<p>To call the five divisional elements or <i>Divisoria</i>
Predicables is to present them as a division of Predicate
Terms on the basis of their relation to the Subject
Term: to suggest that every Predicate Term must be
either a Genus or a Species, or a Differentia, or a
<span class="pagenum"><a name="page107" id="page107"></a>[page&nbsp;107]</span>
Proprium, or an Accidens of the Subject Term. They
are sometimes criticised as such, and it is rightly
pointed out that the Predicate is never a species of or
with reference to the Subject. But, in truth, the five
so-called Predicables were never meant as a division of
predicates in relation to the subject: it is only the title
that makes this misleading suggestion.</p>

<p>To complete the confusion it so happens that
Aristotle used three of the Five terms in what was virtually
a division of Predicates inasmuch as it was a division
of Problems or Questions. In expounding the methods
of Dialectic in the Topica he divided Problems into
four classes according to the relation of the Predicate
to the Subject. The Predicate must either be simply
convertible with the subject or not. If simply convertible,
the two must be coextensive, and the Predicate
must be either a Proprium or the Definition. If
not simply convertible, the Predicate must either be
part of the Definition or not. If part of the Definition
it must be either a Generic Property or a Differentia
(both of which in this connexion Aristotle includes
under Genus): if not part of the Definition, it is an
Accident. Aristotle thus arrives at a fourfold division
of Problems or Predicates:&mdash;<ins title="genos">&gamma;&#941;&nu;&omicron;&sigmaf;</ins> (<i>Genus</i>, including
<i>Differentia</i>, <ins title="diaphora">&delta;&iota;&alpha;&phi;&omicron;&rho;<span style="font-size: 0.9em;">&#8048;</span></ins>);
<ins title="horos"><span style="font-size: 0.9em;">&#8004;</span>&rho;&omicron;&sigmaf;</ins> (Definition);
<ins title="to idion">&tau;<span style="font-size: 0.9em;">&#8056;</span> <span style="font-size: 0.9em;">&#7988;</span>&delta;&iota;&omicron;&nu;</ins>
(<i>Proprium</i>);
and <ins title="to symbebêkos">&tau;<span style="font-size: 0.9em;">&#8056;</span>
&sigma;&upsilon;&mu;&beta;&epsilon;&beta;&eta;&kappa;<span style="font-size: 0.9em;">&#8056;</span>&sigmaf;</ins> (<i>Accidens</i>). The object of it
was to provide a basis for his systematic exposition;
each of the four kinds admitted of differences in
dialectic method. For us it is a matter of simple
curiosity and ingenuity. It serves as a monument of
how much Greek dialectic turned on Definition, and it
corresponds exactly to the division of attributes into
Defining and Non-defining given above. It is sometimes
said that Aristotle showed a more scientific mind
<span class="pagenum"><a name="page108" id="page108"></a>[page&nbsp;108]</span>
than Porphyry in making the Predicables four instead
of five. This is true if Porphyry's list had been meant
as a division of attributes: but it was not so meant.</p>

<p style="margin-top: 2.5em">The distinction between <b>Verbal</b> or <b>Analytic</b> and
<b>Real</b> or <b>Synthetic</b> Predication corresponds to the
distinction between Defining and Non-defining attributes,
and also has no significance except with
reference to some scheme of Division, scientific and
precise or loose and popular.</p>

<p>When a proposition predicates of a subject something
contained in the full notion, concept, or definition of
the subject term, it is called Verbal, Analytic, or
Explicative: <i>verbal</i>, inasmuch as it merely explains
the meaning of a name; <i>explicative</i> for the same
reason; <i>analytic</i>, inasmuch as it unties the bundle of
attributes held together in the concept and pays out
one, or all one by one.</p>

<p>When the attributes of the Predicate are not contained
in the concept of the Subject, the proposition is called
<i>Real</i>, <i>Synthetic</i>, or <i>Ampliative</i>, for parallel reasons.</p>

<p>Thus: "A triangle is a three-sided rectilinear
figure" is Verbal or Analytic; "Triangles have
three angles together equal to two right angles,"
or "Triangles are studied in schools," is Real or
Synthetic.</p>

<p>According to this distinction, predications of the
whole Definition or of a Generic attribute or of a
Specific attribute are Verbal; predications of Accident
are Real. A nice point is whether Propria are Verbal
or Real. They can hardly be classed with Verbal,
inasmuch as one may know the full meaning of the
name without knowing them: but it might be argued
that they are Analytic, inasmuch as they are implicitly
<span class="pagenum"><a name="page109" id="page109"></a>[page&nbsp;109]</span>
contained in the defining attributes as being deducible
from them.</p>

<p>Observe, however, that the whole distinction is really
valid only in relation to some fixed or accepted scheme
of classification or division. Otherwise, what is Verbal
or Analytic to one man may be Real or Synthetic to
another. It might even be argued that every proposition
is Analytic to the man who utters it and Synthetic
to the man who receives it. We must make some
analysis of a whole of thought before paying it out in
words: and in the process of apprehending the meaning
of what we hear or read we must add the other members
of the sentence on to the subject. Whether or not this
is super-subtle, it clearly holds good that what is
Verbal (in the sense defined) to the learned man of
science may be Real to the learner. That the horse
has six incisors in each jaw or that the domestic dog
has a curly tail, is a Verbal Proposition to the Natural
Historian, a mere exposition of defining marks; but
the plain man has a notion of horse or dog into which
this defining attribute does not enter, and to him
accordingly the proposition is Real.</p>

<p>But what of propositions that the plain man would
at once recognise as Verbal? Charles Lamb, for
example, remarks that the statement that "a good
name shows the estimation in which a man is held
in the world" is a verbal proposition. Where is the
fixed scheme of division there? The answer is that
by a fixed scheme of division we do not necessarily
mean a scheme that is rigidly, definitely and precisely
fixed. To make such schemes is the business of
Science. But the ordinary vocabulary of common
intercourse as a matter of fact proceeds upon schemes
of division, though the names used in common speech
<span class="pagenum"><a name="page110" id="page110"></a>[page&nbsp;110]</span>
are not always scientifically accurate, not always the
best that could be devised for the easy acquisition and
sure transmission of thorough knowledge. The plain
man's vocabulary, though often twisted aside by such
causes as we have specified, is roughly moulded on
the most marked distinguishing attributes of things.
This was practically recognised by Aristotle when he
made one of his modes of definition consist in something
like what we have called verifying the meaning
of a name, ascertaining the attributes that it signifies
in common speech or in the speech of sensible men.
This is to ascertain the essence, <ins title="ousia">&omicron;<span style="font-size: 0.9em;">&#8016;</span>&sigma;&#943;&alpha;</ins>, or <i>Substantia</i>,
of things, the most salient attributes that strike the
common eye either at once or after the closer inspection
that comes of long companionship, and form the basis
of the ordinary vocabulary. "Properly speaking,"
Mansel says,<a id="footnotetagPII-ChII1" name="footnotetagPII-ChII1"></a><a href="#footnotePII-ChII1"><sup>1</sup></a>
"All Definition is an inquiry into
<i>Attributes</i>. Our complex notions of Substances can
only be resolved into various Attributes, with the
addition of an unknown <i>substratum</i>: a something to
which we are compelled to regard these attributes
as belonging. <i>Man</i>, for example, is analysed into
Animality, Rationality, and the something which
exhibits these phenomena. Pursue the analysis and
the result is the same. We have a something
corporeal, animated, sensible, rational. An unknown
constant must always be added to complete the
integration." This "unknown constant" was what
Locke called the <i>Real</i> Essence, as distinguished from
the <i>Nominal</i> Essence, or complex of attributes. It
<span class="pagenum"><a name="page111" id="page111"></a>[page&nbsp;111]</span>
is upon this nominal essence, upon divisions of things
according to attributes, that common speech rests,
and if it involves many cross-divisions, this is
because the divisions have been made for limited
and conflicting purposes.</p>

<p class="note1"><a id="footnotePII-ChII1" name="footnotePII-ChII1"></a><a class="footnote" href="#footnotetagPII-ChII1">Footnote 1:</a>
Aldrich's Compendium, Appendix, Note C. The reader
may be referred to Mansel's Notes A and C for valuable historical
notices of the Predicables and Definition.</p>
<span class="pagenum"><a name="page112" id="page112"></a>[page&nbsp;112]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter III.</span></h3>

<h3>ARISTOTLE'S CATEGORIES.</h3>

<p>In deference to tradition a place must be found in
every logical treatise for Aristotle's Categories. No
writing of the same length has exercised a tithe of its
influence on human thought. It governed scholastic
thought and expression for many centuries, being from
its shortness and consequent easiness of transcription
one of the few books in every educated man's library.
It still regulates the subdivisions of Parts of Speech in
our grammars. Its universality of acceptance is shown
in the fact that the words <i>category</i> (<ins title="katêgoria">&kappa;&alpha;&tau;&eta;&gamma;&omicron;&rho;&#943;&alpha;</ins>) and
<i>predicament</i>,
its Latin translation, have passed into
common speech.</p>

<p>The Categories have been much criticised and often
condemned as a division, but, strange to say, few have
inquired what they originally professed to be a division
of, or what was the original author's basis of division.
Whether the basis is itself important, is another
question: but to call the division imperfect, without
reference to the author's intention, is merely confusing,
and serves only to illustrate the fact that the same
objects may be differently divided on different principles
of division. Ramus was right in saying that the
Categories had no logical significance, inasmuch as
<span class="pagenum"><a name="page113" id="page113"></a>[page&nbsp;113]</span>
they could not be made a basis for departments of
logical method; and Kant and Mill in saying that they
had no philosophical significance, inasmuch as they are
founded upon no theory of Knowing and Being: but
this is to condemn them for not being what they were
never intended to be.</p>

<p>The sentence in which Aristotle states the objects to
be divided, and his division of them is so brief and bold
that bearing in mind the subsequent history of the
Categories, one first comes upon it with a certain
surprise. He says simply:&mdash;</p>

<p>"Of things expressed without syntax (<i>i.e.</i>, single
words), each signifies either substance, or quantity, or
quality, or relation, or place, or time, or disposition
(<i>i.e.</i>, attitude or internal arrangement), or appurtenance,
or action (doing), or suffering (being done to)."<a id="footnotetagPII-ChIII1" name="footnotetagPII-ChIII1"></a><a href="#footnotePII-ChIII1"><sup>1</sup></a></p>
<p>The objects, then, that Aristotle proposed to classify
were single words (the <i>themata simplicia</i> of the Schoolmen).<a name="tn" id="tn"></a>
He explains that by "out of syntax"
(<ins title="aneu symplokês"><span style="font-size: 0.9em;">&#7940;</span>&nu;&epsilon;&upsilon;
&sigma;&upsilon;&mu;&pi;&lambda;&omicron;&kappa;<span style="font-size: 0.9em;">&#8134;</span>&sigmaf;</ins>)<a href="#transcriber_note">*</a>
he means without reference to truth or
falsehood: there can be no declaration of truth or
falsehood without a sentence, a combination, or syntax:
"man runs" is either true or false, "man" by itself,
"runs" by itself, is neither. His division, therefore,
was a division of single words according to their differences
of signification, and without reference to the
truth or falsehood of their predication.<a id="footnotetagPII-ChIII2" name="footnotetagPII-ChIII2"></a><a href="#footnotePII-ChIII2"><sup>2</sup></a></p>

<p>Signification was thus the basis of division. But
<span class="pagenum"><a name="page114" id="page114"></a>[page&nbsp;114]</span>
according to what differences? The Categories themselves
are so abstract that this question might be
discussed on their bare titles interminably. But often
when abstract terms are doubtful, an author's intention
may be gathered from his examples. And when Aristotle's
examples are ranged in a table, certain principles
of subdivision leap to the eyes. Thus:&mdash;</p>
<span class="pagenum"><a name="page115" id="page115"></a>[page&nbsp;115]</span>

<table summary="Aristotle's Categories" align="center" border="0" style="margin-top: 2em; margin-bottom: 2em;">
<tr>
       <td class="left" valign="top">Substance<br />
	   (<ins title="ousia">&omicron;&#8016;&sigma;&#943;&alpha;</ins>)<br />
	   (<i>Substantia</i>)
	   </td>
       <td class="left" valign="top"><br />Man<br />
	   (<ins title="anthrôpos">&#7940;&nu;&theta;&rho;&omega;&pi;&omicron;&sigmaf;</ins>)
	   </td>
       <td class="left"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-rightbrace.png" width="15" height="45" alt="brace" border="0" /></td>
       <td class="left"><span class="sc">Common</span><br />
	   <span class="sc">Noun </span></td>
       <td class="left"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-leftbrace.png" width="15" height="45" alt="brace" border="0" /></td>
       <td class="left">Substance</td>
</tr>
<tr>
       <td class="left">Quantity<br />
	   (<ins title="poson">&pi;&omicron;&sigma;&#8056;&nu;</ins>)<br />
	   (<i>Quantitas</i>)<br />
	   Quality<br />
	   (<ins title="poion">&pi;&omicron;&iota;&#8056;&nu;</ins>)<br />
	   (<i>Qualitas</i>)<br />
	   Relation<br />
	   (<ins title="pros ti">&pi;&rho;&#972;&sigmaf; &tau;&iota;</ins>)<br />
	   (<i>Relatio</i>)
	   </td>
       <td class="left">Five-feet-five<br />
	   (<ins title="tripêchu">&tau;&rho;&#943;&pi;&eta;&chi;&upsilon;</ins>)<br /><br />
	    Scholarly<br />
       (<ins title="grammatikon">&gamma;&rho;&alpha;&mu;&mu;&alpha;&tau;&iota;&kappa;&#8056;&nu;</ins>)<br /><br />
	   Bigger<br />
	   (<ins title="meizon">&mu;&epsilon;&#8150;&zeta;&omicron;&nu;</ins>)<br /></td>
	   <td class="left"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-rightbrace2.png" width="21" height="128" alt="brace" border="0" /></td>
       <td class="left">
	   <span class="sc">Adjective</span></td>
       <td class="left"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-leftbrace2.png" width="21" height="128" alt="brace" border="0" /></td>
       <td class="left">Permanent<br /><br /><br /><br />
	   Attribute</td>
</tr>
<tr>
       <td class="left">Place<br />
	   (<ins title="pou">&pi;&omicron;&#8166;</ins>)<br />
	   (<i>Ubi</i>)<br />
	   Time<br />
	   (<ins title="pote">&pi;&omicron;&tau;&#x1F72;</ins>)<br />
	   (<i>Quando</i>)</td>
       <td class="left">In-the-Lyceum<br />
	   (<ins title="en Lykeiô">&#7952;&nu; &Lambda;&upsilon;&kappa;&epsilon;&#943;&#8179;</ins>)<br /><br />
	   Yesterday<br />
	   (<ins title="chthes">&chi;&theta;&#8050;&sigmaf;</ins>)</td>
       <td  class="left"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-rightbrace1.png" width="21" height="84" alt="brace" border="0" /></td>
       <td class="left">&nbsp;&nbsp;<span class="sc">Adverb</span></td>
       <td  class="left" rowspan="2"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-leftbrace4.png" width="21" height="312" alt="brace" border="0" /></td>
       <td class="left" rowspan="2">Temporary<br /><br /><br /><br /><br /><br /><br /><br />
	   Attribute</td>
</tr>
<tr>
       <td class="left">Disposition<br />
	   (<ins title="keisthai">&kappa;&epsilon;&#8150;&sigma;&theta;&alpha;&iota;</ins>)<br />
	   (<i>Positio</i>)<br />
	   Appurtenance<br />
	   (<ins title="echein">&#7956;&chi;&epsilon;&iota;&nu;</ins>)<br />
	   (<i>Habitus</i>)<br />
	   Action<br />
	   (<ins title="poiein">&pi;&omicron;&iota;&epsilon;&#8150;&nu;</ins>)<br />
	   (<i>Actio</i>)<br />
	   Passion<br />
	   (<ins title="paschein">&pi;&#940;&sigma;&chi;&epsilon;&iota;&nu;</ins>)<br />
	   (<i>Passio</i>)
	   </td>
       <td class="left">Reclines<br />
	   (<ins title="anakeitai">&#7936;&nu;&#940;&kappa;&epsilon;&iota;&tau;&alpha;&iota;</ins>)<br /><br />
	   Has-shoes-on<br />
	   (<ins title="hypodedetai">&#8017;&pi;&omicron;&delta;&#941;&delta;&epsilon;&tau;&alpha;&iota;</ins>)<br /><br />
	   Cuts<br />
	   (<ins title="temnei">&tau;&#941;&mu;&nu;&epsilon;&iota;</ins>)<br /><br />
	   Is cut<br />
	   (<ins title="temnetai">&tau;&#941;&mu;&nu;&epsilon;&tau;&alpha;&iota;</ins>)
	   </td>
       <td class="left"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-rightbrace3.png" width="21" height="172" alt="brace" border="0" /></td>
       <td class="left">&nbsp;&nbsp;&nbsp;&nbsp;<span class="sc">Verb</span></td>
      </tr>
</table>

<p>In looking at the examples, our first impression
is that Aristotle has fallen into a confusion. He
professes to classify words out of syntax, yet he
<span class="pagenum"><a name="page116" id="page116"></a>[page&nbsp;116]</span>
gives words with the marks of syntax on them.
Thus his division is accidentally grammatical, a
division of parts of speech, parts of a sentence,
into Nouns, Adjectives, Adverbs, and Verbs. And
his subdivisions of these parts are still followed in
our grammars. But really it is not the grammatical
function that he attends to, but the signification:
and looking further at the examples, we see what
differences of signification he had in his mind. It
is differences relative to a concrete individual,
differences in the words applied to him according
as they signify the substance of him or his attributes,
permanent or temporary.</p>

<p>Take any concrete thing, Socrates, this book, this
table. It must be some kind of a thing, a man, a
book. It must have some size or quantity, six feet
high, three inches broad. It must have some quality,
white, learned, hard. It must have relations with
other things, half this, double that, the son of a
father. It must be somewhere, at some time, in
some attitude, with some "havings," appendages,
appurtenances, or belongings, doing something, or
having something done to it. Can you conceive any
name (simple or composite) applicable to any object
of perception, whose signification does not fall into
one or other of these classes? If you cannot, the
categories are justified as an exhaustive division of
significations. They are a complete list of the most
general resemblances among individual things, in
other words, of the <i>summa genera</i>, the <i>genera generalissima</i>
of predicates concerning this, that or the
other concrete individual. No individual thing is
<i>sui generis</i>: everything is like other things: the
categories are the most general likenesses.</p>
<span class="pagenum"><a name="page117" id="page117"></a>[page&nbsp;117]</span>

<p>The categories are exhaustive, but do they fulfil
another requisite of a good division&mdash;are they mutually
exclusive? Aristotle himself raised this question, and
some of his answers to difficulties are instructive.
Particularly his discussion of the distinction between
Second Substances or Essences and Qualities. Here
he approximates to the modern doctrine of the distinction
between Substance and Attribute as set forth in
our quotation from Mansel at p. 110. Aristotle's
Second Essences
(<ins title="deuterai ousiai">&delta;&epsilon;&#973;&tau;&epsilon;&rho;&alpha;&iota;
&omicron;<span style="font-size: 0.9em;">&#8016;</span>&sigma;&#943;&alpha;&iota;</ins>)
are common nouns
or general names, Species and Genera, <i>man</i>, <i>horse</i>,
<i>animal</i>, as distinguished from Singular names, <i>this
man</i>, <i>this horse</i>, which he calls First Substances
(<ins title="prôtai ousiai">&pi;&rho;<span style="font-size: 0.9em;">&#8182;</span>&tau;&alpha;&iota;
&omicron;<span style="font-size: 0.9em;">&#8016;</span>&sigma;&#943;&alpha;&iota;</ins>),
essences <i>par excellence</i>, to which real existence in
the highest sense is attributed. Common nouns are put
in the First Category because they are predicated in
answer to the question, What is this? But he raises
the difficulty whether they may not rather be regarded
as being in the Third Category, that of Quality
(<ins title="to poion">&tau;<span style="font-size: 0.9em;">&#8056;</span> &pi;&omicron;&iota;<span style="font-size: 0.9em;">&#8056;</span>&nu;</ins>).
When we say, "This is a man," do we not
declare what sort of a thing he is? do we not declare
his Quality? If Aristotle had gone farther along
this line, he would have arrived at the modern point
of view that a man is a man in virtue of his possessing
certain attributes, that general names are applied in
virtue of their connotation. This would have been
to make the line of distinction between the First
Category and the Third pass between First Essence
and Second, ranking the Second Essences with
Qualities. But Aristotle did not get out of the
difficulty in this way. He solved it by falling back
on the differences in common speech. "Man" does
not signify the quality simply, as "whiteness" does.
"Whiteness" signifies nothing but the quality. That
<span class="pagenum"><a name="page118" id="page118"></a>[page&nbsp;118]</span>
is to say, there is no separate name in common
speech for the common attributes of man. His
further obscure remark that general names "define
quality round essence" <ins title="peri ousian">&pi;&epsilon;&rho;&#8054; &omicron;<span style="font-size: 0.9em;">&#8016;</span>&sigma;&#943;&alpha;&nu;</ins>, inasmuch as
they signify what sort a certain essence is, and that
genera make this definition more widely than species,
bore fruit in the medi&aelig;val discussions between Realists
and Nominalists by which the signification of general
names was cleared up.</p>

<p>Another difficulty about the mutual exclusiveness of
the Categories was started by Aristotle in connexion
with the Fourth Category, Relation (<ins title="pros ti">&pi;&rho;&#972;&sigmaf; &tau;&iota;</ins> <i>Ad aliquid</i>,
<i>To something</i>). Mill remarks that "that could not be
a very comprehensive view of the nature of Relation
which would exclude action, passivity, and local situation
from that Category," and many commentators, from
Simplicius down to Hamilton, have remarked that all
the last six Categories might be included under Relation.
This is so far correct that the word Relation is one
of the vaguest and most extensive of words; but the
criticism ignores the strictness with which Aristotle
confined himself in his Categories to the forms of
common speech. It is clear from his examples that in
his Fourth Category he was thinking only of "relation"
as definitely expressed in common speech. In his
meaning, any word is a relative which is joined with
another in a sentence by means of a preposition or
a case-inflection. Thus "disposition" is a relative:
it is the disposition <i>of</i> something. This kind of
relation is perfect when the related terms reciprocate
grammatically; thus "master," "servant," since we
can say either "the master of the servant," or "the
servant of the master". In medi&aelig;val logic the term
<i>Relata</i> was confined to these perfect cases, but the
<span class="pagenum"><a name="page119" id="page119"></a>[page&nbsp;119]</span>
Category had a wider scope with Aristotle. And he
expressly raised the question whether a word might
not have as much right to be put in another Category
as in this. Indeed, he went further than his critics
in his suggestions of what Relation might be made
to include. Thus: "big" signifies Quality; yet a
thing is big with reference to something else, and is
so far a Relative. Knowledge must be knowledge of
something, and is a relative: why then should we put
"knowing" (<i>i.e.</i>, learned) in the Category of Quality.
"Hope" is a relative, as being the hope <i>of</i> a man and
the hope of something. Yet we say, "I have hope,"
and there hope would be in the category of Having,
Appurtenance. For the solution of all such difficulties,
Aristotle falls back upon the forms of common speech,
and decides the place of words in his categories
according to them. This was hardly consistent with
his proposal to deal with separate words out of syntax,
if by this was meant anything more than dealing with
them without reference to truth or falsehood. He did
not and could not succeed in dealing with separate
words otherwise than as parts of sentences, owing
their signification to their position as parts of a transient
plexus of thought. In so far as words have their being
in common speech, and it is their being in this sense
that Aristotle considers in the Categories, it is a
transient being. What being they represent besides is,
in the words of Porphyry, a very deep affair, and one
that needs other and greater investigation.</p>

<p class="note1"><a id="footnotePII-ChIII1" name="footnotePII-ChIII1"></a><a class="footnote" href="#footnotetagPII-ChIII1">Footnote 1:</a>
<ins title="tôn kata mêdemian symplokên legomenôn hekaston êtoi ousian sêmainei, ê poson, ê poion, ê pros ti, ê pou, ê pote, ê keisthai, ê echein, ê poiein, ê paschein.">
&tau;&#8182;&nu; &kappa;&alpha;&tau;&#8048; &mu;&eta;&delta;&epsilon;&mu;&#943;&alpha;&nu;  &sigma;&upsilon;&mu;&pi;&lambda;&omicron;&kappa;&#8052;&nu;
&lambda;&epsilon;&gamma;&omicron;&mu;&#941;&nu;&omega;&nu; &#7957;&kappa;&alpha;&sigma;&tau;&omicron;&nu; &#7970;&tau;&omicron;&iota;
&omicron;&#8016;&sigma;&#943;&alpha;&nu; &sigma;&eta;&mu;&alpha;&#943;&nu;&epsilon;&iota;, &#7970; &pi;&omicron;&sigma;&#8056;&nu;,
&#7970; &pi;&omicron;&iota;&#8056;&nu;, &#7970; &pi;&rho;&#972;&sigmaf; &tau;&iota;, &#7970; &pi;&omicron;&#8166;, &#7970; &pi;&omicron;&tau;&#8050;,
&#7970; &kappa;&epsilon;&#8150;&sigma;&theta;&alpha;&iota;, &#7970; &#7956;&chi;&epsilon;&iota;&nu;, &#7970; &pi;&omicron;&iota;&epsilon;&#8150;&nu;,
&#7970; &pi;&#940;&sigma;&chi;&epsilon;&iota;&nu;</ins>
(Categ. ii. 5.)</p>

<p class="note1"><a id="footnotePII-ChIII2" name="footnotePII-ChIII2"></a><a class="footnote" href="#footnotetagPII-ChIII2">Footnote 2:</a>
To describe the Categories as a grammatical division, as
Mansel does in his instructive Appendix C to Aldrich, is a little
misleading without a qualification. They are non-logical inasmuch
as they have no bearing on any logical purpose. But they
are grammatical only in so far as they are concerned with words.
They are not grammatical in the sense of being concerned with
the function of words in predication. The unit of grammar in
this sense is the sentence, a combination of words in syntax; and
it is expressly with words out of syntax that Aristotle deals, with
single words not in relation to the other parts of a sentence, but in
relation to the things signified. In any strict definition of the
provinces of Grammar and Logic, the Categories are neither
grammatical nor logical: the grammarians have appropriated
them for the subdivision of certain parts of the sentence, but with
no more right than the logicians. They really form a treatise by
themselves, which is in the main ontological, a discussion of substances
and attributes as underlying the forms of common speech.
In saying this I use the word substance in the modern sense: but
it must be remembered that Aristotle's <ins title="ousia">&omicron;&#8016;&sigma;&#943;&alpha;</ins>, translated substantia,
covered the word as well as the thing signified, and that his
Categories are primarily classes of words. The union between
names and things would seem to have been closer in the Greek
mind than we can now realise. To get at it we must note that
every separate word <ins title="to legomenon">&tau;&#8056; &lambda;&epsilon;&gamma;&#972;&mu;&epsilon;&nu;&omicron;&nu;</ins> is conceived as having a being
or thing <ins title="to on">&tau;&#8056; &#8004;&nu;</ins> corresponding to it, so that beings or things
<ins title="ta onta">&tau;&#8048; &#8004;&nu;&tau;&alpha;</ins> are coextensive with single words: a being or thing is
whatever receives a separate name. This is clear and simple
enough, but perplexity begins when we try to distinguish between
this nameable being and concrete being, which last is Aristotle's
category of <ins title="ousia">&omicron;&#8016;&sigma;&#943;&alpha;</ins>, the being signified by a Proper or a Common
as distinguished from an Abstract Noun. As we shall see, it is
relatively to the highest sense of this last kind of being, namely,
the being signified by a Proper name, that he considers the other
kinds of being.</p>
<span class="pagenum"><a name="page120" id="page120"></a>[page&nbsp;120]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter IV.</span></h3>

<h3>THE CONTROVERSY ABOUT UNIVERSALS. &mdash;DIFFICULTIES CONCERNING
THE RELATION  OF GENERAL NAMES TO THOUGHT AND TO REALITY.</h3>

<p>In the opening sentences of his Isagoge, before giving
his simple explanation of the Five Predicables,
Porphyry mentions certain questions concerning
Genera and Species, which he passes over as being
too difficult for the beginner. "Concerning genera and
species," he says, "the question whether they subsist
(<i>i.e.</i>, have real substance), or whether they lie in the
mere thoughts only, or whether, granting them to subsist,
they are corporeal or incorporeal, or whether they
subsist apart, or in sensible things and cohering round
them&mdash;this I shall pass over, such a question being a
very deep affair and one that needs other and greater
investigation."</p>

<p>This passage, written about the end of the third
century, <span class="sc">A.D.</span>, is a kind of isthmus between Greek
Philosophy and Medi&aelig;val: it summarises questions
which had been turned over on every side and most
intricately discussed by Plato and Aristotle and their
successors, and the bald summary became a starting-point
for equally intricate discussions among the
Schoolmen, among whom every conceivable variety of
doctrine found champions. The dispute became known
<span class="pagenum"><a name="page121" id="page121"></a>[page&nbsp;121]</span>
as the dispute about Universals, and three ultra-typical
forms of doctrine were developed, known
respectively as Realism, Nominalism, and Conceptualism.
Undoubtedly the dispute, with all its waste
of ingenuity, had a clearing effect, and we may fairly
try now what Porphyry shrank from, to gather some
simple results for the better understanding of general
names and their relations to thoughts and to things.
The rival schools had each some aspect of the general
name in view, which their exaggeration served to
render more distinct.</p>

<p>What does a general name signify? For logical
purposes it is sufficient to answer&mdash;the points of
resemblance as grasped in the mind, fixed by a name
applicable to each of the resembling individuals. This
is the signification of the general name <i>logically</i>, its
connotation or concept, the identical element of
objective reference in all uses of a general name.</p>

<p>But other questions may be asked that cannot be so
simply answered. What is this concept in thought?
What is there in our minds corresponding to the
general name when we utter it? How is its signification
conceived? What is the signification <i>psychologically</i>?</p>

<p>We may ask, further, What is there in nature that
the general name signifies? What is its relation to
reality? What corresponds to it in the real world?
Has the unity that it represents among individuals no
existence except in the mind? Calling this unity, this
one in the many, the Universal (<i>Universale</i>,
<ins title="to pan">&tau;<span style="font-size: 0.9em;">&#8056;</span> &pi;<span style="font-size: 0.9em;">&#8118;</span>&nu;</ins>),
what is the Universal <i>ontologically</i>?</p>

<p>It was this ontological question that was so hotly
and bewilderingly debated among the Schoolmen.
Before giving the ultra-typical answers to it, it may be
<span class="pagenum"><a name="page122" id="page122"></a>[page&nbsp;122]</span>
well to note how this question was mixed up with still
other questions of Theology and Cosmogony. Recognising
that there is a unity signified by the general
name, we may go on to inquire into the ground of the
unity. Why are things essentially like one another?
How is the unity maintained? How is it continued?
Where does the common pattern come from? The
question of the nature of the Universal thus links itself
with metaphysical theories of the construction of the
world, or even with the Darwinian theory of the origin
of species.</p>

<p>Passing by these remoter questions, we may give
the answers of the three extreme schools to the ontological
question, What is a Universal?</p>

<p>The answer of the Ultra-Realists, broadly put, was
that a Universal is a substance having an independent
existence in nature.</p>

<p>Of the Ultra-Nominalists, that the Universal is a
name and nothing else, <i>vox et pr&aelig;terea nihil</i>; that
this name is the only unity among the individuals of
a species, all that they have in common.</p>

<p>Of the Ultra-Conceptualists, that the individuals
have more in common than the name, that they have
the name plus the meaning, <i>vox</i> + <i>significatio</i>, but that
the Universals, the genera and species, exist only in
the mind.</p>

<p>Now these extreme doctrines, as literally interpreted
by opponents, are so easily refuted and so manifestly
untenable, that it may be doubted whether they were
ever held by any thinker, and therefore I call them
Ultra-Realism, Ultra-Nominalism, and Ultra-Conceptualism.
They are mere exaggerations or caricatures,
set up by opponents because they can be easily knocked
down.</p>
<span class="pagenum"><a name="page123" id="page123"></a>[page&nbsp;123]</span>

<p>To the Ultra-Realists, it is sufficient to say that if
there existed anywhere a substance having all the
common attributes of a species and only these, having
none of the attributes peculiar to any of the individuals
of that species, corresponding to the general name as
an individual corresponds to a Proper or Singular
name, it would not be the Universal, the unity
pervading the individuals, but only another individual.</p>

<p>To the Ultra-Nominalists, it is sufficient to say that
the individuals must have more in common than the
name, because the name is not applied arbitrarily,
but on some ground. The individuals must have in
common that on account of which they receive the
common name: to call them by the same name is
not to make them of the same species.</p>

<p>To the Ultra-Conceptualists, it is sufficient to say
that when we employ a general name, as when we say
"Socrates is a man," we do not refer to any passing
thought or state of mind, but to certain attributes
independent of what is passing in our minds. We
cannot make a thing of this or that species by merely
thinking of it as such.</p>

<p>The ultra-forms of these doctrines are thus easily
shown to be inadequate, yet each of the three, Realism,
Nominalism, and Conceptualism, represents a phase
of the whole truth.</p>

<p>Thus, take Realism. Although it is not true that
there is anything in reality corresponding to the
general name such as there is corresponding to the
singular name, the general name merely signifying
attributes of what the singular name signifies, it
does not follow, as the opponents of Ultra-Realism
hastily assume, that there is nothing in the real
world corresponding to the general name. Three
<span class="pagenum"><a name="page124" id="page124"></a>[page&nbsp;124]</span>
senses may be particularised in which Realism is
justified.</p>

<p>(1) The points of resemblance from which the
concept is formed are as real as the individuals
themselves. It is true in a sense that it is our
thought that gives unity to the individuals of a
class, that gathers the many into one, and so far
the Conceptualists are right. Still we should not
gather them into one if they did not resemble one
another: that is the reason why we think of them
together: and the respects in which they resemble
one another are as much independent of us and
our thinking as the individuals themselves, as much
beyond the power of our thought to change. We
must go behind the activity of the mind in unifying
to the reason for the unification: and the ground of
unity is found in what really exists. We do not
confer the unity: we do not make all men or all
dogs alike: we find them so. The curly tails in a
thousand domestic dogs, which serve to distinguish
them from wolves and foxes, are as real as the
thousand individual domestic dogs. In this sense
the Aristotelian doctrine, <i>Universalia in re</i>, expresses
a plain truth.</p>

<p>(2) The Platonic doctrine, formulated by the Schoolmen
as <i>Universalia ante rem</i>, has also a plain validity.
Individuals come and go, but the type, the Universal,
is more abiding. Men are born and die: man remains
throughout. The snows of last year have vanished,
but snow is still a reality to be faced. Wisdom does
not perish with the wise men of any generation. In
this plain sense, at least, it is true that Universals exist
before Individuals, have a greater permanence, or, if we
like to say so, a higher, as it is a more enduring, reality.</p>
<span class="pagenum"><a name="page125" id="page125"></a>[page&nbsp;125]</span>

<p>(3) Further, the "idea," concept, or universal,
though it cannot be separated from the individual,
and whether or not we ascribe to it the separate
suprasensual existence of the archetypal forms of
Plato's poetical fancy, is a very potent factor in the
real world. Ideals of conduct, of manners, of art, of
policy, have a traditional life: they do not pass away
with the individuals in whom they have existed, in
whom they are temporarily materialised: they survive
as potent influences from age to age. The "idea" of
Chaucer's Man of Law, who always "seemed busier
than he was," is still with us. Medi&aelig;val conceptions
of chivalry still govern conduct. The Universal enters
into the Individual, takes possession of him, makes of
him its temporary manifestation.</p>

<p>Nevertheless, the Nominalists are right in insisting
on the importance of names. What we call the real
world is a common object of perception and knowledge
to you and me: we cannot arrive at a knowledge of
it without some means of communication with one
another: our means of communication is language.
It may be doubted whether even thinking could go far
without symbols with the help of which conceptions
may be made definite. A concept cannot be explained
without reference to a symbol. There is even a sense
in which the Ultra-Nominalist doctrine that the individuals
in a class have nothing in common but the
name is tenable. Denotability by the same name is the
only respect in which those individuals are absolutely
identical: in this sense the name alone is common to
them, though it is applied in virtue of their resemblance
to one another.</p>

<p>Finally, the Conceptualists are right in insisting on
the mind's activity in connexion with general names.
<span class="pagenum"><a name="page126" id="page126"></a>[page&nbsp;126]</span>
Genera and species are not mere arbitrary subjective
collections: the union is determined by the characters
of the things collected. Still it is with the concept in
each man's mind that the name is connected: it is by
the activity of thought in recognising likenesses and
forming concepts that we are able to master the
diversity of our impressions, to introduce unity into
the manifold of sense, to reduce our various recollections
to order and coherence.</p>

<p>So much for the Ontological question. Now for the
<b>Psychological</b>. What is in the mind when we employ
a general name? What is the Universal psychologically?
How is it conceived?</p>

<p>What breeds confusion in these subtle inquiries is
the want of fixed unambiguous names for the things to
be distinguished. It is only by means of such names
that we can hold on to the distinctions, and keep from
puzzling ourselves. Now there are three things to be
distinguished in this inquiry, which we may call the
Concept, the Conception, and the Conceptual or
Generic Image. Let us call them by these names,
and proceed to explain them.</p>

<p>By the Concept, I understand the meaning of the
general name, what the general name signifies: by
the Conception, the mental act or state of him who
conceives this meaning. The concept of "triangle,"
<i>i.e.</i>, what you and I mean by the word, is not my act
of mind or your act of mind when we think or speak of
a triangle. The Conception, which is this act, is an
event or incident in our mental history, a psychical
act or state, a distinct occurrence, a particular fact in
time as much as the battle of Waterloo. The concept
is the objective reference of the name, which is the
same, or at least is understood to be the same, every
<span class="pagenum"><a name="page127" id="page127"></a>[page&nbsp;127]</span>
time we use it. I make a figure on paper with ink
or on a blackboard with chalk, and recognise or conceive
it as a triangle: you also conceive it as such:
we do the same to-morrow: we did the same yesterday:
each act of conception is a different event, but the concept
is the same throughout.</p>

<p>Now the psychological question about the Universal
is, What is this conception? We cannot define it
positively further than by saying that it consists in
realising the meaning of a general name: the act
being unique, we can only make it intelligible by
producing an example of it. But we may define it
negatively by distinguishing it from the conceptual
image. Whenever we conceive anything, "man,"
"horse," there is generally present to our minds an
image of a man or horse, with accidents of size,
colour, position or other categories. But this conceptual
image is not the concept, and the mental act
of forming it is not conception.</p>

<p>This distinction between mental picturing or
imaging and the conception of common attributes is
variously expressed. The correlative terms <i>Intuitive</i>
and <i>Symbolical</i> Thinking, <i>Presentative</i> and <i>Representative</i>
Knowledge have been employed.<a id="footnotetagPII-ChIV1" name="footnotetagPII-ChIV1"></a><a href="#footnotePII-ChIV1"><sup>1</sup></a> But whatever terms
<span class="pagenum"><a name="page128" id="page128"></a>[page&nbsp;128]</span>
we use, the distinction itself is vital, and the want of
it leads to confusion.</p>

<p>Thus the fact that we cannot form a conceptual
image composed solely of common attributes has been
used to support the argument of Ultra-Nominalism,
that the individuals classed under a common name
have nothing in common but the name. What the
word "dog" signifies, <i>i.e.</i>, the "concept" of dog, is
neither big nor little, neither black nor tan, neither
here nor there, neither Newfoundland, nor Retriever,
nor Terrier, nor Greyhound, nor Pug, nor Bulldog.
The concept consists only of the attributes common
to all dogs apart from any that are peculiar to any
variety or any individual. Now we cannot form any
such conceptual image. Our conceptual image is
always of some definite size and shape. Therefore,
it is argued, we cannot conceive what a dog means,
and dogs have nothing in common but the name.
This, however, does not follow. The concept is not
the conceptual image, and forming the image is not
conception. We may even, as in the case of a
chiliagon, or thousand-sided figure, conceive the
meaning without being able to form any definite
image.</p>

<p>How then, do we ordinarily proceed in conceiving,
if we cannot picture the common attributes alone and
apart from particulars? We attend, or strive to attend,
only to those aspects of an image which it has in
common with the individual things denoted. And if
<span class="pagenum"><a name="page129" id="page129"></a>[page&nbsp;129]</span>
we want to make our conception definite, we pass in
review an indefinite number of the individuals, case
after case.</p>

<p>A minor psychological question concerns the nature
of the conceptual image. Is it a copy of some
particular impression, or a confused blur or blend of
many? Possibly neither: possibly it is something
like one of Mr. Galton's composite photographs,
photographs produced by exposing the same surface
to the impressions of a number of different photographs
in succession. If the individuals are nearly alike, the
result is an image that is not an exact copy of any
one of the components and yet is perfectly distinct.
Possibly the image that comes into our mind's eye
when we hear such a word as "horse" or "man"
is of this character, the result of the impressions of a
number of similar things, but not identical with any
one. As, however, different persons have different
conceptual images of the same concept, so we may
have different conceptual images at different times.
It is only the concept that remains the same.</p>

<p>But how, it may be asked, can the concept remain
the same? If the universal or concept psychologically
is an intellectual act, repeated every time we conceive,
what guarantee have we for the permanence of the
concept? Does this theory not do away with all
possibility of defining and fixing concepts?</p>

<p>This brings us back to the doctrine already laid
down about the truth of Realism. The theory of the
concept is not exhausted when it is viewed only
psychologically, as a psychic act. If we would
understand it fully, we must consider the act in its
relations to the real experience of ourselves and
others. To fix this act, we give it a separate name,
<span class="pagenum"><a name="page130" id="page130"></a>[page&nbsp;130]</span>
calling it the conception: and then we must go behind
the activity of the mind to the objects on which it is
exercised. The element of fixity is found in them.
And here also the truth of Nominalism comes in.
By means of words we enter into communication
with other minds. It is thus that we discover what
is real, and what is merely personal to ourselves.</p>

<p class="note1"><a id="footnotePII-ChIV1" name="footnotePII-ChIV1"></a><a class="footnote" href="#footnotetagPII-ChIV1">Footnote 1:</a>
The only objection to these terms is that they have slipped
from their moorings in philosophical usage. Thus instead of
Leibnitz's use of Intuitive and Symbolical, which corresponds
to the above distinction between Imaging and Conception, Mr.
Jevons employs the terms to express a distinction among
conceptions proper. We can understand what a chiliagon
means, but we cannot form an image of it in our minds, except
in a very confused and imperfect way; whereas we can form
a distinct image of a triangle. Mr. Jevons would call the
conception of the triangle <i>Intuitive</i>, of the chiliagon <i>Symbolical</i>.</p>

<p class="note1">Again, while Mansel uses the words Presentative and Representative
to express our distinction, a more common usage is to call
actual Perception Presentative Knowledge, and ideation or
recollection in idea Representative.</p>
<span class="pagenum"><a name="page131" id="page131"></a>[page&nbsp;131]</span>

<h2 style="margin-top: 3em;">PART III.</h2>

<h3>THE INTERPRETATION OF PROPOSITIONS. &mdash;OPPOSITION AND IMMEDIATE INFERENCE.</h3>

<div class="figcenter"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-140.png" width="304" height="35" alt="fancy rule" border="0" /></div>

<h3><span class="sc">Chapter I.</span></h3>

<h3>THEORIES OF PREDICATION.&mdash;THEORIES OF JUDGMENT.</h3>

<p>We may now return to the Syllogistic Forms, and the
consideration of the compatibility or incompatibility,
implication, and interdependence of propositions.</p>

<p>It was to make this consideration clear and simple
that what we have called the Syllogistic Form of
propositions was devised. When are propositions
incompatible? When do they imply one another?
When do two imply a third? We have seen in the
Introduction how such questions were forced upon
Aristotle by the disputative habits of his time. It
was to facilitate the answer that he analysed
propositions into Subject and Predicate, and viewed
the Predicate as a reference to a class: in other words,
analysed the Predicate further into a Copula and a
Class Term.</p>
<span class="pagenum"><a name="page132" id="page132"></a>[page&nbsp;132]</span>

<p>But before showing how he exhibited the interconnexion
of propositions on this plan, we may turn
aside to consider various so-called Theories of Predication
or of Judgment. Strictly speaking, they are not
altogether relevant to Logic, that is to say, as a
practical science: they are partly logical, partly
psychological theories: some of them have no bearing
whatever on practice, but are matters of pure scientific
curiosity: but historically they are connected with the
logical treatment of propositions as having been
developed out of this.</p>

<p>The least confusing way of presenting these theories
is to state them and examine them both logically and
psychologically. The logical question is, Has the
view any advantage for logical purposes? Does it
help to prevent error, to clear up confusion? Does
it lead to firmer conceptions of the truth? The
psychological question is, Is this a correct theory of
how men actually think when they make propositions?
It is a question of <i>what is</i> in the one case, and of
<i>what ought to be for a certain purpose</i> in the other.</p>

<p>Whether we speak of Proposition or of Judgment
does not materially affect our answer. A Judgment is
the mental act accompanying a Proposition, or that
may be expressed in a proposition and cannot be
expressed otherwise: we can give no other intelligible
definition or description of a judgment. So a proposition
can only be defined as the expression of a judgment:
unless there is a judgment underneath them, a
form of words is not a proposition.</p>

<p>Let us take, then, the different theories in turn. We
shall find that they are not really antagonistic, but
only different: that each is substantially right from its
own point of view: and that they seem to contradict
<span class="pagenum"><a name="page133" id="page133"></a>[page&nbsp;133]</span>
one another only when the point of view is misunderstood.</p>

<p>I. <i>That the Predicate term may be regarded as a class
in or from which the Subject is included or excluded.</i>
Known as the Class-Inclusion, Class-Reference, or
Denotative view.</p>

<p>This way of analysing propositions is possible, as we
have seen, because every statement implies a general
name, and the extension or denotation of a general
name is a class defined by the common attribute or
attributes. It is useful for syllogistic purposes:
certain relations among propositions can be most
simply exhibited in this way.</p>

<p>But if this is called a Theory of Predication or
Judgment, and taken psychologically as a theory of
what is in men's minds whenever they utter a
significant Sentence, it is manifestly wrong. When
discussed as such, it is very properly rejected. When
a man says "P struck Q," he has not necessarily a
class of "strikers of Q" definitely in his mind. What
he has in his mind is the logical equivalent of this, but
it is not this directly. Similarly, Mr. Bradley would
be quite justified in speaking of Two Terms and a
Copula as a superstition, if it were meant that these
analytic elements are present to the mind of an
ordinary speaker.</p>

<p>II. <i>That every Proposition may be regarded as affirming
or denying an attribute of a subject.</i> Known sometimes
as the Connotative or the Denotative-Connotative
view. This also follows from the implicit presence of
a general name in every sentence. But it should not
be taken as meaning that the man who says: "Tom
came here yesterday," or "James generally sits there,"
has a clearly analysed Subject and Attribute in his
<span class="pagenum"><a name="page134" id="page134"></a>[page&nbsp;134]</span>
mind. Otherwise it is as far wrong as the other
view.</p>

<p>III. <i>That every proposition may be regarded as an
equation between two terms.</i> Known as the Equational
View.</p>

<p>This is obviously not true for common speech or
ordinary thought. But it is a possible way of regarding
the analytic components of a proposition, legitimate
enough if it serves any purpose. It is a modification
of the Class-Reference analysis, obtained by what is
known as Quantification of the Predicate. In "All S
is in P," P is undistributed, and has no symbol of
Quantity. But since the proposition imports that
All S is a part of P, <i>i.e.</i>, Some P, we may, if we
choose, prefix the symbol of Quantity, and then the
proposition may be read "All S = Some P". And
so with the other forms.</p>

<p>Is there any advantage in this? Yes: it enables
us to subject the formul&aelig; to algebraic manipulation.
But any logical advantage&mdash;any help to thinking?
None whatever. The elaborate syllogistic systems of
Boole, De Morgan, and Jevons are not of the slightest
use in helping men to reason correctly. The value
ascribed to them is merely an illustration of the Bias
of Happy Exercise. They are beautifully ingenious,
but they leave every recorded instance of learned
Scholastic trifling miles behind.</p>

<p>IV. <i>That every proposition is the expression of a
comparison between concepts.</i> Sometimes called the
Conceptualist View.</p>

<p>"To judge," Hamilton says, "is to recognise the
relation of congruence or confliction in which two
concepts, two individual things, or a concept and an
individual compared together stand to each other."</p>
<span class="pagenum"><a name="page135" id="page135"></a>[page&nbsp;135]</span>

<p>This way of regarding propositions is permissible or
not according to our interpretation of the words
"congruence" and "confliction," and the word
"concept". If by concept we mean a conceived
attribute of a thing, and if by saying that two concepts
are congruent or conflicting, we mean that they may
or may not cohere in the same thing, and by saying
that a concept is congruent or conflicting with an
individual that it may or may not belong to that
individual, then the theory is a corollary from
Aristotle's analysis. Seeing that we must pass
through that analysis to reach it, it is obviously not
a theory of ordinary thought, but of the thought of a
logician performing that analysis.</p>

<p>The precise point of Hamilton's theory was that the
logician does not concern himself with the question
whether two concepts are or are not as a matter of
fact found in the same subject, but only with the
question whether they are of such a character that
they may be found, or cannot be found, in the same
subject. In so far as his theory is sound, it is an
abstruse and technical way of saying that we may
consider the consistency of propositions without
considering whether or not they are true, and that
consistency is the peculiar business of syllogistic logic.</p>

<p>V. <i>That the ultimate subject of every judgment is reality.</i></p>

<p>This is the form in which Mr. Bradley and Mr.
Bosanquet deny the Ultra-Conceptualist position.
The same view is expressed by Mill when he says that
"propositions are concerned with things and not with
our ideas of them".</p>

<p>The least consideration shows that there is justice
in the view thus enounced. Take a number of propositions:&mdash;</p>
<span class="pagenum"><a name="page136" id="page136"></a>[page&nbsp;136]</span>

<div class="poem">  <div class="stanza">
<p class="i4">The streets are wet.</p>
<p class="i4">George has blue eyes.</p>
<p class="i4">The Earth goes round the Sun.</p>
<p class="i4">Two and two make four.</p>
  </div>  </div>

<p>Obviously, in any of these propositions, there is a
reference beyond the conceptions in the speaker's mind,
viewed merely as incidents in his mental history.
They express beliefs about things and the relations
among things <i>in rerum natura</i>: when any one understands
them and gives his assent to them, he never
stops to think of the speaker's state of mind, but of
what the words represent. When states of mind
are spoken of, as when we say that our ideas are
confused, or that a man's conception of duty influences
his conduct, those states of mind are viewed as
objective facts in the world of realities. Even when
we speak of things that have in a sense no reality, as
when we say that a centaur is a combination of man
and horse, or that centaurs were fabled to live in the
vales of Thessaly, it is not the passing state of mind
expressed by the speaker as such that we attend to or
think of; we pass at once to the objective reference of
the words.</p>

<p>Psychologically, then, the theory is sound: what is
its logical value? It is sometimes put forward as if it
were inconsistent with the Class-reference theory or
the theory that judgment consists in a comparison of
concepts. Historically the origin of its formal statement
is its supposed opposition to those theories. But
really it is only a misconception of them that it contradicts.
It is inconsistent with the Class-reference view
only if by a class we understand an arbitrary subjective
collection, not a collection of things on the ground of
<span class="pagenum"><a name="page137" id="page137"></a>[page&nbsp;137]</span>
common attributes. And it is inconsistent with the
Conceptualist theory only if by a concept we understand
not the objective reference of a general name, but what
we have distinguished as a conception or a conceptual
image. The theory that the ultimate subject is reality
is assumed in both the other theories, rightly understood.
If every proposition is the utterance of a
judgment, and every proposition implies a general
name, and every general name has a meaning or connotation,
and every such meaning is an attribute of
things and not a mental state, it is implied that
the ultimate subject of every proposition is reality.
But we may consider whether or not propositions
are consistent without considering whether
or not they are true, and it is only their
mutual consistency that is considered in the syllogistic
formul&aelig;. Thus, while it is perfectly correct
to say that every proposition expresses either truth or
falsehood, or that the characteristic quality of a judgment
is to be true or false, it is none the less correct to
say that we may temporarily suspend consideration of
truth or falsehood, and that this is done in what is
commonly known as Formal Logic.</p>

<p>VI. <i>That every proposition may be regarded as
expressing relations between phenomena.</i></p>

