A TREATISE  ON
OR,
THE LAWS OF PURE THOUGHT;
COMPRISING BOTH
THE ARISTOTELIC AND HAMILTONIAN
ANALYSES OF LOGICAL FORMS,
AND SOME CHAPTERS OF
APPLIED LOGIC.
BY FRANCIS BOWEN,
ALFORD PROFESSOR OF MORAL PHILOSOPHY IN HARVARD COLLEGE.
6 Nam neque decipitur ratio, nec decipit unquam."
MANILIUS.
CAMBRIDGE:
SEVER AND FRANCIS,
BOOKSELLERS TO THE UNIVERSITY,
1864.




Entered according to Act of Congress, in the year 1864, by
SEVER AND FRANCIS,
in the Clerk's Office of the District Court of the District of Massachusetts
SECOND  EDI TiONo
UNIVERSITY  PRESS'
WELCH, BIGELOW, AND COIPANY,
CAMBRIDGE.




PREFACE.
HE revival of the study of Logic, at least in
England and America, as an important element of a University education, dates only from the
publication of Dr. Whately's treatise on the subject,
little over thirty years ago. Yet so much has been
accomplished for the advancement of the science
during this short period, that this treatise, with all
its excellences, must be admitted to be now as far
behind the times as were the compilation by Aldrich, and the meagre compendium by Dr. Watts,
the use of which it superseded. Dr. Whately lived
long enough to be able to appropriate to himself
the epigrammatic boast, that he had labored so effectually as to render his own work useless. Without the interest which was awakened in the study
of the science by the publication of his book and
the discussions which it excited, it is not too much
to say that many of the valuable works upon Logic,
which have appeared during the last thirty years,
either would not have been written, or would have
lacked some of their most interesting and important features. Sir William Hamilton's own labors
in this department, by which he certainly accomplished more for the science than has been done by
any one man since Aristotle, began with an elabo



iv                  PREFACE.
rate article on Dr. Whately's treatise in the Edinburg Review, a paper which, as he has himself
declared, contains the germs of all his subsequent
discoveries.  Besides what Hamilton has accomplished, the publications within this period of Professor Mansel, Dr. Thomson, Mr. De Morgan,  Mr.
Boole, Mr. J. S. Mill, and a host of others, have
given an entirely new aspect to the science. Among
recent American works upon Logic, honorable mention ought to be made of those by Mr. Tappan, and
by Dr. W. D. Wilson of Geneva.
The only hope that this volume may be found
to be of some use consists in the fact, that, as I was
the last to enter the field, I have been able to profit
by the labors of my predecessors.  Certainly it
could not have been written without their aid, and
one of the chief objects held in view in the preparation of it has been to gather together, and digest
into system, their several improvements and elucidations of the science.  "At the same time, the
work would not have been carried on in the same
spirit in which they began it, if I had not ventured
respectfully to dissent from some of their doctrines,
and even to present some opinions which will very
likely be found to have no other merit than that
of originality. As Le Clerc remarks, in introducing
his own lucid and thoughtful compendium  of the
science to the reader's notice, "Csi, i' h/acce Loyica,
niihil esse novi, azt plerctaue nova dixerizn, leclorein perinde
fefellero."
When Dr. Whately wrote, it was not so frequent
a practice as it has since become for English scholars to profit by the labors of their German brethren, and hence some of the greatest deficiencies
of his book.  It cannot be said that the study of
Logic ever declined in the schools of Germany, as




PREFACE.                 V
it did in those of France, England, and this country.
Upheld for a time by the genius of Leibnitz and
the indefatigable industry of Wolff, it was at last
reduced to rigorous system, its boundaries were
fixed, and its relations to Psychology and Metaphysics accurately determined, by the master mind of
Kant. Though this great Metaphysician prepared
no distinct work upon the subject, the volume relating to it which passes under his name being a
mere compilation from his loose notes by Jasche,
the science has profited more by his labors than by
those of any other Continental writer of modern
times. Indeed, the publication of his cc Criticism of
Pure Reason" formed hardly less an era in the history of Logic than in that of Metaphysics. In one
respect, it is true, it had an injurious influence, as
it established the practice, which has since become
wellnigh universal in Germany, of modifying the
doctrines of this science in order to furnish a basis
on which might be erected any peculiar scheme
of speculative Philosophy. Since Kant's time, a
multitude of treatises upon Logic have been published by German writers, about half of them havinlg no other purpose than that of preparing the
way, and furnishing the materials, for some extravagant speculations in Metaphysics. This mode of
treatment was carried to an outrageous extent by
HIegel, vho labored to break down altogether the
boundary that had been established by Kant, and
whose elaborate work, bearing the name of Logic,
is a mere perversion and caricature of that science,
(as it is metaphysical from beginning to end. Even
Trendelenburg, who has contributed more than
any other person to the rapid decline of Hegelianism in Germany, is not free from blame in this
respect, his very able work, Logiscew UgztersztchZungee,




vi                  PREFACE.
being devoted in great part to building up a philosophical system of his own.
But the very prevalence of this abuse in Germany furnishes an additional motive for the study
of the subject. A key to German Metaphysics
can be obtained only by a thorough mastery of
the principles and the terminology of Logic. To
some persons, perhaps, this consideration may not
have much weight, as they will object, that it is
of little use to be able to open the door, if the
room  contains little more than rubbish. Still I
cannot but believe —and the opinion is founded
on considerable experience as an instructor in
both departments - that a fair knowledge of Logic is a natural, and eve.n an indispensable, preparation for the successful pursuit of Psychology and
Metaphysics; - may I not add, of any philosophical speculations whatever? It appears certain,
that the University lectures of Kant, Fichte, Schelling, and Hegel could not have been made even
intelligible, much less instructive, to hearers who
had not previously acquired at least the elements
of Logical science. Hence the multitude of manuals and textbooks upon this subject, which have
appeared in Germany during the last three quarters of a century, many of them  having passed
through numerous editions, and each betraying
very plainly the particular system of Philosophy
to which it was intended to serve as an introduction. Some familiarity with the principles of Logic appears essential for a thorough comprehension
even of the metaphysical doctrines of Sir William
Hamilton, which, both in their philosophical and
theological bearings, seem likely to exert a considerable influence over English and American minds
for many years to come.




PREFACE.                V1i
Hlamilton's  "Lectures on Logic 5' are marked
with the inevitable defects of a posthumous publication, the larger portion of which was probably
never intended by the author to be given to the
public; and though very ably edited by Professor
Mansel and Mr. Veitch, they present a mass of
crude material from which a knowledge of the
peculiar doctrines of the writer cannot be extracted but with considerable difficulty. Indeed,
the "Lectures," which form the body of the book,
were evidently prepared in great haste, when the
author's appointment to the Professorship in this
department, in 1836, obliged him to collect at
short notice the materials for an extended course
of instruction. He appears to have met this sudden call by hurriedly translating a series of extracts from the most approved German text-books,
especially those of Krug, Esser, and Bachmann,
merely interpolating here and there some of the
comments, corrections, and additions which could
not fail to occur to so rich a mind as his, while
traversing so broad and familiar a field. These
Lectures, containing only a glimpse of one feature
of the peculiar system which has since become
identified with his name, he seems to have repeated from year to year, during his whole period
of office, with no material enlargement or alteration of the manuscript, though doubtless inserting,
from year to year, many extemporaneous expositions of his corrections of the leading doctrines
of Logical science, as these occurred to him at successive periods.  The whole transaction seems to
me to afford an instructive comment on the futility
of what is called the Professorial mode of teaching,
which has always prevailed in the University of
Edinburgh, and which consists in getting up very




Viu1                PREFACE.
hastily a course of lectures, during the teacher's
first year of office, and repeating them, parrot-like,
from year to year, without any regular use of a
text-book or manual of instruction. If such lectures contain anything really valuable, in addition
to what is already before the world, they are apt
very soon to find their way to the press; if they
are of little worth, they are almost sure to be
repeated, with little alteration, to one class after
another, and with as little profit to the hearer as
exercise to the reader. It may be doubted whether the most fertile and best-trained minds, at least
in the speculative sciences, are capable of preparing every year an entirely new course of lectures,
without either filling them with crudities and truisins, or lapsing into paradox and extravagance,
such as have too frequently characterized the productions of German Professors.
With all his amazing activity of mind and prodigious erudition, Hamilton appears to have been
either too indolent, or too critical of his own labors,
to be able, without great delays, to digest his materials into a shape fit for publication. He was not
an adept in the very low, but very necessary, art
of book-making. But for his controversy with Mr.
De Morgan, I doubt whether he would ever have
worked up into form as much as he did of his
c" New Analytic of Logical Forms," the publication
of which was promised as far back as 1846. Stimulated by opposition, however, though impeded
by ill-health during the later years of his life, he
appears to have labored strenuously, after the lastmentioned date, to fulfil this promise. Death surprised him long before he had completed his preparations; and out of the mass of fragmentary materials which were found among his papers, with




PREFACE.                 i
some aid from the few critical and controversial
articles that he had already printed, his editors
pieced together, with great difficulty, the imnperfect
view of his improved system of Logic, which appears as a long Appendix to the volume of his
Lectures. The manuscripts which they selected
and arranged were judiciously printed just as he
left them, and with very little editorial comment.
The reader must gather from them as best lihe
may, always keeping in view the date attached
to each fragment, a connected view of Sir William
J[Hamilton's latest doctrines upon the subject. This
posthumous work has at least one odd characteristic, as the body of the work and the Appendix
flatly contradict each other, by giving opposite
views of the science to which they relate.
These are the sources whence I have endeavored to collect the materials for a general survey
of the science of Logic in its present state, embracing what is common to all systems, and a review of most of the questions relating to it which
are still open to discussion. Among English authors, after Sir William  Hamilton, I have been
chiefly indebted to Professor Mansel; for without
the aid afforded by his Proleomenena Logica, and the
notes and supplementary matter appended to his
edition of Aldrich, of which Hamilton justly remarks that la sauce vaut qmieuzx que le poisson, this
book would have cost me much more labor, and
yet would have wanted what are now its best
claims to notice. I have also derived much help
from  the excellent c" Outline of the Laws of
Thought," by Dr. Thomson, the present Archbishop of York. Among the German writers, besides all whose names have been already mentioned, I have made profitable use of Kiesewetter,




LX                 PREFACE.
Fries, Beneke, Dressler, and Drobisch, besides consulting a host of others. Of the earlier logicians,
it seems to me that Burgersdyck, with the annotations of Heereboord, gives the clearest account
of the science as it was taught in the schools before the influence of Descartes and Locke began
to be felt; and that the Port Royal "Art of
Thinking," of which an admirable translation, with
Notes and an Appendix, by Mr. Baynes, has recently been published, is far the best of the treatises on the subject which were in use during the
eighteenth century. Throughout the work, I have
kept constantly in view the wants of learners,
much of it having been first suggested while attempting to expound the science in my own classroom. My highest ambition will be satisfied if it
should be found to be of use to other teachers.
CAMBRIDGE, March, 1864.




CONTENTS.
CHAPTER I.
PSYCHOLOGICAL INTRODUCTION.... 1
Intuitions distinguished from Concepts...         1
The Nature of Thought.....                 10
Relations of Thought to Language.                  ~.  16
Mental Characteristics of Brutes...    18
The Formation of Concepts...             19
Language aids Thought....      21
And is often substituted for it...         ~    24
CHAPTER II.
DEFINITION orF LOGIC.....             30
The Form distinguished from the Matter of Thought.      31
Universal distinguished from Special Logic.         34
Divisions of the Science......                         36
Utility of the Study of Logic..                    38
CHAPTER  III.
TEE PRIMARY AxIoMs OF PURE THOUGHT... 47
These Axioms reduced to one Principle....    48
This Principle explicated into three Axioms.      49
Analytic distinguished from Synthetic Thought... 52
Tile Principle of Synthetic Thought explicated.    ~.. 53
Hamilton's Postulate of Logic.         56




xii                          CONTENTS.
CHAPTER IV.
THE DOCTRINE OF CONCEPTS..                           59
The Elements of a Concept....                  62
The twofold Quantity of Concepts.                           66
First and Second Intentions.70
The Relation of the two Quantities to each other                72
Infinitated Concepts..                                      75
The Quality of Concepts.......                                77
The Standards of Nominal and Real Definition                   84
The Relations of Concepts.... 86
The Laws of Homogeneity and Heterogeneity                       90
Definition and Division....                          93
CHAPTER V.
THE DOCTRINE OB JUDGMENTS..  105
The Nature of the Copula.                                    109
The Predicables and the Categories....    112
The Quantity of Judgments, Aristotelic Doctrine.              120
The Quality of Judgments,... 123
Quantity as affected by Quality, "     "                      125
The Relation of Judgments                                      127
Conditional Judgments.......                                 128
The Hamiltonian Doctrine of Judgments.... 132
Explication of Propositions into Judgments....    141
CHAPTER VI.
[HE DOCTRINE OF IIMMEDIATE INFERENCE. 148
_Equipollence or Infinitation.152
Conversion.156
Hamilton's Doctrine of Conversion.160
Opposition and Integration.162
Conspectus of Judgments and Immediate Inference, Aristotelic
Doctrine.166
Hamilton's Doctrine of Opposition and Integration..    168




CONTENTS.                           xSii
CHAPTER VII.
THE DOCTRINE OF MEDIATE INFERENCE: THEE ARISTOTELIC ANALTSIS OF SYLLOGISMS.                  174
The Canon of Categorical Syllogisms.....       175
This Canon explicated into Six Rules.                180
Dictum de omni et nullo....                               187
Figure and Mood........ 190
Reduction to the First. Figure...... 194
The Mood of a Syllogism......197
The Technicalities of Reduction exemplified                   202
Conditional Syllogisms..                            207
Disjunctive Syllogisms....212
Dilemmas or Hypothetico-Disjunctives..                        215
Defective and Complex Syllogisms...              219
Sorites....                                               222
Conspectus of the Aristotelic Doctrine of Syllogisms..    226
CHAPTER VIII.
THE HAMILTONIAN DOCTRINE OF SYLLOGISMS.          228
Analytic and Synthetic Order of Enouncement                   228
Reasoning in the two Quantities.... 234
The Doctrine of the Figures..                               239
The Unfigured Syllogism..                                  244
Hamilton's System of Notation or Symbolization.               246
The Number of Moods increased by Quantifying the Predicate. 251
The worse Relation of Subject and Predicate                   253
Hamiltonian Table of Moods....... 256
Falsity of the Special Rules demonstrated.                  259
Applicability of the different Figures to Deduction and Induction  261
Conditional Syllogisms reduced to Immediate Inferences.. 264
CHAPTER IX.
OF FALLACIES.. *. *                267
Fallacies in dictione improperly so called....    269
Division of Formal and Material Fallacies.            271
Syllogisms of more than Three Terms; Ambiguous Middle         272




X{V     -                   CONTENTS.
Undistributed Middle; Composite and Divisive sense. 278
Illicit Process of the Major and Minor Terms...    281
The Sophism of Eubulides, the Liar. 288
Sophisms respecting the Quality of the Reasoning  290
Violation of the Canons of Hypothetical Reasoning..     293
Material:Fallacies; petitio principii...        294:Fallacy of the Impossibility of Motion... 296
Ignoratio elenchi....   298
Argumentum ad ignorantiam. 300
Non Causa pro Causa; post hoc, ergo propter hoc.    306
Ignava Ratio...309
Achilles and the'Tortoise.                               312
CHAPTER X.
APPLIED LOGIC......... 314
Science formed by Analysis and Synthesis...         317
Classification in Science..... 322
The Relation of Cause and Effect...             324
Necessary Cognitions h priori.. 328
These Cognitions not mere Laws of Thought...    330
Elements of our Concepts of Individual Objects...    334
The preliminary Classifications of Science.                340
Science advances through the improvement of Classifications. 343
Failure of the attempts. made to classify the Sciences..    346
CHAPTER XI.
DEMONSTRATIVE REASONING AND DEDUCTIVE EVIDENCE.. 351
Demonstration applicable to mere Concepts, not to Real Things  352
Why Mathematical reasoning is demonstrative...    353
Mathematical evidence not a mere perception of identity.. 359
Distinction between Pure and Applied Mathematics..    361
The Conclusion not deduced from the Major Premise.. 362
The only New Truth is that enounced in the Subsumption      364
Particular facts not learned, but proved, by Reasoning.  367
Different classes of Major Premises..         371
Technical terms used in the Construction of Science.       3 874




CONTENTS.                          XV
CHAPTER XII.
INDUCTION AND ANALOGY.....    376
Want of Universality in the Sumption fatal to strict Reasoning   376
Induction and Analogy are means for discovering Truth.. 380
Difference between them illustrated.                   381
Analogy is Aristotle's Reasoning from Example.. 382
Analogy leads only to Probable Conclusions..         383
Induction presupposes the correctness of previous Classifications  385
Uniformity of Nature the basis of Induction..    388
This Maxim not an Ultimate Fact.                        389
And not first obtained by Induction...         391
But derived from the Principle of Causality.            395
What is Physical Necessity..                     400
All Induction proceeds by simple enumeration..        401
A universal Logic of Induction cannot be established.   403
A General Fact, a Law of Nature, and a Cause distinguished. 405
How a Law of Nature is discovered.                409
Physical Causes proved by the Laws of Nature subsumed under
them....  414
Induction discovers, the Law of Causality proves.    416
CHAPTER  XIII.
THE SOURcES OP EVIDENCE AND THE CAUSES OF ERROR.               419
Intuition the basis of all Certainty.   419
Intuition of external objects as external....   421
Memory as a Source of Evidence.....    423
The art of Writing an auxiliary to Memory.      426
The experience of others a necessary aid....    427
Testimony distinguished from Authority..      428
And Veracity from Competency...    430
Hume's Argument against Miracles examined.... 432
The Criticism of Tradition and Ancient Writings..    433
The Theory of Probabilities.....            437
Moral Causes of Error....    445








CHAPTER I C
PSYCHOLOGICAL INTRODUCTION.
Intuitions distinguished from Concepts. - Mental Characteristics of Brutes.
- Relations of Thought to Language.
FHE beginning of all knowledge is in single acts of the
Perceptive or Acquisitive faculty, each of which relates immediately to an individual object or event.  Such
acts are called Intuitions or Presentations; the former is the
more generally received appellation.  Each Intuition gives
us a knowledge of its object so far only as this object is
perceived now and here, and also as it is one, or undivided,
though not necessarily indivisible. To recognize, or know
over again, the object as similar to another thing perceived
on a former occasion or in a different place, or to analyze it
into its parts or attributes, or to refer it to a class of things
previously known, and thereby to give it a common name,
requires the aid of a different and higher power of the
mind.  In receiving Intuitions, the mind exerts no conscious
activity whatever; it is passively receptive of any impressions that may be made upon it, and does not in any way
consciously react upon or modify those impressions.  It is
like a mirror reflecting the objects that are held up before
it, perhaps giving distorted or unfaithful images of them
on account of the imperfections of its own surface, but hav1                                A




2            PSYCHOLOGICAL INTRODUCTION.
ing no power to change or in any way affect them by its
own will.
The impression made upon my mind by the portrait of a
friend which I am now looking at, as it hangs before me, or
by the sounds to which I am listening as they are struck
upon a violin; the image now present )to my memory of the
relative whom I have recently lost; the picture of a waterfall in a wood which my imagination at this instant forms;
the consciousness which I have of the present state of my
own mind;- all these are Intuitions, as each one of them
relates to a single object, and each is immnediate, - that is,
it does not come through the intervention of any other state
of mind. But what is denoted by the word man, sound, or
waterfall, is not an Intuition, for it does not refer to one object only, but to many. Man, for instance, includes under
it John, Thomas, William, and many others; and it does
not convey a complete image of any one of these persons,
but only a partial representation equally applicable to any
of them. John, when considered simply as man, is not
regarded as he really is, that is, as possessing all his inlividual attributes and peculiarities, but only as having those
attributes which he possesses in common with all other
men; he is not viewed immediately, but only through the
mediuml of what is called a Concept, or a Thought of what
is common to many. These words, therefore, man, sound,
wate;fhall, and all other common names, do not denote Intuitions, but Thoughts.
The Perceptive or Acquisitive faculty, through which
we receive Intuitions, as it is a merely passive power, or a
capacity of being affected in a certain way, constitutes what
may be called the receptivity of the mind. The Thinking
or Elaborative faculty, - i. e. the Understanding, - as it
has no Intuitions of its own, but voluntarily reacts upon
and modifies those received fiom the Perceptive faculty,
comparing them with each other, and thereby combining




INTUITIONS DISTINGUISHED FROM CONCEPTS.      3
them into one Thought, or disjoining them as dissimilar or
incompatible, belongs to the spontaneity, or self-activity, of
the intellect.
In the ordinary exercise of our faculties, Intuitions are
so intermingled with Thoughts, so quickly pass into them,
and are so closely connected with them, that it is difficult
to illustrate the distinction between the two by giving an
example of an Intuition so isolated and peculiar that there
will be no danger of confounding it with any portion of a
voluntary and more complex process of mind. But a good
illustration may perhaps be found in the case, so firequently
referred to, of a person born entirely blind, and subsequently enabled by a surgical operation, for the first time, to see.
Suppose that the first visual sensation given to such a person
were that of a flash of red light. This sensation, it is evident, would be to him entirely peculiar or sui generis. He
could not, at first, refer it to any class of things with which
he was formerly acquainted; he could not give it a name;
he could not analyze it into parts or attributes. He did
not will to produce or to modify it; it comes to him, so to
speak, of its own accord. He could know it, but not recognize it, as the presentation of an entirely new object, by
which his mind was involuntarily affected in a new and surprising manner.  Such, we may suppose, are the Intuitions
of brutes; and the faculty of Intuitions, as the Perceptive
or Acquisitive faculty may be called, - a mere receptivity,
unmodified by any voluntary act of the patient, -is probably the most prominent of the few mental powers which
brutes possess in common with man. In respect only to
Intuitions produced in him by external causes, man has no
advantage over the lower animals.
But although all our knowledge begins in Intuitions, it
does not end with them. In man, the mere receptivity of
mind is so soon modified by its spontaneity, - the mere Intuition so quickly passes into voluntary or consciously active




4            PSYCHOLOGICAL INTRODUCTION.
Thought properly so called, - that we can hardly tell where
the one ends and the other begins. To recur to the case
just mentioned; the moment the person who has now first
received his sight begins to consider or reflect upon the new
presentation that has thus been made to him, he probably,
in a certain sense, recognizes it as a new sensation, - that is,
he refers it to a class of feelings with which he was formerly acquainted, as coming to him through the other senses,
and which, as similar in some respects, though different in
others, he has ranked together and called by one name,
"' sensations " or " feelings."  Such recognition is an act of
Thought properly so called. It includes comparison of this
Intuition with others, and a conscious discrimination of
those respects in which it is similar to others from those in
which it is unlike them.  The Perceptive faculty gives us
Intuitions of single objects, each of which is to us a distinct
unit, having no connection or relation with anything else;
the Understanding, a higher faculty, gives us Thoughts, or
enables us to analyze each thing into its parts or attributes,
and thus to recognize its various points of resemblance and
difference, and so to form classes of things. The former
power furnishes the rude material —" the Matter," as it
is technically called - of our knowledge; the latter supplies
"the Form," elaborating and disposing this rude material
in a systematic way, or according to regular laws, by throw
ing it into groups, so as to render it conceivable to Thought.
Hence the Understanding has been called the unifying
faculty, by which the many is reduced to unity.
If we look out of a window for the first time upon a
landscape that is entirely new to us, the momentary glance
gives us only an Intuition of the scene, or a confused knowledge of it as one whole, without any distinction of parts,
and without recognition of any of these parts as former
objects of knowledge. This is because the Understanding
requires time to do its work. But if we dwell long enough




INTUITIONS DISTINGUISHED FROM CONCEPTS.       5
upon the scene, first, we recognize (or know over again)
one familiar set of objects, and call them trees; then, other
classes of objects previously known, and call them respectively buildings, rocks, hills, &c. Lastly, we consider the
relations of these objects and classes of objects to each
other and to similar objects formerly known, in respect to
distance, magnitude, color, &c., and are thus enabled to
think the landscape as a whole. This Thought contains a
far more perfect knowledge than the Intuition, which was
all that the senses gave us at the first momentary glance.
Now, how much is implied in the successive recognition
of the component parts of this knowledge as objects previously known, and therefore appropriately designated by a
familiar name? Of course, as the landscape is supposed to
be now seen for tile first time, we do not recognize any individual tree, building, or hill in it as precisely the same
object that we have formerly seen. We mean only that
we recognize it as similar to some former objects of knowledge; that is, having seen many objects which agreed with
each other as similar in many of their parts, - as possessing
trunks, branches, and leaves, - we have formed them into
one class, and called them trees. The object in the new
landscape is then recognized, not as familiar in itself, but as
belonging to a familiar class of things; we do not recognize
it as an Intuition, but as a Concept, - not as this tree, but
as a tree. Conception is that act of the Understanding or
Thinklng faculty whereby we unite similar objects into one
class by overlooking their points of difference and forming
their common attributes into one Concept or Thought, the
name of which thus becomes the common name of all the
individuals included in the class.  Here, again, the unifying office of the Understanding appears; the Concept reduces the many to unity, - brings together many objects
into one Thought or many attributes into one subject.
Thus we are properly said to know many objects which we




6            PSYCHOLOGICAL INTRODUCTION.
have never seen; for, through hearing or reading descriptions of them, we have formed a right Concept of what
they are, and thus are enabled to recognize —i. e. know
them over again — and call them by their appropriate name,
when we do see them. But this evidently is only mediate
knowledge, and is more or less imperfect and inadequate,
depending on the scantiness or falness of the Concept.
As Mlr. Mansel remarks, a Concept "is not the adequate
and actual representative of any single object, but an inadequate and potential representative of many." And again,
" it is not the sensible image of one object, but an intelligible relation between many."
Concepts can never come to us from without, for the external world has no Concepts. It has not even Intuitions
or Percepts, but only real objects, -that is, persons and
things, and their marks or attributes. Every real object
has an indefinite or countless number of such attributes;
for, however long and carefully we may observe it, we can
never be sure that we have ascertained all its elements and
qualities. Carry the chemical analysis of it one step further
than before, or place it in new relations with other real objects, and it will manifest new properties or activities, the
existence of which was formerly unsuspected. Observation,
which proceeds by a series of Intuitions, can make known
to us an indefinite number of these attributes, but can never
exhaust them. Hence the knowledge which we can acquire by Intuition, though constantly increasing in fulness
and complexity, can never become complete, and is always
attended with some uncertainty; as any conclusions that
we form respecting the object may be vitiated by the presence of a quality or element of whose existence we were
ignorant. Moreover, the limited compass and finite powers
of the human mind cannot take in at once all even of those
attributes whose presence is perfectly known. The image
or representation of the object in our minds immediately




INTUITIONS DISTINGUISHED FROM CONCEPTS.        7
becomes confused, when we attempt to make it grasp too
much, or to comprehend, in truth, more than a very few of
the known attributes. Giving up the attempt at completeness, then, we form  a Concept of the object embracing
comparatively few of its ascertained qualities, but selecting
those which are most distinctive and essential, in order
thereby more readily to discriminate it from other objects
of a different class.  Such a Concept is certainly incomplete,
but it is clear in proportion to the narrowness of its dimensions.  We canll more easily grasp it in thought, and contemplate it at once in its entireness, because it has so little
complexity.  On the other hand, the lack of fulness is apt
to render the boundaries of the Concept somewhat less distinct.  Consequently, any object, so far as it is known only
mediately, or through such a Concept, is known only in a
few of its leading attributes; and it may even be doubtful
whether another object, which resembles it in these attributes, but departs very widely fiom it in others, ought to be
ranked in the same class with it, and called by the same
name, or not. If my Concept of tree, for instance, is limited to these few particulars, -a vegetable organism possessing a main trunk, branches, and leaves, - it will be doubtful
whether many small plants ought to be called trees or shrubs.
But if I attempt to enlarge the Concept by introducing
more attributes, so as to distinguish tree fully from all other
plants, the idea becomes cumbrous and confused; we cannot so easily embrace it in a single act of thought.
While the Percept or Intuition belongs only to the particular attribute or object —this one color, house, tree, or
stone-which has impressed it upon the mind, the Concept refers to all the things whose common or similar attributes or traits it conceives (con-capio), or grasps together
into one class and one act of mind.  Thus, for example,
the Concept red color includes all similar red colors of any
object whlatever; the Concept tree refers to all trees, the




8            PSYCHOLOGICAL INTRODUCTION.
Concept house to all houses, &c. And naturally enough;
for though the red or the white of this object is not the
identical red or white of that object - is at least numerically different from it, and separated from it by the accidents of place and time, the one being perceived here
and the other there, the one being seen now and the other
formerly,-  yet as the two produce exactly the same impression upon the mind, or create the same sensation, they
are regarded as virtually the samne color for all the purposes
of thought. Thus, also, though any one tree differs from
every other tree in many other respects besides the accidents of place and time, yet it is common to all trees to
have a root, a trunk, branches, and twigs. Now as the
Concept tree is discriminated from all other Concepts only
by possessing these four Marks or attributes, it must necessarily apply to all trees, which are regarded as the same for
all the purposes of thought.  And so it is with all Concepts.
Hence they are also called Universals, or General Ideas.
As Esser remarks,'" A Concept is the representation of
an object through its distinctive Marks; —that is, not
through those Marks which distinguish it from other objects
in general, but from those which come the nearest to it.
The distinctive Marks of an* object are evidently those
which make it to be this object, and not some other one;
i. e. they are its peculiar and essential Marks.  The common and unessential Marks, therefore, do not necessarily
belong to the Concept; if they were added to it, they
would not only overburden and complicate the Concept,
but would lessen its applicability to other objects of the
same kind.  Hence it is self-evident how tle Concept is
related to the sensible Intuition. Namely, the Concept is
the Intuition stripped of its contingent or unessential (individual) attributes or Marks; and the Intuition is the
Concept clothed with the contingent or unessential (indlividual) Marks."




INTUITIONS DISTINGUISHED FROM CONCEPTS.      9
A Concept may be derived from one object as well as
from many similar ones; that is, it may not represent an
actual, but only a possible, class or plurality of things.
This may be illustrated by the description which a zoilogist would give of a newly discovered animal, that was too
unlike those formerly known to be included in the same
species with any of them. Many slight peculiarities of
such an animal would be passed over altogether, as unessential either to the class to which it belonged, or to any
other. And of the more important Marks, which might
be presuned to be specific and not individual in character,
those only would be selected for careful description which
would serve to distinguish the new object from those which,
through their similarity in other respects, might be presumed to belong to the nearest species, or those most akin
to the strange specimen. The description thus formed,
containing possibly not more than two or three Marks,
would be at once a brief and clear Concept actually drawn
from an individual, but potentially applicable to a whole
class, should other specimens of it be subsequently discovered. In a similar manner, the mind may think any individual object under a Concept consisting of a few wellchosen Marks, instead of knowing it simply by an Intuition as a confused aggregate of many parts and elements,
as brutes would do. We perceive only single things, for
such only are presented to us; we think only actual or possible classes of things, for Nature does not give us classes,
though she furnishes us the resemblances of things, through
which we proceed to classify them. All classification is an
act of the mind, and is more or less arbitrary, depending
on our selection of the attributes or relations in reference
to which we classify them.
It is evident that Concepts must be much clearer representations of things than the confused aggregate of Percepts
or Intuitions on which they are founded.  With their light
1 *




10           PSYCHOLOGICAL INTRODUCTION.
they irradiate and make clearly intelligible everything to
which they are referred, or with which they come together
into consciousness; and thus to explicate and make clear
through Concepts the perceived or represented objects is,
says- Dressler, what it is, in the strict logical acceptation of
the word, to think.  In this sense, therefore, to think is to
make clear through Concepts something already otherwise
represented or known to consciousness.
Esser says, "To think is to designate an object through
a Mark or attribute, or, what is the same thing, to determine a subject through a predicate."  According to Sir
William Hamilton, " Thought is the comprehension of a
thing under a general notion (Concept) or attribute";
and again, "All thought is a comparison, a recognition of
similarity or difference, a conjunction or disjunction; —in
other words, a synthesis or analysis of its objects. In Conception, that is, in the formation of Concepts (or general
notions), it compares, disjoins, or-conjoins attributes; in an
act of Judgment, it compares, disjoins, or conjoins Concepts; in Reasoning, it compares, disjoins, or conjoins Judgments. In each step of this process, there is one essential
element; to think, to compare, to conjoin, or disjoin, it is
necessary to recognize one thing through or under another;
and therefore, in defining Thought proper, we may either
define it as an act of comparison, or as a recognition of one
notion as in or under another." According to other logicians, Thought is the reduction of complexity and plurality
to unity, or the bringing together of what is confused, various, and manifold or multitudinous in our Intuitions into
the clear unity of consciousness.
All these definitions evidently point to one thing, or indicate what is substantially the same process. Comparison
is the means through which we unite what is similar, and
separate what is unlike or opposed; for only through comparison do we recognize likeness or unlikeness, agreement




INTUITIONS DISTINGUISHED FROM CONCEPTS.        11:or opposition.  Now we analyze, divide, and distinguish
only in order subsequently to bring together and combine.
We discriminate the various elements or attributes of objects through comparison of them with each other, and then
unite them with other objects and attributes according to
their similarities as ascertained by a fresh act of comparison;
and this union of many things in one class, this reduction
of a plurality of Intuitions under one Concept or general
notion, is the means through which the infinite variety and
multitude of natural objects are reduced to the limited compass of the human understanding, and made intelligible.
A new individual object is to us an isolated and incomprehensible thing, until we have recognized its similarity with
something else, and thereby assigned it to a class, or comprehended it under a Concept, and given it a common
name.
According to some etymologists, think comes from the
same root as thick,* and originally signified thickening, or
pressing together of many into one; and this exactly describes the special function of the understanding.  As we
have already remarked, while a Percept or Intuition is a single representation, limited to this one thing which excited it
or impressed it upon the mind, a Concept is a collective (general or universal) representation of a whole class of things.
To make a formal definition, we may say that a Concept
is a representation made up from several particular Percepts,
through the union of their similar elements.  It is through
Concepts that we think, - that is, clearly understand, comprehend, or conceive something; for these words mean precisely the same thing, namely, to represent with clearer
consciousness what was already represented in our minds.
Besides the Percept and the Concept, the later German
philosophers distinguish the so-called Idea, as the pattern* The n in t7hink is casual, and does not appear in the participle thought.
So in German, dick, doaenk, qedacht.




12           PSYCHOLOGICAL INTRODUCTION.
representation, ideal Concept, or beacu-ideal, by which we
understand such a representation as surpasses or goes beyond the perceived and the conformed to experience.  The
Idea is that whereby we think an object in its highest possible perfection, and consequently unlike anything which we
have actually witnessed. Hence it does not refer, like the
Intuition, to a single thing, nor, like the Concept, to a
whole class of things; but it wholly surpasses in completeness or perfection the object to which it is referred. Such
are the Ideas of the artist, moral and religious Ideas, &c.
The Kantians use -Bepresentations to designate the genus
which includes, as its several species, Percepts, Concepts,
and Ideas.  The aggregate of the Percepts which any one
has had may be said to constitute his experience.
Intuitions afford the only sure means of first creating,
and of subsequently rectifying and enlarging, our Concepts.
Thus, I may have some scanty knowledge, obtained by
reading perhaps, of a species of plant or flower that I have
never seen. The Concept thus formed may err both by
excess and defect; by excess, because it may include some
parts or attributes which are not peculiar to this species, but
are common to it with many others; by defect, because it,may not comprise enough of the attributes common to all
the plants in this class, and peculiar to them or not belonging to any other plants, to enable me to recognize and distinguish an individual of this species when I see it. It is
only intuitive knowledge, or that gained by direct observation, which can enable me to correct these errors.
Intuitions, then, are the only test of the reality of Concepts; for they alone can determine whether the Concepts
properly correspond to the actual objects in nature which
they are meant to describe. In this sense, Intuitions are
not only the beginning, but the basis and the source, of all
our knowledge. All Concepts, however, are not meant to
represent actual objects; they may be imaginary or fanci



INTUITIONS DISTINGUISHED FROM CONCEPTS.    13
ful. I can conceive a centaur or a griffin, though no such
animal ever lived. Yet even in this case, though the Concept, as a whole, is unreal or imaginary, it must be made up
only of real parts or attributes, - that is, of such as have
been embraced in some preceding Intuition. I have never
seen a centaur; but I have seen the head of a man and the
body of a horse, and I can unite, in Thought, these real parts
into an unreal whole. So, again, I can think or conceive
any combination, however fantastic, of colors that I have
previously seen; but I cannot introduce into the painting,
even in Thought, any color that I have never seen. A
person born blind, and remaining so, cannot conceive any
color whatever; just as one who has never had the sense of
hearing can form no Concept of sound. Intuitions, then,
are the basis, not only of all Knowledge, but of all Thought.
The perception which gives us a new Intuition may take
place either through the external senses, or exclusively
through that internal source of knowledge, sometimes called
an internal sense, but more properly denominated Consciousness, by which we are made aware of the existence
of our own sensations, thoughts, and feelings.
Consciousness, indeed, is the universal witness which
testifies to the reality, not only of sensation and feeling, but
of the external perceptions which come to us through the
outer senses. I see a bright red color, I hear a particular
sound, only so far as I am conscious of that act of seeing
or hearing; if I were not conscious of it, it would be to me
as if it were non-existent. For to know, and to know that 1
know, are phrases that designate one indivisible act of mind;
and to know that I know is a phrase which means the same
thing as to be conscious. Hence, though it is an act of sense
whereby I perceive the red color or hear the sound, it is at
the same time an act of consciousness; as, otherwise, I should
have no knowledge either of the act of perception, or of the
outward phenomenon to the existence of which it testifies.




14           PSYCHOLOGICAL INTRODUCTION.
I am conscious also of internal perceptions, of hunger,
pain, fear, joy, etc. Still further, I am conscious of mnyself,
as the one being that perceives, fears, or rejoices. Every
act of consciousness is twofold, testifying to the existence
both of the subject, - that is, of the being or person who is
conscious,- and of the object,  that is, of the feeling, perception, or other phenomenon of which he is conscious.
The very language which I am compelled to use in making
known the fact to another person testifies to this duality of
the act. Any phrase used for this purpose must contain at
least two terms, one expressive of the subject, and the other
of the object, of consciousness. Thus, in the proposition
"I feel hunger," the pronoun "' I" denotes the person who
feels, and "hunger" the phenomenon which is felt. In
some languages, the whole may be expressed in a single
word, as in the Latin " esurio"; but the expression here is
elliptical, the 1" ego," or the subject of consciousness, being
always understood. The two elements can only be known
together, simultaneously, and in their relation to each other.
One is not known through the other, or in consequence of
the other, or after the other; but they are known together,
in one act of mind. I cannot be conscious of hunger without, at the same moment and in the same act, being conscious of myself as feeling the hunger.
All the phenomena, then, both of the external and internal world, are presented to the mind each in its distinctive
of peculiar Intuition. In other words, any Intuition differs
from every other Intuition, at least in the relations of time
and space. Thus, two successive Intuitions by the same
person, of the same thing, are distinguishable at least in this
respect, that the one preceded the other, or took place at an
earlier time. In like manner,  to borrow an example from
Mr. Mansel, -" I see lying on the table before me a number of shillings of the same coinage. Examined severally,
the image and superscription of each is undistinguishable




INTUITIONS DISTINGUISHED FROM CONCEPTS.     15
from that of its fellow; but in viewing them side by side,
space is a necessary condition of my perception; and the
difference of locality is sufficient to make them distinct,
though similar, individuals."  As already remarked, each
Intuition is of a distinct thing as perceived now and here, —
that is, in its own peculiar relations both to time and space.
On the other hand, a Concept is freed from these relations
of space and time; I can think what is denoted by the
word tree, without identifying it with this or that particular
tree, standing on a particular spot, and seen at a particular
time.
As already remarked, it is the capacity of Thought properly so called which constitutes the immeasurable superiority of the human over the brute mind; but it is also true,
that the necessity of Thought arises from the immeasurable
inferiority of man's intellect to that of his  Creator.  If the
human mind were omniscient and of infinite compass, it
would behold all things intuitively, and would not be confused and overburdened by the multitude of these single
cognitions. But it is far otherwise; the mind is limited
and imperfect, and can grasp at once but few objects,according to the common opinion, only five or six. It can
permanently retain in memory, so as to reproduce at will, it
can accurately -represent in imagination, only a few of its
primary Intuitions.  We must have recourse to the artifice
of Thought; we must discard all individual attributes and
peculiarities, in order, through meagre Concepts, to rise to a
larger and clearer, though consciously imperfect, comprehension of a multitude of things. As will be shown hereafter, it is precisely the scantiness of the general notion in
respect to its import, which renders it more comprehensive
in respect to the number of things which it embraces; in
other words, if we would know more objects, we must
know each of them less perfectly. Unable to master the
vastness and complexity of Nature by taking in detail the




16           PSYCHOLOGICAL INTRODUCTION.
objects which she offers to us, each in its separate Intuition,
we throw them, through discarding their differences, into
groups and classes. The mind can then grasp at once six
or seven of these groups, instead of being limited, as before,
to six or seven individuals. Then, by forming successively
groups of groups, or classes of a higher order of generalization, our mental horizon is enlarged till we can take in, or
comprehend (con-prehendo), all the objects that we have
ever known. But this is like ascending a very high mountain, whence, though we obtain a broader view, the outlines
and colors of objects below are but faintly seen, and many
are wholly lost in the distance.
The nature of Language illustrates this process of the
formation of Thought. In fact, taken in its strictest sense,
Language is the expression of Thought only; it has to do,
not with Intuitions, but with Concepts. Intuitions, from
their very nature, can be designated only by Proper Names;
and words properly so called are Common Names. Every
word has a meaning, and is therefore susceptible of definition, or at least of explanation. But a Proper Name,
strictly speaking, has no meaning; as Mr. J. S. Mill remarks, it is a sign which denotes this one thing, but which
connotes nothing. Like a pointing of the finger, it designates the individual who is meant; but it says nothing as
to the nature or character of that individual. In so far,
indeed, as usage has limited one class of names to males,
and another to females, in so far the names connote sex;
and precisely to this extent they cease to be Proper, and
become Common, Names. If, to a person who does not know
James, I say, " James did this," the effect is precisely the
same as if I had said, "A man or boy did it." If a word
is to express an Intuition, it must be accompanied by other
words, or at least be marked by emphasis or a significant
gesture, so as to restrict its meaning to a determinate single
thing; and these limiting words can be dispensed with only




RELATIONS OF THOUGHT TO LANGUAGE.        17
when the context, or the custom of speech, supplies the
necessary limitations. For example: "this house now before us," "that house on the hill," "'the house in Cambridge which I showed you yesterday," are phrases wherein
the general meaning of the word house is narrowed down
to this or that particular building, which may be known
through an Intuition. In other cases, the context or emphasis suffices to limit the signification of such phrases as
"his house," " John's house," " the house," etc., to the one
thing which was intended.
Dr. Reid puzzles himself in attempting to explain how it
comes to pass, that, whilst all the objects and events which
we perceive are individual or singular, all the words in a
language are general. But the reasons are obvious. First,
we cannot have countless words for the innumerable single
objects which we perceive, as no memory could retain
them: - think, for a moment, of the myriads of leaves,
blades of grass, insects, and other classes of things, which
we are constantly beholding. Secondly, these very instances show, that, at least as far as our perceptions are
concerned, the similarity of objects is often as great as their
diversity, and even greater. Thirdly, one main purpose of
language being the communication of Thought to others,
what we need to know or to communicate is not so often
a particular fact respecting this single object, as it is a general truth respecting a whole class of objects; we do not so
often need to say, Avoid or seek this one thing, as, Avoid
or seek all of which this is a specimen. We are more frequently concerned, in our mnental operations, with classes
than with individuals, though the latter alone furnish employment for our hands. Fourthly, many things are usually
massed together even to our perception, as individual trees
in a forest, and therefore can never be exhaustively designated by one expression. By the law of parsimony, therefore, language makes up its millions of names or designaira




18             PSYCHOLOGICAL INTRODUCTION.
tions out of comparatively few words, just as its thousands
of words are constructed out of some twenty or thirty elementary sounds or letters.
Language, then, deals only with groups or classes of
things; and the process of classification necessarily precedes the formation of language. This theory explains at
once the most striking deficiency of the lower animals,their incapacity of using language.  As they have only
Intuitions, the only names which they can apply or understand are Proper Names,- the appellations of this or that
particular thing. These they can understand. A dog can
easily be taught to know the name of his master, even
when pronounced by another person. They can even be
taught to know the names of particular places and buildings, so that they can understand and obey, when they are
told to go to the barn, the river, or the house.*  But it is
always the particular barn, or other object, with which they
have been taught to associate this sound or significant gesture as its Proper Name.  Carry the animal to a distant
place, near which may be a set of corresponding objects,
and then tell him to go to the barn or the river, and he will
not understand the order as applying to the new set of
objects, but will set off immediately for the old building or
place, with whose Proper Name alone he is familiar. As
Kant remarks, a dog knows (kennt) his master, but does
not recognize him  through his peculiar Mlarks or Attributes
(erkennt), and thereby properly  discriminate him  from
other persons.
These Intuitions, which are common to man and the
X In Mr. Lockhart's amusing account of Sir Walter Scott's first favorite
dog, " Camp," he says: "As the servant was laying the cloth for dinner,
he would address the dog lying on his mat by the fire, and say,'Camp, my
good fellow, the Sheriff's coming home by the ford [or by the hill],' and the
sick animal would immediately bestir himself to welcome his master, going
out at the back door or the front door, according to the direction given, and advancing as far as he was able."




MENTAL CHARACTERISTICS OF BRUTES.              19
brute, and which are mere impressions passively received
by the mind, may be stored up in the memory, but out of
consciousness, as fruits of experience; they may be subsequently recalled to consciousness, or reproduced, either by
casual association or voluntary reminiscence; and, when so
recalled, they may be re-presented, or pictured forth to the
mind, by an act of that faculty which we usually call Imagination. Brutes, as well as men, are capable of all these
acts of Memory, Reproduction, and Imagination, when exercised upon Intuitions alone; for they are all implied in
dreaming, and a dog asleep upon a rug before the fire often
shows, by his barking and growling, that he has vivid
dreams.  Man can remember and reproduce Concepts or
Thoughts, as well as Intuitions. Imagination, whether in
man or the brute, is concerned only with Intuitions, as it
pictures forth nothing but definite images of this or that
particular object or event. Thoughts properly so called
are conceived or understood, but cannot be imaogined.*
Agreeably to what has been said, the mental process of
forming Concepts may be reduced to three steps, viz.:1. Comnparison, whereby, among many attributes or objects, we determine which are similar and which are different or unlike.
2. Combination or Reduction to Unity, whereby, for instance, this, that, and the'other color are recognized and
identified as what is usually called "one and the same"
shade or hue of red; or several quadrupeds are recognized
as all belonging to one class called horse.
3. Abstraction,t whereby we separate and throw aside
- If this simple distinction had been made, the old dispute between the
Nominalists and the Realists could never have arisen. The former clearly
perceived that Concepts could not be imagined; the Realists knew very well
that, in thinking, our thoughts were concerned with something more than
mere words. Both were right.
t This word, according to its etymology (abs-traho, to draw off from), is




20            PSYCHOLOGICAL INTRODUCTION.
— i. e. put out of Thought -the dissimilar or incongruous attributes which, if retained, would prevent the other
elements from flowing together into unity.
Each of these steps evidently involves an act of Judgment, -that is, of that function of the Understanding or
Thinking Faculty whereby we affirm or deny one Intuition
or Concept of another. Hence, we may either consider
Judgments as the elements of Concepts, or Concepts as
the elements of Judgments.  Logicians generally have
treated of the functions of Conception or Simple Apprehension first, and those of Judgment afterwards; and, as
this arrangement is in some respects more convenient, I
shall follow their example, though strict method would perhaps require this order to be reversed.
All men are capable of comparison, and of discerning
those similarities on which the formation of Concepts depends. But it does not so readily appear how many, different persons are naturally led to form the same Concepts,
according as circumstances render them familiar with similar classes of things. This is well explained by Dressier.
Before the elements which are common to the constituent
Intuitions can be really united into Concepts, they must be
excited in consciousness simultaneously, or in immediate
succession; if they arose only separately, and at intervals,
like disjoined fragments, there would be no mutual attraction to draw them together. But when thus brought before the mind at the same time, the synthesis of their
common elements into one Concept is a perfectly natural
process, in which we need no guidance, " as they flow together by a sort of spontaneous attraction for each other,
properly applied to the dissimilar elements which are put aside or abandoned, though, until recently, logicians used it to designate the process of
retaining and combining the similar elements. Sir W. Hamilton would say
that we prescind the similar which is retained, and abstract the different which
is thrown off.