<p>Bain follows Mill in treating this as the final
import of Predication. But he indicates more
accurately the logical value of this view in speaking
of it as important for laying out the divisions of
Inductive Logic. They differ slightly in their lists
of Universal Predicates based upon Import in this
sense&mdash;Mill's being Resemblance, Coexistence, Simple
Sequence, and Causal Sequence, and Bain's being
Coexistence, Succession, and Equality or Inequality.
<span class="pagenum"><a name="page138" id="page138"></a>[page&nbsp;138]</span>
But both lay stress upon Coexistence and Succession,
and we shall find that the distinctions between Simple
Sequence and Causal Sequence, and between Repeated
and Occasional Coexistence, are all-important in the
Logic of Investigation. But for syllogistic purposes
the distinctions have no relevance.</p>
<span class="pagenum"><a name="page139" id="page139"></a>[page&nbsp;139]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter II.</span></h3>

<h3>THE "OPPOSITION" OF PROPOSITIONS.&mdash;THE INTERPRETATION OF "NO".</h3>

<p>Propositions are technically said to be "opposed"
when, having the same terms in Subject and Predicate,
they differ in Quantity, or in Quality, or in both.<a id="footnotetagPIII-ChII1" name="footnotetagPIII-ChII1"></a><a href="#footnotePIII-ChII1"><sup>1</sup></a></p>
<span class="pagenum"><a name="page140" id="page140"></a>[page&nbsp;140]</span>

<p>The practical question from which the technical
doctrine has been developed was how to determine
the significance of contradiction. What is meant by
giving the answer "No" to a proposition put interrogatively?
What is the interpretation of "No"?
What is the respondent committed to thereby?</p>

<p>"Have all ratepayers a vote?" If you answer
"No," you are bound to admit that some ratepayers
have not. O is the <b>Contradictory</b> of A. If A is false,
O must be true. So if you deny O, you are bound to
admit A: one or other must be true: either Some ratepayers
have not a vote or All have.</p>

<p>Is it the case that no man can live without sleep?
Deny this, and you commit yourself to maintaining
that Some man, one at least, can live without sleep.
I is the Contradictory of E; and <i>vice versâ</i>.</p>

<p>Contradictory opposition is distinguished from <b>Contrary</b>,
the opposition of one Universal to another, of
A to E and E to A. There is a natural tendency to
meet a strong assertion with the very reverse. Let it
be maintained that women are essentially faithless or
that "the poor in a lump is bad," and disputants are
apt to meet this extreme with another, that constancy
is to be found only in women or true virtue only among
the poor. Both extremes, both A and E, may be false:
the truth may lie between: Some are, Some not.</p>
<span class="pagenum"><a name="page141" id="page141"></a>[page&nbsp;141]</span>

<p>Logically, the denial of A or E implies only the
admission of O or I. You are not committed to the
full contrary. But the implication of the Contradictory
is absolute; there is no half-way house where the
truth may reside. Hence the name of <b>Excluded
Middle</b> is applied to the principle that "Of two Contradictories
one or other must be true: they cannot
both be false".</p>

<p>While both <b>Contraries</b> may be false, they cannot
both be true.</p>

<p>It is sometimes said that in the case of Singular
propositions, the Contradictory and the Contrary
coincide. A more correct doctrine is that in the case
of Singular propositions, the distinction is not needed
and does not apply. Put the question "Is Socrates
wise?" or "Is this paper white?" and the answer
"No" admits of only one interpretation, provided the
terms remain the same. Socrates may become foolish,
or this paper may hereafter be coloured differently, but
in either case the subject term is not the same about
which the question was asked. Contrary opposition
belongs only to general terms taken universally as
subjects. Concerning individual subjects an attribute
must be either affirmed or denied simply: there is no
middle course. Such a proposition as "Socrates is
sometimes not wise," is not a true Singular proposition,
though it has a Singular term as grammatical subject.
Logically, it is a Particular proposition, of which the
subject-term is the actions or judgments of Socrates.<a id="footnotetagPIII-ChII2" name="footnotetagPIII-ChII2"></a><a href="#footnotePIII-ChII2"><sup>2</sup></a></p>
<span class="pagenum"><a name="page142" id="page142"></a>[page&nbsp;142]</span>

<p>Opposition, in the ordinary sense, is the opposition of
incompatible propositions, and it was with this only
that Aristotle concerned himself. But from an early
period in the history of Logic, the word was extended
to cover mere differences in Quantity and Quality
among the four forms A E I O, which differences have
been named and exhibited symmetrically in a diagram
known as: The Square of Opposition.</p>

<div class="figcenter"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-151-350.png" width="350" height="344" alt="Logic Square" border="0" /></div>

<p>The four forms being placed at the four corners of
the Square, and the sides and diagonals representing
relations between them thus separated, a very pretty
and symmetrical doctrine is the result.</p>

<p><i>Contradictories</i>, A and O, E and I, differ both in
Quantity and in Quality.</p>

<p><i>Contraries</i>, A and E, differ in Quality but not in
Quantity, and are both Universal.</p>

<p><i>Sub-contraries</i>, I and O, differ in Quality but not in
Quantity, and are both Particular.</p>
<span class="pagenum"><a name="page143" id="page143"></a>[page&nbsp;143]</span>

<p><i>Subalterns</i>, A and I, E and O, differ in Quantity but
not in Quality.</p>

<p>Again, in respect of concurrent truth and falsehood
there is a certain symmetry.</p>

<p>Contradictories cannot both be true, nor can they
both be false.</p>

<p>Contraries may both be false, but cannot both be true.</p>

<p>Sub-contraries may both be true, but cannot both be
false.</p>

<p>Subalterns may both be false and both true. If the
Universal is true, its subalternate Particular is true:
but the truth of the Particular does not similarly imply
the truth of its Subalternating Universal.</p>

<p>This last is another way of saying that the truth of
the Contrary involves the truth of the Contradictory,
but the truth of the Contradictory does not imply the
truth of the Contrary.</p>

<p>There, however, the symmetry ends. The sides
and the diagonals of the Square do not symmetrically
represent degrees of incompatibility, or opposition in
the ordinary sense.</p>

<p>There is no incompatibility between two Sub-contraries
or a Subaltern and its Subalternant. Both
may be true at the same time. Indeed, as Aristotle
remarked of I and O, the truth of the one commonly
implies the truth of the other: to say that some of the
crew were drowned, implies that some were not, and
<i>vice versâ</i>. Subaltern and Subalternant also are compatible,
and something more. If a man has admitted
A or E, he cannot refuse to admit I or O, the Particular
of the same Quality. If All poets are irritable, it
cannot be denied that some are so; if None is, that
Some are not. The admission of the Contrary includes
the admission of the Contradictory.</p>
<span class="pagenum"><a name="page144" id="page144"></a>[page&nbsp;144]</span>

<p>Consideration of Subalterns, however, brings to
light a nice ambiguity in Some. It is only when I is
regarded as the Contradictory of E, that it can properly
be said to be Subalternate to A. In that case the
meaning of Some is "not none," <i>i.e.</i>, "Some at least".
But when Some is taken as the sign of Particular
quantity simply, <i>i.e.</i>, as meaning "not all," or "some
at most," I is not Subalternate to A, but opposed to it
in the sense that the truth of the one is incompatible
with the truth of the other.</p>

<p>Again, in the diagram Contrary opposition is represented
by a side and Contradictory by the diagonal;
that is to say, the stronger form of opposition by the
shorter line. The Contrary is more than a denial:
it is a counter-assertion of the very reverse,
<ins title="to enantion">&tau;<span style="font-size: 0.9em;">&#8056;</span> <span style="font-size: 0.9em;">&#7952;</span>&nu;&#940;&nu;&tau;&iota;&omicron;&nu;</ins>.
"Are good administrators always good speakers?"
"On the contrary, they never are." This is a much
stronger opposition, in the ordinary sense, than a
modest contradictory, which is warranted by the
existence of a single exception. If the diagram were
to represent incompatibility accurately, the Contrary
ought to have a longer line than the Contradictory,
and this it seems to have had in the diagram that
Aristotle had in mind (<i>De Interpret.</i>, c. 10).</p>

<p>It is only when Opposition is taken to mean merely
difference in Quantity and Quality that there can be
said to be greater opposition between Contradictories
than between Contraries. Contradictories differ both
in Quantity and in Quality: Contraries, in Quality
only.</p>

<p>There is another sense in which the Particular
Contradictory may be said to be a stronger opposite
than the Contrary. It is a stronger position to take
up argumentatively. It is easier to defend than a
<span class="pagenum"><a name="page145" id="page145"></a>[page&nbsp;145]</span>
Contrary. But this is because it offers a narrower
and more limited opposition.</p>

<p>We deal with what is called Immediate Inference
in the next chapter. Pending an exact definition of
the process, it is obvious that two immediate inferences
are open under the above doctrines, (1) Granted the
truth of any proposition, you may immediately infer
the falsehood of its Contradictory. (2) Granted the
truth of any Contrary, you may immediately infer the
truth of its Subaltern.<a id="footnotetagPIII-ChII3" name="footnotetagPIII-ChII3"></a><a href="#footnotePIII-ChII3"><sup>3</sup></a></p>

<p class="note1"><a id="footnotePIII-ChII1" name="footnotePIII-ChII1"></a><a class="footnote" href="#footnotetagPIII-ChII1">Footnote 1:</a>
This is the traditional definition of Opposition from an early
period, though the tradition does not start from Aristotle. With
him opposition (<ins title="antikeisthai">&#7936;&nu;&tau;&iota;&kappa;&epsilon;&#8150;&sigma;&theta;&alpha;&iota;</ins>) meant, as it still means in ordinary
speech, incompatibility. The technical meaning of Opposition is
based on the diagram (given afterwards in the text) known as the
Square of Opposition, and probably originated in a confused
apprehension of the reason why it received that name. It was
called the Square of Opposition, because it was intended to
illustrate the doctrine of Opposition in Aristotle's sense and the
ordinary sense of repugnance or incompatibility. What the
Square brings out is this. If the four forms A E I O are arranged
symmetrically according as they differ in quantity, or quality,
or both, it is seen that these differences do not correspond
symmetrically to compatibility and incompatibility: that propositions
may differ in quantity or in quality without being
incompatible, and that they may differ in both (as Contradictories)
and be less violently incompatible than when they differ in one
only (as Contraries). The original purpose of the diagram was
to bring this out, as is done in every exposition of it. Hence it
was called the Square of Opposition. But as a descriptive title
this is a misnomer: it should have been the Square of Differences
in Quantity or Quality. This misnomer has been perpetuated by
appropriating Opposition as a common name for difference in
Quantity or Quality when the terms are the same and in the same
order, and distinguishing it in this sense from Repugnance or
Incompatibility (Tataretus in Summulas, <i>De Oppositionibus</i> [1501],
Keynes, <i>The Opposition of Propositions</i> [1887]). Seeing that there
never is occasion to speak of Opposition in the limited sense
except in connexion with the Square, there is no real risk of
confusion. A common name is certainly wanted in that connexion,
if only to say that Opposition (in the limited or diagrammatic
sense) does not mean incompatibility.</p>

<p class="note1"><a id="footnotePIII-ChII2" name="footnotePIII-ChII2"></a><a class="footnote" href="#footnotetagPIII-ChII2">Footnote 2:</a>
Cp. Keynes, pt. ii. ch. ii. s. 57. Aristotle laid down the
distinction
between Contrary and Contradictory to meet another
quibble in contradiction, based on taking the Universal as a whole
and indivisible subject like an Individual, of which a given predicate
must be either affirmed or denied.</p>

<p class="note1"><a id="footnotePIII-ChII3" name="footnotePIII-ChII3"></a><a class="footnote" href="#footnotetagPIII-ChII3">Footnote 3:</a>
I have said that there is little risk of confusion in using the
word Opposition in its technical or limited sense. There is,
however, a little. When it is said that these Inferences are based
on Opposition, or that Opposition is a mode of Immediate Inference,
there is confusion of ideas unless it is pointed out that when
this is said, it is Opposition in the ordinary sense that is meant.
The inferences are really based on the rules of Contrary and
Contradictory Opposition; Contraries cannot both be true, and
of Contradictories one or other must be.</p>
<span class="pagenum"><a name="page146" id="page146"></a>[page&nbsp;146]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter III.</span></h3>

<h3>THE IMPLICATION OF PROPOSITIONS. &mdash;IMMEDIATE FORMAL INFERENCE.&mdash;EDUCATION.</h3>

<p>The meaning of Inference generally is a subject of
dispute, and to avoid entering upon debatable ground
at this stage, instead of attempting to define Inference
generally, I will confine myself to defining what is
called Formal Inference, about which there is comparatively
little difference of opinion.</p>

<p><b>Formal Inference</b> then is the apprehension of what
is implied in a certain datum or admission: the
derivation of one proposition, called the <b>Conclusion</b>,
from one or more given, admitted, or assumed propositions,
called the <b>Premiss</b> or <b>Premisses</b>.</p>

<p>When the conclusion is drawn from one proposition,
the inference is said to be <b>immediate</b>; when more than
one proposition is necessary to the conclusion, the
inference is said to be <b>mediate</b>.</p>

<p>Given the proposition, "All poets are irritable," we
can immediately infer that "Nobody that is not
irritable is a poet"; and the one admission implies
the other. But we cannot infer immediately that
"all poets make bad husbands". Before we can do
this we must have a second proposition conceded,
<span class="pagenum"><a name="page147" id="page147"></a>[page&nbsp;147]</span>
that "All irritable persons make bad husbands".
The inference in the second case is called Mediate.<a id="footnotetagPIII-ChIII1" name="footnotetagPIII-ChIII1"></a><a href="#footnotePIII-ChIII1"><sup>1</sup></a></p>

<p>The modes and conditions of valid Mediate Inference
constitute Syllogism, which is in effect the
reasoning together of separate admissions. With this
we shall deal presently. Meantime of Immediate
Inference.</p>

<p>To state all the implications of a certain form of
proposition, to make explicit all that it implies, is the
same thing with showing what immediate inferences
from it are legitimate. Formal inference, in short, is
the eduction of all that a proposition implies.</p>

<p>Most of the modes of Immediate Inference formulated
by logicians are preliminary to the Syllogistic
process, and have no other practical application. The
most important of them technically is the process
known as Conversion, but others have been judged
worthy of attention.</p>

<h3 style="margin-top: 2em;"><span class="sc">&AElig;quipollent or Equivalent Forms&mdash;Obversion.</span></h3>

<p>&AElig;quipollence or Equivalence (<ins title="Isodynamia">&Iota;&sigma;&omicron;&delta;&upsilon;&nu;&alpha;&mu;&#943;&alpha;</ins>) is defined
as the perfect agreement in sense of two propositions
that differ somehow in expression.<a id="footnotetagPIII-ChIII2" name="footnotetagPIII-ChIII2"></a><a href="#footnotePIII-ChIII2"><sup>2</sup></a></p>

<p>The history of &AElig;quipollence in logical treatises
illustrates two tendencies. There is a tendency on
the one hand to narrow a theme down to definite and
manageable forms. But when a useful exercise is
discarded from one place it has a tendency to break
out in another under another name. A third tendency
<span class="pagenum"><a name="page148" id="page148"></a>[page&nbsp;148]</span>
may also be said to be specially well illustrated&mdash;the
tendency to change the traditional application of logical
terms.</p>

<p>In accordance with the above definition of &AElig;quipollence
or Equivalence, which corresponds with
ordinary acceptation, the term would apply to all cases
of "identical meaning under difference of expression".
Most examples of the reduction of ordinary speech
into syllogistic form would be examples of &aelig;quipollence;
all, in fact, would be so were it not that ordinary
speech loses somewhat in the process, owing to the
indefiniteness of the syllogistic symbol for particular
quality, Some. And in truth all such transmutations
of expression are as much entitled to the dignity of
being called Immediate Inferences as most of the
processes so entitled.</p>

<p>Dr. Bain uses the word with an approach to this
width of application in discussing all that is now most
commonly called Immediate Inference under the title
of Equivalent Forms. The chief objection to this
usage is that the Converse <i>per accidens</i> is not strictly
equivalent. A debater may want for his argument less
than the strict equivalent, and content himself with
educing this much from his opponent's admission.
(Whether Dr. Bain is right in treating the Minor and
Conclusion of a Hypothetical Syllogism as being
equivalent to the Major, is not so much a question of
naming.)</p>

<p>But in the history of the subject, the traditional
usage has been to confine &AElig;quipollence to cases of
equivalence between positive and negative forms of
expression. "Not all are," is equivalent to "Some
are not": "Not none is," to "Some are". In Pre-Aldrichian
text-books, &AElig;quipollence corresponds
<span class="pagenum"><a name="page149" id="page149"></a>[page&nbsp;149]</span>
mainly to what it is now customary to call (<i>e.g.</i>,
Fowler, pt. iii. c. ii., Keynes, pt. ii. c. vii.) Immediate
Inference based on Opposition. The denial of any
proposition involves the admission of its contradictory.
Thus, if the negative particle "Not" is placed before
the sign of Quantity, All or Some, in a proposition,
the resulting proposition is equivalent to the Contradictory
of the original. Not all S is P = Some S is
not P. Not any S is P = No S is P. The medi&aelig;val
logicians tabulated these equivalents, and also the
forms resulting from placing the negative particle
after, or both before and after, the sign of Quantity.
Under the title of &AElig;quipollence, in fact, they considered
the interpretation of the negative particle
generally. If the negative is placed after the universal
sign, it results in the Contrary: if both before and
after, in the Subaltern. The statement of these
equivalents is a puzzling exercise which no doubt
accounts for the prominence given it by Aristotle and
the Schoolmen. The latter helped the student with
the following Mnemonic line: <i>Pr&aelig; Contradic., post
Contrar., pr&aelig; postque Subaltern.</i><a id="footnotetagPIII-ChIII3" name="footnotetagPIII-ChIII3"></a><a href="#footnotePIII-ChIII3"><sup>3</sup></a></p>
<span class="pagenum"><a name="page150" id="page150"></a>[page&nbsp;150]</span>

<p>To &AElig;quipollence belonged also the manipulation
of the forms known after the <i>Summul&aelig;</i> as <i>Exponibiles</i>,
notably <i>Exclusive</i> and <i>Exceptive propositions</i>, such as
None but barristers are eligible, The virtuous alone
are happy. The introduction of a negative particle
into these already negative forms makes a very trying
problem in interpretation. The &aelig;quipollence of the
Exponibiles was dropped from text-books long before
Aldrich, and it is the custom to laugh at them as
extreme examples of frivolous scholastic subtlety: but
most modern text-books deal with part of the doctrine
of the <i>Exponibiles</i> in casual exercises.</p>

<p>Curiously enough, a form left unnamed by the
scholastic logicians because too simple and useless,
has the name &AElig;quipollent appropriated to it, and to
it alone, by Ueberweg, and has been adopted under
various names into all recent treatises.</p>

<p>Bain calls it the <b>Formal Obverse</b>,<a id="footnotetagPIII-ChIII4" name="footnotetagPIII-ChIII4"></a><a href="#footnotePIII-ChIII4"><sup>4</sup></a> and the title of
<span class="pagenum"><a name="page151" id="page151"></a>[page&nbsp;151]</span>
<b>Obversion</b> (which has the advantage of rhyming with
<b>Conversion</b>) has been adopted by Keynes, Miss
Johnson, and others.</p>

<p>Fowler (following Karslake) calls it <b>Permutation</b>.
The title is not a happy one, having neither rhyme
nor reason in its favour, but it is also extensively used.</p>

<p>This immediate inference is a very simple affair to
have been honoured with such a choice of terminology.
"This road is long: therefore, it is not short," is an
easy inference: the second proposition is the Obverse,
or Permutation, or &AElig;quipollent, or (in Jevons's title)
the Immediate Inference by Privative Conception, of
the first.</p>

<p>The inference, such as it is, depends on the Law of
Excluded Middle. Either a term P, or its contradictory,
not-P, must be true of any given subject, S:
hence to affirm P of all or some S, is equivalent to
denying not-P of the same: and, similarly, to deny P,
is to affirm not-P. Hence the rule of Obversion;&mdash;Substitute
for the predicate term its Contrapositive,<a id="footnotetagPIII-ChIII5" name="footnotetagPIII-ChIII5"></a><a href="#footnotePIII-ChIII5"><sup>5</sup></a>
and change the Quality of the proposition.</p>

<div class="poem">  <div class="stanza">
<p class="i4"> All S is P = No S is not-P.</p>
<p class="i6">No S is P = All S is not-P.</p>
<p class="i4">Some S is P = Some S is not not-P.</p>
<p>Some S is not P = Some S is not-P.</p>
  </div>  </div>

<h3 style="margin-top: 2em;"><span class="sc">Conversion.</span></h3>

<p>The process takes its name from the interchange of
the terms. The Predicate-term becomes the Subject-term,
and the Subject-term the Predicate-term.</p>

<p>When propositions are analysed into relations of
<span class="pagenum"><a name="page152" id="page152"></a>[page&nbsp;152]</span>
inclusion or exclusion between terms, the assertion
of any such relation between one term and another,
implies a Converse relation between the second term
and the first. The statement of this implied assertion
is technically known as the <b>Converse</b> of the original
proposition, which may be called the <i>Convertend</i>.</p>

<p>Three modes of Conversion are commonly recognised:&mdash;(<i>a</i>)
<b>Simple Conversion</b>; (<i>b</i>) <b>Conversion</b> <i>per
accidens</i> or by limitation; (<i>c</i>) <b>Conversion by Contraposition</b>.</p>

<p>(<i>a</i>) E and I can be simply converted, only the terms
being interchanged, and Quantity and Quality remaining
the same.</p>

<p>If S is wholly excluded from P, P must be wholly
excluded from S. If Some S is contained in P, then
Some P must be contained in S.</p>

<p>(<i>b</i>) A cannot be simply converted. To know that
All S is contained in P, gives you no information
about that portion of P which is outside S. It only
enables you to assert that Some P is S; that portion
of P, namely, which coincides with S.</p>

<p>O cannot be converted either simply or <i>per accidens</i>.
Some S is not P does not enable you to make any
converse assertion about P. All P may be S, or No
P may be S, or Some P may be not S. All the three
following diagrams are compatible with Some S being
excluded from P.</p>

<div class="figcenter"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-161.png" width="532" height="127" alt="Euler's circles. - Concentric circles of S and P - P in centre, S in one circle and P in another circle. S and P each in a circle, overlapping circle." /></div>

<p>(<i>c</i>) Another mode of Conversion, known by medi&aelig;val
logicians following Boethius as <i>Conversio per contra positionem</i>
<span class="pagenum"><a name="page153" id="page153"></a>[page&nbsp;153]</span>
<i>terminorum</i>, is useful in some syllogistic
manipulations. This Converse is obtained by substituting
for the predicate term its Contrapositive or
Contradictory, not-P, making the consequent change
of Quality, and simply converting. Thus All S is P
is converted into the equivalent No not-P is S.<a id="footnotetagPIII-ChIII6" name="footnotetagPIII-ChIII6"></a><a href="#footnotePIII-ChIII6"><sup>6</sup></a></p>

<p>Some have called it "Conversion by Negation," but
"negation" is manifestly too wide and common a
word to be thus arbitrarily restricted to the process of
substituting for one term its opposite.</p>

<p>Others (and this has some medi&aelig;val usage in its
favour, though not the most intelligent) would call
the form All not-P is not-S (the Obverse or Permutation
of No not-P is S), the Converse by Contraposition.
This is to conform to an imaginary rule
that in Conversion the Converse must be of the same
Quality with the Convertend. But the essence of
Conversion is the interchange of Subject and Predicate:
the Quality is not in the definition except by a bungle:
it is an accident. No not-P is S, and Some not-P is
S are the forms used in Syllogism, and therefore
specially named. Unless a form had a use, it
was left unnamed, like the Subalternate forms of
Syllogism: Nomen habent nullum: nec, si bene
colligis, usum.</p>
<span class="pagenum"><a name="page154" id="page154"></a>[page&nbsp;154]</span>

<h3 style="margin-top: 2em;"><span class="sc">Table of Contrapositive Converses.</span></h3>

<table summary="Table of Contrapositive Converses." align="center">
<tr>
       <td class="left0"><br />All S is P <br />No S is P<br />Some S is not P<br />Some S is P</td>
       <td class="left0">&nbsp;&nbsp;&nbsp;&nbsp;</td>
       <td class="left0">&nbsp;&nbsp;&nbsp;Con. Con.<br />No not-P is S<br />Some not-P is S<br />Some not-P is S<br />None.</td>
</tr>
</table>

<p>When not-P is substituted for P, Some S is P
becomes Some S is not not-P, and this form is
inconvertible.</p>

<h3 style="margin-top: 2em;"><span class="sc">Other Forms of Immediate Inference.</span></h3>

<p>I have already spoken of the Immediate Inferences
based on the rules of Contradictory and Contrary
Opposition (<a href="#page145">see p. 145</a>)</p>

<p>Another process was observed by Thomson, and
named <i>Immediate Inference by Added Determinants</i>.
If it is granted that "A negro is a fellow-creature,"
it follows that "A negro in suffering is a fellow-creature
in suffering". But that this does not follow
for every attribute<a id="footnotetagPIII-ChIII7" name="footnotetagPIII-ChIII7"></a><a href="#footnotePIII-ChIII7"><sup>7</sup></a> is manifest if you take another
case:&mdash;"A tortoise is an animal: therefore, a fast
tortoise is a fast animal". The form, indeed, holds
in cases not worth specifying: and is a mere handle
for quibbling. It could not be erected into a general
rule unless it were true that whatever distinguishes a
species within a class, will equally distinguish it in
every class in which the first is included.</p>

<p><b>Modal Consequence</b> has also been named among
the forms of Immediate Inference. By this is meant
the inference of the lower degrees of certainty from the
<span class="pagenum"><a name="page155" id="page155"></a>[page&nbsp;155]</span>
higher. Thus <i>must be</i> is said to imply <i>may be</i>; and
<i>None can be</i> to imply <i>None is</i>.</p>

<p>Dr. Bain includes also <i>Material Obversion</i>, the
analogue of <i>Formal Obversion</i> applied to a Subject.
Thus Peace is beneficial to commerce, implies that
War is injurious to commerce. Dr. Bain calls this
Material Obversion because it cannot be practised
safely without reference to the matter of the proposition.
We shall recur to the subject in another chapter.</p>

<p class="note1"><a id="footnotePIII-ChIII1" name="footnotePIII-ChIII1"></a><a class="footnote" href="#footnotetagPIII-ChIII1">Footnote 1:</a>
I purposely chose disputable propositions to emphasise the
fact that Formal Logic has no concern with the truth, but only
with the interdependence of its propositions.</p>

 <p class="note1"><a id="footnotePIII-ChIII2" name="footnotePIII-ChIII2"></a><a class="footnote" href="#footnotetagPIII-ChIII2">Footnote 2:</a>
 Mark Duncan, <i>Inst. Log.</i>, ii. 5, 1612.</p>

<p class="note1"><a id="footnotePIII-ChIII3" name="footnotePIII-ChIII3"></a><a class="footnote" href="#footnotetagPIII-ChIII3">Footnote 3:</a>
There can be no doubt that in their doctrine of &AElig;quipollents,
the Schoolmen were trying to make plain a real difficulty in interpretation,
the interpretation of the force of negatives. Their results
would have been more obviously useful if they had seen their way
to generalising them. Perhaps too they wasted their strength in
applying it to the artificial syllogistic forms, which men do not
ordinarily encounter except in the manipulation of syllogisms.
Their results might have been generalised as follows:&mdash;</p>

<p class="note1">(1) A "not" placed before the sign of Quantity contradicts the
whole proposition. Not "All S is P," not "No S is P," not
"Some S is P," not "Some S is not P," are equivalent respectively
to contradictories of the propositions thus negatived.</p>

<p class="note1">(2) A "not" placed after the sign of Quantity affects the
copula, and amounts to inverting its Quality, thus denying the
predicate term of the same quantity of the subject term of which
it was originally affirmed, and <i>vice versâ</i>.</p>

<table align="center" summary="equivalent forms">
<tr>
       <td class="right">All S is "not" P<br />No S is "not" P<br />Some S is "not" P<br />Some S is "not" not P</td>
       <td>&nbsp;=&nbsp; No S is P.<br />&nbsp;=&nbsp; All S is P.<br />&nbsp;=&nbsp; Some S is not P.<br />&nbsp;=&nbsp; Some S is P.</td>
</tr>
</table>

<p class="note1">(3) If a "not" is placed before as well as after, the resulting
forms are obviously equivalent (under Rule 1) to the assertion of
the contradictories of the forms on the right (in the illustration of
Rule 2).</p>

<table align="center" summary="equivalent forms">
<tr>
       <td class="left0">Not<br />Not<br />Not<br />Not</td>
       <td class="left1">All S is "not" P<br />No S is "not" P<br />Some S is "not" P<br /> Some S is "not" not P</td>
       <td class="left0">=&nbsp; No S is P<br />=&nbsp; All S is P<br />=&nbsp; Some S is not P<br /> =&nbsp; Some S is P</td>
       <td class="left1">=&nbsp; Some S is P.<br />=&nbsp; Some S is not P.<br />=&nbsp; All S is P.<br />=&nbsp; No S is P.</td>
</tr>
</table>

<p class="note1"><a id="footnotePIII-ChIII4" name="footnotePIII-ChIII4"></a><a class="footnote" href="#footnotetagPIII-ChIII4">Footnote 4:</a>
<i>Formal</i> to distinguish it from what he called the <i>Material
Obverse</i>, about which more presently.</p>

<p class="note1"><a id="footnotePIII-ChIII5" name="footnotePIII-ChIII5"></a><a class="footnote" href="#footnotetagPIII-ChIII5">Footnote 5:</a>
The medi&aelig;val word for the opposite of a term, the word
Contradictory being confined to the propositional form.</p>

<p class="note1"><a id="footnotePIII-ChIII6" name="footnotePIII-ChIII6"></a><a class="footnote" href="#footnotetagPIII-ChIII6">Footnote 6:</a>
It is to be regretted that a practice has recently crept in of
calling this form, for shortness, the Contrapositive simply. By
long-established usage, dating from Boethius, the word Contrapositive
is a technical name for a terminal form, not-A, and it is
still wanted for this use. There is no reason why the propositional
form should not be called the Converse by Contraposition,
or the Contrapositive Converse, in accordance with traditional
usage.</p>

<p class="note1"><a id="footnotePIII-ChIII7" name="footnotePIII-ChIII7"></a><a class="footnote" href="#footnotetagPIII-ChIII7">Footnote 7:</a>
<i>Cf.</i> Stock, part iii. c. vii.; Bain, <i>Deduction</i>, p.
109.</p>
<span class="pagenum"><a name="page156" id="page156"></a>[page&nbsp;156]</span>


<h3 style="margin-top: 3em;"><span class="sc">Chapter IV.</span></h3>

<h3>THE COUNTER-IMPLICATION OF PROPOSITIONS.</h3>

<p>In discussing the Axioms of Dialectic, I indicated that
the propositions of common speech have a certain
negative implication, though this does not depend
upon any of the so-called Laws of Thought, Identity,
Contradiction, and Excluded Middle. Since, however,
the counter-implicate is an important guide in the
interpretation of propositions, it is desirable to recognise
it among the modes of Immediate Inference.</p>

<p>I propose, then, first, to show that people do
ordinarily infer at once to a counter-sense; second, to
explain briefly the Law of Thought on which such an
inference is justified; and, third, how this law may be
applied in the interpretation of propositions, with a
view to making subject and predicate more definite.</p>

<p>Every affirmation about anything is an implicit
negation about something else. Every say is a gainsay.
That people ordinarily act upon this as a rule of
interpretation a little observation is sufficient to show:
and we find also that those who object to having their
utterances interpreted by this rule often shelter themselves
under the name of Logic.</p>

<p>Suppose, for example, that a friend remarks, when
the conversation turns on children, that John is a good
boy, the natural inference is that the speaker has in his
<span class="pagenum"><a name="page157" id="page157"></a>[page&nbsp;157]</span>
mind another child who is not a good boy. Such an
inference would at once be drawn by any actual hearer,
and the speaker would protest in vain that he said
nothing about anybody but John. Suppose there are
two candidates for a school appointment, A and B,
and that stress is laid upon the fact that A is an
excellent teacher. A's advocate would at once be
understood to mean that B was not equally excellent
as a teacher.</p>

<p>The fairness of such inferences is generally recognised.
A reviewer, for example, of one of Mrs.
Oliphant's historical works, after pointing out some
small errors, went on to say that to confine himself to
censure of small points, was to acknowledge by implication
that there were no important points to find
fault with.</p>

<p>Yet such negative implications are often repudiated
as illogical. It would be more accurate to call them
extra-logical. They are not condemned by any logical
doctrine: they are simply ignored. They are extra-logical
only because they are not legitimated by the
Laws of Identity, Contradiction, and Excluded Middle:
and the reason why Logic confines itself to those laws
is that they are sufficient for Syllogism and its subsidiary
processes.</p>

<p>But, though extra-logical, to infer a counter-implicate
is not unreasonable: indeed, if Definition, clear vision
of things in their exact relations, is our goal rather
than Syllogism, a knowledge of the counter-implicate
is of the utmost consequence. Such an implicate
there must always be under an all-pervading Law of
Thought which has not yet been named, but which
may be called tentatively the law of Homogeneous
Counter-relativity. The title, one hopes, is sufficiently
<span class="pagenum"><a name="page158" id="page158"></a>[page&nbsp;158]</span>
technical-looking: though cumbrous, it is descriptive.
The law itself is simple, and may be thus stated and
explained.</p>

<h3 style="margin-top: 2em;"><i>The Law of Homogeneous Counter-relativity.</i></h3>

<blockquote><p>
Every positive in thought has a contrapositive,
and the positive and contrapositive are of the
same kind.
</p></blockquote>

<p>The first clause of our law corresponds with Dr.
Bain's law of Discrimination or Relativity: it is,
indeed, an expansion and completion of that law.
Nothing is known absolutely or in isolation; the
various items of our knowledge are inter-relative;
everything is known by distinction from other things.
Light is known as the opposite of darkness, poverty of
riches, freedom of slavery, in of out; each shade of
colour by contrast to other shades. What Dr. Bain
lays stress upon is the element of difference in this
inter-relativity. He bases this law of our knowledge
on the fundamental law of our sensibility that change
of impression is necessary to consciousness. A long
continuance of any unvaried impression results in
insensibility to it. We have seen instances of this in
illustrating the maxim that custom blunts sensibility
(p. 74). Poets have been beforehand with philosophers
in formulating this principle. It is expressed with the
greatest precision by Barbour in his poem of "The
Bruce," where he insists that men who have never
known slavery do not know what freedom is.</p>

<div class="poem">  <div class="stanza">
<p>Thus contrar thingis evermare</p>
<p>Discoverings of t' other are.</p>
  </div>  </div>
<span class="pagenum"><a name="page159" id="page159"></a>[page&nbsp;159]</span>

<p>Since, then, everything that comes within our consciousness
comes as a change or transition from
something else, it results that our knowledge is counter-relative.
It is in the clash or conflict of impressions
that knowledge emerges: every item of knowledge has
its illuminating foil, by which it is revealed, over against
which it is defined. Every positive in thought has its
contrapositive.</p>

<p>So much for the element of difference. But this is
not the whole of the inter-relativity. The Hegelians
rightly lay stress on the common likeness that connects
the opposed items of knowledge.</p>

<blockquote><p>
"Thought is not only <i>distinction</i>; it is, at the same time,
<i>relation</i>.<a id="footnotetagPIII-ChIV1" name="footnotetagPIII-ChIV1"></a><a href="#footnotePIII-ChIV1"><sup>1</sup></a>
If it marks off one thing from another, it, at the
same time, connects one thing with another. Nor can either of
these functions of thought be separated from the other: as
Aristotle himself said, the knowledge of opposites is one. A
thing which has nothing to distinguish it is unthinkable, but
equally unthinkable is a thing which is so separated from all
other things as to have no community with them. If then the
<span class="pagenum"><a name="page160" id="page160"></a>[page&nbsp;160]</span>
law of contradiction be taken as asserting the self-identity of
things or thoughts in a sense that excludes their community&mdash;in
other words, if it be not taken as limited by another law which
asserts the <i>relativity</i> of the things or thoughts distinguished&mdash;it
involves a false abstraction.... If, then, the world, as an intelligible
world, is a world of distinction, differentiation, individuality,
it is equally true that in it as an intelligible world there are no
absolute separations or oppositions, no antagonisms which cannot
be reconciled."<a id="footnotetagPIII-ChIV2" name="footnotetagPIII-ChIV2"></a><a href="#footnotePIII-ChIV2"><sup>2</sup></a>
</p></blockquote>

<p>In the penultimate sentence of this quotation Dr.
Caird <i>differentiates</i> his theory against a Logical counter-theory
of the Law of Identity, and in the last sentence
against an Ethical counter-theory: but the point here
is that he insists on the relation of likeness among
opposites. Every impression felt is felt as a change
or transition from something else: but it is a variation
of the same impression&mdash;the something else, the
contrapositive, is not entirely different. Change
itself is felt as the opposite of sameness, difference
of likeness, and likeness of difference. We do not
differentiate our impression against the whole world,
as it were, but against something nearly akin to it&mdash;upon
some common ground. The positive and the
contrapositive are of the same kind.</p>

<p>Let us surprise ourselves in the act of thinking and
we shall find that our thoughts obey this law. We
take note, say, of the colour of the book before us:
we differentiate it against some other colour actually
before us in our field of vision or imagined in our
minds. Let us think of the blackboard as black: the
blackness is defined against the whiteness of the
figures chalked or chalkable upon it, or against the
colour of the adjacent wall. Let us think of a man as
<span class="pagenum"><a name="page161" id="page161"></a>[page&nbsp;161]</span>
a soldier; the opposite in our minds is not the colour
of his hair, or his height, or his birthplace, or his
nationality, but some other profession&mdash;soldier, sailor,
tinker, tailor. It is always by means of some contrapositive
that we make the object of our thoughts
definite; it is not necessarily always the same opposite,
but against whatever opposite it is, they are always
homogeneous. One colour is contradistinguished
from another colour, one shade from another shade:
colour may be contradistinguished from shape, but it
is within the common genus of sensible qualities.</p>

<p>A curious confirmation of this law of our thinking
has been pointed out by Mr. Carl Abel.<a id="footnotetagPIII-ChIV3" name="footnotetagPIII-ChIV3"></a><a href="#footnotePIII-ChIV3"><sup>3</sup></a>
In Egyptian
hieroglyphics, the oldest extant language, we find, he
says, a large number of symbols with two meanings,
the one the exact opposite of the other. Thus the
same symbol represents <i>strong</i> and <i>weak</i>;
<i>above</i>&mdash;<i>below</i>;
<i>with</i>&mdash;<i>without</i>; <i>for</i>&mdash;<i>against</i>. This is what the
Hegelians
mean by the reconciliation of antagonisms in
higher unities. They do not mean that black is white,
but only that black and white have something in
common&mdash;they are both colours.</p>

<p>I have said that this law of Homogeneous Counter-relativity
has not been recognised by logicians. This,
however, is only to say that it has not been explicitly
formulated and named, as not being required for
Syllogism; a law so all-pervading could not escape
recognition, tacit or express. And accordingly we
find that it is practically assumed in Definition: it is
really the basis of definition <i>per genus et differentiam</i>.
When we wish to have a definite conception of
anything, to apprehend what it is, we place it in some
<span class="pagenum"><a name="page162" id="page162"></a>[page&nbsp;162]</span>
genus and distinguish it from species of the same. In
fact our law might be called the Law of Specification:
in obeying the logical law of what we ought to do with
a view to clear thinking, we are only doing with
exactness and conscious method what we all do and
cannot help doing with more or less definiteness in our
ordinary thinking.</p>

<p>It is thus seen that logicians conform to this law
when they are not occupied with the narrow considerations
proper to Syllogism. And another unconscious
recognition of it may be found in most logical text-books.
Theoretically the not-A of the Law of Contradiction&mdash;(A
is not not-A)&mdash;is an infinite term. It stands for
everything but A. This is all that needs to be assumed
for Conversion and Syllogism. But take the examples
given of the Formal Obverse or Permutation, "All men
are fallible". Most authorities would give as the
Formal Obverse of this, "No men are infallible".
But, strictly speaking, "infallible" is of more limited
and definite signification than not-fallible. Not-fallible,
other than fallible, is brown, black, chair, table, and
every other nameable thing except fallible. Thus in
Obversion and Conversion by Contraposition, the
homogeneity of the negative term is tacitly assumed;
it is assumed that A and not-A are of the same kind.</p>

<p style="margin-top: 2.5em">Now to apply this Law of our Thought to the interpretation
of propositions. Whenever a proposition is
uttered we are entitled to infer at once (or <i>immediately</i>)
that the speaker has in his mind some counter-proposition,
in which what is overtly asserted of the ostensible
subject is covertly denied of another subject. And we
must know what this counter-proposition, the counter-implicate
is, before we can fully and clearly understand
<span class="pagenum"><a name="page163" id="page163"></a>[page&nbsp;163]</span>
his meaning. But inasmuch as any positive may have
more than one contrapositive, we cannot tell immediately
or without some knowledge of the circumstances
or context, what the precise counter-implicate is. The
peculiar fallacy incident to this mode of interpretation
is, knowing that there must be some counter-implicate,
to jump rashly or unwarily to the conclusion that it is
some definite one.</p>

<p>Dr. Bain applies the term Material Obverse to the
form, Not-S is not P, as distinguished from the form
S is not not-P, which he calls the Formal Obverse, on
the ground that we can infer the Predicate-contrapositive
at once from the form, whereas we cannot tell the
Subject-contrapositive without an examination of the
matter. But in truth we cannot tell either Predicate-contrapositive
or Subject-contrapositive as it is in the
mind of the speaker from the bare utterance. We can
only tell that if he has in his mind a proposition
definitely analysed into subject and predicate, he must
have contrapositives in his mind of both, and that they
must be homogeneous. Let a man say, "This book
is a quarto". For all that we know he may mean
that it is not a folio or that it is not an octavo: we
only know for certain, under the law of Homogeneous
Counter-relativity, that he means some definite other
size. Under the same law, we know that he has a
homogeneous contrapositive of the subject, a subject
that admits of the same predicate, some other book
in short. What the particular book is we do not
know.</p>

<p>It would however be a waste of ingenuity to dwell
upon the manipulation of formul&aelig; founded on this law.
The practical concern is to know that for the interpretation
of a proposition, a knowledge of the counter-implicate,
<span class="pagenum"><a name="page164" id="page164"></a>[page&nbsp;164]</span>
a knowledge of what it is meant to deny, is
essential.</p>

<p>The manipulation of formul&aelig;, indeed, has its own
special snare. We are apt to look for the counterparts
of them in the grammatical forms of common speech.
Thus, it might seem to be a fair application of our law
to infer from the sentence, "Wheat is dear," that the
speaker had in his mind that Oats or Sugar or Shirting
or some other commodity is cheap. But this would be
a rash conclusion. The speaker may mean this, but
he <i>may</i> also mean that wheat is dear now as compared
with some other time: that is, the Positive subject in
his mind may be "Wheat as now," and the Contrapositive
"Wheat as then". So a man may say, "All
men are mortal," meaning that the angels never taste
death, "angels" being the contrapositive of his subject
"men". Or he may mean merely that mortality is a
sad thing, his positive subject being men as they are,
and his contrapositive men as he desires them to be.
Or his emphasis may be upon the <i>all</i>, and he may
mean only to deny that some one man in his mind
(Mr. Gladstone, for example) is immortal. It would
be misleading, therefore, to prescribe propositions as
exercises in Material Obversion, if we give that name
to the explicit expression of the Contrapositive Subject:
it is only from the context that we can tell what this
is. The man who wishes to be clearly understood
gives us this information, as when the epigrammatist
said: "We are all fallible&mdash;even the youngest of us".</p>

<p>But the chief practical value of the law is as a guide
in studying the development of opinions. Every
doctrine ever put forward has been put forward in
opposition to a previous doctrine on the same subject.
Until we know what the opposed doctrine is, we cannot
<span class="pagenum"><a name="page165" id="page165"></a>[page&nbsp;165]</span>
be certain of the meaning. We cannot gather it with
precision from a mere study of the grammatical or
even (in the narrow sense of the word) the logical content
of the words used. This is because the framers
of doctrines have not always been careful to put them
in a clear form of subject and predicate, while their
impugners have not moulded their denial exactly on
the language of the original. No doubt it would have
been more conducive to clearness if they had done so.
But they have not, and we must take them as they
are. Thus we have seen that the Hegelian doctrine of
Relativity is directed against certain other doctrines in
Logic and in Ethics; that Ultra-Nominalism is a contradiction
of a certain form of Ultra-Realism; and that
various theories of Predication each has a backward
look at some predecessor.</p>

<p>I quote from Mr. A.B. Walkley a very happy application
of this principle of interpretation:&mdash;</p>

<blockquote><p>
"It has always been a matter for speculation why so sagacious
an observer as Diderot should have formulated the wild paradox
that the greatest actor is he who feels his part the least. Mr.
Archer's bibliographical research has solved this riddle. Diderot's
paradox was a protest against a still wilder one. It seems that a
previous eighteenth century writer on the stage, a certain Saint-Albine,
had advanced the fantastic propositions that none but a
magnanimous man can act magnanimity, that only lovers can
do justice to a love scene, and kindred assertions that read like
variations on the familiar 'Who drives fat oxen must himself be
fat'. Diderot saw the absurdity of this; he saw also the essentially
artificial nature of the French tragedy and comedy of his own day;
and he hastily took up the position which Mr. Archer has now
shown to be untenable."
</p></blockquote>

<p>This instance illustrates another principle that has
to be borne in mind in the interpretation of doctrines
from their historical context of counter-implication.
<span class="pagenum"><a name="page166" id="page166"></a>[page&nbsp;166]</span>
This is the tendency that men have to put doctrines in
too universal a form, and to oppose universal to universal,
that is, to deny with the flat contrary, the very
reverse, when the more humble contradictory is all
that the truth admits of. If a name is wanted for this
tendency, it might be called the tendency to Over-Contradiction.
Between "All are" and "None are,"
the sober truth often is that "Some are" and "Some
are not," and the process of evolution has often consisted
in the substitution of these sober forms for their
more violent predecessors.</p>

<p class="note1"><a id="footnotePIII-ChIV1" name="footnotePIII-ChIV1"></a><a class="footnote" href="#footnotetagPIII-ChIV1">Footnote 1:</a>
It is significant of the unsuitableness of the vague unqualified
word Relativity to express a logical distinction that Dr. Bain calls
his law the Law of Relativity simply, having regard to the relation
of difference, <i>i.e.</i>, to Counter-Relativity, while Dr. Caird applies
the name Relativity simply to the relation of likeness, <i>i.e.</i>, to
Co-relativity.
It is with a view to taking both forms of relation
into account that I name our law the Law of Homogeneous
Counter-relativity. The Protagorean Law of Relativity has
regard to yet another relation, the relation of knowledge
to the knowing mind: these other logical laws are of relations
among the various items of knowledge. Aristotle's category of
Relation is a fourth kind of relation not to be confused with the
others. "Father&mdash;son," "uncle&mdash;nephew," "slave&mdash;master," are
<i>relata</i> in Aristotle's sense: "father," "uncle" are homogeneous
counter-relatives, varieties of kinship; so "slave," "freeman" are
counter-relatives in social status.</p>

<p class="note1"><a id="footnotePIII-ChIV2" name="footnotePIII-ChIV2"></a><a class="footnote" href="#footnotetagPIII-ChIV2">Footnote 2:</a>
Dr. Caird's <i>Hegel</i>, p. 134.</p>

<p class="note1"><a id="footnotePIII-ChIV3" name="footnotePIII-ChIV3"></a><a class="footnote" href="#footnotetagPIII-ChIV3">Footnote 3:</a>
See article on Counter-Sense, <i>Contemporary Review</i>, April,
1884.</p>

<span class="pagenum"><a name="page167" id="page167"></a>[page&nbsp;167]</span>

<h2 style="margin-top: 3em;">PART IV.</h2>

<h3>THE INTERDEPENDENCE OF PROPOSITIONS.&mdash;MEDIATE INFERENCE.&mdash;SYLLOGISM.</h3>

<div class="figcenter"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-140.png" width="304" height="35" alt="fancy rule" border="0" /></div>

<h3><span class="sc">Chapter I.</span></h3>

<h3>THE SYLLOGISM.</h3>

<p>We have already defined mediate inference as the
derivation of a conclusion from more than one proposition.
The type or form of a mediate inference fully
expressed consists of three propositions so related that
one of them is involved or implied in the other two.</p>

<div class="poem">  <div class="stanza">
<p class="i6">Distraction is exhausting.</p>
<p class="i6">Modern life is full of distraction</p>
<p class="i4">.<sup>.</sup>. Modern life is exhausting.</p>
  </div>  </div>

<p>We say nothing of the truth of these propositions.
I purposely choose questionable ones. But do they
hang together? If you admit the first two, are you
bound in consistency to admit the third? Is the
truth of the conclusion a necessary consequence of
the truth of the premisses? If so, it is a valid
mediate inference from them.</p>
<span class="pagenum"><a name="page168" id="page168"></a>[page&nbsp;168]</span>

<p>When one of the two premisses is more general than
the conclusion, the argument is said to be Deductive.
You lead down from the more general to the less
general. The general proposition is called the Major
Premiss, or Grounding Proposition, or Sumption: the
other premiss the Minor, or Applying Proposition, or
Subsumption.</p>

<div class="poem">  <div class="stanza">
<p class="i6">Undue haste makes waste.</p>
<p class="i6">This is a case of undue hasting.</p>
<p class="i4">.<sup>.</sup>. It is a case of undue wasting.</p>
  </div>  </div>

<p>We may, and constantly do, apply principles and
draw conclusions in this way without making any
formal analysis of the propositions. Indeed we reason
mediately and deductively whenever we make any
application of previous knowledge, although the
process is not expressed in propositions at all and is
performed so rapidly that we are not conscious of the
steps.</p>

<p>For example, I enter a room, see a book, open it
and begin to read. I want to make a note of something:
I look round, see a paper case, open it, take a
sheet of paper and a pen, dip the pen in the ink and
proceed to write. In the course of all this, I act upon
certain inferences which might be drawn out in the
form of Syllogisms. First, in virtue of previous
knowledge I recognise what lies before me as a book.
The process by which I reach the conclusion, though
it passes in a flash, might be analysed and expressed
in propositions.</p>

<div class="poem1">  <div class="stanza">
<p class="i2">Whatever presents certain outward appearances, contains readable print.</p>
<p class="i2">This presents such appearances.</p>
<p>.<sup>.</sup>. It contains readable print.</p>
  </div>  </div>
<span class="pagenum"><a name="page169" id="page169"></a>[page&nbsp;169]</span>
<p>So with the paper case, and the pen, and the ink. I
infer from peculiar appearances that what I see contains
paper, that the liquid will make a black mark on the
white sheet, and so forth.</p>

<p>We are constantly in daily life subsuming particulars
under known universals in this way. "Whatever has
certain visible properties, has certain other properties:
this has the visible ones: therefore, it has the others"
is a form of reasoning constantly latent in our minds.</p>

<p>The Syllogism may be regarded as the explicit
expression of this type of deductive reasoning; that is,
as the analysis and formal expression of this every-day
process of applying known universals to particular
cases. Thus viewed it is simply the analysis of a
mental process, as a psychological fact; the analysis
of the procedure of all men when they reason from
signs; the analysis of the kind of assumptions they
make when they apply knowledge to particular cases.
The assumptions may be warranted, or they may not:
but as a matter of fact the individual who makes the
confident inference has such assumptions and subsumptions
latent in his mind.</p>

<p>But practically viewed, that is <i>logically</i> viewed, if
you regard Logic as a practical science, the Syllogism
is a contrivance to assist the correct performance of
reasoning together or syllogising in difficult cases. It
applies not to mental processes but to results of such
expressed in words, that is, to propositions. Where
the Syllogism comes in as a useful form is when
certain propositions are delivered to you <i>ab extra</i> as
containing a certain conclusion; and the connexion is
not apparent. These propositions are analysed and
thrown into a form in which it is at once apparent
whether the alleged connexion exists. This form is
<span class="pagenum"><a name="page170" id="page170"></a>[page&nbsp;170]</span>
the Syllogism: it is, in effect, an analysis of given
arguments.</p>

<p>It was as a practical engine or organon that it was
invented by Aristotle, an organon for the syllogising of
admissions in Dialectic. The germ of the invention
was the analysis of propositions into terms. The
syllogism was conceived by Aristotle as a reasoning
together of terms. His prime discovery was that
whenever two propositions necessarily contain or imply
a conclusion, they have a common term, that is, only
three terms between them: that the other two terms
which differ in each are the terms of the conclusion;
and that the relation asserted in the conclusion between
its two terms is a necessary consequence of their
relations with the third term as declared in the
premisses.</p>

<p>Such was Aristotle's conception of the Syllogism
and such it has remained in Logic. It is still, strictly
speaking, a syllogism of terms: of propositions only
secondarily and after they have been analysed. The
conclusion is conceived analytically as a relation
between two terms. In how many ways may this
relation be established through a third term? The
various moods and figures of the Syllogism give the
answer to that question.</p>

<p>The use of the very abstract word "relation" makes
the problem appear much more difficult than it really
is. The great charm of Aristotle's Syllogism is its
simplicity. The assertion of the conclusion is reduced
to its simplest possible kind, a relation of inclusion or
exclusion, contained or not contained. To show that
the one term is or is not contained in the other we
have only to find a third which contains the one and is
contained or not contained in the other.</p>
<span class="pagenum"><a name="page171" id="page171"></a>[page&nbsp;171]</span>

<p>The practical difficulties, of course, consist in the
reduction of the conclusions and arguments of common
speech to definite terms thus simply related. Once
they are so reduced, their independence or the
opposite is obvious. Therein lies the virtue of the
Syllogism.</p>

<p>Before proceeding to show in how many ways two
terms may be Syllogised through a third, we must have
technical names for the elements.</p>

<p>The third term is called the <b>Middle</b> (M) (<ins title="to meson">&tau;<span style="font-size: 0.9em;">&#8056;</span> &mu;&#941;&sigma;&omicron;&nu;</ins>):
the other two the Extremes (<ins title="akra"><span style="font-size: 0.9em;">&#7940;</span>&kappa;&rho;&alpha;</ins>).</p>

<p>The <b>Extremes</b> are the Subject (S) and the Predicate
(P) of the conclusion.</p>

<p>In an affirmative proposition (the normal form) S
is contained in P: hence P is called the <b>Major</b><a id="footnotetagPIV-ChI1" name="footnotetagPIV-ChI1"></a><a href="#footnotePIV-ChI1"><sup>1</sup></a>
term (<ins title="to meizon">&tau;<span style="font-size: 0.9em;">&#8056;</span>
&mu;&epsilon;<span style="font-size: 0.9em;">&#8150;</span>&zeta;&omicron;&nu;</ins>), and S the <b>Minor</b>
(<ins title="to elatton">&tau;<span style="font-size: 0.9em;">&#8056;</span> <span style="font-size: 0.9em;">&#7956;</span>&lambda;&alpha;&tau;&tau;&omicron;&nu;</ins>), being
respectively
larger and smaller in extension. All difficulty
about the names disappears if we remember that in
bestowing them we start from the conclusion. That
was the problem (<ins title="problêma">&pi;&rho;&omicron;&beta;&lambda;<span style="font-size: 0.9em;">&#8134;</span>&mu;&alpha;</ins>) or thesis in dialectic, the
question in dispute.</p>

<p>The two Premisses, or propositions giving the
relations between the two Extremes and the Middle,
are named on an equally simple ground.</p>

<p>One of them gives the relation between the
Minor Term, S, and the Middle, M. S, All or Some,
is or is not in M. This is called the Minor
Premiss.</p>

<p>The other gives the relation between the Major
<span class="pagenum"><a name="page172" id="page172"></a>[page&nbsp;172]</span>
Term and the Middle. M, All or Some, is or is not in
P. This is called the Major Premiss.<a id="footnotetagPIV-ChI2" name="footnotetagPIV-ChI2"></a><a href="#footnotePIV-ChI2"><sup>2</sup></a></p>

<p class="note1"><a id="footnotePIV-ChI1" name="footnotePIV-ChI1"></a><a class="footnote" href="#footnotetagPIV-ChI1">Footnote 1:</a>
Aristotle calls the Major the First (<ins title="to prôton">&tau;&#8056; &pi;&rho;&#8182;&tau;&omicron;&nu;</ins>) and the Minor
the last (<ins title="to eschaton">&tau;&#8056; &#7956;&sigma;&chi;&alpha;&tau;&omicron;&nu;</ins>), probably because that was their order in the
conclusion when stated in his most usual form, "P is predicated
of S," or "P belongs to S".</p>

<p class="note1"><a id="footnotePIV-ChI2" name="footnotePIV-ChI2"></a><a class="footnote" href="#footnotetagPIV-ChI2">Footnote 2:</a>
When we speak of the Minor or the Major simply, the
reference is to the terms. To avoid a confusion into which
beginners are apt to stumble, and at the same time to emphasise
the origin of the names, the Premisses might be spoken of at first
as the Minor's Premiss and the Major's Premiss. It was only in
the Middle Ages when the origin of the Syllogism had been forgotten,
that the idea arose that the terms were called Major and
Minor because they occurred in the Major and the Minor
Premiss respectively.</p>
<span class="pagenum"><a name="page173" id="page173"></a>[page&nbsp;173]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter II</span>.</h3>

<h3>FIGURES AND MOODS OF THE SYLLOGISM.</h3>

<h3 style="margin-top: 2em;">I.&mdash;The First Figure.</h3>

<p>The forms (technically called <b>Moods</b>, <i>i.e.</i>, modes) of
the First Figure are founded on the simplest relations
with the Middle that will yield or that necessarily
involve the disputed relation between the Extremes.</p>

<p>The simplest type is stated by Aristotle as follows:
"When three terms are so related that the last (the
Minor) is wholly in the Middle, and the Middle wholly
either in or not in the first (the Major) there must be
a perfect syllogism of the Extremes".<a id="footnotetagPIV-ChII1" name="footnotetagPIV-ChII1"></a><a href="#footnotePIV-ChII1"><sup>1</sup></a></p>

<p>When the Minor is partly in the Middle, the
Syllogism holds equally good. Thus there are four
possible ways in which two terms (<ins title="horoi"><span style="font-size: 0.9em;">&#8005;</span>&rho;&omicron;&iota;</ins>, plane enclosures)
may be connected or disconnected through a
third. They are usually represented by circles as
being the neatest of figures, but any enclosing outline
answers the purpose, and the rougher and more
irregular it is the more truly will it represent the
extension of a word.</p>
<span class="pagenum"><a name="page174" id="page174"></a>[page&nbsp;174]</span>

<table summary="syllogisms described with circles" align="center" border="0">
<tr>
       <td class="left">Conclusion A.<br />
                        All M is in P.<br />
                        All S is in M.<br />
                        All S is in P.</td>
       <td class="rc"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-183-1-h150.png" width="159" height="150" alt="concentric circles of P, M and S - S in centre" /></td>
</tr>
<tr>
       <td class="left">Conclusion E.<br />
           No M is in P.<br />
           All S is in M.<br />
           No S is in P.</td>
       <td class="rc"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-183-2-h140.png" width="345" height="140" alt="Concentric circles of M and S, S in centre and separate circle of P" /></td>
</tr>
<tr>
       <td class="left">Conclusion I.<br />
           All M is in P.<br />
           Some S is in M.<br />
           Some S is in P.</td>
       <td class="rc"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-183-3-h180.png" width="196" height="180" alt="Concentric circles of P and M, M in centre, both overlapped by circle of S" /></td>
</tr>
<tr>
       <td class="left">Conclusion O.<br />
           No M is in P.<br />
           Some S is in M.<br />
           Some S is not in P.</td>
       <td class="rc"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-183-4-h140.png" width="263" height="140" alt="Circles of M and P touching, each overlapped by circle of S" /></td>
</tr>
</table>

<p>These four forms constitute what are known as the
moods of the First Figure of the Syllogism. Seeing
that all propositions may be reduced to one or other
of the four forms, A, E, I, or O, we have in these
premisses abstract types of every possible valid argument
from general principles. It is all the same
whatever be the matter of the proposition. Whether
the subject of debate is mathematical, physical, social
or political, once premisses in these forms are conceded,
the conclusion follows irresistibly, <i>ex vi form&aelig;,
ex necessitate form&aelig;</i>. If an argument can be analysed
<span class="pagenum"><a name="page175" id="page175"></a>[page&nbsp;175]</span>
into these forms, and you admit its propositions, you
are bound in consistency to admit the conclusion&mdash;unless
you are prepared to deny that if one thing is in
another and that other in a third, the first is in the
third, or if one thing is in another and that other
wholly outside a third, the first is also outside the
third.</p>

<p>This is called the <b>Axiom of Syllogism</b>. The most
common form of it in Logic is that known as the
<i>Dictum</i>, or <i>Regula de Omni et Nullo:</i> "Whatever is
predicated of All or None of a term, is predicated of
whatever is contained in that term". It has been
expressed with many little variations, and there has
been a good deal of discussion as to the best way of
expressing it, the relativity of the word best being often
left out of sight. <i>Best</i> for what purpose? Practically
that form is the best which best commands general
assent, and for this purpose there is little to choose
between various ways of expressing it. To make it
easy and obvious it is perhaps best to have two
separate forms, one for affirmative conclusions and
one for negative. Thus: "Whatever is affirmed of
all M, is affirmed of whatever is contained in M: and
whatever is denied of all M, is denied of whatever is
contained in M". The only advantage of including
the two forms in one expression, is compendious
neatness. "A part of a part is a part of the whole," is
a neat form, it being understood that an individual or
a species is part of a genus. "What is said of a
whole, is said of every one of its parts," is really a
sufficient statement of the principle: the whole being
the Middle Term, and the Minor being a part of it,
the Major is predicable of the Minor affirmatively or
negatively if it is predicable similarly of the Middle.</p>
<span class="pagenum"><a name="page176" id="page176"></a>[page&nbsp;176]</span>

<p>This Axiom, as the name imports, is indemonstrable.
As Aristotle pointed out in the case of the Axiom of
Contradiction, it can be vindicated, if challenged, only
by reducing the challenger to a practical absurdity.
You can no more deny it than you can deny that if a
leaf is in a book and the book is in your pocket, the
leaf is in your pocket. If you say that you have a
sovereign in your purse and your purse is in your
pocket, and yet that the sovereign is not in your
pocket: will you give me what is in your pocket for
the value of the purse?</p>

<h3 style="margin-top: 2em;">II.&mdash;<span class="sc">The Minor Figures Of the Syllogism, And Their Reduction To the First</span>.</h3>

<p>The word Figure (<ins title="schêma">&sigma;&chi;<span style="font-size: 0.9em;">&#8134;</span>&mu;&alpha;</ins>) applies to the form or
figure of the premisses, that is, the order of the terms
in the statement of the premisses, when the Major
Premiss is put first, and the Minor second.</p>

<p>In the First Figure the order is</p>

<div class="poem">  <div class="stanza">
<p>M  P</p>
<p>S  M</p>
  </div>  </div>

<p>But there are three other possible orders or figures,
namely:&mdash;</p>

<table style="margin-left:25%;" summary="possible figures" border="0">
<tr>
       <td class="left2">Fig. ii.<br />&nbsp;&nbsp;PM<br />&nbsp;&nbsp;SM</td>
       <td class="left2">Fig. iii.<br />&nbsp;&nbsp;MP<br />&nbsp;&nbsp;MS</td>
       <td class="left2">Fig. iv.<br />&nbsp;&nbsp;PM<br />&nbsp;&nbsp;MS.</td>
</tr>
</table>

<p>It results from the doctrines of Conversion that
valid arguments may be stated in these forms,
inasmuch as a proposition in one order of terms may
be equivalent to a proposition in another. Thus No
<span class="pagenum"><a name="page177" id="page177"></a>[page&nbsp;177]</span>
M is in P is convertible with No P is in M: consequently
the argument</p>

<div class="poem">  <div class="stanza">
<p>No P is in M</p>
<p>All S is in M,</p>
  </div>  </div>

<p>in the Second Figure is as much valid as when it is
stated in the First&mdash;</p>

<div class="poem">  <div class="stanza">
<p>No M is in P</p>
<p>All S is in M.</p>
  </div>  </div>

<p>Similarly, since All M is in S is convertible into Some
S is in M, the following arguments are equally
valid:&mdash;</p>

<table style="margin-left:25%;" summary="arguments" border="0">
<tr>
       <td class="left2a">&nbsp;&nbsp;&nbsp;Fig. iii.</td>
       <td class="left2a" rowspan="3">&nbsp;&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;</td>
       <td class="left2a">&nbsp;&nbsp;&nbsp;Fig. i.</td>
</tr>
<tr>
       <td class="left2a">All M is in P </td>

       <td class="left2a">All M is in P</td>
</tr>
<tr>
       <td class="left2a">All M is in S</td>

       <td class="left2a">Some S is in M.</td>
</tr>
</table>

<p>Using both the above Converses in place of their
Convertends, we have&mdash;</p>

<table style="margin-left:25%;" summary="arguments" border="0">
<tr>
       <td class="left2a">&nbsp;&nbsp;&nbsp;Fig. iv.</td>
       <td class="left2a" rowspan="3">&nbsp;&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;</td>
       <td class="left2a">&nbsp;&nbsp;&nbsp;Fig. i.</td>
</tr>
<tr>
       <td class="left2a">No P is in M</td>

       <td class="left2a">No M is in P</td>
</tr>
<tr>
       <td class="left2a">All M is in S</td>

       <td class="left2a">Some S is in M.</td>
</tr>
</table>

<p>It can be demonstrated (we shall see presently how)
that altogether there are possible four valid forms or
moods of the Second Figure, six of the Third, and five
of the Fourth. An ingenious Mnemonic of these
various moods and their reduction to the First Figure
by the transposition of terms and premisses has come
down from the thirteenth century. The first line names
the moods of the First, Normal, or Standard Figure.</p>
<span class="pagenum"><a name="page178" id="page178"></a>[page&nbsp;178]</span>

<div class="poem">  <div class="stanza">
<p style="line-height: 150%">BA<i>rb</i>A<i>r</i>A, CE<i>l</i>A<i>r</i>E<i>nt</i>, DA<i>r</i>II, FE<i>r</i>IO<i>que</i> prioris;</p>
<p style="line-height: 150%">CE<i>s</i>A<i>r</i>E, CA<i>m</i>E<i>str</i>E<i>s</i>, FE<i>st</i>I<i>n</i>O, BA<i>r</i>O<i>k</i>O, secund&aelig;;</p>
<p style="line-height: 150%">Tertia DA<i>r</i>A<i>pt</i>I, DI<i>s</i>A<i>m</i>I<i>s</i>, DA<i>t</i>I<i>s</i>I, FE<i>l</i>A<i>pt</i>O<i>n</i>,</p>
<p style="line-height: 150%">BO<i>k</i>A<i>rd</i>O, FE<i>r</i>I<i>s</i>O<i>que</i>, habet; quarta insuper addit,</p>
<p style="line-height: 150%">B<i>r</i>A<i>m</i>A<i>nt</i>IP, CA<i>m</i>E<i>n</i>E<i>s</i>, DI<i>m</i>A<i>r</i>I<i>s</i>, FE<i>s</i>A<i>p</i>O, F<i>r</i>E<i>s</i>I<i>s</i>O<i>n</i>.</p>
  </div>  </div>

<p>The vowels in the names of the Moods indicate the
propositions of the Syllogism in the four forms,
A E I O. To write out any Mood at length you have
only to remember the Figure, and transcribe the propositions
in the order of Major Premiss, Minor Premiss,
and Conclusion. Thus, the Second Figure being</p>

<div class="poem">  <div class="stanza">
<p>PM</p>
<p>SM</p>
  </div>  </div>

<p>FE<i>st</i>I<i>n</i>O is written&mdash;</p>

<div class="poem">  <div class="stanza">
<p>No P is in M.</p>
<p>Some S is in M.</p>
<p>Some S is not in P.</p>
  </div>  </div>

<p>The Fourth Figure being</p>

<div class="poem">  <div class="stanza">
<p>PM</p>
<p>MS</p>
  </div>  </div>

<p>DI<i>m</i>A<i>r</i>I<i>s</i> is</p>

<div class="poem">  <div class="stanza">
<p>Some P is in M.</p>
<p>All M is in S.</p>
<p>Some S is in P.</p>
  </div>  </div>

<p>The initial letter in a Minor Mood indicates that
Mood of the First to which it may be reduced. Thus
Festino is reduced to Ferio, and Dimaris to Darii. In
the cases of Baroko and Bokardo, B indicates that you
may employ Barbara to bring any impugner to confusion,
as shall be afterwards explained.</p>

<p>The letters <i>s</i>, <i>m</i>, and <i>p</i> are also significant. Placed
after a vowel, <i>s</i> indicates that the proposition has to be
simply converted. Thus, FE<i>st</i>I<i>n</i>O:&mdash;</p>

<div class="poem">  <div class="stanza">
<p>No P is in M.</p>
<p>Some S is in M.</p>
<p>Some S is not in P.</p>
  </div>  </div>
<span class="pagenum"><a name="page179" id="page179"></a>[page&nbsp;179]</span>

<p>Simply convert the Major Premiss, and you get FE<i>r</i>IO,
of the First.</p>

<div class="poem">  <div class="stanza">
<p>No M is in P.</p>
<p>Some S is in M.</p>
<p>Some S is not in P.</p>
  </div>  </div>

<p><i>m</i> (<i>muta</i>, or <i>move</i>) indicates that the premisses have
to be transposed. Thus, in CA<i>m</i>E<i>str</i>E<i>s</i>, you have to
transpose the premisses, as well as simply convert the
Minor Premiss before reaching the figure of CE<i>l</i>A<i>r</i>E<i>nt</i>.</p>

<table style="margin-left:25%;" summary="arguments" border="0">
<tr>
       <td class="left2a">All P is in M</td>
       <td class="left2a" rowspan="2" style="line-height:20%;">&nbsp;&nbsp;&nbsp;=&nbsp;&nbsp;&nbsp;</td>
       <td class="left2a">No M is in S</td>
</tr>

<tr>
       <td class="left2a">No S is in M </td>

       <td class="left2a">All P is in M.</td>
</tr>
</table>

<p>From this it follows in CE<i>l</i>A<i>r</i>E<i>nt</i> that No P is in S,
and this simply converted yields No S is in P.</p>

<p>A simple transposition of the premisses in DI<i>m</i>A<i>r</i>I<i>s</i>
of the Fourth</p>

<div class="poem">  <div class="stanza">
<p>Some P is in M</p>
<p>All M is in S</p>
  </div>  </div>

<p>yields the premisses of DA<i>r</i>II</p>

<div class="poem">  <div class="stanza">
<p>All M is in S</p>
<p>Some P is in M,</p>
  </div>  </div>

<p>but the conclusion Some P is in S has to be simply
converted.</p>

<p>Placed after a vowel, <i>p</i> indicates that the proposition
has to be converted <i>per accidens</i>. Thus in FE<i>l</i>A<i>pt</i>O<i>n</i>
of the Third (MP, MS)</p>

<div class="poem">  <div class="stanza">
<p>No M is in P</p>
<p>All M is in S</p>
<p>Some S is not in P</p>
  </div>  </div>

<p>you have to substitute for All M is in S its converse
by limitation to get the premisses of FE<i>r</i>IO.</p>
<span class="pagenum"><a name="page180" id="page180"></a>[page&nbsp;180]</span>

<p>Two of the Minor Moods, Baroko of the Second
Figure, and Bokardo of the Third, cannot be reduced
to the First Figure by the ordinary processes of Conversion
and Transposition. It is for dealing with these
intractable moods that Contraposition is required.
Thus in BA<i>r</i>O<i>k</i>O of the Second (PM, SM)</p>

<div class="poem">  <div class="stanza">
<p>All P is in M.</p>
<p>Some S is not in M.</p>
  </div>  </div>

<p>Substitute for the Major Premiss its Converse by
Contraposition, and for the Minor its Formal Obverse
or Permutation, and you have FE<i>r</i>IO of the First,
with not-M as the Middle.</p>

<div class="poem">  <div class="stanza">
<p>No not-M is in P.</p>
<p>Some S is in not-M,</p>
<p>Some S is not in P.</p>
  </div>  </div>

<p>The processes might be indicated by the Mnemonic
FA<i>cs</i>O<i>c</i>O, with <i>c</i> indicating the contraposition of the
predicate term or Formal Obversion.</p>

<p>The reduction of BO<i>k</i>A<i>rd</i>O,</p>

<div class="poem">  <div class="stanza">
<p>Some M is not in P</p>
<p>All M is in S</p>
<p>Some S is not in P,</p>
  </div>  </div>

<p>is somewhat more intricate. It may be indicated by
DO<i>cs</i>A<i>m</i>O<i>sc</i>. You substitute for the Major Premiss
its Converse by Contraposition, transpose the Premisses
and you have DA<i>r</i>II.</p>

<div class="poem">  <div class="stanza">
<p>All M is in S.</p>
<p>Some not-P is in M.</p>
<p>Some not-P is in S.</p>
  </div>  </div>
<span class="pagenum"><a name="page181" id="page181"></a>[page&nbsp;181]</span>
<p>Convert now the conclusion by Contraposition, and
you have Some S is not in P.</p>

<p>The author of the Mnemonic apparently did not
recognise Contraposition, though it was admitted by
Boethius; and, it being impossible without this to
demonstrate the validity of Baroko and Bokardo by
showing them to be equivalent with valid moods of
the First Figure, he provided for their demonstration
by the special process known as <i>Reductio ad absurdum</i>.
B indicates that Barbara is the medium.</p>

<p>The rationale of the process is this. It is an imaginary
opponent that you reduce to an absurdity or self-contradiction.
You show that it is impossible with
consistency to admit the premisses and at the same
time deny the conclusion. For, let this be done; let it
be admitted as in BA<i>r</i>O<i>k</i>O that,</p>

<div class="poem">  <div class="stanza">
<p>All P is in M</p>
<p>Some S is not in M,</p>
  </div>  </div>

<p>but denied that Some S is not in P. The denial of a
proposition implies the admission of its Contradictory.
If it is not true that Some S is not in P, it must be
true that All S is in P. Take this along with the
admission that All P is in M, and you have a syllogism
in BA<i>rb</i>A<i>r</i>A,</p>

<div class="poem">  <div class="stanza">
<p>All P is in M</p>
<p>All S is in P,</p>
  </div>  </div>

<p>yielding the conclusion All S is in M. If then the
original conclusion is denied, it follows that All S is
in M. But this contradicts the Minor Premiss, which
has been admitted to be true. It is thus shown that
<span class="pagenum"><a name="page182" id="page182"></a>[page&nbsp;182]</span>
an opponent cannot admit the premisses and deny the
conclusion without contradicting himself.</p>

<p>The same process may be applied to Bokardo.</p>

<div class="poem">  <div class="stanza">
<p>Some M is not in P.</p>
<p>All M is in S.</p>
<p>Some S is not in P.</p>
  </div>  </div>

<p>Deny the conclusion, and you must admit that All
S is in P. Syllogised in Barbara with All M is in S,
this yields the conclusion that All M is in P, the
contradictory of the Major Premiss.</p>

<p>The beginner may be reminded that the argument
<i>ad absurdum</i> is not necessarily confined to Baroko and
Bokardo. It is applied to them simply because they
are not reducible by the ordinary processes to the First
Figure. It might be applied with equal effect to
other Moods, DI<i>m</i>A<i>r</i>I<i>s</i>, <i>e.g.</i>, of the Third.</p>

<div class="poem">  <div class="stanza">
<p>Some M is in P.</p>
<p>All M is in S.</p>
<p>Some S is in P.</p>
  </div>  </div>

<p>Let Some S is in P be denied, and No S is in P must
be admitted. But if No S is in P and All M is in S,
it follows (in Celarent) that No M is in P, which an
opponent cannot hold consistently with his admission
that Some M is in P.</p>

<p>The beginner sometimes asks: What is the use of
reducing the Minor Figures to the First? The reason
is that it is only when the relations between the terms
are stated in the First Figure that it is at once apparent
whether or not the argument is valid under the
Axiom or <i>Dictum de Omni</i>. It is then undeniably
evident that if the Dictum holds the argument holds.
<span class="pagenum"><a name="page183" id="page183"></a>[page&nbsp;183]</span>
And if the Moods of the First Figure hold, their
equivalents in the other Figures must hold too.</p>

<p>Aristotle recognised only two of the Minor Figures,
the Second and Third, and thus had in all only fourteen
valid moods.</p>

<p>The recognition of the Fourth Figure is attributed
by Averroes to Galen. Averroes himself rejects it on
the ground that no arguments expressed naturally,
that is, in accordance with common usage, fall into
that form. This is a sufficient reason for not spending
time upon it, if Logic is conceived as a science that
has a bearing upon the actual practice of discussion or
discursive thought. And this was probably the reason
why Aristotle passed it over.</p>

<p>If however the Syllogism of Terms is to be completed
as an abstract doctrine, the Fourth Figure must
be noticed as one of the forms of premisses that contain
the required relation between the extremes. There is
a valid syllogism between the extremes when the
relations of the three terms are as stated in certain
premisses of the Fourth Figure.</p>

<h3 style="margin-top: 2em;">III.&mdash;<span class="sc">The Sorites.</span></h3>

<p>A chain of Syllogisms is called a Sorites. Thus:&mdash;</p>

<div class="poem">  <div class="stanza">
<p class="i4">All A is in B.</p>
<p class="i4">All B is in C.</p>
<p class="i4">All C is in D.</p>
<p class="i8">:</p>
<p class="i8">:</p>
<p class="i8">:</p>
<p class="i8">:</p>
<p class="i4">All X is in Z.</p>
<p class="i2">.<sup>.</sup>. All A is in Z.</p>
  </div>  </div>

<p>A Minor Premiss can thus be carried through a
<span class="pagenum"><a name="page184" id="page184"></a>[page&nbsp;184]</span>
series of Universal Propositions each serving in turn
as a Major to yield a conclusion which can be syllogised
with the next. Obviously a Sorites may contain
one particular premiss, provided it is the first; and
one universal negative premiss, provided it is the last.
A particular or a negative at any other point in the
chain is an insuperable bar.</p>

<p class="note1"><a id="footnotePIV-ChII1" name="footnotePIV-ChII1"></a><a class="footnote" href="#footnotetagPIV-ChII1">Footnote 1:</a>
<ins title="Hotan oun horoi treis autôs echôsi pros allêlous ôste ton eschaton en holô einai tô mesô, kai ton meson en holô tô krôtô ê einai ê mê einai, anankê tôn akrôn einai syllogismon teleion.">
&#8013;&tau;&alpha;&nu; &omicron;&#8018;&nu; &#8005;&rho;&omicron;&iota; &tau;&rho;&epsilon;&#8150;&sigmaf; &alpha;&#8020;&tau;&omega;&sigmaf; &#7956;&chi;&omega;&sigma;&iota;
&pi;&rho;&#8056;&sigmaf; &#7936;&lambda;&lambda;&#942;&lambda;&omicron;&upsilon;&sigmaf; &#8037;&sigma;&tau;&epsilon; &tau;&#8056;&nu; &#7956;&sigma;&chi;&alpha;&tau;&omicron;&nu;
&#7952;&nu; &#8005;&lambda;&#8179; &epsilon;&#7990;&nu;&alpha;&iota; &tau;&#8183; &mu;&#941;&sigma;&#8179;, &kappa;&alpha;&#8054; &tau;&#8056;&nu;
&mu;&#941;&sigma;&omicron;&nu; &#7952;&nu; &#8005;&lambda;&#8179; &tau;&#8183; &kappa;&rho;&#974;&tau;&#8179; &#7970; &epsilon;&#7990;&nu;&alpha;&iota; &#7970;
&mu;&#8052; &epsilon;&#7990;&nu;&alpha;&iota;, &#7936;&nu;&#940;&gamma;&kappa;&eta; &tau;&#8182;&nu; &#7936;&kappa;&rho;&omega;&nu;
&epsilon;&#7990;&nu;&alpha;&iota; &sigma;&upsilon;&lambda;&lambda;&omicron;&gamma;&iota;&sigma;&mu;&#8056;&nu;
&tau;&#941;&lambda;&epsilon;&iota;&omicron;&nu;
</ins> (Anal. Prior.,
i. 4.)</p>
<span class="pagenum"><a name="page185" id="page185"></a>[page&nbsp;185]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter III.</span></h3>

<h3>THE DEMONSTRATION OF THE SYLLOGISTIC MOODS.
&mdash;THE CANONS OF THE SYLLOGISM.</h3>

<p>How do we know that the nineteen moods are the
only possible forms of valid syllogism?</p>

<p>Aristotle treated this as being self-evident upon trial
and simple inspection of all possible forms in each of
his three Figures.</p>

<p>Granted the parity between predication and position
in or out of a limited enclosure (term, <ins title="horos"><span style="font-size: 0.9em;">&#8004;</span>&rho;&omicron;&sigmaf;</ins>), it is a
matter of the simplest possible reasoning. You have
three such terms or enclosures, S, P and M; and you
are given the relative positions of two of them to the
third as a clue to their relative positions to one
another. Is S in or out of P, and is it wholly in or
wholly out or partly in or partly out? You know how
each of them lies toward the third: when can you
tell from this how S lies towards P?</p>

<p>We have seen that when M is wholly in or out of P,
and S wholly or partly in M, S is wholly or partly in
or out of P.</p>

<p>Try any other given positions in the First Figure,
and you find that you cannot tell from them how S
lies relatively to P. Unless the Major Premiss is
Universal, that is, unless M lies wholly in or out of P,
you can draw no conclusion, whatever the Minor
<span class="pagenum"><a name="page186" id="page186"></a>[page&nbsp;186]</span>
Premiss may give. Given, <i>e.g.</i>, All S is in M, it may
be that All S is in P, or that No S is in P, or that
Some S is in P, or that Some S is not in P.</p>

<div class="figcenter"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-195-1.png" width="195" height="136" alt="Circles of M and P, overlapping, with 3 instances of a circle of S: 1. S in M, but not in P; 2. S in the overlap of M and P; 3. S in M, some S in P." /></div>

<p>Again, unless the Minor Premiss is affirmative, no
matter what the Major Premiss may be, you can draw
no conclusion. For if the Minor Premiss is negative,
all that you know is that All S or Some S lies somewhere
outside M; and however M may be situated
relatively to P, that knowledge cannot help towards
knowing how S lies relatively to P. All S may be P,
or none of it, or part of it. Given all M is in P; the
All S (or Some S) which we know to be outside of M
may lie anywhere in P or out of it.</p>

<div class="figcenter"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-195-2.png" width="203" height="212" alt=" Concentric circles of P and M, M in center, with 5 instances of circle of S: 1. S wholly outside P and M; 2. S partly overlapping both P and M, and partly outside both; 3. S overlapping P, but outside M; 4. S wholly within P, but wholly outside M; 5. S touching circle of P, but outside both circles." /></div>

<p>Similarly, in the Second Figure, trial and simple
inspection of all possible conditions shows that there
can be no conclusion unless the Major Premiss is
universal, and one of the premisses negative.</p>

<p>Another and more common way of eliminating the
invalid forms, elaborated in the Middle Ages, is to
formulate principles applicable irrespective of Figure,
<span class="pagenum"><a name="page187" id="page187"></a>[page&nbsp;187]</span>
and to rule out of each Figure the moods that do not
conform to them. These regulative principles are
known as The Canons of the Syllogism.</p>

<p><i><b>Canon I.</b></i> In every syllogism there should be three,
and not more than three, terms, and the terms must
be used throughout in the same sense.</p>

<p>It sometimes happens, owing to the ambiguity of
words, that there seem to be three terms when there
are really four. An instance of this is seen in the
sophism:&mdash;</p>

<div class="poem">  <div class="stanza">
<p class="i4">He who is most hungry eats most.</p>
<p class="i4">He who eats least is most hungry.</p>
<p class="i2">.<sup>.</sup>. He who eats least eats most.</p>
  </div>  </div>

<p>This Canon, however, though it points to a real danger
of error in the application of the syllogism to actual
propositions, is superfluous in the consideration of
purely formal implication, it being a primary assumption
that terms are univocal, and remain constant
through any process of inference.</p>

<p>Under this Canon, Mark Duncan says (<i>Inst. Log.</i>,
iv. 3, 2), is comprehended another commonly expressed
in this form: There should be nothing in the conclusion
that was not in the premisses: inasmuch as if
there were anything in the conclusion that was in
neither of the premisses, there would be four terms in
the syllogism.</p>

<p>The rule that in every syllogism there must be
three, and only three, propositions, sometimes given
as a separate Canon, is only a corollary from Canon I.</p>

<p><i><b>Canon II.</b></i> The Middle Term must be distributed
once at least in the Premisses.</p>

<p>The Middle Term must either be wholly in, or
wholly out of, one or other of the Extremes before
<span class="pagenum"><a name="page188" id="page188"></a>[page&nbsp;188]</span>
it can be the means of establishing a connexion
between them. If you know only that it is partly in
both, you cannot know from that how they lie relatively
to one another: and similarly if you know only that it
is partly outside both.</p>

<p>The Canon of Distributed Middle is a sort of counter-relative
supplement to the <i>Dictum de Omni</i>. Whatever
is predicable of a whole distributively is predicable of
all its several parts. If in neither premiss there is a
predication about the whole, there is no case for the
application of the axiom.</p>

<p><i><b>Canon III.</b></i> No term should be distributed in the
conclusion that was not distributed in the premisses.</p>

<p>If an assertion is not made about the whole of a
term in the premisses, it cannot be made about the
whole of that term in the conclusion without going
beyond what has been given.</p>

<p>The breach of this rule in the case of the Major
term is technically known as the Illicit Process of the
Major: in the case of the Minor term, Illicit Process
of the Minor.</p>

<p>Great use is made of this canon in cutting off invalid
moods. It must be remembered that the Predicate
term is "distributed" or taken universally in O (Some
S is not in P) as well as in E (No S is in P); and
that P is never distributed in affirmative propositions.</p>

<p><i><b>Canon IV.</b></i> No conclusion can be drawn from two
negative premisses.</p>

<p>Two negative premisses are really tantamount to a
declaration that there is no connexion whatever between
the Major and Minor (as quantified in the premisses)
and the term common to both premisses; in short, that
this is not a Middle term&mdash;that the condition of a valid
Syllogism does not exist.</p>
<span class="pagenum"><a name="page189" id="page189"></a>[page&nbsp;189]</span>

<p>There is an apparent exception to this when the
real Middle in an argument is a contrapositive term,
not-M. Thus:&mdash;</p>

<div class="poem">  <div class="stanza">
<p class="i4">Nobody who is not thirsty is suffering from fever.</p>
<p class="i4">This person is not thirsty.</p>
<p class="i2">.<sup>.</sup>. He is not suffering from fever.</p>
  </div>  </div>

<p>But in such cases it is really the absence of a quality
or rather the presence of an opposite quality on which
we reason; and the Minor Premiss is really Affirmative
of the form S is in not-M.</p>

<p><i><b>Canon V.</b></i> If one premiss is negative, the conclusion
must be negative.</p>

<p>If one premiss is negative, one of the Extremes
must be excluded in whole or in part from the Middle
term. The other must therefore (under Canon IV.)
declare some coincidence between the Middle term and
the other extreme; and the conclusion can only affirm
exclusion in whole or in part from the area of this
coincidence.</p>

<p><i><b>Canon VI.</b></i> No conclusion can be drawn from two
particular premisses.</p>

<p>This is evident upon a comparison of terms in all
possible positions, but it can be more easily demonstrated
with the help of the preceding canons. The
premisses cannot both be particular and yield a conclusion
without breaking one or other of those canons.</p>

<p>Suppose both are affirmative, II, the Middle is not
distributed in either premiss.</p>

<p>Suppose one affirmative and the other negative, IO,
or OI. Then, whatever the Figure may be, that is,
whatever the order of the terms, only one term can be
distributed, namely, the predicate of O. This (Canon
II.) must be the Middle. But in that case there must
<span class="pagenum"><a name="page190" id="page190"></a>[page&nbsp;190]</span>
be Illicit Process of the Major (Canon III.), for one of
the premisses being negative, the conclusion is negative
(Canon V.), and P its predicate is distributed. Briefly,
in a negative mood, both Major and Middle must be
distributed, and if both premisses are particular this
cannot be.</p>

<p><i><b>Canon VII.</b></i> If one Premiss is particular the conclusion
is particular.</p>

<p>This canon is sometimes combined with what we
have given as Canon V., in a single rule: "The
conclusion follows the weaker premiss".</p>

<p>It can most compendiously be demonstrated with
the help of the preceding canons.</p>

<p>Suppose both premisses affirmative, then, if one is
particular, only one term can be distributed in the
premisses, namely, the subject of the Universal
affirmative premiss. By Canon II., this must be the
Middle, and the Minor, being undistributed in the
Premisses, cannot be distributed in the conclusion.
That is, the conclusion cannot be Universal&mdash;must be
particular.</p>

<p>Suppose one Premiss negative, the other affirmative.
One premiss being negative, the conclusion must be
negative, and P must be distributed in the conclusion.
Before, then, the conclusion can be universal, all three
terms, S, M, and P, must, by Canons II. and III., be
distributed in the premisses. But whatever the Figure
of the premisses, only two terms can be distributed.
For if one of the Premisses be O, the other must be A,
and if one of them is E, the other must be I. Hence
the conclusion must be particular, otherwise there will
be illicit process of the Minor, or of the Major, or of
the Middle.</p>

<p>The argument may be more briefly put as follows:
<span class="pagenum"><a name="page191" id="page191"></a>[page&nbsp;191]</span>
In an affirmative mood, with one premiss particular,
only one term can be distributed in the premisses, and
this cannot be the Minor without leaving the Middle
undistributed. In a negative mood, with one premiss
particular, only two terms can be distributed, and the
Minor cannot be one of them without leaving either
the Middle or the Major undistributed.</p>

<p style="margin-top: 2.5em">Armed with these canons, we can quickly determine,
given any combination of three propositions in one of
the Figures, whether it is or is not a valid Syllogism.</p>

<p>Observe that though these canons hold for all the
Figures, the Figure must be known, in all combinations
containing A or O, before we can settle a question of
validity by Canons II. and III., because the distribution
of terms in A and O depends on their order in
predication.</p>

<p>Take AEE. In Fig. I.&mdash;</p>

<div class="poem">  <div class="stanza">
<p>All M is in P</p>
<p>No S is in M</p>
<p>No S is in P&mdash;</p>
  </div>  </div>

<p>the conclusion is invalid as involving an illicit process
of the Major. P is distributed in the conclusion and
not in the premisses.</p>

<p>In Fig. II. AEE&mdash;</p>

<div class="poem">  <div class="stanza">
<p>All P is in M</p>
<p>No S is in M</p>
<p>No S is in P&mdash;</p>
  </div>  </div>

<p>the conclusion is valid (Camestres).</p>
<span class="pagenum"><a name="page192" id="page192"></a>[page&nbsp;192]</span>

<p>In Fig. III. AEE&mdash;</p>

<div class="poem">  <div class="stanza">
<p>All M is in P</p>
<p>No M is in S</p>
<p>No S is in P&mdash;</p>
  </div>  </div>

<p>the conclusion is invalid, there being illicit process of
the Major.</p>

<p>In Fig. IV. AEE is valid (Camenes).</p>

<p>Take EIO. A little reflection shows that this combination
is valid in all the Figures if in any, the distribution
of the terms in both cases not being affected
by their order in predication. Both E and I are simply
convertible. That the combination is valid is quickly
seen if we remember that in negative moods both
Major and Middle must be distributed, and that this is
done by E.</p>

<p>EIE is invalid, because you cannot have a universal
conclusion with one premiss particular.</p>

<p>AII is valid in Fig. I. or Fig. III., and invalid in
Figs. II. and IV., because M is the subject of A in I.
and III. and predicate in II. and IV.</p>

<p>OAO is valid only in Fig. III., because only in that
Figure would this combination of premisses distribute
both M and P.</p>

<p>Simple exercises of this kind may be multiplied till
all possible combinations are exhausted, and it is seen
that only the recognised moods stand the test.</p>

<p style="margin-top: 2.5em">If a more systematic way of demonstrating the valid
moods is desired, the simplest method is to deduce
from the Canons special rules for each Figure. Aristotle
arrived at these special rules by simple inspection, but
it is easier to deduce them.</p>
<span class="pagenum"><a name="page193" id="page193"></a>[page&nbsp;193]</span>

<p style="margin-top: 2em">I. In the First Figure, the Major Premiss must be
Universal, and the Minor Premiss affirmative.</p>

<p>To make this evident by the Canons, we bear in
mind the Scheme or Figure&mdash;</p>

<div class="poem">  <div class="stanza">
<p>M in P</p>
<p>S in M&mdash;</p>
  </div>  </div>

<p>and try the alternatives of Affirmative Moods and
Negative Moods. Obviously in an affirmative mood
the Middle is undistributed unless the Major Premiss
is Universal. In a negative mood, (1) If the Major
Premiss is O, the Minor must be affirmative, and M is
undistributed; (2) if the Major Premiss is I, M may
be distributed by a negative Minor Premiss, but in
that case there would be an illicit process of the Major&mdash;P
being distributed in the conclusion (Canon V.) and
not in the Premisses. Thus the Major Premiss can
neither be O nor I, and must therefore be either A or
E, <i>i.e.</i>, must be Universal.</p>

<p>That the Minor must be affirmative is evident, for if
it were negative, the conclusion must be negative
(Canon V.) and the Major Premiss must be affirmative
(Canon IV.), and this would involve illicit process of
the Major, P being distributed in the conclusion and
not in the Premisses.</p>

<p>These two special rules leave only four possible
valid forms in the First Figure. There are sixteen
possible combinations of premisses, each of the four
types of proposition being combinable with itself and
with each of the others.</p>

<table style="margin-left:25%;" summary="The sixteen possible combinations of premisses">
<tr>
       <td class="left2b">AA<br />AE<br />AI<br />AO</td>
       <td class="left2b">EA<br />EE<br />EI<br />EO</td>
       <td class="left2b">IA<br />IE<br />II<br />IO</td>
       <td class="left2b">OA<br />OE<br />OI<br />OO</td>
</tr>
</table>
<span class="pagenum"><a name="page194" id="page194"></a>[page&nbsp;194]</span>

<p>Special Rule I. wipes out the columns on the right
with the particular major premisses; and AE, EE,
AO, and EO are rejected by Special Rule II., leaving
BA<i>rb</i>A<i>r</i>A, CE<i>l</i>A<i>r</i>E<i>nt</i>, DA<i>r</i>II and
FE<i>r</i>IO.</p>

<p style="margin-top: 2em">II. In the Second Figure, only Negative Moods
are possible, and the Major Premiss must be universal.</p>

<p>Only Negative moods are possible, for unless one
premiss is negative, M being the predicate term in
both&mdash;</p>

<div class="poem">  <div class="stanza">
<p>P in M</p>
<p>S in M&mdash;</p>
  </div>  </div>

<p>is undistributed.</p>

<p>Only negative moods being possible, there will be
illicit process of the Major unless the Major Premiss
is universal, P being its subject term.</p>

<p>These special rules reject AA and AI, and the two
columns on the right.</p>

<p>To get rid of EE and EO, we must call in the
general Canon IV.; which leaves us with EA, AE,
EI, and AO&mdash;CE<i>s</i>A<i>r</i>E, CA<i>m</i>E<i>str</i>E<i>s</i>,
FE<i>st</i>I<i>n</i>O
BA<i>r</i>O<i>k</i>O.</p>

<p style="margin-top: 2em">III. In the Third Figure, the Minor Premiss must
be affirmative.</p>

<p>Otherwise, the conclusion would be negative, and
the Major Premiss affirmative, and there would be
illicit process of the Major, P being the predicate term
in the Major Premiss.</p>

<div class="poem">  <div class="stanza">
<p>M in P</p>
<p>M in S.</p>
  </div>  </div>

<p>This cuts off AE, EE, IE, OE, AO, EO, IO, OO,&mdash;the
second and fourth rows in the above list.</p>

<p>II and OI are inadmissible by Canon VI.; which
<span class="pagenum"><a name="page195" id="page195"></a>[page&nbsp;195]</span>
leaves AA, IA, AI, EA, OA, EI&mdash;DA<i>r</i>A<i>pt</i>I,
DI<i>s</i>A<i>m</i>I<i>s</i>,
DA<i>t</i>I<i>s</i>I, FE<i>l</i>A<i>pt</i>O<i>n</i>, BO<i>k</i>A<i>rd</i>O,
FE<i>r</i>I<i>s</i>O&mdash;three affirmative
moods and three negative.</p>

<p style="margin-top: 2em">IV. The Fourth Figure is fenced by three special
rules. (1) In negative moods, the Major Premiss is
universal. (2) If the Minor is negative, both premisses
are universal. (3) If the Major is affirmative, the
Minor is universal.</p>

<p>(1) Otherwise, the Figure being</p>

<div class="poem">  <div class="stanza">
<p>P in M</p>
<p>M in S,</p>
  </div>  </div>

<p>there would be illicit process of the Major.</p>

<p>(2) The Major must be universal by special rule (1),
and if the Minor were not also universal, the Middle
would be undisturbed.</p>

<p>(3) Otherwise M would be undistributed.</p>

<p>Rule (1) cuts off the right-hand column, OA, OE,
OI, and OO; also IE and IO.</p>

<p>Rule (2) cuts off AO, EO.</p>

<p>Rule (3) cuts off AI, II.</p>

<p>EE goes by general Canon IV.; and we are left
with AA, AE, IA, EA, EI&mdash;B<i>r</i>A<i>m</i>A<i>nt</i>I<i>p</i>,
CA<i>m</i>E<i>n</i>E<i>s</i>,
DI<i>m</i>A<i>r</i>I<i>s</i>, FE<i>s</i>A<i>p</i>O,
F<i>r</i>E<i>s</i>I<i>s</i>O<i>n</i>.</p>
<span class="pagenum"><a name="page196" id="page196"></a>[page&nbsp;196]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter IV.</span></h3>

<h3>THE ANALYSIS OF ARGUMENTS INTO SYLLOGISTIC FORMS.</h3>

<p>Turning given arguments into syllogistic form is apt
to seem as trivial and useless as it is easy and
mechanical. In most cases the necessity of the conclusion
is as apparent in the plain speech form as in
the artificial logical form. The justification of such
exercises is that they give familiarity with the instrument,
serving at the same time as simple exercises in
ratiocination: what further uses may be made of the
instrument once it is mastered, we shall consider as
we proceed.</p>

<h3 style="margin-top: 2em;">I.&mdash;<span class="sc">First Figure.</span></h3>

<p>Given the following argument to be put into Syllogistic
form: "No war is long popular: for every war
increases taxation; and the popularity of anything
that touches the pocket is short-lived".</p>

<p>The simplest method is to begin with the conclusion&mdash;"No
war is long popular"&mdash;No S is P&mdash;then to
examine the argument to see whether it yields premisses
of the necessary form. Keeping the form in mind,
Celarent of Fig. I.&mdash;</p>

<div class="poem">  <div class="stanza">
<p>No M is P</p>
<p>All S is M</p>
<p>No S is P&mdash;</p>
  </div>  </div>

<span class="pagenum"><a name="page197" id="page197"></a>[page&nbsp;197]</span>
<p>we see at once that "Every war increases taxation" is
of the form All S is M. Does the other sentence yield
the Major Premiss No M is P, when M represents the
increasing of taxation, <i>i.e.</i>, a class bounded by that
attribute? We see that the last sentence of the argument
is equivalent to saying that "Nothing that
increases taxation is long popular"; and this with the
Minor yields the conclusion in Celarent.</p>

<div class="poem">  <div class="stanza">
<p>Nothing that increases taxation is long popular.</p>
<p>Every war increases taxation.</p>
<p>No war is long popular.</p>
  </div>  </div>

<p style="margin-top: 2.5em">Observe, now, what in effect we have done in thus
reducing the argument to the First Figure. In effect,
a general principle being alleged as justifying a certain
conclusion, we have put that principle into such a form
that it has the same predicate with the conclusion.
All that we have then to do in order to inspect the
validity of the argument is to see whether the subject
of the conclusion is contained in the subject of the
general principle. Is war one of the things that
increase taxation? Is it one of that class? If so,
then it cannot long be popular, long popularity being
an attribute that cannot be affirmed of any of that
class.</p>

<p>Reducing to the first figure, then, amounts simply
to making the predication of the proposition alleged
as ground uniform with the conclusion based upon it.
The minor premiss or applying proposition amounts to
saying that the subject of the conclusion is contained in
the subject of the general principle. Is the subject of
the conclusion contained in the subject of the general
principle when the two have identical predicates? If
<span class="pagenum"><a name="page198" id="page198"></a>[page&nbsp;198]</span>
so, the argument falls at once under the <i>Dictum de
Omni et Nullo</i>.</p>

<p style="margin-top: 2.5em">Two things may be noted concerning an argument
thus simplified.</p>

<p>1. It is not necessary, in order to bring an argument
under the <i>dictum de omni</i>, to reduce the predicate to the
form of an extensive term. In whatever form, abstract
or concrete, the predication is made of the middle term,
it is applicable in the same form to that which is contained
in the middle term.</p>

<p>2. The quantity of the Minor Term does not require
special attention, inasmuch as the argument does not
turn upon it. In whatever quantity it is contained in
the Middle, in that quantity is the predicate of the
Middle predicable of it.</p>

<p>These two points being borne in mind, the attention
may be concentrated on the Middle Term and its
relations with the extremes.</p>

<p>That the predicate may be left unanalysed without
affecting the simplicity of the argument or in any way
obscuring the exhibition of its turning-point, has an
important bearing on the reduction of Modals. The
modality may be treated as part of the predicate without
in any way obscuring what it is the design of the syllogism
to make clear. We have only to bear in mind that
however the predicate may be qualified in the premisses,
the same qualification must be transferred to
the conclusion. Otherwise we should have the fallacy
of Four Terms, <i>quaternio terminorum</i>.</p>

<p>To raise the question: What is the proper form for
a Modal of Possibility, A or I? is to clear up in an
important respect our conceptions of the Universal
proposition, "Victories may be gained by accident".
<span class="pagenum"><a name="page199" id="page199"></a>[page&nbsp;199]</span>
Should this be expressed as A or I? Is the predicate
applicable to All victories or only to Some? Obviously
the meaning is that of any victory it may be true that
it was gained by accident, and if we treat the "mode"
as part of the predicate term "things that may be
gained by accident," the form of the proposition is All
S is in P.</p>

<p>But, it may be asked, does not the proposition that
victories may be gained by accident rest, as a matter
of fact, on the belief that some victories have been
gained in this way? And is not, therefore, the proper
form of proposition Some S is P?</p>

<p>This, however, is a misunderstanding. What we
are concerned with is the formal analysis of propositions
as given. And Some victories have been gained
by accident is not the formal analysis of Victories may
be gained by accident. The two propositions do not
give the same meaning in different forms: the meaning
as well as the form is different. The one is a statement
of a matter of fact: the other of an inference founded
on it. The full significance of the Modal proper may
be stated thus: In view of the fact that some victories
have been gained by accident, we are entitled to say of
any victory, in the absence of certain knowledge, that
it may be one of them.</p>

<p>A general proposition, in short, is a proposition
about a genus, taken universally.</p>

<h3 style="margin-top: 2em;">II.&mdash;<span class="sc">Second Figure.</span></h3>

<p>For testing arguments from general principles, the
First Figure is the simplest and best form of analysis.</p>

<p>But there is one common class of arguments that
fall naturally, as ordinarily expressed, into the Second
<span class="pagenum"><a name="page200" id="page200"></a>[page&nbsp;200]</span>
Figure, namely, negative conclusions from the absence
of distinctive signs or symptoms, or necessary conditions.</p>

<p>Thirst, for example, is one of the symptoms of fever:
if a patient is not thirsty, you can conclude at once
that his illness is not fever, and the argument, fully
expressed, is in the Second Figure.</p>

<div class="poem">  <div class="stanza">
<p class="i4">All fever-stricken patients are thirsty.</p>
<p class="i4">This patient is not thirsty.</p>
<p class="i2">.<sup>.</sup>. He is not fever-stricken.</p>
  </div>  </div>

<p>Arguments of this type are extremely common.</p>

<p>Armed with the general principle that ill-doers are ill-dreaders,
we argue from a man's being unsuspicious
that he is not guilty. The negative diagnosis of the
physician, as when he argues from the absence of sore
throat or the absence of a white speck in the throat
that the case before him is not one of scarlatina or
diphtheria, follows this type: and from its utility in
making such arguments explicit, the Second Figure
may be called the Figure of Negative Diagnosis.</p>

<p>It is to be observed, however, that the character of
the argument is best disclosed when the Major Premiss
is expressed by its Converse by Contraposition. It
is really from the absence of a symptom that the
physician concludes; as, for example: "No patient
that has not a sore throat is suffering from scarlatina".
And the argument thus expressed is in the First
Figure. Thus the reduction of Baroko to the First
Figure by contraposition of the Middle is vindicated as
a really useful process. The real Middle is a contrapositive
term, and the form corresponds more closely
to the reasoning when the argument is put in the First
Figure.</p>
<span class="pagenum"><a name="page201" id="page201"></a>[page&nbsp;201]</span>