RELATIONS OF THOUGHT TO LANGUAGE.          21
each of them being the object of a livelier and clearer consciousness than any of the dissimilar elements. For example; if I see at once, or in quick succession, six different
trees, I perceive their similar properties -i. e. root, trunk,
branches, etc. - six times over, being once for each tree,
and thus have a livelier or stronger consciousness of them
than I have of those which, as dissimilar or peculiar to one
tree, I perceive only once. Moreover, for the very reason
that these common elements are similar —that is, as they
have fewer points of divergence or contrast - they more
easily coalesce and melt into one Concept." As Hamilton
remarks, "the qualities which by comparison are judged
similar are already, by this process, identified in consciousness; for they are only judged similar inasmuch as they
produce in us indiscernible effects."
But this is not all.  "The Concept thus formed by an
abstraction of the resembling from  the non-resembling
qualities of objects would again fall back into the confusion and infinitude from which it has been called out, were
it not rendered permanent for consciousness by being fixed
and ratified in a verbal sign." Hence, Language is necessary, not only that we may communicate our Thoughts to
others, but that we may permanently retain and readily
use these Thoughts for our own purposes.  Concepts are
factitious units, and the particular attributes which constitute them are somewhat arbitrarily selected, being more or
less numerous, and having greater or less resemblance,
according to circumstances.  A  Concept, as we have already remarked, cannot be pictured in Imagination; and
the presence of one of the real objects included under it
does not necessarily suggest the particular attributes out
of which it was formed, to the exclusion of others perhaps
equally prominent to the eye. Hence, a Name must be
given to it, which will be, of course, a Common Name for
all the individuals contained under it; or the factitious




22           PSYCHOLOGICAL INTRODUCTION.
aggregate will be dissolved and lost to memory almost as
soon as formed. The name preserves the unity of the
aggregate just as it was originally constituted, precisely as
a cord holds a bundle of things together, and enables us to
handle many objects as if they were but one. The Memory is then burdened with the retention only of one word,
which, when recalled, by the law of association will suggest
its meaning, instead of being urged to remember a considerable number of attributes, which can neither be separately or collectively pictured in the Imagination. An
Intuition, on the other hand, needs not to be designated
by a Name, as the presence of the object immediately excites it anew in its original perfection, and Imagination can
re-present it almost as adequately and vividly as the reality.
But the'Concept can neither be retained in mind, nor, so to
speak, readily manipulated in Thought, without the aid of
a verbal sign.
This mutual dependence of Thought and Language,
each bearing all the imperfections and perfections of the
other, has been admirably illustrated by Hamilton.
"Though, in general, we must hold that language, as
the product and correlative of thought, must be viewed as
posterior to the act of thinking itself, - on the other hand,
it must be admitted, that we could never have risen above
the very lowest degrees in the scale of thought without the
aid of signs. A sign is necessary to give stability to our
intellectual progress, - to establish each step in our advance as a new starting-point for our advance to another
beyond.
" A  country may be overrun by an, armed host, but it is
only conquered by the establishment of fortresses. Words
are the fortresses of thought. They enable us to realize
our dominion over what we have already overrun in
thought, - to make every intellectual conquest the basis
of operations for others still beyond. Or another illustra



RELATIONS OF THOUGHT TO LANGUAGE.        23
tion: You have all heard of the process of tunnelling, of
tunnelling through a sand-bank. In this operation it is impossible to succeed unless every foot - nay, almost every
inch - in our progress be secured by an arch of masonry,
before we attempt the excavation of another. Now, language is to the mind precisely what the arch is to the tunnel. The power of thinking and the power of excavation
are not dependent on the word in the one case, on the
mason-work in the other; but without these subsidiaries,
neither process could be carried on beyond its rudimentary
commencement.  Though, therefore, we allow that every
movement forward in language must be determined by an
antecedent movement forward in thought, still, unless
thought be accompanied at each point of its evolution by
a corresponding evolution of language, its further development is arrested. Thus it is that the higher exertions of
the higher faculty of Understanding- the classification of
the objects presented and re-presented by the subsidiary
powers in the formation of a hierarchy of notions; the connection of these notions into judgments; the inference of
one judgment from another; and, in general, all our consciousness of the relations of the universal to the particular,
consequently all science strictly so denominated, and every
inductive knowledge of the past and future from the laws
of nature: not only these, but all ascent from the sphere
of sense to the sphere of moral and religious intelligence
are, as experience proves, if not altogether impossible without a language, at least possible to a very low degree.
" Admitting even that the mind is capable of certain elementary Concepts without the fixation and signature of
language, still these are but sparks which would twinkle
only to expire; and it requires words to give them prominence, and, by enabling us to collect and elaborate them
into new Concepts, to raise, out of what would otherwise
be only scattered and transitory scintillations, a vivid and
enduring light."




24           PSYCHOLOGICAL INTRODUCTION.
But Words are not only signs and preservatives, they
are also substitutes, for Thoughts; and this peculiarity of
Language is an excellence or defect in it, according as it is
or is not judiciously used. As Bishop Berkeley remarks,
" It is not necessary, even in the strictest reasonings, that
significant names which stand. for ideas should, every time
they are used, excite in the understanding the ideas they
are made to stand for. In reading and discoursing, names
are for the most part used as letters are in algebra, in
which, though a particular quantity be marked by each letter, yet, to proceed right, it is not requisite that, in every
step, each letter should suggest to your thoughts that particular quantity it was appointed to stand for." Having
once satisfied ourselves, by spreading out in thought all the
attributes which are combined in any Concept, - or, to be
still more careful, by having once called up in Imagination
a picture of some one individual possessing all these attributes, and therefore contained in the class,  that the
meaning of the word, which is the Sign of that Concept
and the Common Name of that class, is within our power,
we proceed to use that word symbolically, — that is, as a
mere signr, and therefore with much more ease and rapidity
than if it were necessary to stop, each time it recurs, and
repeat the process of verifying its meaning. Hence it may
be said that the use of language gives us the power of
thinking in short-hand; words are stenographic thoughts.
Moreover, this abbreviated expression of thought is a great
help to the memory. Having once ascertained by reflection the relation of various Concepts to each other, - that
is, having formed judgments and reasonings, and expressed
them in propositions, - it is a far easier and shorter method
to remember the few words which constitute such a proposition, than to recall successively each of the mental processes which are now embodied in it, and through which it
was first obtained. Language is the great repository of




RELATIONS OF THOUGHT TO LANGUAGE.        25
thought, not only in books, but in our own minds. The
algebraist easily recalls to mind a few brief formulas, which
enable him to perform almost mechanically long numerical
computations, which the mere arithmetician must slowly
and painfully think out step by step. Even when the
meaning of the words is not sufficiently familiar to enable
us to perform the whole process symbolically, or by the use
of words alone, we can often do so in part; - that is, we
need only to explicate, or spread out in our minds, that
particular portion of their meaning which happens to be all
that is necessary for the special purpose which we now have
in view. Thus I may not know the fall meaning of a technical term in some science, or of a certain verb in the Greek
language, and still be enabled to use it without error in that
one of its numerous applications with which use may have
made me familiar. This symbolic knowledge, as it was
termed by Leibnitz, bears about the same relation to the
full thought, of which it is the abbreviated expression, that
our ordinary cursive handwriting does to an ideographic
system, or to the picture-writing of the Mexicans.
On the other hand, it should be remembered that there
is peculiar danger in this use of words as a temporary substitute for thought. Dr. Campbell mentions it as the reason why many persons, even among the judicious and the
well-informed, are sometimes led both to talk and write
nonsense without knowing it. When the use of words is
not checked by a frequent recurrence in thought to the
precise limitations of their meaning, even the best of us
are occasionally betrayed into applications of them which
a moment's reflection would prove to be incongruous and
absurd. The ordinary safeguard against such blunders is,
that, having become familiar by use with certain words in
their ordinary relations and connections with other words,
anything new or peculiar in the combinations in which they
are sometimes found, or in which we may ourselves be
2




26           PSYCHOLOGICAL INTRODUCTION.
tempted to place them, at once attracts our notice, and
puts us upon the lookout to detect a possible absurdity.
Take, for instance, the following stanza, which occurs in
the 1" Song by a Person of Quality," written by Pope to
ridicule this very class of blunders, as frequently committed
by people of fashion in their attempts to string together in
verse the mere commonplaces of poetical expression: 
" Gloomy Pluto, king of terrors,.Armed in adamantine chains,
Lead me to the crystal mirrors
Watering soft Elysian plains."
As chains usually bind and mnirrors reflect, not even the
smoothness of the measure can here cause us to slide over
the absurdity of supposing Pluto to be armed by the former, or plains watered by the latter.
To avoid such blunders, it is not enough to be able
merely to explicate in thought the meaning of each word
taken by itself, or separately, but the combination of words
must express a possible union in thought of what is expressed by them.  Whether this can be done can be ascertained only through the process of what Mr. Mansel calls
"individualizing our Concepts," - that is, of calling up in
imagination a picture of some particular thing denoted by
the words taken together, because possessing together all the
attributes contained in such a union of Concepts. It is only
by the failure of the attempt to form such a mental image,
that we are led to perceive the absurdity of such expressions as a bilinear figure, an iron-gold mountain, or a watering nmirror. Hence it appears, that what is perfectly intelligible in language, when the words are taken separately,
may be absolutely inconceivable in thought. I know what
each of the words bilinear figure means; but such a figure
is inconceivable, and therefore the union of the two words
is absurd.
It was remarked by Burke, in his Essay on the Sublime




RELATIONS OF THOUGHT TO LANGUAGE.        27
and Beautiful, that words are not only used as substitutes
for thoughts, but, through the laws of association, they also
serve to call up the same emotions which are naturally produced by the presence or imagination of the real objects
which they denote. Thus, there are many words which
have feelings of awe, sorrow, or affright so firmly associated with them, by long habit, that the mere utterance of
them in a sermon is enough to solemnize the minds of the
congregation, even before the hearers have time to think of
what they mean.
The doctrine -of the Nominalists, then, is true to this
extent, - that very often, in the use of language, there is
nothing before the minds either of the speakers or the
hearers but mere words; and yet these words are significantly and correctly used, and they answer their purpose
of exciting emotion and imparting knowledge. But it is
also often true, that, in the use of words, all the powers
of the Understanding, or Thinking Faculty, are in active
exercise; — that we compare, combine, discriminate, judge,
and discern new relations before unthought of, the subsidiary powers of the Memory and Imagination, all the while,
furnishing their aid whenever needed; and it is only by
such concomitant activity of the Thinking power, that we
can have full assurance that the words in question are correctly used, and the boundaries of our knowledge are enlarged. Thus, in the thoughtful use of words, we are
continually spreading out;in our minds the attributes of
which the Concepts are made up, individualizing them,
comparing them with each other, discovering new relations
between them, and carrying them up into higher orders of
generalization, or extending them to more objects.
A few remarks may be necessary in explanation of the
nomenclature which has been here employed. The English words thinking, thought, are commonly used, in a very
vague and comprehensive sense, to denote any cognitive




28           PSYCHOLOGICAL INTRODUCTION.
act or object of the mind.  But, as applied in Logic, they
are strictly limited to one well-defined class of our cognitive functions. After the illustrations that have now been
given, the peculiar characteristics of Thought properly so
called are perhaps sufficiently understood.
Hamilton justly observes, that most of the words which
signify operations of the mind have a triple ambiguity, for
they may denote either, 1. the faculty; or, 2. the act; or,
3. the product of the act.' To avoid this uncertainty, the
Understanding is here used exclusively to denote the Faculty of Thinking in the narrower sense, or what Hamilton
calls the "Elaborative Faculty," because it elaborates, or
works up into Thought, the raw material which is furnished
to it by the Perceptive powers. Like any other faculty,
the Understanding at any particular time may, or may not,
be in exercise. Its function or peculiar office is to think;
hence, thinking denotes the act, while Thought signifies the
product, of' this faculty. As will be shown hereafter,
Thought is the generic term, for there are three species
of it; viz. Concepts, Judgments, and Reasonings or Inferences. The old logicians referred the origin of these three
species of Thought to as many distinct faculties, which they
denominated respectively Simple Apprehension, Judgment,
and the Discursive Faculty.  Of these, Simple Apprehension corresponds very nearly to that sort of Thinking which
we now call Conception, its products being denominated
Concepts. In like manner, the products of the Perceptive or Acquisitive Faculty, hitherto called Intuitions, might
more conveniently be termed Percepts, as we should then
have an English verb, perceive, to express the act of that
Faculty of which these are products.  If it were allowable
to coin an English verb to express the act of intuition, answering to the German ansclauen, analogy would direct us
to say intuit.  The Discursive Faculty (from discurrere, to
run to and fro) was so called because, in Reasoning or




INTUITIONS DISTINGUISHED FROM CONCEPTS.    29
drawing Inferences, the mind runs over from one Judgment, as the Ground or Reason, to another, as the Consequence or Conclusion. But the whole Understanding is
more properly called by this name; for, in forming Concepts, the mind runs over the Percepts or Intuitions from
which they are derived, in order to separate the similar
elements from the unlike, and consciously to unite the former into one product of Thought.




30               DEFINITION OGF LOGIC.
CHAPTER II.
DEFINITION OF LOGIC.
Divisions of the Science.- Utility of the Study.
OGIC is the Science of the Necessary Laws of Pure
Thought.
The Greek word, X;gyos, from which Logic is derived,
signifies both the inward thought, and the wvord or outward
form in which this thought is expressed; and thus includes
both the ratio and the oratio of the Latins.  This fact, and
the intimate connection which, as we have already seen,
exists between Thought and Language, has caused some
writers, especially those who adopt the Nominalist theory
to its full extent, to maintain that " Logic is entirely conversant about Language."  But it is not so; for Logic is
primarily and essentially conversant with Thought, and
only secondarily and accidentally with Language; that is,
it treats of Language so far only as this is the vehicle
of Thought. Just the reverse is true of the science of
Grammar, which treats primarily of Language, and only
secondarily of Thought.  Logic might be called the
Grammar of Thought.
Others have held that "' the process or operation of reasoning is alone the appropriate province of Logic."  But
this is putting the part for the whole, and is as inadequate
as it would be to restrict Geometry to the measurement of
spherical bodies, to the exclusion of lines, angles, plane surfaces, and rectilinear solids. There are three classes of the
products of Thought, namely, Concepts, Judgments, and




DEFINITION OF LOGIC.              31
Inferences or Reasonings, with each of which Logic is immediately concerned, as, indeed, no one of them  can be
adequately discussed without consideration of both the others. If, on the one hand, it can be said that conception
and judgment are both subsidiary to the process of reasoning, so, on the other, judgment is the primary and essential
operation, of which conception and inference are only special forms or complex results.
Pure, or, as it is sometimes termed, Formal Thought, is
the mere process of thinking, irrespective of what we are
thinkingy bout. It has already been said that the Acquisitive or Perceptive Faculty furnishes "6the Matter," while
the Understanding supplies " the Form," of our knowledge.
This distinction between Matter and Form is one of considerable importance in the history of philosophy.  The
former is the crude material or the stuff of which anything
consists, or out of which it is made; while the latter is the
peculiar shape or modification given to it by the artist,
whereby it has become this particular thing which it is, and
not something else which might have been fashioned out of
the. same substance.  Thus, wood is the Matter of the desk
on which I am writing, whilst the Form is that which entitles it to be called a desk, rather than a table or a chair.
Vocal sound is the Matter of speech, and articulation is its
Form. It is evident that these are two correlative notions,
each of which implies the other: Matter cannot exist except under, some Form, and there cannot be any Form
except of some given Matter. But though the two cannot
actually be separated, the mind can consider each separately
through that process, called abstraction, whereby the attention is wholly given to the one to the exclusion of the other.
We may think separately of the attributes which are common to a whole class of Forms, disregarding altogether, for
the moment, the Matter of which each of them really consists.  Borrowing algebraic symbols, the Matter in each




32                DEFINITION OF LOGIC.
case may be designated by a letter of the alphabet, the peculiar significance of which is, that it stands for any Matter
whatever, and not for any one in particular. Thus, A is B,
is the Form of an affirmative judgment, wherein A and B
stand for any two Concepts whatever. Hence, whatever is
true of the general formula, A is B, will be true also of
any such particular instances, as Iron is nalleable, Trees are
plants, &c., wherein the Form is associated with some particular Matter. In saying, then, that Logic is concerned
only with the Formrs of Thought, or Pure Thought, or
Thought in the abstract, - for all these expressions signify
the same thing, - we mean only, that what is Material in
Thought is extralogical, and, as logicians, we have nothing
to do with it; just as the geometer has nothing to do with
the particular diagram on the paper before him, except so
far as it is a symbol, or universal Form, of all possible figures of the same general character. As Hamilton remarks:
"The objects (the Matter) of thought are infinite; no one
science can embrace them  all, and therefore to suppose
Logic conversant about the Matter of thought in general, is
to say that Logic is another name for the encyclopoedia —
the ozmne scibile- of human knowledge. The absurdity of
this supposition is apparent.  But if it be impossible for
Logic to treat of all the objects of thought, it cannot be
supposed that it treats of any; for no reason can be given
why it should limit its consideration to some, to the exclusion of others. As Logic cannot, therefore, possibly include
all objects, and as it cannot possibly be shown why it should
include only some, it follows that it must exclude from its
domain the consideration of the Matter of thought altogether; and as, apart from the Matter of thought, there
only remains the Form, it follows that Logic, as a special
science of thought, must be viewed as conversant exclusively about the Form of thought."
Again, the definition of Logic assumes that the process




DIVISIONS OF THE SCIENCE.           33
of Thinking, like every other operation in nature, does not
take place at random, but according to certain fixed Laws
or invariable modes of procedure. There could be no communication of Thought from one mind to another, if the
process of Thinking in all minds were not subject to the
same general rules. We follow these laws for the most
part unconsciously, as a distinct recognition of them is not
by any means necessary for correct thinking; just so, many
persons speak and write correctly without any knowledge
of the grammarian's rules. But they can be discovered
through analysis of their results, and the business of the
logician is to search them out and arrange them in order,
just as the grammarian's duty is to set forth those secondary laws of Thought which control the formation and the
use of Language. Logic, says Dr. Thomson, " like philosophy, of which it is a part, arises from a reflection of the
mind upon its own processes; a logician is not one who
thinks, but one who can declare how he thinks."
But here a distinction is to be made, for Logic takes cognizance not of the contingent, but only of the necessary
and universal, laws of Thought. Psychology, as the science
of the mental phenomena in general, includes, of course, the
procedures of Pure Thought; but it includes them only in
their contingent and phenomenal character, as actually
existing now and then, but not as necessarily existing at all
times. Logic does not consider the subsidiary processes,
such as Perception, Memory, and Imagination, through
which we collect the materials for thinking. The operations
of the Thinking Faculty are also contingently modified by
the coexistence of other powers and affections of the mind;
they are obstructed by indolence, and warped by prejudice
and passion. Logic does not regard these accidental perversions of the Understanding, but takes into view only
those fundamental and absolute principles, to which all
Thought is necessarily subject, and which shine by their
2*o




34               DEFINITION OF LOGIC.
own light, as they cannot be transgressed except by the
idiot or the madman. A violation of one of these Laws is
not so much an error in Thinking, as a negation of Thought.
They are axiomatic in character; that is, they cannot be
proved or deduced from higher principles, for such proof or
deduction would be itself an act of Thought, and therefore
would presuppose the validity of the very principles which it
was intended to guarantee. These Laws cannot be proved,
but they can be enunciated and explained; when understood, their truth is self-evident, for they rest upon the
immediate testimony of consciousness. As necessary and
universally known, they are never consciously broken; but
we may be betrayed into an apparent transgression of'one
or more of them, through an incautious yoking together of
certain words or formulas of expression, without sufficiently
thinking of what they denote. Some Hibernicisms, as they
are termed, are of this character. The judge, who, when
puzzled by the ingenuity of two lawyers who were pleading a cause before him, exclaimed in a pet, "I believe
you are both right,". really violated that universal Law of
Pure Thought, called the Principle of Excluded Middle,
which declares that, of two contradictory propositions, one
must be true, and the other false. Logic, as it proceeds
from axiomatic principles, and derives none of its materials
from experience, but considers only those laws which underlie all experience and first render it possible, is a purely demonstrative science, like algebra or geometry. It treats of
those arguments only which are certain and irrefutable; or
if it indirectly, considers some of those forms which come
short of perfect demonstration, such as Analogy, Imperfect
Induction, and Example, it is only for the purpose of testing them by a reference to the standard forms the validity
of which they presuppose, and which they endeavor, as it
were, to approximate.
Universal Logic considers the Laws of Thought in their




DIVISIONS OF THE SCIENCE.             35
application, not to this or that spe'cial class of objects, but
to all objects whatsoever. *This is the Loyica docens of the
Schoolmen, and contains the abstract theory of the science
in its widest sense, without any of the limitations that arise
from any special purpose or study which the thinker may
have in view. It corresponds to the science of Universal
Grammar, which treats only of those principles which belong to language as such, and therefore are exemplified in
all languages, putting aside altogether the peculiarities of
Hebrew, Greek, German, or any other particular tongue.
On the other hand, Special Logic, or the Logica utens of
the Schools, is the Logic. of Mathematics, or the Logic of
History, or of any other particular science; consequently,
it involves a consideration of the Laws of Thought so far
only as they are exemplified or involved in the processes
of this one science.  Herein Logic becomes subsidiary to
the objects of the special inquiiry which it is intended to
promote or regulate. It presupposes a knowledge of those
objects, and it forms an introduction to that inquiry.
Hence, it is no longer Logic considered for its own sake,.
but it is Geometry, History, or some other science, considered in a logical point of view. The discussion of it is
therefore relegated to treatises on that science of which it
forms a part, and for which it is a special preparatory study.
Legal Logic is a part of the science of Law.  Mathematical Logic is an introduction or an appendage to pure Mathematics.  But, in what now lies before us, it is evident that
we have to do only with Universal Logic, which is one,
while Special Logic is multiform; which is independent,
while that requires an acquaintance with other objects of
study and other modes of investigation; which is a part of
the Philosophy of Mind, or of Philosophy itself in its wider
sense, while that is a portion of a comparatively narrow
science.
There are certain other portions of what has usually




36               DEFINITION OF LOGIC.
been called Logic, which, though they do not properly
belong to the science itself, yet, as they are generally discussed, often at great length, in most treatises upon it, may
properly be defined and explained here, while a full consideration of them may be regarded as an appendix to the
body of the work. Properly speaking, Pure Logic terminates with the consideration of the three classes of products -namely, Concepts, Judgments, and Reasoningswhich are the elements into which all Thought is resolved.
But Thought itself is subsidiary to the attainment of knowledge, - that is, to Science. The question remains, then,
after we have filly treated of Concepts, Judgments, and
Reasonings, taken separately or considered in themselves
alone. what use is to be made of them, taken together,
in the construction of Science. A full answer to this quiestion, as it would involve a study of the objects of Science,
- that is, of the matter of the special sciences, - evidently
falls outside of the province of Logic. But a partial answer
to it, regarding Science in its relation, not to the objects
known, but to the knowing mind, may be considered as a
natural appendage to Logic, as it embraces the conditions
not merely of possible, but of perfect, Thought. Such an
answer is usually called the Doctrine of Method, or Logical Methodology. Pure Logic considers only the Necessary Laws to which all Thought must conform; the Doctrine of Method regards those rules and principles to which
all Thought ought to conform in order to obtain its end,
which is the advancement of Science. Pure Logic treats
merely of the elements of Thought, while Logical Methodology regards the proper arrangement of these elements
into an harmonious whole. All Method is a well-defined
progress towards some end; and the end in this case is the
attainment of truth. Practically speaking, the Doctrine
of Method is a body of rules or precepts looking to the
proper regulation of the Thinking Faculty in the pursuit




DIVISIONS OF THE SCIENCE.            37
of knowledge; and, as such, it necessarily lacks the precision and the demonstrative certainty which are characteristic of the principles of Pure Logic. The Laws of Pure
Thought are absolute; the merits of Perfect Thought are
various, and attainable in different degrees, according to
circumstances.
Another distinction has been tallen, in this science, between Pure and Applied Logic, or, as Sir William Hamilton prefers to call the latter, Modified Logic. The former,
as we have seen, considers the Thinking Faculty alone, as
if it constituted the whole of the human mind, and therefore as if its Laws and Products were unaffected by any
collateral and disturbing influences, but were manifested in
precisely the same manner by different persons. It takes
no account of the defects and hinderances which obstruct
the normal action of the understanding. Modified Logic,
on the other hand, considers Thought as it is, and not
merely as it ought to be. It regards " the Causes of Error
and the Impediments to Truth by which man is beset in
the employment of his Faculties, and what are the means
of their removal." And yet it is a universal science, - as
much so as Pure Logic; — for it does not consider the Matter of Thought. The obstacles and imperfections which it
points out are not those which arise from the objects of inquiry, but from the inquiring mind. They are subjective
or psychological causes of error.  Lord Bacon is probably
the first philosopher who attempted a systematic enumeration of the causes of error. He made a quaint classification
of them, under the significant name of Idols, into the four
genera of Idols of the Tribe, or the necessary faults and
imperfections of the human intellect itself; Idols of the
Den, which arise from the special constitution, education,
and habits of each individual man; Idols of the Forum,
proceeding from the defects of the language which we are
obliged to employ as an instrument of Thought and a means




38               DEFINITION OF LOGIC.
of communication; and Idols of the Theatre, or the various
dogmas of ill-founded systems of philosophy which have
found their way into men's minds through tradition, negligence, and credulity.
But Modified Logic is not properly called Logic, as it is
a branch of Psychology, which treats of the phenomena of
mind in general, and not merely of the normal action and
necessary laws of one special faculty, the Understanding.
As Modified Logic, however, is nearly allied in purpose
with the Doctrine of Method, both looking to the same
general end, - the attainment of truth through the proper
regulation of the Thinking Faculty, - the two may well
be considered together, under the general name of Applied
Logic, as a kind of supplement to the science properly so
called. Moreover, the connection between Thought and
Language being so intimate, as we have seen, that neither
can exist without the other, it would be an injurious, and,
in fact, an impossible refinement, in a Treatise on Logic, to
try to avoid frequent reference to those mistakes in thinking
which proceed from an incautious use of words.
The utility of the study of Logic - at least, of Formal
Logic - has been, perhaps, more generally doubted or denied, during the last two or three centuries, than that of
any other recognized science. In'England especially, ever
since Bacon's time, but more particularly since that of
John Locke, the stucy has been as unreasonably decried as
it was, during an earlier period, unduly exalted. The
popular voice has been against it, and, till within the last
thirty years, it steadily lost ground even in the Universities,
where the popular voice is not often heard or respected.
This unjust depreciation of the study was due in great part
to the extravagant pretensions formerly put forward in its
favor. An age which acknowledged Bacon and Descartes
to be its intellectual leaders was likely to scrutinize with
extreme jealousy the claims of a science long held forth by




UTILITY OF THE STUDY.               39
its votaries as the science or art " of the right use of reason," or " of forming instruments for the direction of the
mind"; as " the head and culminating point of philosophy,"
"' the art of thinlking," "the medicine of the mind," " the
lighthouse of the intellect," " ars artium et scientia scientiarum, qua aperta, omnes alice aperiuntur, et qua clausa,
omnes alice clauduntur."  Especially was this the case, as a
dark shade had already been cast upon this boastful study
by the rapid decline and visibly approaching extinction of
those systems of philosophy, theology, and physical science
which acknowledged the same parentage, and had long
been associated with it in asserted pre-eminence and exclusiveness.
Logic fared not much better in the hands of those, its
later disciples, who abated the extravagance of its pretensions, indeed, and, by throwing aside many of its technicalities and nice distinctions, rendered its aspect less abstruse
and forbidding. But, still adhering to the opinion that its
main purpose was to fulrnish practical rules for the guidance of the understanding in the search after truth, they
destroyed its unity, broke down the boundaries which separate it firom Psychology, Grammar, and Metaphysics, and
encumbered it with a mass of disciplinary precepts which
would be out of place anywhere but in treatises on practical education. The authors of the excellent "Art of Thinking," which commonly passes under the name of the " PortRoyal Logic," deemed it necessary to apologize even for
the limited space which they had devoted to the special
doctrines of this science, on the ground that "' custom has
introduced a sort of necessity of having at least a slight
knowledge of Logic"; and they remarked, that, as the
heads of chapters sufficiently indicated the topics considered
in them, those of exclusively logical import might be omitted in the perusal without serious injury to what remained.
"When we thought any matter might be of service in




40               DEFINITION OF LOGIC.
forming the judgment," they added, "we never scrupled
to insert it, to whatever science it might belong'"; and,
accordingly, "in this Treatise, the reader will find many
things relating to Physics and Ethics, [still more, they
should have added, belonging to Grammar,] and almost as
much Metaphysics as it is necessary to know." This is
equivalent to denying that Logic has any claims to be considered as a distinct science, or that a thorough and systelnatic evolution of its principles would be of any practical
benefit.
The ground of these misapprehensions is entirely removed by the view which has here been given of the
province and the purpose of Logic. Its boundaries are
clearly defined, its pretensions are moderate, and it accomplishes all that it is intended to perform.. As a Formal
Science, it takes no account of the Matter of Thought,
which is all derived from processes of observation or intuition that lie beyond its province. It is not concerned with
the something that is known, but only with the manner of
knowing it. It is not an organon of discovery, then, or a
means to be used for the extension of any science. It analyzes the Laws of Thought; but, as these Laws are necessary and universal, - that is, as they exist in full force even
in the humblest and least-instructed intellect, - it does not
profess to teach anything absolutely new, but only to bring
out into distinct consciousness and scientific arrangement
what exists or takes place implicitly in every mind. These
Laws of Thought exist there in a latent or involved form;
and we follow their guidance unconsciously, just as a person
who has learned to speak and write only by moving in good
society, and following the example of others, uses language
in strict conformity with grammatical laws, though he is
unacquainted with these laws even by name. The test of
the validity of any doctrine in logical science is, that those
to whom it is now for the first time communicated imme



UTILITY OF THE STUDY.               41
diately recognize it as nothing new, except in the form of
statement, but as a principle to which they have always
conformed ever since they began to think. The purpose
of Logic, then, is only to teach us how we always have
thought, and not any new mode of thinking, or new precautions, through which we may avoid the errors to which
we were formerly liable, or by which we may discover
truths that were formerly unattainable. It has no counsels
to give, except to urge careful and uniform compliance with
Laws which every one admits to be authoritative and universal, and to which he has always intended to conform.
As Mr. Mansel remarks, the science advises only the better
performance of existing obligations, and does not attempt
the imposition of new ones.  "A  treatise on Logic is not
designed primarily to give men facility in the practice of
reasoning, any more than a treatise on Optics is intended
to improve their sight; and it would be as correct for a
writer on the mathematical principles of Optics to entitle
his work' Optics, or the Art of improving defective Vision,'
as it is for a writer on the principles of Logic to adopt for
his title,' Logic, or the Art of Reasoning.' " 
Indirectly, indeed, the science may be regarded as a
medicine of the mind. As it brings out into clearer consciousness the laws to which all just thinking must conform,
the indistinctness and confusion of thought to which we are
all liable are dissipated, and the errors which often follow
the symbolic use of language, or the substitution of words
for thought, are exposed and eliminated. In these respects,
we think rightly as soon as we have learned to think clearly; for the necessary forms of the understanding govern
without dispute, when their applicability to the case in hand
has become manifest.  " The progress of the sciences,"
says Hamilton, 6 consists, not merely in the accumulation
of new mnatter, but likewise in the detection of the relations
* Introduction to Aldrich's Logic, third edition, p. lvii




42               DEFINITION OF LOGIC.
subsisting among the materials accumulated; and the reflective abstraction by which this is effected must not only
follow the laws of Logic, but is most powerfully cultivated
by the habits of logical study." As we spread out Concepts into their constituent Intuitions, or individualize them
in particular Imaginations, their true relations to each are
intuitively perceived, and inconsequence or contradiction in
uniting them  becomes impossible. All this, however, is
but the elimination of Formal error; the Matter of thought
comes from other sources; and for the mistakes which arise
from limited observation, or imperfect induction, Logic has
no remedy to offer. It guarantees the correctness neither
of the premises nor of the conclusion, but only the validity
of the inference fiom the former to the latter. Hence,
what is formally correct may be materially false; I may
reason rightly from wrong premises to a false conclusion.
On the other hand, as an error in the Form necessarily
vitiates the whole process of Thought, it may certainly be
said that Logic furnishes us with a negative criterion between truth and falsehood. The blunders which it exposes
are vital, but they are not those which are most insidious,
or even of the most frequent occurrence.
Truth is the agreement of a cognition with the object
which it is intended to represent.  Now Logic, as it takes
no cognizance of the object, which is the Matter of Thought,
is evidently incompetent to determine whether such agreeament exists or not. But there is a preliminary question to
be settled before we come to a consideration of the object;
we inquire whether the cognition agrees with itself,- that
is, whether it is Formally correct. And this question Logic
is competent to- determine with absolute certainty.  The
Formal correctness of a cogniition does not by any means
insure its Material truth; but as Kant remarks, it is to be
regarded as a conditio sine qua non of such truth.
The high place which Logic once held among the proper




UTILITY OF THE STUDY.               43
-studies of a University, and which within a few years it has.
wellnigh reclaimed, is vindicated by the great value of the
effort which is necessary to master it, considered simply as a
vigorous exercise of the understanding.  Indeed, its chief
function is disciplinary, for the effort to acquire it may be
said to equal or surpass in value the subsequent use to be
made of the acquisition. It is not of so much importance
to know, as it is to have strengthened and developed all the
faculties in learning to know. No other study taxes so
severely the power of abstract thought, and hence no one
furnishes better preparatory training for the pursuit of all
the sciences which do not consist mainly in accumulating
facts and registering the materials thus obtained.
Little needs to be said of the intrinsic dignity of the subject. " Admitting," says Heinrich Richter, as translated by
Hamilton, "that this science teaches nothing new, that it
neither extends the boundaries of knowledge, nor unfolds
the mysteries which lie beyond the compass of our reflective
intellect, and that it only investigates the immutable laws
to which the mind in thinking is subjected, still, inasmuch
as it develops the application of these laws, it bestows on
us, to a certain extent, a dominion over our thoughts themselves. And is it nothing to watch the secret workshop in
which nature fabricates cognitions and thoughts, and to
penetrate into the sanctuary of self-consciousness, to the end
that, having learnt to know ourselves, we may be qualified
rightly to understand all else? Is it nothing to seize the
helm of thought, and to be able to turn it at our will? For
through a research into the laws of thinking, Logic gives
us, in a certain sense, a possession of the thoughts themselves. It is true, indeed, that the mind of man is, like the
universe of matter, governed by eternal laws, and follows,
even without consciousness, the invariable canons of its nature.  But to know and understand itself, and out of the
boundless chaos of phenomena presented to the senses to




44                DEFINITION OF LOGIC.
form Concepts, through Concepts to reduce that chaos to
harmony and arrangement, and thus to establish the dominion of intelligence over the universe of existence, -it is'
this alone which constitutes man's grand and distinctive
pre-eminence."  " Our whole dignity," says Pascal, " consists in thought."
It is also argued by Sir William  Hamilton, with great
force, that " Logic is further useful as affording a Nomenclature of the laws by which legitimate thinking is governed,
and of the violation of these laws, through which thought
becomes vicious or null.
"It is said, in Hudibras, —' That all a Rhetorician's rules,
Serve only but to name his tools';
and it may be safely confessed that this is one of the principal utilities of Rhetoric. A mere knowledge of the rules
of Rhetoric can no more enable us to compose well, than a
mere knowledge of the rules of Logic can enable us to
think well. There is required from nature, in both, the
faculty; but this faculty must, in both departments, be cultivated by an assiduous and also a well-directed exercise;
that is, in the one, the powers of Comparison must be exercised according to the rules of a sound Rhetoric, in the
other, according to the rules of a sound Logic. In so far,
therefore, the utility of either science is something more
than a mere naming of their tools. But the naming of
their tools, though in itself of little value, is valuable as the
condition of an important function, which, without this,
could not be performed. Words do not give thoughts; but
without words, thoughts could not be fixed, limited, and
expressed. They are, therefore, in general, the essential
condition of all thinking worthy of the name. Now, what
is true of human thought in general, is true of Logic and
Rhetoric in particular. The nomenclature in these sciences




UTILITY OF THE STUDY.             45
is the nomenclature of certain general analyses and distinctions, which express to the initiated, in a single word, what
the uninitiated could (supposing- what is not probable -
that he could perform the relative processes) neither understand nor express without a tedious and vague periphrasis;
while, in his hands, it would assume only the appearance
of a particular observation, instead of a particular instance
of a general and acknowledged rule. To take a very simple example: — there is in Logic a certain sophism, or act
of illegal inference, by which two things are, perhaps in a
very concealed and circuitous manner, made to prove each
other. Now, the man unacquainted with Logic may perhaps detect and be convinced of the fallacy; but how will
he expose it? He must enter upon a long statement and
explanation, and, after much labor to himself and others, he
probably does not make his objection clear and demonstrative after all. But between those acquainted with Logic,
the whole matter would be settled in two words. It would
be enough to say and show, that the inference in question
involved a circulus in concludendo, and the refutation is at
once understood and admitted. It is in like manner that
one lawyer will express to another the ratio decidendi of a
case in a single technical expression; while their clients will
only perplex themselves and others in their attempts to set
forth the merits of their cause. Now, if Logic did nothing
more than establish a certain number of decided and decisive rules in reasoning, and afford us brief and precise
expressions by which to bring particular cases under these
general rules, it would confer on all who in any way employ
their intellect — that is, on the cultivators of every human
science —the most important obligation. For it is only in
the possession of such established rules, and of such a technical nomenclature, that we can accomplish, with facility,
and to an adequate extent, a criticism of any work of reasoning. Logical language is thus, to the general reasoner,




46              DEFINITION OF LOGIC.
what the notation of Arithmetic, and still more of Algebra,
is to the mathematician. Both enable us to comprehend
and express, in a few significant symbols, what would otherwise overpower us by their complexity; and thus it is, that
nothing would contribute more to facilitate and extend the
faculty of reasoning, than a general acquaintance with the
rules and language of Logic, - an advantage extending indeed to every department of knowledge, but more especially
of importance to those professions which are occupied in
inference, and conversant with abstract matter, such as Theology and Law."




THE PRIMARY AXIOMS OF PURE THOUGHT.       47
CHAPTER III.
THE PRIMARY AXIOMS OF PURE THOUGHT.'AVING defined Logic to be the Science of the Necessary Laws of Pure Thought, our first object must be
to ascertain what are the Fundamental and Universal Laws,
here called Primary Axioms, to which all Thought, as such,
is subject. In the separate consideration, which will come
afterwards, of the three classes of Thoughts, -namely,
Concepts, Judgments, and Reasonings, -we may expect
to find Special Laws or Rules which are applicable only to
one or two of these divisions. Such Special Rules may or
may not be derivative in character; —that is, they may
be either immediate inferences from the Primary Axioms
which govern all the products of the Thinking Faculty, or
they may be independent, as resting upon their own evidence. Of this hereafter. But our first inquiry must be,
whether there are any Axioms of universal applicability,
which underlie and govern every act and product of the
human Understanding; and, if there are such, to determine their character and significance.
If there are such Axioms, they must be few, meagre in
import, not susceptible of proof, and recognizable by all as
familiar truisms, which have always implicitly directed their
thoughts, though perhaps, on account of their very obviousness, they have never been explicitly stated or drawn
out into distinct consciousness. They must have these
characteristics, because they concern only the Forms of
Thought, or the manner of thinking irrespective of what




48      THE PRIMARY AXIOMS OF PURE THOUGHT.
we are thinking about; and as these Forms themselves are
necessarily limited in number and narrow in significance,
the Axioms which underlie them all, and constitute their
common features, must be still fewer and poorer in import.
They cannot admit of proof, as their truth is presupposed
in every act of reasoning, and therefore no argument or
proof is possible unless their veracity is taken for granted\
They must be recognized by all as mere truisms, because
they are thus self-evident, and because their truth has been
acknowledged and acted upon in every Form of Thought
which we have ever experienced. The First Principles of
all the sciences are avowedly thus few and meagre, as is
seen to be the case with the introductory axioms of Geometry and Physics. With still more reason do we expect the
First Principles of all Thought to possess this character, as
they stand in the same relation to the axioms of the special
sciences, that these axioms do to the most advanced theorems which have been built upon them, or which have been
constructed by taking them for granted.
After this explanation, we need not be surprised to find
that all the Primary Axioms of Pure Thought are perhaps
reducible to this single principle: — All Thouyght must be
consistent with itself.  If it be inconsistent, - if, directly or
indirectly, it contradicts itself, - it is self-destructive, and
the Thought is null. Thus stated, the principle is coincident with that which is usually called the Law of Contradiction, though, as Hamilton remarks, it ought rather to be
termed the Law of Non-Contradiction. Practically speaking, every Thought which must be rejected as formally
invalid - that is, which is radically vicious in Form, whatever be its Matter- offends against this principle.  By
logicians generally, however, this principle has been explicated into three general Axioms, called the Law of Identity,
the Law of Contradiction, and the Law of Excluded Middle.
The ground of this explication may be thus set forth.




THE PRIMARY AXIOMS OF PURE THOUGHT.       49
The primary element of all Thought is a Judgment,
which arises from  a Comparison. Hence, all Thought
must proceed either by affirmation or denial, as these are
the only two possible forms of Judgment. Having compared any two Concepts with each other, we either perceive
their identity, similarity, congruence, or some other relation
whereby we affirm their union in one act of Thought; or
we perceive the opposite relation between them, such as
difference, unlikeness, or incompatibility, whereby we deny
one of the other. As any Concept can be compared with
any other, and as the Judgment which follows such comparison must either affirm or deny one of the other, there
being no third form of Judgment conceivable, we have the
Axiom which is usually called the Law of Excluded Third
or Excluded Middle, - Lex _Exclusi Tertii aut Jedii.
Either A is B, or A is not B: if we make any Judgment, - that is, if we think at all, - one of these two
must be true; for no third form is conceivable. It has
been enounced in various forms:- Of two contradictory
judgments, one must be true; Every predicate may be
affirmed or denied of every subject; Every conceivable
thing is either A or not-A. Of course, A and not-A, taken
together, include the universe, - the universe not only of
all that is actual, but of all that is conceivable; for as not-A
excludes A only and nothing else, it includes the universe
excepting A only.
Still further:- Not only are affirmation and negation the
only conceivable forms of Judgment, but, as. contradictory
opposites, they are absolutely incompatible or mutually
destructive. The admission of one is tantamount to a
rejection of the other. If taken together, they destroy
each other, and the Thought is rendered null. To express
this truth algebraically, A +- n ot-A-  O. Here we have
the well-known Law of Contradiction, more properly o
Non-Contradiction, of whic the formula is, A is not ro(A4,
3                            D




50      THE PRIMARY AXIOMS OF PURE THOUGHT.
Evidently this Law is the principle of all logical negation
and discrimination.  It has been variously expressed:Contradictory attributes cannot be affirmed of'the same
subject; What is contradictory is inconceivable. It is less
correctly expressed in the adage,'6It is impossible for the
same thing to be and not to be."  This is a maxim which
concerns the Matter of Thought, and therefore we must
add to it the material limitations, in the same place, at the
same time, in the same respect, &c. It is a mistake, then, to.
maintain that the Axiom, "' Contradictory attributes cannot
be affirmed of the same subject," is not universally true, because we can form such assertions as this: A man can be
both young and not-young, though not at the same time.  In
Logic, where we consider only the Form of the Thought,
a Judgment must be expressed by the present tense of the
verb to be; for what we affirm is not the past or future
union of two real phenomena, but the present coexistence
and agreement of two Concepts in the mind. Hence, the
logical Judgment, this man IS NOT young, is absolutely
incompatible with the assertion, this man Is young, though
it is compatible with the very different assertion, this man
HAS BEEN young.
Once more: The formula, A is not not-A, proves, on
reduction, to be the exact equivalent or consequence of
this, A is A.  Here we have the principle of affirmation
and agreement, as the former was that of negation and difference.  If an object cannot be thought under contradictory attributes, it is because it has a definite character of
its own, excluding one of the contradictories through including the other.  "The universe of conceivable objects,."
to adopt Mr. Mansel's language, "' embraces both A and
not-A; it is only when definitely conceived as the one, that
an object cannot be conceived as the other. Every object
of thought, as such, is thus conceived by limitation and
difference; as having definite characteristics by which it is




THE PRIMARY AXIOMS OF PURE THOUGHT.        51'marked off and distinguished from all others; as being, in
short, itself, and nothing else.'" Here, then, we have a
third Primary Axiom, expressed as the Law of Identity:
Every A is A; Every'object of thought is conceived as
itself; Every thing is equal to itself or agrees with itself;
Every whole is the sum of all its parts.
Thus we have three Primary Axioms of Pure Thought,
- the Law of Identity, the Law of Contradiction, and the
Law of Excluded Middle, - all of which may be regarded as
explications of the single rule, that all Thought must be consistent with itsef, or as corollaries from this one principle,
that Judgment, which is the basis of all Thought, proceeds
only by affirmation and denial. The mutual dependence
and correlation of these three Axioms may be further illustrated thus.
I can think any object only by placing it under a Concept, or Class-notion expressed by a General Term; and I
can do this only by recognizing that it possesses the attributes which belong to this Concept and are common to all
the members of this Class (Law of Identity, affirmation of
similarity or agreement); by discriminating it from other
objects which have different attributes (Law of Contradiction, negation of agreement); and both this affirmation and
denial proceed by the Law of Excluded Middle, which declares, for each given attribute, that the one or the other is
absolutely necessary. Either it does, or does not, belong to
tile object, and the object does or does not belong to the
Class. In respect to the Laws of Identity and Contradiction, says Sir William Hamilton,- "each infers the other,
but only through the principle of Excluded Middle; and
the principle of Excluded.Middle only exists through the
supposition of the two others. Thus, the principles of
Identity and Contradiction cannot move, - cannot be applied, —except through supposing the principle of Excluded
Middle; and this last cannot be conceived existent except




52      THE PRIMARY AXIOMS OF- PURE THOUGHT.
through the supposition of the two former.  They are thus
coordinate, but inseparable.  Begin with any one, the other
two follow as corollaries."
Hence he symbolizes the three Axioms by a Triangle,
thus: -
fl rs'   ---
Excluded Middle.
c is either r or non-r.
These three Axioms are sufficient for all purposes of analytic Thought. There is, however, another large class of
Judgments, which are dependent in part upon a fourth Axiom; and, as a preliminary to the consideration of it, we
must explain the difference between analytic and synthetic
Thought.  Kant was the first to bring this distinction into
notice as one of great importance in philosophy.
In an analytic Judgment, the Predicate affirms nothing
which was not already, though implicitly, contained in the
Concept which forms the Subject.  We analyze a Concept
into the Marks or attributes of which it consists, and then
predicate of it one or more of these Marks. Of course, no
other knowledge is requisite for forming such a Judgment
than is already contained in the Subject itself, as the Predicate affirms nothing more than what is so contained. Thus,
if I say, Body is extended, A circle is round, An equilateral
triangle has three equal sides, I merely repeat, or state
explicitly, what is already implied in the very notion of a
body, a circle, and an equilateral triangle. But in the prop



THE PRIMARY AXIOMS OF PURE THOUGHT.       53
ositions, Body is heavy, A circle is a particular section of a
cone, A triangle is a figure the three angles of which are
equal to two rig#ht angles, the Predicate adds something that
was not previously known and included in the notion of the
Subject. There must be some reason for such addition;
otherwise, all Thought which is not merely analytical in
character would be arbitrary and inconsequent. Pure
Thought, which deals only with the Form, and not with
the Matter, of Thinking, does not ask what this reason is,
and seeks not in any way to determine its character. It
only demands that there should be some reason, - that the
connections of Thought, or those reductions to unity in
which all Thinking consists, should not be merely casual or
capricious; in which case, there would be no proper connection at all.
Besides the first postulate of the Understanding, that all
Thought should be consistent with itself, we have, then, this
second demand, in reference at least to synthetic Judgments, that all Thought should be consequent; that is, that
it should never affirm or deny a union of two Concepts
without any ground for such affirmation or denial.  The
sufficiency of this ground or reason is a material question,
with which the logician, as such, has nothing to do. Leibnitz was wrong, then, in denominating this principle that
of "the Sufficient Reason." The limitation is superfluous,
for the only reason required is one that will make the union
of the predicate with the subject conceivable,- not an actual
union of real things; and the reason which is insufficient
for this end is no reason at all. This axiom, which is properly called that of Reason and Consequent, or the Condition and the Conditioned, is expressed in the formula, affirm
nothing without a ground or reason; or, every affirmation
must have a ground or reason why it is affirmed.
As the former postulate was evolved into three Axioms,
so this one may be explicated into two, such explication




54     -THE PRIMARY AXIOMS OF PURE THOUGHT.
being, in fact, only a statement of the meaning of the words
employed. The first of these derivative Axioms is, that to
affirm the Reason or the Condition is also to affirm the Consequent or the Conditioned; for the Reason would not be
the Reason. unless the Consequent followed it. The second
Axiom is, that to deny the Consequent is also to deny the
Reason; for, again, if the Consequent does not follow, the
Reason cannot exist, since the Reason means only that
which necessitates the Consequent. The two Axioms are
thus pithily stated by the old Logicians: Positad conditione
ponitur conditionatum, sublato conditionato tollitur conditio;
or thus: A ratione ad rationcatum, a negatione rationati ad
neyationem rationis, valet consequentia. 3
Observe, however, that the converse of these two Axioms does not hold good. To affirm the Consequent is not
to affirm any given Reason, since the Consequent may have
followed from some other Reason; and the same consideration shows that it is not competent, from a denial of any
given Reason, to infer a denial of the Consequent. The
primary Axiom asserts only the necessity of some Reason
or other, not of any one Reason. The explication may be
thus summed up in a tabular form: —
There must be a Ground or -Reason for every affirmation.
Affirming the Reason    affirms also the Consequent.
Denying the Reason,    nothing follows.
Affirming the Consequent, nothing follows.
Denying the Consequent denies also the Reason.
Strictly speaking, this Axiom is applicable to all analytic,
as well as to all synthetic Judgments, and therefore, like
each of the other three Axioms, it is a Universal Law of
Thought. But in the case of analytic Judgments this Axiom does not need to be separately considered or enounced,
bfor the ground or reason to which it refers is contained in




THE PRIMARY AXIOMS OF PURE THOUGHT.        55
the Judgment itself; we cannot think the latter without the
former. Thus, we cannot think of body without extension;
and therefore, when we affirm that body is extended, the
Judgment carries its own reason or justification along with
it. But in synthetic Thought, as when we say that matter
is compressible, we see no reason in the Thought itself why
the attribute of compressibility should be affirmed of it, any
more than incompressibility. The Axiom of Excluded Middle tells us that one or the other nmust be so predicated, -
that matter must be either compressible or incompressible.
Another necessary Law of Thought —that of Reason and
Consequent -forbids us to predicate either of these contradictories to the necessary exclusion of the other, without
a ground for such preference; and the reason in this casp
must be derived from some source exterior to the Judgment
itself, as no analysis of the latter will afford any such reason.
We may, indeed, predicate neither; we may leave the
Thought, so far as this pair of contradictories is concerned,
wholly indeterminate. But if we affirm anything of it, beyond what is already contained in it, there must be a reason,
express or implied, for such affirmation.
With obvious propriety, analytic Judgments are also
called explicative, as they merely unfold, and thereby
bring into clearer consciousness, what we already possess.
By them our knowledge is cleared up and rendered explicit, but is not at all enlarged. Synthetic Judgments, on
the other hand, are properly called ampliative, as by them
our sum of knowledge is increased. Each of these requires a reason, as otherwise its result would not be the
enlargement of knowledge, but the caprice of ignorance.
It is rightly observed by Krug, that the relation of Reason and Consequent is something different from that of
Cause and Effect. It is true that Cause and Effect, so far
as they are conceived in thougklt, stand to each other as Reason and Consequent. But the converse is not true; all Rea



56      THE PRIMARY AXIOMS OF PURE THOUGHTo
sons are not Causes, and all Consequents are not Effects.
The two relations may be distinguished from each other as
being respectively what the old logicians called the ratio
cognoscendi and the ratio essendi.  Thus, to take an exampie, the ground being wet is the Reason why I know that it
has rained; this is the ratio cognoscendi, and it is evidently
a relation of one thought to another thought; though the
wetness of the ground is certainly not the *Cause of the
rain, yet, because I know that the ground is wet, I am justified in thinking that the rain has fallen. On the other
hand, the falling of the rain is the Cause of the ground
being wet; this is the ratio essendi, and it is the relation
of one real thing, or actual occurrence, to another; and, as
such, it is independent of any thought, as the one thing
would still cause the other, though there were no mind to
observe their connection. Hence, the relation of Reason
and Consequent is a mere synthesis of thoughts; the
thought of wetness of the ground suggests, and, so to
speak, justifies the thought of rain. But Cause and Effect
expresses an actual union of physical events, the real existence of the one compelling or necessitating the existence of
the other.
This seems the proper place to introduce what is called
"the postulate of Logic," - a precept which Logicians have
always assumed, and acted upon in part, but which, before
Sir William Hamilton's time, they never distinctly enounced,
or carried out consistently in all its consequences. To adopt
his language, -
1" The only postulate of Logic which requires an articulate enouncement is the demand, that, before dealing with a
judgment or reasoning expressed in language, the import of
its terms should be fully understood; in other words, Logic
postulates to be allowed to state explicitly in language what
is implicitly contained in the Thought."
This assumption is grounded upon the two fundamental




THE PRIMARY AXIOMS OF PURE THOUGHT.        57
propositions already stated and explained, namely, that
Logic deals only with the Form, and not with the Matter,
of Thought; and that it is concerned primarily with the
Thought, and only secondarily with the accident of its expression. The science claims, therefore, to fill up the gaps
and elisions of ordinary discourse, wherein much is sacrificed to brevity of speech, and to pare down the complexity
and redundance of rhetorical expression into logical simplicity and precision. For ordinary purposes, and for the
Rhetorician's use, language is a vehicle for the rapid and
effective communication both of Thought and feeling; consequently, it deals much in hints and abbreviated forms of
speech, taking for granted- all that the reader's and hearer's
mind will readily supply, and aiming only to bring his faculties of reasoning, imagination, and emotion into play in
the right direction. The Logician, on the other hand,
seeks to express nothing but Thought; and he aims to
make language a perfect representative of the Thought in
its simplicity and entireness. His proper function is to
point out those minute but frequently recurrent elements
of Thought, which, precisely because frequently recurrent,
are elided or passed over in ordinary discourse. Of course,
the expressions which he thus finds occasion to use will
often appear awkward and redundant, tediously minute,
and even tautological. But he is not responsible for their
rhetorical demerits; the only question for him is, whether
they fully and correctly express ALL that is actually passing
in Thought. Thus, the common form of argumentation is
the Enthymeme, which consists of but two propositions;
hut its Logical form is the Syllogism, consisting of three.
No one but a silly pedant ever speaks or writes Syllogisms,
except in a treatise on Logic. But the only question is,
whether everybody does not think Syllogisms whenever he
speaks or writes Enthymemes. To take another instance,
Hamilton's doctrine of the thoroughgoing quantification of
3*




58      THE PRIMARY AXIOMS OF PURE THOUGHT.
the predicate has been objected to for this reason, among
others, that the propositions which it vindicates are so awkward and unnatural, that they seem "got up for the purpose
of seeing what one can do."  Perhaps so; and yet the
objection is an idle one. For if there are occasions when
we must think affirmative Judgments with universal predicates, and negative Judgments with particular ones, the
Logician's first duty is to express this fact, however awkward and even ludicrous such expression may seem.