<p>The truth is that if the positive term or sign or
necessary condition is prominent as the basis of the
argument, there is considerable risk of fallacy. Sore
throat being one of the symptoms of scarlatina, the
physician is apt on finding this symptom present to
jump to a positive conclusion. This is equivalent
technically to drawing a positive conclusion from
premisses of the Second Figure.</p>

<div class="poem">  <div class="stanza">
<p>All scarlatina patients have sore throat.</p>
<p>This patient has sore throat.</p>
  </div>  </div>

<p>A positive conclusion is technically known as a
Non-Sequitur (Doesn't follow). So with arguments
from the presence of a necessary condition which is
only one of many. Given that it is impossible to pass
without working at the subject, or that it is impossible
to be a good marksman without having a steady hand,
we are apt to argue that given also the presence of this
condition, a conclusion is implicated. But really the
premisses given are only two affirmatives of the
Second Figure.</p>

<blockquote><p>
"It is impossible to pass without working at the subject."
</p></blockquote>

<p>This, put into the form No not-M is P, is to say that
"None who have not worked can pass". This is
equivalent, as the converse by contraposition, with&mdash;</p>

<blockquote><p>
All capable of passing have worked at the subject.
</p></blockquote>

<p>But though Q has worked at the subject, it does not
follow that he is capable of passing. Technically the
middle is undistributed. On the other hand, if he has
not worked at the subject, it follows that he is not
capable of passing. We can draw a conclusion at
<span class="pagenum"><a name="page202" id="page202"></a>[page&nbsp;202]</span>
once from the absence of the necessary condition,
though none can be drawn from its presence alone.</p>

<h3 style="margin-top: 2em;"><span class="sc">Third Figure.</span></h3>

<p>Arguments are sometimes advanced in the form
of the Third Figure. For instance: Killing is not
always murder: for tyrannicide is not murder, and
yet it is undoubtedly killing. Or again: Unpleasant
things are sometimes salutary: for afflictions are
sometimes so, and no affliction can be called pleasant.</p>

<p>These arguments, when analysed into terms, are,
respectively, Felapton and Disamis.</p>

<div class="poem">  <div class="stanza">
<p>No tyrannicide is murder;</p>
<p>All tyrannicide is killing;</p>
<p>Some killing is not murder.</p>
  </div>  </div>

<div class="poem">  <div class="stanza">
<p>Some afflictions are salutary things;</p>
<p>All afflictions are unpleasant things;</p>
<p>Some unpleasant things are salutary things.</p>
  </div>  </div>

<p>The syllogistic form cannot in such cases pretend to
be a simplification of the argument. The argument
would be equally unmistakable if advanced in this
form: Some S is not P, for example, M. Some
killing is not murder, <i>e.g.,</i> tyrannicide. Some unpleasant
things are salutary, <i>e.g.,</i> some afflictions.</p>

<p>There is really no "deduction" in the third figure,
no leading down from general to particular. The
middle term is only an example of the minor. It is
the syllogism of Contradictory Examples.</p>

<p>In actual debate examples are produced to disprove
a universal assertion, affirmative or negative. Suppose
it is maintained that every wise man has a keen sense
of humour. You doubt this: you produce an instance
of the opposite, say Milton. The force of your contradictory
instance is not increased by exhibiting the
<span class="pagenum"><a name="page203" id="page203"></a>[page&nbsp;203]</span>
argument in syllogistic form: the point is not made
clearer.</p>

<p>The Third Figure was perhaps of some use in Yes
and No Dialectic. When you had to get everything
essential to your conclusion definitely admitted, it was
useful to know that the production of an example to
refute a generality involved the admission of two
propositions. You must extract from your opponent
both that Milton was a wise man, and that Milton had
not a keen sense of humour, before you could drive
him from the position that all wise men possess that
quality.</p>

<h3 style="margin-top: 2em;"><i>Examples for Analysis.</i></h3>

<p>Scarlet flowers have no fragrance: this flower has no
fragrance: does it follow that this flower is of a scarlet
colour?</p>

<p>Interest in the subject is an indispensable condition of
learning easily; Z is interested in the subject: he is bound,
therefore, to learn easily.</p>

<p>It is impossible to be a good shot without having a steady
hand: John has a steady hand: he is capable, therefore, of
becoming a good shot.</p>

<p>Some victories have been won by accident; for example,
Maiwand.</p>

<p>Intemperance is more disgraceful than cowardice, because
people have more opportunities of acquiring control
of their bodily appetites.</p>

<p>"Some men are not fools, yet all men are fallible."
What follows?</p>

<p>"Some men allow that their memory is not good: every
man believes in his own judgment." What is the conclusion,
and in what Figure and Mood may the argument
be expressed?</p>

<p>"An honest man's the noblest work of God: Z is an
honest man": therefore, he is&mdash;what?</p>

<p>Examine the logical connexion between the following
<span class="pagenum"><a name="page204" id="page204"></a>[page&nbsp;204]</span>
"exclamation" and "answer": "But I hear some one
exclaiming that wickedness is not easily concealed. To
which I answer, Nothing great is easy."</p>

<p>"If the attention is actively aroused, sleep becomes
impossible: hence the sleeplessness of anxiety, for anxiety
is a strained attention upon an impending disaster."</p>

<p>"To follow truth can never be a subject of regret: free
inquiry does lead a man to regret the days of his childish
faith; therefore it is not following truth."&mdash;<i>J. H. Newman.</i></p>

<p>He would not take the crown: Therefore 'tis certain he
was not ambitious.</p>

<p>As he was valiant, I honour him; as he was ambitious, I
slew him.</p>

<p>The Utopians learned the language of the Greeks with
more readiness because they were originally of the same
race with them.</p>

<p>Nothing which is cruel can be expedient, for cruelty is
most revolting to the nature of man.</p>

<p>"The fifth century saw the foundation of the Frank
dominion in Gaul, and the first establishment of the German
races in Britain. The former was effected in a single long
reign, by the energy of one great ruling tribe, which had
already modified its traditional usages, and now, by the
adoption of the language and religion of the conquered,
prepared the way for a permanent amalgamation with
them." In the second of the above sentences a general
proposition is assumed. Show in syllogistic form how the
last proposition in the sentence depends upon it.</p>

<p>"I do not mean to contend that active benevolence may
not hinder a man's advancement in the world: for advancement
greatly depends upon a reputation for excellence in
some one thing of which the world perceives that it has
present need: and an obvious attention to other things,
though perhaps not incompatible with the excellence itself,
may easily prevent a person from obtaining a reputation for
it." Pick out the propositions here given as interdependent.
Examine whether the principle alleged is sufficiently general
to necessitate a conclusion. In what form would it be so?</p>
<span class="pagenum"><a name="page205" id="page205"></a>[page&nbsp;205]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter V.</span></h3>

<h3>ENTHYMEMES.</h3>

<p>There is a certain variety in the use of the word
Enthymeme among logicians. In the narrowest
sense, it is a valid formal syllogism, with one premiss
suppressed. In the widest sense it is simply an argument,
valid or invalid, formal in expression or informal,
with only one premiss put forward or hinted at, the
other being held in the mind
(<ins title="en thymô"><span style="font-size: 0.9em;">&#7952;</span>&nu; &theta;&upsilon;&mu;<span style="font-size: 0.9em;">&#8183;</span></ins>).
This last is the Aristotelian sense.</p>

<p>It is only among formal logicians of the straitest
sect that the narrowest sense prevails. Hamilton
divides Enthymemes into three classes according as it
is the Major Premiss, the Minor Premiss, or the Conclusion
that is suppressed. Thus, a full syllogism
being:&mdash;</p>

<div class="poem">  <div class="stanza">
<p class="i4">All liars are cowards:</p>
<p class="i4">Caius is a liar:</p>
<p class="i2">.<sup>.</sup>. Caius is a coward:&mdash;</p>
  </div>  </div>

<p>this may be enthymematically expressed in three ways.</p>

<p class="ind">I. Enthymeme of the First Order (<i>Major understood</i>).</p>

<p class="ind1">
Caius is a coward; for Caius is a liar.
</p>

<p class="ind">II. Enthymeme of the Second Order (<i>Minor understood</i>).</p>

<p class="ind1">
Caius is a coward; for all liars are cowards.
</p>
<span class="pagenum"><a name="page206" id="page206"></a>[page&nbsp;206]</span>

<p class="ind">III. Enthymeme of the Third Order (<i>Conclusion
understood</i>).</p>

<p class="ind1">
All liars are cowards, and Caius is a liar.
</p>

<p>The Third Order is a contribution of Hamilton's
own. It is superfluous, inasmuch as the conclusion is
never suppressed except as a rhetorical figure of speech.
Hamilton confines the word Enthymeme to valid arguments,
in pursuance of his view that Pure Logic has
no concern with invalid arguments.</p>

<p>Aristotle used Enthymeme in the wider sense of an
elliptically expressed argument. There has been some
doubt as to the meaning of his definition, but that
disappears on consideration of his examples. He
defines an Enthymeme (Prior Analyt., ii. 27) as "a
syllogism from probabilities or signs"
(<ins title="syllogismos ex eikotôn ê sêmeiôn">&sigma;&upsilon;&lambda;&lambda;&omicron;&gamma;&iota;&sigma;&mu;<span style="font-size: 0.9em;">&#8056;</span>&sigmaf;
<span style="font-size: 0.9em;">&#7952;</span>&xi; &epsilon;<span style="font-size: 0.9em;">&#7984;</span>&kappa;&#972;&tau;&omega;&nu;
<span style="font-size: 0.9em;">&#7970;</span> &sigma;&eta;&mu;&epsilon;&#943;&omega;&nu;</ins>).
The word syllogism in this connexion
is a little puzzling. But it is plain from the
examples he gives that he meant here by syllogism not
even a correct reasoning, much less a reasoning in the
explicit form of three terms and three propositions. He
used syllogism, in fact, in the same loose sense in which
we use the words reasoning and argument, applying
without distinction of good and bad.</p>

<p>The sign, he says, is taken in three ways, in as
many ways as there are Syllogistic Figures.</p>

<p>(1) A sign interpreted in the First Figure is conclusive.
Thus: "This person has been drowned, for he
has froth in the trachea". Taken in the First Figure
with "All who have froth in the trachea have been
drowned" as a major premiss, this argument is valid.
The sign is conclusive.</p>

<p>(2) "This patient is fever-stricken, for he is thirsty."
Assumed that "All fever-stricken patients are thirsty,"
<span class="pagenum"><a name="page207" id="page207"></a>[page&nbsp;207]</span>
this is an argument in the Second Figure, but it is not
a valid argument. Thirst is a sign or symptom of
fever, but not a conclusive sign, because it is indicative
of other ailments also. Yet the argument has a certain
probability.</p>

<p>(3) "Wise men are earnest
(<ins title="spoudaioi">&sigma;&pi;&omicron;&upsilon;&delta;&alpha;<span style="font-size: 0.9em;">&#8150;&omicron;&iota;</span></ins>),
for Pittacus is earnest." Here the suppressed premiss is that
"Pittacus is wise". Fully expressed, the argument is
in the Third Figure:&mdash;</p>

<div class="poem">  <div class="stanza">
<p class="i4">Pittacus is earnest.</p>
<p class="i4">Pittacus is wise.</p>
<p class="i2">.<sup>.</sup>. Wise men are earnest.</p>
  </div>  </div>

<p>Here again the argument is inconclusive and yet it
has a certain probability. The coincidence of wisdom
with earnestness in one notable example lends a
certain air of probability to the general statement.</p>

<p>Such are Aristotle's examples or strict parallels to
them. The examples illustrate also what he says in
his <i>Rhetoric</i> as to the advantages of enthymemes. For
purposes of persuasion enthymemes are better than
explicit syllogisms, because any inconclusiveness there
may be in the argument is more likely to pass undetected.
As we shall see, one main use of the
Syllogism is to force tacit assumptions into light and
so make their true connexion or want of connexion
apparent. In Logic enthymemes are recognised only
to be shown up: the elliptical expression is a cover for
fallacy, which it is the business of the logician to strip
off.</p>

<p>In Aristotle's examples one of the premisses is
expressed. But often the arguments of common
speech are even less explicit than this. A general
principle is vaguely hinted at: a subject is referred to
<span class="pagenum"><a name="page208" id="page208"></a>[page&nbsp;208]</span>
a class the attributes of which are assumed to be
definitely known. Thus:&mdash;</p>

<blockquote><p>
He was too ambitious to be scrupulous in his choice of
means.</p>

<p>He was too impulsive not to have made many blunders.
</p></blockquote>

<p>Each of these sentences contains a conclusion and an
enthymematic argument in support of it. The hearer
is understood to have in his mind a definite idea of the
degree of ambition at which a man ceases to be
scrupulous, or the degree of impulsiveness that is
incompatible with accuracy.</p>

<p>One form of enthymeme is so common in modern
rhetoric as to deserve a distinctive name. It may be
called the <b>Enthymeme of the Abstractly Denominated
Principle</b>. A conclusion is declared to be at variance
with the principles of Political Economy, or contrary
to the doctrine of Evolution, or inconsistent with
Heredity, or a violation of the sacred principle of
Freedom of Contract. It is assumed that the hearer is
familiar with the principles referred to. As a safeguard
against fallacy, it may be well to make the
principle explicit in a proposition uniform with the
conclusion.</p>
<span class="pagenum"><a name="page209" id="page209"></a>[page&nbsp;209]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter VI.</span></h3>

<h3>THE UTILITY OF THE SYLLOGISM.</h3>

<p>The main use of the Syllogism is in dealing with
incompletely expressed or elliptical arguments from
general principals. This may be called Enthymematic
argument, understanding by Enthymeme an argument
with only one premiss put forward or hinted at, the
other being held in the mind. In order to test whether
such reasoning is sound or unsound, it is of advantage
to make the argument explicit in Syllogistic form.</p>

<p>There have been heaps and mazes of discussion
about the use of the Syllogism, much of it being
profitable as a warning against the neglect of Formal
Logic. Again and again it has been demonstrated
that the Syllogism is useless for certain purposes, and
from this it has been concluded that the Syllogism is
of no use at all.</p>

<p>The inventor of the Syllogism had a definite
practical purpose, to get at the simplest, most convincing,
undeniable and irresistible way of putting
admitted or self-evident propositions so that their
implication should be apparent. His ambition was to
furnish a method for the Yes and No Dialectician, and
the expounder of science from self-evident principles.
A question being put up for discussion, it was an
advantage to analyse it, and formulate the necessary
<span class="pagenum"><a name="page210" id="page210"></a>[page&nbsp;210]</span>
premisses: you could then better direct your interrogations
or guard your answers. The analysis is similarly
useful when you want to construct an argument from
self-evident principles.</p>

<p>All that the Syllogism could show was the consistency
of the premisses with the conclusion. The
conclusion could not go beyond the premisses, because
the questioner could not go beyond the admissions of
the respondent. There is indeed an advance, but not
an advance upon the two premisses taken together.
There is an advance upon any one of them, and this
advance is made with the help of the other. Both
must be admitted: a respondent may admit one without
being committed to the conclusion. Let him
admit both and he cannot without self-contradiction
deny the conclusion. That is all.</p>

<p>Dialectic of the Yes and No kind is no longer
practised. Does any analogous use for the Syllogism
remain? Is there a place for it as a safeguard against
error in modern debate? As a matter of fact it is
probably more useful now than it was for its original
purpose, inasmuch as modern discussion, aiming at
literary grace and spurning exact formality as smacking
of scholasticism and pedantry, is much more flabby and
confused. In the old dialectic play there was generally
a clear question proposed. The interrogative form
forced this much on the disputants. The modern
debater of the unpedantic, unscholastic school is not
so fettered, and may often be seen galloping wildly
about without any game in sight or scent, his maxim
being to&mdash;</p>

<div class="poem">  <div class="stanza">
<p>Spur boldly on, and dash through thick and thin,</p>
<p>Through sense and nonsense, never out nor in.</p>
  </div>  </div>
<span class="pagenum"><a name="page211" id="page211"></a>[page&nbsp;211]</span>

<p>Now the syllogistic analysis may often be of some
use in helping us to keep a clear head in the face of a
confused argument. There is a brilliant defence of
the syllogism as an analysis of arguments in the <i>Westminster
Review</i> for January, 1828. The article was a
notice of Whately's Logic: it was written by J. S.
Mill. For some reason it has never been reprinted,
but it puts the utility of the Syllogism on clearer
ground than Mill afterwards sought for it.</p>

<p>Can a fallacy in argument be detected at once?
Is common-sense sufficient? Common-sense would
require some inspection. How would it proceed?
Does common-sense inspect the argument in a lump
or piecemeal? All at once or step by step? It
analyses. How? First, it separates out the propositions
which contribute to the conclusion from those
which do not, the essential from the irrelevant. Then
it states explicitly all that may have been assumed
tacitly. Finally, it enumerates the propositions in
order.</p>

<p>Some such procedure as this would be adopted by
common-sense in analysing an argument. But when
common-sense has done this, it has exhibited the
argument in a series of syllogisms.</p>

<p>Such is Mill's early defence of the Syllogism. It is
weak only in one point, in failing to represent how
common-sense would arrive at the peculiar syllogistic
form. It is the peculiar form of logical analysis that
is the distinction of the syllogism. When you have
disentangled the relevant propositions you have not
necessarily put them in this form. The arguments
given in text-books to be cast into syllogistic form,
consist only as a rule of relevant propositions, but they
are not yet formal syllogisms. But common-sense
<span class="pagenum"><a name="page212" id="page212"></a>[page&nbsp;212]</span>
had only one other step to make to reach the distinctive
form. It had only to ask after analysing the
argument, Is there any form of statement specially
suitable for exhibiting the connexion between a conclusion
and the general principle on which it is alleged
to depend? Ask yourself the question, and you will
soon see that there would be an obvious advantage in
making the conclusion and the general principle
uniform, in stating them with the same predicate.
But when you do this, as I have already shown (p. 197)
you state the argument in the First Figure of the
Syllogism.</p>

<p style="margin-top: 2.5em">It must, however, be admitted that it is chiefly for
exhibiting, or forcing into light, tacit or lurking
assumptions that the Syllogistic form is of use.
Unless identity of meaning is disguised or distorted by
puzzling difference of language, there is no special
illuminative virtue in the Syllogism. The argument
in a Euclidean demonstration would not be made
clearer by being cast into formal Syllogisms.</p>

<p>Again, when the subject matter is simple, the
Syllogistic form is not really required for protection
against error. In such enthymemes as the following
for example:&mdash;</p>

<div class="poem">  <div class="stanza">
<p>She must be clever: she is so uncompromisingly ugly.</p>
<p>Romeo must be in love: for is he not seventeen?</p>
  </div>  </div>

<p>it is plain to the average intelligence without any
knowledge of Syllogism that the argument takes for
granted a general proposition and what the general
proposition is.</p>

<p>Another thing is plain to the average intelligence,
perhaps plainer than to a proficient in the use of the
<span class="pagenum"><a name="page213" id="page213"></a>[page&nbsp;213]</span>
Syllogism. Clearly we cannot infer with certainty
that a woman is clever because she is ugly, unless it
is the case that all ugly women are clever. But a
Syllogiser, seeing that no certain conclusion can be
drawn except upon this condition, is apt to dismiss
the argument as altogether worthless. This may be
specified as an error incident to the practice of the
Syllogism, that it inclines us to look for necessarily
conclusive premisses, and to deny all weight to anything
short of this. Now in ordinary life it is comparatively
seldom that such premisses can be found.
We are obliged to proceed on maxims that are not of
universal scope, and which lend only a more or less
strong colour of probability to cases that can be brought
under them. "A little learning is a dangerous thing;"
"Haste makes waste;" "Slowness of speech is a sign
of depth of thought;" "Vivacity is a sign of shallowness:"
such are the "endoxes" or commonplaces of
popular knowledge that men bring to bear in daily life.
They are not true for all cases, but some of them are true
for most or for a good many, and they may be applied
with a certain probability though they are not rigidly
conclusive. The plain man's danger is that he apply
them unthinkingly as universals: the formal logician's
danger is that, seeing them to be inapplicable as universals,
he dismisses them as being void of all
argumentative force.</p>

<p>It helps to fix the limits of Formal Logic to remember
that it lies outside its bounds to determine the degree
of probability attaching to the application of approximate
truths, such as are the staple of arguments in
ordinary affairs. Formal Logic, we may repeat, is
not concerned with degrees of truth or falsehood,
probability or improbability. It merely shows the
<span class="pagenum"><a name="page214" id="page214"></a>[page&nbsp;214]</span>
interdependency of certain arguments, the consistency
of conclusion with premisses.</p>

<p>This, however, is a function that might easily be
underrated. Its value is more indirect than direct. In
showing what is required for a certain conclusion, it
puts us on the road to a more exact estimate of the
premisses alleged, a sounder judgment of their
worth. Well begun is half done: in undertaking the
examination of any argument from authority, a
formal syllogism is a good beginning.</p>
<span class="pagenum"><a name="page215" id="page215"></a>[page&nbsp;215]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter VII.</span></h3>

<h3>CONDITIONAL ARGUMENTS.&mdash;HYPOTHETICAL SYLLOGISM,
DISJUNCTIVE SYLLOGISM, AND DILEMMA.</h3>

<p>The justification of including these forms of argument
in Logic is simply that they are sometimes used
in debate, and that confusion may arise unless the
precise meaning of the premisses employed is understood.
Aristotle did not include them as now given in
his exposition of the Syllogism, probably because they
have no connexion with the mode of reasoning together
to which he appropriated the title. The fallacies connected
with them are of such a simple kind that to
discuss as a question of method the precise place they
should occupy in a logical treatise is a waste of
ingenuity.<a id="footnotetagPIV-ChVII1" name="footnotetagPIV-ChVII1"></a><a href="#footnotePIV-ChVII1"><sup>1</sup></a></p>

<h3 style="margin-top: 2em;">I.&mdash;<span class="sc">Hypothetical Syllogisms.</span></h3>

<table align="center" summary="Hypothetical Syllogisms">
<tr>
       <td class="left2a">&nbsp;If A is B, C is D<br />&nbsp;&nbsp;&nbsp;&nbsp;A is B<br />.<sup>.</sup>. C is D</td>
       <td class="left2a"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-rightbrace.png" width="15" height="45" alt="rightbrace" border="0" /></td>
       <td class="left2a"><span class="sc">Modus</span><br /><span class="sc">Ponens.</span></td>
</tr>
<tr>
       <td class="left2a">&nbsp;If A is B, C is D<br />&nbsp;&nbsp;&nbsp;&nbsp;C is not D<br />.<sup>.</sup>. A is not B</td>
       <td class="left2a"><img src="https://brian.carnell.com/wiki/_media/etext:w:william-minto-logic-inductive-and-deductive-rightbrace.png" width="15" height="45" alt="rightbrace" border="0" /></td>
       <td class="left2a"><span class="sc">Modus</span><br /><span class="sc">Tollens.</span></td>
</tr>
</table>
<span class="pagenum"><a name="page216" id="page216"></a>[page&nbsp;216]</span>

<p>A so-called Hypothetical Syllogism is thus seen to
be a Syllogism in which the major premiss is a
<b>Hypothetical Proposition</b>, that is to say, a complex
proposition in which two propositions are given as so
related that the truth of one follows necessarily from
the truth of the other.</p>

<p>Two propositions so related are technically called
the <b>Antecedent</b> or Reason, and the <b>Consequent</b>.</p>

<p>The meaning and implication of the form, If A is B,
C is D, is expressed in what is known as the <b>Law of
Reason and Consequent</b>:&mdash;</p>

<p>"<i>When two propositions are related as Reason and
Consequent, the truth of the Consequent follows from the
truth of the Antecedent, and the falsehood of the Antecedent,
from the falsehood of the Consequent</i>".</p>

<p>If A is B, C is D, implies that If C is not D, A is
not B. If this subject is educative, it quickens the
wits; if it does not quicken the wits, it is not educative.</p>

<p>Admitted, then, that the law of Reason and Consequent
holds between two propositions&mdash;that If A is B,
C is D: admitted also the Antecedent, the truth of
the Consequent follows. This is the <b>Modus Ponens</b>
or Positive Mode, where you reach a conclusion by
obtaining the admission of the Antecedent. Admit the
Antecedent and the truth of the Consequent follows.</p>

<p>With the same Major Premiss, you may also, under
the Law of Reason and Consequent reach a conclusion
by obtaining the denial of the Consequent. This is
the <b>Modus Tollens</b> or Negative Mode. Deny the Consequent
and one is bound to deny the Antecedent.</p>

<p>But to guard against the fallacy technically known
as <b>Fallacia Consequentis</b>, we must observe what the
relation of Reason and Consequent does not imply.
<span class="pagenum"><a name="page217" id="page217"></a>[page&nbsp;217]</span>
The truth of the Consequent does not involve the
truth of the Antecedent, and the falsehood of the Antecedent
does not involve the falsehood of the Consequent.</p>

<p>"If the harbour is frozen, the ships cannot come
in." If the harbour is not frozen, it does not follow
that the ships can come in: they may be excluded by
other causes. And so, though they cannot come in, it
does not follow that the harbour is frozen.</p>

<h3 style="margin-top: 2em;">Questions Connected with Hypothetical Syllogisms.</h3>

<p>(1) <i>Are they properly called Syllogisms?</i> This is
purely a question of Method and Definition. If we
want a separate technical name for forms of argument
in which two terms are reasoned together by means of
a third, the Hypothetical Syllogism, not being in such
a form, is not properly so called. The fact is that for
the purposes of the Hypothetical Argument, we do not
require an analysis into terms at all: it is superfluous:
we are concerned only with the affirmation or denial of
the constituent propositions as wholes.</p>

<p>But if we extend the word Syllogism to cover all
arguments in which two propositions necessarily
involve a third, the Hypothetical Argument is on this
understanding properly enough called a Syllogism.</p>

<p>(2) <i>Is the inference in the Hypothetical Syllogism
Mediate or Immediate?</i></p>

<p>To answer this question we have to consider whether
the Conclusion can be drawn from either of the two
premisses without the help of the other. If it is
possible immediately, it must be educible directly
either from the Major Premiss or from the Minor.</p>

<p>(<i>a</i>) Some logicians argue as if the Conclusion were
immediately possible from the Major Premiss. The
Minor Premiss and the Conclusion, they urge, are
<span class="pagenum"><a name="page218" id="page218"></a>[page&nbsp;218]</span>
simply equivalent to the Major Premiss. But this is
a misunderstanding. "If A is B, C is D," is not
equivalent to "A is B, <i>therefore</i> C is D". "If the
harbour is frozen, the ships cannot come in" is not to
say that "the harbour is frozen, and therefore," etc.
The Major Premiss merely affirms the existence of the
relation of Reason and Consequent between the two
propositions. But we cannot thereupon assert the
Conclusion unless the Minor Premiss is also conceded;
that is, the inference of the Conclusion is Mediate,
as being from two premisses and not from one
alone.</p>

<p>(<i>b</i>) Similarly with Hamilton's contention that the
Conclusion is inferrible immediately from the Minor
Premiss, inasmuch as the Consequent is involved in
the Reason. True, the Consequent is involved in the
Reason: but we cannot infer from "A is B" to "C is
D," unless it is conceded that the relation of Reason
and Consequent holds between them; that is, unless
the Major Premiss is conceded as well as the Minor.</p>

<p>(3) <i>Can Hypothetical Syllogism be reduced to the
Categorical Form?</i></p>

<p>To oppose Hypothetical Syllogisms to Categorical
is misleading, unless we take note of the precise
difference between them. It is only in the form of the
Major Premiss that they differ: Minor Premiss and
Conclusion are categorical in both. And the meaning
of a Hypothetical Major Premiss (unless it is a mere
arbitrary convention between two disputants, to the
effect that the Consequent will be admitted if the
Antecedent is proved, or that the Antecedent will be
relinquished if the Consequent is disproved), can
always be put in the form of a general proposition,
from which, with the Minor Premiss as applying
<span class="pagenum"><a name="page219" id="page219"></a>[page&nbsp;219]</span>
proposition, a conclusion identical with the original
can be drawn in regular Categorical form.</p>

<p>Thus:&mdash;</p>

<div class="poem">  <div class="stanza">
<p class="i4">If the harbour is frozen, the ships cannot come in.</p>
<p class="i4">The harbour is frozen.</p>
<p class="i2">.<sup>.</sup>. The ships cannot come in.</p>
  </div>  </div>

<p>This is a Hypothetical Syllogism, <i>Modus Ponens</i>.
Express the Hypothetical Major in the form of the
general proposition which it implies, and you reach a
conclusion (in <i>Barbara</i>) which is only grammatically
different from the original.</p>

<div class="poem">  <div class="stanza">
<p class="i4">All frozen harbours exclude ships.</p>
<p class="i4">The harbour is frozen.</p>
<p class="i2">.<sup>.</sup>. It excludes ships.</p>
  </div>  </div>

<p>Again, take an example of the <i>Modus Tollens</i>&mdash;</p>

<div class="poem">  <div class="stanza">
<p class="i4">If rain has fallen, the streets are wet.</p>
<p class="i4">The streets are not wet.</p>
<p class="i2">.<sup>.</sup>. Rain has not fallen.</p>
  </div>  </div>

<p>This is reducible, by formulating the underlying
proposition, to <i>Camestres</i> or <i>Baroko</i> of the Second
Figure.</p>

<div class="poem">  <div class="stanza">
<p class="i4">All streets rained upon are wet.</p>
<p class="i4">The streets are not wet.</p>
<p class="i2">.<sup>.</sup>. They are not streets rained upon.</p>
  </div>  </div>

<p>Hypothetical Syllogisms are thus reducible, by
merely grammatical change<a id="footnotetagPIV-ChVII2" name="footnotetagPIV-ChVII2"></a><a href="#footnotePIV-ChVII2"><sup>2</sup></a>,
or by the statement of
<span class="pagenum"><a name="page220" id="page220"></a>[page&nbsp;220]</span>
self-evident implications, to the Categorical form.
And, similarly, any Categorical Syllogism may be
reduced to the Hypothetical form. Thus:&mdash;</p>

<div class="poem">  <div class="stanza">
<p class="i4">All men are mortal.</p>
<p class="i4">Socrates is a man.</p>
<p class="i2">.<sup>.</sup>. Socrates is mortal.</p>
  </div>  </div>

<p>This argument is not different, except in the expression
of the Major and the Conclusion, from the following:&mdash;</p>

<div class="poem">  <div class="stanza">
<p class="i4">If Socrates is a man, death will overtake him.</p>
<p class="i4">Socrates is a man.</p>
<p class="i2">.<sup>.</sup>. Death will overtake him.</p>
  </div>  </div>

<p>The advantage of the Hypothetical form in argument
is that it is simpler. It was much used in Medi&aelig;val
Disputation, and is still more popular than the
Categorical Syllogism. Perhaps the prominence given
to Hypothetical Syllogisms as syllogisms in Post-Renaissance
text-books is due to the use of them in
the formal disputations of graduands in the Universities.
It was the custom for the Disputant to expound his
argument in this form:&mdash;</p>

<div class="poem">  <div class="stanza">
<p class="i4">If so and so is the case, such and such follows.</p>
<p class="i4">So and so is the case.</p>
<p class="i2">.<sup>.</sup>. Such and such follows.</p>
  </div>  </div>

<p>To which the Respondent would reply: <i>Accipio
antecedentem, nego consequentiam</i>, and argue accordingly.
Petrus Hispanus does not give the Hypothetical
Syllogism as a Syllogism: he merely explains the true
law of Reason and Consequent in connexion with the
Fallacia Consequentis in the section on Fallacies.
(<i>Summul&aelig;. Tractatus Sextus.</i>)</p>
<span class="pagenum"><a name="page221" id="page221"></a>[page&nbsp;221]</span>

<h3 style="margin-top: 2em;">II.&mdash;<span class="sc">Disjunctive Syllogisms.</span></h3>

<p>A Disjunctive Syllogism is a syllogism in which the
Major Premiss is a <b>Disjunctive Proposition</b>, <i>i.e.</i>, one
in which two propositions are declared to be mutually
incompatible. It is of the form Either A is B, or C is
D.<a id="footnotetagPIV-ChVII3" name="footnotetagPIV-ChVII3"></a><a href="#footnotePIV-ChVII3"><sup>3</sup></a></p>

<p>If the disjunction between the alternatives is really
complete, the form implies four hypothetical propositions:&mdash;</p>

<div class="poem">  <div class="stanza">
<p>(1) If A is B, C is not D.</p>
<p>(2) If A is not B, C is D.</p>
<p>(3) If C is D, A is not B.</p>
<p>(4) If C is not D, A is B.</p>
  </div>  </div>

<p>Suppose then that an antagonist has granted you
a Disjunctive Proposition, you can, using this as a
Major Premiss, extract from him four different Conclusions,
if you can get him also to admit the requisite
Minors. The Mode of two of these is technically
called <b>Modus Ponendo Tollens</b>, the mode that denies
the one alternative by granting the other&mdash;A is B,
<i>therefore</i> C is not D; C is D, <i>therefore</i> A is not B.
The other Mode is also twice open, the <b>Modus
Tollendo Ponens</b>&mdash;A is not B, <i>therefore</i> C is D; C is
not D, <i>therefore</i> A is B.</p>

<p>Fallacy is sometimes committed through the Disjunctive
form owing to the fact that in common speech
there is a tendency to use it in place of a mere
<span class="pagenum"><a name="page222" id="page222"></a>[page&nbsp;222]</span>
hypothetical, when there are not really two incompatible
alternatives. Thus it may be said "Either the
witness is perjured, or the prisoner is guilty," when the
meaning merely is that if the witness is not perjured
the prisoner is guilty. But really there is not a valid
disjunction and a correct use of the disjunctive form,
unless four hypotheticals are implied, that is, unless
the concession of either involves the denial of the
other, and the denial of either the concession of the
other. Now the prisoner may be guilty and yet the
witness be perjured; so that two of the four hypotheticals,
namely&mdash;</p>

<div class="poem">  <div class="stanza">
<p>If the witness is perjured, the prisoner is not guilty,</p>
<p>If the prisoner is guilty, the witness is not perjured&mdash;</p>
  </div>  </div>

<p>do not necessarily hold. If, then, we would guard
against fallacy, we must always make sure before
assenting to a disjunctive proposition that there is
really a complete disjunction or mutual incompatibility
between the alternatives.</p>

<h3 style="margin-top: 2em;">III.&mdash;<span class="sc">The Dilemma.</span></h3>

<p>A Dilemma is a combination of Hypothetical and
Disjunctive propositions.</p>

<p>The word has passed into common speech, and its
ordinary use is a clue to the logical structure. We are
said to be in a dilemma when we have only two courses
open to us and both of them are attended by unpleasant
consequences. In argument we are in this position
when we are shut into a choice between two admissions,
and either admission leads to a conclusion which
we do not like. The statement of the alternatives as
the consequences hypothetically of certain conditions
is the major premiss of the dilemma: once we admit
<span class="pagenum"><a name="page223" id="page223"></a>[page&nbsp;223]</span>
that the relations of Antecedent and Consequent are
as stated, we are in a trap, if trap it is: we are on the
horns of the dilemma, ready to be tossed from one to
the other.</p>

<p>For example:&mdash;</p>

<blockquote><p>
If A is B, A is C, and if A is not B, A is D. But A
either is or is not B. Therefore, A either is C or is D.</p>

<p>If A acted of his own motive, he is a knave; if A
did not act of his own motive, he is a catspaw. But
A either acted of his own motive or he did not.
Thereupon A is either a knave or a catspaw.
</p></blockquote>

<p>This is an example of the <i>Constructive</i> Dilemma, the
form of it corresponding to the common use of the
word as a choice between equally unpleasant alternatives.
The standard example is the dilemma in which
the custodians of the Alexandrian Library are said to
have been put by the Caliph Omar in 640 <span class="sc">A.D.</span></p>

<blockquote><p>
If your books are in conformity with the Koran, they
are superfluous; if they are at variance with it, they
are pernicious. But they must either be in conformity
with the Koran or at variance with it. Therefore
they are either superfluous or pernicious.
</p></blockquote>

<p>Where caution has to be exercised is in accepting
the clauses of the Major. We must make sure that
the asserted relations of Reason and Consequent really
hold. It is there that fallacy is apt to creep in and
hide its head. The Alexandrian Librarians were rash
in accepting the first clause of the conqueror's Major:
it does not follow that the books are superfluous unless
the doctrines of the Koran are not merely sound but
contain all that is worth knowing. The propounder
of the dilemma covertly assumes this. It is in the
facility that it affords for what is technically known as
<span class="pagenum"><a name="page224" id="page224"></a>[page&nbsp;224]</span>
<i>Petitio Principii</i> that the Dilemma is a useful instrument
for the Sophist. We shall illustrate it further
under that head.</p>

<p>What is known as the <i>Destructive</i> Dilemma is of a
somewhat different form. It proceeds upon the denial
of the Consequent as involving the denial of the
Antecedent. In the Major you obtain the admission
that if a certain thing holds, it must be followed by one
or other of two consequences. You then prove by way
of Minor that neither of the alternatives is true. The
conclusion is that the antecedent is false.</p>

<p>We had an example of this in discussing whether
the inference in the Hypothetical Syllogism is Immediate.
Our argument was in this form:&mdash;</p>

<blockquote><p>
If the inference is immediate, it must be drawn
either from the Major alone or from the Minor alone.
But it cannot be drawn from the Major alone, neither
can it be drawn from the Minor alone. Therefore, it is
not immediate.
</p></blockquote>

<p>In this form of Dilemma, which is often serviceable
for clearness of exposition, we must as in the other
make sure of the truth of the Major: we must take
care that the alternatives are really the only two
open. Otherwise the imposing form of the argument
is a convenient mask for sophistry. Zeno's famous
dilemma, directed to prove that motion is impossible,
covers a <i>petitio principii</i>.</p>

<blockquote><p>
If a body moves, it must move either where it is or
where it is not. But a body cannot move where it
is: neither can it move where it is not. Conclusion,
it cannot move at all, <i>i.e.</i>, Motion is impossible.
</p></blockquote>

<p>The conclusion is irresistible if we admit the Major,
because the Major covertly assumes the point to be
<span class="pagenum"><a name="page225" id="page225"></a>[page&nbsp;225]</span>
proved. In truth, <i>if</i> a body moves, it moves neither
where it is nor where it is not, but from where it is to
where it is not. Motion consists in change of place:
the Major assumes that the place is unchanged, that is,
that there is no motion.</p>

<p class="note1"><a id="footnotePIV-ChVII1" name="footnotePIV-ChVII1"></a><a class="footnote" href="#footnotetagPIV-ChVII1">Footnote 1:</a>
For the history of Hypothetical Syllogism see Mansel's
<i>Aldrich</i>, Appendix I.</p>

<p class="note1"><a id="footnotePIV-ChVII2" name="footnotePIV-ChVII2"></a><a class="footnote" href="#footnotetagPIV-ChVII2">Footnote 2:</a>
It may be argued that the change is not merely grammatical,
and that the implication of a general proposition in a hypothetical
and <i>vice versâ</i> is a strictly logical concern. At any rate such an
implication exists, whether it is the function of the Grammarian
or the Logician to expound it.</p>

<p class="note1"><a id="footnotePIV-ChVII3" name="footnotePIV-ChVII3"></a><a class="footnote" href="#footnotetagPIV-ChVII3">Footnote 3:</a>
Some logicians prefer the form Either A is, or B is. But the
two alternatives are propositions, and if "A is" represents a proposition,
the "is" is not the Syllogistic copula. If this is
understood it does not matter: the analysis of the alternative
propositions is unessential.</p>
<span class="pagenum"><a name="page226" id="page226"></a>[page&nbsp;226]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter VIII.</span></h3>

<h3>FALLACIES IN DEDUCTIVE ARGUMENT.&mdash;PETITIO PRINCIPII AND IGNORATIO ELENCHI.</h3>

<p>The traditional treatment of Fallacies in Logic follows
Aristotle's special treatise
<ins title="Peri sophistikôn elenchôn">&Pi;&epsilon;&rho;<span style="font-size: 0.9em;">&#8054;</span>
&sigma;&omicron;&phi;&iota;&sigma;&tau;&iota;&kappa;<span style="font-size: 0.9em;">&#8182;</span>&nu;
<span style="font-size: 0.9em;">&#7952;</span>&lambda;&#941;&gamma;&chi;&omega;&nu;</ins>&mdash;Concerning
Sophistical Refutations&mdash;Pretended Disproofs&mdash;Argumentative
Tricks.</p>

<p>Regarding Logic as in the main a protection against
Fallacies, I have been going on the plan of taking each
fallacy in connexion with its special safeguard, and in
accordance with that plan propose to deal here with
the two great types of fallacy in deductive argument.
Both of them were recognised and named by Aristotle:
but before explaining them it is worth while to indicate
Aristotle's plan as a whole. Some of his Argumentative
Tricks were really peculiar to Yes-and-No Dialectic
in its most sportive forms: but his leading types, both
Inductive and Deductive, are permanent, and his plan
as a whole has historical interest. Young readers
would miss them from Logic: they appeal to the
average argumentative boy.</p>

<p>He divides Fallacies broadly into Verbal Fallacies
(<ins title="para tên lexin">&pi;&alpha;&rho;<span style="font-size: 0.9em;">&#8048;</span>
&tau;<span style="font-size: 0.9em;">&#8052;</span>&nu; &lambda;&#941;&xi;&iota;&nu;</ins>,
<i>in dictione</i>), and Non-Verbal Fallacies
(<ins title="exô tês lexeôs"><span style="font-size: 0.9em;">&#7956;</span>&xi;&omega; &tau;<span style="font-size: 0.9em;">&#8134;</span>&sigmaf;
&lambda;&#941;&xi;&epsilon;&omega;&sigmaf;</ins>), <i>extra dictionem</i>).</p>

<p>The first class are mere Verbal Quibbles, and hardly
deserve serious treatment, still less minute subdivision.
The world was young when time was spent
<span class="pagenum"><a name="page227" id="page227"></a>[page&nbsp;227]</span>
upon them. Aristotle names six varieties, but they
all turn on ambiguity of word or structure, and some
of them, being dependent on Greek syntax, cannot
easily be paralleled in another tongue.</p>

<p>(1) Ambiguity of word (<ins title="homônymia"><span style="font-size: 0.9em;">&#8001;</span>&mu;&omega;&nu;&upsilon;&mu;&#943;&alpha;</ins>). As if one were
to argue: "All cold can be expelled by heat: John's
illness is a cold: therefore it can be expelled by heat".
Or: "Some afflictions are cheering, for afflictions are
sometimes light, and light is always cheering". The
serious confusion of ambiguous words is met by
Definition, as explained at length in pt. ii. c. i.</p>

<p>(2) <i>Ambiguity of structure</i>
(<ins title="amphibolia"><span style="font-size: 0.9em;">&#7936;</span>&mu;&phi;&iota;&beta;&omicron;&lambda;&#943;&alpha;</ins>).</p>

<p>"What he was beaten with was what I saw him
beaten with: what I saw him beaten with was my
eye: therefore, what he was beaten with was my eye."</p>

<p>"How do you do?" "Do? Do what?" "I mean,
how do you feel?" "How do I feel? With my
fingers, of course; but I can see very well." "No,
no; I mean, how do you find yourself?" "Then why
did you not say so? I never exactly noticed, but I
will tell you next time I lose myself."</p>

<p>(3) <i>Illicit conjunction</i> (<ins title="synthesis">&sigma;&#973;&nu;&theta;&epsilon;&sigma;&iota;&sigmaf;</ins>).</p>

<p>Socrates is good. Socrates is a musician. Therefore
Socrates is a good musician.</p>

<p>(4) <i>Illicit disjunction</i> (<ins title="diairesis">&delta;&iota;&alpha;&#943;&rho;&epsilon;&sigma;&iota;&sigmaf;</ins>).</p>

<p>Socrates is a good musician. Therefore he is a good
man.</p>

<p>(5) <i>Ambiguity of pronunciation</i> (<ins title="prosôdia">&pi;&rho;&omicron;&sigma;<span style="font-size: 0.9em;">&#8179;</span>&delta;&#943;&alpha;</ins>),
<i>fallacia accentus</i>).</p>

<p>Analogies to words that differ only in accent, such
as <ins title="ou-with accents {psili and persipomeni}">&omicron;<span style="font-size: 0.9em;">&#8022;</span></ins> and
<ins title="ou-with accents {psili and oxia}">&omicron;<span style="font-size: 0.9em;">&#8020;</span></ins>,
may be found in differences of pronunciation.
"Hair very thick, sir," said a barber to a
customer, whose hair was bushy, but beginning to turn
grey. "Yes, I daresay. But I would rather have it
<span class="pagenum"><a name="page228" id="page228"></a>[page&nbsp;228]</span>
thick than thin." "Ah, too thick to-day, sir." "But
I don't want to dye it." "Excuse me, sir, I mean the
hair of the hatmosphere, t-o-d-a-y, to-day."</p>

<p>"He said, saddle me the ass. And they saddled
<i>him</i>."</p>

<p>(6) <i>Ambiguity of inflexion</i> (<ins title="schêma tês lexeôs">&sigma;&chi;<span style="font-size: 0.9em;">&#8134;</span>&mu;&alpha;
&tau;<span style="font-size: 0.9em;">&#8134;</span>&sigmaf; &lambda;&#941;&xi;&epsilon;&omega;&sigmaf;</ins>, <i>Figura dictionis</i>).</p>

<p>This is not easy to make intelligible in English.
The idea is that a termination may be ambiguously
interpreted, a neuter participle, <i>e.g.</i>, taken for an active.
Thus: "George is ailing". "Doing what, did you
say? Ailing? What is he ailing? Ginger-aleing?"</p>

<p>Non-Verbal Fallacies, or Fallacies in thought, are
a more important division. Aristotle distinguishes
seven.</p>

<p>Of these, three are comparatively unimportant and
trifling. One of them, known to the Schoolmen as
<i>Fallacia Plurium Interrogationum</i>, was peculiar to
Interrogative disputation. It is the trick of putting
more than one question as one, so that a simple Yes
commits the respondent to something implied. "Have
you left off beating your father?" If you answer Yes,
that implies that you have been in the habit of beating
him. "Has the practice of excessive drinking ceased
in your part of the country?" Such questions were
unfair when the Respondent could answer only Yes
or No. The modern disputant who demands a plain
answer Yes or No, is sometimes guilty of this trick.</p>

<p>Two others, the fallacies known as <i>A dicto simpliciter
ad dictum secundum quid</i>, and <i>A dicto secundum quid ad
dictum simpliciter</i>, are as common in modern dialectic as
they were in ancient. The trick, conscious or unconscious,
consists in getting assent to a statement with a
qualification and proceeding to argue as if it had been
<span class="pagenum"><a name="page229" id="page229"></a>[page&nbsp;229]</span>
conceded without qualification, and <i>vice versâ</i>. For
example, it being admitted that culture is good, a
disputant goes on to argue as if the admission applied
to some sort of culture in special, scientific, &aelig;sthetic,
philosophical or moral. The fallacy was also known
as <i>Fallacia Accidentis</i>. Proving that the Syllogism is
useless for a certain purpose, and then claiming to
have proved that it is useless for any purpose is another
example. Getting a limited admission and then
extending it indefinitely is perhaps the more common
of the two forms. It is common enough to deserve a
shorter name.</p>

<p>The <i>Fallacia Consequentis</i>, or <i>Non-Sequitur</i>, which
consists specially in ignoring the possibility of a
plurality of causes, has already been partly explained
in connexion with the Hypothetical Syllogism, and
will be explained further in the Logic of Induction.</p>

<p><i>Post hoc ergo proper hoc</i> is a purely Inductive Fallacy,
and will be explained in connexion with the Experimental
Methods.</p>
<p>There remain the two typical Deductive Fallacies,
<b>Petitio Principii</b> (Surreptitious Assumption) and <b>Ignoratio
Elenchi</b> (Irrelevant Argument) about which we
must speak more at length.</p>

<p>The phrase of which Petitio Principii or Begging the
Question is a translation&mdash;<ins title="to en archê aiteisthai">&tau;<span style="font-size: 0.9em;">&#8056;</span>
<span style="font-size: 0.9em;">&#7952;</span>&nu;
<span style="font-size: 0.9em;">&#7936;</span>&rho;&chi;<span style="font-size: 0.9em;">&#8135;</span>
&alpha;<span style="font-size: 0.9em;">&#7984;</span>&tau;&epsilon;<span style="font-size: 0.9em;">&#8150;</span>&sigma;&theta;&alpha;&iota;</ins>&mdash;was
applied by Aristotle to an argumentative trick in
debate by Question and Answer. The trick consisted
in taking for granted a proposition necessary to the
refutation without having obtained the admission of it.
Another expression for the same thing&mdash;<ins title="to en archê lambanein">&tau;<span style="font-size: 0.9em;">&#8056;</span>
<span style="font-size: 0.9em;">&#7952;</span>&nu; <span style="font-size: 0.9em;">&#7936;</span>&rho;&chi;<span style="font-size: 0.9em;">&#8135;</span>
&lambda;&alpha;&mu;&beta;&#940;&nu;&epsilon;&iota;&nu;</ins>&mdash;taking the principle for granted&mdash;is more
descriptive.</p>

<p>Generally speaking, Aristotle says, Begging the
<span class="pagenum"><a name="page230" id="page230"></a>[page&nbsp;230]</span>
Question consists in not demonstrating the theorem.
It would be in accordance with this general description
to extend the name to all cases of tacitly or covertly,
unwittingly to oneself or to one's opponent, assuming
any premiss necessary to the conclusion. It is the
fallacy of Surreptitious Assumption, and all cases of
Enthymematic or Elliptical argument, where the
unexpressed links in the chain of argument are not
fully understood, are examples of it. By contrast, the
articulate and explicit Syllogism is an <i>Expositio Principii</i>.
The only remedy for covert assumptions is to force
them into the light.<a id="footnotetagPIV-ChVIII1" name="footnotetagPIV-ChVIII1"></a><a href="#footnotePIV-ChVIII1"><sup>1</sup></a></p>

<p><i>Ignoratio Elenchi</i>, ignoring the refutation
(<ins title="tou elenchou agnoia">&tau;&omicron;<span style="font-size: 0.9em;">&#8166;</span>
<span style="font-size: 0.9em;">&#7952;</span>&lambda;&#941;&gamma;&chi;&omicron;&upsilon;
<span style="font-size: 0.9em;">&#7940;</span>&gamma;&nu;&omicron;&iota;&alpha;</ins>), is simply arguing beside the point, distracting
the attention by irrelevant considerations. It
often succeeds by proving some other conclusion which
is not the one in dispute, but has a superficial resemblance
to it, or is more or less remotely connected with
it.</p>

<p>It is easier to explain what these fallacies consist in
than to illustrate them convincingly. It is chiefly in
long arguments that the mischief is done. "A Fallacy,"
says Whately, "which when stated barely in a few
sentences would not deceive a child, may deceive half
the world if diluted in a quarto volume." Very rarely
is a series of propositions put before us in regular form
and order, all bearing on a definite point. A certain
conclusion is in dispute, not very definitely formulated
perhaps, and a mixed host of considerations are
tumbled out before us. If we were perfectly clear-headed
<span class="pagenum"><a name="page231" id="page231"></a>[page&nbsp;231]</span>
persons, capable of protracted concentration of
attention, incapable of bewilderment, always on the
alert, never in a hurry, never over-excited, absolutely
without prejudice, we should keep our attention fixed
upon two things while listening to an argument, the
point to be proved, and the necessary premisses. We
should hold the point clearly in our minds, and watch
indefatigably for the corroborating propositions. But
none of us being capable of this, all of us being subject
to bewilderment by a rapid whirl of statements, and all
of us biased more or less for or against a conclusion,
the sophist has facilities for doing two things&mdash;taking
for granted that he has stated the required premisses
(<i>petitio principii</i>), and proving to perfect demonstration
something which is not the point in dispute, but which
we are willing to mistake for it (<i>ignoratio elenchi</i>).</p>

<p>It is chiefly in the heat of argument that either
Petitio or Ignoratio succeeds. When a fallacy continues
to perplex us in cold blood, it must have in its
favour either some deeply-rooted prejudice or some
peculiar intricacy in the language used, or some
abstruseness in the matter. If we are not familiar
with the matter of the argument, and have but a vague
hold of the words employed, we are, of course, much
more easily imposed upon.</p>

<p>The famous Sophisms of antiquity show the fascination
exercised over us by proving something, no matter
how irrelevant. If certain steps in an argument are
sound, we seem to be fascinated by them so that we
cannot apply our minds to the error, just as our senses
are fascinated by an expert juggler. We have seen
how plausibly Zeno's argument against the possibility
of motion hides a Petitio: the Fatalist Dilemma is
another example of the same sort.</p>
<span class="pagenum"><a name="page232" id="page232"></a>[page&nbsp;232]</span>

<blockquote><p>
If it is fated that you die, you will die whether you
call in a doctor or not, and if it is fated that you will
recover, you will recover whether you call in a doctor
or not. But it must be fated either that you die or
that you recover. <i>Therefore</i>, you will either die or
recover whether you call in a doctor or not.
</p></blockquote>

<p>Here it is tacitly assumed in the Major Premiss that
the calling in of a doctor cannot be a link in the fated
chain of events. In the statement of both the alternative
conditions, it is assumed that Fate does not act
through doctors, and the conclusion is merely a
repetition of this assumption, a verbal proposition
after an imposing show of argument. "If Fate does
not act through doctors, you will die whether you call
in a doctor or not."</p>

<p>The fallacy in this case is probably aided by our
veneration for the grand abstraction of Fate and the
awful idea of Death, which absorbs our attention and
takes it away from the artful <i>Petitio</i>.</p>

<p>The Sophism of Achilles and the Tortoise is the
most triumphant of examples of <i>Ignoratio Elenchi</i>.</p>

<p>The point that the Sophism undertakes to prove is
that Achilles can never overtake a Tortoise once it
has a certain start: what it really proves, and proves
indisputably, is that he cannot overtake the Tortoise
within a certain space or time.</p>

<p>For simplicity of exposition, let us assume that the
Tortoise has 100 yards start and that Achilles runs ten
times as fast. Then, clearly, Achilles will not come
up with it at the end of 100 yards, for while he has run
100, the Tortoise has run 10; nor at the end of 110, for
then the Tortoise has run 1 more; nor at the end of 111,
for then the Tortoise has run <span style="font-size: 0.8em"><sup>1</sup></span>&frasl;<span style="font-size: 0.8em"><sub>10</sub></span> more; nor at the end
of 111<span style="font-size: 0.8em"><sup>1</sup></span>&frasl;<span style="font-size: 0.8em"><sub>10</sub></span>, for then the Tortoise has gained
<span style="font-size: 0.8em"><sup>1</sup></span>&frasl;<span style="font-size: 0.7em"><sub>100</sub></span> more.
<span class="pagenum"><a name="page233" id="page233"></a>[page&nbsp;233]</span>
So while Achilles runs this <span style="font-size: 0.8em"><sup>1</sup></span>&frasl;<span style="font-size: 0.8em"><sub>100</sub></span>, the Tortoise runs
<span style="font-size: 0.8em"><sup>1</sup></span>&frasl;<span style="font-size: 0.8em"><sub>1000</sub></span>; while he runs the
<span style="font-size: 0.8em"><sup>1</sup></span>&frasl;<span style="font-size: 0.8em"><sub>1000</sub></span>,
it runs <span style="font-size: 0.8em"><sup>1</sup></span>&frasl;<span style="font-size: 0.8em"><sub>10000</sub></span>. Thus
it would seem that the Tortoise must always keep
ahead: he can never overtake it.</p>

<p>But the conclusion is only a confusion of ideas: all
that is really proved is that Achilles will not overtake
the Tortoise while running</p>

<div class="poem">  <div class="stanza">
<p>100 + 10 + 1 + <span style="font-size: 0.8em"><sup>1</sup></span>&frasl;<span style="font-size: 0.8em"><sub>10</sub></span> +
<span style="font-size: 0.8em"><sup>1</sup></span>&frasl;<span style="font-size: 0.8em"><sub>100</sub></span> +
<span style="font-size: 0.8em"><sup>1</sup></span>&frasl;<span style="font-size: 0.8em"><sub>1000</sub></span> +
<span style="font-size: 0.8em"><sup>1</sup></span>&frasl;<span style="font-size: 0.8em"><sub>10000</sub></span>, etc.</p>
  </div>  </div>

<p>That is, that he will not overtake it till he has completed
the sum of this series, 111<span style="font-size: 0.8em"><sup>1</sup>&frasl;</span><span style="font-size: 0.8em"><sub>9</sub></span> yards. To prove
this is an <i>ignoratio elenchi</i>; what the Sophist undertakes
to prove is that Achilles will never overtake it, and he
really proves that Achilles passes it between the 111th
and 112th yards.</p>


<p>The exposure of this sophism is an example also of
the value of a technical term. All attempts to expose
it without using the term <i>Ignoratio Elenchi</i> or something
equivalent to it, succeed only in bewildering the
student. It is customary to say that the root of the
fallacy lies in assuming that the sum of an infinite
series is equal to infinity. This profound error may be
implied: but if any assumption so hard to understand
were really required, the fallacy would have little force
with the generality.</p>

<p>It has often been argued that the Syllogism involves
a <i>petitio principii</i>, because the Major Premiss contains
the Conclusion, and would not be true unless the
Conclusion were true. But this is really an <i>Ignoratio
Elenchi</i>. The fact adduced, that the Major Premiss
contains the Conclusion, is indisputable; but this does
not prove the Syllogism guilty of Petitio. <i>Petitio
principii</i> is an argumentative trick, a conscious or
unconscious act of deception, a covert assumption, and
<span class="pagenum"><a name="page234" id="page234"></a>[page&nbsp;234]</span>
the Syllogism, so far from favouring this, is an <i>expositio
principii</i>, an explicit statement of premisses such that,
if they are true, the conclusion is true. The Syllogism
merely shows the interdependence of premisses and
conclusion; its only tacit assumption is the <i>Dictum de
Omni</i>.</p>

<p>If, indeed, an opponent challenges the truth of the
conclusion, and you adduce premisses necessarily
containing it as a refutation, that is an <i>ignoratio elenchi</i>
unless your opponent admits those premisses. If he
admits them and denies the conclusion, you convict
him of inconsistency, but you do not prove the truth
of the conclusion. Suppose a man to take up the
position: "I am not mortal, for I have procured the
<i>elixir vit&aelig;</i>". You do not disprove this by saying, "All
men are mortal, and you are a man". In denying
that he is mortal, he denies that all men are mortal.
Whatever is sufficient evidence that he is not mortal,
is sufficient evidence that all men are not mortal.
Perhaps it might be said that in arguing, "All men
are mortal, and you are a man," it is not so much
<i>ignoratio elenchi</i> as <i>petitio principii</i> that you commit.
But be it always remembered that you may commit
both fallacies at once. You may both argue beside
the point and beg the question in the course of one
and the same argument.</p>

<p class="note1"><a id="footnotePIV-ChVIII1" name="footnotePIV-ChVIII1"></a><a class="footnote" href="#footnotetagPIV-ChVIII1">Footnote 1:</a>
Cp. Mr. Sidgwick's instructive treatise on Fallacies, International Scientific Series, p. 199.</p>
<span class="pagenum"><a name="page235" id="page235"></a>[page&nbsp;235]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter IX.</span></h3>

<h3>FORMAL OR ARISTOTELIAN INDUCTION.&mdash;INDUCTIVE ARGUMENT.</h3>

<p>The distinction commonly drawn between Deduction
and Induction is that Deduction is reasoning from
general to particular, and Induction reasoning from
particular to general.</p>

<p>But it is really only as modes of argumentation that
the two processes can be thus clearly and fixedly opposed.
The word Induction is used in a much wider sense
when it is the title of a treatise on the Methods of
Scientific Investigation. It is then used to cover all
the processes employed in man's search into the
system of reality; and in this search deduction is
employed as well as induction in the narrow sense.</p>

<p>We may call Induction in the narrow sense Formal
Induction or Inductive Argument, or we may simply
call it Aristotelian Induction inasmuch as it was the
steps of Inductive argument that Aristotle formulated,
and for which he determined the conditions of validity.</p>

<p>Let us contrast it with Deductive argument. In
this the questioner's procedure is to procure the admission
of a general proposition with a view to forcing
the admission of a particular conclusion which is in
dispute. In Inductive argument, on the other hand, it
is a general proposition that is in dispute, and the
<span class="pagenum"><a name="page236" id="page236"></a>[page&nbsp;236]</span>
procedure is to obtain the admission of particular cases
with a view to forcing the admission of this general
proposition.</p>

<p>Let the question be whether All horned animals
ruminate. You engage to make an opponent admit
this. How do you proceed? You ask him whether
he admits it about the various species. Does the ox
ruminate? The sheep? The goat? And so on.
The bringing in of the various particulars is the induction
(<ins title="epagôgê"><span style="font-size: 0.9em;">&#7952;</span>&pi;&alpha;&gamma;&omega;&gamma;&#942;</ins>).</p>

<p>When is this inductive argument complete? When
is the opponent bound to admit that all horned animals
ruminate? Obviously, when he has admitted it about
every one. He must admit that he has admitted it
about every one, in other words, that the particulars
enumerated constitute the whole, before he can be held
bound in consistency to admit it about the whole.</p>

<p>The condition of the validity of this argument is
ultimately the same with that of Deductive argument,
the identity for purposes of predication of a generic
whole with the sum of its constituent parts. The
Axiom of Inductive Argument is, <i>What is predicated of
every one of the parts is predicable of the whole.</i> This is
the simple converse of the Axiom of Deductive argument,
the <i>Dictum de Omni</i>, "What is predicated of the
whole is predicable about every one of the parts".
The Axiom is simply convertible because for purposes
of predication generic whole and specific or individual
parts taken all together are identical.</p>

<p>Practically in inductive argument an opponent is
worsted when he cannot produce an instance to the
contrary. Suppose he admits the predicate in question
to be true of this, that and the other, but denies that
this, that and the other constitute the whole class in
<span class="pagenum"><a name="page237" id="page237"></a>[page&nbsp;237]</span>
question, he is defeated in common judgement if he
cannot instance a member of the class about which the
predicate does not hold. Hence this mode of induction
became technically known as <i>Inductio per enumerationem
simplicem ubi non reperitur instantia contradictoria</i>.
When this phrase is applied to a generalisation of fact,
Nature or Experience is put figuratively in the position
of a Respondent unable to contradict the inquirer.</p>

<p>Such in plain language is the whole doctrine of
Inductive Argument. Aristotle's Inductive Syllogism
is, in effect, an expression of this simple doctrine
tortuously in terms of the Deductive Syllogism. The
great master was so enamoured of his prime invention
that he desired to impress its form upon everything:
otherwise, there was no reason for expressing the process
of Induction syllogistically. Here is his description of
the Inductive Syllogism:&mdash;</p>

<blockquote><p>
"Induction, then, and the Inductive Syllogism, consists
in syllogising one extreme with the middle through the
other extreme. For example, if B is middle to A and C, to
prove through C that A belongs to B."<a id="footnotetagPIV-ChIX1" name="footnotetagPIV-ChIX1"></a><a href="#footnotePIV-ChIX1"><sup>1</sup></a>
</p></blockquote>

<p>This may be interpreted as follows: Suppose a
general proposition is in dispute, and that you wish to
make it good by obtaining severally the admission of
all the particulars that it sums up. The type of a
general proposition in Syllogistic terminology is the
Major Premiss, All M is P. What is the type of the
particulars that it sums up? Obviously, the Conclusion,
S is P. This particular is contained in the
Major Premiss, All M is P; its truth is accepted as
<span class="pagenum"><a name="page238" id="page238"></a>[page&nbsp;238]</span>
contained in the truth of All M is P. S is one of the
parts of the generic whole M; one of the individuals or
species contained in the class M. If you wish, then,
to establish P of All M by Induction, you must establish
P of all the parts, species, or individuals contained
in M, that is, of all possible S<i>s:</i> you must make good
that this, that and the other S is P, and also that this,
that and the other S constitute the whole of M.
You are then entitled to conclude that All M is P: you
have syllogised one Extreme with the Middle through
the other Extreme. The formal statement of these
premisses and conclusion is the Inductive Syllogism.</p>

<div class="poem1">  <div class="stanza">
<p class="i4">This, that and the other S is P, <i>Major</i>.</p>
<p class="i4">This, that and the other S is all M, <i>Minor</i>.</p>
<p class="i2">.<sup>.</sup>. All M is P, <i>Conclusion</i>.</p>
<p class="i2">This, that and the other magnet (<i>i.e.</i>, magnets individually) attract iron.</p>
<p class="i2">This, that and the other magnet (<i>i.e.</i>, the individuals  separately admitted) are all magnets.</p>
<p>.<sup>.</sup>. All magnets attract iron.</p>
  </div>  </div>

<p>This, that and the other S being simply convertible
with All M, you have only to make this conversion
and you have a syllogism in Barbara where this, that
and the other S figures as the Middle Term.</p>

<p>The practical value of this tortuous expression is not
obvious. Medi&aelig;val logicians shortened it into what
was known as the Inductive Enthymeme: "This,
that and the other, therefore all," an obvious conclusion
when this, that and the other constitute all. It
is merely an evidence of the great master's intoxication
with his grand invention. It is a proof also that
Aristotle really looked at Induction from the point of
view of Interrogative Dialectic. His question was,
<span class="pagenum"><a name="page239" id="page239"></a>[page&nbsp;239]</span>
When is a Respondent bound to admit a general
conclusion? And his answer was, When he has
admitted a certain number of particulars, and cannot
deny that those particulars constitute the whole whose
predicate is in dispute. He was not concerned
primarily with the analysis of the steps of an inquirer
generalising from Nature.</p>

<p class="note1"><a id="footnotePIV-ChIX1" name="footnotePIV-ChIX1"></a><a class="footnote" href="#footnotetagPIV-ChIX1">Footnote 1:</a>
<ins title="epagôgê men oun esti kai ho ex epagôgês syllogismos to dia tou eterou thateron akron tô mesô syllogisasthai; Oion ei tôn A G meson to B, dia tou G deixai to A tô B hyparchon.">
&#7952;&pi;&alpha;&gamma;&omega;&gamma;&#8052; &mu;&#8050;&nu; &omicron;&#8022;&nu; &#7952;&sigma;&tau;&#8054; &kappa;&alpha;&#8054;
&#8001; &#7952;&xi; &#7952;&pi;&alpha;&gamma;&omega;&gamma;&#8134;&sigmaf; &sigma;&upsilon;&lambda;&lambda;&omicron;&gamma;&iota;&sigma;&mu;&#8056;&sigmaf;
&tau;&#8056; &delta;&iota;&#8048; &tau;&omicron;&#8166; &#7957;&tau;&#941;&rho;&omicron;&upsilon; &theta;&#7940;&tau;&epsilon;&rho;&omicron;&nu;
&#7940;&kappa;&rho;&omicron;&nu; &tau;&#8183; &mu;&#941;&sigma;&#8183;
&sigma;&upsilon;&lambda;&lambda;&omicron;&gamma;&#943;&sigma;&alpha;&sigma;&theta;&alpha;&iota;;
&Omicron;&#7991;&omicron;&nu; &epsilon;&#7984; &tau;&#8182;&nu; &Alpha; &Gamma; &mu;&#941;&sigma;&omicron;&nu; &tau;&#8056; &Beta;,
&delta;&iota;&#8048; &tau;&omicron;&#8166; &Gamma; &delta;&epsilon;&#8150;&xi;&alpha;&iota; &tau;&#8056; &Alpha; &tau;&#8183; &Beta; &#8017;&pi;&#940;&rho;&chi;&omicron;&nu;.
</ins> &nbsp;&nbsp;(An. Prior., ii. 23.)</p>
<span class="pagenum"><a name="page240" id="page240"></a>[page&nbsp;240]</span><br />
<span class="pagenum"><a name="page241" id="page241"></a>[page&nbsp;241]</span>

<h1 style="margin-top: 3em">BOOK II.</h1>

<h2>INDUCTIVE LOGIC, OR THE LOGIC OF SCIENCE.</h2>
<span class="pagenum"><a name="page242" id="page242"></a>[page&nbsp;242]</span><br />
<span class="pagenum"><a name="page243" id="page243"></a>[page&nbsp;243]</span>

<h3 style="margin-top: 3.5em;">INTRODUCTION.</h3>

<p>Perhaps the simplest way of disentangling the leading
features of the departments of Logic is to take them
in relation to historical circumstances. These features
are writ large, as it were, in history. If we recognise
that all bodies of doctrine have their origin in practical
needs, we may conceive different ages as controlled
each by a distinctive spirit, which issues its mandate
to the men of the age, assigning to them their distinctive
work.</p>

<p>The mandate issued to the age of Plato and Aristotle
was <i>Bring your beliefs into harmony one with another</i>.
The Aristotelian Logic was framed in response to this
order: its main aim was to devise instruments for
making clear the coherence, the concatenation, the
mutual implication of current beliefs.</p>

<p>The mandate of the Medi&aelig;val Spirit was <i>Bring your
beliefs into harmony with dogma</i>. The medi&aelig;val logic
was contracted from Aristotle's under this impulse.
Induction as conceived by him was neglected, allowed
to dwindle, almost to disappear from Logic. Greater
prominence was given to Deduction.</p>

<p>Then as Dogmatic Authority became aggressive,
and the Church through its officials claimed to pronounce
on matters outside Theology, a new spirit was
roused, the mandate of which was, <i>Bring your beliefs
into harmony with facts</i>. It was under this impulse that
<span class="pagenum"><a name="page244" id="page244"></a>[page&nbsp;244]</span>
a body of methodical doctrine vaguely called Induction
gradually originated.</p>

<p>In dealing with the genesis of the Old Logic, we
began with Aristotle. None can dispute his title
to be called its founder. But who was the founder
of the New Logic? In what circumstances did it
originate?</p>

<p>The credit of founding Induction is usually given
to Francis Bacon, Lord Verulam. That great man
claimed it for himself in calling his treatise on the
Interpretation of Nature the <i>Novum Organum</i>. The
claim is generally conceded. Reid's account of the
matter represents the current belief since Bacon's own
time.</p>

<blockquote><p>
"After man had laboured in the search of truth
near two thousand years by the help of Syllogisms,
[Lord] Bacon proposed the method of <span class="sc">Induction</span> as a
more effectual engine for that purpose. His <i>Novum
Organum</i> gave a new turn to the thoughts and labours
of the inquisitive, more remarkable and more useful
than that which the <i>Organon</i> of Aristotle had given
before, and may be considered as a second grand era
in the progress of human nature.... Most arts have
been reduced to rules after they had been brought to a
considerable degree of perfection by the natural sagacity
of artists; and the rules have been drawn from
the best examples of the art that had been before
exhibited; but the art of philosophical induction was
delineated by [Lord] Bacon in a very ample manner
before the world had seen any tolerable example
of it."<a id="footnotetagB2-Intro1" name="footnotetagB2-Intro1"></a><a href="#footnoteB2-Intro1"><sup>1</sup></a>
</p></blockquote>

<p>There is a radical misconception here, which, for
reasons that I hope to make plain, imperatively needs
<span class="pagenum"><a name="page245" id="page245"></a>[page&nbsp;245]</span>
to be cleared up. It obscures the very essence of
"philosophical induction".</p>

<p>There are three ways in which movement in any
direction may be helped forward, Exhortation, Example,
and Precept. Exhortation: a man may exhort to
the practice of an art and thereby give a stimulus.
Example: he may practise the art himself, and show
by example how a thing should be done. Precept: he
may formulate a clear method, and so make plain how
to do it. Let us see what was Bacon's achievement
in each of those three ways.</p>

<p>Undoubtedly Bacon's powerful eloquence and high
political position contributed much to make the study
of Nature fashionable. He was high in place and
great in intellect, one of the commanding personalities
of his time. Taking "all knowledge for his province,"
though study was really but his recreation, he sketched
out a plan of universal conquest with a clearness and
confidence that made the mob eager to range themselves
under his leadership. He was the magnificent
demagogue of science. There had been champions of
"Induction" before him, but they had been comparatively
obscure and tongue-tied.</p>

<p>While, however, we admit to the full the great
services of this mighty advocate in making an "Inductive"
method popular, we should not forget that he
had pioneers even in hortatory leadership. His
happiest watchword, the Interpretation of Nature, as
distinguished from the Interpretation of Authoritative
Books, was not of his invention. If we read Whewell's
<i>History of the Inductive Sciences</i>, we shall find that
many before him had aspired to "give a new turn to
the labors of the inquisitive," and in particular to
substitute inquisition for disquisition.</p>
<span class="pagenum"><a name="page246" id="page246"></a>[page&nbsp;246]</span>

<p>One might compile from Whewell a long catalogue
of eminent men before Bacon who held that the study
of Nature was the proper work of the inquisitive:
Leonardo da Vinci (1452-1519), one of the wonders of
mankind for versatility, a miracle of excellence in many
things, painter, sculptor, engineer, architect, astronomer,
and physicist; Copernicus (1473-1543), the
author of the Heliocentric theory; Telesius (1508-1588),
a theoretical reformer, whose <i>De Rerum Natura</i>
(1565) anticipated not a little of the <i>Novum Organum</i>;
Cesalpinus (1520-1603), the Botanist; Gilbert (1540-1603),
the investigator of Magnetism. By all these
men experiment and observation were advocated as the
only way of really increasing knowledge. They all
derided mere book-learning. The conception of the
world of sense as the original MS. of which systems of
philosophy are but copies, was a familiar image with
them. So also was Bacon's epigrammatic retort to
those who wish to rest on the wisdom of the ancients,
that antiquity is the youth of the world and that we
are the true ancients. "We are older," said Giordano
Bruno, "and have lived longer than our predecessors."</p>

<p>This last argument, indeed, is much older than the
sixteenth century. It was used by the Doctor
Mirabilis of the thirteenth, the Franciscan Friar,
Roger Bacon (1214-1292). "The later men are, the
more enlightened they are; and wise men now are
ignorant of much the world will some day know." The
truth is that if you are in search of a Father for
Inductive Philosophy, the medi&aelig;val friar has better
claims than his more illustrious namesake. His
enthusiasm for the advancement of learning was not
less nobly ambitious and far-reaching, and he was
himself an ardent experimenter and inventor. His
<span class="pagenum"><a name="page247" id="page247"></a>[page&nbsp;247]</span>
<i>Opus Majus</i>&mdash;an eloquent outline of his projects for a
new learning, addressed in 1265 to Pope Clement IV.,
through whom he offered to give to the Church the
empire of the world as Aristotle had given it to
Alexander&mdash;was almost incredibly bold, comprehensive
and sagacious. Fixing upon Authority, Custom,
Popular Opinion, and the Pride of Supposed Knowledge,
as the four causes of human ignorance, he urged a
direct critical study of the Scriptures, and after an
acute illustration of the usefulness of Grammar and
Mathematics (widely interpreted), concluded with
Experimental Science as the great source of human
knowledge. I have already quoted (p. 15) the Friar's
distinction between the two modes of Knowing,
Argument and Experience, wherein he laid down that
it is only experience that makes us feel certain. It
were better, he cried in his impatience, to burn Aristotle
and make a fresh start than to accept his conclusions
without inquiry.</p>

<blockquote><p>
Experimental Science, the sole mistress of Speculative
Science, has three great Prerogatives among
other parts of Knowledge. First, she tests by experiment
the noblest conclusions of all other sciences.
Next, she discovers respecting the notions which other
sciences deal with, magnificent truths to which these
sciences can by no means attain. Her third dignity
is that she by her own power and without respect to
other sciences investigates the secret of Nature.
</p></blockquote>

<p>So far, then, as Exhortation goes, King James's
great lawyer and statesman was not in advance of
Pope Clement's friar. Their first principle was the
same. It is only by facts that theories can be tested.
Man must not impose his own preconceptions
(<i>anticipationes mentis</i>) on nature. Man is only the
<span class="pagenum"><a name="page248" id="page248"></a>[page&nbsp;248]</span>
interpreter of nature. Both were also at one in holding
that the secrets of nature could not be discovered by
discussion, but only by observation and experiment.</p>

<p>Francis Bacon, however, went beyond all his predecessors
in furnishing an elaborate Method for the
interpretation of Nature. When he protested against
the intellect's being left to itself (<i>intellectus sibi permissus</i>),
he meant more than speculation left unchecked by
study of the facts. He meant also that the interpreter
must have a method. As man, he says, cannot move
rocks by the mere strength of his hands without
instruments, so he cannot penetrate to the secrets of
Nature by mere strength of his intellect without
instruments. These instruments he undertakes to
provide in his Inductive Method or <i>Novum Organum</i>.
And it is important to understand precisely what his
methods were, because it is on the ground of them that
he is called the founder of Inductive Philosophy, and
because this has created a misapprehension of the
methods actually followed by men of science.</p>

<p>Ingenious, penetrating, wide-ranging, happy in
nomenclature, the <i>Novum Organum</i> is a wonderful
monument of the author's subtle wit and restless
energy; but, beyond giving a general impulse to
testing speculative fancies by close comparison with
facts, it did nothing for science. His method&mdash;with
its Tables of Preliminary Muster for the Intellect
(<i>tabul&aelig; comparenti&aelig; prim&aelig; instantiarum ad intellectum</i>,
facts collected and methodically arranged for the intellect
to work upon); its Elimination upon first inspection
of obviously accidental concomitants (<i>Rejectio sive
Exclusiva naturarum</i>); its Provisional Hypothesis
(<i>Vindemiatio Prima sive Interpretatio Inchoata</i>); its
advance to a true Induction or final Interpretation by
<span class="pagenum"><a name="page249" id="page249"></a>[page&nbsp;249]</span>
examination of special instances (he enumerates
twenty-seven, 3 × 3 × 3, <i>Prerogativas Instantiarum</i>,
trying to show the special value of each for the
inquirer)<a id="footnotetagB2-Intro2" name="footnotetagB2-Intro2"></a><a href="#footnoteB2-Intro2"><sup>2</sup></a>&mdash;was beautifully regular and imposing, but
it was only a vain show of a method. It was rendered
so chiefly by the end or aim that Bacon proposed for
the inquirer. In this he was not in advance of his
age; on the contrary, he was probably behind Roger
Bacon, and certainly far behind such patient and
concentrated thinkers as Copernicus, Gilbert, and
Galileo&mdash;no discredit to the grandeur of his intellect
when we remember that science was only his recreation,
the indulgence of his leisure from Law and State.</p>

<p>In effect, his method came to this. Collect as many
instances as you can of the effect to be investigated,
and the absence of it where you would expect it,
arrange them methodically, then put aside guesses at
the cause which are obviously unsuitable, then draw
up a probably explanation, then proceed to make this
exact by further comparison with instances. It is when
we consider what he directed the inquirer to search for
that we see why so orderly a method was little likely
to be fruitful.</p>

<p>He starts from the principle that the ultimate
object of all knowledge is use, practice (<i>scimus ut operemur</i>).
We want to know how Nature produces things
that we may produce them for ourselves, if we can.
The inquirer's first aim, therefore, should be to find
out how the qualities of bodies are produced, to discover
the <i>form&aelig;</i> or formal causes of each quality. An
<span class="pagenum"><a name="page250" id="page250"></a>[page&nbsp;250]</span>
example shows what he meant by this. Gold is a
crowd or conjugation of various qualities or "natures";
it is yellow, it has a certain weight, it is malleable or
ductile to a certain degree, it is not volatile (loses
nothing under fire), it can be melted, it is soluble. If
we knew the <i>forma</i> or formal cause of each of those
qualities, we could make gold, provided the causes
were within our control. The first object, then, of the
investigator of Nature is to discover such <i>form&aelig;</i>, in
order to be able to effect the transformation of bodies.
It may be desirable also to know the <i>latens processus</i>,
any steps not apparent to the senses by which a body
grows from its first germs or rudiments, and the
<i>schematismus</i> or ultimate inner constitution of the body.
But the discovery of the <i>form&aelig;</i> of the constituent
qualities (<i>natur&aelig; singul&aelig;</i>), heat, colour, density or
rarity, sweetness, saltness, and so forth, is the grand
object of the Interpreter of Nature; and it is for this
that Bacon prescribed his method.</p>

<p>The <i>Sylva Sylvarum</i>, or Natural History, a miscellaneous
collection of facts and fictions, observations
and traditions, with guesses at the explanation of
them, affords us a measure of Bacon's own advancement
as an interpreter of Nature. It was a posthumous
work, and the editor, his secretary, tells us that he
often said that if he had considered his reputation he
would have withheld it from the world, because it was
not digested according to his own method: yet he
persuaded himself that the causes therein assigned were
far more certain than those rendered by others, "not
for any excellence of his own wit, but in respect of his
continual conversation with Nature and Experience,"
and mankind might stay upon them till true Axioms
were more fully discovered. When, however, we
<span class="pagenum"><a name="page251" id="page251"></a>[page&nbsp;251]</span>
examine the causes assigned, we find that in practice
Bacon could not carry out his own precepts: that he
did not attempt to creep up to an explanation by slow
and patient ascent, but jumped to the highest
generalisations: and that his explanatory notions were
taken not from nature, but from the ordinary traditions
of medi&aelig;val physical science. He deceived himself, in
short, in thinking that he could throw aside tradition
and start afresh from observation.</p>

<p>For example. He is struck by the phenomenon of
bubbles on water: "It seemeth somewhat strange
that the air should rise so swiftly, while it is in the
water, and when it cometh to the top should be stayed
by so weak a cover as that of the bubble is". The
swift ascent of the air he explains as a "motion of
percussion," the water descending and forcing up the
air, and not a "motion of levity" in the air itself.
"The cause of the enclosure of the bubble is for that
the appetite to resist separation or discontinuance,
which is strong in solids, is also in liquors, though
fainter and weaker." "The same reason is of the
roundness of the bubble, as well for the skin of
water as for the air within. For the air likewise
avoideth discontinuance, and therefore casteth itself
into a round figure. And for the stop and arrest of
the air a little while, it showeth that the air of itself
hath little or no appetite of ascending."<a id="footnotetagB2-Intro3" name="footnotetagB2-Intro3"></a><a href="#footnoteB2-Intro3"><sup>3</sup></a>
These notions
were not taken direct from the facts: they descended
from Aristotle. He differs from Aristotle, however,
in his explanation of the colours of birds' feathers.
"Aristotle giveth the cause vainly" that birds are more
in the beams of the sun than beasts. "But that is
<span class="pagenum"><a name="page252" id="page252"></a>[page&nbsp;252]</span>
manifestly untrue; for cattle are more in the sun
than birds, that live commonly in the woods or
in some covert. The true cause is that the excrementitious
moisture of living creatures, which maketh as
well the feathers in birds as the hair in beasts, passeth
in birds through a finer and more delicate strainer
than it doth in beasts. For feathers pass through
quills, and hair through skin." It is an instance of
percolation or filtering: other effects of the same cause
being the gums of trees, which are but a fine passage or
straining of the juice through the wood and bark, and
Cornish Diamonds and Rock Rubies, which are in like
manner "fine exudations of stone".<a id="footnotetagB2-Intro4" name="footnotetagB2-Intro4"></a><a href="#footnoteB2-Intro4"><sup>4</sup></a></p>

<p>These examples of Bacon's Inductions are taken
from the <i>Sylva</i> at random. But the example which
best of all illustrates his attitude as a scientific
investigator is the remark he makes in the <i>Novum
Organum</i> about the Copernican theory. Elsewhere he
says that there is nothing to choose between it and the
Ptolemaic; and in the <i>Novum Organum</i> (lib. ii. 5) he
remarks that "no one can hope to terminate the
question whether in diurnal motion it is really the
earth or the sky that rotates, unless he shall first have
comprehended the nature of spontaneous rotation".
That is, we must first find out the <i>forma</i> or formal
cause of spontaneous rotation. This is a veritable
<i>instantia crucis</i>, as fixing Bacon's place in the medi&aelig;val
and not in the new world of scientific speculation.</p>

<p>Bacon, in short, in the practice of induction did not
advance an inch beyond Aristotle. Rather he retrograded,
inasmuch as he failed to draw so clear a line
between the respective spheres of Inductive collection
<span class="pagenum"><a name="page253" id="page253"></a>[page&nbsp;253]</span>
of facts and Explanation. There are two sources of
general propositions, according to Aristotle, Induction
and Nous. By Induction he meant the generalisation
of facts open to sense, the summation of observed
particulars, the <i>inductio per enumerationem simplicem</i> of
the schoolmen. By Nous he meant the Reason or
Speculative Faculty, as exercised with trained sagacity
by experts. Thus by Induction we gather that all
horned animals ruminate. The explanation of this
is furnished by the Nous, and the explanation that
commended itself to the trained sagacity of his time
was that Nature having but a limited amount of hard
material and having spent this on the horns, had none
left for teeth, and so provided four stomachs by way of
compensation. Bacon's guesses at causes are on the
same scientific level with this, only he rather confused
matters by speaking of them as if they were inductions
from fact, instead of being merely fancies superinduced
upon fact. His theory of interpretation, it is true, was
so far an advance that he insisted on the necessity of
verifying every hypothesis by further appeal to facts,
though in practice he himself exercised no such
patience and never realised the conditions of verification.
Against this, again, must be set the fact that by calling
his method induction, and laying so much stress on
the collection of facts, he fostered, and, indeed, fixed
in the public mind the erroneous idea that the whole
work of science consists in observation. The goal of
science, as Herschel said, is Explanation, though
every explanation must be made to conform to fact,
and explanation is only another term for attaining to
higher generalisations, higher unities.</p>

<p>The truth is that Induction, if that is the name we
use for scientific method, is not, as Reid conceived, an
<span class="pagenum"><a name="page254" id="page254"></a>[page&nbsp;254]</span>
exception to the usual rule of arts in being the invention
of one man. Bacon neither invented nor practised it.
It was perfected gradually in the practice of men of
science. The birthplace of it as a conscious method
was in the discussions of the Royal Society of London,
as the birthplace of the Aristotelian Logic was in the
discussions of the Athenian schools. Its first great
triumph was Newton's law of Gravitation. If we are
to name it after its first illustrious practitioner, we
must call it the Newtonian method, not the Baconian.
Newton really stands to the Scientific Method of
Explanation as Aristotle stands to the Method of
Dialectic and Deduction. He partly made it explicit
in his <i>Regul&aelig; Philosophandi</i> (1685). Locke, his friend
and fellow-member of the Royal Society, who applied
the method to the facts of Mind in his <i>Essay Concerning
Human Understanding</i> (1691), made it still further
explicit in the Fourth Book of that famous work.</p>

<p>It was, however, a century and a half later that an
attempt was first made to incorporate scientific method
with Logic under the name of Induction, and add it as
a new wing to the old Aristotelian building. This was
the work of John Stuart Mill, whose System of Logic,
Deductive and Inductive, was first published in 1843.</p>

<p>The genesis of Mill's System of Logic, as of other
things, throws light upon its character. And in
inquiries into the genesis of anything that man makes
we may profitably follow Aristotle's division of causes.
The Efficient Cause is the man himself, but we have
also to find out the Final Cause, his object or purpose
in making the thing, the Material Cause, the sources
of his material, and the Formal Cause, the reason why
he shaped it as he did. In the case of Mill's system
we have to ask: What first moved him to formulate
<span class="pagenum"><a name="page255" id="page255"></a>[page&nbsp;255]</span>
the methods of scientific investigation? Whence did
he derive his materials? Why did he give his scientific
method the form of a supplement to the old Aristotelian
Logic? We cannot absolutely separate the three
inquiries, but motive, matter and form each had a
traceable influence on the leading features of his
System.</p>

<p>First, then, as to his motive. It is a mistake to
suppose that Mill's object was to frame an organon
that might assist men of science as ordinarily understood
in making discoveries. Bacon, his secretary
tells us, was wont to complain that he should be
forced to be a Workman and a Labourer in science
when he thought he deserved to be an Architect in this
building. And men of science have sometimes rebuked
Mill for his presumption in that, not being himself an
investigator in any department of exact science, he should
volunteer to teach them their business. But Mill was
really guilty of no such presumption. His object, on
the contrary, was to learn their method with a view to
its application to subjects that had not yet undergone
scientific treatment. Briefly stated, his purpose
was to go to the practical workers in the exact
sciences, Astronomy, Chemistry, Heat, Light, Electricity,
Molar and Molecular Physics; ascertain,
not so much how they made their discoveries as
how they assured themselves and others that their
conclusions were sound; and having ascertained their
tests of truth and principles of proof, to formulate these
tests so that they might be applied to propositions
outside the range of the exact sciences, propositions in
Politics, Ethics, History, Psychology. More particularly
he studied how scientific men verify, and when
they accept as proved, propositions of causation, explanations
<span class="pagenum"><a name="page256" id="page256"></a>[page&nbsp;256]</span>
of the causes of things. In effect, his survey
of scientific method was designed to lead up to the
Sixth Book in his System, the Logic of the Moral
Sciences. There are multitudes of floating endoxes
or current opinions concerning man and his concerns,
assigning causes for the conduct and character of
individuals and of communities. Mill showed himself
quite aware that the same modes of investigation may
not be practicable, and that it may not be possible,
though men are always ready to assign causes with
confidence, to ascertain causes with the same degree
of certainty: but at least the conditions of exact verification
should be the same, and it is necessary to see
what they are in order to see how far they can be
realised.</p>

<p>That such was Mill's design in the main is apparent
on internal evidence, and it was the internal evidence
that first struck me. But there is external evidence as
well. We may first adduce some essays on the Spirit
of the Age, published in the <i>Examiner</i> in 1831, essays
which drew from Carlyle the exclamation, "Here is a
new Mystic!" These essays have never been republished,
but they contain Mill's first public expression
of the need for a method in social inquiries. He starts
from the Platonic idea that no state can be stable in
which the judgment of the wisest in political affairs is
not supreme. He foresees danger in the prevalent
anarchy of opinion. How is it to be averted? How
are men to be brought to accept loyally the judgment
of the expert in public affairs? They accept at once
and without question the decisions of the specially
skilled in the physical sciences. Why is this? For
one reason, because there is complete agreement
among experts. And why is there this complete
<span class="pagenum"><a name="page257" id="page257"></a>[page&nbsp;257]</span>
agreement? Because all accept the same tests of
truth, the same conditions of proof. Is it not possible
to obtain among political investigators similar
unanimity as to their methods of arriving at conclusions,
so as to secure similar respect for their
authority?</p>

<p>We need not stop to ask whether this was a vain
dream, and whether it must not always be the case
that to ensure confidence in a political or moral
adviser more is needed than faith in his special knowledge
and trained sagacity. Our point is that in
1831 Mill was in search of a method of reasoning in
social questions. Opportunely soon after, early in
1832, was published Herschel's <i>Discourse on the Study
of Natural Philosophy</i>, the first attempt by an eminent
man of science to make the methods of science
explicit. Mill reviewed this book in the <i>Examiner</i>,
and there returns more definitely to the quest on which
he was bent. "The uncertainty," he says, "that
hangs over the very elements of moral and social
philosophy proves that the means of arriving at the
truth in those sciences are not yet properly understood.
And whither can mankind so advantageously turn, in
order to learn the proper means and to form their
minds to the proper habits, as to that branch of knowledge
in which by universal acknowledgment the
greatest number of truths have been ascertained and
the greatest possible degree of certainty arrived at?"</p>

<p>We learn from Mill himself that he made an attempt
about this time, while his mind was full of Herschel's
Discourse, to connect a scientific method with the
body of the Old Logic. But he could not make the
junction to his satisfaction, and abandoned the attempt
in despair. A little later, in 1837, upon the appearance
<span class="pagenum"><a name="page258" id="page258"></a>[page&nbsp;258]</span>
of Whewell's <i>History of the Inductive Sciences</i>, he
renewed it, and this time with happier results.
Whewell's <i>Philosophy of the Inductive Sciences</i> was
published in 1840, but by that time Mill's system was
definitely shaped.</p>

<p>It was, then, to Herschel and Whewell, but
especially to the former, that Mill owed the raw materials
of his Inductive Method. But why did he desire to
concatenate this with the old Logic? Probably
because he considered that this also had its uses for
the student of society, the political thinker. He had
inherited a respect for the old Logic from his father.
But it was the point at which he sought to connect the
new material with the old, the point of junction
between the two, that determined the form of his
system. We find the explanation of this in the history
of the old Logic. It so happened that Whately's
Logic was in the ascendant, and Whately's treatment
of Induction gives the key to Mill's.</p>

<p>Towards the end of the first quarter of this century
there was a great revival of the study of Logic at
Oxford. The study had become mechanical, Aldrich's
Compendium, an intelligent but exceedingly brief
abstract of the Scholastic Logic, being the text-book
beyond which no tutor cared to go. The man who
seems to have given new life to the study was a tutor
who subsequently became Bishop of Llandaff, Edward
Copleston. The first public fruits of the revival begun
by him was Whately's article on Logic in the <i>Encyclop&aelig;dia
Metropolitana</i>, published as a separate book in
1827. Curiously enough, one of Whately's most
active collaborators in the work was John Henry
Newman, so that the common room of Oriel, which
Mr. Froude describes as the centre from which
<span class="pagenum"><a name="page259" id="page259"></a>[page&nbsp;259]</span>
emanated the High Church Movement, may also be
said to have been the centre from which emanated the
movement that culminated in the revolution of Logic.</p>

<p>The publication of Whately's Logic made a great stir.
It was reviewed by Mill, then a young man of twenty-one,
in the <i>Westminster Review</i> (1828), and by Hamilton, then
forty-five years of age, in the <i>Edinburgh</i> (1833). There
can be no doubt that it awakened Mill's interest in the
subject. A society formed for the discussion of philosophical
questions, and called the Speculative Society,
met at Grote's house in 1825, and for some years
following. Of this society young Mill was a member,
and their continuous topic in 1827 was Logic, Whately's
treatise being used as a sort of text-book.</p>

<p>It is remarkable that Mill's review of Whately, the
outcome of these discussions, says very little about
Induction. At that stage Mill's chief concern seems
to have been to uphold the usefulness of Deductive
Logic, and he even goes so far as to scoff at its
eighteenth century detractors and their ambition to
supersede it with a system of Induction. The most
striking feature of the article is the brilliant defence of
the Syllogism as an analysis of arguments to which I
have already referred. He does not deny that an
Inductive Logic might be useful as a supplement, but
apparently he had not then formed the design of supplying
such a supplement. When, however, that design
seriously entered his mind, consequent upon the felt need
of a method for social investigations, it was Whately's
conception of Induction that he fell back upon. Historically
viewed, his System of Logic was an attempt
to connect the practical conditions of proof set forth in
Herschel's discourse with the theoretic view of Induction
propounded in Whately's. The tag by which he
<span class="pagenum"><a name="page260" id="page260"></a>[page&nbsp;260]</span>
sought to attach the new material to the old system
was the Inductive Enthymeme of the Schoolmen as
interpreted by Whately.</p>

<p>Whately's interpretation&mdash;or misinterpretation&mdash;of
this Enthymeme, and the conception of Induction
underlying it, since it became Mill's ruling conception
of Induction, and virtually the formative principle of
his system, deserves particular attention.</p>

<blockquote><p>
"This, that and the other horned animal, ox, sheep,
goat, ruminate; <i>therefore</i>, all horned animals ruminate."
</p></blockquote>

<p>The traditional view of this Enthymeme I have given
in my chapter on Formal Induction (p. 238). It is
that a Minor Premiss is suppressed: "This, that
and the other constitute the whole class". This is
the form of the Minor in Aristotle's Inductive Syllogism.</p>

<p>But, Whately argued, how do we know that this,
that and the other&mdash;the individuals we have examined&mdash;constitute
the whole class? Do we not assume that
what belongs to the individuals examined belongs to
the whole class? This tacit assumption, he contended,
is really at the bottom of the Enthymeme, and its
proper completion is to take this as the Major Premiss,
with the enumeration of individuals as the Minor.
Thus:&mdash;</p>

<div class="poem1">  <div class="stanza">
<p>What belongs to the individuals examined belongs to the whole class.</p>
<p>The property of the ruminating belongs to the individuals examined, ox, sheep, goat, etc.</p>
<p><i>Therefore</i>, it belongs to all.</p>
  </div>  </div>

<p>In answer to this, Hamilton repeated the traditional
view, treating Whately's view merely as an instance of
<span class="pagenum"><a name="page261" id="page261"></a>[page&nbsp;261]</span>
the prevailing ignorance of the history of Logic. He
pointed out besides that Whately's Major was the
postulate of a different kind of inference from that
contemplated in Aristotle's Inductive Syllogism,
Material as distinguished from Formal inference.
This is undeniable if we take this syllogism purely as
an argumentative syllogism. The "all" of the conclusion
simply covers the individuals enumerated and
admitted to be "all" in the Minor Premiss. If a
disputant admits the cases produced to be all and can
produce none to the contrary, he is bound to admit
the conclusion. Now the inference contemplated by
Whately was not inference from an admission to what
it implies, but inference from a series of observations
to all of a like kind, observed and unobserved.</p>

<p>It is not worth while discussing what historical
justification Whately had for his view of Induction.
It is at least arguable that the word had come to mean,
if it did not mean with Aristotle himself, more than a
mere summation of particulars in a general statement.
Even Aristotle's respondent in the concession of his
Minor admitted that the individuals enumerated constituted
all in the truly general sense, not merely all
observed but all beyond the range of observation. The
point, however, is insignificant. What really signifies
is that while Hamilton, after drawing the line between
Formal Induction and Material, fell back and entrenched
himself within that line, Mill caught up Whately's
conception of Induction, pushed forward, and made it
the basis of his System of Logic.</p>

<p>In Mill's definition, the mere summation of particulars,
<i>Inductio per enumerationem simplicem ubi non
reperitur instantia contradictoria</i>, is Induction improperly
so called. The only process worthy of the name is
<span class="pagenum"><a name="page262" id="page262"></a>[page&nbsp;262]</span>
Material Induction, inference to the unobserved. Here
only is there an advance from the known to the
unknown, a veritable "inductive hazard".</p>

<p>Starting then with this conception of inference to
the unobserved as the only true inference, and with an
empirical law&mdash;a generality extended from observed
cases to unobserved&mdash;as the type of such inference,
Mill saw his way to connecting a new Logic with the
old. We must examine this junction carefully, and
the brilliant and plausible arguments by which he
supported it; we shall find that, biased by this desire
to connect the new with the old, he gave a misleading
dialectic setting to his propositions, and, in effect,
confused the principles of Argumentative conclusion
on the one hand and of Scientific Observation and
Inference on the other. The conception of Inference
which he adopted from Whately was too narrow on
both sides for the uses to which he put it. Be it
understood that in the central methods both of Syllogistic
and of Science, Mill was substantially in accord
with tradition; it is in his mode of junction, and the
light thereby thrown upon the ends and aims of both,
that he is most open to criticism.</p>

<p>As regards the relation between Deduction and
Induction, Mill's chief proposition was the brilliant
paradox that all inference is at bottom Inductive, that
Deduction is only a partial and accidental stage in a
process the whole of which may be called Induction.
An opinion was abroad&mdash;fostered by the apparently
exclusive devotion of Logic to Deduction&mdash;that all
inference is essentially Deductive. Not so, answered
Mill, meeting this extreme with another: all inference
is essentially Inductive. He arrives at this through
the conception that Induction is a generalisation from
<span class="pagenum"><a name="page263" id="page263"></a>[page&nbsp;263]</span>
observed particulars, while Deduction is merely the
extension of the generalisation to a new case, a new
particular. The example that he used will make his
meaning plain.</p>

<p>Take a common Syllogism:&mdash;</p>

<div class="poem">  <div class="stanza">
<p>All men are mortal.</p>
<p>Socrates is a man.</p>
<p>Socrates is mortal.</p>
  </div>  </div>

<p>"The proposition," Mill says, "that Socrates is mortal
is evidently an inference. It is got at as a conclusion
from something else. But do we in reality conclude
it from the proposition, All men are mortal?" He
answers that this cannot be, because if it is not true that
Socrates is mortal it cannot be true that all men are
mortal. It is clear that our belief in the mortality of
Socrates must rest on the same ground as our belief
in the mortality of men in general. He goes on to
ask whence we derive our knowledge of the general
truth, and answers: "Of course from observation.
Now all which man can observe are individual cases.... A
general truth is but an aggregate of particular
truths. But a general proposition is not merely a
compendious form for recording a number of particular
facts.... It is also a process of inference. From
instances which we have observed we feel warranted
in concluding that what we have found true in those
instances, holds in all similar ones, past, present, and
future. We then record all that we have observed
together with what we infer from our observations, in
one concise expression." A general proposition is
thus at once a summary of particular facts and a
memorandum of our right to infer from them. And
when we make a deduction we are, as it were,
<span class="pagenum"><a name="page264" id="page264"></a>[page&nbsp;264]</span>
interpreting this memorandum. But it is upon the
particular facts that the inference really rests, and Mill
contends that we might if we chose infer to the
particular conclusion at once without going through
the form of a general inference. Thus Mills seeks to
make good his point that all inference is essentially
Inductive, and that it is only for convenience that the
word Induction has been confined to the general
induction, while the word Deduction is applied to the
process of interpreting our memorandum.</p>

<p>Clear and consecutive as this argument is, it is
fundamentally confusing. It confuses the nature
of Syllogistic conclusion or Deduction, and at the
same time gives a partial and incomplete account of
the ground of Material inference.</p>

<p>The root of the first confusion lies in raising the
question of the ground of material inference in connexion
with the Syllogism. As regards the usefulness
of the Syllogism, this is an <span class="sc">Ignoratio Elenchi</span>. That
the Major and the conclusion rest upon the same ground
as matters of belief is indisputable: but it is irrelevant.
In so far as "Socrates is mortal" is an inference from
facts, it is not the conclusion of a Syllogism. This is
implicitly and with unconscious inconsistency recognised
by Mill when he represents Deduction as the
interpretation of a memorandum. To represent
Deduction as the interpretation of a memorandum&mdash;a
very happy way of putting it and quite in accordance
with Roger Bacon's view&mdash;is really inconsistent with
regarding Deduction as an occasional step in the
process of Induction. If Deduction is the interpretation
of a memorandum, it is no part of the process of
inference from facts. The conditions of correct
interpretation as laid down in Syllogism are one thing,
<span class="pagenum"><a name="page265" id="page265"></a>[page&nbsp;265]</span>
and the methods of correct inference from the facts, the
methods of science that he was in search of, are
another.</p>

<p>Let us emphasise this view of Deduction as the
interpretation of a memorandum. It corresponds
exactly with the view that I have taken in discussing
the utility of the Syllogism. Suppose we want to
know whether a particular conclusion is consistent
with our memorandum, what have we to look to? We
have to put our memorandum into such a form that it
is at once apparent whether or not it covers our
particular case. The Syllogism aspires to be such a
form. That is the end and aim of it. It does not
enable us to judge whether the memorandum is a
legitimate memorandum or not. It only makes clear
that if the memorandum is legitimate, so is the conclusion.
How to make clear and consistent memoranda
of our beliefs in words is a sufficiently complete description
of the main purpose of Deductive Logic.</p>

<p>Instead, then, of trying to present Deduction and
Induction as parts of the same process, which he was
led to do by his desire to connect the new and the old,
Mill ought rather, in consistency as well as in the
interests of clear system, to have drawn a line of
separation between the two as having really different
ends, the conditions of correct conclusion from accepted
generalities on the one hand, and the conditions of
correct inference from facts on the other. Whether the
first should be called inference at all is a question of
naming that ought to have been considered by itself.
We may refuse to call it inference, but we only confuse
ourselves and others if we do not acknowledge that
in so doing we are breaking with traditional usage.
Perhaps the best way in the interests of clearness is to
<span class="pagenum"><a name="page266" id="page266"></a>[page&nbsp;266]</span>
compromise with tradition by calling the one Formal
Inference and the other Material Inference.</p>

<p>It is with the latter that the Physical Sciences are
mainly concerned, and it was the conditions and
methods of its correct performance that Mill desired to
systematise in his Inductive Logic. We have next to
see how his statement of the grounds of Material
Inference was affected by his connexion of Deduction
and Induction. Here also we shall find a reason for a
clearer separation between the two departments of
Logic.</p>

<p>In his antagonism to a supposed doctrine that all
reasoning is from general to particular, Mill maintained
<i>simpliciter</i> that all reasoning is from particulars to
particulars. Now this is true only <i>secundum quid</i>, and
although in the course of his argument Mill introduced
the necessary qualifications, the unqualified thesis was
confusing. It is perfectly true that we may infer&mdash;we
can hardly be said to reason&mdash;from observed particulars
to unobserved. We may even infer, and infer correctly,
from a single case. The village matron, called in to
prescribe for a neighbour's sick child, infers that what
cured her own child will cure the neighbour's, and
prescribes accordingly. And she may be right. But
it is also true that she may be wrong, and that no
fallacy is more common than reasoning from particulars
to particulars without the requisite precautions. This
is the moral of one of the fables of Camerarius. Two
donkeys were travelling in the same caravan, the one
laden with salt, the other with hay. The one laden with
salt stumbled in crossing a stream, his panniers dipped
in the stream, the salt melted, and his burden was
lightened. When they came to another stream, the
donkey that was laden with hay dipped his panniers
<span class="pagenum"><a name="page267" id="page267"></a>[page&nbsp;267]</span>
in the water, expecting a similar result. Mill's illustrations
of correct inference from particulars to particulars
were really irrelevant. What we are concerned with in
considering the grounds of Inference, is the condition
of correct inference, and no inference to an unobserved
case is sound unless it is of a like kind with the
observed case or cases on which it is founded, that
is to say, unless we are entitled to make a general
proposition. We need not go through the form of
making a general proposition, but if a general proposition
for all particulars of a certain description is not
legitimate, no more is the particular inference. Mill,
of course, did not deny this, he was only betrayed by
the turn of his polemic into an unqualified form of
statement that seemed to ignore it.</p>