THE DOCTRINE OF CONCEPTS.                      59
CHAPTER IV.
THE DOCTRINE OF CONCEPTS.
1. Their Quantity; 2. Their Quality; 3. Their Relation; 4. Their Definition and Division.
CONCEPT  is a combination, or a reduction to unity
in Thought, of those elements and  qualities of the
objects which we are thinking  of, whereby they are distinguished from  all other objects, and especially from  those
which, in other respects, are most similar to them.* These
distinguishing attributes, which are the elements of the
Concept, are called its Marks; for through them  the objects of Thought are determined, or known  to  be what
they are, and discriminated from  what they are not.  The
word, or General Term, which is the appellation of the
Concept, is, consequently, the Common Name of all the
objects that are included under it. It is a convenient use
of language, (though the words are sometimes applied in
a different manner,) to say that the word or Name connotes
* The words Concept and Notion, often used as synonymes, are perhaps
best distinguished etymologically; - Concept (con-capere) as the grasping
up together of a plurality of attributes into one Thought; Notion (noscere
notis, to know an object by its Marks), as the taking note of the several
Marks or characteristics of an object.  The meaning of Notion might,
perhaps, be conveniently limited to the apprehension of.any single Mark
(nota), while C6ncept signifies the comprehension of all the attributes which
are characteristic of a, certain class of things. Thus, I have a Notion of
each of the Marks, cold-blooded, vertebrated, animal, breathing by means of gills,
and living in the water, taken singly; and I have a Concept of them taken
together, as the characteristic Marks of a Fish, or of the whole class of
Fishes. As thus limited, Notions are a subordinate class of Concepts.




60                THE DOCTRINE OF CONCEPTS.
the attributes or Marks which make up its signification,-~
and denotes the individual things contained under it which
possess those  attributes.  Thus, the name Man connotes
biped, two-handed, rational, animal, and denotes all individual men and classes of men.
It has already been  explained, that a Concept is not
necessarily the Thought of an actual, but only of a possible, class of objects;  that is, its name  may  actually
denote only one thing, as, for example, the one animal,
just discovered, of a species hitherto unknown. Hence,
Esser was led to define a Concept as'the representation
of an (one) object through its distinguishing Marks."   But
even in this case, the representation, in order to be a Concept, must be a partial representation; that is, it must
represent, not all the Marks, but only the distinguishing
Marks.  Thus it becomes the representative  of a possible class or plurality of things; if other specimens should
be subsequently discovered possessing these distinguishing
Marks, the Concept would include them  also.  It is only
when the object is immediately presented before us either
by the Senses or the Imagination, so that we have a
Presentation or Intuition of it, as one whole, with all its
* " as these qualities or modes are only identified with the thing by a
mental attribution, they are called attributes; as it is only in and through
them that we say or enounce aught of a thing, they are called predicates,
predicables, and predicaments, or categories (these words being here used in
their more extensive signification); as it is only in and through them that
we recognize a thing for what it is, they are called notes, signs, marks, chiaracters; finally, as it is only in and through them that we become aware that
a thing is possessed of a peculiar and determinate existence, they are called
properties, differences, determinations. As consequent on, or resulting from.
the existence of a thing, they have likewise obtained the name of consequents.
What in reality has no qualities has no existence in thought, —it is a
logical nonentity; hence e converso, the scholastic aphorism, non-entis nullas
sunt predicata.  What, again, has no qualities attributed to it, though attributable, is said to be indetermined; it is only a possible object of thought."
- HAMIILTON, Lectures on Logic, Am. ed., p. 55.




THEIR CONTENTS.                   61
attributes, that its Name is a Proper Name strictly so
called; for if it is present only in Thought, our representation of it is necessarily partial, as not including all its
Marks, and its Name is then virtually Common, as the
designation of a possible plurality of things. Thus, if I
am contrasting in Thought two historical characters, as
Cesar and Pompey, these two names to my conception
become General Terms, as several individuals may each
possess the few  Marks which, for the purposes of this
contrast, I attribute to those two old Romans. Gray's
affecting lines may be attributed to any churchyard: —,, Some mute inglorious Milton there may rest,
Some Cromwell, guiltless of his country's blood."
Still further; not merely may a Concept actually denote
only one thing, it may actually connote only one Mark.
But here, as before, there is a possible plurality in actual
unity. Thus, in the present state of my knowledge, my
Notion or Concept of red color may be absolutely simple,that is, it may have but this one Mark of redness.  But
additional acquaintance with the science of Optics would
teach me that this red color is an element of white light,
and that it has a certain degree of refrangibility, by virtue
of which its position in the solar spectrum is at one end of
the scale.  Here are three additional Marks of red color.
In like manner, every Concept, though actually simple,
must be regarded as containing a possible plurality of
Marks.  I say, it must be so regarded; for every Concept
must denote some existing object, - existing, that is, either
really or potentially; and no such object can be conceived
of except as possessing a possible plurality of Marks.
For every object can be conceived to be what it is, only
by discriminating it from several things which it is not;
and such discrimination is possible only through a plurality
of attributes.




62,           THE DOCTRINE OF CONCEPTS.
This will be more evident, if we consider for a moment
the various kinds of Marks by which one Concept may
be distinguished from another. The following enumeration
of them, which might be much enlarged, is taken in great
part firom Esser.
Marks are divided, -l. Into affirmative and negative, according as we know through them either what the object
is, or what it is not; thus, rational is an Affirmative, imperfect a Negative, Mark of Man. 2. Into internal and
external, according as the Mark -is attributed to the object
either in and for itself, or on the ground of the relation
in which it stands to some other object; thus, biped is an
Internal,.Father or Son an External, Mark of Man.  3.
Into permanent and transitory, according as they are always, or only sometimes, found in the object; thus, metallic
is a Permanent, hot is a Transitory, Mark of Iron.  4. Into
peculiar and common, according as they belong to these
only, or also to other objects; thus, right-angled is a Peculiar, plane-figure is a Common, Mark of a Square. 5.
Into essential or necessary, and accidental or contingent,
according as they can, or cannot, be separated friom the
object; thus, rational is an Essential, learned an Accidental, Mark of Man.  6. Into original or immediate, and
derivative or mediate, according as they are either Marks
of the thing itself, or only Marks of other Marks of it;
thus, free-willed is an Original, able to compute by numbers
a Derivative, Mark of Man, the latter being only a consequent or Mark of rationality.
We gain another view of the elements of a Concept
by dividing them into, - 1. Kinds of Existence; 2. Qualities, or Modes of Existence; and 3. Relations, or Forms
of Intermediate Existence.
First, in order to conceive, we must conceive something,- i. e. some being or existence,- which, as an object
of Thought, may be distinguished from other things, and




THEIR CONTENTS.                 - 63
to which qualities can be' attributed.  If there is no such
entity, at'the bottom of the Concept, to give it unity, the
Thought is null; non-entis nulla sunt predicata.  There
are but two kinds of Being or Existence, one of which is
thlus necessarily presupposed in Thought; namely, Real
and Imaginary or Potential.  One or the other must enter
into every Concept, not. as attributed to it, but as presupposed in forming it. In other words, every Thought must
be of some real or imaginary thing.
Secondly, whatever exists must exist in some; determinate mode; that is to say, it must have one or more
qualities. Being or existence, as defined above, includes
all things, both real and possible; hence, in order to think
any particular thing, we must discriminate it from other
things; and we can do this' only by attributing to it
Qualities, or particular modes of existence. By presupposing existence, then, we have a thing, or object of possible Thought; by giving to it qualities, we have a definite
thing, or object of actual Thought. The thing exists in
itself, per se; the quality exists only in the thing, — that
is, in something different from itself, per aliud, or, as the
logicians say, per accidens.
Thirdly, a Relation exists neither in itself, per se, nor
in the thing as different from itself, per aliud, but between
the thing and some other thing with which it is compared..
This intermediate state of existence is the only characteristic feature of Relations, whereby they are distinguished
from other Qualities.  The Relation does not merely result
from a comparison and discrimination, for this is true of
all Qualities; but it only exists as between one thing and
another, thereby necessitating a Thought of both. Thus,
the Relation of. Husband and Wife exists in neither of
them, but between them, and can be apprehended only
by thinking of the two together.
"' Every object," says Drobisch, "is thought as a deter



64           THE DOCTRINE OF CONCEPTS.
mninate object only through the Marks appertaining to it,
by means of which it is comparable, in respect to its nature,
with other things, and is distinguishable from them. Without these Marks, it is only an indeterminate something, a
thing or being without further determination; just as, on
the other hand, these Marks have no independent being in
and for themselves, but they can be separated only ill
Thought from the object in which they exist. In the
Concept of the object, then, there is the Thought of
an independent but indeterminate something, united with
determinate, but (in themselves considered) dependent,
Marks; the Concept of the object is the union of the two.
(Thus, my Concept of Man is a living, rational, organic
SOMETHING, having a mortal body and an immortal soul.)
The Marks are the manifold, the plurality, and the indeterminate something is that which gives unity to these
Marks, in the Concept of an object. The Concept is complex, therefore, and admits of separation into its elements;
and this separation is called Analysis."
It is obvious enough, that the distinction between Concept and Marks is not absolute, but relative; they may
be used interchangeably. Any Concept may become the
Mark of some other Concept; and every Notion, which
may appear in one Thought as a Mark, becomes in
another an independent Concept. Thus, the Concept animal is a Mark of man; and metal, which is a Mark of
iron, is itself a Concept, including under it iron, tin,
lead, &c. The only distinction consists in the two different uses which are made of them in Thought. If a
Concept is used only as a means of determining some
other Concept, and so without direct reference to the objects or things which it denotes, it is a Mark; but if used
as a Class-notion of certain objects, and with only secondary reference to the attributes or qualities involved in it,
it is a Concept in the stricter sense. In other words, if




THEIR CONTENTS.                65
used connotatively, it is called a Mark; if used denotatively, it is called a Concept.
The only law of pure Thought applicable to the formation of Concepts is the Axiom of Non-contradiction. A
Concept must not have contradictory Marks, as these destroy each o'ther, and the Thought so far becomes void or
null. Thus, looking only to the Form of Thought, to the
Concept A may be attributed the Marks B, C, D, and so
on without limitation; but B and not-B cannot be so
attributed.
Looking to the Matter of the Thought, however, a
further limitation arises. Considered in relation to each
other, Marks are either Congruent or Repugnant; the
former can, and the latter cannot, be attributed to the
same Concept. Thus, sweet and red are Congruent, as the
same apple may have both Marks; but sweet and bitter
are Repugnant, since they cannot be united in the same
object. If the tyro should object, that one part of it may
be sweet, and another part bitter, the answer is, that the
two parts are two different objects. Marks are said to be
Contradictory, when the one is a simple or direct negation
of the other; as sweet and not-sweet, B and not-B. They
are Repugnant or Contrary, when the negation is indirect,
as when the one is denied, not directly, but by putting in
its place, or in the same Concept, another Mark with which
it is incompatible. The mere Form of the Marks tells
me whether they are Contradictory or not; but to know
whether they are Congruent or Repugnant, I must know
the Matter of the Thought, — that is, I must have recourse to experience.
Again, if considered as mere Marks, or with reference
to their connotation only, the attributes which are united
in the same object are disparate Nlotions, for they are
different without any similarity. This holds true of Congruent, as well as of Repugnant, Marks; thus, sweet and
BE




66            THE DOCTRINE OF CONCEPTS.
red are Disparate, for the quality of sweetness has no resemblance whatever with that of redness.  On the other
hand, if considered as Concepts, or with reference to what
they denote, they are properly called disj'unct or discrete
Notions, for they are only relatively different; they have
at least so much in common, that they can be co-ordinated
under some higher Concept. Thus, sweet apples and red
apples are so far similar, that they both belong under the
Class-notion apples or fruits.  It is only stating the same
distinction ill other words to say, that Disparate Notions
are Congruent, for they can be united in the same Concept; but they do not denote any objects. On the other
hand, the Disjunct do denote Objects, but they are not
Congruent, for they cannot be united in, but are only
contained under, the same Concept.
To apprehend still further the nature of Concepts, they
must be viewed in three aspects. First, if considered in
themselves alone, they have* Quantity; secondly, if considered in reference to the mind or thinking subject in
which they are conceived, they have Quality; thirdly, if
considered in reference to each other, they have Relation.
1. THE QUANTITY OF CONCEPTS.
It follows from the definition which has been given,
that a Concept is a magnitude or Quantity, and that this
Quantity is twofold. First, it has a number of Marks,
which are reduced to unity in Thought, because they are
all conceived as inhering in one object or thing. This is
its Quantity of Intension. Secondly, it denotes a numnber
of objects, which are reduced to unity in Thought as one
class or species, because each of them possesses all these
Marks.  This is its Quantity of Extension.  Thus, the
Intension of bird is a winged, feathered, vertebrated, biped,
animal; in its Extension are contained all individual birds




THEIR. QUANTITY.                        67:and. classes of birds, as eagles, vultu res, halwks, pigeons, &c.
The plurality. of objects which are  denoted by thee Con,cept are said  to  constitute a Logical-whole, or the whole
of Extension; the  plurality  of Marks  connoted  by  the
Concept form a Metaphysical. whole, or the whole of
Intension.
This distinction of.Quantity has been  expressed by Logicians in various ways, which are here enumerated for
convenience of reference, though the forms of expression
already given will be adhered to in the present work. 
A Logical or Universal whole   A Metaphysical or Formal whole*
has Extension,   has Intension,
Breadth,           Depth,
Sphere;            Comprehension;
contains under it,  contains in it,
denotes,         connotes,
Objects,         Marks,
Things.          Attributes.
This twofold Quantity of Concepts enables us to understand the seemingly opposite assertions, that the Subject
of a proposition is in the Predicate, and yet that the Predicate is in the  Subject.  With  reference to the  Quantity
* Besides the Logical and the Metaphysical, three other sorts of wholes
have been distinguished by Logicians.
1. The Essential or Physical whole is that which consists of Matter and
Form, or substance and accident, as its essential parts.  The characteristic
of this whole is, that, as its parts do not exist out of each other, they cannot
be separated except in Thought.  As Burgersdyck says, "the Form permeates the Matter, and informs all its parts," so that Form and Matter are
inseparable. 
2. The Mathematical or, Integral whole, on the other hand, has parts
which are external to each other, so that they can be divided asunder.
This: is the case with geometrical figures, as the t~riangle, the parallelogram,
and with the human body and the limbs.  These have partes extra partes.
3. A  Collective whole, or whole of Aggregation, has its parts separate
and accidentally thrown' together;. as, an army, a hieap of stones.




68            THE DOCTRINE OF CONCEPTS.
of Intension, the Predicate is in the Subject, inasmuch
as it is but one of several Marks which make up our
Notion of the Subject.  Thus, Nan is animal; animal may
be regarded as a part of man, because it is a part of the
meaning of the word; and, when taken in connection with
the other parts, living, two-handed, rational, makes up the
whole Intension of the Concept man.  But in respect to
the Quantity of Extension, man is contained under animal, - the Subject in the Predicate,- since he is but one
out of many kinds, all denoted by this one General Term,
or contained under this one Concept, animal.
" We find two expressions in Aristotle, both of which
are sometimes rendered by' being in,' - inesse. 1. VrdpXEV,
by which the Predicate is said to be in the Subject. This
is equivalent to KamryopeuOat. To A v7rapXeL 7raVTL 7T B = — 
A KaTnyopELTaL KaTa rauTvrTo Too B= A inest omni B  (= A  is
predicated of every B = All B is A).  2. etva e'v, by which
the Subject is said to be in the Predicate.  A EcrrTv iv o5A
T9  = — Omne A est B (All A is B).  This is exactly the
reverse of Kar77yopETrat. The English language is defective
in not having, like the Greek and Latin, a proper Copula
to express the relation of Intension as well as that of Extension. Thus the relation expreesed by v7rapXEs and inest
can only be strictly rendered into English by a circumlocution,' A is a quality belonging to B.' With the ordinary Copula, both must be translated into the language of
Extension." X
Besides the Concepts which are formed from individual
things, by abstracting their differences and uniting their
common or similar elements, we can, by a perfectly similar
process, form Concepts of Concepts; and then, again repeating this process, we obtain Concepts of these Concepts,
and so on indefinitely.  In this way, we have in each case
* MANSEL, Notes to Aldrich, p. 45.




THEIR QUANTITY.                 69
a hierarchy of Concepts, of which only the lowest in order
directly denotes individuals, while all the others directly
denote other Concepts or classes, and only indirectly denote
the individuals contained in those classes.  Thus, spaniel,
terrier, hound, mastiff, &c. are Concepts of the first or
lowest order, each of them directly denoting certain individual animals, whose common attributes have become, in
Thought, the Marks of their class. Then, abstracting the
differences of these classes, we have dog as a Concept of
the second order, directly denoting spaniel, terrier, &c., and
indirectly denoting the same individuals as before. Having
formed in a similar manner secondary Concepts of cat, wolf,
fox, bear, &c., by comparing all of these with dog, abstracting
the differences and combining the similarities, we obtain the
tertiary Concept carnivora. Again, comparing carnivora
with rodents, marsupials, ruminants, &c., we have a Concept of the next higher order, mammal, of which the Marks,
forming the Intension, are vertebrate, viviparous, warm-blooded, animal, suckinyg its young. It is evident that we can
go on in this manner, rising through Concepts successively
broader and broader in generalization, till we reach the
limit of human Thought in the Concept thing, entity, or
object of Thou#ght, which connotes nothing but existence
(real or potential), and denotes everything.
I have here intentionally taken an illustration of the logical process of generalization from Natural History, as the
science in which classification is most extensive and precise,
though with the disadvantage of introducing here a number
of technical names peculiar to that science, and with which,
as belonging to the Matter of Thought, Logic has nothing
to do. But every word in our language, or in any language,
perfectly corresponds to one of these zoological technicalities, in that it occupies a definite place in some one of the
countless hierarchies of Concepts which the human mind,
for various purposes, has been led to form. The greater




-70           THE DOCTRINE OF CONCEPTS.
part of'our mental life is spent in generalizing by successive;
steps,  that is, in forming Concepts of Concepts; but
always, except in the science of Logic, with special reference to the particular things denoted by these Concepts.
Logic, which deals only with the Form, and not the Matter,
of Thought, needs a set of technicalities of its own, to describe these steps of generalization, and all other processes
~of pure Thought, with reference, not to the things which
they denote, but to each other and to the thinking mind.
This is precisely the distinction, so famous in the Scholastic:philosophy, between first and second intentions,   a distinction which has been ignorantly ridiculed by those who did
not understand it, but which in itself is perfectly intelligible,
and is as necessary as other technical distinctions in science,
all of which, before they can be understood, require a
knowledge of the elements of the special science in which
they are taken.  The burlesque question, utrum chimeera
bombinans in vacuo posset comiedere secundas intentiones, is a
good specimen of the fun which for a long time was heaped
on the study of Scholastic Logic.
A first intention or notion is a Concept, whether of a low
or a high order, which denotes things.  Thus, in the illustration just given, spaniel, dog, carnivor, mammal, -each
and all denote certain animals; they are First Intentions.
On the other hand, a second intention or notion is a Concept
which denotes first intentions - i. e. the former Conceptsin their relation, not to the things denoted, but to each other.
Thus, if the three lower steps in every hierarchy of Concepts are denominated respectively, Variety, Species, Genus,
then these three names, applicable not only to spaniel, dog,
carnivor, but to every other corresponding set of three successive steps of generalization, express second intentions.' First Intentions," says Mr. Manllsel, "as conceptions of
things, are predicable of the individuals conceived under
them. Thus we may say,' Socrates is man, animal, &c.'




THEIR QUANTITY.                  71
Second Intentions are not so predicable; we cannot say,' Socrates is species, genus, &c.' So, when Genus is said to
be predicable of Species, it is not meant that we can predicate the one Second Intention of the other, so as to say,'Species is Genus'; but that the First Intention animal
is predicable of the First Intention man, the relation of the
one to the other being expressed by the Second Intentions
genus and species.  For this reason, Logic was said to treat
of second intentions applied to first." *
It is obvious that Second Intentions are the peculiar technicalities of the abstract sciences of Logic and Grammar.
In the physical sciences, we have to deal only with Concepts of things; but Logic and Grammar need Concepts
of our modes of thinking and speaking of things, so far as
these modes are related to each other.  Thus, we need the
technical terms Genus and Species to express the relations
in which the several Concepts, that form any one hierarchy
or series, stand to each other. These relations are indicated in the following table.
* Notes to Aldrich, p. 20.




72                THE DOCTRINE  OF CONCEPTS.
Second Intentions,
or Concepts of Con-  oirst Intentions,  Intension,         Extension,
cepts,                       of    or Marks connoted.   or Objects denoted.
atively to each other.
Summum Genus. T/ing or Entity. Existing.               Everything.
Species or subal-    Animal.      Existing, organized, Every Vertebrate,
tern Genus.                       sentient.            Mollusk, Articulate, and Radiate.
Species or subal-    Mammal.    Existing, organized, Every  vertebrattern Genus.                       sentient, suckling   ed animal which
their young.       suckles its young.
Species or subal-    Carnivor.    Existing, organized, Bears,    wolves,
tern Genus.                       sentient, suckling    foxes,   lions,
their young, eat-   tigers, &c.
ing flesh.
Species or subal-      Dog.       Existing, organized, Mastiffs, spaniels,
tern Genus.                       sentient, suckling    hounds,  territheir young, eat-   ers, &c.
ifig flesh, digitigrade quadruped,
&c.
Infima Species.      Spanie.      Silky-haired, water- All  individual
dog, having all the   spaniels.
preceding Marks.
Put any other, an  entirely different, series of First Intentions in the place of those given in the table, - take,
for instance, the series 3lan, European, Frenchman, Parisian, —  and it is evident that the relations of these  Concepts also to each other will be correctly indicated by the
same Second Intentions as before. AlMan is now the Summum  Genus, Parisian is the Infima Species, and the intermediate Concepts are the Subaltern Genera or Species.
A  mere inspection of the  table  also brings to light the
one law  of Thought which  determines the  Quantity  of
Concepts.  It is, that Intension  and  Extension, the two
Quantities of every Concept, are always in inverse ratio  to
each other. They must both be present; there must be at




THEIR QUANTITY.                 73
least a minimum of each; for a Concept must always connote something and always denote something. But if we
take a great number of objects, we can find but few attributes or Marks which are common to them all, while a few
objects may have many common attributes. Looking at
the table, we see that, in the Summum Genus, the Intension is least: in the case there given, only one Mark —
existing - is connoted; while the Extension is greatest, for
the same Concept denotes everything. Descending from
the Highest Genus, we see that the Intension steadily increases through the Subaltern Genera, while the Extension
regularly diminishes. In the Lowest Species, the Intension
is at its maximum, as Spaniel connotes all the Marks of the
higher Genera and one or two additional Marks, and the
Extension is at its minimum, as there are fewer,Sjpaniels
than Dogs, still fewer than Carnivora, &c. It is only stating the same law in other words to say, with reference to
any one hierarchy or series of Concepts, that any increase
of the Intension produces, ipso facto, a diminution of the
Extension, and any diminution of the former an increase
of the latter.  Observe, however, that it is only the original and essential lMarks of which we speak, when we say
that the' number of Marks is inversely proportional to the
number of objects denoted.  The Original Marks carry
their Derivatives along with them by necessary implication; and therefore we do not really increase the Intension,
but only render it more explicit, when we annex certain
Derivative attributes which were not formerly expressed -
perhaps not even thought - as belonging to it. Thus, the
Intension of triangle, as a plane figure having only three
sides and three angles, is not at all enlarged by adding this
Mark, the sum of these three angles being equal to two right
angles, even though I now for the first time learn that this
is their sum. Though I did not, therefore, previously think
this Mark of the Concept, it did nevertheless belong to it
4




74            THE DOCTRINE OF CONCEPTS.
implicitly, or by necessary inference; and hence its express
recognition does not alter either Quantity.  In like manner, it is only the Essential Marks which determine the
boundaries of a Concept; we do not enlarge the Intension
of man as a rational animal, by adding this Accidental
]Mark, sometimes learned.  As for the Ma:lk copab6le of
learning, that is a Derivative from rational.
The metaphysical meaning of essence is, that internal
constitution of a thing which makes it what it is, - which is
not only the source of its attributes, but is necessary to its
existence.  In this sense, of course, no finite mind can
attain to a knowledge of the Essence of any real thing
whatever.  Passing by the disputes on this head as beyond our province, it is enough to say that Logic (which
has nothing to do with "real things," as they belong to
the Matter of Thought) considers the Essence of a Concept to be the aggregate of its Jlarks, or, in other words,
the sum of the attributes wzhich it connotes. Still further: -
Formal Logic cannot inquire into the nature of these attributes, but designates them indifferently by letters of
the alphabet, as being all of the same kind.  It necessarily
presupposes, as above stated, that only Original and Essential attributes are used as Marks of a Concept; and
hence it looks only to their number, and not to their
quality.  Therefore, the law is universal and absolute,add or subtract a single Mark, and the Extension, or
number of objects denoted, is thereby diminished or increased.  Essential means insejparable or necessary; take
away an Essential attribute, and the Concept ceases to be
what it was, and becomes another Concept with a wider
Extension.  Thus, fronom man as a rational animal, remove
the Mark of rationality, which is Essential to him, and
the remaining Concept is animal, which denotes all men
and brutes also.
aGenerification, usually called Generalization, is the pro



THEIR QUANTITY.                 75
cess of rising, through the successive abstraction of Marks,
fiom lower to higher Concepts.  It is so called because the
lower Concept is relatively a Species, and the higher one,
to which we proceed, is relatively a Genus, having a wider
Extension. Thus, we proceed from the lower Concept
JIammal, which is in this relation a Species, to the higher
Concept Animal, which is in the same relation a Genus,
by throwing out the Mark suckling their young.  The
name of this process, therefore, correctly indicates the act
of becoming a Genus.
The contrary process, of descending from higher to lower Concepts through the successive assumption of Marks,
is called Determination, -more properly Specification, as
it expresses the act of becoming a Species. It has been
well said, that it is the process of "thinking out objects
by thinking in attributes."  Thus, we descend from the
Genus Nlammalia to the Species Caornivora, by throwing
out all herbivorous animals, through bringing in the Mark,
eating flesh.
It has already been observed, in treating of the Axiom
of Excluded Middle and its applications, that every pair
of Contradictory attributes, A and not-A, divide the universe between them, as one or the other must belong to
everything. Because a given attribute, A, can be affirmed
only of a certain number of objects, it must be denied of
all other objects; and we may express such denial by
saying, all these others are Not-A.  Hence we have a
peculiar class of Concepts, called Negative or Privative,
more properly Infinitated, of which the characteristic is,
that they denote almost everything, and connote'next to
nothing,? - that is, nothing positive. Thus they afford a
curious illustration of the law, that the two quantities of a
Concept exist only in an inverse proportion to each other.
Logically considered, the Extension of the Concept rNot-A
is infinite, embracing the universe of existence both real




176           THE DOCTRINE OF CONCEPTS.
and potential; for the subtraction of a finite quantity, A,
does not diminish infinity. Consequently, its Intension is
zero; for it does not connote any Mark, but only the
absence of the Mark, 2A.
Practically considered, however, or with reference to
the Matter of the Thought, " the universe " in such cases
is not thought absolutely, but relatively; it means only
the totality of that class of objects which we are thinking
of, and to which A belongs. Thus, the two Concepts
Frenchman and not-Frenchman are not thought to include
all things, (which, if taken strictly, they would do,) but
only all men. In like manner, not-male, which, if rigidly
construed, would denote every stock and stone, besides
many animals, is actually thought merely as a synonyme
for female, and so denotes only about one half of the animal kingdom. Sometimes, the name is seemingly positive,
but the Concept or thought is truly negative.  Thus,
parallels are lines that do not meet; therefore, as two
negatives destroy each other, not-parallel are lines that do
meet,- a really positive Concept under a Privative or
Infinitated form. For this reason, some writers have argued that infinite, i. e. not-finite, is not thought negatively,
but positively; for finite, meaning limited or bounded, is a
restriction or negation of the magnitude which infinity
asserts positively. On the other hand, it is maintained
that the essence of Thought, as such, consists in limitation
or restriction; for we cannot think any object except by
distinguishing it, through its peculiar Marks, from other
objects; consequently, to deny this restriction or negation,
is to deny that the object in question has any peculiar
Marks, or that it is distinguished from other objects in any
manner whatever, and thereby to reduce the Thought of
it to zero.




THEIR QUALITY.                 77
2. THE QUALITY OF CONCEPTS.
When considered in relation to the mind or thinking
subject in which they are conceived, Concepts may be
said to have Quality, according as they more or less
perfectly represent to this mind the objects which they
denote, and the Marks or attributes by which those objects
are distinguished. The three virtues of Clearness, Distinctness, and Adequacy constitute the perfection of Thought.
The corresponding vices, of course, which render Thought
imperfect, are Obscurity, Indistinctness, and Inadequacy.
The Quality of a Concept depends on the degree in which
it possesses each of these merits or faults.
It is evident, from this account, that the Quality of
Concepts, depending on the characteristics not merely of
possible, but of perfect, Thought, properly belongs either
to the Doctrine of Method, or to what Hamilton calls
Modified Logic, rather than to Pure Universal Logic. As
the subsidiary processes of Definition and Division, however,
by which the Qualities of Clearness, Distinctness, and Adequacy are obtained, are applicable to all Concepts, and,
in a certain degree, regulate their formation and use in all
minds, there is sufficient reason for considering the subject
here, instead of regarding it as a mere appendage to the
science, to be treated only at the close. It is sometimes
convenient to depart a little from a rigorously systematic
arrangement, more being gained than lost by the sacrifice.
For this reason, and even as a matter of necessity, several
matters properly appertaining to the Relation of Concepts
have been partially considered in the preceding section,
under the head of their Quantity. The filiation and interdependence of the parts of a science are often such, that
it is impossible to give a proper explanation of any one
of them without presupposing some knowledge of the
others.




78'           THE DOCTRINE OF CONCEPTS.
A  Concept, being the reduction of a plurality both of
Marks and Objects to unity, supposes the power of thinking
one and many both separately, and in their relation to each
other, or together.  We think the Concept clearly as a
unity, when we can clearly distinguish it as one whole
from. other unities, - that is, from other Concepts regarded
as wholes. We think it distinctly as a plurality, when
we can distinguish both the Marks and the Objects which
constitute it from  each other.  The Clearness of my
Concept of a given metal - iron, for instance — depends
on the fulness and precision with which I distinguish it
as one whole from other Concepts, especially of those
substances which, like the other metals, tin, copper, platinum, as nearest or most similar, would be most likely to
be confounded with it.  The opposite of this merit is Obscurity. On the other hand, the Distinctness of a Concept
depends on the fulness and precision whereby I apprehend
it as a plurality, — that is, as connoting many attributes
or Marks, which I clearly distinguish from  each other,
and as denoting many Objects, which also I can clearly
distinguish from each other. The former, or the distinct apprehension of the several Marks, is its Internal
Distinctness; the latter, the distinct apprehension of the
several Objects contained under it, is its External Distinctness. The opposite of this merit is Indistinctness.
It is evident that these qualities of a perfect Concept
may exist in an indefinite number of degrees; and it is
also evident, that a Concept may be quite Clear, while
it is but very imperfectly Distinct. A young child may
have a very Clear notion of a clock, as distinguished from
the other objects in the room, and still have but a very
Indistinct apprehension of its parts, properties, and uses,
or. of the various kinds of horological instruments all
denoted by this name. On the other hand, Distinctness
necessarily involves Clearness; I cannot have a Distinct




THEIR QUALITY.                 79
apprehension of all the Marks of a Concept, without being
thereby enabled clearly to distinguish it as one whole from
other Concepts. The fact, that we may be- able very
clearly to discriminate a whole from  other wholes, or a
Concept from other Concepts, though we can but indistinctly separate in thought the parts or the Marks which
constitute that whole or that Concept, is thus illustrated
by Hamilton, from  the analogy of our Perceptive and
Representative Faculties.
4' We are all acquainted with many, say a thousand, individuals; that is, we recognize'such and such a countenance
as the countenance of John, and as not the countenance of
James, Thomas, Richard, or any of the other 999.  This'*
we do with a clear and certain knowledge. But the countenances which we thus distinguish from each other are,
each of them, a complement made up of a great number
of separate traits or features; and it might, at first view,
be supposed that, as a whole is only the sum of its parts,
a clear cognition of a whole countenance can only be realized through a distinct knowledge of each of its constituent features. But the slightest consideration will prove
that this is not the case. For how few of us are able to
say of any, the most familiar face, what are the particular
traits which go to form the general result: and yet, on
that account, we hesitate neither in regard to our own
knowledge of an individual, nor in regard to the knowledge possessed-, by others. Suppose a witness be adduced
in a court of justice to prove the identity or non-identity
of a certain individual with the perpetrator of a certain
crime, the commission of which he had chanced to see;would the counsel be allowed to invalidate the credibility
of the witness by, first of all, requiring him to specify the
various elements of which the total likeness of the accused
was compounded, and then by showing that, as the witness
either could not specify the several traits, or specified




80            THE DOCTRINE OF CONCEPTS.
what did not agree with the features of the accused, he
was therefore incompetent to prove the identity or nonidentity required?  This would not be allowed. For the
court would hold that a man might have a clear perception
and a clear representation of a face and figure, of which,
however, he had not separately considered, and could not
separately image to himself, the constituent elements.
Thus, even the judicial determination of life and death
supposes, as real, the difference between a clear and a
distinct knowledge: for a distinct knowledge lies in the
knowledge of the constituent parts; while a clear knowledge is only of the constituted whole.
"' Continuing our illustrations from the human countenance; we all have a clear knowledge of any face which
we have seen, but few of us have distinct knowledge even
of those with which we are,familiar; but the painter, who,
having looked upon a countenance, can retire and reproduce its likeness in detail, has necessarily both a clear and
a distinct knowledge of it. Now, what is thus the case
with perceptions and representations, is equally the case
with notions. We'nay be able clearly to discriminate one
concept from another, although the degree of consciousness
does not enable us distinctly to discriminate the various
component characters of either concept from each other."
Clearness and Distinctness, with their opposites, were
first regarded as qualities of vision merely, being applied
only to objects as seen, their signification being afterwards
extended by analogy to the other senses, and finally to
Thought. The distinction between them, first fully pointed
out by Leibnitz, was admirably illustrated by Krug, in a
passage which is thus paraphrased by Hamilton.
"11In darkness - the complete obscurity of night -we
see nothing,- there is no perception,.- no discrimination
of objects. As the light dawns, the obscurity diminishes,
the deep and uniform sensation of darkness is modified, -




THEIR QUALITY.                   81
we are conscious of a change, —we see something, but
are still unable to distinguish its features, -we know not
what it is. As the light increases, the outlines of wholes
begin to appear, but still not with a distinctness sufficient
to allow us to perceive them completely; but when this
is rendered possible, by the rising intensity of the light,
we are then said to see clearly.  We then recognize
mountains, plains, houses, trees, animals, etc., that is, we
discriminate these objects as wholes, as unities, from each
other.  But their parts, — the manifold of which these
unities are the sum,- their parts still lose themselves in
each other; they are still but indistinctly visible.  At
length, when the daylight has fully sprung, we are enabled likewise to discriminate their parts; we now  see
distinctly what lies around us.  But still we see as yet
only the wholes which lie proximately around us, and of
these, only the parts which possess a certain size.  The
more distant wholes, and the smaller parts of nearer
wholes, are still seen by us only in their conjoint result,
only as they concur in making up that whole which is for
us a visible minimum.  Thus it is, that in the distant forest, or on the distant hill, we perceive a green surface;
but we see not the several leaves, which in the one, nor
the several blades of grass, which in the other, each contributes its effect to produce that amount of impression
which our consciousness requires.....  Clearness and
distinctness are thus only relative.  For between the extreme of obscurity and the extreme of distinctness there
are in vision an infinity of intermediate degrees.  Now,
the same thing occurs in thought.  For we may either be
conscious only of the concept in general, or we may also
be conscious of its various constituent attributes, or both
the concept and its parts may be lost in themselves to consciousness, and only recognized to exist by effects which
indirectly evidence their existence."
4 *




82            THE DOCTRINE OF CONCEPTS.
The Adequacy of a Concept depends on the number
and the relative importance of the Marks which constitute
it, considered as more or less perfectly representing the
objects which it denotes. A Concept may be perfectly
Clear and perfectly Distinct, and still be a very Inadequate
representation of the class of things for which it stands;
for it may connote but two or three out of the many
attributes which they possess, and even these two or three
may be relatively insignificant, or of trifling import as compared with several of those which are omitted.  The old
Concept of man, happily ridiculed by Aristotle, which
described him as a two-legged animal without feathers, is
Clear, for it enables us easily to distinguish man from all
other animals; and it is Distinct, for its three Marks are
easily distinguishable from each other; but it is very
Inadequate, as it omits man's crowning and peculiar attribute as a rational being.  We may have a very Clear
and Distinct Concept of an elephant, as a quadruped that
drinks through its nostrils; obviously, however, this is a
very Inadequate representation of that sagacious and gigantic brute.
The difference between the artificial system of Botany
invented by Linnnus and the Natural System  of Jussieu
illustrates very well the importance of making a proper
selection, and taking a sufficient number, of attributes
wherewith to determine the classes of things which we
think.  Every plant may be perfectly distinguished from
all other plants, and easily referred to its proper class, in
a system founded, like that of Linnmus, exclusively upon
the number, situation, and connection of its stamens and
pistils. Such a system furnishes an easy mode of ascertaining the names of plants, just as the alphabetical
arrangement of words in a dictionary is the easiest way
of enabling one to find any word that he wants. But
the arrangement is artificial and arbitrary, the number




THEIR QUALITY.                 83
and relative situation of the stamens and pistils in a plant
no more determining its leading and essential characteristics, than the significance and mutual relations of words
depend upon the position which their initial letters happen
to occupy in the alphabet. In the Natural System, these
prominent and essential attributes of plants are made to
mark out the classes into which they are divided, and
thus the relations which actually exist between the things
themselves stand out with the same relative prominence
in the thoughts wherein they are represented to consciousness. The Concepts here not only denote their objects,
but represent them in a manner which approximates, though
distantly, the fulness of Intuition.
The three merits of Clearness, Distinctness, and Adequacy, which constitute the Quality of a Concept, presuppose a reference to some standard, which, for the very
reason that it is a standard, must be independent of our
Thought,- that is, not subject to arbitrary change in
Thought. Strictly speaking, every Concept considered
merely as such, or as an individual Thought in consciousness, must have its own degree of each of these merits,
and cannot change this degree without becoming a different Concept from what it was. Whatever faults may
be imputed to it when it is compared with some standard,
it may still be said of it, even in its present state, that
it connotes something and denotes something, and thus
has all the essential characteristics which enter into our
definition of a Concept. Any change to which it may
be subjected is not an improvement of this Concept, but
the substitution of another in its place, having different
Marks, and therefore denoting not the same objects as
before. Such a change or substitution can be required
only through a reference in Thought to some standard, to
which this Concept, or the Concept as it now stands,
does not conform, but to which it was previously implied
that it ought to conform.




84            THE DOCTRINE OF CONCEPTS.
There are two standards, one of the name and the othex
of the thing, to one or the other of which every Concept
which the mind can form is, at least tacitly, referred.
Words, which are the names of Concepts, are the means
of- communicating our Thought to others; and they cannot
perform this office unless they have the same signification
to the hearer as to the speaker; that is, each name must
call up the same Concept in the minds of both. A Concept may be faulty, then, not as a Concept, (for in this
respect, or in reference to the mere Form of Thought,
one Concept is as good as another,) but because it has a
wrong name, whereby it improperly assumes to be the same
Thought which is designated by that name in the minds of
other persons generally. Thus it is that language, among
its other offices, has an important influence in the regulation and fixation of Thought. We do not classify things
and form Concepts of them arbitrarily, each one according
to his own preferences; but the necessity of maintaining
intercourse with other minds imposes on us a constant
reffort to approximate our Thoughts to theirs, -that is,
to the Thoughts which they have fixed and established
for general use through stamping upon them certain names.
The Thoughts which I attach to the words church, state,
government, for instance, may be as correct and proper,
in themselves considered, as the connotation which you
attach to them; but it is a decisive objection to my mode
of thinking, if I attach these old and familiar names to
peculiar combinations of Thought which they never before
designated, and to which people generally do not now
give these appellations. Owing to the symbolic use of
language, in which, as already explained, words are employed as temporary substitutes for Thoughts, we are
continually learning and using words before we have fully
learned their meaning. Gradually, by a process of induction, we accommodate our use of these words to their




THEIR QUALITY.                 85'
established usage; and it is while thus learning, that our
Thoughts are said to be wanting in Clearness, Distinctness,
and Adequacy. In truth, it is not our Thoughts which
are thus faulty; but our apprehension of other people's
Thoughts, or, what is the same thing, of the meaning
which they attach to certain words. My own Concepts
of church, state, &c. are Clear and Distinct enough, unless
indeed I now hear these words for the first time; but I
cannot clearly distinguish what I imperfectly understand
to be your Concepts of them from certain other kindred
or nearly allied Thoughts; or I have but an Indistinct
knowledge of the several Marks which are connoted in
the Concepts which you and other men have of them;
or my connotation of these Marks is Inadequate, — that
is to say, not so full as other people's.
The second standard to which our Concepts are referred,
when they are said to be deficient in Quality, is the class
of things which they denote, and which they consequently
ought to represent as perfectly as possible. Thus, every
artisan, through long use, has a more Adequate, Clear,
and Distinct Concept of each of the tools of his trade,
each of the objects which he works upon, and each of the
processes to which these objects are subjected, than it is
possible for other persons to possess who have no special
familiarity with the business. The Concepts which these
other persons have may be perfect enough for the correct
use of language; that is, they may apply the technical
names rightly. But when compared with the full and
accurate Notions which have been acquired by experts,
they appear to be, as they are, very imperfect representations of the things themselves.
The difference between these two standards to which all
Concepts, in respect to their Quality or degree of perfection, are referred, enables us to understand the distinction
which logicians long ago established between nominal and




86            THE DOCTRINE OF CONCEPTS.
real Definitions. This distinction has been very imperfectly
apprehended by many, especially by those who, unable to
find any other mode of distinguishing the two sorts of
definition, leave held that a Nominal one consisted only in
explaining the meaning of the word by synonymes, or by
unfolding its etymology. Such a process would be Grammatical rather than Logical; rightly considered, it is no
definition at all. A  Nominal Definition is the distinct
explication of all the Marks which are connoted in the name
of the Concept by general consent, as evinced in the use
of language.  But language is imperfect, and words in
common use often signify much less than exact science
requires.  A  Real Definition is a distinct explication of
all those Marks, and those only, which a careful examination
of the class of things denoted by the word proves to be both
Original and Essential.  It is obvious that the Nominal
and the Real Definition of a Concept will often coincide.
This is usually the case with the technical terms in every
science, especially those of recent origin, whose connotations are usually determined with great care before their
names are invented.  In other cases, as already explained,
the two definitions may differ very widely from each other.
The further consideration of Definition, and of Division
also, as the subsidiary processes by which the Quality of
Concepts may be improved, must be postponed till after
we have treated of
3. THE RELATIONS OF CONCEPTS.
The Relation of Concepts, as already remarked, is a
technical phrase, which is understood to mean their Relations to each other only, and not to the other forms of
Thought, which will be considered hereafter.
A series or hierarchy of Concepts, formed by successive
steps of Generification, like the one given in the table on




THEIR RELATIONS.                 87
page 72, represents a succession of Concepts as subordinated to each other in their two Quantities of Extension
and Intension.  But the names of the Second Intentions,
which express the Relations of these Concepts or classes
to each other, are given with primary reference to the
Extension only.  Unless express notice is given to the
contrary, therefore, we shall always speak only of their
Relation in Extension.  Of any two Concepts in such a
series, that one is called the Superior, Higher, or Broader,
which has the greater Extension,- that is, which denotes the larger number of individual objects; it may
also be called the Superordinate.  The other, having less
Extension, or denoting fewer Individuals, is called Inferior, Lower, Narrower, or Subordinate.  Thus, referring
to the table again, animal is Superior or Superordinate to
mammal, which, as included under it, or denoting fewer
individuals, is called Inferior or Subordinate. The Superior, also as the more general notion, and as obtained by
the process of Generification or throwing out Marks, is
called the Genus; while the Inferior, as more specific, and
obtained by the process of Specification, or thinking in
Marks, is called the Species.  These names being merely
relative, it is evident that the same Concept is, at the
same time, a. Genus to any lower Concept, and a Species
to any higher one.
The Highest or Broadest Concept in such a series,
denoting most individuals and connoting fewest Marks, is
called the Summum Genus; hence, it is defined by logicians to be a Genus which cannot become a Species.  On
the other hand, the lowest Concept in the series, as denoting the least and connoting the most, is called an Infima
Species.  In fact, it denotes individuals only, and not any
classes or Species of individuals; therefore it is defined to
be a Species whic7z cannot become a Genus.  Each intermediate Concept, as we have just said, is a Species to those




88           THE DOCTRINE OF CONCEPTS.
above it, and a Genus to those below it. Its next Higher
neighbor is called its proximate Genus; and its next lower
one might be termed a proximate Species, though this term
is not in frequent use.
When the name of any Higher Concept is applied as the
name of a Lower one, or of an individual, it is called its
abstract name, or its denomination in the abstract; the peculiar or proper appellation of this lower Concept or individual is called its concrete name. Thus, animal is an
Abstract, and man the Concrete, name of a rational animal;
and again, relatively, man is the Abstract, and John the
Concrete, appellation of the individual, this man whom we
are speaking of. These names obviously have reference
to the Intension of the Concept, the Abstract name being
obtained by Abstraction, that is, by throwing out Marks,
and the Concrete signifying all the Marks taken together
(con-cresco, grown together), or the whole Intension.
According to another and more frequent use of language,
an "Abstract name " has a narrower signification than the
one here indicated, being applicable only to one peculiar
Species of Higher Concept, instead of denoting the Abstract
use of any Higher Concept whatever. What appears only
as a Mark of the Concept in its Lower or Concrete use, is
itself a Higher Concept; and if its denotation is then
altered, - that is, if it no longer denotes things as before,
but only various kinds and degrees of that attribute which
the Concrete term  connotes, -it is then, and then only,
commonly called an Abstract term. Thus, to recur to the
instance already given, man connoting rational animal, we
may take rational instead of animal as the Higher Concept; and then, altering its denotation, we may understand
it to mean, not rational beings, but various kinids and degrees of rationality. Hence, such terms as rationality,
redness, whiteness, humanity, &c. are called Abstract
names. According to this use, anl Abstract term is one




THEIR RELATIONS.                 89
which denotes that which, in its Concrete application, it connoted; it is a Mark or attribute considered as a thing.
The Relations thus far explained, as arising from the
higher or lower position of a Concept in the series or
hierarchy to which it belongs, are all denominated Relations of Subordination.  They may be aptly symbolized by
a series of concentric circles, thus: -
Here, A, having the greatest
extent, and so containing all the
others under it, represents the
/It\D  Summum Genus; while F, as
least extended, and  denoting
only  individuals, not classes,
represents the Infima Species.
Any intermediate circle, C, is a
subaltern Genus or Species, being Genus to D and Species to B.
If we were to use the same diagram to symbolize the
Relations of Intension, since the two Quantities are in
inverse ratio to each other, the order of the letters would
be reversed.  F, as connoting the most Marks or having
the largest Intension, would be the outermost circle, and
A, having the least Intension, would be the innermost or
smallest.
In general, and for practical purposes, the terms Summum  Genus and Infima Species are applied not in an
absolute, but only in a relative sense; - relative, that is,
not to the totality or the smallest class of all conceivable
things, but to the totality or the smallest convenient class of
those things only which we are now thinking of; say, all the
objects of some particular science. Thus, in Zo5ilogy, animnal is considered as the Summum Genus, no notice being
taken of vegetables and minerals; and what is usually
termed a "Variety" or " Sub-Variety" -King Charles
Spaniel, for instance - is an Infima Species.