<p>But this was not the worst defect of Mill's attempt
at a junction of old and new through Whately's conception
of Induction. A more serious defect was due
to the insufficiency of this conception to represent all
the modes of scientific inference. When a certain
attribute has been found in a certain connexion in this,
that, and the other, to the extent of all observed
instances, we infer that it will be found in all, that the
connexion that has obtained within the range of our
actual experience has obtained beyond that range and
will obtain in the future. Call this an observed uniformity
of nature: we hold ourselves justified in
expecting that the observed uniformities of nature will
continue. Such an observed uniformity&mdash;that All
animals have a nervous system, that All animals die,
that Quinine cures ague&mdash;is also called an Empirical
Law.</p>

<p>But while we are justified in extending an empirical
law beyond the limits within which it has been
<span class="pagenum"><a name="page268" id="page268"></a>[page&nbsp;268]</span>
observed to hold good, it is a mistake to suppose that
the main work of science is the collection of empirical
laws, and that the only scientific inference is the
inference from the observed prevalence of an empirical
law to its continuance. With science the collection of
empirical laws is only a preliminary: "the goal of
science," in Herschel's phrase, "is explanation". In
giving such prominence to empirical laws in his theory,
Mill confined Induction to a narrower scope than
science ascribes to it. Science aims at reaching "the
causes of things": it tries to penetrate behind observed
uniformities to the explanation of them. In fact, as long
as a science consists only of observed uniformities, as
long as it is in the empirical stage, it is a science only
by courtesy. Astronomy was in this stage before the
discovery of the Law of Gravitation. Medicine is
merely empirical as long as its practice rests upon such
generalisations as that Quinine cures ague, without
knowing why. It is true that this explanation may
consist only in the discovery of a higher or deeper uniformity,
a more recondite law of connexion: the point
is that these deeper laws are not always open to
observation, and that the method of reaching them is
not merely observing and recording.</p>

<p>In the body of his Inductive Logic, Mill gave a
sufficient account of the Method of Explanation
as practised in scientific inquiry. It was only his
mode of approaching the subject that was confusing,
and made it appear as if the proper work of science
were merely extending observed generalities, as when
we conclude that all men will die because all men have
died, or that all horned animals ruminate because all
hitherto observed have had this attribute. A minor
source of confusion incident to the same controversy
<span class="pagenum"><a name="page269" id="page269"></a>[page&nbsp;269]</span>
was his refusing the title of Induction proper to a mere
summary of particulars. He seemed thereby to cast
a slight upon the mere summation of particulars.
And yet, according to his theory, it was those
particulars that were the basis of the Induction
properly so called. That all men will die is an
inference from the observation summed up in the
proposition that all men have died. If we refuse
the name of Induction to the general proposition of
fact, what are we to call it? The truth is that the
reason why the word Induction is applied indifferently
to the general proposition of fact and the general proposition
applicable to all time is that, once we are sure
of the facts, the transition to the inference is so simple
an affair that it has not been found necessary in
practice to distinguish them by different names.</p>

<p>Our criticism of Mill would itself mislead if it were
taken to mean that the methods of science which he
formulated are not the methods of science or that his
system of those methods is substantially incomplete.
His Inductive Logic as a system of scientific method
was a great achievement in organisation, a veritable
<i>Novum Organum</i> of knowledge. What kept him substantially
right was that the methods which he
systematised were taken from the practice of men of
science. Our criticism amounts only to this, that in
correlating the new system with the old he went upon
a wrong track. For more than two centuries Deduction
had been opposed to Induction, the <i>ars disserendi</i> to the
<i>ars inveniendi</i>. In trying to reconcile them and bring
them under one roof, Mill drew the bonds too tight.
In stating the terms of the union between the two
partners, he did not separate their spheres of work
with sufficient distinctness.</p>
<span class="pagenum"><a name="page270" id="page270"></a>[page&nbsp;270]</span>

<p>Mill's theory of Deduction and Induction and the
voluminous criticism to which in its turn it has been
subjected have undoubtedly been of great service in
clearing up the foundations of reasoning. But the
moral of it is that if we are to make the methods of
Science a part of Logic, and to name this department
Induction, it is better to discard altogether the questions
of General and Particular which are pertinent
to Syllogism, and to recognise the new department
simply as being concerned with a different kind of
inference, inference from facts to what lies beyond
them, inference from the observed to the unobserved.</p>

<p>That this is the general aim and proper work of
Science is evident from its history. Get at the secrets
of Nature by the study of Nature, penetrate to what
is unknown and unexperienced by help of what is
known and has been experienced, was the cry of the
early reformers of Science. Thus only, in Roger
Bacon's phrase, could certainty&mdash;assured, well grounded,
rational belief&mdash;be reached. This doctrine, like every
other, can be understood only by what it was intended
to deny. The way of reaching certainty that Roger
Bacon repudiated was argument, discussion, dialectic.
This "concludes a question but does not make us feel
certain, or acquiesce in the contemplation of truth that
is not also found in Experience". Argument is not
necessarily useless; the proposition combated is only
that by it alone&mdash;by discussion that does not go beyond
accepted theories or conceptions&mdash;rational belief about
the unknown cannot be reached. The proposition
affirmed is that to this end the conclusions of argument
must be tested by experience.</p>

<p>Observation of facts then is a cardinal part of the
method of Science. The facts on which our inferences
<span class="pagenum"><a name="page271" id="page271"></a>[page&nbsp;271]</span>
are based, by which our conclusions are tested, must
be accurate. But in thus laying emphasis on the
necessity of accurate observation, we must beware of
rushing to the opposite extreme, and supposing that
observation alone is enough. Observation, the accurate
use of the senses (by which we must understand
inner as well as outer sense), is not the whole work of
Science. We may stare at facts every minute of our
waking day without being a whit the wiser unless we
exert our intellects to build upon them or under them.
To make our examination fruitful, we must have
conceptions, theories, speculations, to bring to the test.
The comparison of these with the facts is the inductive
verification of them. Science has to exercise its
ingenuity both in making hypotheses and in contriving
occasions for testing them by observation. These
contrived occasions are its artificial experiments, which
have come to be called experiments simply by contrast
with conclusive observations for which Nature herself
furnishes the occasion. The observations of Science
are not passive observations. The word experiment
simply means trial, and every experiment, natural or
artificial, is the trial of a hypothesis. In the language
of Leonardo da Vinci, "Theory is the general, Experiments
are the soldiers".</p>

<p>Observation and Inference go hand in hand in the
work of Science, but with a view to a methodical
exposition of its methods, we may divide them broadly
into Methods of Observation and Methods of Inference.
There are errors specially incident to Observation, and
errors specially incident to Inference. How to observe
correctly and how to make correct inferences from our
observations are the two objects of our study in Inductive
Logic: we study the examples of Science because
<span class="pagenum"><a name="page272" id="page272"></a>[page&nbsp;272]</span>
they have been successful in accomplishing those
objects.</p>

<p>That all inference to the unobserved is founded on
facts, on the data of experience, need not be postulated.
It is enough to say that Inductive Logic is concerned
with inference in so far as it is founded on the data of
experience. But inasmuch as all the data of experience
are not of equal value as bases of inference, it is
well to begin with an analysis of them, if we wish to
take a comprehensive survey of the various modes of
inference and the conditions of their validity.</p>

<p class="note1"><a id="footnoteB2-Intro1" name="footnoteB2-Intro1"></a><a class="footnote" href="#footnotetagB2-Intro1">Footnote 1:</a>
Hamilton's <i>Reid</i>, p. 712.</p>

<p class="note1"><a id="footnoteB2-Intro2" name="footnoteB2-Intro2"></a><a class="footnote" href="#footnotetagB2-Intro2">Footnote 2:</a>
The <i>Novum Organum</i> was never completed. Of the nine
heads of special aids to the intellect in the final interpretation he
completed only the first, the list of Prerogative Instances.</p>

<p class="note1"><a id="footnoteB2-Intro3" name="footnoteB2-Intro3"></a><a class="footnote" href="#footnotetagB2-Intro3">Footnote 3:</a>
<i>Sylva Sylvarum</i>, Century <span class="sc">I</span>, 24.</p>

<p class="note1"><a id="footnoteB2-Intro4" name="footnoteB2-Intro4"></a><a class="footnote" href="#footnotetagB2-Intro4">Footnote 4:</a>
<i>Sylva Sylvarum</i>, Century <span class="sc">I</span>, 5.</p>
<span class="pagenum"><a name="page273" id="page273"></a>[page&nbsp;273]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter I.</span></h3>

<h3>THE DATA OF EXPERIENCE AS GROUNDS OF INFERENCE OR RATIONAL BELIEF.</h3>

<p>If we examine any of the facts or particulars on which
an inference to the unobserved is founded, we shall
find that they are not isolated individuals or attributes,
separate objects of perception or thought, but relations
among things and their qualities, constituents, or
ingredients.</p>

<p>Take the "particular" from which Mill's village
matron inferred, the fact on which she based her
expectation of a cure for her neighbour's child. It is a
relation between things. We have the first child's
ailment, the administration of the drug, and the
recovery, a series of events in sequence. This observed
sequence is the fact from which she is said to infer, the
datum of experience. She expects this sequence to
be repeated in the case of her neighbour's child.</p>

<p>Similarly we shall find that, in all cases where we
infer, the facts are complex, are not mere isolated
things, but relations among things&mdash;using the word
thing in its widest sense&mdash;relations which we expect to
find repeated, or believe to have occurred before, or to
be occurring now beyond the range of our observation.
These relations, which we may call coincidences or
conjunctions, are the data of experience from which we
<span class="pagenum"><a name="page274" id="page274"></a>[page&nbsp;274]</span>
start in our beliefs or inferences about the unexperienced.</p>

<p>The problem of Inductive Logic being to determine
when or on what conditions such beliefs are rational,
we may begin by distinguishing the data of coincidence
or conjunction accordingly. There are certain coincidences
that we expect to find repeated beyond the
occasions on which we have observed them, and others
that we do not expect to find repeated. If it is a sound
basis of inference that we are in search of, it is evidently
to these first, the coincidences that we are assured of
finding again, that we must direct our study. Let us
see whether they can be specified.</p>

<p>(1) If there is no causal connexion between A and
B, using these as symbols for the members of a
coincidence&mdash;the objects that are presented together&mdash;we
do not expect the coincidence to be repeated. If A
and B are connected as cause and effect, we expect the
effect to recur in company with the cause. We expect
that when the cause reappears in similar circumstances,
the effect also will reappear.</p>

<p>You are hit, <i>e.g.</i>, by a snowball, and the blow is
followed by a feeling of pain. The sun, we shall
say, was shining at the moment of the impact of the
snowball on your body. The sunshine preceded your
feeling of pain as well as the blow. But you do not
expect the pain to recur next time that the sun shines.
You do expect it to recur next time you are hit by a
snowball.</p>

<p>The taking of food and a certain feeling of strength
are causally connected. If we go without food, we are
not surprised when faintness or weariness supervenes.</p>

<p>Suppose that when our village matron administered
her remedy to her own child, a dog stood by the
<span class="pagenum"><a name="page275" id="page275"></a>[page&nbsp;275]</span>
bedside and barked. The barking in that case would
precede the cure. Now, if the matron were what we
should call a superstitious person, and believed that
this concomitant had a certain efficacy, that the dog's
barking and the cure were causally connected, she
would take the dog with her when she went to cure
her neighbour's child. Otherwise she would not. She
would say that the barking was an accidental, casual,
fortuitous coincidence, and would build no expectation
upon it.</p>

<p>These illustrations may serve to remind us of the
familiar fact that the causal nexus is at least one of
the things that we depend on in our inferences to the
unobserved. To a simple sequence we attach no
importance, but a causal sequence or consequence that
has been observed is a mainstay of inference.</p>

<p>Whether the causal sequence holds or not as a
matter of fact, we depend upon it if we believe in it as
a matter of fact. But unless it does hold as a matter
of fact, it is valueless as a guide to the unknown, and
our belief is irrational. Clearly, therefore, if rational
belief is what we aim at, it is of importance that we
should make sure of cause and effect as matter of fact
in the sequence of events.</p>

<p>One large department of Inductive Logic, the so-called
Experimental Methods, is designed to help us in
thus making sure, <i>i.e.</i>, in ascertaining causal sequence
as a matter of fact. It is assumed that by careful
observation of the circumstances, we can distinguish
between mere simple sequence and causal sequence or
consequence, and methods are recommended of observing
with the proper precautions against error.</p>

<p>Observe that these methods, though called Inductive,
are not concerned with arriving at general propositions.
<span class="pagenum"><a name="page276" id="page276"></a>[page&nbsp;276]</span>
The principle we go upon is simply this, that if it can be
ascertained as matter of fact that a certain thing is
related to another as cause and effect, we may count
upon the same relation as holding in unobserved
Nature, on the general ground that like causes produce
like effects in like circumstances.</p>

<p>Observe, also, that I deliberately speak of the causal
relation as a relation among phenomena. Whether
this use of the words cause and effect is philosophically
justifiable, is a question that will be raised and partly
discussed later on. Here I simply follow the common
usage, in accordance with which objects of perception,
<i>e.g.</i>, the administration of a drug and the recovery of
a patient, are spoken of as cause and effect. Such
observable sequences are causal sequences in the
ordinary sense, and it is part of the work of Science to
observe them. I do not deny that the <i>true</i> cause, of
the cause that science aims ultimately at discovering,
is to be found in the latent constitution or composition
of the things concerned. Only that, as we shall see
more precisely, is a cause of another description.
Meantime, let us take the word to cover what it
undoubtedly covers in ordinary speech, the perceptible
antecedent of a perceptible consequent.</p>

<p>Strictly speaking, as we shall find, Science has only
one method of directly observing when events are in
causal sequence. But there are various indirect
methods, which shall be described in some sort of
order.</p>

<p>For the practical purposes of life, a single ascertained
causal sequence is of little value as a basis of inference,
because we can infer only to its repetition in identical
circumstances. Suppose our village matron had been
able to ascertain as a matter of fact&mdash;a feat as we shall
<span class="pagenum"><a name="page277" id="page277"></a>[page&nbsp;277]</span>
find not to be achieved by direct observation&mdash;that the
drug did cure her child, this knowledge by itself would
have been practically valueless, because the only
legitimate inference would have been that an exactly
similar dose would have the same effect in exactly
similar circumstances. But, as we shall find, though
practically valueless, a single ascertained causal
sequence is of supreme value in testing scientific
speculations as to the underlying causes.</p>

<p>(2) We have next to see whether there are any other
rational expectations based on observed facts. We
may lay down as a principle the following:&mdash;</p>

<p><i>If a conjunction or coincidence has constantly been
repeated within our experience, we expect it to recur and
believe that it has recurred outside our experience.</i></p>

<p>How far such expectations are rational, and with
what degrees of confidence they should be entertained,
are the questions for the Logic of Inference, but
we may first note that we do as a matter of habit
found expectations on repeated coincidence, and indeed
guide our daily life in this way. If we meet a man
repeatedly in the street at a certain hour, we go out
expecting to meet him: it is a shock to our expectations,
a surprise, when we do not. If we are walking along
a road and find poles set up at regular intervals, we
continue our walk expecting to find a pole coincident
with the end of each interval.</p>

<p>What Mill calls the uniformities of Nature, the
uniformities expressed in general propositions, are from
the point of view of the observer, examples of repeated
coincidence. Birth, growth, decay, death, are not
isolated or variable coincidences with organised being:
all are born, all grow, all decay, and all die. These
uniformities constitute the order of Nature: the coincidences
<span class="pagenum"><a name="page278" id="page278"></a>[page&nbsp;278]</span>
observed are not occasional, occurring once in
a way or only now and then; they turn up again and
again. Trees are among the uniformities on the
varied face of Nature: certain relations between the
soil and the plant, between trunk, branches, and leaves
are common to them. For us who observe, each
particular tree that comes under our observation is a
repetition of the coincidence. And so with animals:
in each we find certain tissues, certain organs, conjoined
on an invariable plan.</p>

<p>Technically these uniformities have been divided
into uniformities of Sequence and uniformities of
Coexistence. Thus the repeated alternation of day
and night is a uniformity of Sequence: the invariable
conjunction of inertia with weight is a uniformity of
Coexistence. But the distinction is really immaterial
to Logic. What Logic is concerned with is the observation
of the facts and the validity of any inference
based on them: and in these respects it makes no
difference whether the uniformity that we observe and
found upon is one of Sequence or of Coexistence.</p>

<p>It was exclusively to such inferences, inferences
from observed facts of repeated coincidence, that Mill
confined himself in his theory of Induction, though not
in his exposition of the methods. These are the
inferences for which we must postulate what he calls
the Uniformity of Nature. Every induction, he says,
following Whately, may be thrown into the form of a
Syllogism, in which the principle of the Uniformity of
Nature is the Major Premiss, standing to the inference
in the relation in which the Major Premiss of a
Syllogism stands to the conclusion. If we express this
abstractly denominated principle in propositional form,
and take it in connexion with Mill's other saying that
<span class="pagenum"><a name="page279" id="page279"></a>[page&nbsp;279]</span>
the course of Nature is not a uniformity but uniformities,
we shall find, I think, that this postulated Major
Premiss amounts to an assumption that the observed
Uniformities of Nature continue. Mill's Inductive
Syllogism thus made explicit would be something like
this:&mdash;</p>

<div class="poem1">  <div class="stanza">
<p>All the observed uniformities of Nature continue.</p>
<p>That all men have died is an observed uniformity.</p>
<p><i>Therefore</i>, it continues; <i>i.e.</i>, all men will die and did die before the beginning of record.</p>
  </div>  </div>

<p>There is no doubt that this is a perfectly sound
postulate. Like all ultimate postulates it is indemonstrable;
Mill's derivation of it from Experience did not
amount to a demonstration. It is simply an assumption
on which we act. If any man cares to deny it,
there is no argument that we can turn against him.
We can only convict him of practical inconsistency, by
showing that he acts upon this assumption himself
every minute of his waking day. If we do not believe
in the continuance of observed uniformities, why do we
turn our eyes to the window expecting to find it in its
accustomed order of place? Why do we not look for
it in another wall? Why do we dip our pens in ink,
and expect the application of them to white paper to
be followed by a black mark?</p>

<p>The principle is sound, but is it our only postulate
in inference to the unobserved, and does the continuance
of empirical laws represent all that Science
assumes in its inferences? Mill was not satisfied
about this question. He pointed out a difficulty which
a mere belief in empirical continuity does not solve.
Why do we believe more confidently in some uniformities
than in others? Why would a reported breach of
<span class="pagenum"><a name="page280" id="page280"></a>[page&nbsp;280]</span>
one be regarded with more incredulity than that of
another? Suppose a traveller to return from a strange
country and report that he had met men with heads
growing beneath their shoulders, why would this be
pronounced more incredible than a report that he had
seen a grey crow? All crows hitherto observed have
been black, and in all men hitherto observed the heads
have been above the shoulders: if the mere continuity
of observed uniformities is all that we go upon in our
inferences, a breach of the one uniformity should be
just as improbable as a breach of the other, neither
more nor less. Mill admitted the difficulty, and
remarked that whoever could solve it would have
solved the problem of Induction. Now it seems to me
that this particular difficulty may be solved, and yet
leave another behind. It may be solved within the
limits of the principle of emperical&mdash;meaning by that
observational&mdash;continuity. The uniform blackness of
the crow is an exception within a wider uniformity:
the colour of animals is generally variable. Hence we
are not so much surprised at the reported appearance
of a grey crow: it is in accordance with the more
general law. On the other hand, the uniform position
of the head relative to other parts of the body is a
uniformity as wide as the animal kingdom: it is a
coincidence repeated as often as animals have been
repeated, and merely on the principle that uniformities
continue, it has an absolutely uncontradicted series in
its favour.</p>

<p>But is this principle really all that we assume? Do
we not also assume that behind the observed fact
uniformity, there is a cause for it, a cause that does
not appear on the surface of the observation, but must
be sought outside of its range? And do not the various
<span class="pagenum"><a name="page281" id="page281"></a>[page&nbsp;281]</span>
degrees of confidence with which we expect a repetition
of the coincidence, depend upon the extent of our
knowledge of the producing causes and the mode of
their operation? At bottom our belief in the continuance
of the observed uniformities rests on a belief in
the continuance of the producing causes, and till we
know what these are our belief has an inferior warrant:
there is less reason for our confidence.</p>

<p>To go back to the illustrations with which we
started. If we have met a man every day for months
at a certain place at a certain hour, it is reasonable to
expect to meet him there to-morrow, even if our knowledge
does not go beyond the observed facts of repeated
coincidence. But if we know also what brings him
there, and that this cause continues, we have a stronger
reason for our expectation. And so with the case of
poles at regular intervals on a road. If we know why
they are placed there, and the range of the purpose,
we expect their recurrence more confidently within the
limits of that purpose. This further knowledge is a
warrant for stronger confidence, because if we know
the producing causes, we are in a better position for
knowing whether anything is likely to defeat the
coincidence. A uniformity is said to be explained
when its cause is known, and an inference from an
explained uniformity is always more certain than an
inference from a uniformity that is merely empirical in
the sense of being simply observed.</p>

<p>Now, the special work of Science is to explain, in
the sense of discovering the causes at work beneath
what lies open to observation. In so doing it follows
a certain method, and obeys certain conditions of
satisfactory explanation. Its explanations are inferences
from facts, inasmuch as it is conformity with
<span class="pagenum"><a name="page282" id="page282"></a>[page&nbsp;282]</span>
observed facts, with outward signs of underlying causal
nexus, that is the justification of them. But they are
not inferences from facts in the sense above described
as empirical inference. In its explanations also
Science postulates a principle that may be called the
Uniformity of Nature. But this principle is not
merely that observed uniformities continue. It may be
expressed rather as an assumption that the underlying
causes are uniform in their operation, that as they have
acted beneath the recorded experiences of mankind, so
they have acted before and will continue to act.</p>

<p style="margin-top: 2.5em">The foregoing considerations indicate a plan for a
roughly systematic arrangement of the methods of
Induction. Seeing that all inference from the data of
experience presupposes causal connexion among the
data from which we infer, all efforts at establishing
sound bases of inference, or rational ground for expectation
fall, broadly speaking, under two heads: (1)
Methods of ascertaining causal connexion among
phenomena as a matter of fact, that is, Methods of
Observation; and (2) Methods of ascertaining what
the causal connexion is, that is, Methods of Explanation.</p>

<p>These constitute the body of Inductive Logic. But
there is a preliminary and a pendant. Without
raising the question of causal connexion, we are liable
to certain errors in ascertaining in what sequence
and with what circumstances events really occurred.
These tendencies to error deserve to be pointed out by
way of warning, and this I shall attempt in a separate
chapter on observation of facts of simple sequence.
This is preliminary to the special methods of observing
causal sequence. Then, by way of pendant, I shall
consider two modes of empirical inference from data in
<span class="pagenum"><a name="page283" id="page283"></a>[page&nbsp;283]</span>
which the causal connexion has not been ascertained
or explained&mdash;Inference from approximate generalisations
to particular cases, and Inference from Analogy.</p>

<p>Most of these methods in one form or another were
included by Mill in his system of Inductive Logic, and
the great merit of his work was that he did include them,
though at some sacrifice of consistency with his introductory
theory. With regard to the kind of empirical
inference which that theory, following the lead of
Whately, took as the type of all inference, Logic has
really little to say. It was this probably that was in
Mill's mind when he said that there is no Logic of
Observation, ignoring the fact that the Experimental
Methods are really methods of observation, as well as
the Methods of Eliminating Chance by calculation of
Probability. There is no method of observing uniformities
except simply observing them. Nor indeed
is there any "method" of inferring from them: we
can only point out that in every particular inference
from them we assume or postulate their continuance
generally. As regards their observation, we may point
out further that a special fallacy is incident to it, the
fallacy of ignoring exceptions. If we are prepossessed
or prejudiced in favour of a uniformity, we are apt to
observe only the favourable instances, and to be blind
to cases where the supposed invariable coincidence
does not occur. Thus, as Bacon remarked among his
<i>Idola</i>, we are apt to remember when our dreams come
true, and to forget when they do not. Suppose we
take up the notion that a new moon on a Saturday is
invariably followed by twenty days of unsettled
weather, one or two or a few cases in which this notably
holds good are apt to be borne in mind, while cases
where the weather is neither conspicuously good nor
<span class="pagenum"><a name="page284" id="page284"></a>[page&nbsp;284]</span>
bad are apt to be overlooked. But when a warning
has been given against this besetting fallacy, Logic
has nothing further to say about empirical uniformities,
except that we may infer from them with some degree
of reasonable probability, and that if we want ground
for a more certain inference we should try to explain
them.</p>
<span class="pagenum"><a name="page285" id="page285"></a>[page&nbsp;285]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter II.</span></h3>

<h3>ASCERTAINMENT OF SIMPLE FACTS IN THEIR ORDER.&mdash;PERSONAL OBSERVATION.&mdash;HEARSAY EVIDENCE&mdash;METHOD OF TESTING TRADITIONAL EVIDENCE.</h3>

<p>All beliefs as to simple matter of fact must rest
ultimately on observation. But, of course, we believe
many things to have happened that we have never
seen. As Chaucer says:&mdash;</p>

<div class="poem">  <div class="stanza">
<p>But God forbed&euml; but men should&euml; 'lieve</p>
<p>Wel mor&euml; thing than men han seen with eye.</p>
<p>Man shall not weenen everything a lie</p>
<p>But if himself it seeth or els&euml; doth.</p>
  </div>  </div>

<p>For the great bulk of matters of fact that we believe
we are necessarily dependent on the observations of
others. And if we are to apply scientific method to
the ascertainment of this, we must know what errors
we are liable to in our recollections of what we have
ourselves witnessed, and what errors are apt to arise in
the tradition of what purports to be the evidence of
eye-witnesses.</p>

<h3 style="margin-top: 2em;"><span class="sc">I.&mdash;Personal Observation.</span></h3>

<p>It is hard to convince anybody that he cannot trust
implicitly to his memory of what he has himself seen.
<span class="pagenum"><a name="page286" id="page286"></a>[page&nbsp;286]</span>
We are ready enough to believe that others may be
deceived: but not our own senses. Seeing is believing.
It is well, however, that we should realise that all
observation is fallible, even our own.</p>

<p>Three great besetting fallacies or tendencies to error
may be specified:&mdash;</p>

<p>1. Liability to have the attention fastened on special
incidents, and so diverted from other parts of the
occurrence.</p>

<p>2. Liability to confuse and transpose the sequence
of events.</p>

<p>3. Liability to substitute inference for fact.</p>

<p>It is upon the first of these weaknesses in man as
an observing machine that jugglers chiefly depend on
working their marvels. Sleight of hand counts for
much, but diverting the spectator's eyes for a good
deal more. That is why they have music played and
patter incessantly as they operate. Their patter is not
purposeless: it is calculated to turn our eyes away
from the movements of their nimble hands.</p>

<p>It must be borne in mind that in any field of vision
there are many objects, and that in any rapid succession
of incidents much more passes before the eyes than the
memory can retain in its exact order. It is of course
in moments of excitement and hurry, when our observation
is distracted, that we are most subject to
fallacious illusions of memory. Unconsciously we
make a coherent picture of what we have seen, and
very often it happens that the sequence of events is
not what actually passed, but what we were prejudiced
in favour of seeing. Hence the unlikelihood of finding
exact agreement among the witnesses of any exciting
occurrence, a quarrel, a railway accident, a collision at
sea, the incidents of a battle.</p>
<span class="pagenum"><a name="page287" id="page287"></a>[page&nbsp;287]</span>

<p>"It commonly happens," says Mr. Kinglake,<a id="footnotetagB2-ChII1" name="footnotetagB2-ChII1"></a><a href="#footnoteB2-ChII1"><sup>1</sup></a> "that
incidents occurring in a battle are told by the most
truthful bystanders with differences more or less wide."
In the attack on the Great Redoubt in the Battle of the
Alma, a young officer, Anstruther, rushed forward and
planted the colours of the Royal Welsh&mdash;but where?
Some distinctly remembered seeing him dig the butt-end
of the flagstaff into the parapet: others as distinctly
remembered seeing him fall several paces before he
reached it. Similarly with the incidents of the death of
the Prince Imperial near the Italezi Hills in the Zulu
War. He was out as a volunteer with a reconnoitring
party. They had off-saddled at a kraal and were
resting, when a band of Zulus crept up through the
long grass, and suddenly opened fire and made a rush
forward. Our scouts at once took horse, as a reconnoitring
party was bound to do, and scampered off,
but the Prince was overtaken and killed. At the
Court-Martial which ensued, the five troopers gave
the most conflicting accounts of particulars which an
unskilled investigator would think could not possibly
have been mistaken by eye-witnesses of the same event.
One said that the Prince had given the order to mount
before the Zulus fired: another that he gave the order
directly after: a third was positive that he never gave
the order at all, but that it was given after the surprise
by the officer in command. One said that he saw the
Prince vault into the saddle as he gave the order:
another that his horse bolted as he laid hold of the
saddle, and that he ran alongside trying to get up.</p>

<p>The evidence before any Court of Inquiry into an
exciting occurrence is almost certain to reveal similar
<span class="pagenum"><a name="page288" id="page288"></a>[page&nbsp;288]</span>
discrepancies. But what we find it hard to realise is
that we ourselves can possibly be mistaken in what
we have a distinct and positive recollection of having
seen. It once happened to myself in a London street
to see a drunken woman thrown under a cab by her
husband. Two cabs were running along, a four-wheeler
and a hansom: the woman staggered almost
under the first, and was thrown under the second. As
it happened the case never got beyond the police
station to which the parties were conveyed after
fierce opposition from some neighbours, who sympathised
entirely with the man. The woman herself,
when her wounds were dressed, acknowledged the
justice of her punishment, and refused to charge her
husband. I was all the more willing to acquiesce in
this because I found that while I had the most distinct
impression of having seen the four-wheeler run over the
woman's body, and should have been obliged to swear
accordingly, there could be no doubt that it was really
the hansom that had done so. This was not only the
evidence of the neighbours, which I suspected at the time
of being a trick, but of the cabdriver, who had stopped
at the moment to abide the results of the accident. I
afterwards had the curiosity to ask an eminent police
magistrate, Sir John Bridge, whether this illusion of
memory on my part&mdash;which I can only account for by
supposing that my eyes had been fixed on the sufferer
and that I had unconsciously referred her injuries to
the heavier vehicle&mdash;would have entirely discredited
my testimony in his Court. His answer was that it
would not; that he was constantly meeting with such
errors, and that if he found a number of witnesses of
the same occurrence exactly agreed in every particular,
he would suspect that they had talked the matter over
<span class="pagenum"><a name="page289" id="page289"></a>[page&nbsp;289]</span>
and agreed upon what they were to say. This was
the opinion of an experienced judge, a skilled critic of
the defects of personal observation. An Old Bailey
counsel for the defence, who is equally acquainted with
the weakness of human memory, takes advantage of
the fact that it is not generally understood by a Jury,
and makes the fallacious assumption that glaring
discrepancies are irreconcilable with the good faith of
the witnesses who differ.<a id="footnotetagB2-ChII2" name="footnotetagB2-ChII2"></a><a href="#footnoteB2-ChII2"><sup>2</sup></a></p>

<h3 style="margin-top: 2em;"><span class="sc">II.&mdash;Tradition.&mdash;Hearsay Evidence</span>.</h3>

<p>Next in value to personal observation, we must place
the report, oral or written, of an eye-witness. This is
the best evidence we can get if we have not witnessed
an occurrence ourselves. Yet Courts of Law, which
in consideration of the defects of personal observation
require more than one witness to establish the truth,
exclude hearsay evidence altogether in certain cases,
and not without reason.</p>
<span class="pagenum"><a name="page290" id="page290"></a>[page&nbsp;290]</span>

<p>In hearing a report we are in the position of observers
of a series of significant sounds, and we are subject to all
the fallacies of observation already mentioned. In an
aggravated degree, for words are harder to observe than
visible things. Our attention is apt to be more listless
than in presence of the actual events. Our minds dwell
upon parts of the narrative to the neglect of other parts,
and in the coherent story or description that we retain
in our memories, sequences are apt to be altered and
missing links supplied in accordance with what we
were predisposed to hear. Thus hearsay evidence is
subject to all the imperfections of the original observer,
in addition to the still more insidious imperfections of
the second observer.</p>

<p>How quickly in the course of a few such transmissions
hearsay loses all evidentiary value is simply illustrated
by the game known as Russian Scandal. One of a
company, A, writes down a short tale or sketch, and
reads it to B. B repeats it to C, C to D, and so on.
When it has thus gone the round of the company, the
last hearer writes down his version, and it is compared
with the original. With every willingness to play fair,
the changes are generally considerable and significant.</p>

<p>Sometimes it is possible to compare an oral tradition
with a contemporary written record. In one of Mr.
Hayward's Essays&mdash;"The Pearls and Mock Pearls of
History"&mdash;there are some examples of this disenchanting
process. There is, for instance, a pretty story of
an exchange of courtesies between the leaders of the
French and English Guards at the battle of Fontenoy.
The tradition runs that Lord Charles Hay stepped
in front of his men and invited the French Guards
to fire, to which M. d'Auteroche with no less
chivalry responded: "Monsieur, we never fire first;
<span class="pagenum"><a name="page291" id="page291"></a>[page&nbsp;291]</span>
you fire". What really passed we learn from a letter
from Lord Charles Hay to his mother, which happens
to have been preserved. "I advanced before our
regiment, and drank to the Frenchmen, and told them
we were the English Guards, and hoped they would
stand till we came, and not swim the Scheldt as they
did the Maine at Dettingen." Tradition has changed
this lively piece of buffoonery into an act of stately and
romantic courtesy. The change was probably made
quite unconsciously by some tenth or hundredth
transmitter, who remembered only part of the story,
and dressed the remainder to suit his own fancy.</p>

<p>The question has been raised, For how long can oral
tradition be trusted? Newton was of opinion that it
might be trusted for eighty years after the event.
Others have named forty years. But if this means
that we may believe a story that we find in circulation
forty years after the alleged events, it is wildly extravagant.
It does injustice to the Mythop&oelig;ic Faculty
of man. The period of time that suffices for the
creation of a full-blown myth, must be measured by
hours rather than by years. I will give an instance
from my own observation, if that has not been entirely
discredited by my previous confessions. The bazaars
of the East are generally supposed to be the peculiar
home of myth, hotbeds in which myths grow with the
most amazing speed, but the locality of my myth is
Aberdeen. In the summer of 1887 our town set up in
one of its steeples a very fine carillon of Belgian bells.
There was much public excitement over the event: the
descriptions of enthusiastic promoters had prepared us
to hear silvery music floating all over the town and
filling the whole air. On the day fixed for the inauguration,
four hours after the time announced for
<span class="pagenum"><a name="page292" id="page292"></a>[page&nbsp;292]</span>
the first ceremonial peal, not having heard the bells, I
was in a shop and asked if anything had happened to
put off the ceremony. "Yes," I was told; "there had
been an accident; they had not been properly hung,
and when the wife of the Lord Provost had taken hold
of a string to give the first pull, the whole machinery
had come down." As a matter of fact all that had
happened was that the sound of the bells was faint,
barely audible a hundred yards from the belfry, and not
at all like what had been expected. There were
hundreds of people in the streets, and the myth had
originated somehow among those who had not heard
what they went out to hear. The shop where it was
repeated circumstantially to me was in the main street,
not more than a quarter of a mile from where the
carillon had been played in the hearing of a large but
disappointed crowd. I could not help reflecting that if
I had been a medi&aelig;val chronicler, I should have gone
home and recorded the story, which continued to
circulate for some days in spite of the newspapers:
and two hundred years hence no historian would have
ventured to challenge the truth of the contemporary
evidence.</p>

<h3 style="margin-top: 2em;"><span class="sc">III.&mdash;Method of Testing Traditional Evidence</span>.</h3>

<p>It is obvious that the tests applied to descriptive
testimony in Courts of Law cannot be applied to the
assertions of History. It is a supreme canon of
historical evidence that only the statements of contemporaries
can be admitted: but most even of their
statements must rest on hearsay, and even when the
historian professes to have been an eye-witness, the
range of his observation is necessarily limited, and he
<span class="pagenum"><a name="page293" id="page293"></a>[page&nbsp;293]</span>
cannot be put into the witness-box and cross-examined.
Is there then no way of ascertaining historical fact?
Must we reject history as altogether unworthy of
credit?</p>

<p>The rational conclusion only is that very few facts
can be established by descriptive testimony such as
would satisfy a Court of Law. Those who look for
such ascertainment are on a wrong track, and are
doomed to disappointment. It is told of Sir Walter
Raleigh that when he was writing his History of the
World, he heard from his prison in the Tower a
quarrel outside, tried to find out the rights and the
wrongs and the course of it, and failing to satisfy
himself after careful inquiry, asked in despair how he
could pretend to write the history of the world when he
could not find out the truth about what occurred under
his own windows. But this was really to set up an
impossible standard of historical evidence.</p>

<p>The method of testing historical evidence follows
rather the lines of the Newtonian method of Explanation,
which we shall afterwards describe. We must
treat any historical record as being itself in the first
place a fact to be explained. The statement at least is
extant: our first question is, What is the most rational
way of accounting for it? Can it be accounted for
most probably by supposing the event stated to have
really occurred with all the circumstances alleged? Or
is it a more probable hypothesis that it was the result
of an illusion of memory on the part of the original
observer, if it professes to be the record of an eye-witness,
or on the part of some intermediate transmitter,
if it is the record of a tradition? To qualify
ourselves to answer the latter kind of question with
reasonable probability we must acquaint ourselves
<span class="pagenum"><a name="page294" id="page294"></a>[page&nbsp;294]</span>
with the various tendencies to error in personal
observation and in tradition, and examine how far any
of them are likely to have operated in the given case.
We must study the operation of these tendencies
within our experience, and apply the knowledge thus
gained. We must learn from actual observation of
facts what the Mythop&oelig;ic Faculty is capable of in
the way of creation and transmutation, and what
feats are beyond its powers, and then determine with
as near a probability as we can how far it has been
active in the particular case before us.</p>

<p class="note1"><a id="footnoteB2-ChII1" name="footnoteB2-ChII1"></a><a class="footnote" href="#footnotetagB2-ChII1">Footnote 1:</a>
<i>The Invasion of the Crimea</i>, iii. 124</p>

<p class="note1"><a id="footnoteB2-ChII2" name="footnoteB2-ChII2"></a><a class="footnote" href="#footnotetagB2-ChII2">Footnote 2:</a>
The truth is, that we see much less than is commonly supposed.
Not every impression is attended to that is made on the
retina, and unless we do attend we cannot, properly speaking, be
said to see. Walking across to college one day, I was startled by
seeing on the face of a clock in my way that it was ten minutes to
twelve, whereas I generally passed that spot about twenty minutes
to twelve. I hurried on, fearing to be late, and on my arrival
found myself in very good time. On my way back, passing the
clock again, I looked up to see how much it was fast. It marked
ten minutes to eight. It had stopped at that time. When I
passed before I had really seen only the minute hand. The whole
dial must have been on my retina, but I had looked at or attended
to only what I was in doubt about, taking the hour for granted.
I am bound to add that my business friends hint that it is only
absorbed students that are capable of such mistakes, and that alert
men of business are more circumspect. That can only be because
they are more alive to the danger of error.</p>
<span class="pagenum"><a name="page295" id="page295"></a>[page&nbsp;295]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter III.</span></h3>

<h3>ASCERTAINMENT OF FACTS OF CAUSATION.</h3>

<h3 style="margin-top: 2em"><span class="sc">I.&mdash;<i>Post Hoc ergo Propter Hoc</i></span>.</h3>

<p>One of the chief contributions of the Old Logic to
Inductive Method was a name for a whole important
class of misobservations. The fallacy entitled <i>Post
Hoc ergo Propter Hoc</i>&mdash;"After, therefore, Because of"&mdash;consisted
in alleging mere sequence as a proof of
consequence or causal sequence. The sophist appeals
to experience, to observed facts: the sequence which
he alleges has been observed. But the appeal is
fallacious: the observation on which he relies amounts
only to this, that the one event has followed upon the
other. This much must be observable in all cases of
causal sequence, but it is not enough for proof. <i>Post
hoc ergo propter hoc</i> may be taken as a generic name for
imperfect proof of causation from observed facts of
succession.</p>

<p>The standard example of the fallacy is the old
Kentish peasant's argument that Tenterden Steeple
was the cause of Goodwin Sands. Sir Thomas More
(as Latimer tells the story in one of his Sermons to
ridicule incautious inference) had been sent down into
Kent as a commissioner to inquire into the cause of
the silting up of Sandwich Haven. Among those who
came to his court was the oldest inhabitant, and
<span class="pagenum"><a name="page296" id="page296"></a>[page&nbsp;296]</span>
thinking that he from his great age must at least have
seen more than anybody else, More asked him what
he had to say as to the cause of the sands. "Forsooth,
sir," was the greybeard's answer, "I am an old
man: I think that Tenterden Steeple is the cause of
Goodwin Sands. For I am an old man, and I may
remember the building of Tenterden Steeple, and I
may remember when there was no steeple at all there.
And before that Tenterden Steeple was in building,
there was no manner of speaking of any flats or sands
that stopped the haven; and, therefore, I think that
Tenterden Steeple is the cause of the destroying and
decaying of Sandwich Haven."</p>

<p>This must be taken as Latimer meant it to be, as a
ridiculous example of a purely imbecile argument from
observation, but the appeal to experience may have
more show of reason and yet be equally fallacious.
The believers in Kenelm Digby's "Ointment of
Honour" appealed to experience in support of its
efficacy. The treatment was to apply the ointment,
not to the wound, but to the sword that had inflicted
it, to dress this carefully at regular intervals, and,
meantime, having bound up the wound, to leave it
alone for seven days. It was observed that many cures
followed upon this treatment. But those who inferred
that the cure was due to the bandaging of the sword,
failed to observe that there was another circumstance
that might have been instrumental, namely, the
exclusion of the air and the leaving of the wound
undisturbed while the natural healing processes went
on. And it was found upon further observation that
binding up the wound alone answered the purpose
equally well whether the sword was dressed or not.</p>

<p>In cases where <i>post hoc</i> is mistaken for <i>propter hoc</i>,
<span class="pagenum"><a name="page297" id="page297"></a>[page&nbsp;297]</span>
simple sequence for causal sequence, there is commonly
some bias of prejudice or custom which fixes
observation on some one antecedent and diverts
attention from other circumstances and from what
may be observed to follow in other cases. In the
minds of Digby and his followers there was probably
a veneration for the sword as the weapon of honour,
and a superstitious belief in some secret sympathy
between the sword and its owner. So when the
practice of poisoning was common, and suspicion was
flurried by panic fear, observation was often at fault.
Pope Clement VIII. was said to have been killed by
the fumes of a poisoned candle which was placed in
his bedroom. Undoubtedly candles were there, but
those who attributed the Pope's death to them took no
notice of the fact that a brazier of burning charcoal was
at the same time in the apartment with no sufficient
outlet for its fumes. Prince Eugene is said to have
received a poisoned letter, which he suspected and immediately
threw from him. To ascertain whether his
suspicions were well founded the letter was administered
to a dog, which, to make assurance doubly sure, was
fortified by an antidote. The dog died, but no inquiry
seems to have been made into the character of the
antidote.</p>

<p>Hotspur's retort to Glendower showed a sound sense
of the true value to be attached to mere priority.</p>

<div class="poem3">  <div class="stanza">
<p><i>Glendower</i>.</p>
<p class="i26" style="margin-top: -1.1em;">At my nativity</p>
<p class="i8">The front of heaven was full of fiery shapes,</p>
<p class="i8">Of burning cressets: and at my birth</p>
<p class="i8">The frame and huge foundation of the earth</p>
<p class="i8">Shaked like a coward.</p>
  </div><div class="stanza">
<p><i>Hotspur</i>. Why so it would have done at the same season, if</p>
<p>your mother's cat had but kittened, though yourself had never</p>
<p>been born.</p>
  </div><div class="stanza">
<p class="i32" style="margin-top: -2em; margin-bottom: 2em;">1 Hen. IV., 3, 1, 13.</p>
  </div>  </div>
<span class="pagenum"><a name="page298" id="page298"></a>[page&nbsp;298]</span>

<p>We all admit at once that the retort was just.
What principle of sound conclusion was involved in
it? It is the business of Inductive Logic to make such
principles explicit.</p>

<p>Taking <i>Post Hoc ergo Propter Hoc</i> as a generic name
for fallacious arguments of causation based on
observed facts, for the fallacious proof of causation
from experience, the question for Logic is, What more
than mere <i>sequence</i> is required to prove <i>consequence?</i>
When do observations of <i>Post Hoc</i> warrant the conclusion
<i>Propter Hoc?</i></p>

<h3 style="margin-top: 2em;"><span class="sc">II.&mdash;Meaning of "Cause".&mdash;Methods of Observation&mdash;Mill's
Experimental Methods.</span></h3>

<p>The methods formulated by Mill under the name of
Experimental Methods are methods actually practised
by men of science with satisfactory results, and are
perfectly sound in principle. They were, indeed, in
substance, taken by him from the practice of the
scientific laboratory and study as generalised by
Herschel. In effect what Mill did was to restate them
and fit them into a system. But the controversies
into which he was tempted in so doing have somewhat
obscured their exact function in scientific inquiry.
Hostile critics, finding that they did not serve the ends
that he seemed to claim for them, have jumped to the
conclusion that they are altogether illusory and serve
no purpose at all.</p>

<p>First, we must dismiss the notion, encouraged by
Mill's general theory of Inference, that the Experimental
Methods have anything special to do with the
observation and inferential extension of uniformities
such as that death is common to all organised beings.
<span class="pagenum"><a name="page299" id="page299"></a>[page&nbsp;299]</span>
One of the Methods, as we shall see, that named by
Mill the Method of Agreement, does incidentally and
collaterally establish empirical laws in the course of
its observations, and this probably accounts for the
prominence given to it in Mill's system. But this is
not its end and aim, and the leading Method, that
named by him the Method of Difference, establishes
as fact only a particular case of causal coincidence.
It is with the proof of theories of causation that
the Experimental Methods are concerned: they are
methods of observing with a view to such proof.<a id="footnotetagB2-ChIII1" name="footnotetagB2-ChIII1"></a><a href="#footnoteB2-ChIII1"><sup>1</sup></a></p>

<p>The next point to be made clear is that the facts of
causation with which the Methods are concerned are
observable facts, relations among phenomena, but that
the causal relations or conditions of which they are
the proof are not phenomena, in the meaning of being
manifest to the senses, but rather noumena, inasmuch
as they are reached by reasoning from what is manifest.</p>

<p>Take, for example, what is known as the <i>quaquaversus</i>
principle in Hydrostatics, that pressure upon a liquid
is propagated equally in all directions. We cannot
observe this extension of pressure among the liquid
particles directly. It cannot be traced among the
particles by any of our senses. But we can assume
that it is so, consider what ought to be visible if it is
so, and then observe whether the visible facts are in
accordance with the hypothesis. A box can be made,
filled with water, and so fitted with pistons on top and
bottom and on each of its four sides that they will
<span class="pagenum"><a name="page300" id="page300"></a>[page&nbsp;300]</span>
indicate the amount of pressure on them from within.
Let pressure then be applied through a hole in the top,
and the pistons show that it has been communicated
to them equally. The application of the pressure and
the yielding of the pistons are observable facts, facts
in causal sequence: what happens among the particles
of the liquid is not observed but reasonably conjectured,
is not <i>phenomenal</i> but <i>noumenal</i>.</p>

<p>This distinction, necessary to an understanding of
the scope of the Methods, was somewhat obscured by
Mill in his preliminary discussion of the meaning of
"cause". Very rightly, though somewhat inconsistently
with his first theory of Induction, he insists that "the
notion of Cause being the root of the whole theory of
Induction, it is indispensable that this idea should at the
very outset of our inquiry be, with the utmost practicable
degree of precision, fixed and determined". But in this
determination, not content with simply recognising
that it is with phenomena that the Experimental
Methods primarily deal, it being indeed only phenomena
that can be the subjects of experimental management
and observation, he starts by declaring that science
has not to do with any causes except such as are
phenomenal&mdash;"when I speak of the cause of any
phenomenon, I do not mean a cause which is not itself
a phenomenon"&mdash;and goes on to define as the only
correct meaning of cause "the sum total of conditions,"
including among them conditions which are not
phenomenal, in the sense of being directly open to
observation.</p>

<p>When Mill protested that he had regard only to
phenomenal causes, he spoke as the partisan of a
philosophical tradition. It would have been well if
he had acted upon his own remark that the proper
<span class="pagenum"><a name="page301" id="page301"></a>[page&nbsp;301]</span>
understanding of the scientific method of investigating
cause is independent of metaphysical analysis of what
cause means. Curiously enough, this remark is the
preface to an analysis of cause which has but slight
relevance to science, and is really the continuation of
a dispute begun by Hume. This is the key to his use
of the word phenomenon: it must be interpreted with
reference to this: when he spoke of causes as
phenomenal, he opposed the word to "occult" in some
supposed metaphysical sense.<a id="footnotetagB2-ChIII2" name="footnotetagB2-ChIII2"></a><a href="#footnoteB2-ChIII2"><sup>2</sup></a>
And this irrelevant
discussion, into the vortex of which he allowed himself
to be carried, obscured the fact, elsewhere fully recognised
by Mill himself, that science does attempt to get
beyond phenomena at ultimate laws which are not
themselves phenomena though they bind phenomena
together. The "colligation" of the facts, to use
Whewell's phrase, is not a phenomenon, but a
noumenon.</p>

<p>The truth is that a very simple analysis of "cause"
is sufficient for the purposes of scientific inquiry. It is
enough to make sure that causal sequence or consequence
shall not be confounded with simple sequence.
Causal sequence is simple sequence and something
more, that something more being expressed by calling
it causal. What we call a cause is not merely
antecedent or prior in time to what we call its effect:
it is so related to the effect that if it or an equivalent
event had not happened the effect would not have
happened. Anything in the absence of which a
<span class="pagenum"><a name="page302" id="page302"></a>[page&nbsp;302]</span>
phenomenon would not have come to pass as it did
come to pass is a cause in the ordinary sense. We
may describe it as an indispensable antecedent, with
this reservation (which will be more fully understood
afterwards), that if we speak of a general effect, such
as death, the antecedents must be taken with corresponding
generality.</p>

<p>It is misleading to suggest, as Mill does, by defining
cause as "the sum total of conditions"&mdash;a definition
given to back up his conception of cause as phenomenal&mdash;that
science uses the word cause in a different
meaning from that of ordinary speech. It is quite true
that "the cause, philosophically speaking, is the sum
total of the conditions, positive and negative, taken
together: the whole of the contingencies of every
description, which being realised, the consequent
invariably follows". But this does not imply any
discrepancy between the scientific or philosophical
meaning and the ordinary meaning. It is only another
way of saying that the business of science or philosophy
is to furnish a complete explanation of an event, an
account of all its indispensable antecedents. The
plain man would not refuse the name of cause to
anything that science or philosophy could prove to
be an indispensable antecedent, but his interest in
explanation is more limited. It is confined to what he
wants to know for the purpose he has in hand. Nor
could the man of science consistently refuse the name
of cause to what the plain man applies it to, if it really
was something in consequence of which the event
took place. Only his interest in explanation is
different. The indispensable antecedents that he
wants to know may not be the same. Science or
philosophy applies itself to the satisfaction of a wider
<span class="pagenum"><a name="page303" id="page303"></a>[page&nbsp;303]</span>
curiosity: it wants to know all the causes, the whole
why, the sum total of conditions. To that end the
various departments of science interest themselves in
various species of conditions. But all understand the
word cause in the ordinary sense.</p>

<p>We must not conclude from accidental differences in
explanation or statement of cause, dependent on the
purpose in view, that the word Cause is used in
different senses. In answering a question as to the
cause of anything, we limit ourselves to what we
suppose our interrogator to be ignorant of and desirous
of knowing. If asked why the bells are ringing, we
mention a royal marriage, or a victory, or a church
meeting, or a factory dinner hour, or whatever the
occasion may be. We do not consider it necessary to
mention that the bells are struck by a clapper. Our
hearer understands this without our mentioning it.
Nor do we consider it necessary to mention the
acoustic condition, that the vibration of the bells is
communicated to our ears through the air, or the
physiological condition, that the vibrations in the
drums of our ears are conveyed by a certain mechanism
of bone and tissue to the nerves. Our hearer may not
care to know this, though quite prepared to admit
that these conditions are indispensable antecedents.
Similarly, a physiographer, in stating the cause of the
periodical inundation of the Nile, would consider it
enough to mention the melting of snow on the mountains
in the interior of Africa, without saying anything
of such conditions as the laws of gravity or the laws of
liquefaction by heat, though he knows that these conditions
are also indispensable. Death is explained by
the doctor when referred to a gunshot wound, or a
poison, or a virulent disease. The Pathologist may
<span class="pagenum"><a name="page304" id="page304"></a>[page&nbsp;304]</span>
inquire further, and the Moral Philosopher further
still. But all inquiries into indispensable conditions
are inquiries into cause. And all alike have to be on
their guard against mistaking simple sequence for
consequence.</p>

<p>To speak of the sum total of conditions, as the
Cause in a distinctively scientific sense, is misleading
in another direction. It rather encourages the idea
that science investigates conditions in the lump, merely
observing the visible relations between sets of antecedents
and their consequents. Now this is the very
thing that science must avoid in order to make progress.
It analyses the antecedent situation, tries to separate
the various coefficients, and finds out what they are
capable of singly. It must recognise that some of the
antecedents of which it is in search are not open to
observation. It is these, indeed, for the most part
that constitute the special subject-matter of the
sciences in Molar as well as in Molecular Physics.
For practical every-day purposes, it is chiefly the
visible succession of phenomena that concerns us, and
we are interested in the latent conditions only in as far
as they provide safer ground for inference regarding
such visible succession. But to reach the latent
conditions is the main work of science.</p>

<p>It is, however, only through observation of what is
open to the senses that science can reach the underlying
conditions, and, therefore, to understand its
methods we must consider generally what is open to
observation in causal succession. What can be
observed when phenomena follow one another as
cause and effect, that is, when the one happens in consequence
of the happening of the other? In Hume's
theory, which Mill formally adopted with a modification,<a id="footnotetagB2-ChIII3" name="footnotetagB2-ChIII3"></a><a href="#footnoteB2-ChIII3"><sup>3</sup></a>
<span class="pagenum"><a name="page305" id="page305"></a>[page&nbsp;305]</span>
there is nothing observable but the constancy or
invariability of the connexion. When we say that
Fire burns, there is nothing to be observed except that
a certain sensation invariably follows upon close
proximity to fire. But this holds good only if our
observation is arbitrarily limited to the facts enounced
in the expression. If this theory were sound, science
would be confined to the observation of empirical laws.
But that there is something wrong with it becomes
apparent when we reflect that it has been ascertained
beyond doubt that in many observed changes, and
presumably in all, there is a transference of energy
from one form to another. The paralogism really lies
in the assumption from which Hume deduced his
theory, namely, that every idea is a copy of some
impression. As a matter of fact, we have ideas that
are not copies of any one impression, but a binding
together, colligation, or intellection of several impressions.
Psychological analysis shows us that even when
we say that things exist with certain qualities, we are
expressing not single impressions or mental phenomena,
but supposed causes and conditions of such,
<i>noumena</i> in short, which connect our recollections of
many separate impressions and expectations of more.</p>

<p>The Experimental Methods proceed on the assumption
that there is other outward and visible evidence
<span class="pagenum"><a name="page306" id="page306"></a>[page&nbsp;306]</span>
of causal connexion than invariability of sequence. In
the leading Method it is assumed that when events
may be observed to follow one another in a certain
way, they are in causal sequence. If we can make
sure that an antecedent change is the only change that
has occurred in an antecedent situation, we have proof
positive that any immediately subsequent change in
the situation is a consequent, that the successive
changes are in causal sequence. Thus when Pascal's
barometer was carried to the top of Puy le Dome, and
the mercury in it fell, the experimenters argued that
the fall of the mercury was causally connected with
the change of elevation, all the other circumstances
remaining the same. This is the foundation of the
so-called Method of Difference. To determine that the
latent condition was a difference in the weight of the
atmosphere, needed other observations, calculations
and inferences; but if it could be shown that the
elevation was the only antecedent changed in a single
instance, causal connexion was established between
this and the phenomenon of the fall of the barometer.</p>

<p>It is obvious that in coming to this conclusion we
assume what cannot be demonstrated but must simply
be taken as a working principle to be confirmed by its
accordance with experience, that nothing comes into
being without some change in the antecedent circumstances.
This is the assumption known as the Law of
Causation&mdash;<i>ex nihilo nihil fit</i>.</p>

<p>Again, certain observable facts are taken as evidence
that there is no causal connexion. On the assumption
that any antecedent in whose absence a phenomenon
takes place is not causally connected with it, we set
aside or eliminate various antecedents as fortuitous or
non-causal. This negative principle, as we shall see,
<span class="pagenum"><a name="page307" id="page307"></a>[page&nbsp;307]</span>
is the foundation of what Mill called the Method of
Agreement.</p>

<p>Be it remarked, once for all, that before coming to
a conclusion on the Positive Method or Method of
Difference, we may often have to make many observations
on the Negative Method. Thus Pascal's experimenters,
before concluding that the change of altitude
was the only influential change, tried the barometer in
exposed positions and in sheltered, when the wind
blew and when it was calm, in rain and in fog, in
order to prove that these circumstances were indifferent.
We must expound and illustrate the methods separately,
but every method known to science may have
in practice to be employed in arriving at a single
conclusion.</p>

<p class="note1"><a id="footnoteB2-ChIII1" name="footnoteB2-ChIII1"></a><a class="footnote" href="#footnotetagB2-ChIII1">Footnote 1:</a>
This is implied, as I have already remarked, in the word
Experimental. An experiment is a proof or trial: of what? Of a
theory, a conjecture.</p>

<p class="note1"><a id="footnoteB2-ChIII2" name="footnoteB2-ChIII2"></a><a class="footnote" href="#footnotetagB2-ChIII2">Footnote 2:</a>
If we remember, as becomes apparent on exact psychological
analysis, that things and their qualities are as much <i>noumena</i> and
not, strictly speaking, <i>phenomena</i> as the attraction of gravity or
the quaquaversus principle in liquid pressure, the prejudice against
occultism is mitigated.</p>

<p class="note1"><a id="footnoteB2-ChIII3" name="footnoteB2-ChIII3"></a><a class="footnote" href="#footnotetagB2-ChIII3">Footnote 3:</a>
The modification was that causation is not only "invariable"
but also "unconditional" sequence. This addition of unconditionality
as part of the meaning of cause, after defining cause
as the sum total of the conditions, is very much like arguing in a
circle. After all, the only point recognised in the theory as
observable is the invariability of the sequence. But this is less
important than the fact that in his canons of the Experimental
Methods Mill recognised that more is observable.</p>
<span class="pagenum"><a name="page308" id="page308"></a>[page&nbsp;308]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter IV.</span></h3>

<h3>METHODS OF OBSERVATION.&mdash;SINGLE DIFFERENCE.</h3>

<h3 style="margin-top: 2em">I.&mdash;<span class="sc">The Principle of Single Difference.&mdash;
Mill's "Canon".</span></h3>

<p>On what principle do we decide, in watching a succession
of phenomena, that they are connected as
cause and effect, that one happened in consequence
of the happening of another? It may be worded as
follows:&mdash;</p>

<blockquote><p>
<i>When the addition of an agent is followed by the
appearance or its subtraction by the disappearance
of a certain effect, no other influential circumstance
having been added or subtracted at the same time
or in the meantime, and no change having occurred
among the original circumstances, that agent is a
cause of the effect.</i>
</p></blockquote>

<p>On this principle we would justify our belief in the
causal properties of common things&mdash;that fire burns,
that food appeases hunger, that water quenches thirst,
that a spark ignites gunpowder, that taking off a tight
shoe relieves a pinched foot. We have observed the
effect following when there was no other change in the
antecedent circumstances, when the circumstance to
which we refer it was simply added to or subtracted
from the prior situation.</p>
<span class="pagenum"><a name="page309" id="page309"></a>[page&nbsp;309]</span>

<p>Suppose we doubt whether a given agent is or is not
capable of producing a certain effect in certain circumstances,
how do we put it to the proof? We add it
singly or subtract it singly, taking care that everything
else remains as before, and watch the result. If we
wish to know whether a spoonful of sugar can sweeten
a cup of tea, we taste the tea without the sugar, then
add the sugar, and taste again. The isolated introduction
of the agent is the proof, the experiment. If we
wish to know whether a pain in the foot is due to a
tight lacing, we relax the lacing and make no other
change: if the pain then disappears, we refer it to the
lacing as the cause. The proof is the disappearance of
the pain on the subtraction of the single antecedent.</p>

<p>The principle on which we decide that there is causal
connexion is the same whether we make the experimental
changes ourselves or merely watch them as
they occur&mdash;the only course open to us with the great
forces of nature which are beyond the power of human
manipulation. In any case we have proof of causation
when we can make sure that there was only one
difference in the antecedent circumstances corresponding
to the difference of result.</p>

<p>Mill's statement of this principle, which he calls the
Canon of the Method of Difference, is somewhat more
abstract, but the proof relied upon is substantially the
same.</p>

<blockquote><p>
<i>If an instance in which the phenomenon under
investigation occurs, and an instance in which it
does not occur, have every circumstance in common
save one, that one occurring only in the former, the
circumstance in which alone the two instances differ
is [the effect, or]<a id="footnotetagB2-ChIV1" name="footnotetagB2-ChIV1"></a><a href="#footnoteB2-ChIV1"><sup>1</sup></a> the cause, or an indispensable part
of the cause, of the phenomenon.</i>
</p></blockquote>
<span class="pagenum"><a name="page310" id="page310"></a>[page&nbsp;310]</span>

<p>Mill's statement has the merit of exactness, but
besides being too abstract to be easy of application, the
canon is apt to mislead in one respect. The wording
of it suggests that the two instances required must be
two separate sets of circumstances, such as may be
put side by side and compared, one exhibiting the
phenomenon and the other not. Now in practice it is
commonly one set of circumstances that we observe
with a special circumstance introduced or withdrawn:
the two instances, the data of observation, are furnished
by the scene before and the scene after the experimental
interference. In the case, for example, of a man shot
in the head and falling dead, death being the phenomenon
in question, the instance where it does not occur
is the man's condition before he received the wound,
and the instance where it does occur is his condition
after, the single circumstance of difference being the
wound, a difference produced by the addition or
introduction of a new circumstance. Again, take the
common coin and feather experiment, contrived to
show that the resistance of the air is the cause of the
<span class="pagenum"><a name="page311" id="page311"></a>[page&nbsp;311]</span>
feather's falling to the ground more slowly than the
coin. The phenomenon under investigation is the
retardation of the feather. When the two are dropped
simultaneously in the receiver of an air-pump, the air
being left in, the feather flutters to the ground after
the coin. This is the instance where the phenomenon
occurs. Then the air is pumped out of the receiver,
and the coin and the feather being dropped at the
same instant reach the ground together. This is the
instance where the phenomenon does not occur. The single
circumstances of difference is the presence of air
in the former instance, a difference produced by the
subtraction of a circumstance.</p>

<p>Mill's Canon is framed so as to suit equally whether
the significant difference is produced by addition to or
subtraction from an existing sum of circumstances.
But that is misleading in so far as it suggests that the
two instances must be separate sets of circumstances,
is shown by the fact that it misled himself when he
spoke of the application of the method in social
investigations, such as the effect of Protection on
national wealth. "In order," he says, "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. We must
have two nations alike in all natural advantages and
disadvantages; resembling each other in every quality
physical and moral; habits, usages, laws, and institutions,
and differing only in the circumstance that the
one has a prohibitory tariff and the other has not." It
being impossible ever to find two such instances, he
concluded that the Method of Difference could not be
applied in social inquiries. But really it is not necessary
<span class="pagenum"><a name="page312" id="page312"></a>[page&nbsp;312]</span>
in order to have two instances that we should
have two different nations: the same nation before
and after a new law or institution fulfils that requirement.
The real difficulty, as we shall see, is to satisfy
the paramount condition that the two instances shall
differ in a single circumstance. Every new enactment
would be an experiment after the Method of Difference,
if all circumstances but it remained the same till its
results appeared. It is because this seldom or never
occurs that decisive observation is difficult or impossible,
and the simple method of difference has to be
supplemented by other means.</p>

<p>To introduce or remove a circumstance singly is the
typical application of the principle; but it may be employed
also to compare the effects of different agents,
each added alone to exactly similar circumstances. A
simple example is seen in Mr. Jamieson's agricultural
experiments to determine the effects of different
manures, such as coprolite and superphosphate, on
the growth of crops. Care is taken to have all the
antecedent circumstances as exactly alike as possible,
except as regards the agency whose effects are to be
observed. A field is chosen of uniform soil and even
exposure and divided into plots: it is equally drained
so as to have the same degree of moisture throughout;
the seed is carefully selected for the whole sowing.
Between the sowing and the maturing of the crop all
parts of the field are open to the same weather. Each
plot may thus be regarded as practically composing
the same set of conditions, and any difference in the
product may with reasonable probability be ascribed to
the single difference in the antecedents, the manures
which it is desired to compare.</p>

<span class="pagenum"><a name="page313" id="page313"></a>[page&nbsp;313]</span>

<h3 style="margin-top: 2em;"><span class="sc">II.&mdash;Application of the Principle.</span></h3>

<p>The principle of referring a phenomenon to the only
immediately preceding change in antecedent circumstances
that could possibly have affected it, is so simple
and so often employed by everybody every day, that
at first we do not see how there can be any difficulty
about it or any possibility of error. And once we
understand how many difficulties there are in reaching
exact knowledge even on this simple principle, and
what care has to be taken, we are apt to overrate its
value, and to imagine that it carries us further than it
really does. The scientific expert must know how to
apply this principle, and a single application of it with
the proper precautions may take him days or weeks,
and yet all that can be made good by it may carry but
a little way towards the knowledge of which he is in
search.</p>

<p>When the circumstances are simple and the effect
follows at once, as when hot water scalds, or a blow
with a stick breaks a pane of glass, there can be no
doubt of the causal connexion so far, though plenty
of room for further inquiry into the why. But the
mere succession of phenomena may be obscure. We
may introduce more than one agent without knowing
it, and if some time elapses between the experimental
interference and the appearance of the effect, other
agents may come in without our knowledge.</p>

<p>We must know exactly what it is that we introduce
and all the circumstances into which we introduce it.
We are apt to ignore the presence of antecedents that
are really influential in the result. A man heated by
work in the harvest field hastily swallows a glass of
water, and drops down dead. There is no doubt that
<span class="pagenum"><a name="page314" id="page314"></a>[page&nbsp;314]</span>
the drinking of the water was a causal antecedent, but
the influential circumstance may not have been the
quantity or the quality of the liquid but its temperature,
and this was introduced into the situation as well as a
certain amount of the liquid components. In making
tea we put in so much tea and so much boiling water.
But the temperature of the pot is also an influential
circumstance in the resulting infusion. So in chemical
experiments, where one might expect the result to
depend only upon the proportions of the ingredients,
it is found that the quantity is also influential, the
degree of heat evolved entering as a factor into the
result. Before we can apply the principle of single
difference, we must make sure that there is really only
a single difference between the instances that we
bring into comparison.</p>

<p>The air-pump was invented shortly before the foundation
of the Royal Society, and its members made
many experiments with this new means of isolating
an agent and thus discovering its potentialities. For
example, live animals were put into the receiver, and
the air exhausted, with the result that they quickly
died. The absence of the air being the sole difference,
it was thus proved to be indispensable to life. But air
is a composite agent, and when means were contrived
of separating its components, the effects of oxygen
alone and of carbonic acid alone were experimentally
determined.</p>

<p>A good example of the difficulty of excluding agencies
other than those we are observing, of making sure that
none such intrude, is found in the experiments that
have been made in connexion with spontaneous
generation. The question to be decided is whether
life ever comes into existence without the antecedent
<span class="pagenum"><a name="page315" id="page315"></a>[page&nbsp;315]</span>
presence of living germs. And the method of determining
this is to exclude all germs rigorously from a
compound of inorganic matter, and observe whether
life ever appears. If we could make sure in any one case
that no germs were antecedently present, we should
have proved that in that case at least life was
spontaneously generated.</p>

<p>The difficulty here arises from the subtlety of the
agent under observation. The notion that maggots
are spontaneously generated in putrid meat, was
comparatively easy to explode. It was found that
when flies were excluded by fine wire-gauze, the
maggots did not appear. But in the case of microscopic
organisms proof is not so easy. The germs are
invisible, and it is difficult to make certain of their
exclusion. A French experimenter, Pouchet, thought
he had obtained indubitable cases of spontaneous
generation. He took infusions of vegetable matter,
boiled them to a pitch sufficient to destroy all germs
of life, and hermetically sealed up the liquid in glass
flasks. After an interval, micro-organisms appeared.
Doubts as to the conclusion that they had been
spontaneously generated turned upon two questions:
whether all germs in the liquid had been destroyed by
the preliminary boiling, and whether germs could have
found access in the course of the interval before life
appeared. At a certain stage in Pouchet's process he
had occasion to dip the mouths of the flasks in mercury.
It occurred to Pasteur in repeating the experiments
that germs might have found their way in from the
atmospheric dust on the surface of this mercury. That
this was so was rendered probable by his finding that
when he carefully cleansed the surface of the mercury
no life appeared afterwards in his flasks.</p>
<span class="pagenum"><a name="page316" id="page316"></a>[page&nbsp;316]</span>

<p>The application of the principle in human affairs is
rendered uncertain by the immense complication of
the phenomena, the difficulty of experiment, and the
special liability of our judgments to prejudice. That
men and communities of men are influenced by circumstances
is not to be denied, and the influence of
circumstances, if it is to be traced at all, must be
traced through observed facts. Observation of the
succession of phenomena must be part at least of any
method of tracing cause and effect. We must watch
what follows upon the addition of new agencies to a
previously existing sum. But we can seldom or never
get a decisive observation from one pair of instances,
a clear case of difference of result preceded by a single
difference in the antecedents. The simple Method of
Experimental Addition or Subtraction is practically
inapplicable. We can do nothing with a man analogous
to putting him into a hermetically sealed retort. Any
man or any community that is the subject of our
observations must be under manifold influences.
Each of them probably works some fraction of the
total change observable, but how are they to be disentangled?
Consider, for example, how impossible it
would be to prove in an individual case, on the strict
principle of Single Difference, that Evil communications
corrupt good manners. Moral deterioration may
be observed following upon the introduction of an evil
companion, but how can we make sure that no other
degrading influence has operated, and that no original
depravity has developed itself in the interval? Yet
such propositions of moral causation can be proved
from experience with reasonable probability. Only it
must be by more extended observations than the strict
Method of Difference takes into account. The method
<span class="pagenum"><a name="page317" id="page317"></a>[page&nbsp;317]</span>
is to observe repeated coincidences between evil companionship
and moral deterioration, and to account for
this in accordance with still wider observations of the
interaction of human personalities.</p>

<p>For equally obvious reasons the simple Method of
Difference is inapplicable to tracing cause and effect
in communities. Every new law or repeal of an old
law is the introduction of a new agency, but the effects
of it are intermixed with the effects of other agencies
that operate at the same time. Thus Professor Cairnes
remarks, concerning the introduction of a high Protective
Tariff into the United States in 1861, that before
its results could appear in the trade and manufacture
of the States, there occurred (1) The great Civil War,
attended with enormous destruction of capital; (2)
Consequent upon this the creation of a huge national
debt, and a great increase of taxation; (3) The issue
of an inconvertible paper currency, deranging prices
and wages; (4) The discovery of great mineral
resources and oil-springs; (5) A great extension of
railway enterprise. Obviously in such circumstances
other methods than the Method of Difference must be
brought into play before there can be any satisfactory
reasoning on the facts observed. Still what investigators
aim at is the isolation of the results of single
agencies.</p>

<p class="note1"><a id="footnoteB2-ChIV1" name="footnoteB2-ChIV1"></a><a class="footnote" href="#footnotetagB2-ChIV1">Footnote 1:</a>
Prof. Bain, who adopts Mill's Canon, silently drops the words
within brackets. They seem to be an inadvertence. The "circumstance,"
in all the examples that Mill gives, is an antecedent
circumstance. Herschel's statement, of which Mill's is an adaptation,
runs as follows: "If we can either find produced by
nature, or produce designedly for ourselves, two instances which
agree exactly in all but one particular and differ in that one, its
influence in producing the phenomenon, if it have any, must
thereby be rendered apparent".</p>

<span class="pagenum"><a name="page318" id="page318"></a>[page&nbsp;318]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter V.</span></h3>

<h3>METHODS OF OBSERVATION.&mdash;ELIMINATION.&mdash;SINGLE AGREEMENT.</h3>

<h3 style="margin-top: 2em">I.&mdash;<span class="sc">The Principle of Elimination.</span></h3>

<p>The essence of what Mill calls the Method of Agreement
is really the elimination<a id="footnotetagB2-ChV1" name="footnotetagB2-ChV1"></a><a href="#footnoteB2-ChV1"><sup>1</sup></a>
of accidental, casual, or
fortuitous antecedents. It is a method employed when
we are given an effect and set to work to discover the
cause. It is from the effect that we start and work
back. We make a preliminary analysis of the antecedents;
call the roll, as it were, of all circumstances
present before the effect appeared. Then we proceed
to examine other instances of the same effect, and
other instances of the occurrence of the various antecedents,
and bring to bear the principle that any
antecedent in the absence of which the effect has
appeared or on the presence of which it has not
appeared may be set aside as fortuitous, as being not
<span class="pagenum"><a name="page319" id="page319"></a>[page&nbsp;319]</span>
an indispensable antecedent. This is really the
guiding principle of the method as a method of
observation.</p>

<p>Let the inquiry, for example, be into the cause of
Endemic Goitre. Instances of the disease have been
collected from the medical observations of all countries
over many years. Why is it endemic in some localities
and not in others? We proceed on the assumption
that the cause, whatever it is, must be some circumstance
common to all localities where it is endemic.
If any such circumstance is obvious at once, we may
conclude on the mere principle of repeated coincidence
that there is causal connexion between it and the
disease, and continue our inquiry into the nature of
the connexion. But if no such circumstance is obvious,
then in the course of our search for it we eliminate, as
fortuitous, conditions that are present in some cases but
absent in others. One of the earliest theories was that
endemic goitre was connected with the altitude and
configuration of the ground, some notorious centres of
it being deeply cleft mountain valleys, with little air
and wind and damp marshy soil. But wider observation
found it in many valleys neither narrower nor
deeper than others that were exempt, and also in wide
exposed valleys such as the Aar. Was it due to the
geological formation? This also had to be abandoned,
for the disease is often incident within very narrow
limits, occurring in some villages and sparing others
though the geological formation is absolutely the same.
Was it due to the character of the drinking-water?
Especially to the presence of lime or magnesia? This
theory was held strongly, and certain springs characterised
as goitre-springs. But the springs in some
goitre centres show not a trace of magnesia. The
<span class="pagenum"><a name="page320" id="page320"></a>[page&nbsp;320]</span>
comparative immunity of coast regions suggested that
it might be owing to a deficiency of iodine in the
drinking-water and the air, and many instances were
adduced in favour of this. But further inquiries made
out the presence of iodine in considerable quantities,
in the air, the water, and the vegetation of districts
where goitre was widely prevalent; while in Cuba it is
said that not a trace of iodine is discoverable either in
the air or the water, and yet it is quite free from goitre.
After a huge multiplication of instances, resulting in
the elimination of every local condition that had been
suggested as a possible cause, Hirsch came to the
conclusion that the true cause must be a morbid poison,
and that endemic goitre has to be reckoned among the
infectious diseases.<a id="footnotetagB2-ChV2" name="footnotetagB2-ChV2"></a><a href="#footnoteB2-ChV2"><sup>2</sup></a></p>

<p>On this negative principle, that if a circumstance
comes and goes without bringing the phenomenon in
its train, the phenomenon is causally independent of
it, common-sense is always at work disconnecting
events that are occasionally coincident in time. A bird
sings at our window, for example, and the clock ticks
on the mantelpiece. But the clock does not begin to
tick when the bird begins to sing, nor cease to tick
when the bird flies away. Accordingly, if the clock
should stop at any time, and we wished to inquire into
the cause, and anybody were to suggest that the
stoppage of the clock was caused by the stoppage of
a bird's song outside, we should dismiss the suggestion
at once. We should eliminate this circumstance from
our inquiry, on the ground that from other observations
we knew it to be a casual or fortuitous concomitant.
<span class="pagenum"><a name="page321" id="page321"></a>[page&nbsp;321]</span>
Hotspur's retort to Glendover (p. 297) was based on
this principle. When poetic sentiment or superstition
rejects a verdict of common-sense or science, it is
because it imagines a causal connexion to exist that is
not open to observation, as in the case of the grandfather's
clock which stopped short never to go again
when the old man died.</p>

<h3 style="margin-top: 2em;">II.&mdash;<span class="sc">The Principle of Single Agreement.</span></h3>

<p>The procedure in Mill's "Method of Agreement"
consists in thus eliminating fortuitous antecedents or
concomitants till only one remains. We see the
nature of the proof relied upon when we ask, How far
must elimination be carried in order to attain proof of
causal connexion? The answer is that we must go on
till we have eliminated all but one. We must multiply
instances of the phenomenon, till we have settled of each
of the antecedents except one that it is not the cause.
We must have taken account of all the antecedents,
and we must have found in our observations that all
but one have been only occasionally present.</p>

<blockquote><p>
<i>When all the antecedents of an effect except one can be absent
without the disappearance of the effect, that one is causally
connected with the effect, due precautions being taken
that no other circumstances have been present besides
those taken account of.</i>
</p></blockquote>

<p>Mill's Canon of the Method of Agreement is substantially
identical with this:&mdash;</p>

<blockquote><p>
When two or more instances of the phenomenon under
investigation have only one circumstance in common,
the circumstance in which alone all the instances
agree is the cause (or effect) of the given phenomenon.
</p></blockquote>
<span class="pagenum"><a name="page322" id="page322"></a>[page&nbsp;322]</span>

<p>Herschel's statement, on which this canon is
founded, runs as follows: "Any circumstance in
which all the facts without exception agree, may be the
cause in question, or if not, at least a collateral effect
of the same cause: if there be but one such point of
agreement, the possibility becomes a certainty".</p>

<p>All the instances examined must agree in one
circumstance&mdash;hence the title Method of Agreement.
But it is not in the agreement merely that the proof
consists, but the agreement in one circumstance combined
with difference in all the other circumstances,
when we are certain that every circumstance has come
within our observation. It is the singleness of the
agreement that constitutes the proof just as it is the
singleness of the difference in the Method of Difference.<a id="footnotetagB2-ChV3" name="footnotetagB2-ChV3"></a><a href="#footnoteB2-ChV3"><sup>3</sup></a></p>

<p>It has been said that Mill's Method of Agreement
amounts after all only to an uncontradicted <i>Inductio
per enumerationem simplicem</i>, which he himself stigmatised
as Induction improperly so called. But this is
not strictly correct. It is a misunderstanding probably
caused by calling the method that of agreement simply,
instead of calling it the Method of Single Agreement,
so as to lay stress upon the process of elimination by
which the singleness is established. It is true that
in the course of our observations we do perform an
induction by simple enumeration. In eliminating, we
<span class="pagenum"><a name="page323" id="page323"></a>[page&nbsp;323]</span>
at the same time generalise. That is to say, in
multiplying instances for the elimination of non-causes,
we necessarily at the same time multiply instances
where the true causal antecedent, if there is only one
possible, is present. An antecedent containing the
true cause must always be there when the phenomenon
appears, and thus we may establish by our eliminating
observations a uniformity of connexion between two
facts.</p>

<p>Take, for example, Roger Bacon's inquiry into the
cause of the colours of the rainbow. His first notion
seems to have been to connect the phenomenon with
the substance crystal, probably from his thinking of
the crystal firmament then supposed to encircle the
universe. He found the rainbow colours produced by
the passage of light through hexagonal crystals. But
on extending his observations, he found that the
passage of light through other transparent mediums
was also attended by the phenomenon. He found it
in dewdrops, in the spray of waterfalls, in drops
shaken from the oar in rowing. He thus eliminated
the substance crystal, and at the same time established
the empirical law that the passage of light through
transparent mediums of a globular or prismatic shape
was a causal antecedent of the rainbow colours.<a id="footnotetagB2-ChV4" name="footnotetagB2-ChV4"></a><a href="#footnoteB2-ChV4"><sup>4</sup></a></p>

<p>Ascertainment of invariable antecedents may thus
proceed side by side with that of variable antecedents,
the use of the elimination being simply to narrow the
scope of the inquiry. But the proof set forth in Mill's
Canon does not depend merely on one antecedent or
<span class="pagenum"><a name="page324" id="page324"></a>[page&nbsp;324]</span>
concomitant being invariably present, but also on the
assumption that all the influential circumstances have
been within our observation. Then only can we be
sure that the instances have <i>only one</i> circumstance in
common.</p>

<p>The truth is that owing to the difficulty of fulfilling
this condition, proof of causation in accordance with
Mill's Canon is practically all but impossible. It is
not attained in any of the examples commonly given.
The want of conclusiveness is disguised by the fact
that both elimination and positive observation of mere
agreement or uniform concomitance are useful and
suggestive in the search for causes, though they do not
amount to complete proof such as the Canon describes.
Thus in the inquiry into the cause of goitre, the
elimination serves some purpose though the result is
purely negative. When the inquirer is satisfied that
goitre is not originated by any directly observable local
conditions, altitude, temperature, climate, soil, water,
social circumstances, habits of exertion, his search is
profitably limited. And mere frequency, much more
constancy of concomitance, raises a presumption of
causal connexion, and looking out for it is valuable as
a mode of reconnoitring. The first thing that an
inquirer naturally asks when confronted by numerous
instances of a phenomenon is, What have they in
common? And if he finds that they have some one
circumstance invariably or even frequently present,
although he cannot prove that they have no other
circumstance in common as the Cannon of Single
Agreement requires, the presumption of causal connexion
is strong enough to furnish good ground for
further inquiry. If an inquirer finds an illness with
marked symptoms in a number of different households,
<span class="pagenum"><a name="page325" id="page325"></a>[page&nbsp;325]</span>
and finds also that all the households get their milk
supply from the same source, this is not conclusive
proof of causation, but it is a sufficient presumption
to warrant him in examining whether there is any
virulent ingredient in the milk.</p>

<p>Thus varying the circumstances so as to bring out
a common antecedent, though it does not end in exact
proof, may indicate causal connexion though it does
not prove what the nature of the connexion is. Roger
Bacon's observations indicated that the production of
rainbow colours was connected with the passage of
light through a transparent globe or prism. It was
reserved for Newton to prove by other methods that
white light was composed of rays, and that those rays
were differently refracted in passing through the transparent
medium. We have another example of how far
mere agreement, revealed by varying the circumstances,
carries us towards discovery of the cause, in Wells's
investigation of the cause of dew. Comparing
the numerous instances of dew appearing without
visible fall of moisture, Wells found that they
all agreed in the comparative coldness of the surface
dewed. This was all the agreement that he established
by observation; he did not carry observation to the
point of determining that there was absolutely no other
common circumstance: when he had simply discovered
dewed surfaces, he tried next to show by reasoning
from other knows facts how the coldness of the surface
affected the aqueous vapour of the neighbouring air.
He did not establish his Theory of Dew by the
Method of Agreement: but the observation of an agreement
or common feature in a number of instances was
a stage in the process by which he reached his theory.</p>

<span class="pagenum"><a name="page326" id="page326"></a>[page&nbsp;326]</span>

<h3 style="margin-top: 2em;">III.&mdash;<span class="sc">Mill's "Joint Method of Agreement and
Difference".</span></h3>

<p>After examining a variety of instances in which an
effect appears, and finding that they all agree in the
antecedent presence of some one circumstance, we
may proceed to examine instances otherwise similar
(<i>in pari materia</i>, as Prof. Fowler puts it) where the
effect does not appear. If these all agree in the
absence of the circumstance that is uniformly present
with the effect, we have corroborative evidence that
there is causal connexion between this circumstance
and the effect.</p>

<p>The principle of this method seems to have been
suggested to Mill by Wells's investigations into Dew.
Wells exposed a number of polished surfaces of various
substances, and compared those in which there was a
copious deposit of dew with those in which there was
little or none. If he could have got two surfaces, one
dewed and the other not, identical in every concomitant
but one, he would have attained complete proof
on the principle of Single Difference. But this being
impracticable, he followed a course which approximated
to the method of eliminating every circumstance
but one from instances of dew, and every circumstance
but one in the instances of no-dew. Mill sums up as
follows the results of his experiments: "It appears
that the instances in which much dew is deposited,
which are very various, agree in this, and, <i>so far as we
are able to observe, in this only</i>, that they either radiate
heat rapidly or conduct it slowly: qualities between
which there is no other circumstance of agreement
than that by virtue of either, the body tends to lose
heat from the surface more rapidly than it can be
<span class="pagenum"><a name="page327" id="page327"></a>[page&nbsp;327]</span>
restored from within. The instances, on the contrary,
in which no dew, or but a small quantity of it, is
formed, and which are also extremely various, agree
(<i>as far as we can observe</i>) <i>in nothing except</i> in <i>not</i> having
this same property. We seem therefore to have
detected the characteristic difference between the substances
on which the dew is produced, and those on
which it is not produced. And thus have been realised
the requisitions of what we have termed the Indirect
Method of Difference, or the Joint Method of Agreement
and Difference." The Canon of this Method is
accordingly stated by Mill as follows:&mdash;</p>

<blockquote><p>
If two or more instances in which the phenomenon
occurs have only one circumstance in common,
while two or more instances in which it does not
occur have nothing in common save the absence of
that circumstance; the circumstance in which alone
the two sets of instances differ, is the effect, or the
cause, or an indispensable part of the cause, of the
phenomenon.
</p></blockquote>

<p>In practice, however, this theoretical standard of
proof is never attained. What investigators really
proceed upon is the presumption afforded, to use Prof.
Bain's terms, by Agreement in Presence combined
with Agreement in Absence. When it is found that
all substances which have a strong smell agree in
being readily oxidisable, and that the marsh gas or
carbonetted hydrogen which has no smell is not
oxidisable at common temperatures, the presumption
that oxidation is one of the causal circumstances in
smell is strengthened, even though we have not succeeded
in eliminating every circumstance but this one
from either the positive or the negative instances. So
in the following examples given by Prof. Fowler there
<span class="pagenum"><a name="page328" id="page328"></a>[page&nbsp;328]</span>
is not really a compliance with the theoretical requirements
of Mill's Method: there is only an increased
presumption from the double agreement. "The Joint
Method of Agreement and Difference (or the Indirect
Method of Difference, or, as I should prefer to call it,
the Double Method of Agreement) is being continually
employed by us in the ordinary affairs of life. If when
I take a particular kind of food, I find that I invariably
suffer from some particular form of illness,
whereas, when I leave it off, I cease to suffer, I entertain
a double assurance that the food is the cause of
my illness. I have observed that a certain plant is
invariably plentiful on a particular soil; if, with a
wide experience, I fail to find it growing on any other
soil, I feel confirmed in my belief that there is in this
particular soil some chemical constituent, or some
peculiar combination of chemical constituents, which
is highly favourable, if not essential, to the growth of
the plant."</p>

<p class="note1"><a id="footnoteB2-ChV1" name="footnoteB2-ChV1"></a><a class="footnote" href="#footnotetagB2-ChV1">Footnote 1:</a>
Elimination, or setting aside as being of no concern, must not
be confounded with the exclusion of agents practised in applying
the Method of Difference. We use the word in its ordinary sense
of putting outside the sphere of an argument. By a curious slip,
Professor Bain follows Mill in applying the word sometimes to
the process of singling out or disentangling a causal circumstance.
This is an inadvertent departure from the ordinary usage, according
to which elimination means discarding from consideration as being
non-essential.</p>

<p class="note1"><a id="footnoteB2-ChV2" name="footnoteB2-ChV2"></a><a class="footnote" href="#footnotetagB2-ChV2">Footnote 2:</a>
Hirsch's <i>Geographical and Historical Pathology</i>, Creighton's
translation, vol. ii. pp. 121-202.</p>

<p class="note1"><a id="footnoteB2-ChV3" name="footnoteB2-ChV3"></a><a class="footnote" href="#footnotetagB2-ChV3">Footnote 3:</a>
The bare titles Difference and Agreement, though they have
the advantage of simplicity, are apt to puzzle beginners inasmuch
as in the Method of Difference the agreement among the instances
is at a maximum, and the difference at a minimum, and <i>vice versâ</i>
in the Method of Agreement. In both Methods it is really the
isolation of the connexion between antecedent and sequent that
constitutes the proof.</p>

<p class="note1"><a id="footnoteB2-ChV4" name="footnoteB2-ChV4"></a><a class="footnote" href="#footnotetagB2-ChV4">Footnote 4:</a> That rainbows in the sky are produced by the passage of light
through minute drops in the clouds was an inference from this
observed uniformity.</p>

<span class="pagenum"><a name="page329" id="page329"></a>[page&nbsp;329]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter VI.</span></h3>

<h3>METHODS OF OBSERVATION.&mdash;MINOR METHODS.</h3>

<h3 style="margin-top: 2em"><span class="sc">I.&mdash;Concomitant Variations.</span></h3>

<blockquote><p>
<i>Whatever phenomenon varies in any manner whenever
another phenomenon varies in some particular manner,
is either a cause or an effect of that phenomenon, or is
connected with it through some fact of causation.</i>
</p></blockquote>

<p>This simple principle is constantly applied by us in
connecting and disconnecting phenomena. If we hear
a sound which waxes and wanes with the rise and fall
of the wind, we at once connect the two phenomena.
We may not know what the causal connexion is, but
if they uniformly vary together, there is at once a
presumption that the one is causally dependent on the
other, or that both are effects of the same cause.</p>

<p>This principle was employed by Wells in his
researches into Dew. Some bodies are worse conductors
of heat than others, and rough surfaces radiate
heat more rapidly than smooth. Wells made observations
on conductors and radiators of various degrees,
and found that the amount of dew deposited was
greater or less according as the objects conducted heat
slowly or radiated heat rapidly. He thus established
what Herschel called a "scale of intensity" between
the conducting and radiating properties of the bodies
bedewed, and the amount of the dew deposit. The
<span class="pagenum"><a name="page330" id="page330"></a>[page&nbsp;330]</span>
explanation was that in bad conductors the surface
cools more quickly than in good conductors because
heat is more slowly supplied from within. Similarly
in rough surfaces there is a more rapid cooling because
heat is given off more quickly. But whatever the
explanation might be, the mere concomitant variation
of the dew deposit with these properties showed that
there was some causal connexion between them.</p>

<p>It must be remembered that the mere fact of concomitant
variation is only an index that some causal
connexion exists. The nature of the connexion must
be ascertained by other means, and may remain a
problem, one of the uses of such observed facts being
indeed to suggest problems, for inquiry. Thus a
remarkable concomitance has been observed between
spots on the sun, displays of Aurora Borealis, and
magnetic storms. The probability is that they are
causally connected, but science has not yet discovered
how. Similarly in the various sciences properties are
arranged in scales of intensity, and any correspondence
between two scales becomes a subject for investigation
on the assumption that it points to a causal connexion.
We shall see afterwards how in social investigations
concomitant variations in averages furnish material
for reasoning.</p>

<p>When two variants can be precisely measured, the
ratio of the variation may be ascertained by the
Method of Single Difference. We may change an
antecedent in degree, and watch the corresponding
change in the effect, taking care that no other agent
influences the effect in the meantime. Often when we
cannot remove an agent altogether, we may remove it
in a measurable amount, and observe the result. We
cannot remove friction altogether, but the more it is
<span class="pagenum"><a name="page331" id="page331"></a>[page&nbsp;331]</span>
diminished, the further will a body travel under the
impulse of the same force.</p>

<p>Until a concomitant variation has been fully
explained, it is merely an empirical law, and any
inference that it extends at the same rate beyond the
limits of observation must be made with due caution.
"Parallel variation," says Professor Bain, "is sometimes
interrupted by critical points, as in the expansion
of bodies by heat, which suffers a reverse near the
point of cooling. Again, the energy of a solution
does not always follow the strength; very dilute
solutions occasionally exercise a specific power not
possessed in any degree by stronger. So, in the
animal body, food and stimulants operate proportionally
up to a certain point, at which their further operation
is checked by the peculiarities in the structure of the
living organs.... We cannot always reason from
a few steps in a series to the whole series, partly
because of the occurrence of critical points, and partly
from the development at the extremes of new and
unsuspected powers. Sir John Herschel remarks that
until very recently 'the formul&aelig; empirically deduced
for the elasticity of steam, those for the resistance of
fluids, and on other similar subjects, have almost
invariably failed to support the theoretical structures
that have been erected upon them'."<a id="footnotetagB2-ChVI1" name="footnotetagB2-ChVI1"></a><a href="#footnoteB2-ChVI1"><sup>1</sup></a></p>

<h3 style="margin-top: 2em;">II.&mdash;<span class="sc">Single Residue.</span></h3>

<blockquote><p>
<i>Subduct from any phenomenon such part as previous induction
has shown to be the effect of certain antecedents, and the
residue of the phenomenon is the effect of the remaining
antecedents.</i>
</p></blockquote>

<p>"Complicated phenomena, in which several causes
<span class="pagenum"><a name="page332" id="page332"></a>[page&nbsp;332]</span>
concurring, opposing, or quite independent of each
other, operate at once, so as to produce a compound
effect, may be simplified by subducting the effect of all
the known causes, as well as the nature of the case
permits, either by deductive reasoning or by appeal to
experience, and thus leaving as it were a <i>residual
phenomenon</i> to be explained. It is by this process, in
fact, that science, in its present advanced state, is
chiefly promoted. Most of the phenomena which
nature presents are very complicated; and when the
effects of all known causes are estimated with exactness,
and subducted, the residual facts are constantly
appearing in the form of phenomena altogether new,
and leading to the most important conclusions."<a id="footnotetagB2-ChVI2" name="footnotetagB2-ChVI2"></a><a href="#footnoteB2-ChVI2"><sup>2</sup></a></p>

<p>It is obvious that this is not a primary method of
observation, but a method that may be employed with
great effect to guide observation when a considerable
advance has been made in accurate knowledge of
agents and their mode of operation. The greatest
triumph of the method, the discovery of the planet
Neptune, was won some years after the above passage
from Herschel's Discourse was written. Certain perturbations
were observed in the movements of the
planet Uranus: that is to say, its orbit was found not
to correspond exactly with what it should be when
calculated according to the known influences of the
bodies then known to astronomers. These perturbations
were a residual phenomenon. It was supposed
that they might be due to the action of an unknown
planet, and two astronomers, Adams and Le Verrier,
simultaneously calculated the position of a body such
as would account for the observed deviations. When
<span class="pagenum"><a name="page333" id="page333"></a>[page&nbsp;333]</span>
telescopes were directed to the spot thus indicated, the
planet Neptune was discovered. This was in September,
1846: before its actual discovery, Sir John
Herschel exulted in the prospect of it in language that
strikingly expresses the power of the method. "We
see it," he said, "as Columbus saw America from
the shores of Spain. Its movements have been felt,
trembling along the far-reaching line of our analysis,
with a certainty hardly inferior to that of ocular
demonstration."<a id="footnotetagB2-ChVI3" name="footnotetagB2-ChVI3"></a><a href="#footnoteB2-ChVI3"><sup>3</sup></a></p>

<p>Many of the new elements in Chemistry have been
discovered in this way. For example, when distinctive
spectrums had been observed for all known substances,
then on the assumption that every substance has a
distinctive spectrum, the appearance of lines not referable
to any known substance indicated the existence
of hitherto undiscovered substances and directed search
for them. Thus Bunsen in 1860 discovered two new
alkaline metals, C&aelig;sium and Rubidium. He was
examining alkalies left from the evaporation of a large
quantity of mineral water from Durkheim. On applying
the spectroscope to the flame which this particular
salt or mixture of salts gave off, he found that some
bright lines were visible which he had never observed
before, and which he knew were not produced either
by potash or soda. He then set to work to analyse
the mixture, and ultimately succeeded in separating
two new alkaline substances. When he had succeeded
in getting them separate, it was of course by the
Method of Difference that he ascertained them to be
capable of producing the lines that had excited his
curiosity.</p>

<p class="note1"><a id="footnoteB2-ChVI1" name="footnoteB2-ChVI1"></a><a class="footnote" href="#footnotetagB2-ChVI1">Footnote 1:</a>
Bain's <i>Logic</i>, vol. ii. p. 64.</p>

<p class="note1"><a id="footnoteB2-ChVI2" name="footnoteB2-ChVI2"></a><a class="footnote" href="#footnotetagB2-ChVI2">Footnote 2:</a>
Herschel's <i>Discourse</i>, &#167; 158.</p>

<p class="note1"><a id="footnoteB2-ChVI3" name="footnoteB2-ChVI3"></a><a class="footnote" href="#footnotetagB2-ChVI3">Footnote 3:</a>
De Morgan's <i>Budget of Paradoxes</i>, p. 237.</p>
<span class="pagenum"><a name="page334" id="page334"></a>[page&nbsp;334]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter VII.</span></h3>

<h3>THE METHOD OF EXPLANATION.</h3>

<p>Given perplexity as to the cause of any phenomenon,
what is our natural first step? We may describe it as
searching for a clue: we look carefully at the circumstances
with a view to finding some means of assimilating
what perplexes us to what is already within our
knowledge. Our next step is to make a guess, or
conjecture, or, in scientific language, a hypothesis.
We exercise our Reason or <i>Nous</i>, or Imagination, or
whatever we choose to call the faculty, and try to
conceive some cause that strikes us as sufficient to
account for the phenomenon. If it is not at once
manifest that this cause has really operated, our third
step is to consider what appearances ought to present
themselves if it did operate. We then return to the
facts in question, and observe whether those appearances
do present themselves. If they do, and if there
is no other way of accounting for the effect in all its
circumstances, we conclude that our guess is correct,
that our hypothesis is proved, that we have reached a
satisfactory explanation.</p>

<p>These four steps or stages may be distinguished in
most protracted inquiries into cause. They correspond
to the four stages of what Mr. Jevons calls the Inductive
Method <i>par excellence</i>, Preliminary Observation,
<span class="pagenum"><a name="page335" id="page335"></a>[page&nbsp;335]</span>
Hypothesis, Deduction and Verification. Seeing that
the word Induction is already an overloaded drudge,
perhaps it would be better to call these four stages the
Method of Explanation. The word Induction, if we
keep near its original and most established meaning,
would apply strictly only to the fourth stage, the
Verification, the bringing in of the facts to confirm our
hypothesis. We might call the method the Newtonian
method, for all four stages are marked in the prolonged
process by which he made good his theory of Gravitation.</p>

<p>To give the name of Inductive Method simply to all
the four stages of an orderly procedure from doubt to a
sufficient explanation is to encourage a widespread
misapprehension. There could be no greater error
than to suppose that only the senses are used in
scientific investigation. There is no error that men of
science are so apt to resent in the mouths of the non-scientific.
Yet they have partly brought it on themselves
by their loose use of the word Induction, which
they follow Bacon in wresting from the traditional
meaning of Induction, using it to cover both Induction
or the bringing in of facts&mdash;an affair mainly of Observation&mdash;and
Reasoning, the exercise of Nous, the
process of constructing satisfactory hypotheses. In
reaction against the popular misconception which
Bacon encouraged, it is fashionable now to speak of the
use of Imagination in Science. This is well enough
polemically. Imagination as commonly understood is
akin to the constructive faculty in Science, and it is
legitimate warfare to employ the familiar word of high
repute to force general recognition of the truth. But
in common usage Imagination is appropriated to
creative genius in the Fine Arts, and to speak of
Imagination in Science is to suggest that Science
<span class="pagenum"><a name="page336" id="page336"></a>[page&nbsp;336]</span>
deals in fictions, and has discarded Newton's declaration
<i>Hypotheses non fingo</i>. In a fight for popular
respect, men of science may be right to claim for
themselves Imagination; but in the interests of clear
understanding, the logician must deplore that they
should defend themselves from a charge due to their
abuse of one word by making an equally unwarrantable
and confusing extension of another.</p>

<p>Call it what we will, the faculty of likely guessing,
of making probable hypotheses, of conceiving in all its
circumstances the past situation or the latent and
supramicroscopical situation out of which a phenomenon
has emerged, is one of the most important of the
scientific man's special gifts. It is by virtue of it that
the greatest advancements of knowledge have been
achieved, the cardinal discoveries in Molar and
Molecular Physics, Biology, Geology, and all departments
of Science. We must not push the idea of
stages in explanatory method too far: the right
explanation may be reached in a flash. The idea of
stages is really useful mainly in trying to make clear
the various difficulties in investigation, and the fact
that different men of genius may show different powers
in overcoming them. The right hypothesis may occur
in a moment, as if by simple intuition, but it may be
tedious to prove, and the gifts that tell in proof, such
as Newton's immense mathematical power in calculating
what a hypothesis implies, Darwin's patience in
verifying, Faraday's ingenuity in devising experiments,
are all great gifts, and may be serviceable at different
stages. But without originality and fertility in
probable hypothesis, nothing can be done.</p>

<p>The dispute between Mill and Whewell as to the
place and value of hypotheses in science was in the
<span class="pagenum"><a name="page337" id="page337"></a>[page&nbsp;337]</span>
main a dispute about words. Mill did not really
undervalue hypothesis, and he gave a most luminous
and accurate account of the conditions of proof. But
here and there he incautiously spoke of the "hypothetical
method" (by which he meant what we have
called the method of Explanation) as if it were a
defective kind of proof, a method resorted to by science
when the "experimental methods" could not be
applied. Whether his language fairly bore this construction
is not worth arguing, but this was manifestly
the construction that Whewell had in his mind when
he retorted, as if in defence of hypotheses, that "the
inductive process consists in framing successive
hypotheses, the comparison of these with the ascertained
facts of nature, and the introduction into them
of such modifications as the comparison may render
necessary". This is a very fair description of the
whole method of explanation. There is nothing really
inconsistent with it in Mill's account of his "hypothetical
method"; only he erred himself or was the
cause of error in others in suggesting, intentionally or
unintentionally, that the Experimental Methods were
different methods of proof. The "hypothetical method,"
as he described it, consisting of Induction, Ratiocination,
and Verification, really comprehends the principles
of all modes of observation, whether naturally or artificially
experimental. We see this at once when we
ask how the previous knowledge is got in accordance
with which hypotheses are framed. The answer must
be, by Observation. However profound the calculations,
it must be from observed laws, or supposed
analogues of them, that we start. And it is always by
Observation that the results of these calculations are
verified.</p>
<span class="pagenum"><a name="page338" id="page338"></a>[page&nbsp;338]</span>

<p>Both Mill and Whewell, however, confined themselves
too exclusively to the great hypotheses of the
Sciences, such as Gravitation and the Undulatory
Theory of Light. In the consideration of scientific
method, it is a mistake to confine our attention to
these great questions, which from the multitude of
facts embraced can only be verified by prolonged and
intricate inquiry. Attempts at the explanation of the
smallest phenomena proceed on the same plan, and the
verification of conjectures about them is subject to
the same conditions, and the methods of investigation
and the conditions of verification can be studied most
simply in the smaller cases. Further, I venture to
think it a mistake to confine ourselves to scientific
inquiry in the narrow sense, meaning thereby inquiry
conducted within the pale of the exact sciences. For
not merely the exact sciences but all men in the
ordinary affairs of life must follow the same methods
or at least observe the same principles and conditions,
in any satisfactory attempt to explain.</p>