90'THE DOCTRINE OF CONCEPTS.
Absolutely speaking, logicians maintain that Summum.
Genus and Infima Species are both unattainable, - that
they are limits of classification in Thought, which we can
approximate, but never reach.  They express this impossibility under the form of two Laws of Thought. The first
of these, called the Law of Homogeneity, affirms that things
the most dissimilar must, in some respects, be similar or
homogeneous; and consequently, any two Concepts, how
unlike. soever, may still both be subordinated under some
highler Concept.  Thus, animals and veyetables, distinct as
they are from each other, are both contained under the
higher Concept organized natural objects.  And even from
this connotation, if we subtract the Mark organized, the remainder will be a still higher Concept, natural objects, which
will include minerals, as well as animals and vegetables.
On this ground, Mr. Mansel and other logicians maintain that thing or entity, connoting but one attribute, existence (real or imaginary), which would seem  to be an
absolute' Summum  Genus, is. not thinkable.  They deny
that it is a possible object of Thought, on the ground seemingly that it does not contain a plurality of attributes.
But'as reasons have already been assigned (page 61) why
a Concept, as actually thought by us, may have only one
attribute or distinguishing Mark, I cannot see why ens is
not thinkable, as distinguished from nihil, which has not
even this one attribute of (real or imaginary) existence, and
is therefore certainly not conceivable. That it is a very
vague and indefinite Thought, is admitted; this is a consequence of its connotation being reduced to a minimum.
But to say, that "' distinguishable from nothing " is tantamount to affirming that it is not distinguishable at all, seems
to me in this connection, or for the purposes of pure
Thought, a mnere quibble.  I can certainly think a difference - that is, a relation - between being and no-being,
though only one term  of the relation is positive, and the




THEIR RELATIONS.                 91
other is merely negative.  The algebraist finds a very distinct relation between plus a and minus a, as the presence
of one in place of the other affects the results of his calculation very sensibly; and both these expressions are clearly
distinguishable from zero. It is too much of a paradox to
affirm that there is no difference in Thought between something and nothing.
About the second principle, called the Law of Heterogeneity, there is no dispute. According to this Law, things the
most similar must, in some respects, be dissimilar or heterogeneous; and consequently, any Concept, however large
its Intension may be, may still have that Intension increased, without thereby descending to individuals.  What
is relatively an Infima Species, or considered as such for
the purposes of some particular science, may be again subdivided into two or more, and so on indefinitely. Thus,
King Charles Spaniel may be subdivided into such Spaniels
one year- old, and those of two years or older; into those
born in _Europe, and those born in Anterica; into those above,
and those below, three pounds in weight, &c.  Though, as
Air. Mansel remarks, " as far as the Laws of Thought are
concerned, it is permitted to unite in an act of conception
all attributes which are not contradictory of each other, it
is impossible in practice to go beyond a very limited number. The number of attributes in the universe not logically
repugnant to each other is infinite; and the mind can therefore find no absolute limits to its downward progress in the
formation of subordinate notions."' 
The Relation of Co-ordination exists between different
Species which have the same Proximate Genus; two or
more Species are thus said to be Co-ordinate when each
excludes the other from its own Extension, but both or all
are included under the Extension of the same nearest
Higher Concept.  For instance, dog, wolf, cat, lion, bear,
* Prolegyolena Logica, p. 169.




92'           THE DOCTRINE OF CONCEPTS.
&c. are Co-ordinate Species under the same Genus, Carnivora; each excludes the other, - what is wolf is not cat,
— but all alike are Carnivora.  As the two Quantities of a
Concept are in inverse ratio, and as, in reference to Extension, the Species is contained under the Genus, so, in
reference to Intension, the Genus is contained in the Species. Thus, the Intension of every Species contains the
Genus, -that is,.the aggregate of Marks which characterize the Genus, - and the Specific Difference, - that is,
the aggregate of Marks by which this Species is distinguished both from the Genus to which it is Subordinate,
and from the other Species with which it is Co-ordinate.
Man is a rational animal — here, animal expresses the
Genus to which man belongs, and rational is the Specific
Difference whereby man is distinguished from other Species
of animals.
Two things may be said to be generically different, when
they belong to different Genera; specifically different, when
they belong to different Species; individually or numerically different, when they do not constitute one and the
same reality. But as every member of the hierarchy,
except the highest and the lowest, may be viewed indifferently as either Genus or Species, yeneric difference and
specific difference are only various expressions for the same
thing.
"Individual existences," as Krug remarks, "can only
be perfectly discriminated by external or internal Perception, and their numerical differences are endless; for of
all possible Contradictory attributes, the one or the other
must, on the principles of Contradiction and Excluded
Middle, be considered as belonging to each individual
thing.  On the other hand, Species and Genera may be
perfectly discriminated by one or few characters. For
example, triangle is distinguished firom  every Genus or
Species of geometrical figures by the single character of




THEIR DEFINITION AND DIVISION.           93
trilaterality. It is, therefore, far easier adequately to describe a Genus or Species than an Individual; as, in the
latter case, we must select, out of the infinite multitude
of characters which an Individual comprises, a few of the
most prominent, or those by which the thing may most
easily be recognized."  We may describe, but cannot define,
an Individual, as there would be no end to the enumeration of its peculiar attributes.  In such case, the only
adequate definition is a view - an Intuition - of the thing
itself.  Omnis intuitiva notitia est definitio.
The other Relations of Concepts to each other may be
very briefly indicated.  Concepts are said to intersect,
when the Extension of one coincides in part, and only in
part, with the Extension of the other.  Thus, Erenchman
and Protestant are Intersecting Concepts, for some Frenchmen are Protestants and some are not, some Protestants
are Frenchmen and some are not.  These may be symbolized by two circles whose circumferences cut or intersect
each other. Exclusive Concepts —animal and vegetable,
for instance — do not coincide in any part of their Extension, and may therefore by symbolized by two circles
which lie wholly apart the one from  the other.  ReciZrocating, Convertible, or Coextensive Concepts are those
which have precisely the same Extension, as living being
and organized being, since everything which lives is organized. Two circles of the same diameter, and laid one
upon the other so as to coincide throughout, would aptly
represent Convertible Concepts.
4.  DEFINITION AND DIVISION.
It has already been said, that a Concept is internally
Distinct when we can fully enumerate and clearly distinguish from each other all its original and essential Marks.
The process through which this is accomplished is called




94            THE DOCTRINE OF CONCEPTS.
Definition. Again, a Concept is externcdly Distinct when
we can fully enumerate all its subordinate Genera and
Species. This process is called the Division of the Concept. Both processes have reference to one or the other
of the two standards, - the name and the thing, — by
which it is determined whether the Concept in our minds
is, what it purports to be, a faithful copy or representation
of what is generally designated by that name, or a full
enumeration of the original and essential attributes of the
class of things so designated.  We will first consider
Definition of namzes only, Division relating only to classes
of things, the object of both processes being not to determine and render distinct the Concepts which we already
possess, but to substitute others for them which shall more
perfectly answer our purposes.  The Concept to be defined
should be called'the definiendum, the Definition itself
being the definientia.
A Definition consists primarily of two parts, the Proximate Genus and the Specific Difference of the Concept
defined; for these two elements, as we have just seen,
make up the whole Intension of every class.  Thus,
carnivor is a flesh-eating mammal; the word mammal here
denotes the Proximate Genus, and flesh-eating the Specific
Difference which distinguishes carnivora from other mammals.  Such a Definition, however, is incomplete, as it is
further necessary to define the Genus which makes a part
of it;- and this can be done only by considering this Genus
(mammal) as a Species, and assigning to it its own Proximate Genus (the next higher one in the hierarchy), animal, and its Specific Difference, suckling its young.  We
proceed in this manner till we have reached the Summum
Genus, each Specific Difference successively taken up being the Mark which was abstracted in the original process
of Generification, and the sum of these Differences being,
therefore, the aggregate of all the Marks which make up




THEIR DEFINITION AND DIVISION.          95
the Intension of the Concept first proposed to be defined.
What may be called the secondary or proper Definition,
then, as before stated, is the distinct explication of all the
Marks which are connoted in the name of the Concept.
Thus, having successively defined dog as carnivor, carnivor
as mammal, mammal as animal, and animal as thing,
annexing in each case the corresponding Specific Difference, we then sum up all these Specific Differences, and
thus form the proper Definition consisting solely of these
Differences, - that is, of all the Marks which the definiendum  connotes.  Hence it appears, that though the
defining analysis is of the Intension only, yet it is regulated by the Extension, as the Extension determines the
order in which the Intension is resolved into the Marks
which are its elements.
It is obvious also, that Definition by Genus and Specific
Difference in all its successive steps supposes a previous
knowledge of the whole hierarchy of Concepts through
which it ascends, and therefore it only explicitly enumerates the Marks which were already implicitly known.
The Classification here precedes, and is the means through
which we form, the Definition.  Usually, however, we
proceed in the inverse order of this process: we seek first
for the Definition, — that is, for a knowledge of all the
original and essential attributes of a class of things, - as
a preliminary step towards determining the Classification,
or assigning the class to its proper place in a hierarchy
of Concepts. Here, the Definition is primarily of the
thing, and only secondarily of the name, the problem being how to determine the sum of the original and essential
characteristics of this class of things. The following are
the Rules usually given by Logicians for the solution of
this problem, -that is, for the proper formation of Definitions.
1. A Definition must be adequate; that is, it must have




96           THE DOCTRINE OF CONCEPTS.
precisely the same Extension as the thing defined. If
not, if the Predicate defining denotes more objects than the
Subject defined, the Definition is too Wide; if it denotes
fewer objects, it is too Narrow. Thus, when a triangle
is defined "a figure having three rectilinear sides," the
Definition is too Narrow, as there are spherical triangles
to which it will not apply. If we say, " water is a compound of oxygen and hydrogen," the Definition is too
Wide, as it includes not only water, but something else, -
a deutoxide of hydrogen. When this rule is complied
with, the Definition and the thing defined are Reciprocating or Convertible Concepts; consequently, everything
to which the Definition applies, and nothing to which it
does not apply, is the thing defined. When this is the
case, our Concept of this class of things has become perfectly Clear, or distinguishable from all other Concepts.
2. The Definition must not be tautological; that is, it
must not contain the name of the thing defined, as this
is precisely the word which we are bound to explain. It
is equally a violation of this rule to allow any of the
derivatives of this name, or any of its correlative notions,
either one of which can be explained only through the
other, to constitute a part of the definition. This fault is
called "defining in a circle."  Lexicographers often fall
into it unawares, as when they define a board to be " a thin
plank," and then a plank to be " a thick board"; or when
they say that life is "vitality, the state of being alive,
the opposite of death."
3. A Definition ought not to proceed by Negative or
Disjunctive attributes, when it is possible to avoid both.
You cannot teach me what a notion is, by merely declaring what it is not, or that it is one of several things
without indicating which one is intended. It is no real
Definition to say of parallels, that they are "lines which
do not meet," or of oxygen, that it is " one of the gases




THEIR DEFINITION AND DIVISION.         97
fit for respiration." But convenience often requires what
Logicians call division by dichotomy, in which a Genus is
divided into two Species having Contradictory Marks; that
is, one of these Species has, and the other has not, certain well-defined characteristics, the latter, of course, being
capable only of Definition by negation.  Thus Cuvier,
having determined with great precision the attributes of
Vertebrated animals, found it convenient to regard all
other animals as Invertebrates, that is, as not possessing
these attributes.
4. A Definition must be precise,- that is, it must contain nothing unessential or superfluous. Thus, all Derivative Marks should be excluded as superfluous, after their
Originals have been enumerated; for they are virtually
contained in those Marks from which they are deducible
by the necessary Laws of Thought, so that the mention
of them only cumbers the Definition without really enlarging it. That a triangle is half of a parallelogram, is no
proper part of the Definition of a triangle, inasmuch as
it is a necessary consequence of this figure having three
sides and three angles. Unessential attributes are also
superfluous; that man is a featherless biped is an accident,
not an essential trait, of his humanity.  Give him a coat
of feathers, and he is still man; but deprive him of rationality, and he is no longer human.
5. A Definition must be perspicuous; for we define
only in order to make more clear, and obscure or figurative
expressions do not conduce to this end, but only increase
the difficulty.  " Tropes and figures," says Krug, 1" are logical hieroglyphics: they do not indicate the thing itself,
but only something similar," But many expressions, originally metaphorical, have ceased to be so through long
use in their secondary meaning.  Their original signification has become obsolete, and no longer recurs to perplex
us. This is the case with nearly all the words which




98            THE DOCTRINE OF CONCEPTS.
now denote mind and its operations, though they were
first applied only to what is material.
Dr. Thomson takes a wider view of Definition, as including any Predicate which may be "useful to mark out
for us more clearly the limits of the subject defined, and
is therefore capable of being employed as a Definition for
some thinker or other."  6 Any of the Predicates we
propose to include," he continues, " though not the absolute
Definition, not the Genus and Difference, may be employed as a Definition by some particular person, and may
to him fulfil the purpose of the best logical Definition
which can be given, 6'and therefore ought, if possible,
to be comprehended under the same head." In conformity
with this view, he enumerates the following six sources
from which convenient Definitions may arise.
"'i. From Resolution, when the Marks of the definitum
are made its definition; as in'a pension is an allowance
for past services.' It is not necessary that the Marks
should be completely enumerated, -- that the conception
should be strictly adequate, -but only that the Marks
should suffice for the identification of the Subject, as belonging to it all and to it alone; so that Aristotle's Property
would be included in it. ii. From Composition, the reverse
of the last method, in which the definitum, a conception of
which the component Marks are enumerated, stands Subject
to a Definition implicitly containing those Marks; as,' those
who encroach upon the property of others are dishonest.'
iii. From Division, where we define the Subject by enumerating its Dividing Members; as,'Britons are those who
dwell in England, Scotland, or Wales.' All the judgments called disjunctives are under this head. iv. From
Colligation, the exact reverse of the last; where the Dividing Members of a conception are enumerated in the Subject,
and the divided conception itself added to define them; as,'historical, phlilosophical, and mathematical sciences are the




THEIR DEFINITION AND DIVISION.             99
sum (i. e. are all, or equal) of human knowledge.'  This
is the form which Inductive Judgments naturally assume.
v. From change of Symbol, where both Subject and Predicate are symbolic conceptions, the latter being given as a
substitute for the former on a principle of expedience only;
as,'probity is honesty.'  This is the nominal definition of
some logic-books. vi. From Casual Substitution, where
one representation is put for another on a principle of
expedience only, as serving to recall the Marks, which
both possess in common, more readily to the hearer's
mind; as,'the science of politics is the best road to success in life.; pleasure is the opposite of pain.'
"TABLE OF DEFINITION.
By its In- i being unfolded, = i.  Resolution, or
~By its i ~n-           B     ~Definition
tension (or
Marks),
Marks)   8 being reunited,  ii.  Composition.
By its Ex-  being divided,= iii. Division.
o      tension (or
A  Sphere)    being reunited, = iv. Colligation.
By  Acci-           of a Symbol, = v.  Nominal Definition.
dental Codental Co-    of Notation, = vi. Accidental Defiincidence                       nition."
As absolute Definition resolves the Intension of a Concept into its constituent Marks, so -Division resolves the
Extension into its constituent Genera and Species. In its
most general acceptation, division is the separation of any
whole into its parts.  But Logical Division, with which
alone we are here concerned, is such a separation of a Logical Whole only,- that is, of a class containing under it other
classes, which are regarded as its parts.  An individual
is so called (in-divido) because it cannot be (logically)
divided; the process of cutting it apart is properly called
Partition, not Division.  The Mathematical or Integral
whole is such an individual, and can be sundered into its




100           THE DOCTRINE OF CONCEPTS.
parts only by Partition.  The parts of an Essential or
Physical whole, as they interpenetrate and inform each
other, cannot be separated at all except in Thought.  But
a Logical whole is itself a creation of Thought, formed
out of lesser wholes of the same kind, into which it can
be resolved by mental analysis.
By Partition, triangle may be resolved into smaller triangles, or into angles and sides; the former Partition may
be actual, while the latter can only be ideal, -that is, it
is possible only in Thought. By Division, on the other
hand, triangle is resolved into rectilinear and curvilinear
triangles, or into equilateral, isosceles, and scalene triangles,
as these are Species comprehended under one Genus.
The Genus to be divided is called the divisum, and
the constituent Species into which it is resolved are the
dividing members (membra dividentia).  Agreeably to the
nature of a hierarchy of Concepts, the parts which result
from such a Division are in themselves wholes containing
other parts under them, and the dividing process repeated
upon these is called a Subdivision. The same Concept
may likewise be differently divided from different points
of view, each separate analysis proceeding on what is
technically termed its own fundamentum  divisionis, or
peculiar Ground of Division. Thus, man may be divided
geographically into -European, Asiatic, American, &c.; or,
in reference to color, into white, red, and blaclk men; or,
in reference to religion, into Christians, Mohammedans, and
Pagans; - local position, color, and religion being here
the successive fundamenta divisionis.  So the books in
a library may be arranged either according to size, as
folios, quartos, octavos, &c.; or according to the languages
in which they are written, as Latin, French, English,
&c.; or according to the subjects of which they treat, as
theological, scientific, historical, &c. Perhaps the most
important point in the philosophy of the Classificatory




THEIR DEFINITION AND DIVISION.       101
Sciences is the right selection of a fundcamentum divisionis,
or Ground of Division.
If a Division has only two parts or members, it is called
a dichotomy; and if such a Dichotomy is exhaustive, as it
should be, these two members are evidently Contradictories
of each other; for whatever is contained in one is thereby
excluded from the other, and the two, taken together,
constitute the whole. Accordingly, these two Dividing
Members can always be expressed under the formula B
and not-B. Thus, in dividing triangle, instead of calling
the two members rectilinear and curvilinear, it is better
to denominate them  rectilinear and non-rectilinear.  A
Division into three members may be called a trichotomy;
into many, a polytomy.
Logicians have commonly given the following Rules for
the proper Division of a Concept.
1. Each Division should have but one fundamentum
divisionis, by which every part of the process is regulated.
The intervention of more than one Ground of Division
in the same process is the Logical fault which is called a
Cross Division. Thus, a Division of man into European,
American, Negro, and Pagan is faulty, because the Ground
of Division for the first two Dividing Members is local
position; for the third, it is color; and for the fourth, it
is religion. The consequence of this blunder -is, that the
same individual might be contained in each of the iBst
three Members; — for he may be at once American, Negro,
and Pagan. Whatever we may select as a Ground of
Division, it must evidently be a Mark or attribute of the
Divisuml, and the number of distinct forms or varieties,
under which this attribute appears in the class of things
to be divided, will determine the number of Dividing
Members. One of the Dividing Members, however, and
but one, may be marked only by the absence of this
attribute.




102           THE DOCTRINE OF CONCEPTS.
2. The Mark selected as the Ground of Division should
be an Essential attribute of the Divisuln, and one which
has as many Derivatives, or which determines as many
of its other attributes, as possible; otherwise, the Division
will be complex and purposeless. Thus, the color of the
hair is an unessential attribute of man; mankind might
be divided into a large number of classes in this respect,
but as very few of his physical, and none of the intellectual
or moral, qualities of a man can be inferred from the fact
that he has red, brown, or black hair, the Division would
be useless. On the other hand, a classification of men
according to their nationality or race, their geographical
position, or their religion, is found to be an eminently
fruitful one, as many of their other attributes are found
in invariable connection with these leading characteristics,
so as to be readily determined by them. The purpose
for which a Division is made often determines the selection
of its Ground. Thus, soldiers may be conveniently divided
into cavalry and infantry, as this distinction is one of great
moment in military affairs; but to divide men in general
into foot and horsemen would be absurd.
3. No Dividing Member must by itself exhaust the
Divisum; and the Dividing Members, taken together,
must exhaust, and no more than exhaust, the Divisum.
As the Genus and the Co-ordinate Species into which it; - -iivided stand to each other in the relation of a whole
to its parts, the propriety of this rule is manifest. Mlan
cannot be divided into rational and irrational, for the one
class of rational beings includes all men, so that neither
of the Dividing Members is a part, or the result of a
Division, properly so called.  Again, as all the parts are
required to constitute a whole, if the Co-ordinate Species,
taken together, do not exhaust the Genus, the Division is
obviously imperfect; one or more members remain to be
supplied.  If, on the other hand, they overlap the Genus,




THEIR DEFINITION AND DIVISION.        103
there is somewhere an excess, which ought to be subtracted and referred to another class.  Government cannot
be divided into monarchical, aristocratic, and democratic;
as there, is a fourth class, the mixed. The old Division
of the science of language into Grammar, Logic, and
Rhetoric is redundant, as Logic is concerned with the
laws of thought rather than of utterance, and therefore
properly belongs to the science of mind.
4. The Co-ordinate Species into which a Genus is divided must be reciprocally exclusive; that is, no one of
them  must, in whole or in part, contain any other. In
order to ascertain whether this rule, the propriety of
which is obvious, has been complied with, Logicians apply
the test of:Dichotomy, to which any other Division, however complex, may be reduced. Thus, all the Co-ordinate
Species, B, C, D, E, &c., of any Genus, A, may be represented under any one of the formulas, B and not-B; C and
not-(J; D and not-D, &c. If the Dividing Members are
mutually exclusive, C, D, and E will each be found under
not-B; B, D, and E, under not-C; B, C, and E, under
not-D; and so on. This rule is violated in a Cross Division, where, as we have already seen, the same individuals
may appear under two or more of the Dividing Members;
and also when a Member of a Subdivision is improperly
co-ordinated with the Members of a primary Division.
This last fault, however, is properly ranked under the next
following rule.  The ten Categories of Aristotle are now
generally -condemned as a faulty Division, because the
last six of them are only subdivisions of the fourth, Relation.
" For the Category where is the relation of a thing to
other things in space; the category when is the relation
of a thing to other things in time; action and passion
constitute a single relation, - that of agent and patient'";
5. A  Division must proceed step by step, in regular




104            THE DOCTRINE OF CONCEPTS.
order, from  proximate to remote differences, not overleaping any step which is properly intermediate.  In other
words, each Species, as it appears among the Dividing
Members, must emerge directly from the Division of its,
own Proximate Genus.  Divisio ne fiat per saltum vel hiaturn.  Even the ordinary Division of all natural objects
into animals, vegetables, and minerals is faulty in this respect, its three Species not being properly co-ordinate, as
one step has been omitted. The primary Division should
be by Dichotomy into organic and inorganic things, animals
and vegetables appearing subsequently as a subdivision of
the organic.




THE DOCTRINE OF JUDGMENTS.            105
CHAPTER V.
THE DOCTRINE OF JUDGMENTS;
1. The Predicables and the Categories. - 2. The Quantity, Quality, and Relation of Judgments according to the Aristotelical Doctrine. — 3. The
Hamiltonian Doctrine of Judgments. - 4. The Explication of Propositions into Judgments.
UDGMENT is that act of mind whereby the relation of one Concept to another, or of an individual
thing to a Concept, is determined, and, as a consequence
of such determination, that two Concepts, or the individual
thing and the Concept, are reduced to unity in Thought.
A Judgment expressed in words is a Proposition, the
two terms of the Judgment being called the Subject and
Predicate of the Proposition.  The assertions, iron is malleable, John is brave, determine a relation of agreement
between the two terms involved in each, whereby these
two are conceived as one, and thus expressed, malleable
iron, brave John. On the other hand, the'Judgment,
quadrupeds are not rational, determines the relation of
disagreement between the two Terms, so that one is now
denied to be a Mark of the other, or, what is the same
thing, the negative Mark, irrational, is now attached to
the Concept, quadruped.
As we have already defined a Concept to be a representation of one or more objects through their distinctive
Marks, it is evident that Judgment is the process through
which Concepts are formed. In fact, to judge is to recognize a particular Mark or attribute as belonging, or not
5* 




106          THE DOCTRINE OF JUDGMENTS.
belonging, to a certain object or class of objects. The
Judgment is not, strictly speaking, a comparison, but it
is the mental act of conjoining or disjoining two things
which results from a previous comparison of them with
each other, and a consequent recognition of their agreement or disagreement.  Hence, as Hamilton remarks,
"every Concept is a Judgment fixed and ratified in a
sign"; and, again, "a Concept may be viewed as an
implicit or undeveloped Judgment; a Judgment as an
explicit and developed Concept."  Thus, the Concept
man, which has the four Marks biped, two-handed, rational,
animal, is the combined result of four separate Judgments
which affirmed each of these attributes to be characteristic
of man. Aristotle, the Father of Logic, seems to have
regarded Judgments as the primary elements, out of
which Concepts are formed; for his whole system is based
upon an analysis of Judgments. Modern writers have preferred, as more convenient, and at least equally correct,
the view which has here been taken, that Concepts are
the elements of Judgments. In truth, each presupposes
the other. If it be asked which, in the order of the
mind's development, comes first, the answer is, neither;
but a partial and confused apprehension of a thing, which
is a young child's substitute for a Concept, and which is
first cleared up by a succession of Judgments producing
Concepts properly so called. Judgment is not arbitrary
or dependent upon the will; I must, in Thought, affirm
the union or the separation of the two Terms, according
as the relation of agreement or disagreement is perceived
to exist between them. Hence, the Judgment is always,
at least subjectively, true; the Proposition, which is only
the verbal affirmation, may be either true or false, according as it does, or does not, agree with the mental Judgment.
The mere succession or coexistence of two Thoughts in
the mind does not constitute a Judgment. I may think




THE DOCTRINE OF JUDGMENTS.          107
first of man, and then of animal; but no Judgment takes
place until I affirm in Thought a perceived relation between
them, - until I think man Is animal. Such a relation cannot be perceived between them unless one is regarded as
an attribute or determination of the other; - that is, one
must be regarded as determining, and the other as determined. For if both were viewed as determining, there
would be nothing determined; and both cannot be determined, unless there is something determining them. Hence
there are three necessary parts of a Judgment; -first, the
Concept or thing determined, which is called the Subject;
secondly, the determining or attributive notion, which is
called the Predicate; and, thirdly, that which expresses
the relation of determination between the Subject and the
Predicate is called the Copula. The Subject and Predicate
are called the Termns (termini) or Extremes of the Judgment; and the Copula may therefore be symbolized as a
straight line connecting the two points which are its Terms
or ends.
Though a Judgment necessarily consists of two Terms,
it is nevertheless a single act of mind. There is a separate
act of mind, whereby I perceive or conceive each of the two
Terms taken separately; but it is only one act by which I
perceive and affirm the relation between these two Terms,
and thereby unite them into one process of Thought.
When the mental Judgment comes to be expressed in
words as a Proposition, each of its three parts does not
necessarily appear as a distinct word. The idiom of language often requires or enables us to express two, or even
all three, of them by a single word; but, in accordance
with the general Postulate of Logic, that we must be allowed to express ll that is implicitly thought, we cannot
deal logically with the Proposition until its form is so modified as to allow all the three elements to appear separately.
Moreover, as has been already remarked, the Copula of a




108              THE DOCTRINE OF JUDGMENTS.
Judgment, since it expresses the present union of two
thoughts now before the mind, must always appear as the
present tense of a verb, -  usually of the verb to be: is or
Is NOT is commonly regarded as the only distinctive expression of the logical Copula.  Thus the Propositions, the sun
shines; pluit; cogito, ergo sum; he came yesterday; John
will arrive; if reduced to their logical form  as Judgments,
must be thus expressed: the sun is shining; the rain  is
falling; lam  thinking, therefore I am  existing; he is the
person who came yesterday; John is he who will arrive.  In
each of these cases, all that precedes the Copula, is or am,
is the Subject, and all that follows the Copula is the Predicate.* The substantive verb, when used as a Copula,
* Hence we perceive how unfounded is the objection which has been made
to the science of Formal Logic, on the ground that it does not expound the
whole theory of reasoning, because it furnishes no explanation of an inference so obvious as this:A is greater than B;
therefore, B is less than A.
But here the Predicate is not B or A, but " greater than B" and " less than
A "; the meaning of these two expressions, therefore, belongs to the Matter
of Thought, with which, as a logician, I have nothing more to do than with
the meaning of A or B taken alone. That these two expressions have a
correlative meaning, is a fact which belongs to the science of language rather
than to that of Thought. Instead of regarding one of them as an inference
from the other, it would be more correct to say that the two are equivalent
statements of the same fact; they express one relation between two Concepts. That two lines converge from A to B is only another way of saying
that the same two lines diverge from B to A; there is but one thing to be
said, though there are two modes of saying it.  In like manner, we may say,
but we do not argue, that
Socrates is the husband of Xantippe;
therefore, Xantippe is the wife of Socrates.
God alone is omnipotent;
therefore, no one is omnipotent but God.
In such cases, the second proposition is an interpretation of the preceding
one, not an inference from it. We learn from a dictionary, not from a
treatise on Logic, what different phrases are equivalent statements of one
and the same Thought.




THE DOCTRINE OF JUDGMENTS.            109
never means exists; but the idea of existence, when it is
intended to be conveyed, forms the Predicate. He is, in
the sense of he exists, is logically interpreted, he is existing.
Fuit Ilium; Troy is that which has been, - is that which
exists no longer.
Logicians generally maintain that the Copula is precisely
equivalent to the mathematical sign of equality. In many
cases, this is undoubtedly true. If the Predicate is simply
a definition of the Subject, or if the Proposition in any
manner expresses the entire equivalence of its two Terms,
it can then be expressed in the manner of an equation.
Thus, Saltpetre =  nitrate of Potash; Alexander = the son
of Philip.  But the two Terms of a Judgment are not
always convertible or equivalent.  What is thought and
expressed is always a relation between the two Terms, but
is not always a relation of equivalence or identity. Sometimes, as in a negative Judgment, it is a relation of disagreement; sometimes the Predicate expresses merely one
attribute of the Subject, and then the relation is that of a
whole to its part, since only a portion of the Subject's Intension is affirmed of the Subject. When we say, the apple
is red, we do not mean apple = red, but only that a red
color is one out of many attributes of the apJple, - is a part
of its Intension. In this case, the Copula signifies rather
possession, to have, than equality, to be. The form of the
Judgment as thought is, the apple has a red color as one of
its many attributes.
It is evident, then, that there are two classes of Judgments, properly distinguished by Dr. Thomson as Substitutive and Attributive. In Substitutive Judgments, the sign
of equality may be used as the Copula; the Predicate is
properly identified with the Subject, or made convertible
with it, and therefore every attribute of the one may also
be affirmed of the other.  If A =  B, then every x of A
is also x of B; all that is true of I "Alexander " is also true




110          THE DOCTRINE OF JUDGMENTS.
of "the son of Philip."  But if the Judgment is only Attributive, the sign of equality cannot be used; the two
Terms are not convertible, and consequently it cannot be
inferred that they possess the same attributes. Sweetness
or sourness is a quality of the apple, but not of the red
color which belongs to the apple.
The distinction here explained is a valid and important
one in respect to Judgments considered simply as such, or
as mere phenomena of Thought, irrespective of any use to
be subsequently made of them in reasoning or other mental
processes.  In Attributive Judgments, the Predicate is
actually thought only connotatively, as a Mark or attribute
of the Subject, and not denotatively, as the name of a class
of things. And hence Mr. Mill is led to maintain, that
such Judgments never express truths of classification, and,
therefore, that the generally received doctrine of Predication, that it consists in placing something in a class or excluding something from a class, is entirely unfounded.
"When I say that snow is white," he argues, " I may and
ought to be thinking of snow as a class; but I am certainly
not thinking of white objects as a class; I am thinking of
no white object whatever except snow, but only of that, and
of the sensation'of white which it gives me."
All this is granted. At the moment of forming the Judyment, white is not consciously before the mind as the name
of a class of things. We then think of it only connotatively,
- only as a Mark. But it is still true that we originally
learned the meaning of the word white not only as a Mark
connoting a quality, but also as a Concept denoting a class
of things, - namely, white objects; otherwise, it would not
be, what it certainly is, a Common Name of snow, milk,
chalk, and many other things. And though this its denotative meaning - its Extension - is not consciously before
the mind when it is used as a Mark or as a Predicate, it is
still there potentially, and must be brought out or expressed




THE DOCTRINE OF JUDGMENTS.           111
when we attempt to found an inference upon this Judgment, or to employ.it as one of the premises in a syllogism.
To borrow Mr. Mill's own instance, —if I am in doubt
whether Chimborazo is snow-covered, I may reason
thus:
All mountains of a certain altitude, and whose summits
are perpetually white, are snow-covered.
But Chimborazo's lofty summit is always white, -that
is, it is one of this class of mountains.
Therefore, Chimborazo is snow-covered.
As already observed (p. 64), "the distinction between
Concepts and Marks is not absolute, but relative; they
may be used interchangeably."  That a Concept or Common Name is sometimes used only as a Mark, or with no
eonscious reference at the moment to its denotation, is
surely no proof that it is always so used, or even that the
denotative meaning, or Extension, is not potentially present
in this very case, so that it may be revived, if need be,
and an inference founded upon it. Because words are
sometimes used symbolically, or without spreading out in
Thought all their signification, it does not follow that they
are. always so used, or that such use of them may not be
checked, and kept from falling into error, by occasionally
bringing up into consciousness what they always potentially
signify in Thought. It follows, then, that although a Judgment, as actually thought, may not be a truth of classification,
and therefore that the Copula may not be equivalent to the
mathematical sign of equality, yet it may always be reduced
to the form of such a truth, and then this mathematical
sign fully expresses its proper form; and in reasoning,
such a reduction is generally necessary. Though it is not
true that apple = red, it is true that apples =- some red
objects; or, as it is more commonly expressed by Conversion, some red objects are apples.




112          THE DOCTRINE OF JUDGMENTS.
1. THE PREDICABLES AND THE CATEGORIES.
In his analysis of Judgments, Aristotle was led to con.
sider how many kinds of Predicates there are, when
viewed relatively to their Subjects; —in other words, to
determine the Second Intentions of Predicates considered
in relation to Subjects. Thus was formed his celebrated
doctrine of the Predicables, - a doctrine which was considerably modified, but not improved, by his followers,
Porphyry and the Schoolmen. According to Aristotle,
every Judgment affirms or denies one of four relations of
a Predicate to its Subject. It expresses either,-1. the
Genus, i. e. the class under which it is included, as when
we say, man is an animal; or, 2. the Definition, which,
as we have seen, is the Genus and the Specific Difference
taken together, and may be reduced to an enumeration
of all the essential Marks of the Subject, as, a Carnivor
is a flesh-eating Mammal; or, 3. a Property, that is, some
peculiar attribute of the Subject, belonging to it universally, belonging to nothing else, and yet not regarded as
essential to it, for we could conceive of the thing without
it, - as polarity is a Property (proprium) of the mnagnet,
and risibility of man; or, 4. an Accident, which is an
attribute that happens to belong to the Subject, but, as
unessential, is separable from it, as man is learned.
Two of these Predicables, namely, the Definition and
the Property, are convertible with the Subject, or may
change places with it; and of these two, the former expresses the whole Essence (all the essential qualities), while
the latter, strictly speaking, is no part of the Essence; for
we can conceive of man as not having the attribute of
risibility, but we cannot conceive of him as deprived of
rationality. So, the magnet can be conceived of without
polarity, as its magnetic or attractive power was known
long before its property of pointing to the north was dis



THE PREDICABLES AND THE CATEGORIES.         113
covered; but its magnetic or attractive quality is essential
to our conception of it. Of the two other Predicables,
Genus and Accident, neither is convertible with the Subject; and, again, the former expresses a part of the Essence,
and the latter does not.  Thus we have the following
scheme of the Predicables:
Definition   expressing the whole Essence  convertible
Property   expressing no part of the Essence  with the Subject.
Genus      expressing a part of the Essence  inconvertible
Accident   expressing no part of the Essence  with the Subject.
Porphyry and the Schoolmen modified this analysis, but
did not improve it, in their attempt to make it conform
to their philosophical doctrine of Realism. The Realists
maintained, that Universals or Species are not mere classes
of things arbitrarily formed by the mind, but are real existences, with perfectly well-defined limits, existing in things,
and yet independently of them and of our conceptions
of them.  Each Universal is the common and essential
element - the Essence - of all the individual things which
are included under it and denoted by its Name.  Whatever other attributes these individuals possess do not belong
to their Essence, but are considered as their Properties
or Accidents. According to this view, Species has a determinate and fixed meaning, corresponding very nearly
to what we have termed the Infima Species; it was
absolutely the lowest class to which anything can be referred, and not merely the lowest relatively, as we have
defined it. Every Specific Difference, moreover, signifies
absolutely the attribute whereby a given Species is distinguished from every other Species of the same Genus.
Both Species and Genus are thus supposed to be absolutely
determined, following the patterns or archetypes of them
which exist in the Divine Mind, and which presided over
their creation, instead of being mere creatures of our
Thought, and springing from arbitrary classifications, ac



114          THE DOCTRINE OF JUDGMENTS.
cording to which the same individual may be referred to
any one of several different Species, and again the same
Species to one Genus or another, according as it suits our
purpose.  The Realists maintained that the hierarchy of
classification is not fluctuating and arbitrary, formed by
man for his own convenience, and therefore always changing to suit his ever-varying purposes;- but they held that
it resulted from the real nature of things, as determined
by the Creator, and therefore is a perfect and immutable
copy of the Divine Thought.  To adopt Mr. Mill's language, "they did not admit every class which could be
divided into other classes to be a Genus, or every class
which could be included in a larger class to be a Species.
Animal was by them considered a Genus; and man and
brute, co-ordinate Species under that Genus: biped would
not have been admitted to be a Genus with reference to
man, but a proprium  or accidens only. It was requisite,
according to their theory, that Genus and Species should
be of the Essence of the Subject. Animal was of the
Essence of man; biped was not. And in every classification, they considered some one class as the lowest or
Infima Species; man, for instance, was a lowest Species.
Any other divisions into which the class might be capable of being further broken down, aa man into white, black,
and red man, or into priest and layman, they did not
admit to be Species." They wrongly assumed, -1. that
the Divine Mind classifies at all (see p. 15); 2. that it
would be possible for man to follow the thought of the
Creator so far as to copy without error such classification,
even if it existed; 3. that there is no occasion, even for
purposes of human science and convenience, to distribute
the same individual things into different systems of classification, assuming various Grounds of Division, according
to the special ends in view.
Adopting the Realist hypothesis, the Schoolmen distin



T.HE PREDICABLES AND THE CATEGORIES.      115
guished these five Predicables, - Genus, Species, Difference, Property, and Accident.  Comparing this list with
that of Aristotle, we perceive that Definition is. omitted,
being resolved into its two elements, Genus and Specific
Difference, both of which are admitted into this scheme,
and that Species also is added. The Species here intended
is the Infima Species, or proximate class, and is usually defined as being the whole Essence of the individuals of
which it is predicated.  Difference is also taken absolutely, being regarded as predicable of this class and of
none other, - that is, as serving to distinguish this Species,
not merely from the other Species in the same Genus, but
from  all others whatever. Aristotle omitted Difference
from his list, because, as he says, it is "of the nature of
Genus," or, as we should say, it is interchangeable with
Genus. In truth, each of the two elements of a Definition
is a Genus; they are two communicant or overlapping
Genera. But it is more convenient to regard one as determined, and the other as determining, - that is, one as
Genus and the other as Difference.  Thus, man is a rational animal; here are two Genera, rational beings and
animal beings, which partially include, and partially exclude, each other.  As there are some rational beings
which are not animal (angels, for instance), so there are
some animals (brutes) which are not rational; but man is
both animal and rational, - that is, he is the common part
of the two overlapping Genera. He is, therefore, a rational
animal being, or, what is precisely the same thing, he is an
animalized rational being. In the former case, animal is the
Genus and rational is the Specific Difference; in the latter
case, this is reversed, rational
being the Genus and animal
the Difference. Thus:Let A = animal;                         C     B
B -  rational;
then, C  - rational animal.




116          THE DOCTRINE OF JUDGMENTS.
Aristotle evidently perceived, what his followers did not,
that there is no real distinction between Genus and Difference; that both of them are, in truth, Genera; and hence
that Difference, being of the nature of Genus, cannot be
admitted into the list of distinct Predicables.
Having ascertained the Second Intentions of Predicates,
which are the Predicables, Aristotle attempted to carry the
analysis of Judgments one step farther, by determining their
First Intentions, and was thus led to form his celebrated
list of the ten Categories or Predicaments. In other words,
having determined how many sorts of Predicates there are
in relation to their Subjects, he next inquired how many
and what particular things may be predicated of any Subject. Considering every Judgment as the answer to a
question, he sought to ascertain how many and what different questions may be asked concerning a Subject, - what
are the several determinations of which it is capable. The
inquiry evidently concerns the Matter, and not the Form,
of Thought, and therefore does not properly fall within the
province of Logic, which is exclusively occupied with Second Intentions. But the Categories may be regarded as a
curiosity in the history of the science, and as a monument
of the genius of its founder for abstract thought and comprehensive  generalization.  Great ingenuity has been
wasted upon the discussion of them by his followers. For
many centuries, during which the boundaries of the science
were not so strictly defined as they now are, the doctrine
of the Categories occupied a prominent place in every
treatise upon Logic. A very brief explanation of it will
answer our present wants.
The Greek verb from which category is derived properly
signifies to accuse, or to affirm something of any one, and
hence, to predicate. But the noun has been diverted by
logicians from signifying affirmation or predication, and
applied to a list or class of things of the same kind which
may be predicated of any Subject.  Aristotle affirms that




THE PREDICABLES AND THE CATEGORIES.            117
there are ten Categories, or classes of things that may be so
predicated, - namely, 1. Substance; 2. Quantity; 3. Quality; 4. Relation; 5. Place; 6. Time; 7. Posture; 8. Possession; 9. Action; 10. Passion.  According to a fashion
very common among the Scholastic logicians, of manufacturing Latin verses as aids to the memory in retaining the
technicalities of the science, the several Categories are indicated in the two following lines, though in a somewhat
different order from  that given above, as shown by the
numerals prefixed.
1   2   3     4      9    10
Arbor sex servos fervore refrigerat ustos;
5   6   7         8
Ruri eras stabo, nec tunicatus ero.
The four Predicables, argues Aristotle, -" the Accident,
the Genus, the Property, and the Definition, — will always
be in one of these Categories [or classes]; since, through
these, all propositions signify either what the Subject is, or
how much it is, or what sort of a thing it is, or some one of
the other Categories"; as, what relation it bears to some
other thing, or its place, its time, its posture, what it has,
or does, or suffers. Adopting Aristotle's own examples of
predication under each of these classes, we may, for instance, affirm  of anything, -- 1. under the Category of
Substance, that it is a man, a horse, or the like; 2'. under
that of Quantity, that it is two cubits long, three cubits,
&c.; 3. under that'of Quality, that it is white, grammatical, &c.; 4. under that of Relation, that it is double, half
as large, greater, &c.; 5. under that of Place, in the
Lyceum, in the Forum, &c.; 6. under that of Time, yesterday, last year, &c.; 7. under Posture, standing, seated,
&c.;  8. under Possession, having shoes or armor, &c.;
* Many writers have interpreted Aristotle's seventh Category, KE0(rOat, as
Situation. But, as Situation is identical with Place, this interpretation makes
the'seventh redundant and unnecessary. Besides, the examples here selected
prove that Aristotle here understands Kceo-Oat to signify Posture.