<p>Tares appear among the wheat. Good seed was
sown: whence, then, come the tares? "An enemy
has done this." If an enemy has actually been
observed sowing the tares, his agency can be proved
by descriptive testimony. But if he has not been seen
in the act, we must resort to what is known in Courts
of Law as circumstantial evidence. This is the
"hypothetical method" of science. That the tares
are the work of an enemy is a hypothesis: we examine
all the circumstances of the case in order to prove, by
inference from our knowledge of similar cases, that
thus, and thus only, can those circumstances be
accounted for. Similarly, when a question is raised as
to the authorship of an anonymous book. We first
<span class="pagenum"><a name="page339" id="page339"></a>[page&nbsp;339]</span>
search for a clue by carefully noting the diction, the
structure of the sentences, the character and sources of
the illustration, the special tracks of thought. We
proceed upon the knowledge that every author has
characteristic turns of phrase and imagery and
favourite veins of thought, and we look out for such
internal evidence of authorship in the work before us.
Special knowledge and acumen may enable us to
detect the authorship at once from the general resemblance
to known work. But if we would have clear
proof, we must show that the resemblance extends to
all the details of phrase, structure and imagery: we
must show that our hypothesis of the authorship of
XYZ explains all the circumstances. And even this
is not sufficient, as many erroneous guesses from
internal evidence may convince us. We must establish
further that there is no other reasonable way of
accounting for the matter and manner of the book; for
example, that it is not the work of an imitator. An
imitator may reproduce all the superficial peculiarities
of an author with such fidelity that the imitation can
hardly be distinguished from the original: thus few
can distinguish between Fenton's work and Pope's in
the translation of the Odyssey. We must take such
known facts into account in deciding a hypothesis of
authorship. Such hypotheses can seldom be decided
on internal evidence alone: other circumstantial evidence&mdash;other
circumstances that ought to be discoverable
if the hypothesis is correct&mdash;must be searched for.</p>

<p>The operation of causes that are manifest only in
their effects must be proved by the same method as the
operation of past causes that have left only their effects
behind them. Whether light is caused by a projection
of particles from a luminous body or by an agitation
<span class="pagenum"><a name="page340" id="page340"></a>[page&nbsp;340]</span>
communicated through an intervening medium cannot
be directly observed. The only proof open is to
calculate what should occur on either hypothesis, and
observe whether this does occur. In such a case there
is room for the utmost calculating power and experimental
ingenuity. The mere making of the general
hypothesis or guess is simple enough, both modes of
transmitting influence, the projection of moving matter
and the travelling of an undulation or wave movement,
being familiar facts. But it is not so easy to calculate
exactly how a given impulse would travel, and
what phenomena of ray and shadow, of reflection,
refraction and diffraction ought to be visible in its
progress. Still, no matter how intricate the calculation,
its correspondence with what can be observed is
the only legitimate proof of the hypothesis.</p>

<h3 style="margin-top: 2em;">II.&mdash;<span class="sc">Obstacles to Explanation.&mdash;Plurality of
Causes and Intermixture of Effects.</span></h3>

<p>There are two main ways in which explanation may
be baffled. There may exist more than one cause
singly capable of producing the effect in question, and
we may have no means of determining which of the
equally sufficient causes has actually been at work.
For all that appears the tares in our wheat may be
the effect of accident or of malicious design: an
anonymous book may be the work of an original author
or of an imitator. Again, an effect may be the joint
result of several co-operating causes, and it may be
impossible to determine their several potencies. The
bitter article in the <i>Quarterly</i> may have helped to kill
John Keats, but it co-operated with an enfeebled
<span class="pagenum"><a name="page341" id="page341"></a>[page&nbsp;341]</span>
constitution and a naturally over-sensitive temperament,
and we cannot assign its exact weight to each of these
coefficients. Death may be the result of a combination
of causes; organic disease co-operating with
exposure, over-fatigue co-operating with the enfeeblement
of the system by disease.</p>

<p>The technical names for these difficulties, Plurality
of Causes and Intermixture of Effects, are apt to confuse
without some clearing up. In both kinds of
difficulty more causes than one are involved: but in
the one kind of case there is a plurality of possible or
equally probable causes, and we are at a loss to decide
which: in the other kind of case there is a plurality of
co-operating causes; the effect is the result or product
of several causes working conjointly, and we are unable
to assign to each its due share.</p>

<p>It is with a view to overcoming these difficulties
that Science endeavours to isolate agencies and ascertain
what each is capable of singly. Mill and Bain
treat Plurality of Causes and Intermixture of Effects
in connexion with the Experimental Methods. It is
better, perhaps, to regard them simply as obstacles to
explanation, and the Experimental Methods as methods
of overcoming those obstacles. The whole purpose of
the Experimental Methods is to isolate agencies and
effects: unless they can be isolated, the Methods are
inapplicable. In situations where the effects observable
may be referred with equal probability to more than
one cause, you cannot eliminate so as to obtain a
single agreement. The Method of Agreement is
frustrated. And an investigator can get no light from
mixed effects, unless he knows enough of the causes at
work to be able to apply the Method of Residues. If
he does not, he must simply look out for or devise
<span class="pagenum"><a name="page342" id="page342"></a>[page&nbsp;342]</span>
instances where the agencies are at work separately,
and apply the principle of Single Difference.</p>

<p>Great, however, as the difficulties are, the theory of
Plurality and Intermixture baldly stated makes them
appear greater than they are in practice. There is a
consideration that mitigates the complication, and
renders the task of unravelling it not altogether
hopeless. This is that different causes have distinctive
ways of operating, and leave behind them marks of
their presence by which their agency in a given case
may be recognised.</p>

<p>An explosion, for example, occurs. There are
several explosive agencies, capable of causing as much
destruction as meets the eye at the first glance. The
agent in the case before us may be gunpowder or it
may be dynamite. But the two agents are not so
alike in their mode of operation as to produce results
identical in every circumstance. The expert inquirer
knows by previous observation that when gunpowder
acts the objects in the neighbourhood are blackened;
and that an explosion of dynamite tears and shatters in
a way peculiar to itself. He is thus able to interpret
the traces, to make and prove a hypothesis.</p>

<p>A man's body is found dead in water. It may be
a question whether death came by drowning or by
previous violence. He may have been suffocated and
afterwards thrown into the water. But the circumstances
will tell the true story. Death by drowning
has distinctive symptoms. If drowning was the cause,
water will be found in the stomach and froth in the
trachea.</p>

<p>Thus, though there may be a plurality of possible
causes, the causation in the given case may be brought
home to one by distinctive accompaniments, and it is
<span class="pagenum"><a name="page343" id="page343"></a>[page&nbsp;343]</span>
the business of the scientific inquirer to study these.
What is known as the "ripple-mark" in sandstone
surfaces may be produced in various ways. The most
familiar way is by the action of the tides on the sand
of the sea-shore, and the interpreter who knows this
way only would ascribe the marks at once to this
agency. But ripple-marks are produced also by the
winds on drifting sands, by currents of water where no
tidal influence is felt, and in fact by any body of water
in a state of oscillation. Is it, then, impossible to
decide between these alternative possibilities of
causation? No: wind-ripples and current-ripples and
tidal-ripples have each their own special character and
accompanying conditions, and the hypothesis of one
rather than another may be made good by means of
these. "In rock-formations," Mr. Page says,<a id="footnotetagB2-ChVII1" name="footnotetagB2-ChVII1"></a><a href="#footnoteB2-ChVII1"><sup>1</sup></a> "there
are many things which at first sight seem similar,
and yet on more minute examination, differences are
detected and conditions discovered which render it
impossible that these appearances can have arisen
from the same causation."</p>

<p>The truth is that generally when we speak of
plurality of causes, of alternative possibilities of causation,
we are not thinking of the effect in its individual
entirety, but only of some general or abstract aspect
of it. When we say, <i>e.g.</i>, that death may be produced
by a great many different causes, poison, gunshot
wounds, disease of this or that organ, we are thinking
of death in the abstract, not of the particular case
under consideration, which as an individual case, has
characters so distinctive that only one combination of
causes is possible.</p>
<span class="pagenum"><a name="page344" id="page344"></a>[page&nbsp;344]</span>

<p>The effort of science is to become less and less
abstract in this sense, by observing agencies or combinations
of agencies apart and studying the special
characters of their effects. That knowledge is then
applied, on the assumption that where those characters
are present, the agent or combination of agencies has
been at work. Given an effect to be explained, it is
brought home to one out of several possible alternatives
by <i>circumstantial evidence</i>.</p>

<p>Bacon's phrase, <i>Instantia Crucis</i>,<a id="footnotetagB2-ChVII2" name="footnotetagB2-ChVII2"></a><a href="#footnoteB2-ChVII2"><sup>2</sup></a> or Finger-post
Instance, might be conveniently appropriated as a
technical name for a circumstance that is decisive
between rival hypotheses. This was, in effect, proposed
by Sir John Herschel,<a id="footnotetagB2-ChVII3" name="footnotetagB2-ChVII3"></a><a href="#footnoteB2-ChVII3"><sup>3</sup></a> who drew attention to
the importance of these crucial instances, and gave the
following example: "A curious example is given by
M. Fresnel, as decisive, in his mind, of the question
between the two great opinions on the nature of light,
which, since the time of Newton and Huyghens, have
divided philosophers. When two very clean glasses
are laid one on the other, if they be not perfectly flat,
but one or both in an almost imperceptible degree
convex or prominent, beautiful and vivid colours will
be seen between them; and if these be viewed through
a red glass, their appearance will be that of alternate
dark and bright stripes.... Now, the coloured stripes
thus produced are explicable on both theories, and are
appealed to by both as strong confirmatory facts; but
there is a difference in one circumstance according as
one or the other theory is employed to explain them.
In the case of the Huyghenian doctrine, the intervals
<span class="pagenum"><a name="page345" id="page345"></a>[page&nbsp;345]</span>
between the bright stripes ought to appear <i>absolutely
black</i>; in the other, <i>half bright</i>, when viewed [in a
particular manner] through a prism. This curious
case of difference was tried as soon as the opposing
consequences of the two theories were noted by M.
Fresnel, and the result is stated by him to be decisive
in favour of that theory which makes light to consist
in the vibrations of an elastic medium."</p>

<h3 style="margin-top: 2em;">III.&mdash;<span class="sc">The Proof of a Hypothesis.</span></h3>

<p>The completest proof of a hypothesis is when that
which has been hypothetically assumed to exist as a
means of accounting for certain phenomena is afterwards
actually observed to exist or is proved by
descriptive testimony to have existed. Our argument,
for example, from internal evidence that Mill in writing
his Logic aimed at furnishing a method for social
investigations is confirmed by a letter to Miss Caroline
Fox, in which he distinctly avowed that object.</p>

<p>The most striking example of this crowning verification
in Science is the discovery of the planet
Neptune, in which case an agent hypothetically
assumed was actually brought under the telescope as
calculated. Examples almost equally striking have
occurred in the history of the Evolution doctrine.
Hypothetical ancestors with certain peculiarities of
structure have been assumed as links between living
species, and in some cases their fossils have actually
been found in the geological register.</p>

<p>Such triumphs of verification are necessarily rare.
For the most part the hypothetical method is applied
to cases where proof by actual observation is impossible,
such as prehistoric conditions of the earth or of life
<span class="pagenum"><a name="page346" id="page346"></a>[page&nbsp;346]</span>
upon the earth, or conditions in the ultimate constitution
of matter that are beyond the reach of the strongest
microscope. Indeed, some would confine the word
hypothesis to cases of this kind. This, in fact, was
done by Mill: hypothesis, as he defined it, was a conjecture
not completely proved, but with a large amount
of evidence in its favour. But seeing that the procedure
of investigation is the same, namely, conjecture,
calculation and comparison of facts with the calculated
results, whether the agency assumed can be brought
to the test of direct observation or not, it seems better
not to restrict the word hypothesis to incompletely
proved conjectures, but to apply it simply to a conjecture
made at a certain stage in whatever way it may
afterwards be verified.</p>

<p>In the absence of direct verification, the proof of
a hypothesis is exclusive sufficiency to explain the
circumstances. The hypothesis must account for all
the circumstances, and there must be no other way of
accounting for them. Another requirement was mentioned
by Newton in a phrase about the exact meaning
of which there has been some contention. The first
of his Regul&aelig; Philosophandi laid down that the cause
assumed must be a <i>vera causa</i>. "We are not," the
Rule runs, "to admit other causes of natural things
than such as both are true, and suffice for explaining
their phenomena."<a id="footnotetagB2-ChVII4" name="footnotetagB2-ChVII4"></a><a href="#footnoteB2-ChVII4"><sup>4</sup></a></p>

<p>It has been argued that the requirement of "verity"
is superfluous; that it is really included in the requirement
of sufficiency; that if a cause is sufficient to
explain the phenomena it must <i>ipso facto</i> be the true
<span class="pagenum"><a name="page347" id="page347"></a>[page&nbsp;347]</span>
cause. This may be technically arguable, given a
sufficient latitude to the word sufficiency: nevertheless,
it is convenient to distinguish between mere sufficiency
to explain the phenomena in question, and the proof
otherwise that the cause assigned really exists <i>in rerum
natura</i>, or that it operated in the given case. The
frequency with which the expression <i>vera causa</i> has
been used since Newton's time shows that a need is
felt for it, though it may be hard to define "verity"
precisely as something apart from "sufficiency". If we
examine the common usage of the expression we shall
probably find that what is meant by insisting on a <i>vera
causa</i> is that we must have some evidence for the cause
assigned outside the phenomena in question. In
seeking for verification of a hypothesis we must extend
our range beyond the limited facts that have engaged
our curiosity and that demand explanation.</p>

<p>There can be little doubt that Newton himself aimed
his rule at the Cartesian hypothesis of Vortices. This
was an attempt to explain the solar system on the
hypothesis that cosmic space is filled with a fluid in
which the planets are carried round as chips of wood
in a whirlpool, or leaves or dust in a whirlwind. Now
this is so far a <i>vera causa</i> that the action of fluid
vortices is a familiar one: we have only to stir a cup
of tea with a bit of stalk in it to get an instance. The
agency supposed is sufficient also to account for the
revolution of a planet round the sun, given sufficient
strength in the fluid to buoy up the planet. But if
there were such a fluid in space there would be other
phenomena: and in the absence of these other
phenomena the hypothesis must be dismissed as
imaginary. The fact that comets pass into and out
of spaces where the vortices must be assumed to be
<span class="pagenum"><a name="page348" id="page348"></a>[page&nbsp;348]</span>
in action without exhibiting any perturbation is an
<i>instantia crucis</i> against the hypothesis.</p>

<p>If by the requirement of a <i>vera causa</i> were meant
that the cause assigned must be one directly open to
observation, this would undoubtedly be too narrow a
limit. It would exclude such causes as the ether which
is assumed to fill interstellar space as a medium
for the propagation of light. The only evidence for
such a medium and its various properties is sufficiency
to explain the phenomena. Like suppositions as to
the ultimate constitution of bodies, it is of the nature
of what Professor Bain calls a "Representative
Fiction": the only condition is that it must explain all
the phenomena, and that there must be no other way of
explaining all. When it is proved that light travels
with a finite velocity, we are confined to two alternative
ways of conceiving its transmission, a projection of
matter from the luminous body and the transference of
vibrations through an intervening medium. Either
hypothesis would explain many of the facts: our
choice must rest with that which best explains all.
But supposing that all the phenomena of light were
explained by attributing certain properties to this
intervening medium, it would probably be held that
the hypothesis of an ether had not been fully verified
till other phenomena than those of light had been
shown to be incapable of explanation on any other
hypothesis. If the properties ascribed to it to explain
the phenomena of light sufficed at the same time to
explain otherwise inexplicable phenomena connected
with Heat, Electricity, or Gravity, the evidence of its
reality would be greatly strengthened.</p>

<p>Not only must the circumstances in hand be
explained, but other circumstances must be found to
<span class="pagenum"><a name="page349" id="page349"></a>[page&nbsp;349]</span>
be such as we should expect if the cause assigned
really operated. Take, for example, the case of
Erratic blocks or boulders, huge fragments of rock
found at a distance from their parent strata. The
lowlands of England, Scotland, and Ireland, and the
great central plain of Northern Europe contain many
such fragments. Their composition shows indubitably
that they once formed part of hills to the northward of
their present site. They must somehow have been
detached and transported to where we now find them.
How? One old explanation is that they were carried
by witches, or that they were themselves witches accidentally
dropped and turned into stone. Any such
explanation by supernatural means can neither be
proved nor disproved. Some logicians would exclude
such hypotheses altogether on the ground that they
cannot be rendered either more or less probable by subsequent
examination.<a id="footnotetagB2-ChVII5" name="footnotetagB2-ChVII5"></a><a href="#footnoteB2-ChVII5"><sup>5</sup></a>
The proper scientific limit, however,
is not to the making of hypotheses, but to the
proof of them. The more hypotheses the merrier:
only if such an agency as witchcraft is suggested, we
should expect to find other evidence of its existence in
other phenomena that could not otherwise be explained.
Again, it has been suggested that the erratic boulders
may have been transported by water. Water is so far
a <i>vera causa</i> that currents are known to be capable of
washing huge blocks to a great distance. But blocks
transported in this way have the edges worn off by the
friction of their passage: and, besides, currents strong
enough to dislodge and force along for miles blocks
as big as cottages must have left other marks of their
<span class="pagenum"><a name="page350" id="page350"></a>[page&nbsp;350]</span>
presence. The explanation now received is that
glaciers and icebergs were the means of transport.
But this explanation was not accepted till multitudes
of circumstances were examined all tending to show
that glaciers had once been present in the regions
where the erratic blocks are found. The minute habits
of glaciers have been studied where they still exist:
how they slowly move down carrying fragments of
rock; how icebergs break off when they reach water,
float off with their load, and drop it when they melt;
how they grind and smooth the surfaces of rocks over
which they pass or that are frozen into them: how
they undercut and mark the faces of precipices past
which they move; how moraines are formed at the
melting ends of them, and so forth. When a district
exhibits all the circumstances that are now observed
to attend the action of glaciers the proof of the
hypothesis that glaciers were once there is complete.</p>

<p class="note1"><a id="footnoteB2-ChVII1" name="footnoteB2-ChVII1"></a><a class="footnote" href="#footnotetagB2-ChVII1">Footnote 1:</a>
Page's <i>Philosophy of Geology</i>, p. 38.</p>

<p class="note1"><a id="footnoteB2-ChVII2" name="footnoteB2-ChVII2"></a><a class="footnote" href="#footnotetagB2-ChVII2">Footnote 2:</a>
Crux in this phrase means a cross erected at the parting of
ways, with arms to tell whither each way leads.</p>

<p class="note1"><a id="footnoteB2-ChVII3" name="footnoteB2-ChVII3"></a><a class="footnote" href="#footnotetagB2-ChVII3">Footnote 3:</a>
<i>Discourse</i>, &#167; 218.</p>

<p class="note1"><a id="footnoteB2-ChVII4" name="footnoteB2-ChVII4"></a><a class="footnote" href="#footnotetagB2-ChVII4">Footnote 4:</a>
Causas rerum naturalium non plures admitti debere quam
qu&aelig; et veri&aelig; sint et carum phenomenis explicandis sufficiant.</p>

<p class="note1"><a id="footnoteB2-ChVII5" name="footnoteB2-ChVII5"></a><a class="footnote" href="#footnotetagB2-ChVII5">Footnote 5:</a>
See Prof. Fowler on the Conditions of Hypotheses, <i>Inductive
Logic</i>, pp. 100-115.</p>
<span class="pagenum"><a name="page351" id="page351"></a>[page&nbsp;351]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter VIII.</span></h3>

<h3>SUPPLEMENTARY METHODS OF INVESTIGATION.</h3>

<h3 style="margin-top: 2em">I.&mdash;<span class="sc">The Maintenance of Averages.</span>&mdash;<span class="sc">Supplement
to the Method of Difference.</span></h3>

<p>A certain amount of law obtains among events that
are usually spoken of as matters of chance or accident
in the individual case. Every kind of accident recurs
with a certain uniformity. If we take a succession of
periods, and divide the total number of any kind of
event by the number of periods, we get what is called
the average for that period: and it is observed that
such averages are maintained from period to period.
Over a series of years there is a fixed proportion
between good harvests and bad, between wet days and
dry: every year nearly the same number of suicides
takes place, the same number of crimes, of accidents
to life and limb, even of suicides, crimes, or injuries by
particular means: every year in a town nearly the
same number of children stray from their parents and
are restored by the police: every year nearly the same
number of persons post letters without putting an
address on them.</p>

<p>This maintenance of averages is simple matter of
observation, a datum of experience, an empirical law.
Once an average for any kind of event has been
noted, we may count upon its continuance as we count
upon the continuance of any other kind of observed
<span class="pagenum"><a name="page352" id="page352"></a>[page&nbsp;352]</span>
uniformity. Insurance companies proceed upon such
empirical laws of average in length of life and
immunity from injurious accidents by sea or land:
their prosperity is a practical proof of the correctness
and completeness of the observed facts and the soundness
of their inference to the continuance of the average.</p>

<p>The constancy of averages is thus a guide in practice.
But in reasoning upon them in investigations of
cause, we make a further assumption than continued
uniformity. We assume that the maintenance of the
average is due to the permanence of the producing
causes. We regard the average as the result of the
operation of a limited sum of forces and conditions,
incalculable as regards their particular incidence, but
always pressing into action, and thus likely to operate
a certain number of times within a limited period.</p>

<p>Assuming the correctness of this explanation, it
would follow that <i>any change in the average is due to
some change in the producing conditions</i>; and this derivative
law is applied as a help in the observation and
explanation of social facts. Statistics are collected
and classified: averages are struck: and changes in
the average are referred to changes in the concomitant
conditions.</p>

<p>With the help of this law, we may make a near
approach to the precision of the Method of Difference.
A multitude of unknown or unmeasured agents may
be at work on a situation, but we may accept the
average as the result of their joint operation. If then
a new agency is introduced or one of the known agents
is changed in degree, and this is at once followed by a
change in the average, we may with fair probability
refer the change in the result to the change in the
antecedents.</p>
<span class="pagenum"><a name="page353" id="page353"></a>[page&nbsp;353]</span>

<p>The difficulty is to find a situation where only one
antecedent has been changed before the appearance
of the effect. This difficulty may be diminished in
practice by eliminating changes that we have reason
to know could not have affected the circumstances in
question. Suppose, for example, our question is
whether the Education Act of 1872 had an influence
in the decrease of juvenile crime. Such a decrease
took place <i>post hoc</i>; was it <i>propter hoc</i>? We may at
once eliminate or put out of account the abolition of
Purchase in the Army or the extension of the Franchise
as not having possibly exercised any influence on
juvenile crime. But with all such eliminations, there
may still remain other possible influences, such as an
improvement in the organisation of the Police, or an
expansion or contraction in employment. "Can you
tell me in the face of chronology," a leading statesman
once asked, "that the Crimes Act of 1887 did not
diminish disorder in Ireland?" But chronological
sequence alone is not a proof of causation as long as
there are other contemporaneous changes of condition
that may also have been influential.</p>

<p>The great source of fallacy is our proneness to
eliminate or isolate in accordance with our prejudices.
This has led to the gibe that anything can be proved
by statistics. Undoubtedly statistics may be made to
prove anything if you have a sufficiently low standard
of proof and ignore the facts that make against your
conclusion. But averages and variations in them are
instructive enough if handled with due caution. The
remedy for rash conclusions from statistics is not no
statistics, but more of them and a sound knowledge of
the conditions of reasonable proof.</p>
<span class="pagenum"><a name="page354" id="page354"></a>[page&nbsp;354]</span>

<h3 style="margin-top: 2em;">II.&mdash;<span class="sc">The Presumption from Extra-Casual
Coincidence.</span></h3>

<p>We have seen that repeated coincidence raises a
presumption of causal connexion between the coinciding
events. If we find two events going repeatedly
together, either abreast or in sequence, we infer that
the two are somehow connected in the way of causation,
that there is a reason for the coincidence in the
manner of their production. It may not be that the
one produces the other, or even that their causes are
in any way connected: but at least, if they are independent
one of the other, both are tied down to happen
at the same place and time,&mdash;the coincidence of both
with time and place is somehow fixed.</p>

<p>But though this is true in the main, it is not true
without qualification. We expect a certain amount of
repeated coincidence without supposing causal connexion.
If certain events are repeated very often
within our experience, if they have great positive
frequency, we may observe them happening together
more than once without concluding that the coincidence
is more than fortuitous.</p>

<p>For example, if we live in a neighbourhood possessed
of many black cats, and sally forth to our daily business
in the morning, a misfortune in the course of the day
might more than once follow upon our meeting a
black cat as we went out without raising in our minds
any presumption that the one event was the result of
the other.</p>

<p>Certain planets are above the horizon at certain
periods of the year and below the horizon at certain
other periods. All through the year men and women
are born who afterwards achieve distinction in various
<span class="pagenum"><a name="page355" id="page355"></a>[page&nbsp;355]</span>
walks of life, in love, in war, in business, at the bar,
in the pulpit. We perceive a certain number of
coincidences between the ascendancy of certain planets
and the birth of distinguished individuals without
suspecting that planetary influence was concerned in
their superiority.</p>

<p>Marriages take place on all days of the year: the
sun shines on a good many days at the ordinary time
for such ceremonies; some marriages are happy, some
unhappy; but though in the case of many happy
marriages the sun has shone upon the bride, we regard
the coincidence as merely accidental.</p>

<p>Men often dream of calamities and often suffer
calamities in real life: we should expect the coincidence
of a dream of calamity followed by a reality to
occur more than once as a result of chance. There
are thousands of men of different nationalities in
business in London, and many fortunes are made: we
should expect more than one man of any nationality
represented there to make a fortune without arguing
any connexion between his nationality and his success.</p>

<p>We allow, then, for a certain amount of repeated
coincidence without presuming causal connexion: can
any rule be laid down for determining the exact
amount?</p>

<p>Prof. Bain has formulated the following rule:
"Consider the positive frequency of the phenomena
themselves, how great frequency of coincidence
must follow from that, supposing there is neither connexion
nor repugnance. If there be greater frequency,
there is connexion; if less, repugnance."</p>

<p>I do not know that we can go further definite in
precept. The number of casual coincidences bears a
certain proportion to the positive frequency of the
<span class="pagenum"><a name="page356" id="page356"></a>[page&nbsp;356]</span>
coinciding phenomena: that proportion is to be determined
by common-sense in each case. It may be
possible, however, to bring out more clearly the principle
on which common-sense proceeds in deciding
what chance will and will not account for, although
our exposition amounts only to making more clear
what it is that we mean by chance as distinguished
from assignable reason. I would suggest that in
deciding what chance will not account for, we make
regressive application of a principle which may be
called the principle of Equal and Unequal Alternatives,
and which may be worded as follows:&mdash;</p>

<blockquote><p>
Of a given number of possible alternatives, all equally
possible, one of which is bound to occur at a given
time, we expect each to have its turn an equal
number of times in the long run. If several of the
alternatives are of the same kind, we expect an
alternative of that kind to recur with a frequency
proportioned to their greater number. If any of
the alternatives has an advantage, it will recur with
a frequency proportioned to the strength of that
advantage.
</p></blockquote>

<p>Situations in which alternatives are absolutely equal
are rare in nature, but they are artificially created for
games "of chance," as in tossing a coin, throwing
dice, drawing lots, shuffling and dealing a pack of
cards. The essence of all games of chance is to construct
a number of equal alternatives, making them as
nearly equal as possible, and to make no prearrangement
which of the number shall come off. We then
say that this is determined by chance. If we ask why
we believe that when we go on bringing off one alternative
at a time, each will have its turn, part of
<span class="pagenum"><a name="page357" id="page357"></a>[page&nbsnbsp;357]</span>
the answer undoubtedly is that given by De Morgan,
namely, that we know no reason why one should be
chosen rather than another. This, however, is probably
not the whole reason for our belief. The rational
belief in the matter is that it is only in the long run
or on the average that each of the equal alternatives
will have its turn, and this is probably founded on the
experience of actual trial. The mere equality of the
alternatives, supposing them to be perfectly equal,
would justify us as much in expecting that each would
have its turn in a single revolution of the series, in one
complete cycle of the alternatives. This, indeed, may
be described as the natural and primitive expectation
which is corrected by experience. Put six balls in a
wicker bottle, shake them up, and roll one out: return
this one, and repeat the operation: at the end of six
draws we might expect each ball to have had its turn of
being drawn if we went merely on the abstract equality
of the alternatives. But experience shows us that in
six successive draws the same ball may come out
twice or even three or four times, although when
thousands of drawings are made each comes out nearly
an equal number of times. So in tossing a coin,
heads may turn up ten or twelve times in succession,
though in thousands of tosses heads and tails are
nearly equal. Runs of luck are thus within the
rational doctrine of chances: it is only in the long run
that luck is equalised supposing that the events are
pure matter of chance, that is, supposing the fundamental
alternatives to be equal.</p>

<p>If three out of six balls are of the same colour, we
expect a ball of that colour to come out three times as
often as any other colour on the average of a long
succession of tries. This illustrates the second clause
<span class="pagenum"><a name="page358" id="page358"></a>[page&nbsp;358]</span>
of our principle. The third is illustrated by a loaded
coin or die.</p>

<p>By making regressive application of the principle
thus ascertained by experience, we often obtain a clue
to special causal connexion. We are at least enabled
to isolate a problem for investigation. If we find one
of a number of alternatives recurring more frequently
than the others, we are entitled to presume that they
are not equally possible, that there is some inequality
in their conditions.</p>

<p>The inequality may simply lie in the greater possible
frequency of one of the coinciding events, as when
there are three black balls in a bottle of six. We
must therefore discount the positive frequency before
looking for any other cause. Suppose, for example,
we find that the ascendancy of Jupiter coincides more
frequently with the birth of men afterwards distinguished
in business than with the birth of men
otherwise distinguished, say in war, or at the bar, or
in scholarship. We are not at liberty to conclude
planetary influence till we have compared the positive
frequency of the different modes of distinction.
The explanation of the more frequently repeated
coincidence may simply be that more men altogether
are successful in business than in war or law or
scholarship. If so, we say that chance accounts for
the coincidence, that is to say, that the coincidence
is casual as far as planetary influence is concerned.</p>

<p>So in epidemics of fever, if we find on taking a long
average that more cases occur in some streets of a
town than in others, we are not warranted in concluding
that the cause lies in the sanitary conditions of
those streets or in any special liability to infection
without first taking into account the number of families
<span class="pagenum"><a name="page359" id="page359"></a>[page&nbsp;359]</span>
in the different streets. If one street showed on the
average ten times as many cases as another, the
coincidence might still be judged casual if there were
ten times as many families in it.</p>

<p>Apart from the fallacy of overlooking the positive
frequency, certain other fallacies or liabilities to error
in applying this doctrine of chances may be specified.</p>

<p>1. We are apt, under the influence of prepossession
or prejudice, to remember certain coincidences better
than others, and so to imagine extra-casual coincidence
where none exists. This bias works in confirming all
kinds of established beliefs, superstitious and other,
beliefs in dreams, omens, retributions, telepathic communications,
and so forth. Many people believe that
nobody who thwarts them ever comes to good, and can
produce numerous instances from experience in support
of this belief.</p>

<p>2. We are apt, after proving that there is a residuum
beyond what chance will account for on due allowance
made for positive frequency, to take for granted that we
have proved some particular cause for this residuum.
Now we have not really explained the residuum by the
application of the principle of chances: we have only
isolated a problem for explanation. There may be
more than chance will account for: yet the cause may
not be the cause that we assign off-hand. Take, for
example, the coincidence that has been remarked
between race and different forms of Christianity in
Europe. If the distribution of religious systems were
entirely independent of race, it might be said that you
would expect one system to coincide equally often with
different races in proportion to the positive number
of their communities. But the Greek system is found
almost solely among Slavonic peoples, the Roman
<span class="pagenum"><a name="page360" id="page360"></a>[page&nbsp;360]</span>
among Celtic, and the Protestant among Teutonic.
The coincidence is greater than chance will account
for. Is the explanation then to be found in some
special adaptability of the religious system to the
character of the people? This may be the right
explanation, but we have not proved it by merely discounting
chance. To prove this we must show that
there was no other cause at work, that character was
the only operative condition in the choice of system,
that political combinations, for example, had nothing
to do with it. The presumption from extra-casual
coincidence is only that there is a special cause: in
determining what that is we must conform to the
ordinary conditions of explanation.</p>

<p>So coincidence between membership of the Government
and a classical education may be greater than
chance would account for, and yet the circumstance of
having been taught Latin and Greek at school may
have had no special influence in qualifying the members
for their duties. The proportion of classically educated
in the Government may be greater than the proportion
of them in the House of Commons, and yet their
eminence may be in no way due to their education.
Men of a certain social position have an advantage
in the competition for office, and all those men have
been taught Latin and Greek as a matter of course.
Technically speaking, the coinciding phenomena may
be independent effects of the same cause.</p>

<p>3. Where the alternative possibilities are very
numerous, we are apt not to make due allowance for
the number, sometimes overrating it, sometimes underrating
it.</p>

<p>The fallacy of underrating the number is often seen
in games of chance, where the object is to create a vast
<span class="pagenum"><a name="page361" id="page361"></a>[page&nbsp;361]</span>
number of alternatives, all equally possible, equally
open to the player, without his being able to affect
the advent of one more than another. In whist, for
example, there are some six billions of possible hands.
Yet it is a common impression that, one night with
another, in the course of a year, a player will have
dealt to him about an equal number of good and bad
hands. This is a fallacy. A very much longer time
is required to exhaust the possible combinations.
Suppose a player to have 2000 hands in the course of
a year: this is only one "set," one combination, out
of thousands of millions of such sets possible. Among
those millions of sets, if there is nothing but chance
in the matter, there ought to be all proportions of good
and bad, some sets all good, some all bad, as well as
some equally divided between good and bad.<a id="footnotetagB2-ChVIII1" name="footnotetagB2-ChVIII1"></a><a href="#footnoteB2-ChVIII1"><sup>1</sup></a></p>

<p>Sometimes, however, the number of possible alternatives
is overrated. Thus, visitors to London often
remark that they never go there without meeting somebody
from their own locality, and they are surprised
at this as if they had the same chance of meeting their
fellow-visitors and any other of the four millions of
the metropolis. But really the possible alternatives
of rencounter are far less numerous. The places
frequented by visitors to London are filled by much
more limited numbers: the possible rencounters are
to be counted by thousands rather than by millions.</p>

<p class="note1"><a id="footnoteB2-ChVIII1" name="footnoteB2-ChVIII1"></a><a class="footnote" href="#footnotetagB2-ChVIII1">Footnote 1:</a>
See De Morgan's <i>Essay on Probabilities</i>, c. vi., "On Common
Notions of Probability".</p>
<span class="pagenum"><a name="page362" id="page362"></a>[page&nbsp;362]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter IX.</span></h3>

<h3>PROBABLE INFERENCE TO PARTICULARS&mdash;THE MEASUREMENT OF PROBABILITY.</h3>

<p>Undoubtedly there are degrees of probability. Not
only do we expect some events with more confidence
than others: we may do so, and our confidence may
be misplaced: but we have reason to expect some
with more confidence than others. There are different
degrees of rational expectation. Can those degrees be
measured numerically?</p>

<p>The question has come into Logic from the mathematicians.
The calculation of Probabilities is a
branch of Mathematics. We have seen how it may
be applied to guide investigation by eliminating what
is due to chance, and it has been vaguely conceived by
logicians that what is called the calculus of probabilities
might be found useful also in determining by
exact numerical measurement the probability of single
events. Dr. Venn, who has written a separate treatise
on the Logic of Chance, mentions "accurate quantitative
apportionment of our belief" as one of the goals
which Logic should strive to attain. The following
passage will show his drift.<a id="footnotetagB2-ChIX1" name="footnotetagB2-ChIX1"></a><a href="#footnoteB2-ChIX1"><sup>1</sup></a></p>

<blockquote><p>
A man in good health would doubtless like to know
whether he will be alive this time next year. The fact
<span class="pagenum"><a name="page363" id="page363"></a>[page&nbsp;363]</span>
will be settled one way or the other in due time, if he can
afford to wait, but if he wants a present decision, Statistics
and the Theory of Probability can alone give him any
information. He learns that the odds are, say five to
one that he will survive, and this is an answer to his
question as far as any answer can be given. Statisticians
are gradually accumulating a vast mass of data of this
general character. What they may be said to aim at is to
place us in the position of being able to say, in any given
time or place, what are the odds for or against any at
present indeterminable fact which belongs to a class
admitting of statistical treatment.</p>

<p>Again, outside the regions of statistics proper&mdash;which
deal, broadly speaking, with events which can be numbered
or measured, and which occur with some frequency&mdash;there
is still a large field as to which some better approach
to a reasoned intensity of belief can be acquired. What
will be the issue of a coming war? Which party will win
in the next election? Will a patient in the crisis of a
given disease recover or not? That statistics are lying
here in the background, and are thus indirectly efficient
in producing and graduating our belief, I fully hold; but
there is such a large intermediate process of estimating,
and such scope for the exercise of a practised judgment,
that no direct appeal to statistics in the common sense
can directly help us. In sketching out therefore the
claims of an Ideal condition of knowledge, we ought
clearly to include a due apportionment of belief to every
event of such a class as this. It is an obvious defect that
one man should regard as almost certain what another
man regards as almost impossible. Short, therefore, of
certain prevision of the future, we want complete agreement
as to the degree of probability of every future event:
and for that matter of every past event as well.
</p></blockquote>

<p>Technically speaking, if we extend the name
Modality (<a href="#page78">see p. 78</a>) to any qualification of the certainty
of a statement of belief, what Dr. Venn here
<span class="pagenum"><a name="page364" id="page364"></a>[page&nbsp;364]</span>
desiderates, as he has himself suggested, is a more
exact measurement of the Modality of propositions.
We speak of things as being certain, possible, impossible,
probable, extremely probable, faintly probable,
and so forth: taking certainty as the highest degree of
probability<a id="footnotetagB2-ChIX2" name="footnotetagB2-ChIX2"></a><a href="#footnoteB2-ChIX2"><sup>2</sup></a>
shading gradually down to the zero of the
impossible, can we obtain an exact numerical measure
for the gradations of assurance?</p>

<p>To examine the principles of all the cases in which
chances for and against an occurrence have been calculated
from real or hypothetical data, would be to
trespass into the province of Mathematics, but a few
simple cases will serve to show what it is that the
calculus attempts to measure, and what is the practical
value of the measurement as applied to the probability
of a single event.</p>

<p>Suppose there are 100 balls in a box, 30 white and
70 black, all being alike except in respect of colour, we
say that the chances of drawing a black ball as against
a white are as 7 to 3, and the probability of drawing
black is measured by the fraction <sup>7</sup>&frasl;<sub>10</sub>. In believing
this we proceed on the principle already explained
(p. 356) of Proportional Chances. We do not know
for certain whether black or white will emerge, but
knowing the antecedent situation we expect black
<span class="pagenum"><a name="page365" id="page365"></a>[page&nbsp;365]</span>
rather than white with a degree of assurance corresponding
to the proportions of the two in the box. It
is our degree of rational assurance that we measure by
this fraction, and the rationality of it depends on the
objective condition of the facts, and is the same for all
men, however much their actual degree of confidence
may vary with individual temperament. That black
will be drawn seven times out of every ten on an
average if we go on drawing to infinity, is as certain
as any empirical law: it is the probability of a single
draw that we measure by the fraction <sup>7</sup>&frasl;<sub>10</sub>.</p>

<p>When we build expectations of single events on
statistics of observed proportions of events of that
kind, it is ultimately on the same principle that
rational expectation rests. That the proportion will
obtain on the average we regard as certain: the ratio
of favourable cases to the whole number of possible
alternatives is the measure of rational expectation
or probability in regard to a particular occurrence.
If every year five per cent. of the children of a town
stray from their guardians, the probability of this or
that child's going astray is <sup>1</sup>&frasl;<sub>20</sub>. The ratio is a correct
measure only on the assumption that the average is
maintained from year to year.</p>

<p>Without going into the combination of probabilities,
we are now in a position to see the practical value of
such a calculus as applied to particular cases. There
has been some misunderstanding among logicians on
the point. Mr. Jevons rebuked Mill for speaking disrespectfully
of the calculus, eulogised it as one of the
noblest creations of the human intellect, and quoted
Butler's saying that "Probability is the guide of life".
But when Butler uttered this famous saying he was
probably not thinking of the mathematical calculus of
<span class="pagenum"><a name="page366" id="page366"></a>[page&nbsp;366]</span>
probabilities as applied to particular cases, and it was
this special application to which Mill attached comparatively
little value.</p>

<p>The truth is that we seldom calculate or have any
occasion to calculate individual chances except as a
matter of curiosity. It is true that insurance offices
calculate probabilities, but it is not the probability of
this or that man dying at a particular age. The
precise shade of probability for the individual, in so
far as this depends on vital statistics, is a matter of
indifference to the company as long as the average is
maintained. Our expectations about any individual
life cannot be measured by a calculation of the chances
because a variety of other elements affect those expectations.
We form beliefs about individual cases, but
we try to get surer grounds for them than the chances
as calculable from statistical data. Suppose a person
were to institute a home for lost dogs, he would doubtless
try to ascertain how many dogs were likely to go
astray, and in so doing would be guided by statistics.
But in judging of the probability of the straying of a
particular dog, he would pay little heed to statistics
as determining the chances, but would proceed upon
empirical knowledge of the character of the dog and
his master. Even in betting on the field against a
particular horse, the bookmaker does not calculate
from numerical data such as the number of horses
entered or the number of times the favourite has been
beaten: he tries to get at the pedigree and previous
performances of the various horses in the running.
We proceed by calculation of chances only when we
cannot do better.</p>

<p class="note1"><a id="footnoteB2-ChIX1" name="footnoteB2-ChIX1"></a><a class="footnote" href="#footnotetagB2-ChIX1">Footnote 1:</a>
<i>Empirical Logic</i>, p. 556.</p>

<p class="note1"><a id="footnoteB2-ChIX2" name="footnoteB2-ChIX2"></a><a class="footnote" href="#footnotetagB2-ChIX2">Footnote 2:</a>
Mr. Jevons held that all inference is merely probable and that
no inference is certain. But this is a purposeless repudiation of
common meaning, which he cannot himself consistently adhere
to. We find him saying that if a penny is tossed into the air it
will <i>certainly</i> come down on one side or the other, on which
side being a matter of probability. In common speech probability
is applied to a degree of belief short of certainty, but to say that
certainty is the highest degree of probability does no violence to
the common meaning.</p>
<span class="pagenum"><a name="page367" id="page367"></a>[page&nbsp;367]</span>

<h3 style="margin-top: 3em;"><span class="sc">Chapter X.</span></h3>

<h3>INFERENCE FROM ANALOGY.</h3>

<p>The word Analogy was appropriated by Mill, in accordance
with the usage of the eighteenth century, to
designate a ground of inference distinct from that on
which we proceed in extending a law, empirical or
scientific, to a new case. But it is used in various
other senses, more or less similar, and in order to
make clear the exact logical sense, it is well to specify
some of these. The original word
<ins title="analogia"><span style="font-size: 0.9em;">&#7936;</span>&nu;&alpha;&lambda;&omicron;&gamma;&#943;&alpha;</ins>,
as employed by Aristotle, corresponds to the word Proportion
in Arithmetic: it signified an equality of ratios,
<ins title="isotês logôn"><span style="font-size: 0.9em;">&#7984;</span>&sigma;&#972;&tau;&eta;&sigmaf; &lambda;&#972;&gamma;&omega;&nu;</ins>:
two compared with four is analogous to four
compared with eight. There is something of the same
meaning in the technical use of the word in Physiology,
where it is used to signify similarity of function as
distinguished from similarity of structure, which is
called homology: thus the tail of a whale is analogous
to the tail of a fish, inasmuch as it is similarly used
for motion, but it is homologous with the hind legs of
a quadruped; a man's arms are homologous with a
horse's fore legs, but they are not analogous inasmuch
as they are not used for progression. Apart from
these technical employments, the word is loosely used
in common speech for any kind of resemblance. Thus
De Quincey speaks of the "analogical" power in
memory, meaning thereby the power of recalling things
<span class="pagenum"><a name="page368" id="page368"></a>[page&nbsp;368]</span>
by their inherent likeness as distinguished from their
casual connexions or their order in a series. But even
in common speech, there is a trace of the original
meaning: generally when we speak of analogy we
have in our minds more than one pair of things, and
what we call the analogy is some resemblance between
the different pairs. This is probably what Whately
had in view when he defined analogy as "resemblance
of relations".</p>

<p>In a strict logical sense, however, as defined by
Mill, sanctioned by the previous usage of Butler and
Kant, analogy means more than a resemblance of
relations. It means a preponderating resemblance
between two things such as to warrant us in inferring
that the resemblance extends further. This is a
species of argument distinct from the extension of an
empirical law. In the extension of an empirical law,
the ground of inference is a coincidence frequently
repeated within our experience, and the inference is
that it has occurred or will occur beyond that experience:
in the argument from analogy, the ground of
inference is the resemblance between two individual
objects or kinds of objects in a certain number of
points, and the inference is that they resemble one
another in some other point, known to belong to the
one, but not known to belong to the other. "Two
things go together in many cases, therefore in all,
including this one," is the argument in extending a
generalisation: "Two things agree in many respects,
therefore in this other," is the argument from analogy.</p>

<p>The example given by Reid in his <i>Intellectual Powers</i>
has become the standard illustration of the peculiar
argument from analogy.</p>

<blockquote><p>
We may observe a very great similitude between this
<span class="pagenum"><a name="page369" id="page369"></a>[page&nbsp;369]</span>
earth which we inhabit, and the other planets, Saturn,
Jupiter, Mars, Venus and Mercury. They all revolve round
the sun, as the earth does, although at different distances
and in different periods. They borrow all their light from
the sun, as the earth does. Several of them are known to
revolve round their axis like the earth, and by that means
have like succession of day and night. Some of them have
moons, that serve to give them light in the absence of
the sun, as our moon does to us. They are all, in their
motions, subject to the same law of gravitation as the earth
is. From all this similitude it is not unreasonable to think
that these planets may, like our earth, be the habitation
of various orders of living creatures. There is some probability
in this conclusion from analogy.<a id="footnotetagB2-ChX1" name="footnotetagB2-ChX1"></a><a href="#footnoteB2-ChX1"><sup>1</sup></a>
</p></blockquote>

<p>The argument from analogy is sometimes said to
range through all degrees of probability from certainty
to zero. But this is true only if we take the word
analogy in its loosest sense for any kind of resemblance.
If we do this, we may call any kind of argument an
argument from analogy, for all inferences turn upon
resemblance. I believe that if I throw my pen in the
air it will come down again, because it is like other
ponderable bodies. But if we use the word in its
limited logical sense, the degree of probability is much
nearer zero than certainty. This is apparent from the
conditions that logicians have formulated of a strict
argument from analogy.</p>

<p>1. The resemblance must be preponderating. In
estimating the value of an argument from analogy, we
must reckon the points of difference as counting against
the conclusion, and also the points in regard to which
we do not know whether the two objects agree or
differ. The numerical measure of value is the ratio of
<span class="pagenum"><a name="page370" id="page370"></a>[page&nbsp;370]</span>
the points of resemblance to the points of difference
<i>plus</i> the unknown points. Thus, in the argument that
the planets are inhabited because they resemble the
earth in some respects and the earth is inhabited, the
force of the analogy is weakened by the fact that we
know very little about the surface of the planets.</p>

<p>2. In a numerical estimate all circumstances that
hang together as effects of one cause must be reckoned
as one. Otherwise, we might make a fallaciously
imposing array of points of resemblance. Thus in
Reid's enumeration of the agreements between the
earth and the planets, their revolution round the sun
and their obedience to the law of gravitation should
count as one point of resemblance. If two objects
agree in <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i>, <i>e</i>, but <i>b</i> follows
from <i>a</i>, and <i>d</i> and <i>e</i>
from <i>c</i>, the five points count only as two.</p>

<p>3. If the object to which we infer is known to
possess some property incompatible with the property
inferred, the general resemblance counts for nothing.
The moon has no atmosphere, and we know that air is
an indispensable condition of life. Hence, however
much the moon may resemble the earth, we are
debarred from concluding that there are living creatures
on the moon such as we know to exist on the earth.
We know also that life such as it is on the earth is
possible only within certain limits of temperature, and
that Mercury is too hot for life, and Saturn too cold, no
matter how great the resemblance to the earth in other
respects.</p>

<p>4. If the property inferred is known or presumed to
be a concomitant of one or more of the points of
resemblance, any argument from analogy is superfluous.
This is, in effect, to say that we have no occasion to
argue from general resemblance when we have
<span class="pagenum"><a name="page371" id="page371"></a>[page&nbsp;371]</span>
reason to believe that a property follows from something
that an object is known to possess. If we knew
that any one of the planets possessed all the conditions,
positive and negative, of life, we should not require
to reckon up all the respects in which it resembles
the earth in order to create a presumption that it is
inhabited. We should be able to draw the conclusion
on other grounds than those of analogy. Newton's
famous inference that the diamond is combustible is
sometimes quoted as an argument from analogy. But,
technically speaking, it was rather, as Professor Bain
has pointed out, of the nature of an extended generalisation.
Comparing bodies in respect of their densities and
refracting powers, he observed that combustible bodies
refract more than others of the same density; and
observing the exceptionally high refracting power of
the diamond, he inferred from this that it was combustible,
an inference afterwards confirmed by experiment.
"The concurrence of high refracting power
with inflammability was an empirical law; and
Newton, perceiving the law, extended it to the adjacent
case of the diamond. The remark is made by Brewster
that had Newton known the refractive powers of the
minerals <i>greenockite</i> and <i>octohedrite</i>, he would have
extended the inference to them, and would have been
mistaken."<a id="footnotetagB2-ChX2" name="footnotetagB2-ChX2"></a><a href="#footnoteB2-ChX2"><sup>2</sup></a></p>

<p>From these conditions it will be seen that we cannot
conclude with any high degree of probability from
analogy alone. This is not to deny, as Mr. Jevons
seems to suppose, that analogies, in the sense of
general resemblances, are often useful in directing
investigation. When we find two things very much
alike, and ascertain that one of them possesses a
<span class="pagenum"><a name="page372" id="page372"></a>[page&nbsp;372]</span>
certain property, the presumption that the other has
the same is strong enough to make it worth while
trying whether as a matter of fact it has. It is said
that a general resemblance of the hills near Ballarat
in Australia to the Californian hills where gold had been
found suggested the idea of digging for gold at Ballarat.
This was a lucky issue to an argument from analogy,
but doubtless many have dug for gold on similar
general resemblances without finding that the resemblance
extended to that particular. Similarly, many
of the extensions of the Pharmacopeia have proceeded
upon general resemblances, the fact that one drug
resembles another in certain properties being a sufficient
reason for trying whether the resemblance goes
further. The lucky guesses of what is known as
natural sagacity are often analogical. A man of wide
experience in any subject-matter such as the weather,
or the conduct of men in war, in business, or in
politics, may conclude to the case in hand from some
previous case that bears a general resemblance to it,
and very often his conclusions may be perfectly sound
though he has not made a numerical estimate of the
data.</p>

<p>The chief source of fallacy in analogical argument
is ignoring the number of points of difference. It
often happens that an amount of resemblance only
sufficient for a rhetorical simile is made to do duty as
a solid argument. Thus the resemblance between a
living body and the body politic is sometimes used to
support inferences from successful therapeutic treatment
to State policy. The advocates of annual
Parliaments in the time of the Commonwealth based
their case on the serpent's habit of annually casting
its skin.</p>
<span class="pagenum"><a name="page373" id="page373"></a>[page&nbsp;373]</span>

<div class="poem">  <div class="stanza">
<p>Wisest of beasts the serpent see,</p>
<p>Just emblem of eternity,</p>
<p class="i2">And of a State's duration;</p>
<p>Each year an annual skin he takes,</p>
<p>And with fresh life and vigour wakes</p>
<p class="i2">At every renovation.</p>
  </div>
  <div class="stanza">
<p>Britain! that serpent imitate.</p>
<p>Thy Commons House, that skin of State,</p>
<p class="i2">By annual choice restore;</p>
<p>So choosing thou shall live secure,</p>
<p>And freedom to thy sons inure,</p>
<p class="i2">Till Time shall be no more.</p>
  </div>  </div>

<p>Carlyle's saying that a ship could never be taken
round Cape Horn if the crew were consulted every
time the captain proposed to alter the course, if taken
seriously as an analogical argument against Representative
Government, is open to the objection that the
differences between a ship and a State are too great
for any argument from one to the other to be of
value. It was such fallacious analogies as these that
Heine had in view in his humorous prayer, "Heaven
defend us from the Evil One and from metaphors".</p>

<p class="note1"><a id="footnoteB2-ChX1" name="footnoteB2-ChX1"></a><a class="footnote" href="#footnotetagB2-ChX1">Footnote 1:</a>
Hamilton's <i>Reid</i>, p. 236.</p>

<p class="note1" style="margin-bottom: 5em;"><a id="footnoteB2-ChX2" name="footnoteB2-ChX2"></a><a class="footnote" href="#footnotetagB2-ChX2">Footnote 2:</a>
Bain's <i>Logic</i>, ii. 145.</p>

<hr class="full" />

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