118          THE DOCTRINE OF JUDGMENTS.
9. under Action, it cuts, burns, &c.; 10. under Passion,
it is cut, is burned, &c.
The purpose of Aristotle in framing his scheme of the
Categories, and the nature of the Categories themselves,
have been very differently understood by different writers,
who, in commenting upon them, seem to have had much
more reference to their own systems of metaphysical philosophy than to a fair interpretation of the text of their
author. Thus, Kant assumes that Aristotle's intention was
to form a complete list of the a priori conceptions of the
intellect, or of the forms which the mind imposes upon
things by its own mode of thinking them. Under this interpretation, he asserts very truly, that the analysis is not
formed upon any one principle; that the enumeration is
incomplete; that empirical notions are intruded among the
pure, and derivative among those which are original.
Mr. Mill supposes that the Categories are c" an enumeration of all things capable of being named, -an enumeration by the summa genera; that is, the most extensive
classes into which things could be distributed; which,
therefore, were so many highest Predicates, one or other
of which was supposed capable of being affirmed with
truth of every namable thing whatsoever."  Taken in
this light, he finds, of course, that the list is both redundant and defective; that Relation includes Action, Passion,
and several others; and that "mental states," which, in
Mr. Mill's opinion, are neither substances nor attributes,
are omitted entirely.
Sir William Hamilton's interpretation of the Categories
agrees very nearly with that of Mr. Mill. He finds that
they are an enumeration of the highest genera of Being
or Existence, - that is, of all things whatsoever; and,
under this view, justly objects that Being ought first to be
divided by dichotomy, into absolute and relative Being,
the first of which coincides with Aristotle's first Category,




THE PREDICABLES AND THE CATEGORIES.        119
that of Substance, while the second includes the' other
nine; and that the last six may all be reduced to the
fourth, that of Relation.. Trendelenburg, who is followed by Mr. Mansel, maintains that the Categories are, to adopt the language of the
latter, "an enumeration of the different modes of naming
things, classified primarily according to the grammatical
distinctions of speech, and gained, not from the observation
of objects, but from the analysis of assertions." This
doctrine seems to be correct; but it is obviously irrelevant,
for it explains only the genesis, not the nature, of the
Categories. To show the source of the classification, or
how Aristotle was led to make it, is very different from
explaining the nature of the things classified, and the real
distinctions between the several classes.
And the ground for the other criticisms falls away when
it is considered, that the distinction between the Form and
the Matter of Thought -that is, between Logic and
Metaphysics - is but very imperfectly preserved by Aristotle. But although much of what properly belongs to
Metaphysics is intruded into his treatises upon Logic, and
vice versa, it is never considered there primarily in its
metaphysical nature, but only in its logical relations. The
doctrine of the Categories, as conceived by him, is not
an attempt to enumerate the highest classes into which
things in general can be distributed; for this would be a
purely metaphysical speculation, and, as such,-open to
criticism on metaphysical grounds. But it is a classification
of things in so far only as these things are predicates,that is, of things considered merely in one of their logical
aspects.  To such a classification, metaphysical objections,
like those of Kant, Mill, and Hamilton, are evidently
irrelevant. For instance: - metaphysically, Place is included under Relation, for it is the relation of a subject
to a fixed point in space. But, logically, these two Cate



120          THE DOCTRINE OF JUDGMENTS.
gories are distinct, for it is one thing to assign a Subject
to a fixed point in space; a second, to assign its relation to
another thing in quantity or quality; and a third and fourth,
to assign its quantity and quality absolutely. Aristotle's
scheme or general conception of the Categories may be
censured, as depending on a mixture of two incongruous
aspects of Thought, the logical and the metaphysical; but
for all that appears, it is as well executed as such a hybrid
scheme can be.
2. THE QUANTITY, QUALITY, AND RELATION OF JUDGMENTS, ACCORDING TO THE ARISTOTELIC DOCTRINE.
The question now arises, how many things can be determined about a Judgment considered merely as such,
that is, by considering its mere Form, without reference
to the Matter of the Concepts which are its Terms. In
the first place, we may inquire concerning the number
of objects about which we judge, and thus determine the
Quantity, or Extension, of the Judgment. Secondly, we
may ask what sort of a Judgment we form respecting the
two Terms,  that is, whether we affirm a relation of
agreement or of disagreement between them; we thus
ascertain the Quality of the Judgment, or whether it is
affirmative or negative. Thirdly, we may inquire respecting the different modes in which a relation of agreement
or difference between the two terms may be affirmed, and
thus determine what is called the Relation of a Judgment.
In this manner are answered the three questions which
may be asked concerning any Judgment or Proposition
whatsoever, - Quanta 2 qualis. quce?
A fourth question has generally been asked by logicians,
as to the degree of certainty with which a Judgment is
affirmed. This was called the Modality of the Judgment,
being the mode or measure in which we hold it to be true.




THEIR QUANTITY, QUALITY, AND RELATION.    121
Several degrees of it were usually distinguished, according
to the following formulas:Judgments are either
Pure       A is B.       AssertoricaL.
or        A may be B    Contingent or Problematic.
~Moda.l    ) A must be B.   Necessary..A cannot be B. Impossible. Demonstrative.
A can be B.   Possible.
But the whole doctrine of Modality is now rightfully
banished from  Pure Logic, as it evidently belongs not to
the Form, but to the Matter, of Thought.  Any number
of Modal Propositions may be firamed, all of which would
have as good a claim to consideration as those just specified.
Thus, A  is rightfully B, A  is justly B, A  is maliciously
B, are as good Modals as A is possibly B, or A is certainly
B. In truth, since the Copula in Logic is only a sign
of equality, or the present tense of the verb to be, the
qualifying word must be logically regarded as a portion
of the Predicate; thus, A is a possible, or a necessary B.
Hence it is manifest that the signs of Modality belong
to the Matter of the Thought, with which here we have
no concern.
In respect to Quantity, according to the Aristotelic
logicians, Judgments are either Universal or Particular.
A Universal Judgment is one in which the Predicate is
affirmed of the whole Subject taken distributively. Thus,.
All men (i. e. each and every man) are mortal; 2No quadruped (i. e. not any one out of all quadrupeds) is rational;
are Universal Judgments.
A Particular Judgment is one in which the Predicate
is affirmed only of a part - an indefinite part — of the
Subject. For example: Some men (i. e. some at least,
some -I know not how many) are learned; Some trees are,zot deciduous.
On the other hand, all taken collectively (as, All the
Greeks — i. e. the Greek nation - conquered the Persians),
6




122           THE DOCTRINE OF JUDGMENTS.
is the sign of a Singular or Individual Judgment, in which
a Predicate is affirmed of one thing, or of a class of things
taken as one whole. But as here also the Predicate is
affirmed of the whole Subject, Singular Judgments, for all
logical purposes, are considered as Universals.
In like manner, some certain - some, a definite partembracing these very cases which I am thinking of and
no other- is the sign, not of a Particular, but of a
Singular Judgment, and is therefore properly ranked with
Universals.' Individual names," says Mr. Mansel, " are distinguished as individua signata, expressed by a proper name,
as Socrates; individua demonstrativa, by a demonstrative
pronoun, hie homo; individua vaga, by an indefinite pronoun, aliquis homo, quidam homo."  But he properly objects that this last class, the indefinites, ought to be considered as Particulars rather than as Singulars.'6 If we say
quidam conscionatur, quidam legit, there is no evidence that
the same person is spoken of in the two propositions; while
Socrates, except by a mere quibble, will always designate
the same person. There may, indeed, be two persons of
the same name; but, in this case, the name fails to accomplish the intended distinction, and we must specify,- Socrates the son of Sophroniscus."
The logicians formerly distinguished another class of
Judgments as Indefinite, meaning those in which the Subject, having no sign or predesignation of Quantity affixed
to it, is not expressly declared to be either Universal, Singular, or Particular.  Thus, Elephants are sagacious animals; --  Learned men are to be found at Oxford.  But this
omission of the predesignation of Quantity is merely an
accident of expression, and therefore belongs only to Propositions, and not to Judgments, which are always thought as
having some one of the three specified kinds of Quantity.
According to the Postulate of Logic, which requires us to




THEIR QUANTITY, QUALITY, AND RELATION.    123
state explicitly all that is implicitly thought, the two examples just given are logically stated thus: All elephants are
sagacious; —Some learned men are found at Oxford.
An improved classification or nomenclature of Judgments
in respect to Quantity is proposed by Sir William Hamilton.
Since both Universals and Singulars have a determinate or
known Quantity, - namely, the whole either of a class or
of a unit, - he would call them Definite Judgments; while
Particulars, expressing an indeterminate or unknown part
of a whole, should be called Indefinite.  But as confusion
might arise from abandoning technical terms which have
been so long in use, we shall continue to distinguish Judgments in respect to Quantity as either Universal or Particular, Singular being ranked with the former, and the latter
expressing an indefinite part.
In respect to Quality, Judgments are distinguished as
either Affirmative or Negative, according as they affirm a
union or a disjunction of their two Terms. In every real
Negative Judgment, the negative particle, wherever in
the sentence it may appear, belongs only to the Copula;
since the question always is, whether a union of the
Subject and Predicate is, or is not, affirmed.  Hence the
presence of a negative particle in the proposition is not a
sure sign that it is a Negative Judgment, for this particle
may belong in thought to one of the two Terms. Thus,
" Nil admirari prope res est una, Numici"; —
" Not to admire is all the art I know"; —
"2Eneas potuit - non vincere Turnum ";are Affirmative Judgments. This, also, is an affirmation: -
" Una salus victis - nullam sperare salutem."
"The only chance of preservation for the vanquished is, not to hope for
preservation."
Hence, by an easy artifice, a Negative Judgment may
be changed, in Form, to an Affirmative one of equivalent




124             THE DOCTRINE OF JUDGMENTS.
meaning, by taking off the negation from the Copula, and
affixing it to the Predicate. Thus, X is not Y, is the
same as, X is not-Y; for if the universe is divided into
only two parts, Y and not- Y, the exclusion of X from one
of these parts is necessarily an inclusion of it in the other.
And as two negatives cancel each other, an Affirmative
may be made to take the Form of a Negative Judgment,
by negativing both the Copula and the Predicate.  X  is
Y, may be changed into, X  is not not-Y.  "The -soul is
indivisible," is equivalent to " The soul is not divisible";
and " All the righteous are happy," is the same as " Not
any of the righteous are unhappy." We shall soon see
what use can be made of this artifice in the doctrine of
Immediate Inference.
By combining the Quantity and Quality, as there are
two kinds of each, we have four distinct forms of Judgments, which are designated by the four vowels A, E,
I, 0.  To aid the memory, these distinctions have been
expressed in this Latin distich: —
Asserit A, negat E, sed universaliter ambse,
Asserit I, negat 0, sed particulariter ambo.
These lines have been thus translated into English doggerel:iA, it affirms of this, these, all,
Whilst E denies of any;
I, it affirms, whilst O denies,
Of some (or few or many).*
Examples of these Propositional Forms, as they are
called, are given in the following table:Symbols.     Examples.         Quality.    Quantity.
A. All animals are sentient.  Affirmative. Universal
E. No plant is sentient.  Negative.
I.  Some men are honest.  Affirmative.
0. Some trees are not maples. Negative.   Particular.
It is suggested by Hamilton, with great plausibility, that these four
letters were selected because A and I are the first two vowels in affirmo, E
and 0 the two vowels in nego.




THEIR QUANTITY, QUALITY, AND RELATION.    125
Observe, however, that though the predesignation all
is the sign of A, a Universal Affirmative, not all is not
the sign of E, a Universal Negative, but is always Particular, and leaves the Quality ambiguous, as it may be
either Affirmative or Negative. Not all denies universality, and is a direct assertion that some are not, and an
implied assertion that some are. Thus, Not all is gold that
glitters, asserts directly that some glittering things are not
gold, and, by implication, that some glittering things are
gold.  "Not every one who says unto me, Lord! Lord!
shall enter into the kingdom  of Heaven"; — i. e. some
who say this shall not enter.
The predesignation some is likewise ambiguous. It may
mean some at least,- -i. e. some, perhaps all; or it may
mean some at most, —i. e. some, not all. Thus, a chemist
might say, Some metals are dissolved by acids, meaning
" Perhaps all metals are thus soluble, but at any rate, some
are."  On the other hand, he may say, Some metals are
malleable, meaning, some - excluding all, for he knows that
some metals are not malleable. In a Negative Judgment,
if we. consider some to mean perhaps all, it is evident that
"' Some X is not Y" may be construed " Perhaps no X is
Y"; but if some signifies not all, then some is not excludes,
or is inconsistent with, none-not one.  The wholly indefinite meaning, some, perhaps all, is the one generally received in Logic; the other meaning is called by Sir W.
Hamilton semi-definite, because, by excluding all, it is so far
definite. Though this latter meaning has been generally
neglected by logicians, it leads, as we shall see hereafter,
to some important additional inferences, and modifies, to a
considerable extent, the old doctrines concerning Opposition.
Hitherto we have considered the Quantity of the Judgment only, and we have now to consider the Quantity of
the two Terms as affected by the Judgment in which they
stand. A Term is said to be distributed when it is taken




126          THE DOCTRINE OF JUDGMENTS.
distributively, or in the whole of its Extension,- that is,
when it is affected, or should be affected, by the predesignations all, each, none, &c.; it is not distributed when. it' is
taken only in an indefinite part of its Extension, - as
usually signified by the predesignations some, not all, &c.
The received or Aristotelic doctrine upon this matter is,
that the distribution of the Subject depends upon the Quantity of the Judgment, thus; — in Universal Judgments, the
Subject is distributed, but in Particular Judgments, it is
not distributed.  1No unjust action is expedient;- this is a
Universal Proposition, and its Subject is evidently distributed, as the meaning is, not any one out of all unjust
actions is expedient.  But in the Particular Proposition,
Some men are learned, it is obvious that tile Subject, men,
is not distributed.
On the other hand, the distribution of the Predicate
lepends upon the Quality of the Judgmeiit, thus; -in
Negative Judgments, the Predicate is distributed, but ill
Affirmatives, it is not distributed.  This rule is evidently
founded upon the doctrine that all predication is classification; and consequently, that when we affirm, we thereby
include the Subject in the class denoted by the Predicate,
not meaning that the Subject constitutes the whole of that
class, but only a part of it; and that, when we deny, we
thereby exclude the Subject wholly, or from any part of
the class. Thus, when we say, "' Men are animals," we
mean, "Men are some animals," since it is not true that
all animals are men.  On the other hand, when we say,
"No man is immortal," we mean to exclude man from
every part of the class of "'immortal beings," so that no
immortal whatever can be human. And even in the case
of Particular Negatives, as, "Some Frenchmen are not
Parisians," we still mean absolute or total exclusion,that not any Parisian whatever is one of the "Some
Frenchmen "- say, inhabitants of Lyons - whom we were
speaking of.




THEIR QUANTITY, QUALITY, AND RELATION.    127
According to this doctrine, the four fundamental Judgments, if the statements are intended to convey the whole
Thought which is implied in them, must be thus expressed: -
A. All X are some Y. All animals are some sentient
beings.
E. No X is any Y. No plant is any sentient being.
I. Some X are some Y. Some men are some honest
persons.
O. Some X are not any Y. Some trees are not any maples.
Hence the rule for the distribution of the two Terms
in a Judgment may be thus briefly expressed: —In A,
only the Subject is distributed; in 0, only the Predicate;
in I, neither; in E, both.
Those who maintain this doctrine are perfectly aware,
of course, that the Predicate is sometimes taken universally
in Affirmative Judgments, as when we -predicate either
Definition or Property; but they assert that this results
from considering the Matter, not the Form, of the Judgment, and therefore is not entitled to notice in Pure Logic.
And they further maintain, that the Predicate is never
quantified particularly in a Negative Judgment. Sir W.
Hamilton, however, as we shall see, has denied both portions of the doctrine, and, by substituting for it his own
theory of 1" the thoroughgoing quantification of the Predicate," has revolutionized the whole science of Logic.
In respect to the Relation of the Predicate to the Subject,
Judgments are divided into simple or absolute, and conditional.  In the former, which are technically called
Cateyorical, the Predicate is conceived as a Mark, and is
therefore absolutely affirmed or denied of the Subject,
there being no other ground or reason for the attribution
or denial than what is contained in the Subject itself. All




128           THE DOCTRINE OF JUDGMENTS.
Categorical Judgments are included under these two formulas, A is B, A is not B. Conditional Judgments are
those in which the Predicate is affirmed or denied of the
Subject, not absolutely, but only under some condition
or prerequisite,  This condition may be conceived as primarily affecting the Subject, or the Predicate, or both;
and hence we have three forms of Conditional Judgments,
distinguished as Hypothetical, Disjunctive, and Dilemmatic
or Hypothetico-Disjunctive. Thus, in respect to Relation,
we have four kinds of Judgments, as distinguished in the
following table.
Categorical.                  A is B, or, A is not B.
( ypothetical.       If A is B, A is C.
Dilemmatic, or
( Hypothetica-Disjurctive.  If A is B, then C is either D or E.
In a Categorical Judgment, Maan ts mortal, there is
evidently no ground or reason for the attribution but an
internal one; the Mark of mortality is conceived as an
essential attribute of man under all circumstances or conditions whatsoever.  But in each of the other forms, the
attribution is conditional. In the Hypothetical Judgment,
If death is a transition to a happier life, then it is desirable,
we do not affirm  absolutely that death is desirable, but
affirm  it only under a condition affecting the Subject,
death.  In a Disjunctive, as, Every deliberate action is either
good or evil, the condition evidently affects the Predicate,
as neither of its two forms is affirmed absolutely, but
either is affirmed only on condition that the other is denied.  The Dilemmatic, as it has two conditions, the
one affecting the Subject and the other the Predicate, is
obviously a combination of the two preceding forms, and
is therefore properly called the Hypothetico-Disjunctive.
All Hypothetical Judgments obviously consist of two parts,
the first of which is called the Condition or Antecedent,
and the second, the Consequent; and the assertion X




THEIR QUANTITY, QUALITY, AND RELATION.    129
Judgment is, that if the Condition exists, the Consequent
follows.
A Conditional Judgment, though seemingly complex, is
really simple, and expresses only a single act of Thought;
it contains but one assertion. Thus, in the Hypothetical
just cited, we do not assert that death is a transition, or
that death is desirable; but only, if it is a-transition, then
it is desirable. Hence the affirmation is evidently single,
and the particles'if and then form the Copula of this
Judgment, as they connect its two parts together. In a
Disjunctive, either is and or is form the Copula, which
reduces an apparently complex Judgment to a simple one.
Sometimes where and there take the place of either, or,
in a Conditional Judgment; as, where fire is, there is heat;
where light is, there is shadow.
In Hypotheticals, the Consequence, or tie which binds
together the Antecedent and the Consequent, may be
either mediate or immediate. It is Mediate, only when
there is nothing in the Terms of either of the two parts
which binds them together; as when we say,
If A is B, C is D.
jf the air is still and cloudless, the dew will fall.
If God is just, sinners will be punished.
In such cases, the Consequence may be valid, but it is
not Immediate; for, as there are four distinct Terms, the
two Parts have no common Term, and are therefore connected only by some unknown cause, or by:what is in the
mind, but is not expressed. The unexpressed medium,
which binds the two Parts together in the last case, is our
knowledge that God governs the world, and that justice
consists in rewarding the good and punishing sinners; therefore, if God is just, sinners will be punished.
The Consequence is Immediate, when there are only
three Terms in the two Parts, so that, since one of these
6*                              I




130           THE DOCTRINE OF JUDGMENTS.
Terms is necessarily repeated, it forms an immediate connection of the Parts with each other.  In order that
there may be this repetition of one of the Terms, either
the two Parts must have the same Subject, or the same
Predicate, or the Predicate of the first must be the
Subject of the second, or the Subject of the first must
be the Predicate of the second. In other words, the
Hypothetical must appear under one of the four following
formulas.
If A is B, A is C.    If men do wrong, they deserve punishment.
If A is B, C is B.    If metals are fusible, gold is fusible.
If A is B, B is C.    If patience be a virtue, virtue may
be painful.
If A is B, C is A.    If happiness is mere freedom from
pain, insensibility is happiness.
In each of these cases, the Consequence is Immediate,
because it results from a general rude, which is presupposed
in the Proposition that is before us, and may be evolved
from it without any further appeal to experience. Because
"all C is A," we can immediately infer that, "if A is B,
C is B "; or conversely, because the latter Proposition
is universally true, the- former can be deduced from it by
necessary implication. I-f the earth is immovable, and is
lighted in all parts by the sun, the sun revolves round it;this is true so far as concerns the dependence of the one
Proposition upon the other, though either Proposition,
taken separately, is false. Hence, we do not deny a
Hypothetical Judgment by denying either or both of its
parts, but only by denying the Consequence of one fi-om
the other. This is usually done, in Latin, by placing the
negation at the beginning.
Non si miserum fortuna Sinonem
Finxit, vanum etiam mendacemque improba finget.




THEIR QUANTITY, QUALITY, AND RELATION.    131
In English, we may deny a Hypothetical by substituting
although, or some equivalent, for if in the Reason, and
then negativing the Consequent.
If you eat of the forbidden fruit, you scall die.
Although you eat, tic., you shall not die.
Or the Proposition may be thus denied.
It is not true that if you eat, &c.
Disjunctives are denied in. the same manner.
Conditional Judgments can be reduced to Categoricals,
though, for logical purposes, it is more convenient to retain
them in the Conditional form. The Condition is equivalent to a limitation, and therefore can always be expressed
by a limiting adjective (see page 143). In the formula,
If A is B, then A is C, it is not asserted that all A is C,
but only those A which are B.  Let d represent such A;
then the equivalent Categorical formula is, dA  are C.
To take a concrete instance: —If the iron is mancnetic, it
has the attribute of polarity; this is equivalent to the
Categorical Judgment, magnetic iron is polar. Conversely,
if any Categorical Judgment has its Subject limited by a
qualifying word, the limitation can be resolved into a
condition, and the Judgment thus becomes Conditional.
Thus, Virtuous men are happy, is equivalent to If men are
virtuous, they are happy.
Disjunctives are reduced in a similar manner to as many
Categoricals as there are disjunct members of the Predicate. Thus, -
(All those A which are not B are C,
A is either B br C-                  and
All those A which are not C are B;
and if d represents the former and f the latter, we have
dA are C, and fA are B.  Even then, the Thought is not
complete until we add, dA + fA =  all A.  It amounts
to the same thing to say, that a Disjunctive may be first




132            THE DOCTRINE OF JUDGMENTS.
resolved into as many Hypotheticals as it has disjunct
members; and each of these may then be reduced, as
before, to a Categorical.  Thus, If A  is not B, it is C;
and, If ~A is not C, it is B.  Evidently, then, Disjunctives
are only complex Hypotheticals.
3. TiHE HAMILTONIAN DOCTRINE OF JUDGMENTS.
According to the Aristotelic doctrine, as we liave seen,
in all Affirmative Judgments, the Predicate is Particular,
while in all Negative Judgments it is Universal.  Thus
we have but four fundamental Judgments or Propositional
Forms, which have been designated by the four vowels
A, E, I, and 0.  According to Sir William  Hamilton's
doctrine of " the thorough-going  quantification of the
Predicate," in both Affirmative and Negative Judgments,
the Predicate may be distributed or undistributed, - that
is, may be either Universal or Particular.  This doctrine
gives us eight Propositional Forms, which are thus indicated:-A  signifies that the Term to which it corresponds,
whether Subject or Predicate, is universal, whilst I signifies
that it is particular; f,* standing in the place of the
Copula, signifies that the Judgment is affirmative, whilst
n* signifies that it is negative.  Thus we have the following table of Hamilton's eight fundamental Judgments,
those of them which are recognized under the Aristotelic
doctrine being also indicated, as before, by the four vowels.
Affirmatives.
Afa. All X are all Y.  e. g. All copperas is all sulphate of iron. (1.)
(A.) Aft. All X are some Y.' All whales are some mammals.  (2.)
Ifa. Some X are all Y. " Some men are all logicians.  (3.)
(I.) Ifi.  Some X are some Y. " Some quadrupeds are some amphibious.                    (4.)
* These two letters are selected because they are the two first consonants
of affirmo and nego.




THE HAMILTONIAN ANALYSIS.               133
Negatives.
(E.) Ana. Not any X is any Y.  e. g. Not any fish is any warmblooded.             (5.)
Ani. Not any X is some Y.  " N6t any Englishman is some
Briton (Scotch).     (6.)
(O.) Ina. Some X are not any Y.  ", Some Frenchmen are not any
Parisians.           (7.)
Ini.  Some X are not some Y. " Some trees (oaks) are not some
trees (maples).      (8.)
The question is, whether these four:iorms, viz. Afa, Ifa,
Ani, and Ini, which have been added to the list by Sir
W. Hamilton, are legitimate and natural Forms of Thought,
- whether we do not have frequent occasion to think them
as Judgments, though we seldom or never express them as
Propositions. It is admitted that the predesignations of
quantity, some, all, any, here italicized as belonging to the
Predicate, are usually elided in expression. This is the case
even with the old Forms, A, E, I, and 0; for language
aims always at brevity, and therefore usually omits all that
is so obvious as to be easily understood, since its expression
would only cumber and lengthen the sentence unnecessarily.  Thus, we usually say, Men are animals; but nearly all
logicians acknowledge that the Thought, of which this is an
abbreviated expression, is, All men are some animals.  But
the peculiar function of Logic is to analyze, not language,
but Thought; it deals, not with Propositions, but with Judgments.  Hence its necessary postulate, that we must be
allowed to express logically all that is contained in what
we think.  The question is, whether we are not often
obliged to think Judgments under the Forms, All are all,
Some are all, Not any is some, and Some are not some.
Now the evidence in favor of the first two of these
Forms, the affirmatives Afa and Ifa, is so strong, that the
only wonder is, how they could have been almost universally rejected by logicians for over two thousand years,
down to the time of Sir W. Hamilton. In the first place,




134          THE DOCTRINE OF JUDGMENTS.
any process of inductive reasoning can be properly reduced
to logical Form only in this manner:X, Y, Z, &c. are B.
But X, Y, Z, &c. are (or represent) all A.
Therefore, all A are B.
Here the second premise is materially false; but with
this fault, as logicians, we have nothing to do. Logic does
not guarantee the truth of the premises, but only the validity of the inference from the premises to the conclusion.
And that this inference is valid in the preceding formula
may be seen by taking an instance in which neither of the
premises is faulty. If I am playing chess, and my king is
in fatal check, I must reason thus: —
I can neither move my king, nor interpose a man, nor
capture the attacking piece.
But these three are all the modes of obviating check.
Then I am checkmated.
Here the Predicate of the second premise is quantified
universally; and men reason in this manner every day,
when they are reduced to a choice among a few only possible modes of action, and each of these modes is fatal. The
following example shows how we reason inductively: —
Copper, tin, lead, iron, &c. are fusible.
But copper, tin, lead, &c. are (or represent) all metals.
Then all metals are fusible.
As already hinted, every adequate Definition -that is,
every one in which the Definiendum and the Definition are
convertible terms —has its Predicate universally quantified
in Thought. To take the instance already given, All copperas is sulphate of iron, or, conversely, All sulphate of iron
is all copperas. So, also, every exhaustive Division must
be thought as a Judgment with a universal Predicate.
Thus, the geometer, having demonstrated a certain proposition successively of equilateral, isosceles, and scalene
triangles, adds in Thought, But these are all triangles;
therefore, the theorem holds good of all triangles.




THE HAMILTONIAN ANALYSIS.                135
" Ifi fact," says Hamilton, " ordinary language quantifies
the Predicate so often as this determination becomes of the
smallest import. This it does directly, by adding all, some,
or their equivalent predesignations, to the Predicate; or it
accomplishes the same end indirectly, in an exceptive or
limitative form.
"a) Directly, —as, Peter, John, James, etc. are all the
Alpostles;-   liercury, Venus, etc. are all the planets.
4 b) But this is more frequently accomplished indirectly,
by the equipollent forms of Limitation or Inclusion, andException.*
" For example, by the limitative designations, alone or
only, we say, God alone is good, which is equivalent to
saying, God is all good, that is, God is all that is good;
Virtue is the only nobility, that is, Virtue is all noble, that
is, all that is noble. The symbols of the Catholic and
Protestant divisions of Christianity may afford us a logical
illustration of the point.  The Catholics say, Faith, Hope,
and Charity alone justify; that is, the three heavenly virtues
together are all-justifying, that is, all that justifies; omne
justificans, justutn  faciens.  The Protestants say, _Faith
alone justifies; that is, _Faith, which they hold to comprise
the other two virtues, is all-justifying, that is, all that
justifies; omne justificans.  In either case, if we translate
the watchwords into logical simplicity, the predicate appears predesignated.
"Of animals man alone is rational; that is, hMian is all
rational animal.  What is rational is alone or only risible;
that is, All rational is all risible, etc.
"I now  pass on to the Exceptive Form.  To take the
motto overhead,' On earth there is nothing great but
man.'  What does this mean?  It means, Man - is -  all
* The English Exclusive particles a're, one, only, alone, exclusively, precisely, just, sole, solely, nothing, but, &c. These particles annexed to the Subject predesignate the Predicate universally, or to its whole extent.




136          THE DOCTRINE OF JUDGMENTS.
earthly great.  (Homo  est-omne magnum terrestre.)
And the second clause — -' In man there is nothing great
but mind'- in like manner gives, as its logical equipollent,
Mind- is -all humanly great, that is, all that is great in
man. (lMens est onne magnum humanum.)"
The case may not seem so clear in respect to the two
negative Forms, Ani and Ini, in which the Predicate is
Particular; for the expression of them in language is so
awkward and unnatural as to have provoked the remark,
that they seem to be got up as if for the purpose of showing what one could do. It would certainly be accounted a
forced and uncouth assertion, to say that not any iron is
some metal, -i. e. is not lead; or that some men (Englishmen) are not some men (Frenchmen). Dr. Thomson admits that they are conceivable, but denies that they are
actual, cases of negative predication. He argues that
" such a Judgment is never actually made, because it has
the semblance only, and not the power, of a denial. True
though it is, it does not prevent our making another Judgment of the affirmative kind from the same Terms."  It
would be more correct to say that we can make " another
Proposition," instead of "another Judgment," from  the
same Terms; for the " some metal" in the Predicate of the
negative Judgment is not thought as the same "some metal"
in the Predicate of the affirmative. The two assertions
are incompatible in Thought, though they happen to be
identical in expression. Thus, -
Iron is not some metal, - i. e. is not lead.
Iron is some metal, — i. e. is iron.
Englishmen are not some men, - not Frenchmen.
Englishmen are some men, - Englishmen.
In fact, the law of Division, that the Dividing Members
must exclude each other, compels us to think some are not
some, - these are not those, - these are different from those.
As already shown, negation is only the affirmation of dif



THE HAMILTONIAN ANALYSIS.            137
ference or exclusion;' A is not B,' is equivalent to 6 A is
not-B.' Now we never have occasion to affirm difference
or exclusion except for the purpose of distinguishing coordinate Species from each other; for if the two classes were
not recognized as belonging to the same Genus,- that is,
as similar in some respects,- it would not be necessary to
think or to say that they differ in certain other respects.
We never say, Fishes are not stars, since the two things are
so unlike that there is no danger of confounding them.
But we think and say, Oaks are not maples, Spaniels are
not terriers, as the classes are here thought as belonging to
the same proximate Genera, trees and dogs. In Thought,
therefore, these two Judgments are explicated thus: Some
trees are not some trees;, Some dogs are not some dogs.
Even the Aristotelic doctrine admits that Unskilful are
some physicians is a legitimate Judgment, for it is the simple converse of Some physicians are unskilfcul.  But it
amounts to precisely the same thing whether we say, Unskilful are, &c., or Not (any) skilful are some physicians.
Considered as Propositions, one of these may be condemned as faulty in expression; but as Judgments, one
cannot be admitted and the other rejected, for they are one
and the same Judgment.
Again, whenever we predicate a Genus of a Species, the
Predicate is obviously quantified as Particular; and some,
which is the predesignation of particularity, must then be
thought in its semi-definite sense, as some, excluding all.
In this sense, we cannot think that some are, ufnless we also
think that some are not. Then, every such Judgment
carries with it by necessary inference, or as a part of itself,
another Judgment, negative in Form and with a Particular
Predicate.  Thus the Judgment, Men are some animals
(rational bipeds), is incomplete and even impossible in
Thought, unless we also think, Men are not some (other) animals (brutes). Either of these two assertions thus carrying




1-38         THE DOCTRINE OF JUDGMENTS.
the other along with it by necessary implication, it is more
natural to adopt in words the affirmative form, as the more
frequent and familiar one, even when the negative meaning
is more prominent in Thought. As Hamilton remarks,
"'men naturally preferred to attribute positively a part of
one notion to another, than to deny a part."
It has already been argued, (page 110,) that although
the Predicate in any Judgment may be actually thought
only connotatively, or as a Mark, it is still potentially a
Concept, and as* such, it denotes a class, or has Extension.
To predicate, therefore, is virtually to classify, or to assign a Subject to its proper place in a class, thereby attributing to it all the Marks of that class. Now it is argued
by Mr. Baynes, with great force, " that when we bring an
object under a notion, that is, when we predicate of itthat it belongs to such a class, we must know that it occupies a certain place in that class. For if we were uncertain what place the individual object occupied in the class,
or whether it occupied any place at all, we should not
know the class, and could not therefore bring any object
under it;- e. g. if I do not know whether rose comes
under the Concept flower,  whether it is equal to some
part, or the whole, or superior to it, - I cannot, of course,
predicate flower of rose, since I do not know what the
Concept means, what it contains, and what it does not.
If, therefore, we understand the object at all, we must fix,
in Thought, the sphere which it occupies under the class to
which, in predication, we have assigned it. In other words,
if we comprehend what we utter, every notion holding the
place of predicate in a proposition must have a determinate
quantity in thought." *  We cannot, for instance, predicate
bird successfully of pigeons, of winged and feathered bipeds,
and of animals, unless we know at least so much of the
characteristics of the class bird as to be able to think that
X* Baynes's New Analytic of Logical Forms, pp. 9, 10.




THE HAMILTONIAN ANALYSIS.            139
"all pigeons are some birds," "all winged and feathered
bipeds are all birds," and "some animals are all birds."
In like manner, we cannot exclude a Subject from a given
Concept or class, - as when we say, Whales are not fish,
unless we either think fish as cold-blooded, vertebrated animals, living in the water and breathing by gills, in which
case we think "whales are not any fish"; or accept the
vulgar notion of fish as finned animals living in the water,
and then think " whales are not some fish," - viz. not coldblooded fish. This leads us to remark, that, in fact, any limitation of the predicated class by a limiting adjective is equivalent to quantifying that Predicate particularly; - e. g.
Pines are not deciduous trees — =Pines are not some trees.
These reasons, and others which will be mentioned when
we come to treat of Conversion, seem conclusive in favor
of Sir W. Hamilton's doctrine, that, potentially at least,
the Predicate is always quantified either universally or particularly, both in affirmative and negative Judgments.
But if each of the two Terms of a Judgment has its own
quantity assigned to it in Thought, then, for still stronger
reasons than those which have already (pp. 64, 110) been
assigned, the distinction between Subject and Predicate
ceases to be of any moment.  In fact, every Judgment
comes from an act of comparing two quantified Terms with
each other; and as the result of such comparison, we have
an equation, or non-equation, established between these
Terms, and it is completely indifferent which of them is
placed first. Thus, having compared two Concepts, A and
B, I find either that they agree, or do not agree, with each
other. This agreement or difference may be expressed
equally well in either of the following formulas: -
A is B.                        A is not B.
B is A.                       B is not A.
A and B are equal.            A and B are not equal.
Convertible or equal are A and B. Unconvertible are A and B.




140            THE DOCTRINE OF JUDGMENTS.
In these last two formulas, the two compared notions do
not stand to each other as Subject and Predicate, but are,
in the same proposition, either both Subjects or both Predicates.
In common language, if the two Terms are both quantified universally in Thought, it is admitted to be of no
consequence which is placed first; usually, that which is
prior or pre-eminent in Thought appears as the Subject.
Thus, we say either, Electricity is not the nervous fluid, or,
The nervous fluid is not electricity; Common salt is chloride
of sodium, or, Chloride of sodium is common salt.
But if the two Terms differ in Quantity, the convenience
of language requires, in most cases (not in all *), that the
one which has the wider Extension should appear as the
Predicate, and that its Quantity, though present in Thought,
should be silently passed over in expression. It is more convenient that the Term which has the less Extension, as it is
more definite or limited in meaning, and therefore can be
more easily grasped in Thought, should be placed first; and
then, the Quantity of the Predicate, as it is known to be
greater than that of the Subject, (and it matters not how
much greater it is,) may be omitted in expression for the
sake of brevity.  Metals are fusible substances is a shorter
and more natural expression than Some fusible substances
are metals, though the two propositions convey precisely
- Such propositions as these, for instance, are common: -
It is disgraceful to be a slave to passion.
Turpe est obsequi libidini.
lHappy is he who is able to know the causes of things.
Felix qui potuit rerum cognoscere causas.
It is rain which has fallen.
It is foolish to listen to flattereers.
If the Term of the wider Extension must be the Predicate, we should
say, - To be a slave to passion is disgraceful; He who can discover the causes
of things is happy; That which has fallen is rain; To listen to flatterers is
folly.




EXPLICATION OF PROPOSITIONS INTO JUDGMENTS. 141
the same meaning. Hence the old logicians, having more
regard to Language than to Thought, maintained that the
former order was the only legitimate one; they analyzed
this order only, and based upon it their whole system.
" Natural, or regular, or direct predication they held to be
that in which the genus is predicated of the species, the
species of the individual, the attribute of its subject, and,
in general, the extensive whole of its part; and in which,
therefore, the Subject notion was always of less extent than
the Predicate notion. Unnatural, indirect, or irregular
predication was the reverse of this, - that, to wit, in which
the species was predicated of the genus, the subject of its
attribute, and, in general, the extensive part of its whole."*
But when it is acknowledged that Logic has to do primarily with Thought, and only secondarily with Language; that each of the two Terms has its own Quantity
assigned to it in Thought; and that the purport of the
Judgment is merely to affirm the agreement or non-agreement of these two quantified Terms, —it becomes evident that every proposition is logically reduced to an
equation, or non-equation, of two Terms, the relative position of which is of no importance whatever. All metals
are some fusible things, and Some fusible things are all metals, are two statements of precisely the same import. And
in like manner with negatives;- Some EFrenchmen are
not any Parisians, is the same Judgment as, Not any Parisians are some,Frenchmen.
4. THE EXPLICATION OF PROPOSITIONS INTO JUDGMENTS.
Strictly speaking, as we have seen, Pure Logic deals
only with Judgments, and refers to the science of Language for the doctrine of Propositions, or the proper expression of Judgments in words. But the claims of Logic
* Baynes's Analytic,, p. 12.




142          THE DOCTRINE OF JUDGMENTS.
to be regarded as a universal science, and its doctrine that
all Thought can be reduced to distinct Judgments, so that
the logical theory of Judgments is applicable to every
mental product into which Thought enters, cannot be defended, or even properly understood, until it is clearly
shown how all Propositions, even the most complex in
character, may be reduced to simple Judgments.  We
shall therefore consider the explication of Propositions
here, though the subject properly belongs to Applied
Logic.
Every pure Judgment corresponds to one of these two
forms, -A is B, or A is not B; and if thus expressed in
words, it is called a Simple Proposition.  In this case,
neither Subject nor Predicate necessarily consists of a
single word; either or both may be described in many
words, provided that the union of these words expresses
but one Judgment or a single act of Thought. Thus, Well
organized and skilfully administered governments are productive of hlappiness to their subjects, is a Simple Proposition, as
well as John is sick.  On the other hand, several acts of
Thought combined in one statement constitute a Cormpound
Proposition, the plurality of which may reside either in the
Subject, or in the Predicate, or in both.  Thus, James and
William are young and healthy, is a Compound Proposition,
which may be resolved into these four Simple ones: -
James is young; James is healthy; William  is young;
William is healthy. A distinct Judgment is evidently necessary for each of these affirmations, whether they are
expressed separately, or united into one Compound Proposition.  Such a Proposition obviously may be partly true
and partly false, according as all, or only some, of the Predicates are truly affirmed of all, or only some, of the Subjects.
But as a Simple Proposition contains only one Subject
and one Predicate, it would seem that it must be either




EXPLICATION OF PROPOSITIONS INTO JUDGMENTS.  143
wholly true or wholly false. And so it would be, but that
there are many Propositions, seemingly Compound, but
really Simple, whose Subject or Predicate is a Complex
term, containing by implication other Judgments, that may
be called incidental.  In these, the incidental Judgment
may be false, while the main Proposition may be true. In
those which are properly called Complex Propositions, the
incidental or implied Judgment may appear, either as a part
of the: Subject or of the Predicate, with which it is joined
by a relative pronoun, whose office it is to combine several
Propositions into one, or only as a limiting or defining adjective, or participle, or adjective clause.  Thus, it is the
same thing to say, God, who is invisible, created the world,
which is visible; or, The invisible God created the visible
world.  It is justly remarked by the Port Royal Logicians, that these incidental Judgments are to be regarded
not so much as Propositions which we now make, but as
Judgments formerly made, the Predicate of which is now
regarded as a simple Mark or attribute of one of the
Terms in our present main Proposition. Hence it is still
true, that the Complex Proposition is Simple, because it
expresses but one Judgment made at the moment.
The incidental Judgment expressed in an additional
word or clause may be either explicative or limitative. It is
Explicative, when it is of the nature of a complete or partial
definition, and therefore belongs to the Term to which it is
annexed in the whole of its Extension.  Thus, Man, who
is born of woman, is of few days and full of trouble;here, the adjunct clause, born of woman, is to be understood
as a definition applicable to all men. But in such a Proposition as this, Men who are avaricious are unhappy, the
relative clause restricts or limits the predication of unhappiness to some men, —to those only who are avaricious.
It is only these Complex Limitative Propositions which are
equivalent to Hypotheticals — thus, All iron which is may



144           THE DOCTRINE OF JUDGMENTS.
netic is polar, has the same meaning as, If iron is magnetic, it is polar.  It depends upon the Matter of the
Thought, and can usually be determined by the context or
the nature of the subject, whether the adjunct word or
clause is to be considered as Explicative or Limitative.
With regard to Explicatives, it should be observed, that
the falsehood of the incidental does not affect the truth of
the principal Proposition. Thus, in the Proposition, JHarmodius and Aristogeiton killed Hipparchus, who was a
tyrant, or, killed the tyrant Hipparchus, the main assertion
would still be true, even though Hipparchus was not a
tyrant.  If, however, there is an implied Inference or argument, that the principal Proposition is true because the
incidental one is a correct definition, then the falsity of
the latter becomes a reason for doubting, not for denying,
the truth of the former. Thus, the Proposition, The soul,
which is an extended substance, must occupy space, becomes
doubtful when the incidental affirmation, that it is extended,
is disproved; but it may still be true, for other reasons,
that the soul must have some position in space.
In respect to Limitatives, no question can arise concerning the truth or falsity of the incidental Proposition; for
its Predicate is not affirmed of the Subject to which the
relative refers, nor is the existence of any such Subject
affirmed.  If I say, Judges who never do anything by
request orfavor are worthy of praise, the only assertion is a
Hypothetical one. I do not affirm, that Judges never do
anything by request or favor, or that there are any such
Judges; but only, that if there are any such, then they deserve praise. The most orthodox believer in the atoning
virtue of the death of Christ may still admit, that a man who
has never sinned, and is not sinful by nature, stands in no
need of an atonement.  So far, indeed, as such a statement
contains any implication that such a human being ever
lived, it is false; but if construed strictly, it implies nothing of the kind.




EXPLICATION OF PROPOSITIONS INTO JUDGMENTS.  145
Compound Propositions are divided into those which
obviously contain a plurality of Judgments, and therefore
do not need analysis and exposition; and those in which
the plurality is concealed, so that it is apt to escape notice.
The latter are called Exponibles, because they need to be
analyzed and explained. These are divided into Exclusives, Exceptives, and Restrictives.
Exclusive Propositions limit the Predicate to this one
Subject, thereby excluding it from every other Subject.
Hence, every Exclusive contains two Propositions, one of
which affirms the Predicate of A, and the other denies it
of all not-A. Thus,
Only  A    B   A is B.
i No not-A is B.
G  od is to be worshipped.
God alone is to be worshipped    No other being is to be
worshippyed.
Hamilton, as we have seen, reduces these Compounds
to Simple Propositions, by showing that the Exclusive
particle annexed to the Subject quantifies the Predicate
universally; thus: —
Only A is B - A is all B;
whence we infer immediately, by Infinitation, that
NVo not-A is B.
Sometimes the Exclusive particles only, one, sole, &c.,
are annexed adjectively to the Predicate, and then have
the same meaning as all. Thus, God is the sole object to
be worshipped;- i. e. God is all that should be worshipped.
Annexed adverbially to the Copula and Predicate taken
together, the Exclusive particle limits the Subject to this
one Predicate, thereby excluding it from every other
Predicate.
Peter only plays; i. e. he plays, and he does nothing else.
James is only a lawyer; i. e. he is a lawyer, and nothing
else.
7                          3




146           THE DOCTRINE OF JUDGMENTS.
But, James is the only lawyer =  he is all the lawyer that
you can find.
Exceptive Propositions state the Subject universally, yet
with a specified exception, to which it is implied that the
Predicate is not attributed.  These also are equivalent to
two Judgments, and these two, as in the case of Exclusives
also, differ in Quality.
(Nearly) all have disapAll but one have disappeared -=              ha  isad
but one has not disapp peared.
In respect to Quantity, Exceptives are to be considered
as Universals. For although a part is excluded from the
whole of the Subject, so that the Predicate is referred
only to the remainder, yet this remainder constitutes a
whole in itself, of which the Predicate is affirmed or
denied.
It is obvious that an Exclusive and an Exceptive are
only two modes of expressing the same thing, as it is easy
to change them reciprocally from the one to the other;
but the direct affirmation in one becomes the implied
assertion in the other.  A fool thinks that no method except his own is right; in other words, that his own is the
only right method.
Restrictive Propositions are of two kinds, both of which
are Limitative in meaning. The first sort restricts the
assertion by a special clause, which determines more narrowly the signification of the Subject or the Predicate.
_Ethics, considered merely as a doctrine of the expedient, is
no longer a science of morality: —this is equivalent to
the two Judgments, -Ethics is a science of morality, but
a mere doctrine of expediency is not such a science.  Here
the Subject is the restricted Term; but in the following
example, it is the Predicate.  A good magistrate is merdiful to offenders, as far as the demands of justice will permit.




EXPLICATION OF PROPOSITIONS INTO JUDGMENTS. 147
The second sort of Restriction is called Reduplicative, as
it consists in a repetition of the restricted Term. A judge,
as judge, ought never to receive presents; - that is, he may
receive them, like other men, on ordinary occasions, but
never in connection with the performance of his official
duties. Here, also, the two Judgments into which the
Proposition is explicated differ in Quality.




148     THE DOCTRINE OF IMMEDIATE INFERENCE.
CHAPTER VI.
THE DOCTRINE OF IMMEDIATE INFERENCE.
1. tAquipollence or Infinitation. - 2. Conversion. - 3. Opposition and
Integration.
INFERENCE or Reasoning is that act of Pure Thought
whereby one Judgment is derived from another, or
from two others. The Judgment from which another is
deduced is called the Premise; and that which is derived is
called the Conclusion. If the Conclusion is drawn directly
from one Premise only, without the aid either of an
Intuition or another Judgment, it is said to be an Immediate Inference. Thus, from the Premise that No quadruped
is rational, I know at once, or by Immediate Inference,that is, by an act of Pure Thought, - that _Every quadruped is irrational, and that No rational thing is a quadruped.
If the Conclusion can be drawn only through the intervention of a third Judgment, -in other words, if two Premises are necessary, -the result is a Mediate Inference,
or Syllogism.
But in either case, the act of Reasoning or Inference,
whether Mediate or Immediate, is simple, being one indivisible act of mind.  The Premises are considered as
given, and their truth is taken for granted; the Inference
is the act of deduction, or drawing out the Conclusion from
the Premises, and this act is necessarily simple. If it is
performed in accordance with the Laws of Pure Thought,
it is apodeictic or absolutely certain, as any opposite Conclusion would be Contradictory and absurd. In respect to




THE DOCTRINE OF IMMEDIATE INFERENCE.    149
their Malitter, both the Premises and the Conclusion may be
false; and yet the Form of Inference, or the transition
from one to the other, may be intuitively true. Thus, the
Mediate Inference,
Everything material is mortal;
The Soul is mnaterial;.
Therefore the Soul is mortal;
is false in each of its three Judgments. Yet its Conclusion
is as correctly drawn, and the Syllogism is therefore just as
valid, as in the following instance, where each of the three
Judgments is true.
Everything material is divisible;
Gold is material;
Therefore Gold is divisible.
Hence, the material truth of the Conclusion depends upon
the material truth of the Premises; its formal validity is
the correctness of the process whereby it was deduced from
the Premises. Pure Logic has to do only with the latter.
Every correct step of Reasoning, considered simply as such,
or in reference to its Form, is as indisputable as one of
those Primary Axioms of Pure Thought on which it is
based, or of which it is an application. The uncertainty or
disputable character. of much of what is improperly called
Reasoning lies altogether in the Premises, and is referable
to imperfect observation, to an improper use of words where
language has become a substitute for Thought, or to overhasty generalization. But the mere process of Reasoning,
irrespective of the data about which we reason, is the same
in the moral and physical, as in the purely mathematical,
sciences; it is equally demonstrative in all, for it is conditioned by the absolute laws of Pure Thought. The longest chain of argument is but a series or repetition of Inferences, whether Mediate or Immediate, in which the
formal validity of each step, taken by itself, is intuitively
perceived.




150     THE DOCTRINE OF IMMEDIATE INFERENCE.
Logic, as Hamilton remarks, "is exclusively conversant
about Thought strictly so denominated; and Thought
proper, we have seen, is the cognition of one object of
thought by another, in or under which it is mentally included;-in other words, Thought is the knowledge of
a thing through a Concept or General Notion, or of one
Notion through another. In Thought, all that we think
about is considered either as something containing, or as
something contained; — in other words, every process of
Thought is only a cognition of the necessary relations of
our Concepts. This being the case, it need not move our
wonder that Logic, within its proper sphere, is of such
irrefragable certainty, that, in the midst of all the revolutions of philosophical doctrines, it has stood, not only
unshattered, but unshaken.  In this respect, Logic and
Mathematics stand alone among the sciences, and their
peculiar certainty flows from the same source. Both are
conversant about the relations of certain a priori forms of
intelligence; - Mathematics about the necessary forms of
Imagination; Logic about the necessary forms of Understanding; - Mathematics about the relations of our representations of objects, as out of each other in space and time;
Logic about the relations of our Concepts of objects, as in
or under each other, that is, as in different relations respectively containing and contained. Both are thus demonstrative, or absolutely certain, sciences, only as each develops
what is given, - what is given as necessary, in the mind
itself. The laws of Logic are grounded on the mere
possibility of a knowledge through the Concepts of the
Understanding, and, through these, we know only by comprehending the many under the one. Concerning the
nature of the objects delivered by the Subsidiary Faculties
to the Elaborative, Logic pronounces nothing, but restricts
its consideration to the laws according to which their
agreement or disagreement is affirmed."




THE DOCTRINE OF IMMEDIATE INFERENCE.      151' It is of itself manifest that every science must obey
the laws of Logic.  If it does not, such pretended science
is not founded on reflection, and is only an irrational
absurdity.  All Inference, evolution, concatenation, is conducted on logical principles, —principles which are ever
valid, ever imperative, ever the same. But an extension of
any science through Logic is absolutely impossible; for by
conforming to logical canons, we acquire no knowledge,
receive nothing new, but are only enabled to render
what is already obtained more intelligible, by analysis and
arrangement.  Logic is only the negative condition of
truth.  To attempt by a mere logical knowledge to amplify
a science, is an absurdity as great as if we should attempt,
by a knowledge of the grammatical laws of a language, to
discover whlat is written in this language, without a perusal
of the several writings themselves.  But though Logic
cannot extend, cannot amplify, a science by the discovery
of new facts, it is not to be supposed that it does not contribute to the progress of science.  The progress of the
sciences consists not merely in the accumulation of new
matter, but likewise in the detection of the -relations subsisting among the materials accumulated; and the reflective abstraction by which this is effected must not only
follow the laws of Logic, but is most powerfully cultivated
by the habits of logical study."
Aristotle has defined Inference as 44a thought or proposition in which, from something laid down and admitted,
something distinct from what we have laid down follows of
necessity." But this definition, though it describes the
Syllogism accurately, seems at first to be inapplicable to
Immediate Inference, in which, as there is only one premise,
and as the act of Pure Thought through which we reason
cannot add any new Matter (that is, any new Intuition or
Concept), it would appear that the Conclusion cannot contain anything distinct from what has already been laid down.




152     THE DOCTRINE OF IMMEDIATE INFERENCE.
And this is true; it cannot contain any new Matter, but it
may represent this Matter under a new Form, so that the
Conclusion and the Premise will be perfectly distinct Judgments. Thus, in the instance just given, "6quadruped'"
and 1"rational " are the only Terms that appear in either
of the two Conclusions, " irrational " being only the equivalent of'6 non-rational "; and both of these are contained
in the Premise. And yet the Inference is not a mere
repetition, but the Judgments which it involves are new
and distinct from what was previously laid down; for one
of them is affirmative, while the Premise is negative; and
the other denies a certain Mark of any " rational thing,"
while the Premise denies a certain other Mark of any
"6 quadruped."  If it be argued further, that such Conclu.sions are virtually contained in the Premise, inasmuch as
they become evident to any one who fully apprehends it,
the answer is, that this is true of all Reasoning, even of
Syllogisms and Inductions.  That a certain step is obvious
and easily taken, is surely no proof that it is no step at all,
or that we can get along without taking it.
1.   QUIPIOLLENCE OR INFINITATION.
The first sort of Immediate Inference which we have to
consider is that which the Greek logicians called co8vat alaa,
and the Latins, AXquipollence; its more appropriate name
is Infinitation. It has already been said, that every pair
of Concepts, such as A and not-A, of which one is merely
the Contradictory or the privative of the other, divide the
universe between them. According to the axiom of Excluded Middle, either A, or its Infinitated correlative, notA, must belong to everything, and must include everything;
and according to the axiom of Non-Contradiction, the presence of one in any given case insures the exclusion of the
other.  Hence arise a number of Immediate Inferences,




AEQUIPOLLENOE OR INFINITATION.        153
some of which are of frequent occurrence in our ordinary
processes of thought.  As already remarked, a negative
Judgment can always be changed in Form to an affirmative, or an affirmative to a negative, simply by Infinitating
one of its Terms, or by dropping its Infinitation; and the
result is a new Judgment, the truth of which is an Immediate Inference from the truth of the antecedent Judgment
whence it was derived. HIere the Inference is only an
application of the well-known grammatical rule, that two
negatives cancel each other, and thus become equivalent to
an affirmative. But the idiom of every language sanctions
a greater or smaller number of exceptions to this general
rule, none of which, however, are admissible in Logic,
where every negation must be construed rigorously.
The following memoriter lines, which I copy from Burgersdyck, enumerate the more frequent forms of 2equipollence and of the idiomatic force of negative expressions;
but of course, all of them do not hold good in this meaning
in any other language than the Latin.
Non omnis = quidam non; omnis non quasi nullus.
Non nullus - quidam; sed nullus non valet omnis.
Non aliquis - nullus; non quidam non valet omnis.
Non alter  = neuter; neuter non prcestat uterque.
In all cases of Immediate Inference by Infinitation, the
dependence of the Conclusion upon the Premise is so obvious, and so directly governed by the Primary Axioms of
Pure Thought, that no mistake is likely to arise, except
from a momentary doubt as to the position or the proper
force of the negative particle. The two following rules
comprehend at least all the more important cases, and
they hold true, I believe, without exception, for the four
Propositional Forms which are recognized in the Aristotelic system.
R RULE I.  To change the Infinitation of the Predicate
(either by Infinitating it, or by dropping its Infinita7*




154       THE DOCTRINE OF IMMEDIATE INFERENCE.
tion), change the  Quality of the Judgment; —-the
Quantity of the Judgment then remains unaltered.
RULE II.  To change the Infinitation of the  Subject,
convert the Judgment (i. e. make the Subject and the
Predicate change places with each other), and then
either change the Quality, or change the Infinitation
of the (old) Predicate also; - here, also, the Quantity
of the Judgment remains unchanged.
The following are instances, both in the abstract and the
concrete, of the application of these two Rules to all four
of the fundamental Judgments, A, E  I, and 0, and also
to their Infinitated  forms, here designated as A', E', I',
and 0/.   This enumeration  was first made  out by Mr.
DeMorgan. It will be seen that it contains no instance of
mere Conversion, as the cases under that head will be afterwards separately considered.  To avoid a confasing repetition of the negative particle not, words compounded with
the negative prefixes un and in have been adopted whenever it was practicable. For the same reason, right is used
for not-wrong; brutes for not-men; pitiless for not-compassionate; &c.
PREMISES.                    CONCLUSIONS.
By Rule I.            By Rule II.
A. Every X is Y.   -— No X is not-Y.     — Every not-Y is not-X.
All metals are fu-  = -No metal is infusi- = All infusible things are
sible.              ble.                 unmetallic.
0. Some X are not Y. -- Some X are not-Y. -Some not-Y are not not-X.
Some men are not = Some men are piti-    Some pitiless beings are
compassionate.     less.*                not mere brutes (not-men).
E. No X is Y.      -Every X is not-Y.   -Every Y is not-X.
No avaricious man  -=Every  avaricious  -=Every happy man is free
is happy.           man is unhappy.      from avarice.
* Strictly speaking, or according to the rules of Logic, "not-compassionate" has the same meaning as "pitiless," for it is the contradictory of
"compassionate."  But in common parlance, there is a slight difference in
the meaning of the two words; A" not-compassionate," like most other epithets compounded with a negative particle, means, not entire privation of the
quality, but only the existence of it in a very low degree.




-EQUIPOLLENCE OR INFNITATIONE.                   155
1. Some X are Y.    - SomeXare not not-Y.= Some Y are not not-X.
Some wrong acts  =Some wrong acts  =Some excusable acts are
are excusable.      are not inexcusable. L    not right acts.
not-Y.          No not                         is X.
Every unjust act   =No unjust act is ex-  = Every (truly) expedient
is inexpedient.      pedient.              act is just.*
0'. Some not-X are     Some neot-X are Y. = Some Y are not X.
Some invisible things: -Some invisible   = Some tangible things are
are not intangible.    things are tangible. Q    not visible.
El. No not-X is not -Y. =Every not-X is Y.  -Every not-Y is X.
No mortal who-is- (-Every mortal who-    Every  mortal who-is-innot-a-brate is in-      is-not-a-brute  is  very  mortal wo-is-inot-a-brute  ias in-.     capable-of-sin  is a brate.
capable of sin.      capable of sin.
II. Some not-X are }  Some not-X are not Y.= Some not-Y are not X.
not-Y.
Some invertebrates  = Some invertebrates  = Some wingless  animals
are wingless.        are not winged.       are not vertebrates.
The Infinitation of the four additional Judgments first
considered by Sir W. Hamilton  cannot with equal facility
be reduced to rule. As either Afa or Afa' is a perfect expression  of the  absolute identity of what the two Terms
denote, either may be deduced by Infinitation from the
other, and, by the same means, several other less perfect
expressions of the same identity may be obtained. But of
these less perfect expressions some may more properly be
regarded as inferences by Subalternation. Thus, -
Aa. All X are all)   ( No X is not-Y        )     Everynot-Yis not-X.
Y   No Y is not-X          - All X are Y.
Afa'. All not-X are
a. All not-X nre  Every not-Xis not-Y     All Y are X.
all not-Y
All extended are all divisible =  All unextended are all indivisible.
On the other hand, as Ini and Ini' are indefinite expressions of the partial disagreement of the two Ternms, they
s Some writers upon the theory of morals, who have strenuously maintained that "no unjust act is expedient," have yet been very unwilling to
admit that "every expedient act is just."  Yet the latter proposition is a
necessary inference from the former.




156       THE DOCTRINE OF IMMEDIATE INFERENCEO
yield  no inferences by  Infinitation  properly  so called;
though, if some be taken in its semi-definite sense, they
yield a number of unimportant inferences by what Sir W.
Hamilton calls Integration.
The following are the more common inferences by Infinitation from the two remaining pairs of these four Judgments.  In these it will be observed that the Quantity of
the Conclusion often differs from that of the Premise.
Ifa. Some X are all Y.   -- All not-X are not-Y. _ No Y is not-X.
Some curvilinearsare  - All rectilinears are { = No circular is recall circulars.       not-circulars.        tilinear.
Ani. No X is some Y.       Some not-X are not   Some Yare not-XS
not-YNo tyrants are some  tS — Som   are not} -Some kings are
kings.          tyrannical are not      not-tyrannica.
kings.               unroyal.
Ifa'. Some not-X are all      No X is not       Soe nt-  ar
X iYs.                                   -not Y.
Some unsentient are = No sentient thing is  = Some  unsentient
all inorganic.        inorganic.          are not organic.
Ani'. sot  any not-X  is ~ - Some X are not Y.  = Some not-Y are X.
some not-Y.     )
Not any dishonest is  = Some honest are not = Some  imprudent
some imprudent.      prudent.              are honest.
2. CoNVERSION.
A  Judgment is said to be converted when its Subject
and Predicate have been made to change places with ehch
other.   Before  Conversion, the Judgment is called the
Convertend; after Conversion, it is the  Converse.   The
logical doctrine of Immediate Inference by Conversion
shows us when and why the truth of the Converse is a
necessary consequence of the truth of the Convertend.
In other words, Logic takes notice only of what is called
illative Conversion, in which the Convertend and the Converse must either both be true, or both be false, together.
Thus, the Conversion of No A is B, into No B is A, is illative; we can say,




CONVERSION.                  157
No carnivorous animal is ruminant;
therefore, No ruminant animal is carnivorous.
But the Conversion of Some A are not B, into Some B are
not A, is not illative; because we can say, Some men are not i
logicians, it does not follow that Some logicians are not men.
In Conversion of Judgments, the learner must remember that the whole Predicate must change places with the
whole Subject; — that is, whatever belongs to the Predicate must be transferred to the Subject's place, and whatever relates to the Subject to the Predicate's place. For
example; — Some temple is in the city, is not converted into
Some city is in the temple, but into Something in the city is
a temple. Again,- the Predicate of Every old man has
been a boy, is not boy, but has been a boy; therefore, it is
not converted into Some boy has been an old man, but into
Some one who has been a boy is an old man.  To avoid mistakes of this sort, every proposition, before Conversion, -
or, indeed, before it is subjected to any logical treatment
whatever, - should be reduced to its simplest logical form,
— that is, to the formula A is B, or A is not B.  Then no
error can arise, if we remember that all which precedes the
Copula, is or is not, is the Subject, and that all which follows the Copula is Predicate.
In treating of Conversion, as well as in other portions of
the subject, we first consider exclusively the doctrine of the
Aristotelic system, which admits only of four fundamental
Judgments, and reserve for subsequent treatment the
Hamiltonian theory of eight Judgments.
There are three sorts of Conversion. The first is applicable to E  and I, Universal Negatives and Particular
Affirmatives, and is called Simple Conversion, because both
the Quantity and the Quality of the Judgment remain unchanged; that is, E is converted into E, and I into I. If
it is true that No man is immortal, it follows by Immediate
Inference that No immortal is man; for if any one immor



158     THE DOCTRINE OF IMMEDIATE INFERENCE.
tal were a man, it would not be true that No man is immnortal. Likewise, if Some men are just, it follows immediately that Some just beings are men; because the assertion
that No just being is a man, would contradict the Convertend. By Simple Conversion, then, a Universal Negative passes over into a Universal Negative, and a Particular
Affirmative into a Particular Affirmative.
The second sort is Conversion per accidens, in which the
Quantity is changed from Universal to Particular, but the
Quality remains unaltered. This is applicable to A, and
also may be applied to E, though the latter, as we have
just seen, may also be converted simply. But A cannot
be converted simply; because, though all men are animals,
it does not follow that all animals are men. The Judgment
in the Convertend is, that men are included under the class
of animals, not that they constitute all animals; they are
only some animals. Hence the Converse is, Some animals
are men. We have already seen that E is converted simply into E; but 0 also is obtained by Immediate Inference
from IE; for, if None are, it follows that Some are not.
Hence, the Convertend, No man is immortal, yields as its
Converse, not only E, No immortal is man, but 0, Some
immortals are not men.  Conversion per accidens, then,
changes A into I, and E into 0, the Quantity in both
cases being diminished, but the Quality remaining unchanged.
The Judgment O remains, and this cannot be converted
either simply or per accidens.  From  the Convertend,
Some men are not learned, we cannot infer that Some
learned beings are not men.  Indeed, properly speaking,
0 cannot be converted at all on the Aristotelic system;
but by an artifice which is called Contraposition, the third
sort of Conversion, another Judgment can be inferred
from it, which; is called its Converse, though it is properly the Converse of its Elquipollent or Infinitated equiv



CONVERSION.                       159
alent.  In order to convert by Contraposition, then, first
infinitate the Convertend by Rule First, and then convert
simply. Thus, -
Convertend.         Some A are not B.  Some men are not learned.
Infinitated equivalent. Some A are not-B.  Some men are unlearned.
Converse of this.  Some not-B are A.  Some unlearned persons are men.
Hence I is the Converse by Contraposition of 0; and
in like manner, A  by Contraposition yields E, the effect
of this sort of Conversion being to change the Quality of
the Convertend, while its Quantity remains unaltered. A
is thus contraponed:Convertend.        All A is B.        All men are rational.
Infinitated equivalent. No A is not-B.  No man is irrational.
Converse of this.    No not-B is A.   No irrational being is a man.
No inference can be obtained from I by Contraposition;
for if infinitated, I becomes 0, which cannot be converted
except by infinitating it back again.  Logicians seem  to
have overlooked the fact that E can be contraponed into
I, though the inferred Judgment in this case, because its
Quantity is diminished, is weak and comparatively worthless.  Thus, -
NVo A is B.               No fish is warm-blooded.
Every A is not-B.        Every fish is cold-blooded.
Some not-B are A.        Some cold-blooded animals are fishes.
The results of the three sorts of Conversion have been
summed up in this (nonsense) mnemonic line, in which
each dissyllable contains the vowel-symbol first of the Convertend and then of its Converse; and each pair of these
dissyllables is followed by the (italicized) abbreviation of
the kind of Conversion by which the two preceding inferences have been obtained; simp. =  Simple; Ace. =per
accidens; and  Cont.-  Contraposition.
Ecce tibi, simp.; armi-geros, ace.; ante boni, Cont.
The same thing is more briefly  indicated  in these two
Latin words, lToc capessit, in which oe-ca signifies that O
and A  are.converted by Contraposition; ap2e, A  and E per
accidens; essi, E and I simply.




160       THE DOCTRINE OF IMMEDIATE INFERENCE.
The most striking merit of Sir W. Hamilton's system  of
the thorough-going quantification of the Predicate is, that
it abolishes at once this whole cumbrous system of Conversion in three kinds, with its attendant rules, and substitutes for it the universal and self-evident process of Simple Conversion. As it has already been demonstrated, that
each Term of every Judgment has its own Quantity in
Thought, and consequently, that the distinction of Subject
and Predicate may be, for most logical purposes, left entirely out of view, every Judgment being reduced to an
equation, in which, of course, it makes no difference which
of the equated quantities is placed first, Conversion becomes at once a simple, uniform, and self-evident process.
As an old logician (Du Hamel, as quoted by Mr. Baynes),
remarks, " omnes conversionum leges pendent a cohmesione,
vel potius ab identitate, subjecti et attributi; quod si enim
subjectum  conjungitur et identifteatur, ut aiunt, cum attributo, necesse est pariter attributum uniri et identificari
cum subjecto." Though it is hardly necessary even for
the youngest learner, I give examples of the Hamiltonian
mode of converting each of the eight Judgments.
Converted.                  Converse.
Afa.    All rationalareallmoral = a. All moral are all rational
beings                         beings.
Afi (A). All lilies are (some) fra-      Ifa.  Some fragrant things are all
-grant                        lilies.
Ifa.     Some plants are all trees -Afi. All trees are (some) plants.
Ifi (I).   Some vicious men are rich = Ifi.  Some rich men are vicious.
N  mter cmove itself =  Ana. Nothing that can move itself
Ana (E). No matter can move itself -.    is matter.
Ani.     Not (any) indistinct are  = Ina. Some sounds are not indissome sounds                   tinct.
Ina (0). Some virtuous men are i   Ani. Not (any) happy are some
not happy                      virtuous men.
Ini.     Some singers are not some  — Ini.  Some musicians are not
(good) musicians              some singers.
Conversion per aceidens, says Mr. Mansel, is so called




CONVERSION.                 161
because it is not a Conversion of the Universal per se, but
only of the Particular which happens to be included in the
Universal. "Some B is A," is primarily the Converse of
"Some A is B," and only secondarily of " All A is B," or
because "All A" includes " Some A." Properly speaking, then, it is no Conversion at all, but only an Immediate
Inference by Subalternation from the proper Converse.
This is clearly seen in the case of the Universal Negative,
E; No A is B, is first converted into E, No B is A, whence
we obtain by Subalternation O, Some B are not A.
Moreover, it is evident that, by reconverting the Converse, we ought to regain the Convertend. But this cannot be done after converting per accidens; we first convert
A into I, and then reconvert I, not into A, but into I.
For example;- All men are mortal, yields by accidental
Conversion, Some mortals are men; and this is reconverted
simply into Some mnen are mortals.
It is further argued by Hamilton, that the Aristotelic
doctrine applies Conversion to the naked Terms only, —
to the Subject and Predicate of the Convertend without
regard to the Quantity of either; it thus changes all to
some, and, as we have just seen, it makes the total Quantity of the Converse inferior to that of the Convertend.
But this is evidently wrong; for the quantified Terms are
the Concepts which were compared in Thought in the
Convertend, and these only ought to appear after Conversion, and appear unchanged. Contraposition, as we have
already shown, is a mediate process, the Conversion being
possible only through a previous Infinitation; for the original Judgment, on the Aristotelic doctrine, is not convertible at all. But as every Judgment is certainly the result
of a comparison, to assert that it is inconvertible, is to
maintain that A can be compared with B, while, at the
same moment, B is not compared with A; —which is
absurd. Comparison is necessarily bilateral.
ar




162      THE DOCTRINE OF IMMEDIATE INFERENCE.
3. OPPOSITION AND INTEGRATION.
Opposition is said to exist between Judgments which
have the same Matter (i. e. the same naked or unquantifled Subject and Predicate), but differ in Quantity, or in
Quality, or in both. The logical doctrine of Opposition
shows us what can be immediately inferred as to the truth
or falsity of one Judgment, from positing or sublating
(i. e. affirming or denying) one of its Opposites. Thus,
from positing E, No A is B, I can immediately infer the
truth of its Subaltern Opposite; 0, Some A are not B, and
the falsity of its Contradictory Opposite, I, Some A are B;
but I cannot infer, from sublating B, the truth of its Contrary Opposite, A, All A are B.
But here the word Opposition must be taken in a technical and qualified sense. It was first applied only to the
relations between two Contraries, or two Contradictories;
and this is its proper or strict meaning, as any two such
Judgments are opposed to each other, the one negativing
the other, and it is impossible that the two should be true
together. But as it was convenient for Logicians to consider the relations of Subalternation and Sub-Contrariety
under the same head with the two former, the meaning of
the word was extended so as to cover all the relations
existing between two Judgments of the same Matter, but
of different Form, although some of these are relations not
of opposition, but of congruity.
There are four sorts of Opposition. The first and most
perfect of these is that of Contradiction, which exists between two Judgments which differ from each other both in
Quantity and Quality; that is, between A and 0, and between E and I. This sort of Opposition is governed by
the Axiom  of Excluded Middle, which declares that of
two Contradictories, - that is, of two Judgments between
which there is no "6 Middle," no intermediate Judgment, -




OPPOSITION AND INTEGRATION.          163
one must be true; and then the Axiom  of Non-Contradiction adds, that the other must be false. Now, A and
O are two such Judgments, and likewise E and I; so also
the two Singular Judgments, Socrates is wise, and Socrates
is not wise.  Between either of these pairs, no "third" or
intermediate Judgment is conceivable. Hence the universal rule for this sort of Opposition, that Contradictories can-,not both be true, and cannot both be false.  Therefore, as
both cannot be true, if I posit (affirm) one, I immediately
infer that the other is sublated (denied); and as both cannot be false, if I sublate one, the other is posited. For
example; — if E is not true, that No quadruped is rational,
I must be true, that Some quadrupeds are rational.
Observe that two Judgments properly contradict each
other only when that which is affirmed by the one is denied by the other, - 1. in the same manner; 2. in the same
respect; 3. in the same degree; and 4. at the same time.
Thus, to borrow some examples from Aldrich, -1. A dead
body is, and is not, a man; that is, it is a dead man, but
not a living one. 2. Zoilus is, and is not, black; that is,
black-haired, but red-faced.  3. Socrates is, and is not,
long-haired; that is, he is so, if you compare him with
Scipio, but is not so, if you compare him with Xenophon.
4. Nestor is, and is not, an old man, according as you
speak of him when in childhood, or when he was at the
siege of Troy.
The second sort of Opposition is that of Contrariety,
which exists between two Universal Judgments, that differ
in Quality, but are alike in Quantity; that is, between A
and E.  Here the Axiom of Excluded Middle does not
apply; for between A and E, there is a "Middle" or
intermediate Judgment, namely, I.  Though it is not true,
either that all men are wise, or that no man is wise, it is
true that some men are wise. Hence both Contraries may
be false, so that I cannot infer the truth of one from the




164      THE DOCTRINE OF IMMEDIATE INFERENCE.
falsity of the other.  On the other hand, as one of these
Contraries affirms what the other denies, the Axiom of
Non-Contradiction applies; both Contraries cannot be true;
and, therefore, from the truth of one I can immediately
infer the falsity of the other. Accordingly, the rule is,
Contraries may be false together, but both cannot be true.
Therefore, from positing either A or E, I can immediately
infer that the other is sublated; but from sublating either,
I cannot infer that the other is posited.
The third sort of Opposition is that of Sub-Contrariety,
which exists between two Particular Judgments, that differ
in Quality, but are alike in Quantity; that is, between I
and 0. To these, the Axiom of Excluded Middle is
applicable; for there is no third, or intermediate, Judgment
conceivable between Some are, and Some are not. Accordingly, both cannot be false, but one must be true. On the
other hand, if I and O are considered as Propositions, that
is, if the Judgments are expressed in words, the Axiom of
Non-Contradiction does not apply to them; for both may
be true. Though some men are learned, it is also true that
some men are not learned. But observe, that the " some
men " in the latter case are not the same " some men " as
in the former; though expressed by the same words, they
are thought as different. To make the former Proposition
true, " some men" may be thought to be " graduates of
Oxford"; to make the latter true, " some men" may
mean " American Indians." As Propositions, then, and
possibly as Judgments, the two assertions do not contradict
each other, but may both be true.  Hence the rule, that
Sub- Contraries may be true together, but cannot both befalse.
Therefore, by sublating either I or O, we immediately infer
that the other is posited; but by positing either, we cannot infer that the other is sublated.  Of course, SubContraries can be called " opposites" only in a qualified
and technical sense; they are actually congruent, or, to




OPPOSITION AND INTEGRATION.            165
adopt one of Hamilton's newly-coined words, they are
"compossible."
The fourth sort of Opposition is that of Subalternation,
which exists between Judgments alike in Quality, but different in Quantity; that is, between A and I, and between
E  and 0.  Here, again, it is evident that the " Opposition" is merely technical, the two Judgments being not
merely consistent, but so nearly allied that the Particular
can be inferred from its Universal by the Axiom of Identity.  Since all includes some, if we affirm A, All A are B,
we thereby also affirm I, Some A are B; and in like manner, to posit E is also to posit O. The same Axiom compels us to think, that sublating I sublates A also, and
sublating 0 sublates E also. In this sort of inference, the
Universal may be called the Subalternans, and the Particular, the Subalternate.  Hence we have this rule for inference by Subalternation, that if the Subalternans is true, the
Subalternate is true also; and if the Subalternate is false,
the Subalternans is false also.
Summing up, we have the following list of Immediate
Inferences by Opposition.
i If A is true, 0 is false, E false, and I true.
If E is true, I is false, A false, and 0 true.
g If I is false, E is true, 0 true, and A false.
If 0 is false, A is true, I true, and E false.
If A is false, 0 is true,  the others unknown.
If E is false, I is true,
If I is true, E is false,  the others unknown.
If 0 is true, A is false,
Hence it appears, that from the truth of a Universal or
the falsehood of a Particular, we may infer the character of
all the opposed Judgments; but from the falsehood of a
Universal or truth of a Particular, we can know the character only of the Contradictory.




166           CONSPECTUS OF THE DOCTRINE OF
JUDGMENTS, considered
in reference to              Affrmative Predesignations of UViver.
QUANTITY, are either Univer-               sal Judgments.
sat or Particular; to         All - Every - Each- This - That
QUALITY, are either. Afrma-   -  These -Those-  a Proper
tive or Negative; to
QUANTITY and QUALITY, are             A. Universal Affirmative.
of four sorts:-                  e.g.     All X is Y.
All metals are lustrous.
IMMEDIATE INFERENCE proceeds
BY INFINITATION
of the Terms of a Judgment, or by dropping their Infinitation, the Judgments thus produced being, in certain
cases, cequipollent, or equivalent to those from  which
they were derived.
BY OPPOSITION,                                  FOUR  KINDS
or the relation that  A        conrar1. CONTRADICTION
be twerel    a     Conthary.    E exists between Judgments
exists between Judg-                         which differ both in Quanments  which  have.          \Ac.tity and Quality.
ent         w hc heRule. - Contradictories canthe  same naked or d    \ gnot both be true and cannot
both be false. Hence,
unquantified Subject,                        to posit A is to sublate O
E         "..
and  Predicate, but                         to sublate A is to posit 
differ  in  Quantity, ~                  i    "    El "  "   I
cdiffer iln  Quant~ity,:/X                and conversely,
or Quality, or both.  I   Sub-Contrary.  0   to posit 0 is to sublate A
BY CONVERSION,                            THREE  KINDS
or causing the Subject and               1. SIMPLE, E & I,
Predicate  of a Judgment without changing either the Quantity
to change places with each    or the Quality.  (Ecce-tibi.)
other, but in  such  man- Convertend. No X is Y.         E into
Converse.  No Y is X.     E.
her that if the Convertend  Coaverse.  No Y is X.
Convertend. Some X are Y. I into
is true, then the Converse  Converse.   Some Y are X. I.
will be true also.




JUDGMENTS AND  IMMEDIATE. INFERENCE.                     167
Negative Predesignations of Univer- Predesignations of Particular Judgsal Judgments.                ments, either Affirmative or Nega-.
tire.
None -  Not any -  Not one - Not
this -Not that --' Not " prefixed  Some - Not all - or any indication
or suffixed to a Proper Name.         of an indefinite part of a whole.
E. Universal Negative.  I. Particular Affirmative.  O. Particular Negative
No X is Y.              Some X are Y.          Some X are not Y.
No quadruped is rational.  Some swans are black.  Some men are not famous.
Two KINDS OF INFINITATION.
Rule. -  To change the Infinitation of Rule.- To change the Infinitation of
the Predicate, either by infinitating    the Subject, convert the Judgment,
it or by dropping its Infinitation,    and then either change the Quality,
change the Quality of the Judg-    or change the Infinitation of the
ment; the Quantity of the Judg-    (old) Predicate also.  Here, also,
ment remains unaltered.               the Quantity is unaltered.
OF OPPOSITION.
2. CONTRARIETY          3. SUB-CONTRARIETY        4. SUBALTERNATION
exists between  Universal exists between Particular exists between Judgments
Judgments that differ in   Judgments that differ in   alike in Quality, but differQuality, but are alike in   Quality, but are alike in   ent in Quantity.
Quantity.                Quantity.               Rule. —If the Subalternans
Rule.-Both Contraries may Rule. — Sub-Contraries may   (the Universal) is true, the
be false, but both cannot   both be true, but cannot   Subalternate (the Particube true. Hence,          both be false. Hence,     lar) is also true i and if the
to posit A is to sublate E    to sublate I is to posit O    Subalternate is false, the
"   E"   "   A            "     0  "        I"    Subalternans is false also.
Hence,
to posit A is to posit I
"   E   "   "   O
to sublate I is to sublate A
"    0"    "   E
OF CONVERSION.   (HOC  capessit.)
2. PtER ACCIDENS, A  & E,          3. BY CONTRAPOSITION, A  & 0,
changing the Quantity, but not the changing, not the Quantity, but the
Quality. (Armi-geros.)                Quality, through infinitating the
Convertend. All X is Y.      A  into    Predicate.  (Ante-boni.)
Converse.  Some Y is X.    I.         Convertend. All men are mortal. A.
Convertend. No X is Y.       E into  Converse.   No immortal is man. E.
Converse.  Some Y is not X. 0.        Convertend. Some  men  are  not
white.          0.
Converse. Some not-white are men. I.




168     THE DOCTRINE OF IMMEDIATE INFERENCE.
That the various points in the doctrine of this sort of
Immediate Inference might be more easily remembered,
the old logicians contrived,
A         Contrary.      E
not some mnemonic verses,
as on other occasions, but
the  accompanying  ingeSo a              ir GS/&/X nious diagram, which may
m, be called the Square of
i  Opposition.  It is very
easy to retain the whole
theory in  the memory,
when we observe the
I       Sub-Contrary.       D proper position, upon this
square, of the vowels which
indicate the four species of Judgments.'The upper line
belongs to the Universals, A and E; the lower line to the
Particulars, I and 0; the left hand to the Affirmatives,
A and I; and the right to the Negatives, E and 0.  Then
it is easily remembered, that the two diagonals represent
Contradiction, the upper line Contrariety, the lower one
Sub-Contrariety, and each of the two sides Subalternation.
For the further convenience of learners, I have brought
together in the preceding Conspectus the principal technicalities and rules in the Aristotelic doctrine of Judgments
and Immediate Inference.
Hamilton has considerably enlarged and modified the
doctrine of Immediate Inference by Opposition, by introducing, what the logicians had hitherto neglected, the
semi-definite meaning of some, —that is, some at most,some excluding all and none. In the Aristotelic doctrine,
some was applied exclusively in its wholly indefinite meaning, as some at least, - some, perhaps all; - and in negatives, some, perhaps none. Yet, as Hamilton remarks, some
is always thought as semi-definite when the other Term
of the Judgment is Universal; and it is only when both




OPPOSITION AND INTEGRATION.          169
Terms are Particular, that the some of each is left wholly
indefinite.  Thus, when we say, Some nmen are (all) black,
we mean to deny that all are black; Some flowers are not
(any) fragrant, denies that none are fragrant.
But in the case of Subalternation, which Hamilton prefers to call Restriction, if we introduce this semi-definite
meaning, and think some as some only -not all, instead of
having an Inference from the Subalternans to the Subalternate, we find a true Opposition between them; to adopt
the Hamiltonian word, the two Judgments are Incompossible. Thus, Some (only - not all) men are yellow, is really
opposed to All men are yellow, instead of being an Inference from it; and in like manner, Some (not all) bipeds
are not men, is opposed to No bipeds are men. This new
sort of Opposition or Incompossibility, as it exists between
two Judgments which are alike in Quality, either both
Affirmatives or both Negatives, while the other two sorts,
Contradiction and Contrariety, differ in Quality, is called
Inconsistency.  Of course, as two Inconsistents, like any
other two Incompossibles or Opposites, cannot both be
true, the true Inference is, that by positing either A or I,
E or 0, the other is sublated. To express the whole doctrine of Subalternation or Restriction in one rule; —If
some means some — perhaps all, the Subalternate is a direct
Inference from positing the Subalternans; but if some
means some -not all, the Subalternans and Subalternate
are Opposite or Incompossible, so that, by positing either,
the other is sublated.
Again, it has already been shown that Sub-Contrariety
is properly no Opposition at all, so that both Judgments
may be true; though, as both cannot be false, sublating one
enables us to posit the other. But if we introduce the
semi-definite meaning of some here also, we have a new
Inference from one to the other;  from the one some,
which is a part, to the other some, which is the remaining
8




170     THE DOCTRINE OF IMMEDIATE INFERENCE.
part necessary to constitute the whole.  This sort of Inference Hamilton would call Integration, as its effect is, after
determining one part, to reconstitute the whole by bringing
into view the remaining part. Thus, if I know that Some
(not all) men are white, I can immediately infer that Some
(other) men are not white; and if Some poets are not pvhilosophers, it follows that Some (other) poets are philosophers.
In such cases, though the two Judgments are different in
Quality, they are not opposed, but congruent; and the
Inference may be not only to all others definitely, but to
some others indefinitely.  It is valid, also, whether some
appears in the Subject or Predicate.  Thus, from Men are
some animals, we immediately infer that JMEen are not some
(other) animals (say, brutes). Here, the Inference concerns the Predicate, while in the preceding cases it concerned the Subject.
To apply the whole doctrine of Incompossibility and Integration, in both meanings of the word some, to the eight
HEamiltonian Judgments, is evidently a long and complex
process. The following table (page 172), in which the
whole process is worked out, is borrowed fi-om Sir William
Hamilton, and placed here, not, of course, that it may be
committed to memory, but because the examination of it
will be a useful exercise for the learner. In explanation
of it, observe that the Incompossibility, or the fact that the
two Judgments cannot both be true, - and in some cases,
the Restriction (Subalternation) and the Integration, —
may be bilateral (here marked bi), as affecting both Subject
and Predicate; thus,
All physical laws are all efficient causes.
Not any physical law is any efficient cause.
Or unilateral (un), as affecting either the Subject onlythus,
All men are all rational.
Some men are not (any) rational.




OPPOSITION AND INTEGRATION.           171
Or the Predicate only; thus,- some in the second Judgment being semi-definite,
All dogs are all barking animals.
All dogs are some barking animals.
Or it may be unilateral cross (un. or.), as reversing in
the one Judgment the relation of Genus and Species —
containing and contained - which exists between the
Terms of the other Judgment; thus, some being semidefinite,
All whites are some civilized.
Some whites are all civilized.
Or bilateral cross (hi. cr.), as affecting both Terms, but in
opposite relations, - as from Particular to Universal in
the Subject, and from Universal to Particular in the Predicate; thus, some being semi-definite,
Some blacks are all Africans.
Not any black is some Africans.
Or bilateral direct (hi. di.), as affecting both Terms, and
excluding any intermediate or third Judgment, both propositions remaining the same after conversion; thus,
Some men are (some) irrational.
Not any man is (any) irrational.




I.                                                                                            II.
Common to I. and sI.,          INCOMPOSSIJILITY                              INFERENCE
5' 1   ~ e     a  in either of which         of Proposition with Proposition,        from Proposition to Proposition, on the         H           S)
all Propositions are related.                 either as                                two Systems.
1.               2.                               1.                2.
Numbered as11    Vale.    Wholly Indefinite.   Semi-Definite.                 Wholly Indefinite.   Semi-Definite.
on pp 13 213                       0nrpom  -to.                                                                           -32,13
D(Some, perhapsall.)  (Some, notall.) iA(Someo  -erheastall.).   (So. R                               tr.    all.)
0 a         AfNiregat.
c         1-2       Afa - Afi                       Incons. un.           1-2          Restr. un.                           e
i..          1-3        Afa -Ifa                        Incons. un.           1-3          Restr. un.
4  P        1 —4       Afa — Ifi                                             1-4          Restr. bi.     Restr. bi.
1 X a      62 —3       Afi -   a                      Incons. un.,cr.                                                                       
]i               2-4-        Afi - Ifi                                            2-4          Restr. un.     Restr. un.
0"l ^  b 3 —4       Ifa  - Ifi                                            3-4          Restr. un.     Restr. un.          o  o
5 —6                       Ana- A                          Incons. un.           5 —6         Restr. un.'d.      ~    o  5 —7      Ana - Ina                       Incons. un.           5-7          Restr. un.                         L  0 
aI   U a       5-8       Ana - Ini                                             5-8          Restr. bi.      Restr. hi.         H.6-7       Ani — Ina   Doubtful, cr.    Doubtful, c.                                                             0
5. ~' ~    26-8      Ani — Ini                                             6-8          Restr. un.      Restr. un.?    0         7 —8      Ina — Ini                                             7-8          Restr. un.      Restr. un.
1 —5      Afa - Ana  Contrar. bi.         Contrar. bi.  i
1-6       Afa - Ani  Contrar. un.         Contrar. un. 
CD.        2o 1 —7    Afa - Ina   Contrar. un.    Contrar. un.                                               &       i
1-8       A Aa  — Ini                                           1 —8                         Res. & Int:. b/.    Q
IJt q       3~2-5     Afi — Ana  Contrar. un.         Contrar. un.'              2 —6      Aft — Ano                                             2-6                          Integr. in. 
U     2-7        Afi - Ina   Repugn. bi. cr.  Contrar. bi. cr.                                                           H
2-8       Afi - Ini                                             2-8                          Res. & Int. un.    _
8 3-5           Ifa  -Ana  Contrar. un.         Contrar. un.                                                          0,
3 —6      Ifa  -  An   Repugn. bi. cr.  Contrar. bi. cr.   
3-7       Ifa  - Ina                                            3-7                          Integr. un.'* ~j       3-8        Ifa  -                                                 -Ini  -8                   Res. & Int. un.:
C D      4-5        Ifi  — Ana  Repugn. bi. di.  Contrar. bi. di.                                                            0
0           4-6        Ifi  - Ani                                        4-6, 6-4                        Res. & Int. un.
11       4-7        Ifi  -Ina                                          4-7, 7-4                       Res. & Int...
~ t>      4-8        1fi  -  ni                                        4-8. 8-4                        Integr. hi.           o




OPPOSITION AND INTEGRATION.          178
It appears from this Table, that Afi and Ina (A and 0),
which, on the Aristotelic doctrine, are Contradictories, become only Contraries when we admit the semi-definite
meaning of some; for by sublating Ina, which denies only
a part (some only), we know not whether to posit Aft,
which affirms the whole, or Ifi, which affirms only some
(other) part, or Ana, which denies the whole; since each
of these three is incompossible with Ina.  For the same
reason, Ifa and Ani, which are only A and O converted,
are merely Contraries on this system, though Contra*dictories on the other, wherein some means perhaps all.
Indeed, there can be no Contradiction on this system,
wherein whole and part negative each other, just as much
as affiration and negation.  The only Contradictories are
those in which the distinction of whole and part does not
exist;- Judgments about Singulars or Individuals, for
instance, and about Universals regarded as Singulars or
as undivided wholes.  Thus, Common salt is chloride of
sodium  contradicts Common salt is not chloride of sodium; for Common salt, though really a General Term,
is here actually thought as undivided, so that the two
Judgments contradict each other as directly as do these
two Singulars, -John is sick, John is not sick. If either
Judgment in one of these pairs is sublated, the other is
necessarily posited.
"'The propositional form Ifi is consistent with all the
affirmatives; Ini is not only consistent with all the negatives, but is compossible with every other form  in universals.  It is useful only to divide a class, and is
opposed only by the negation of divisibility."
The whole scheme of Opposition upon this system may
be safely characterized as too complex to be of any practical use, though the learner may be profited by some
study of its details.




174        MEDIATE INFERENCE OR SYLLOGISM.
CHAPTER VII.
THE DOCTRINE OF MEDIATE INFERENCE: THE ARISTOTELIC
ANALYSIS OF SYLLOGISMS.
1. Figure and Mood. - 2. Conditional Syllogisms. - 3. Defective and
Complex Syllogisms.
MEDIATE  Inference is that act of Pure Thought,
whereby the relation of the two Terms of a possible Judgment to each other is ascertained by comparing
each of them separately with a third Term. Thus, if I
cannot immediately determine whether A is, or is not, B,
I can compare each with M. If, as the result of such comparison, it is found that A is 1 and B is M, then we infer
mediately - that is, through this relation of each to a third
- that A is B.  But if this comparison shows that one of
these Terms is, and the other is not, M, then we infer
mediately that A is not B. The affirmative conclusion is
evidently governed by the Axiom of Identity, which declares that A is B, if it is that (M) which is the equivalent
of B; or to use language more consonant with the phraseology hitherto employed, and converting B is M into Mtis
B, we say that B is a Mark of A, when it is a Mark of
that (M) which is a Mark of A, - nota notce est nota rei
ipsius.  The negative conclusion results from the Axiom
of Non-Contradiction, which declares that A is not B, when
it is equivalent to that (or has for a Mark that) (M),
which is not B; or, what is the same thing, when it is not
equivalent to that (M) which is B.
The fundamental principle of Mediate Inference or Syl



THE ARISTOTELIC ANALYSIS.           175
logism is thus traced to those Axioms which, as we have
already seen, must govern all the processes of Pure
Thought; or rather, Mediate Inference itself is but one of
the special applications of those Axioms. Instead of using
these Primary Axioms themselves, logicians have usually,
in order to demonstrate the processes of syllogistic reasoning, preferred to employ certain intermediate principles or
maxims, one of which we have just mentioned, —that the
iark of a lMark is a Marki of the thing itself.  But as these;
maxims can be directly deduced from the original Axioms,
to which, indeed, they owe all their validity, it seems better to test the legitimacy of each step by a reference to the
primary, rather than to any derivative, principle.
Thus far, A  and B, in their comparison with M, have
been regarded simply as undivided wholes; but it is evident that the same considerations will hold good if we substitute, for either or both of them, all, or any indefinite part,
of a divided Universal. Thus, if we find that Some A are
X, and Some B are 1, we are compelled to conclude, by
the Axiom  of Identity, that Some A  are (some) B; or,
taking a negative instance, if Some A are 3M, and Not any
B  is 3, then we infer that Some A are not (any) B.
Hence we see the correctness of the derivative or intermediate principle which Sir W. Hamilton enounces as
6" the supreme Canon of Categorical Syllogisms," - IN so
FAR AS two Notions'(Concepts or Individuals), either both
agree, or, one agreeing, the other does not agree, with a common third Notion, IN SO FAR these Notions do or do not
agree with each other. But if, by calling it " supreme," he
means that it is the ultimate and original Canon, his position may be doubted; for it is evidently a compound
statement, embracing, with an unimportant change of
phraseology, the two Primary Axioms of Identity and
Non-Contradiction, and guarding them with those limitations under which alone are they ever applicable.




176        MEDIATE INFERENCE OR SYLLOGISM.
We have seen that, though either or both of the two
Terms be quantified Particularly, the Syllogism still holds
good, - at least, to the extent to which the two Terms
are quantified. But the third Term must be taken Universally at least once in comparing it with the other
Notions; otherwise, we have no security that these others
are compared with the same, or "' a common," third Term.
Though we know, for instance, that A is some M, and B
is some M, still we cannot conclude that A is B; for the
6" some M " which is A may not be the same "some M"
which is B. Though Some learned men are pedants, and
Some learned men are wise, it does not follow that Pedants
are wise; for two very different classes of learned persons
are here spoken of. Hence we have this general rule for
all Syllogisms, that the Middle Term must be distributed
(i. e. taken Universally) in at least one of the comparisons
which are instituted between it and the other two Terms.
We say, " at least one" of the two comparisons; for the
other may be quantified Particularly without injury to the
reasoning. Thus, if All men are mortal, and X, Y, and Z
are (some) men, we may legitimately conclude that X, Y,
and Z are mortals; for to whatever class these " some men "
belong, they are necessarily included under 6 all men,"
who are declared to be mortal.
A Syllogism evidently comprises three Judgments, one
of which affirms the agreement or non-agreement of its
two Terms with each other to be the necessary consequence
of two other Judgments, in which a common third Term
is affirmed to agree with both, or with one only, of these
two Terms. The main Judgment is called the Conclusion;
the two subsidiary Judgments, on which it depends, are
termed the Premises; and the necessary connection between the Premises and the Conclusion — that which
entitles us to infer the one from the other —is the Consequence. The essence of the Syllogism, and all that is




THE ARISTOTELIC ANALYSIS.           177
actually affirmed in it, is this necessary consequence of the
Conclusion from the Premises.  Hence'the Syllogism is
really one, —a single and indivisible act of Thought.
Though apparently complex - though, in a certain sense,
including three Judgments - it does not affirm either one
of them taken separately, but only the necessary dependence of one upon the two others. Thus, as we have seen,
both Premises may be false, and the Conclusion may be
false; and yet the Syllogism may be valid or correct in
Form, for the latter may be legitimately deduced from the
former. The following, for example, is a valid inference,
though each of the Propositions is false.
All men are immortal,
All bipeds are men;
Therefore, all bipeds are immortal.
Hence, in order to dispute or deny a Syllogism as such, we
do not need to deny either of its.three Judgments, but
only the Consequence, or the dependence of the Conclusion upon the Premises; in other words, a single negation
denies all that the Syllogism, which is but one act of
Thought, asserts. We say, it does not follow that A is B
BECAUSE A is some M  and B is some I; though possibly
A is B for some other reason.
In explanation of the terms employed to denote the process of reasoning, the following passage is borrowed from
Sir William Hamilton's Lectures on Logic: " Reasoning
is a modification from the French raisonner (and this is a
derivation from the Latin ratio) and corresponds to ratiocinatio, which has, indeed, been immediately transferred
into our language under the form ratiocination. Ratiocination denotes properly the process, but improperly also the
product, of reasoning; ratiocinium marks exclusively the
product.  The original meaning of ratio was computation,
and from the calculation of numbers it was transferred to
the process of mediate comparison in general. -Discourse
8*                              L - 




178         MEDIATE INFERENCE OR SYLLOGISM.
(discursus,  catvota) indicates the operation of comparison,
the running backwards and forwards between the characters or notes of objects; this term may therefore be
properly applied to the Elaborative Faculty in general
[the Understanding]. The terms discourse and discursus
are, however, often, nay generally, used for the reasoning
process strictly considered, and discursive is even applied
to denote Mediate, in opposition to Intuitive [or Immediate], judgment, as is done by Milton.' Whence the soul
Reason receives, and reason is her being,
Discursive or intuitive; discourse
Is oftest yours.'
The compound term, discourse of reason, unambiguously
marks its employment in this sense.,A beast that wants discourse of reason
Would have mourned longer.'
Argumentation is derived from  argumentari, which means
argumentis uti.  Argument again  (argumentum) -  what
is assumed in order to argue something -is properly the
middle notion in a reasoning, — that through which the
Conclusion is established.  It is often, however, applied
as coextensive with argumentation.   Inference or illation
(from infero) indicates the carrying out into the last Proposition what was virtually contained in the antecedent
Judgments.  To conclude (concludere), again, signifies the
act of connecting and shutting into the last Proposition the
two notions which stood apart in the two first. A conclusion is usually taken, in its strict and proper signification,
to mean the last Proposition of a reasoning; it is sometimes, however, used to express the product of the whole
process. To syllogize means to form Syllogisms. Syllogism
(avXXo7t,/yo) seems originally, like ratio, to have denoted
a computation, - an adding up, -  and, like the greater part
of the technical terms in Logic in general, was borrowed




THE ARISTOTELIC ANALYSIS.          179
by Aristotle from  the mathematicians.  This primary
meaning of these two words favors the theory of those
philosophers who, like Hobbes and Leidenfrost, maintain
that all Thought is, in fact, at bottom, only a calculation,
a reckoning.  vUXXokory-6jl  may, however, be considered
as expressing only what the composition of the word denotes, — a collecting together; for o-vXxo/t[eo-OaL comes
from  o-vXXeyeLv, which signifies to collect.  Finally, in
Latin, a Syllogism is called collectio, and to reason, colligere.
This refers to the act of collecting, in the Conclusion, the
two notions scattered in the Premises."
Thus the un'ifying office of the Understanding, to which
we have before adverted, is again brought to view. As a
Judgment is an act whereby the two notions which are its
Terms are brought together into one, so a Syllogism —
Reasoning proper - Mediate Inference -- is that act of
Pure Thought whereby the two Judgments which are its
Premises are collected and summed up into one in the
Conclusion.; or, what is the same thing expressed in relation
to the Terms, whereby three notions are reduced to unity.
" Without the power of Reasoning," says Hamilton,
6"we should have been limited in our knowledge (if
knowledge under such a limitation would deserve the
name of knowledge at all)- I say, without Reasoning,
we should have been limited to a knowledge of what is
given by Immediate Intuition; we should have been
unable to draw any inference from this knowledge, and.
have been shut out from the discovery of that countless
multitude of truths, which, though of high, of paramount
importance, are not self-evident. This faculty is likewise
of peculiar utility, in order to protect us in our cogitations
from error and falsehood, and to remove these, if they
have already crept in.  For every, even the most complex, web of thought' may be reduced to simple Syllogisms; and when this is done, their truth or falsehood, at




180        MEDIATE INFERENCE OR SYLLOGISM.
least in a logical relation, flashes into view."  Hence, as
Dr. Whately remarks, " the Syllogistic theory does not
profess to furnish a peculiar method of reasoning, but only
to set forth a method of analyzing that mental process which
must invariably take place in all correct reasoning "; and
again, " a Syllogism is evidently not a peculiar kind of
argument, but only a peculiar form of expression in which
every argument may be stated."
The power of reasoning, of drawing Mediate Inferences,
like that of framing Concepts, is at once a proof of man's
superiority over the brutes, and of his inferiority to his
Creator. Brutes cannot reason, nor even form Judgments
respecting classes of things, their knowledge being confined, as we' have seen, to Intuitions,- to Singulars.  On
the other hand, the Infinite Mind knows immediately or
intuitively the relation of one thing or class of things to another, without being compelled to ascertain indirectly their
agreement or non-agreement through their relations to a
third or Middle Term. The power of Mediate Inference is
a help for an imperfect intellect; Omniscience needs no help.
The brief view which has now been given comprises all
the essential principles of Mediate Inference, - that is, all
the rules to which all Syllogisms, whatever may be their
peculiarities in other respects, must conform. They may
be summed up as follows --
1. A Syllogism  must contain three Terms, and no more;
namely, the two whose agreement or disagreement we wish
to ascertain, and the Third or Middle, with which each of
these is separately compared. If there were four Terms,
two of them must be intermediate, not appearing in the Conclusion; but then the Premises would have no common Term.
If we know only that A is _/ and B is V, we have no
means of ascertaining the relation of A and B to each other.
2. A Syllogism  must contain three Judgments, and no
more; namely, the two in which each of the Terms of the




THE ARISTOTELIC ANALYSIS.           181
Conclusion is compared with the Middle Term, and that in
which these two are compared with each other.
3. The Middle Term mnust be distributed (taken universally) in at least one of -the Premises.  The necessity of
this Rule arises, as we have seen, from the fact that the
two Extremes, in order to be compared with each other,
must have been separately compared with the same common Middle.  If we consider no other kinds of Quantity
than all and some (Universal and Particular), the Rule as
here expressed is sufficient. But if we take into more
definite view the Quantity of some, - namely, whether it
does or does not exceed.one half,- the Rule may be made
seemingly less stringent. It is enough that the quantifications of the Middle Term in both Premises, added together,
should exceed unity, - that is, exceed its possible totality
or its distribution in any one; for tle amount of such
excess over unity then constitutes a common Middle Term.
Something {more than all the Middle Term has been mentioned in the Premises; and both Terms in the Conclusion
must have this excess as a common element.  If A is three
fourths of X, and B is one half of M, then at least one
fourth of 1f is common to A and B; and their agreement
with this common term is enough to insure their agreement
with each other. This is called by Hamilton the ultra-total
quantification of the Middle Term. It deserves mention, but
as it is of very infrequent use, the Rule as first enounced
for the quantification of the Middle is practically sufficient.
4. One Premise at least must be affirmative; for if both
Premises are negative, the Middle Term agrees with
neither of the two others, and therefore affords no ground
for any Inference as to their agreement or non-agreement
with each other. Though we know that A is not M and
B is not M, we do not thereby know whether A is or is not
B.  A good general is not a coward, and Pompey was not
a coward; but these two assertions furnish no reason for believing that Pompey either was, or was not, a good general.




182           MEDIATE INFERENCE OR SYLLOGISM.
5. If either Premise is negative, the Conclusion is negative; for as one Premise, according to the preceding Rule,
must be affirmative, if the other Premise is negative, there
is a difference in the relation of the two principal Terms to
the Middle Term, and hence a non-agreement between the
two Terms themselves.
6. Neither Term  must be distributed in the Conclusion if
it was not distributed in the Premise; for if only some is
premised, we cannot conclude all.
Logicians have usually added two other Rules, that the
Conclusion follows the weaker part, a Negative being regarded as Weaker than an Affirmative, and a Particular as
weaker than  a Universal; and that no Conclusion can be
drawn from  two Particular Premises.  But both of these
result only from a combination of Rules 5 and 6 with 3;
hence they hardly need to be considered here, but I append a demonstration of them  in the note.*  No syllogism
* As the two additional Rules were constructed with special reference to
the Aristotelic doctrine of Judgments, they can be conveniently demonstrated only by bearing in mind the following maxims, which have already
been laid down in the exposition of that doctrine.
1. By Subalternation, Particular Judgments are included under their
corresponding Universals; that is, if A is true, I is also true; and the
same holds good of E and 0.
2. The Subject of a Judgment, taken universally or particularly, is that
which renders the Judgment itself Universal or Particular.
3. The Predicate of an Affirmative Judgment is always considered as
Particular.
4. The Predicate of a Negative Judgment is always regarded as Universal,- that is, as distributed.
Now there must always be in the Premises one more Term distributed than in
the Conclusion; for by Rule 3, the Middle Term (which does not appear in
the Conclusion) must be distributed in at least one of the Premises; and
by Rule 6, if any Term is distributed which does appear in the Conclusion, it must also be distributed in the Premises. Then it follows that no
Conclusion can be drawn from two Particular Premises.  For if these are I
and I, as neither Subject nor Predicate of I is Universal, the Middle Term
is not distributed.  If they are I and 0, then, by Rule 5, the Conclusion is




THE ARISTOTELIC  ANALYSIS.                     183
can be invalid which does not violate one or more of the
six Rules first enounced.
After the usual manner of logicians, the foregoing Rules
have been summed up in these mnemonic hexameters —
Distribuas medium, nec quartus terminus adsit;
Utraque nec proemissa negans, nec particularis;
Sectetur partem conclusio deteriorem,
Et non distribuat nisi curm prmemissa, negetve.
But the application of these rules may become a matter
of considerable complexity, when it is considered that, from
the same naked (unquantified) Terms, a great variety
of different Syllogisms may be formed.  Each of the three
Terms may be either Particular or Universal; each of the
three Judgments, either Affirmative or Negative; the Judgments may be placed in any order with respect to each
negative; then its Predicate is distributed; and Rule 6, taken in conjunction with what has just been stated respecting the number of distributed
Terms in the Premises, requires one of these Premises to be Universal.
Again, if either Premise is Particular, the Conclusion must be Particular.
For the Subject of a Universal Affirmative Conclusion must be Universal;
therefore, in the Premise wherein this Subject appears, it must, by Rule 6,
be Universal, and the Middle Term, which is therein joined with it, must
consequently be Particular, since it must be the Predicate of an Affirmative
Judgment. Then the Middle Term, in order to be once distributed, must
be the Universal Subject of the other Premise. Hence, if the Conclusion is
Universal Affirmative, both Premises must be Universal.
And if the Conclusion is Universal Negative, both Premises must also be
Universal. For both Terms of the Conclusion are then distributed; and as
the Middle Term  must also be distributed, there must be at least three
Terms distributed in the Premises.  But this cannot be, unless both Premises are Universal, since both of them, by Rule 4, cannot be Negative.
Hence, whether the Conclusion is Affirmative or Negative, if it be Universal, both Premises must be Universal. Then, if either Premise is Particular,
the Conclusion must be Particular.
But according to Rule 5, if either Premise is Negative, the Conclusion
is Negative.  Then, the Conclusion must follow the weaker part; - that is, it
must be Particular, if either Premise is Particular, and Negative, if either
Premise is Negative. - Q. E. D.




184        MEDIATE INFERENCE OR SYLLOGISM.
other, and for three Judgments, six different orders of position are possible; and each of the three Terms may be
either Subject or Predicate in either or both of the Premises, the two principal Terms also assuming either place in
the Conclusion. The larger portion of the numerous Syllogisms thus formed, it is true, are invalid, as offending
against one or more of the preceding Rules. We need
some more succinct mode than that of severally applying
to each Syllogism all these Rules, before we can be satisfied
that it is impeccable. Many of these Syllogistic forms,
moreover, are equivalents of each other; that is, the Reasoning may be changed from one form to another, without impairing its validity, or even changing its signification
in any essential respect. But of these equivalent forms
some are more natural and obvious than the others; the
mind seeks for these by preference; and when the process
of reasoning appears in one of these natural and preferred
forms, its validity is determined with ease and in a moment.  The application of the Rules to such cases is made
with the quickness of instinct, and may be reduced almost
to a mechanical process.
A highly ingenious, though artificial, system has been
contrived of classifying these numerous Syllogistic forms
under a few heads, throwing out at once all that are illegitimate, immediately recognizing the remainder, and then
transmuting those which are valid in substance, but unnatural and obscure in form, into the easy and familiar
types in which the mind quickly perceives their legitimacy.
The study of this. system, a ready use of which may be
said to constitute the art of Syllogizing, is facilitated by a
series of mnemonic contrivances, many of them of marvellous ingenuity and completeness.  The notation and
most of the operations are of an algebraic character; and
attempts'have not been wanting of late years to enlarge
and perfect the system by a further introduction of mathe



MHE ARISTOTELIC ANALYSIS.           185
matical signs and processes.  The failure of such an undertaking is not to be wondered at, for it proceeds, as it seems
to me, upon a mistaken opinion as to the relative position
of the two sciences. Logic is not a department of mathematics.  Rather the reverse is true.  Mathematics is the
science of pure quantity, - of reasoning about dimensions
and numbers in the abstract, or as unmodified by any of
the differences of quality by which all the objects of thought
are actually distinguished; and it is, therefore, only a department, or a special application, of the far more comprehensive science which has for its object Reasoning itself
and all its subsidiary processes, and thus covers the whole
domain of Pure Thought. All computation is reasoning;
but all reasoning is not computation, and therefore cannot
be carried on by the processes, or be made subject to the
special laws, of pure mathematics.
Syllogistic forms are classified with respect to Hood and
Pigure, the former having regard to the value of the three
component Judgments, and the latter to the relative position of the three Terms in these Judgments.  It will be
convenient, then, to have a uniform mode of designating
these three Terms. In future, S will stand for the Subject, and P for the Predicate, of the Conclusion, and Mfor
the Middle Term.  The Consequence, or what we usually
express by the words therefore, consequently, &c., will be
indicated by three dots placed thus.'. For example: -
Mis P;
S is M;.'. S is P.
To facilitate reference, the Logicians have given special
names to these several Terms and Judgments.  The
Predicate of the Conclusion is called the Major Term, and
its Subject the Minor Term.  The Premise in which the
Major is compared with the Middle Term is called the
Major Premise, and that in which the Minor is compared




186        MEDIATE INFERENCE OR SYLLOGISM
with the Middle, is the Minor Premise.  These names
have reference to the Quantity of Extension only, and are
founded upon the received doctrine, that the natural order
of predication is that in which the Genus is predicated of the
Species, the Species of the Individual, and, generally, the
Extensive whole of its part. Then the more Extensive
Term, the Major, usually occupies, at least in Affirmative
Judgments, the Predicate's place.  "This,"  says Dr.
Thomson, "is the natural, though not invariable, order;
and it is worthy of remark, that, even in Negative Judgments, where, from the negation, the two Terms cannot be
set together to determine their respective Extension, if,
apart from the Judgment, we know that the one is a small
and the other a large class, - the one a clearly determined
and the other a vague notion,- we naturally take the
small and clearly determined Concept for the Subject.
Thus, it is more natural to say that the Apostles are not
deceivers, than that No deceivers are Apostles. So that, if
our minds are. not influenced by some previous thought to
give greater prominence to the wider notion, and so make
it the Subject," thus reversing the primary and natural
order, the Term  of mctor Extension will always be the
Predicate, and that of minor Extension, the Subject.
As these names -Major, Middle, and Minor — thus
correctly indicate the comparative Extension of the three
Terms, an Affirmative Syllogism in which these Terms
occupy their natural place is conveniently symbolized by
three concentric circles, of which the outermost and largest
indicates the Predicate of the Conclusion, or the Major
Term; the innermost and smallest, the Subject of the Conclusion, or the Minor; and the intermediate one, the
Middle Term.  Thus:- 
All mammals are viviparous;   All M are P.
All whales are mammals;  All S are M..o. All whales are viviparous.,e. All S are P.




THE ARISTOTELIC ANALYSIS.            187
Here the reasbning is, that S, which is a part of 1M,
must also be a part of P, -since Mis a part of P.  We are
thus led to another mode of enunciating the governing
principle of all Syllogisms, that a part of a part is a part
of the whole; or, as Leibnitz expresses it, contentum contenti
est conztentum continentis.  This principle agrees in every
essential respect with the famous Dictum of Aristotle,
usually called the Dictum de omni et nullo, that whatever is
predicated (affirmed or denied) universally of any Class
(i. e. of any whole), may be also predicated of any part of that
Class.  Both principles have been already recognized and
applied in the doctrine of Subalternation.  The name of
this Dictumn is derived from the two forms which it assumes
as applied either to affirmative or negative Conclusions;
the Dictum de omni being thus expressed, Quicquid de
omni valet, valet etiam de quibusdam  et singulis; and the
Dictum de nullo being, Quicquid de nullo valet, nec de quibusdam nee de singulis valet.  Both of these principles are
evidently of a secondary or derivative character, their affirmative and negative forms being grounded respectively
upon the two Axioms of Identity and Non-Contradiction;
for as a whole is identical with the sum of all its parts,
whatever is affirmed or denied (distributively) of the
whole is. thereby affirmed or denied of each of its parts.
Burgersdyck remarks, that, for the purpose of applying the
Dictum to Syllogisms, it may more conveniently be thus
expressed: Whatever Predicate is universally affirmed or
denied of any Middle Term or Part is also affirmed or denied of any Subject which is contained under that intermediate Term or Part.
The mode of symbolizing the mutual relations of the
three Terms of a Syllogism, which is applied above to a
Universal Affirmative, may be extended to Negatives and
Particulars.  The total disagreement of two Terms with
each other, which is expressed by a Negative Judgment, is




188        MEDIATE INFERENCE OR SYLLOGISM.
properly indicated by two Circles which do not coincide in
any part. Thus:No M is P;
All S is M;
No S is P.
Both the partial agreement, and the partial disagreement,
of two Terms,- as these are merely two aspects of one
and the same Thought, —
are properly indicated by
the same symbol, namely,
two circles which intersect.
s  [
Some S are 1, and Some
S are not M, are both expressed by this symbol.
Excepting this ambiguity,
all Syllogisms can be adequately symbolized by some combination of the preceding diagrams.
Hitherto we have regarded the Syllogism  only as a
means of evincing the relation of two Terms to each other
through the relation of each to a common or Third Term.
But the Dictum as expressed'by Burgersdyck indicates
another aspect of the Syllogism, equivalent indeed to the
former one, but in certain respects more convenient for
use. The Judgment in which "a Predicate is universally
affirmed or denied of any Middle Term or Part" is a General Rule; the Judgment that a given'" Subject is contained under that intermediate Term or part," is the Subsumption of this Subject under the condition of that Rule;
and then tile Conclusion following, that the given Subject is
governed by that Rule, is a solution of the doubt with which
we commenced, whether S is, or is not, P. Every Syllogism,




THE ARISTOTELIC ANALYSIS.           189
then, must consist of three Judgments, one of which must
be a General -Rule, or, as Hamilton expresses it, a Sumption; another must be the Subsumption of a certain Subject under that Rule; and the third is the Conclusion,
that this Subject is determined by the Rule. Thus:Sumption.    No one who is content is miserable;
Subsumntion. Some of the poor are content;
Conclusion.   Some of the.poor are not miserable.
It is not difficult to prove, say the Port Royal logicians,
that all the Rules which we have given serve only to show
that the Conclusion is contained under (or embraced in the
Extension of) one of the Premises, which is a General
Rule or Sumption, and that the other Premise, the Subsumption, shows this; and that arguments are vicious only
when they fail to observe this method, and are always good
when it is observed.
Kant expresses the general law of the Syllogism, as thus
conceived, in the following formula: Whatever stands
under the condition of a Rule, that stands also under the
Rule itself.  As the former view regards chiefly the three
Terms, so this one has primary reference to the three
Judgments, of which every Syllogism is composed.  The
former view does not contradict the latter; they are. only
two aspects of the same thing. But what we have hitherto
termed the Major Premise, though it is usually the same
Judgment that is here called the Sumption, is not always
so. Thus, in the following Syllogism, (called by the
Logicians )Disamis of the Third Figure,) the first Judgment, as it contains the Predicate of the Conclusion, is the
Major Premise; but the. second Judgment is the Sumption.
Some wicked persons are men of high rank;
All the wicked are miserable..-. Some miserable persons are men of high rank.
As it has been demonstrated that from two Particulars no
Conclusion can be drawn, every Syllogism must have for a




190        MEDIATE INFERENCE OR SYLLOGISM.
Premise at least one Universal Judgment; that is, one of
its Premises must be a Sumption or General Rule. In the
First Figure, which is the only natural and obvious form
of reasoning, and to which all the other forms can be reduced, the Sumption is always the Major Premise.
1. FIGURE AND MooD.
The Etigure of a Syllogism depends upon the relative
position of its three Terms, and is determined by the position of the Middle Term in the Premises. Now the Middle Term may be either the Subject of the Major Premise,
and the Predicate of the Minor, in which case we say the
Syllogism is of the First Figure; or it may be the Predicate of both, which is the Second Figure; or it may be the
Subject,of both, thus constituting the Third Figure; or it
may be the Predicate of the Major and the Subject of the
Minor, thus converting the First, and giving rise to the
Fourth Figure. Accordingly, the four Figures are thus
indicated.
I.          II.           III.         IV.
MP           PM           MP            PM
SM           SM           MS            M S.. SP. S  P..   S P. S P
They are also indicated in the following mnemonic
line: -
Sub prce; turnm prce prce; turn sub sub; turnm pnce sub.
The line should be read thus: -The Middle Term is, first,
Subject, Predicate; then, Predicate, Predicate; then, Subject, Subject; lastly, Predicate, Subject.
The Fourth Figure is not recognized by Aristotle, but is
accepted, if at all, on the supposed authority of Galen.
Most modern logicians reject it, not as invalid, but as unnatural and unnecessary. As we have already said, the




FIGURE AND MOOD.                191
natural order of predication is that in which the Genus is
predicated of the Species, or the more Extensive of the less
Extensive Term. Then it follows that the First is the
only natural and obvious Figure, as it is the only one
which observes this order throughout.  Here, the Predicate
of the Conclusion, which is the Term of widest Extension,
appears as the Predicate of the Major Premise; and the
Subject of the Conclusion, being the Term of least Extension, is the Subject of the Minor Premise, - the Middle
Term appearing, as it ought, intermediate between the
two, being of less Extension than P, and greater than S.
Here also, as Dr. Thomson remarks, the Conclusion in no
way disturbs the order of Terms which was first established
in the Premises; for the Subject of the Conclusion appears
also as a Subject in the Premises, and the Predicate as a
Predicate; - that is, no Thought which was primary becomes secondary, nor any secondary primary. Take, for
instance, the following Syllogism in the First Figure:1. No boaster deserves respect;
Some heroes are (some) boasters;.'. Some heroes do not deserve respect.
Here, everything is in its natural place; each Subject is of
less Extension than its Predicate, and the Terms preserve
the same relative places in the Conclusion which they
occupied in the Premises.
But change this Syllogism into the Second Figure, by
converting the Major Premise, thus: —
2. No person deserving respect is a boaster;
Some heroes are (some) boasters;.'. Some heroes do not deserve respect.
Here, the natural order is violated in one half of the reasoning; for the Subject of the Major is the Predicate of
the Conclusion, and has wider Extension than its own
Predicate.




192        MEDIATE INFERENCE OR SYLLOGISM.
Again, change the same Syllogism into the Third Figure, by converting the Minor Premise, thus -
3. No boaster deserves respect;
Some boasters are (some) heroes;.'. Some heroes do not deserve respect.
Here, the other half of the reasoning appears unnatural
and forced. The Predicate of the Minor Premise becomes
the Subject of the Conclusion, and is of less Extension
than its own Slibject.
To change this Syllogism into the Fourth Figure, we
must convert both Premises, thus:4. No person deserving respect is a boaster;
Some boasters are (some) heroes;-.-. Some heroes do not deserve respect.
Here, both halves of the reasoning are contorted, so that it
appears wholly unnatural. Not only is -the Predicate of
the Minor the Subject of the Conclusion and of less Extent
than its own Subject, but the Subject of the Major is the
Predicate of the Conclusion, and of greater Extent than its
own Predicate.  The mind revolts at this perversion;
striving to preserve the same order in the Conclusion
which it observed in the Premises, the Conclusion which it
would naturally draw from these two Premises is this:No person deserving respect is (some) hero.
Now, this Conclusion, which is natural and obvious, is the
Converse of the former one, which was unnatural; and it
reduces the Syllogism (changing the order of the Premises)
from the Fourth to the First Figure.  Hence it appears,
that what is called the Fourth Figure is only the First
with a converted Conclusion; that is, we do not actually
reason in the Fourth, but only in the First, and then, if
occasion requires, convert the Conclusion of the First.
The reasoning is indirect, or Mediate in a double sense;
the nominal Conclusion of the Fourth is actually, but in



FIGURE AND MOOD.                19%
directly, obtained by converting the Conclusion of the
First.  Hence, many Logicians exclude the Fourth altogether, and call those Syllogistic forms which would otherwise fall under it "' indirect Moods of the First Figure."
But we can also obtain, if we see fit, indirect Moods from
the Second or Third Figure, by converting their Conclusions also.  There is no Teason, then, for giving a special
class of these 6"indirect Moods " to the First Figure, any
more than to the Second or Third; that is, there is no
reason for considering the Moods of the so-called Fourth
Figure at all.  It is not only unnatural, but wholly unnecessary.  We need only state, that, after obtaining the
ordinary mediate Conclusions from either of the three Figures, we may, if occasion requires, obtain a second set of
Conclusions immediately, by converting the former ones.
But we observe, secondly, that the natural but unexpressed Conclusion of the so-called Fourth,
1" No person deserving respect is (some) hero,"is a shocking one for the Aristotelians, for it is a Negative
with an undistributed Predicate.  They will not allow that
such a Judgment is possible; but here it appears as actual,
— nay, as the only natural result of Premises to which,
according to the Aristotelic doctrine, only a wholly unnatural Conclusion can be given by inventing a so-called
Fourth Figure, otherwise not needed, and in every respect
perverted and contrary to nature.  Of course, Sir William
Hamilton, whose system expressly recognizes these Negative Judgments (Ani) with undistributed Predicates, has
taken adcvantage of this fact, and pressed it as an unanswerable argument against his opponents..
But to return to the Aristotelic doctrine.  The reason
ordinarily given for awarding a decided preference to the
First over the other Figures is not either of the two here
alleged, but one which immediately results from them,
namely, that the Dictam  de omni et nullo, which is held to
9                               IM




194        MEDIATE INFERENCE OR SYLLOGISM.
be a universal principle of all reasoning, is directly applicable only to the First Figure.  This Dictum, which has
respect exclusively to the Quantity of Extension, riecessarily supposes that the order of Extension is strictly followed in the Syllogism; that is, that the Predicate in each
of its three Judgments should be of wider Extension than
the Subject.  This is the case in the First Figulre; but as
we have seen, it is not so with the others.  In the Second,
the Subject of the Major, and in the Third, the Subject of
the Minor Premise, has a wider Extension than the corresponding Predicate.  In order to show that the Dictum is
universally applicable, we must be able to reduce all Syllogisms, in whatever class they may at first be ranked, to the
First Figure. Now, to judge from tile instance just given,
in which we have carried the same Syllogism successively
through each of the four Figures, such a Reduction can be
very easily accomplished.  It is only necessary to convert
one orboth of the Premises.  Recurring for a moment to
the first mode of indicating the variations of Figure,I.           II.           III.         IV.
MIP          Pik           MP PP PM
SM           SM            M S           MS.. SP.. SP.. S P.. SP
it is easy to see that the Second Figure is reduced to the
First by converting its Major Premise; the Third, by con-verting its Minor; and the Fourth, by converting both.
But as the order of the Premises may be transposed, as the
Sumption and the Major Premise do not always coincide,
and as the Judgment 0, on the strict Aristotelic doctrine,
is not convertible at all, it is not always easy to tell which
Premise ought to be converted, and the process of Reduction practically becomes so complex and intricate, that,
to facilitate it, an elaborate system and a whole set of
mnemonics have been contrived.  These will be explained
hereafter.




FIGURE AND MOOD.               195
The Aristotelic logicians appear to hesitate, or be in
doubt, as to the motives for reducing the three lower Figures to the First. At times, they speak as if the only
reason for such Reduction were the one already mentioned,
- to reduce all Syllogistic forms to system by showing that
they are all controlled by one governing principle, the -Dictum de omni et nullo. The implication then is, that they
are valid or competent forms of reasoning, even before such
Reduction; and that they are reduced, therefore, only to
render them more systematic and orderly in appearance.
Then, again, they speak of proving them by this Reduction,
as if otherwise'they were weak and needed proof, even if
they were not invalid. The truth is, the reasoning under
either of these Figures is just as conclusive as under the
First. In neither case can the Conclusion be denied without involving the denier in an absurdity, - that is, in a contradiction of one of the Primary Axioms of Pure Thought.
Nay, more; in certain cases, it is, in one' sense,:more
natural to make inferences by the Second or Third Figure,
than by the First; that is, the particular object which we
have in view in the general investigation or course of argument which we are pursuing, may more directly lead us to
the former than to the latter. Thus, when we wish to
exclude something from a class to which it had been
wrongly assigned, or to disprove something which has been
asserted, we are most frequently led to argue in the Second
Figure, since any Conclusion in this Figure must be negative; for as the Middle Term is here Predicate in both
Premises, it cannot be distributed unless one of the Premises is negative, and then, by Rule 5, the Conclusion is
negative. "The arguments," says Whately, "used in the
process called Abscissio infiniti, will, in general, be the most
easily referred to this Figure. This phrase was applied by
some logicians to a series of arguments used in any inquiry
in which we go on excluding, one by one, certain suppo




196        MEDIATE INFERENCE OR SYLLOGISM.
sitions, or certain classes of things, from that.whose real
nature we are seeking to ascertain."
Again, if our design is to establish exceptions to a pretended law or rule, - that is, if we would disprove the asserted universality of the Proposition,- the Third Figure
will most commonly answer our purpose, for here all Conclusions must be Particular; we prove that Some are, or
Some are not, and thus disprove the assertion that All are
not, or All are. Conclusions in the Third Figure must be
Particular, because both Terms of the Conclusion appear
as Predicates in the two Premises; hence, if these Premises are both Affirmatives, their Predicates are Particular;
and if one of them is Negative, the Conclusion can only be
a Particular Negative, since a Universal Negative distributes both its Terms.
Because the two lower Figures are thus not only valid
in themselves, but peculiarly appropriate for certain purposes, some logicians hold that it is unnecessary to reduce
them to the First Figure.  Each of the three, they maintain, has its own functions and its own governing principle.
The principle which is assigned to the First, needs but to
be slightly modified in order to be directly applicable to
the Second or the Third; since all three are but various
applications of the same Axioms of Thought.  Thus, if the
Dictum de omni et nullo be considered as the principle for
the First Figure, for the Second we have the -Dictum de
diverso, - that if one Term is contained in, and another excludedfrom, a third Term, then they are excluded from each
other.  For the Third Figure, the principle is called the
Dictum de exemplo, - that two Terms which contain a common part partly agree; or, if one contains a part which the
other does not, they partly differ.
Reduction is not essential, therefore, but it is certainly
convenient; the reasoning does not become more cogent by
being reduced to the First Figure, but it is rendered more




FIGURE AND MOOD.               197
perspicuous, more simple and natural in expression, and
any fallacies in it, which might otherwise escape notice,
become at once so obvious that they cannot avoid detection.
The whole theory of argumentation, moreover, is rendered
more systematic and elegant, when its numerous modes
are reduced to a very few fundamental forms, the validity
of which is so manifest that they do not need to be tested
by the application of previously determined rules.
The proper relative position of the three Judgments of
a Syllogism appears so obvious, on the Aristotelic doctrine,
that it has usually been taken for granted. If we reason
only in order to instruct, to convince, or to refute, -and
no other purpose seems to have been contemplated by the
old logicians, - the natural order of Thought seems to be,
that the Ground or Reason should precede the Consequence; that is, that the Premises, as their name imports,
should precede, and, as it were, effectuate the Conclusion.
And as regards the two Premises, if the reasoning is exclusively in the Quantity of Extension, the Major should
be placed before the Minor, the Sumption or General Rule
before the Subsumption.
The Mood of a Syllogism is the value of its three Judgments considered in respect to their Quantity and Quality.
Since there are but four kinds of Judgments as thus viewed,
indicated respectively by the four vowels A, E, I, and 0,
it is evident that three of these letters must express any
possible Mood. When we have ascertained its Mood and
Figure, the classified place and formal value of a Syllogism
are determined. For instance, E I O, Fig. I., and A A I,
Fig. III., are thus expressed: —
FIG. I.                  FIG. III.
No M is P;          E        All M are P;       A
Some S are M;       I        All M are S;       A.'. Some S are not P.   0.. Some S are P. 




198        MEDIATE INFERENCE OR SYLLOGISM.
As only four Judgments are possible, and three are
necessary to constitute a Syllogism, the whole number of
Moods can be numerically determined.  Only sixvty-four
different arrangements can be made out of four letters
taken three at a time; hence, sixty-four Moods are conceivable. But the greater number of these are invalid, as
contradicting one or more of the General Rules which
govern, as we have seen, all forms of Mediate Inference.
The elimination of these invalid forms can be more easily
effected, if we first reduce the expression of a lMood to its
simplest form.
Strictly speaking, only the two letters which denote the
Premises need to be taken into account; for the Quantity
and Quality (and therefore the letter) of the Conclusion
are determined by those'of the Premises. Each Mood,
then, being designated by only two letters, and only sixteen different arrangements being possible of four letters
taken two at a time, all conceivable Moods are contained
in the following list:- 
i.) A A        2.) E A        3.) IA        4.)     A
A E              _E          BI t'         O E
AI             EI             II            o01
AO             BO             0             00
The Rule that from two Negative Premises no Conclusion
can be drawn, excludes four from this list, namely, E B,
] 0, O E, and O O. The Rule that no Conclusion can be
drawn from two Particular Premises, excludes three more,
nlamely, I I, I 0, and 0 I. Finally, I E is excluded because its Negative Conclusion distributes the Major Term,
which is undistributed in I, the Major Premise; but
according to Rule 6, neither Term can be distributed in the
Conclusion, if it was not distributed in the Premise.  We
may here observe, that the violation of this last Rule, in
respect to the Major Term, is called illicit process of the




FIGURE AND MOOD.                199
Mfajor; in respect to the Minor Term, it is called illicit
process of the Minor.,
These exclusions being effected, there remain but eight
valid Moods, namely, A A, A E, A I, A 0, E A, E I,
I A, and O A. Not all, even of these eight, however,
afford a valid Syllogism in each of the four Figures; for
the altered position of the Middle Term may cause the
greater number of them to offend against the Rules which
forbid both anl undistributed Middle and an Illicit Process
whether of the Major or Mr inor Term. Special Rules
have been enounced for each of the Figures, which will
enable us to make the further exclusions that are requisite.
It should be observed, that these Special Rules contain no
new  principle, but are immediately deducible from  the
General Rules, that have already been established for all
Syllogisms; taking these General Rules in connection, however, with the two axioms by which the Aristotelians determine the implicit Quantity of the Predicate; namely,
that, in all Affirmative Judgments, the Predicate is Particular, and that, in all Negative Judgments, the Predicate
is Universal. This deduction may be left as an exercise
for tmhe learner. We will here consider the Special Rules
under that theory which regards every Mediate Inference
as proceeding from the Subsumption of a particular case
under a General Rule or Sumption; little more than an
alteration of phraseology will be needed to adapt them to
the theory in which we speak only of Major and Minor
Premises.
The Special Rules for the First Figure are,1. The Sumption must be Universal;
2. The Subsumption must be Affirmative.
These two Rules exclude I A, 0 A, A EBC, and A 0.
There remain A A, E A, A I, and. I, as the only valid:Moods in this Figure; and these are named Barbara, Celarent, cDari, and Ferio.  Observe that the three vowels




200        MEDIATE INFERENCE OR SYLLOGISM.
in each of these names denote the Mood of the Syllogism
to which it is applied; and the same is true of the technical
names which will be given to the valid Moods in the other
Figures.
The Special Rules for the Second Figure are, -
1. The Sumption must be Universal;
2. One of the Premises must be Negative, and therefore the Conclusion must be Negative.
These Rules exclude I A, 0 A, A A, and A I; thle
there remain as valid in the Second Figure only the four
Moods which have been named Cesare, Camestres,:FestinoQ
and Baroko.
The Special Rules for the Third Figure are, —
1. The Subsumption must be Affirmative;
2. The Conclusion must be Particular.
Throwing out A E and A 0 under these Rules, there
remain for tile Third Figure six Moods, named Darati.
Disamis, cDatisi, Felapton, Bokardo, and _Ferison.
The Special Rules for the Fourth Figure are, -
1. If the Sumption is Affirmative, the Subsumption
must be Universal.
2. If either Premise is Negative, the Sumption must be
Universal.
3. If the Subsumption is Affirmative, the Conclusion
must be Particular.
Rejecting A  I, A  0, and 0 A, as offending against
these Rules, there remain only five Moods, called Bramnantip, CUamenes, Dimaris, Fesapo, and.Fresison, as valid
in the Fourth Figure.
Taking the four Figures together, therefore, there are
nineteen valid Moods; but as fifteen of these can be reduced to those of the First Figure, there are only four
Moods which are at once valid, natural, and perspicuous.
Regarding the last vowel in the names of these four (Barbara, Celarent, D)arii, Ferio), we see that these are just




FIGURE AND MOOD.                201
sufficient to prove the four fundamental Judgments, A, E,
I, and O.
If we exclude the Fourth Figure altogether, considering
Bramantip, Ccamenes, &c. as indirect Moods of the First,
there are but fourteen direct Moods. On the other hand,
since from every Syllogism with a Universal Conclusion
we can obtain, by Subalternation, a Particular Conclusion
also, there are five other indirect Moods, which are anonymous, making twenty-four in all. Thus, A A in the First
yields I, as well as A, for a Conclusion; and from E A in
the Second, we may conclude not only E, but 0. But
these anonymous Moods, besides being indirect, are practically useless; since it is idle to infer some only, when the
Premises warrant the inference of all.
Rejecting the Fourth Figure and the indirect Moods,
it will be seen, from examining the last vowel in each of
the names, that A is proved only in one Figure and one
Mood; E in two Figures and three Moods; I in two Figures and four Moods; and O in three Figures and six
Moods. " For this reason," says Mr. Mansel, "A is declared by Aristotle to be the most difficult proposition to
establish, and the easiest to overthrow; 0, the reverse.
And, generally, Universals'are most easily overthrown,
Particulars more easily established."
The names of all the valid Moods have been put together into the following mnemonic hexameters, which
deserve careful study, not only as a complete artificial
system for the Reduction of all the Moods of the subordinate Figures to those of the First, (for which purpose the
names were invented,) but as a literary curiosity. They
have been in use in the Schools, as an aid to the memory, for over six centuries, their authorship being unknown.  Mr. DeMorgan calls them  "the magic words
which are more full of meaning than any that ever were
made."  Sir William Hamilton says of them that "there
9*




202        MEDIATE INFERENCE OR SYLLOGISM
are few human inventions which display a higher ingenuity."
BARBARA, CELARENT, DARII, FERIOQUE prioris.
CESARE, CAMESTRES, FESTINO, BAROKO secundm.
Tertia DARAPTI, DISAMIS, DATISI, FELAPTON,
BOKARDO, FERISON habet. Quarta insuper addit
BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON.
If, rejecting the Fourth Figure, we consider its contents
as indirect Moods of the First, instead of the first line, the
two following should be substituted: —
BARBARA, CELARENT, DARII, FERIO, B3AALIp-ton,
CELANTES, DABITIS, FAPESMO, FRISESOM-0rum,
the final syllables in italics being only euphonic.
As already mentioned, the three vowels in each of these
names indicate the Quantity and Quality of the three Judgments which form the Syllogism. The consonants in the
names belonging to the First Figure have no special meaning; but of those in the other Figures, every consonant
(except T and N, which are merely euphonic) indicates
some step to be taken in the process of reducing the Mood
to a Mood of the First Figure.
The initial consonant, which is either B, C, D, or F,
indicates that Mood of the First Figure (Barbara, Celarent, Darii, or ETerio) to which the Reduction brings us.
Thus, Cesare and Camestres are reduced to Celarent; EPestino, Felapton, &c., to EFerio. The other consonants show
how the Reduction is made. M indicates that the Premises
are to be transposed; s and P, that the Judgment indicated
by the vowel immediately preceding is to be converted,
s, that it is to be converted simply, while P signifies the
conversion per accidens.
K, which occurs in the names of only two Moods, Baroko and Bokardo, denotes that the Judgment indicated
by the preceding vowel is to be left out, another substituted for it, and the process to be then completed by




FIGURE AND MOOD.                   203
a Reduction per inpossi6ile, which will be explained hereafter.
A  few  examples will sufficiently illustrate the process.
The name Disamis indicates the following Syllogism  of
the Third Figure, which is to be reduced to D)arii of the
First, by converting simply its Major Premise, transposing
its Premises, and then converting its Conclusion.
DISAMIS        reduced to        DARTI.
Some M are P;                    All M are S;
All 31 are S;                     Some P are Ml;.-. Some S are P..'. Some P are S.
Some wars are justifiable;    All wars are inexpedient;
All wars are inexpedient;    Some justifiable acts are wars;
e'. Some inexpedient acts are.'. Some justifiable acts are inexjustifiable.                 pedient.
Festino of the Second is reduced to Eerio of the First
Figure, by converting simply its Major Premise.
FESTINO         reduced to       FERIO.
No P is M;                    No M is P;
Some S are M;                 Some S are M;
le. Some S are not P..o. Some S are not P.
No ruminant is solid-hoofed;    No solid-hoofed animal is
ruminant;
Some herbivora are solid-        Some herbivora are solidhoofed;                         hoofed;.'. Some herbivora are not rumi-.. Some herbivora are not
nant.                           ruminant.
Eesapo of the Fourth is reduced to Eerio of the First
Figure, by converting both its Premises, the Major simply,
and the Minor per accidens.
FESAPO         reduced to        FERIO.
No P is M;                     No M is P;
All M are S;                   Some S are  1;.-. Some S are not P..-. Some S are not P.




204        MEDIATE INFERENCE OR SYLLOGISM.
No Hindoo is white;            No white is a Hindoo;
All whites are civilized;      Some civilized are whites.'. Some civilized are not Hindoos.,. Some civilized are not
Hindoos.
Baroko and Bokardo have been stumbling-blocks to the
logicians. In order to reduce either of them to the First
Figure, the Premise which needs to be converted is O;
but according to the old doctrine, O is inconvertible. To
overcome this difficulty, the logicians invented the awkward, roundabout, and operose process which they called
Reduction per Impossibile. Through a Syllogism in Barbara, they proved, not directly that the Conclusion in
Baroko and Bokardo is true, but that its Contradictory is
false; now, according to the Axiom of Excluded Middle
(that two Contradictories cannot both be false), this is an
indirect method of proving that the Conclusion is true.
The process is as follows.
Of course, both Premises in every Syllogism  are presumed to be true; then, any Conclusion which contradicts
either one of them must be false. Now, K indicates, that,,
instead of the Premise signified by the vowel (0) immediately preceding, we are to substitute the Contradictory
of the Conclusion; and as this Conclusion is 0, its Contradictory is A.  But from  the two Premises (A A) thus
obtained, we have a Conclusion which contradicts the original Premise, 0.  Then the substituted Judgment in A
(which is the Contradictory of the original Conclusion)
must be false; and therefore the original Conclusion itself
is true. This is not exactly reducing the Syllogism to the
First Figure, but it is indirectly proving, through the First
_Figure, that the Conclusion of the Syllogism must be true,
because its Contradictory is false.
BAROKO    reduced to      BARBARA.
All P are M;        All P are M;               [elusion.)
Some S are not M;   All S are P; (Contradictory of former Con..'. Some S are not P..'. All S are M. (Contradicts former Minor
Premise.)




FIGURE AND MOOD.                  205
BOKARDO     reduced to       BARBARA.
Some M are not P;    All S are P; (Contradictory of former
All M are S;         All M are S;   Conclusion).. Some S are not P..'. All M  are P. (Contradicts former Major
Premise.)
As this Conclusion  in Barbara cannot be true, its
Premise, which is the Contradictory of the former Conclusion, must be false; then the original Conclusion itself
is true.
All this is awkward  enough.  Whately and others
rightly remark, that these two difficult Syllogisms can be
reduced in a much simpler and more elegant manner,
through converting one of their Premises by Contraposition.  Thus, let Baroko be now called Fakoro, and let
Bokardo be named -Dokamok (the substitution of these two
names will not spoil the mnemonic hexameters); and let
K indicate Conversion by Contraposition.
FAKORO        reduced to      FERIO.
All P are M;               No not-M is P;
Some S are not M;         Some S are not-M;.-. Some S are not P..-. Some S are not P.
All murders are intentional;    No unintentional act is a
murder;
Some homicides are not inten-   Some homicides are unintional;                         tentional;.'. Some homicides are not mur-.-. Some homicides are not
ders.                           murders.
DOKAMOK       reduced to    DARII.
Some M are not P;        All M are S;
All M are S;             Some not-P are M;.'. Some S are not P..'. Some not-P are S; (or, convert
by Contraposition,).'. Some S are not P.
Some imprudent acts are    All imprudent acts are foolish;
not vicious;
All imprudent acts are foolish; Some not-vicious  acts  are
imprudent;




206        MEDIATE INFERENCE OR SYLLOGISM.. Some foolish acts are not.~. Some not-vicious  acts are
vicious.                  foolish;.-.Some foolish acts are not
vicious.
These examples show that, after Dokamnok has been reduced to Darii, the Conclusion must be contraponed back
again, if we would have it in its original form.
Ingenious as this whole system of Reduction is, it is
needlessly artificial and complex. The sole reason for reducing Syllogisms to the First Figure, we have said, is
to exhibit the reasoning in its simplest and most natural
form, and in that in which its validity, or invalidity, is most
readily perceived. A few simple Rules may be given
which will enable the learner to accomplish this object at
once, in whatever Figure the argumentation may originally
be propounded, and even without knowing what this Figure is.
1. Every process of reasoning must consist of a Judgment which is to be proved, and of one or two other Judgments alleged in its support; the former is the Conclusion,
the latter are the Premises. The first step is to reduce
each of these Judgments to its simplest logical form, —
that is, to a Subject and Predicate connected by the present tense (affirmative or negative) of the verb to be. Care
must, be taken to determine accurately the Quantity and
Quality of each of the Judgments.
2. The Middle Term is that which does not appear in
the Conclusion. If no such Term is found in the Premises, the Inference is Immediate, and must be tried by the
principles laid down in the preceding chapter, concerning
Conversion, Opposition, &c. If there is a Middle Term,
the Inference is Mediate; then the Major Premise is that
Judgment in which this Middle Term appears connected
with the Predicate of the Conclusion; the Minor Premise,
that in which it is connected with the Subject of the




CONDITIONAL SYLLOGISMS.           207
Conclusion. If only one Premise is given in the original
statement, the other may be easily supplied by a moment's
consideration, as its two naked Terms are known, and its
Quantity and Quality may be inferred, through the General
Rules already given for all Syllogisms, from the Quantity
and Quality of the Conclusion and the given Premise.
3. The First Figure requires the Middle Term to be the
Subject of the Major, and the Predicate of the Minor,
Premise. If, in the Premises as determined, the Terms do
not already appear in this order, one or both must be converted, either simply, or per aceidens, or by Contraposition.
There can be no difficulty in the application of these
Rules, which does not arise from some ambiguity in the language of the original statement; and to resolve such ambiguity is the business, not of the logician, but of the grammarian and the lexicographer. But a few cases will be
incidentally resolved when we come to treat of Fallacies, a
subject which cannot be fully considered without sometimes stepping out of the province of Pure Thought.
2. CONDITIONAL SYLLOGISMS.
Thus far we have treated exclusively of the purely Categorical Syllogism, in which each of the component Judgments call be reduced to one or the other of the two Categorical formulas, A is B, or A is not B. The reasoning in
this case, as we have seen, depends upon the two Axioms
of Identity and Non-Contradiction.  We come now to
another class of Syllogisms, -dependent upon the Axioms
of Reason and Consequent, and Excluded Middle.
A Conditional Syllogism is one of which the Major Prem2ie, and only the Major Premise, is a Conditional Judgment.
There are three kinds of such Syllogisms, corresponding to
the three classes into which Conditional Judgments are
divided; namely, the Hypothetical, the Disj'unctive, and the




208        MEDIATE INFERENCE OR SYLLOGISM.
)Dilemmatic or Jfypothetico-Disjunctive. The following are
examples of each.
Hypothetical.             Disjunctive.
If A is B, C is D;        A is either B or C;
Ais B;                     AisB;.'. C is D..'. A is not C.
Dilemmatic or Hypothetico-Disjunctive.
If A is B, C is either D or E;
C is neither D nor E;. A is not B.
These Terms may be quantified in the Minor Premise,
as in Categorical Syllogisms, and the Conclusion will still
be valid, if its proper Quantity be assigned to it according
to the Rules already given. Thus, if the Minor Premise
of the preceding Hypothetical be' All A are B," we may
conclude that "All C are D"; but if we know only that' Some A are B," we can only conclude that "Some C
are D." We may likewise use the quantification of Singulars, and say, " this A," or " in certain cases, A is B ";
then, " in this case," or " in the same cases," C is D.
Dr. Thomson seems to be wrong, therefore, when he
gives the following as an instance of a Hypothetical Syllogism, Figure I. in which each of the three Judgments is
Hypothetical.
In cases where M is N, C is D.
In cases where A is B, M is N.
In cases where A is B, C is D.
Here, the supposed Condition, "in cases where A is B,"
is only an awkward quantification of the Minor Premise
and the Conclusion, equivalent to " in certain cases," or
"some M is N "; therefore, in these cases, or some, C is D.
The reasoning does not turn upon this phrase, "in cases
where A is B," as a condition, the Consequent being
evolved from' it; it turns upon it only as a limitation,




CONDITIONAL SYLLOGISMS.          209
showing in how many-cases the reasoning is applicable.
The reasoning does rest exclusively upon the Major
Premise, where the corresponding phrase, "' in cases where
M is N," is a true condition, the Consequent being evolved
from it, and the whole argumentation being governed by
the Axiom of Reason and Consequent.
This error has led Dr. Thomson into a more serious one.
Not perceiving that Hypothetical Reasoning is distinct in
kind from Categorical, being governed by a different Axiom
of Thought, he has overlooked the principle that, from
affirming the Consequent of a Reason, no Conclusion can be
drawn, and has presented the following as a valid Syllogism:In cases where C is D, M is N;
In cases where A is B, M is N;..In cases where A is B, C is D.
But here the Minor Premise only affirms that " M is N,9
which is the Consequent of the hypothesis in the Major
Premise; and therefore the Conclusion is illogical; the
Middle Term is not distributed. This can be easily seen
from the following example, the Conclusion of which is
evidently a non sequitur.
If you whip him, the boy cries;
If you take away his toys, the boy cries;. If you take away his toys, you whip him.
Then, in a Conditional Syllogism, it is only the Major
Premise -which is a Conditional Judgment; for the reasoning turns upon the relation of Reason and Consequent, and
this relation, being once affirmed in the Major Premise,
affords all the material requisite for the Inference. Both
the Minor Premise and the Conclusion must be Categorical;
the Major contains all the Terms which appear in either of
them; whereas, the Minor Premise of a Categorical Syllogism contains a new Term, which did not appear in the
Major. If, then, both Premises, or one Premise and Cons
N




21u       MEDIATE INFERENCE OR SYLLOGISM.
elusion, are Conditional Judgments, the reasoning is, in
fact, Categorical, and depends upon the Axioms of Identity
and Non-Contradiction. This is easily seen in the case of
a Disjunctive Syllogism, whose form is determined by the
Axiom of Excluded Middle.
Every A is either X or Y;
But B is A;
Then B is either X or Y.
Here the reasoning is evidently Categorical; the Minor
Premise introduces a new Term, B, not contained in the
Major Premise, and therefore the Conclusion is also Disjunetive.
Endeavoring to prove that, in a Disjunctive Syllogism,
not only the. Major, but the Minor Premise or the Conclusion, may be a Disjunctive Judgment, Dr. Thomson presents the following as a valid example: —
C, D, and E are B;
C, D, and E - A;.. A is B.
This is not a Disjunctive Syllogism at all, as neither of the
three Judgments is Disjunctive; the three Concepts which
constitute the Middle Term  are not taken disjunctively,
but collectively; that is, one of them does not exclude the
others, but requires the presence of the others, in order to
constitute the Predicate. They form one compound Term.
Thus, let C, D, and E - 1X, and mnake the substitution.
Then the Syllogism assumes this form, and is evidently
Categorical.
M is B;
M A;.'. A is B.
The Axiom of Reason and Consequent is explicated, as
we have seen, into these two principles; — to affirm the.Reason or the Condition is also to affirm the Consequent or
the Conditioned; and to deny the Consequent is also to deny




CONDITIONAL SYLLOGISMS.           211
the Reason. The application of these principles gives us,
from the same Major Premise, two, and only two, valid
Moods of the Hypothetical Syllogism, - namely, the
Modus Ponens and the Modus Tollens. Thus:If A is B, C is D.
MODUS PONENS.          MODUS TOLLENS.
A is B;               C is not D;
Then C is D.         Then A is not B.
The following are examples of these formulas:MODUS PONENS.
If matter is essentially inert, every change in it must be
produced by mind;
But matter is essentially inert;
Then all changes in it are produced by mind.
MODUS TOLLENS.
If the moon shines by its own light, it must always be full;
But it is not always full;
Then it does not shine by its own light.
We have said that there are only two valid Moods, because, from denying the Reason, or from affirming the Consequent, nothing follows. The Consequent may follow from
some other Reason than the particular one assigned in the
Major Premise; and the original Axiom only affirms the
necessity of some Reason or other, not of any particular
one. It is true, that the Minor Premise may be quantified
with the predesignations all, some, or this, and corresponding Conclusions will follow. The different forms which
thus result may, if we please, be called Moods also.
The Major Premise, or Sumption, in either of the preceding examples, may be converted by Contraposition;
and the result will be, that what was the Modus Tollens
becomes the Miodus Ponens, and vice versa. These two
Moods are thus shown to be really one; and this is precisely what we should -expect, for the two principles by




212       MEDIATE INFERENCE OR SYLLOGISM.
which they are governed are only two explications of one
Axiom of Thought. Thus, the last preceding example,
which is now the Modus Tollens, becomes the following, if
we contrapone the Sumption: —
If the moon is not always full, it does not shine by its own
light;
But it is not always full;
Then it does not shine by its own light.
Here the Subsumption posits what is now the Reason,
(though both are negative in form,) and therefore the
Conclusion posits the Consequent. Hence the reasoning
has now become the Modus Ponens.
Summing up what has been said, it appears that the
Hypothetical Syllogism is subject to these three Special
Rules: -
1. It consists of three Judgments, and only three; but in
these Judgments there may be more than three Terms.
2. In respect to Quantity and Quality, the Sumption
must always be Affirmative and Universal, while the Subsumption may vary in either of these relations.
3. The Conclusion is regulated, both in Quantity and
Quality, by that member of the Sumption which is not
subsumed, agreeing with it in both these respects in the
Modus Ponens, and differing from it in both in the Modus
Tollens.
The Sumption in the last example (after Contraposition)
may seem not to conform to the second of these Rules; for
it appears to be Negative in Quality. But if closely examined, the negative particle not will be found to belong
to each of the two parts (Reason and Consequent) taken
separately; while the Sumption, as a whole, affirms the
connection of these two negative parts with each other.
Agreeably to what has been said, a -Disjunctive Syllogism
is one of which the Major Premise is a -Disjunctive Judy.




CONDITIONAL SYLLOGISMS.                 213
wment, while the ]Yinor Premise and the Conclusion are Categorical Judgments. The Axiom of Excluded Middle, by
which this sort of Syllogism is governed, affirms that, of
two Contradictories, one must be true and the other must
be false. Accordingly, if the Major Premise presents
three or more Disjunct Members, the Axiom will not be
immediately applicable; these three or more Members are
only Contraries with respect to each other, and they must
be reduced to two Contradictories, before we can obtain a
ground of inference, from positing or sublating one of them,
to sublating or positing the other. The number of such
Members can always be thus reduced by considering, for
the moment, two or more of them as one. After this reduction is accomplished, the Minor Premise and Conclusion
appear in their true character, not as Disjunctive, but as
Categorical Judgments. For example: —
Complete Formula.           Reduced Formula.
A is either B, C, or D;           Let B or C =fX.
But A is neither B nor C;   A is either X or D;
Then A is D.*                  But A is not X;
Then A is D.
This formula, as reduced, presents the universal type of
Disjunctive reasoning.  As its two Disjunct Members are
Contradictories of each other, the Axiom of Excluded Middle authorizes us, from positing either one of them, to sublate the other.  This is called the Modus ponendo tollens,
and it has two forms, according as we posit one or the
other of the two Disjunct Members.  The same Axiom
* A story is told to illustrate the sagacity of a dog. Following his
master by the scent, the animal came to a place where three roads met, and
having ascertained by his nose, at two of them, that the object of his search
had not taken either of the two, he immediately darted off by the third, without pausing to try whether this path also was scentless. The story is unquestionably a fiction; but, if true, the dog must have reasoned by this form
of the Disjunctive Syllogism,, in the modus tollendo ponens.




214         MEDIATE INFERENCE OR SYLLOGISM.
permits us, from sublating either of the two, to posit the
other.  This is called the Modus tollendo ponens, and has
two forms like the other. Hence, every Disjunctive Syllogism  affords, from  the same Major Premise, two valid
Moods, each containing two forms. It is obvious, that the
remaining Term, A, of the Major Premise, may be quantified as all or this, and the Conclusion will appear accordingly as Universal or Singular.  The two Moods and four
forms of a Disjunctive Syllogism  are exhibited in the following example:Major Premise.  Every Judgment is either Affirmative or
Negative.
MODUS PONENDO TOLLENS.
Eirst form.    This Judgment is Affirmative;
Then it is not Negative.
Second form.  This Judgment is Negative;
Then it is not Affirmative.
MODUS TOLLENDO PONENS.
First form.    This Judgment is not Affirmative;
Then it is Negative.
Second form.  This Judgment is not Negative;
Then it is Affirmative.
For those who are fond of mnemonic hexameters, Hamilton has presented all four forms in the following verses:Ponendo tollens.  Falleris aut fallor; fallor; non falleris ergo.
Falleris aut fallor; tu falleris; ergo ego nedum.
Tollendo ponens. Falleris aut fallor; non fallor; falleris ergo.
Falleris aut fallor; non falleris; ergo ego fallor.
Three Special Rules have been framed for Disjunctive
Syllogism, though they are so obvious that their formal
enouncement is hardly necessary.
1. A regular Disjunctive Syllogism must consist of
three Judgments only, in which, if the Major Premise
be reduced  to its proper logical form, there, can  be




CONDITIONAL SYLLOGISMS.           215
only three Terms, all of which must appear in the Major
Premise.
2. The Major Premise must be Universal and Affirmative; the Minor Premise may be of either Quality and of
either Quantity.
3. The Conclusion must be of the same Quantity, but of
opposite Quality, with the Minor Premise.
Agreeably to what was said in treating of Disjunctive
Judgments, each Mood of a Disjunctive Syllogism may be
resolved into a Hypothetical Syllogism, and then its two
forms appear as the two Moods of the Hypothetical reasoning. For instance, the example last cited may be thus
transformed: -
If any Judgment is not Affirmative, it is Negative.
Modus Ponens.        Modus Tollens.
This Judgment is not Af- This Judgment is not Negfinmative;                  ative;
Then it is Negative.        Then it is Affirmative.
As a Dilemmatic Syllogism consists of a Hypothetical
and a Disjunctive combined, and as these two may be combined in several different ways, the resulting forms are
numerous and complex. Most of them are really compound, and a full analysis would need to resolve them
into several simple and subordinate Syllogisms. It would
be tedious to analyze them all, and this is not necessary,
as the principles already established for the Hypothetical
and the Disjunctive Syllogisms taken separately, still govern them when taken in connection; and the learner in
each case may make the analysis and apply the principles
for himself. What follows is to be regarded only as illustrating the method to be pursued.
What has already been presented as a type of the Dilemmatic Syllogism is, in fact, only a Hypothetical disguised, as the Disjunction is not resolved, and therefore its




216        MEDIATE INFERENCE OR SYLLOGISM.
Disjunct Members, whether two or more, may be regarded
as a single Term.
If A is B, C is either D or E.
MODUS PONENS.              MODUS TOLLENS.
But A is B;             C is neither D nor E;.'. C is either D or E..'. A is not B.
In practice, however, the Disjunction is usually resolved,
in the Modus tollens, by two subordinate (abridged) Syllogisms, by which it is first separately proved that C is not D,
and that C is not SE; and then the Conclusion of the compound Modus tollens follows, that A is not B.  Thus:If man cannot be virtuous, either he must be unable to
know what is right, or unable to will what is right.
But he is not unable to know what is right, for he is intelligent; and he is not unable to will what is right,
for he is free.
Therefore, he can be virtuous.
Hence, the Dilemma was called by the old logicians
the Cornutus or horned syllogism, because, in the Sumption, -the Disjunct Members are opposed like horns to the
assertion of the adversary; with these, we throw it from
one side to the other in the Subsumption, in order to toss
it altogether away in the Conclusion.
Krug remarks: " The Cornutus and Crocodilinus of the
ancients must not be confounded with the Dilemma which
we are here speaking of. The former were sophismata
heterozeteseos, sophisms of counter-questioning; the latter is
a legitimate mode of reasoning." But it may be shown
that the old Cornutus is a legitimate Dilemma in Form,
and is of the type which we are now considering, the fallacy being in the Matter. The Litigiosus, for instance,
which is one illustration of this old fallacy, may be thus
resolved.




CONDITIONAL SYLLOGISMS.           217
Protagoras agreed for a large sum to educate Euathlus
as a lawyer, one half of the price to be paid down, and
the other half on the day when the pupil should plead and
gain his first cause. Some time elapsed, and Protagoras,
thinking that his disciple intentionally delayed the completion of his contract, sued him in court for the remainder
of the fee', and propounded this Dilemma.
If Euathlus is to be released from the payment of this
sum, it must be either because the judgment of this court
will be in his favor, or against him.
But if the judgment is in his favor, then he has pleaded
and gained his first cause, and the money is due me under
the contract.
If the judgment is against him, the money is due me
under the decision of the court.
Thus, both the Disjunct Members of the Consequent
being disproved by subordinate Syllogisms, the Conclusion
of the compound Modus tollens follows, that Euathlus is
not to be released from the payment.
The Dilemma is here correct in Form, but there is a
Material Fallacy in the Major Premise, since the Disjunction is not complete. There is a third horn to it, as Protagoras had no right, under the contract, to invoke the
judgment of the court at all, so that the judges ought to
have dismissed the case without a hearing. Before a judgment was rendered, Protagoras had no ground of action.
Euathlus is said to have retorted upon his antagonist, by
propounding a Dilemma in the same Form in which it had
just been urged against him. " If the decision be favorable to me, I shall pay nothing under the sentence of the
court; if adverse, I pay nothing in virtue of the compact,
because I shall not have gained my first cause."
"In sifting a proposed Dilemma," says Krug, "we are
to look closely to the three following particulars:1. Whether, in the Sumption, the Consequent is a legiti10




218    iMEDIATE INFERENCE OR SYLLOGISM.
mate inference from  the Antecedent; 2. Whether the
Disjunction in the Consequent is complete; 3. Whether,
in the Subsumption, the Disjunct Members are properly
sublated.  The following Dilemma is faulty in each of
these respects.
"' If Philosophy be of any value, it must procure for us
power, riches, or honor.
" But it procures neither of them. Therefore, &c.
"Here, 1. the inference is wrong, as Philosophy may be
worth something, though it does not secure any of these
external advantages; 2. the Disjunction is incomplete, as
there are other goods, besides the three here enumerated;
3. the Subsumption is false, as Philosophy has often been
the means of procuring these very advantages."
In another form of the Dilemma, the Sumption is a
Hypothetical Judgment with more than one Antecedent,
and the Subsumption is a Disjunctive of which these several Antecedents are the Disjunct Members.
IfAisB, CisD; and ifEisF, CisD;
But either A is B or E is F;.-. C is D.
Here, the several Antecedents have the same Consequent, and therefore the Conclusion is Categorical.  If
they had different Consequents, the Conclusion would be
Disjunctive. Thus:If A is B, C is D; and if E is F, G is H;
But either A is B or E is F;.'. Either C is D, or G is H.
In this case, the Modus tollens is also valid; if we disjunctively deny the Consequents, we may, in the Conclusion, disjunctively deny the Antecedents.
Either C is not D, or G is not H... Either A is not B, or E is not F.
In the preceding case, where the Antecedents had the




DEFECTIVE AND COMPLEX SYLLOGISMS.      219
same Consequent, if we deny this one Consequent, we must
deny the Antecedents taken collectively, and not disjunctively; then the Syllogism will be exclusively Hypothetical, as neither Judgment will be disjunctive. Thus:If A is B, Cis D; and if E is F, C is D;
But C is not D;.'. Then A is not B, and E is not F.
The nature of a Disjunction is, that any one of the Disjunct Members exists, or is posited, only by the non-existence, or sublation, of all the others. Hence, the particles,
either- or, have a Disjunctive force; but the corresponding
negative particles, neither -nor, have a Conjunctive force,
as they denote the exclusion of both or all, and not merely
the exclusion of one on condition of the inclusion of all the
others. A is either B or C, means that A is B only on condition that A is not C. But A is neither B nor C, means
that A is not B and is not C.
It has been remarked, that the Mod-us tollens of the Dilemma, in the form in which it was here first proposed, is
nothing but a Negative induction.
If A is B, C is either D, E, or F;
But C is neither D, E, nor F;
Then A is not B.
This can be resolved into a Categorical Syllogism of
Induction. Thus -
C is not D, is not E, and is not F;
But these are all the possible cases of A being B;
Then A is not B.
3. DEFECTIVE AND COMPLEX SYLLOGISMS.
It has already been mentioned, that men do not usually
speak or write complete Syllogisms; nay, it is almost only
in treatises on Logic that we find Syllogisms completely




220        MEDIATE INFERENCE OR SYLLOGISM.
enounced, or with all their parts expressed. The abridged
form is preferred on all ordinary occasions, because at least
one of the three Judgments is so obvious, both to the
speaker and the hearer, that it would be a waste of time
and words - a sin against brevity, and even against perspicuity - to propound it openly; for unnecessary words
do not elucidate, but obscure, the Thought. We usually
express a single process of reasoning by two Judgments,
connected by an illative particle, because, then, therefore,
&c.; sometimes only by a conjunctive particle, and. The
following are instances of reasoning thus enounced.
Aldebaran is a star; therefore, it shines by its own light.
No avaricious person can be happy; because he who is
never free from fear cannot be happy.
A liar ought not to be believed; and this witness has been
proved to be a liar.
Such sentences as these are called Enthymemes, because
they are abridged statements of a process of reasoning, one
of the three Judgments necessary to constitute the Syllogism being Ev OvpL6, in the mind, but not expressed. In
the first case, the suppressed Judgment is the Major Premise, - all stars shine by their own light; in the second, it
is the Minor Premise, - an avaricious person is never free
from fear, the Conclusion also, as is frequently the case in
Enthymemes, being placed first, instead of last; in the
third case, the suppressed Judgment is the Conclusion, —
this witness ought not to be believed.
An Enthymeme, then, is not a peculiar kind of Syllogism, but only an abridged expression of a Syllogism. Of
course, the doctrine of Enthymemes properly belongs, not
to Logic, but to Rnetoric, for it concerns expression, not
thought; and it would never have been obtruded into the
former science but for the authority of Aristotle, who employed the name, indeed, in a different and now disused




DEFECTIVE AND COMPLEX SYLLOGISMS.       221
meaning, signifying by it " a reasoning from signs and likelihoods."
Hitherto, we have treated only of the so-called Mlonosyllogism, -that is, of a Syllogism considered as one independent whole, without reference to the continuous chain
of reasoning, of which, in an abridged form of expression,
it usually constitutes a single link. Many truths - most
of the theorems in  Geometry, for instance- can be
proved only by a Chain of Reasoning; —that is, by a
connected series of Syllogisms, the several portions of
which are dependent upon each other. A Conclusion of
one -may become a Premise of the next succeeding Syllogism, and is then called, in reference to its successor, a
Prosyllogism; while the latter, in reference to the one
which preceded it, is called an Episyllogism. A Prosyllogism, then, is a Syllogism whose Conclusion is a Premise of
that which follows; and an Episyllogism is one whose Premise is a Conclusion of that which precedes. As, in a hierarchy
of Concepts, the same class-notion is at once a Genus to
the class below and a Species to the class above; so, in a
Chain of Reasoning, the same Syllogism is at once a Prosyllogism and an Episyllogism in its opposite relations.
Only that which contains the primary or highest reason
can be exclusively called a Prosyllogism; only that which
enounces the last or lowest consequent is exclusively an
Episyllogism.
The Syllogism constituting a Chain may be either partly
complete and partly abbreviated, or all equally abbreviated.
In the former case, the complex Syllogism which results is
called an Epicheirema; in the latter, it is called a Sorites.
A Syllogism is called an Epicheirema, when, to either or
both of its two Premises, there is attached a reason for its
support. The Premise with such a rider annexed is, in
fact, a Prosyllogism abbreviated, - that is, an Enthymeme
used to prove one of the branches of the main Syllogism.
Thus:



222        MEDIATE INFERENCE OR SYLLOGISM.
NI is P;                 The flesh of ruminants is good for
food;
S is M, because it is N;   These animals are ruminants, because they have cloven hoofs;.S. S is P..-. These animals are good for food.
Here, the Enthymeme, which is a rider of the Minor
Premise, may be thus explicated into a complete Prosyllogism.
All animals which have cloven hoofs are ruminant;
These animals have cloven hoofs;.'. These animals are ruminants.
It has already been said, that every Syllogism may be
regarded as an application of the general and self-evident
principle, that a part of a part is a part of the whole.  If, in
the application of this principle, we do not stop at the first
or proximate whole, but, before drawing any expressed Conclusion, proceed step by step to remoter parts and more
comprehensive wholes, and, in the Conclusion, finally place
the smallest part under the largest whole; the complex
abbreviated reasoning thus formed is called a Chain-Syllogism, or Sorites.  It may be aptly symbolized by a series
of concentric circles.
2. AisB; 
2. B is'C;
3. C is D;
4. D) is E;
Therefore, A is E.
A Sorites of this sort may be described as a series of
Enthymemes with suppressed Conclusions, in which the Predicate of each is the Subject of the next, and the Conclusion
of the whole is formed from the first Subject and last Predicate of the Premises. The Conclusion being thus formed,




DEFECTIVE AND COMPLEX SYLLOGISMS.        223
it is evident that there must be as many Middle Terms
(i. e. Terms intervening between the first Subject and last
Predicate, that is, again, between the smallest part and the
greatest whole which the reasoning connects) as there are
Premises minus one; consequently, every Sorites may be
explicated into as many distinct Syllogisms as there are
Premises minus one. The first Judgment in the Sorites is
the only Minor Premise that is expressed; each of the
other Minor Premises is the Conclusion of the separate
Syllogism next preceding. Hence, each of the Judgments
in the Sorites except the first is the Major Premise of a
distinct Syllogism.  The preceding Sorites, for instance,
may be thus explicated into three Syllogisms, the correctness of the explication being made very evident by a reference to the diagram.
I.              Il.               III.
2. B is C,        3. C is D,        4. D is E,
1. AisB;            A is C;            A is D;. 0A is C..'. A is 1)..A. A is EE.
An invalid Mood occurring anywhere in  the series
before the last Syllogism would not only be wrong itself,
but, as furnishing a Premise to its successors, would vitiate
all that follow. Hence, in a Sorites, out of all the Premises, only the one first expressed may be Particular; because, in the First Figure, to which all the separate Syllogisms belong, the Minor Premise may be Particular, but
not the Major; and all the Judgments in the Sorites,
except the first and the Conclusion, are Major Premises.
In the Sorites, also, only the last Judgment may be Negative; for if any other of its Judgments were Negative, the
Syllogism formed -from the next following Judgment would
have a Negative Minor Premise, which the First Figure
does not admit. A Sorites in the Modus tollens, then, can
be stated only in.one form;- from denying the last Con



224        MEDIATE INFERENCE OR SYLLOGISM.
sequent of the last Antecedent, we go back to denying
this same Consequent of the first Antecedent. Thus, if
we say that D is not E, we must conclude that A is not BE.
The three distinct Syllogisms already given are not all
that may be formed from the given Sorites. - Instead of beginning with the first Judgment, and thereby finally concluding that A is E, we may begin with the second Judgment, first concluding that B is D, and then that B is E;
and again, beginning with the third, we may conclude that
C is _. Hence, from a Sorites with four Premises, we
may form in all six distinct Syllogisms. If there were five
Premises, there would be ten resultant Syllogisms. "The
formula," says Dr. Thomson, "for ascertaining the number of Conclusions is this:  Let the number of Premises
= n; the number of terms = n + 1; then the number
of Conclusions   n (n -21.2
Goclenius invented another form of the Sorites, to which
his name has been attached; it is the same as the common
form, except that the Premises are reversed. Referring to
the diagram again, it is evident that, instead of beginning
with the Terms of least Extension, represented by the innermost circles, we may begin with the more Extended
Terms in the outer circles. Then the Subject of each
Judgment becomes the Predicate of the next; while, in
the common form, it is the Predicate of the former which
becomes the Subject of the latter. The Goclenian Sorites
is thus stated:D is E,
C is D,
B is C,
A is B;.-.A is E.
Here, Extension is more prominent, as we start with the
wider Terms; hence, this form is better suited for deduc



DEFECTIVE AND COMPLEX SYLLOGISMS.           225
tion. In the common form, Intension predominates, as
the narrower Terms come first; Induction naturally assumes this Form.
" A'pretty quarrel' long existed amongst logicians,"
says Dr. Thomson, "which of the two was to be called
progressive and which regressive.  It was a mere strife
about words. If we are discovering truth by the inductive
method, the Aristotelian form  is progressive; if we are
teaching truth, or trying our laws upon new facts, we use
deduction, and the Goclenian form  is progressive.  In an
apt but familiar figure,- if I am on the ground floor, and
wish to fetch something that is above, my going up stairs is
my progress towards my object, and my coming down is a
regression; if the positions of myself and the thing are reversed, going down would be progress, and returning up,
regress. The inductive truth-seeker is on the ground-floor
of facts, and goes up to seek a law; the deductive teacher
is on a higher story, and carries his law down with him  to
the facts.
6" This will be clearer from a pair of examples.
Goclenian or descending Sorites.  Aristotelian or ascending Sorites.
Sentient beings seek happiness;  Caius is a man;
All finite beings are sentient;    All men are finite beings;
All men are finite beings;     All finite beings are sentient;
Caius is a man;                All sentient beings seek happiness;
Therefore  Caius seeks happi- Therefore Caius seeks happi.
ness.                          ness."
By way of recapitulation, the chief principles and rules
of the Aristotelic doctrine of Syllogism  are brought together, in the following Conspectus.




226             CONSPECTUS OF THE ARISTOTELIC
MEDIATE INFERENCE OR SYLLO-                                 SYLLOGISMS
GISM
CATEGORICAL,
is that act of Thought whereby the in which each of the three Judgments can be
relation of the two Terms of a pos-   expressed under one or the other of these
sible Judgment to each other is  two Formulas:ascertained by comparing each of          X is B;        is not B.
them separately with a Third Term.
GENERAL CANON                              This Canon is explicated
of Categorical Syllogisms. In so far         I.                II
as two Notions, (Concepts or Indi- A  Syllogism  must A  Syllogism  must
viduals,) either both agree, or, one  contain three Terms,  contain three Judgagreeing, the other does not agree,  and no more.     ments, and no more.
with a common Third Notion, in
so far these Notions do, or do not,
agree with each other.
THE FIGURE                                  Let S = Subject of the
Figure I. MP;
of a Syllogism  is determined by the               SM;
relative position of the Middle Term.. S P.
in the two Premises.
THE MOOD                                              VALID
of a Syllogism is the value of its three            Fig. I.
Judgments in respect to their Quan-          A A A; Barbara.
E A E.; Celarent.
tity and Quality, as indicated in            A I I;  Darii.
each case by the four Judgments,             E I O0  Ferio.
A, E, I, and 0.
REDUCTION
of the valid Moods of the three lower   B = Reduce the Mood to Barbara.
Figures to those of the First Fig-    C=    CC    c        Celarent.
D       "     "     Darii.
ure may be accomplished by per-       F       "     "     Ferio.
forming the processes indicated by
the following letters in the names
of those Moods.
GENERAL CANON                             This Canon produces, from
of Hypothetical Syllogisms. To affirm                      Major Premise,
the Reason or the Condition is to             Modus Ponens.
affirm the Consequent; and to deny                A is B
the Consequent is also to deny the
Reason.
GENERAL CANON                             This Canon produces, from
of Disjunctive Syllogisms.  Of two                         Major Premise,
Contradictories, one must be true         Modus ponendo tollens.
and the other must be false.                   1.  AisB;... A is not C.
2. Ais C;.'. A is not B.




DOCTRINE OF SYLLOGISM.                               227
AREI EITHER
OR CONDITIONsL,
in which the Major Premise, and only the Major Premise, is a Conditional Judgment; andr
these are subdivided into
Hypothetical;                Disjunctive;         Dilemmatic or Hypotheti.
Major Premise,              Major Premise,                  cal Disjunctive.
If A is B, C is D.          A is either B or C.            Major Premise,
If A is B, C is either D or E.
into these six General Rules.
III.                 IV.                   V.                   VI.
The  Middle  Term  One Premise at least If either Premise is Neither Term  must
must be distributed   must be Affirmative.  Negative, the Con-  be distributed in the
in at least one of the                    clusion must be Neg-  Conclusion, if it was
Premises.                                 ative.               not distributed  in
the Premise.
Conclusion; P = Predicate of the Conclusion; M = Middle Term. Then,
Figure II. P M;            Figure III. M P i           Figure IV. P Mi
SM;                         MS;            I            MS;.. SP. o'.SP.                                  I.. SP.
MOODS. 
MooDs.
Fig. II.                    Fig. III.                        Fig. IV.
E A E; Cesare.             A A I; Darapti.                  A A I; Bramantip.
A E E; Camestres.           I A I i Disamis.                A E E; Camenes.
E I 0;    Festino.         A I I; Datisi.                  I A I; Dimaris.
A  0;  Baroko (Fakoro).  EJ A 0; Felapton.                  E A 0; Fesapo.
All Negative Conclusions.  0 A 0   Bokardo (Dokamolc).   E I 0; Fresison.
E  -'O. Ferison.
All Particular Conclusions.
m = Transpose the Premises.       Barbara, Celarent, Darii, Ferioque, prioris;
s = Convert simply.              Cesare, Camestres, Festino, Baroko, secunde;
p = Convert per accidens.         Tertia Darapti, Disamis, Datisi, Felapton,
k = Reduce per impossibile for Bokardo, Ferison habet; Quarta insuper addit
Baroko & Bokardo;         Bramantip, Camenes, Dimaris, Fesapo, Fresison.
Convert by Contraposition for
Fakoro & Dokamok.
the same Premise, two valid Moods.
If A is B, C is D.
Modus Tollens.
C is not D;.. A is not B.
the same Premise, two valid Moods, each having two forms.
A is either B or C.
MIodus tollendo ponens.
1. A is not B;.. A is C.
2.  A is not C;
o-. A is B.




228        MEDIATE INFERENCE OR SYLLOGISM.
CHAPTER VIII.
THE HAMILTONIAN DOCTRINE OF SYLLOGISMS.
IR  William  Hamilton's innovations in the doctrine
of Syllogisms, which had been generally received
up to this time, are not limited to such as are the direct
consequences of his theory of the thorough-going quantification of the Predicate. On several minor points, also,
he has considerably modified the Aristotelic doctrine.
These changes, it is true, were probably suggested by his
system of quantifying the Predicate; but they are not so
closely connected with it as to prevent them from being
received, even by those logicians who, wholly or in part,
reject that system. All of them deserve consideration, as
they involve a discussion of some incidental questions of
much interest, affecting the whole theory of Logic.
As to the order of enouncement, the old doctrine was,
that the Premises, as their name imports, should precede
the Conclusion. Hamilton observes that the reverse order
is more natural, that it more faithfully represents the
progress of the mind in the investigation or discovery of
truth, and that it effectually relieves the Syllogism from
the imputation, which has been thrown upon it for more
than three centuries, of being founded upon a mere petitio
principii, or a begging of the question.  "Mentally one,"
he says, " the Categorical Syllogism, according to its order
of enouncement, is either Analytic, if what is inappropriately styled the' Conclusion' be expressed first, and
what are inappropriately styled the  Premises' be then




THE HAMILTONIAN ANALYSIS.           229
stated as its reasons; or Synthetic, if the Premises precede
and, as it were, effectuate the Conclusion."  In the Analytic order, the " Conclusion " would be more properly
called the Qucesitum, and the  "Premises" should be
denominated the Proofs.
Now, the Analytic order, it is argued, is the more natural, because the Problem or Question, which it is the
purpose of the Syllogism to solve or answer, and which is
therefore the leading thought in the mind, is propounded
first. When we are in doubt whether A is, or is not, B,
it is surely more natural to argue, A is B, because A is C,
and all C is B, than to reason in the old order, placing the
solution of the Problem last.' In point of fact, the Analytic Syllogism is not only the more natural, it is even presupposed by the Synthetic."  As already stated, the Syllogistic process in the mind is really one and undivided, consisting only in the inference of the Conclusion from the
Premises. But in order to state this single process in
words, we must analyze it, and therefore the Conclusion,
which is the compound result, ought to be stated first, so
as to admit of analysis. It may be stated generally, that a
process of investigation or research, looking towards truth
not yet discovered, is always Analytic. The most that can
be said for the Synthetic method is, that it may be successfully used for teaching, or proving the truth that is
already known. To adopt an old illustration, in order to
find out for ourselves how a clock is made and how it does
its work, we must take it to pieces; having done this, the
best way to teach another person how to make a clock is
to take those pieces and put them together again.
The common objection to the validity of the Syllogistic
process is, that the Conclusion is virtually contained in the
Premises, so that we have to assume it to be true in the
very propositions by which we attempt to prove it. This
objection is thus forcibly stated by Mr. Mill. "When we
say, -




230-       MEDIATE INFERENCE OR SYLLOGISM.
All men are mortal;
Socrates is a man;
Therefore, Socrates is mortal;
it is unanswerably urged by the adversaries of the Syllogistic theory, that the proposition,' Socrates is mortal,' is
presupposed in the more general assumption,' All men
are mortal'; that we cannot be assured of the mortality of all men, unless we were previously certain of
the mortality of every individual man; that if it be still
doubtful whether Socrates, or any other individual you
choose to name, be mortal or not, the same degree of uncertainty must hang over the assertion,'All men are
mortal'; that the general principle, instead of being given
as evidence of the particular case, cannot itself be taken
for true without exception, until every shadow of doubt
which could affect any case comprised with it is dispelled
by evidence aliunde; and then, what remains for the Syllogism to prove? that, in short,'no reasoning from generals
to particulars can, as such, prove anything: since, from a
general principle, you cannot infer any particulars but those
which the principle itself assumes as foreknown."
But if the Syllogism be stated in the Analytic form,
it is obvious that this objection is inapplicable.  When we
argue,
Socrates is mortal,
Because Socrates is a man,
And all men are mortal, —
we do not assume the point which ought to be proved, but
we prove that it is right to predicate mortality of Socrates,
by showing that Socrates belongs to the class man, all the
members of which are universally admitted to be mortal.
We appeal to the admitted Universal truth only after we
have established, what is here the main point of the argument, the applicability of the truth to this case, - the fact
that Socrates is a man.  Mr. Mill mistakes the compara



THE HAMILTONIAN ANALYSIS.           231
tive importance of the two Premises; in Analytic reasoning, -in drawing an inference for the purpose of investigation or discovery, —the proof turns chiefly upon the
Subsumption; and Aristotle therefore correctly places this
Premise first. Thus, if I am in doubt with respect to a
new substance which I have found, whether it be fusible or
not, the doubt may be resolved by ascertaining that this
substance is a metal.  Only after this fact is ascertained,
and then only in order to complete the thought, or to silence cavil, I refer to the admitted truth that all metals are
fusible.  Men usually reason in this manner, as is shown
by the frequent recurrence of such Enthymemes as these:
This iron is not malleable, for it is cast-iron; The man is
dishonest, for he has taken what is not his own; this line is
equal to that, for they are both radii of the same circle, &c.
There is certainly a mental reference in such cases to a
Major Premise, - to the well-known truths, that No castiron is malleable, All radii of the same circle are equal, &c.
But precisely because such Premises are well known and
obvious, though thought, they are not usually expressed.
The bald truisms which are usually taken as examples
of the Syllogistic process are unfortunately chosen, as they
render more plausible the imputation that this process itself
is futile and needless.  Any kind of reasoning appears
puerile, when it is applied only to establish a puerile Conclusion. Nobody wishes any proof of the fact that Socrates was mortal.  Adopt any supposition which will make
it appear that there was a real doubt in the case, and that
the point to be determined was one of some importance,
and the Syllogism employed loses its frivolous aspect, and
seems grave and pertinent. Suppose that the impulsive
Athenians of his day had made the same mistake in relation to Socrates, that those of a later time committed in
regard to Paul and Barnabas, and had begun to offer sacrifices to him as an immortal being; it would have been




232        MEDIATE INFERENCE OR SYLLOGISM.
dignified and conclusive on his part to argue with them, as
the Apostle did, by saying, "  PYe are men of like passions
with you," and worship is due only unto God. The first
question for the inquirer or disputant is, not whether this
case has already been decided, and therefore included
under this General Rule, which is supposed to be already
found; but under what Class-notion can this case be put,
which shall afford a General Rule that will be applicable
for the solution of the doubt. The difficulty is, how to
find the right Rule, and not, as Mr. Mill supposes, how to
interpret it when found. The astronomer proceeds in this
manner, when he seeks to know whether a comet, which
has just appeared in the heavens, will return at a future
period, or disappear forever. By determining three or
more points in its path, he ascertains either that its orbit is
an ellipse or an hyperbola; this is the Subsumption, and
when found, the question is really answered, for the application of the Sumption - that the ellipse is a curve which
returns into itself, while the hyperbola does not —is so
obvious, that it is unnecessary, except for a child, to be
reminded of it. But though not expressed, the thought
without it is certainly incomplete, and the main question is
not answered.
Mr. Mill's doctrine is, that "we much oftener conclude
from particulars to particulars directly, than through the
intermediate agency of any general proposition."  For example, "it is not only the village matron, who, when
called to a consultation upon the case of a neighbor's child,
pronounces on the evil and its remedy simply on the recollection and authority of what she accounts the similar
case of her Lucy."
We have already observed (page 9) that a Concept may
be derived from one object, as well as from many similar
ones; that is, it may not represent an actual, but only a
possible, class or plurality of things. The hasty and sweep



THE HAMILTONIAN ANALYSIS.           239
ing inductions of the vulgar are of this character; they are
often generalizations from a single instance. The medicine
which they have once successfully tried is believed by them
to be a panacea. The unhesitating confidence with which
the village matron pronounces, not merely on one case of
measles or whooping-cough in her neighbor's family, but
on every one that occurs in the village, proves that she
has generalized her Lucy's case.
All general truths are not learned by induction from
particulars. They are sometimes first obtained by Intuition, as in the case of axioms and other necessary truths,
or by reasoning firom the causes or conditions on which
they depend; and then, individual truths are proved by
deduction from these generals. Most of the truths of pure
mathematics are thus acquired. To borrow an example
from Hobbes, - because we know how a circle is generated, namely, by the circumduction of a body one end of
which is fixed, we know that all radii of the same circle
are equal. Most of the beautiful applications of algebraic
theorems to the solution of arithmetical and geometrical
problems were first ascertained to be possible long after the
general theorems themselves were discovered. Such metaphysical. principles as these, Every event must have a cause,
All attributes presuppose a substance, Space is infinite and
indestructible, were not first made known to us by induction, and cannot be proved by that method. Yet the objection to the Syllogistic process, that the Major Premise
could not be posited if the truth of the Conclusion were
not already known, has neither force nor relevancy, if it
be not proved that all general truths are obtained by induction, and that the induction was so perfect that it must
have consciously included the very case which we are now
seeking to deduce from the general rule.
Hamilton's next innovation in the theory of Logic —
and it is one which was propounded by him at an earlier




234        MEDIATE INFERENCE OR SYLLOGISM.
day than his doctrine of the quantification of the Predicate
- was to draw attention to the fact, that reasoning does
not proceed, as had formerly been taught, solely in the
Quantity of Extension, but also in the Quantity of Intension, the relations of whole and part, on which he considers
that the whole process depends, being reversed in these
opposite Quantities. It has already been mentioned, that,
in one sense, the Predicate of every Judgment includes the
Subject, and therefore, as the greater or more Extensive
Term, it was called the Major, and the Subject was designated as the Minor Term. As thus construed, the Judgment, Man is an animal, means that the class AMan is ineluded under, or forms a part of, the class animal. But in
another sense, - that is, in the Quantity of Intension,the Subject includes the Predicate, and the relations of
whole and part are reversed. Interpreted Intensively, this
Judgment signifies that all the attributes of animal are
contained in or among - form a part of- the attributes of
man. The Subject is now the Major Term, and the Predicate is the Minor; and the rule being still adhered to, that
the Major Premise must be stated first, the order of the
Premises is reversed.
Hamilton gives the following example of reasoning in
Extension.
All responsible agents are free agents;
But man is a responsible agent;
Therefore, man is a free agent.
The Premises are. stated in this order on the supposition
that "'free agents," as the more Extensive class, is the
whole or the Major Term, that 1" man," having the least
Extension, is the smallest part or the Minor Term, and
that the Middle Term, "responsible agent," as intermediate between the two, is made the Subject of the former,
as contained under it, and the Predicate of the latter, which
is only a part of it. In other words, man is a part of that




THE HAMILTONIAN ANALYSIS.            235
Term responsible agent, which is itself a part of the Term
free agent; and therefore, as a part of a part is a part of
the whole, man is a free agent.
Now reverse the Premises.
Man is a responsible agent;
But a responsible agent is a free agent;
Therefore, man is a free agent.
Here, the notion free agent, which was the greatest whole,
becomes the smallest part; and the notion man, which was
the smallest part, becomes the greatest whole.'" The
notion responsible agent remains the Middle quantity or
notion in both, but its relation to the two notions is reversed; what was formerly its part being now its whole,
and what was formerly its whole being now its part."
Hence, in the First Figure (but not, as we shall see, in
the two other Figures), the order in which the two Premises are placed always indicates the Quantity in which we
are reasoning. If the Major Premise contains the Subject
of the Conclusion, then this Subject is the Major Term, and
the reasoning is in Intension. But if the Predicate of the
Conclusion appears in the first Premise, then this Predicate
is the Major quantity, and the reasoning is in Extension.
But as this indication is a faint one, and may mislead in
the case of the -Second or the Third Figure, it is easy to
change the phraseology of the Judgments, so as to enounce
explicitly whether the reasoning concerns the Intensive,
metaphysical, whole (the whole of the Marks connoted), or
the Extensive, logical, whole (the whole of the Individuals
and Species denoted). Thus, for the latter, we may say,All responsible agents are included in the class of free
agents;
But man is a responsible agent;
Therefore, man is included in the class of free agents.
And the reasoning of Intension mav be thus stated: -




236        MEDIATE INFERENCE OR SYLLOGISM.
The notion or Concept, man, includes the notion of responsibility;
But the notion of responsibility includes that of free
agency;
Therefore, the notion, man, includes the notion of freeagency.
It is the more remarkable that nearly all the logicians
since Aristotle should have contemplated exclusively reasoning in Extension, as Aristotle himself seems to have
regarded reasoning in Intension as coextensive with the
former, even if not paramount to it. Hamilton has only
restored the doctrine of tile great founder of Logic, which
had been strangely overlooked by nearly the whole tribe
of his commentators and followers. As already remarked,
the being in a Subject and the being predicated of a Subject are used by Aristotle as synonymous phrases.  "A
is predicated of all B," means All B is A; "A is in (or
inheres in, vra'pev) all B," also means All B  is A.
The meaning evidently is, that, in the Quantity of Intension, the Predicate is in the Subject because it constitutes
a part, and only a part, of the Intension of the Subject.
Animal is in mran, because man has all the attributes or
Marks of animal, and other attributes also.
But the relation of whole and part is not precisely the
same thing in the one Quantity as in the other. In Extension, the whole is the Genus, and the parts are the subordinate Species; and the first Rule for the division is, that
the parts, or the co-ordinate Species, must exclude each
other.  But in Intension, the parts are not Species, but
attributes or Marks; and these do not exclude each other.
Each part or attribute here interpenetrates, so to speak,
and informs, the whole. Black is a part of neyro in the
sense of being only one of his attributes, since he has many
others, such as being long-heeled, prognathous, &c.; but it
is a part which colors the whole, for the negro is black all




THE HAMILTONIAN ANALYSIS.           237
over. But if we consider the Extension, if the Genus man
is subdivided into the co-ordinate Species white man and
black man, these parts exclude each other; no one man
can belong at the same time to both Species, - can be both
white and black.
Hence the maxim, that a part of a part is also a part of
the whole, is not a universal maxim of all reasoning; as it
refers only to co-exclusive parts, it is applicable only to
reasoning in Extension. The corresponding maxim for
reasoning in Intension is, that a Mark of a Mark is also a
fark of the thing itself, - of the whole thing; nota notce
est nota rei ipsius. PFree agency, which is a Mark of
responsibility, is also a Mark of man, because responsibility
is a Mark of the whole man.  On the other hand, reasoning Extensively, we say, men are a part or class of responsible agents, and are, therefore, also a part of free agents,
because responsible agents are a part of free agents.
By not attending to this distinction, Hamilton was betrayed on one occasion into propounding as a valid syllogism one, which, if the language be construed literally, is,
illogical; and into censuring as illogical another, which, as
stated, is certainly irrecusable. It is true that the error
consisted entirely in the use of language. As he understood them, his approbation of the one and his censure of
the other are correct; but from his use of language, no
other person would so understand them. In his Lectures
on Logic, while illustrating the Special Rule of an Intensive Syllogism (page 223, Am. ed.), that the Sumption
must be Affirmative, and the Subsumption Universal, he
states the following as a valid Syllogism:" S comprehends M;
M does not comprehend P;
Therefore S does not comprehend P."     Q  




238        MEDIATE INFERENCE OR SYLLOGISM.
If the language be interpreted literally, the Conclusion
here is illogical; for it is evident, from the diagram which
we have annexed, that, though S comprehends M, and M
excludes P, it may yet be true that S comprehends P.
On the same page, he censures the following as a non
sequitur, though the diagram here annexed demonstrates it
to be valid.
S  does  not comprehend M; 
But M comprehends;          s
Therefore S does not
comprehend P.
But instead of the proposition "S comprehends M," substitute the meaning which was intended, that S has M for
one of its Marks or attributes, and make the corresponding
change throughout, and Hamilton's verdict upon the two
Syllogisms becomes correct. M, though only one of the
attributes of S, affects or colors the whole of S; therefore,
P, which is not an attribute of M,   does not affect any
part of M,- is not an attribute of S;-S does not include P among its attributes. The Syllogism which is approved corresponds, in Form, to the following, which is
evidently valid.
A negro has a black skin;
But a black skin is not an invariable sign of a brute intellect;
Therefore, a negro ls not necessarily brutish in intellect.
And the Syllogism which is rejected is the following: —
A negro is not white;
But whites are civilized;
Therefore, a negro is not civilized.
In fact, the mode of symbolizing Syllogisms by circles, as




THE HAMILTONIAN ANALYSIS.            239
well as the maxim, a part of a part is also a part of the
whole, is inapplicable to the Intensive Syllogism; for here
the " parts" are Marks or attributes; and these are not
co-exclusive. They are notpartes extra partes.
It is with some reason, then, that Mr. DeMorgan objects
to considering the Intension of a Concept as a quantity.
In the vague sense of being susceptible of more and less, it
is a quantity; but so far as it is incapable of exact measurement, it is not a quantity.  "As to extent," he says, "200
instances bear a definite ratio to 100, which we can use,
because our instances are homogeneous. But different qualities or descriptions can never be numerically summed as
attributes to any purpose arising out of their number.
Does the idea of rational animal, two descriptive terms,
suggest any useful idea of duplication, when compared with
that of animal alone?  When we say that a chair and a
table are more furniture than a chair, which is true, we
never can cumulate them to any purpose, except by extracting some homogeneous idea, as of bulk, price, weight,
&c..To give equal quantitative weight to attributes, as
attributes, seems to me absurd; to use them numerically
otherwise, is at present impossible." Perhaps this is only
saying that a logician's idea of quantity is not the same as
a mathematician's; to the latter, it is always numerically
definite, or may be made so; to the former, it is never so.
Perhaps, if Mr. DeMorgan had kept this fact steadily in
view, a good many of his attempted innovations in Logic
might have appeared, even to him, irrelevant.
Hamilton has made no specific innovation in the doctrine
of the Figures, but his speculations upon the subject have
thrown a flood of light not only upon the essential nature
of these varieties of the Syllogism, but upon the theories
of former logicians in respect to them.  To Aristotle, on
account of his peculiar method of stating a Judgment,
with reference to the Intension instead of the Extension of




240        MEDIATE INFERENCE OR SYLLOGISM.
its Terms, that is, placing the Predicate first and the Subject last, —the Middle Term was intermediate between
the two others, not only in nature, but in position. Thus,
the following are only two different expressions of the same
Syllogism.
Aristotle's form.                 Later or common form.
P inheres in (is predicated of) all M;  All M are P;
M inheres in all S;                   All S are M;.'. P inheres in all S..-. All S are P.
Here, in Aristotle's form, P, one of the Extremes, appears
first, and S, the other Extreme, comes last; M, the Middle
Term, in both of its expressions, being intermediate, or
coming between them.  In the later form, it is not so.
As a consequence of this mode of statement, in his definition of the Second Figure, Aristotle says that the Middle
Term is, by its position, the first; to us, on the contrary,
it is the last. In fact, in his reduction of the Second and
Third Figures to the First, Aristotle seems to have had in
view, not only the establishment of the dictumn de omni et
nrullo as the universal principle of all Syllogistic reasoning,
but the restoration of the Middle Term to its proper intermediate position. He was evidently thinking most of
reasoning in Intension, and his followers of what is more
frequent in use, though not more natural,- reasoning in
Extension.  In the later form, if the Minor Premise is
stated first, the Middle Term  becomes intermediate in
position, as in the Aristotelic formula.
In this exposition of Aristotle's mode of enouncement,
as contrasted with that of the later logicians, Hamilton has
merely followed Barth6lemy St. Hilaire; in what follows,
he is more original.
"' When logicians," he says, " came to enounce propositions and Syllogisms in common language, the Subject
being usually first, they had one or other of two difficulties




THE HAMILTONIAN ANALYSIS.            241
to encounter, and submit they must to either; for they
must either displace the Middle Term from its intermediate position in the First Figure, to say nothing of reversing its order in the Second and Third; or, if they kept it
in an intermediate position in the First Figure (in the
Second and Third, the Aristotelic order could not be kept),
it behooved them to enounce the Minor Premise first."
Most of the older logicians adopted the latter alternative,
stating the Minor Premise first in all the Figures; and
this seems the more natural order, if the Syllogism is used
for the purpose of investigation and discovery. At a later
period, when instruction, disputation, and proof came to
be the chief purposes for which Syllogisms were formally
enounced, the former alternative was adopted, and the
Middle Term lost its proper intermediate position, the
Major Premise being placed first in all the Figures.
In the First Figure, according to any mode of enouncement, the Middle Term must be the Subject of one of the
Extremes (the two Terms of the Conclusion), and the
Predicate of the other. Hence, in this Figure, there is a
determinate Major and Minor Premise for reasoning in
either Quantity, and but one direct or proximate Conclusion. If, in the Major Premise, the MIiddle Term is Predicate to the Subject of the Conclusion, then, in each of the
three Judgments, the Subject includes the Predicate, and the
reasoning is in the Quantity of Intension.  If, on the contrary, in the Major Premise, the hiddle Term is Subject to
the Predicate of the Conclusion, then, in each of the three
Judgments, the Predicate includes the Subject, and the reasoning is in the Quantity of Extension.  The relative position
of the two Premises is really unimportant as respects the
nature of the reasoning; this depends upon the nature of
the Middle Term, as including, or included under, the Subject of the Conclusion.  But following the established
order of logical Quantity, that the greater should be placed
ii                     r~~~~~~~




242        MEDIATE INFERENCE OR SYLLOGISM.
first, the Middle Term as Subject, and the Predicate of
the Conclusion as Predicate, should be the first or Major
Premise for reasoning in Extension; and the Middle Term
as Predicate, with the Subject of the Concelusion as Subject, should be the first or Major Premise in Intension.
Thus:In Extension.             In Intension.
M is P;'               S is M;
S is M;                     M is P;.. S is [included under] P..'. S is [includes] P.
Here, the relation of the Terms to each other in the
Premises determines their relation to each other in the Conclusion. If, in the Premises, M is included under P, and
S included under M, then, in the Conclusion, S must be
included under P. But if, in the Premises, S includes M,
and M includes P, then, in the Conclusion, S must include
P. Hence, in the First Figure, there can be but one
direct Conclusion.
In the two other Figures, it is not so. The Middle
Term is not Subject of one and Predicate of the other Extreme, but is either, as in the Second Figure, Predicate of
both, or, as in the Third, Subject of both. Consequently,
in each of these Figures, the Middle Term either includes
both the Extremes, or is included under both. As there
is nothing, then, to determine the relative Quantity of the
two Extremes to each other, either may be considered as
Major in the Conclusion; — we may conclude either that
S is P, or that P is S.
Though the First Figure has but one direct or immediate
Conclusion, we may, by the medium of Conversion, obtain
from it another Conclusion, which is then properly called
indirect or mediate. Thus, in the formulas just given, having concluded directly that All S is P, we may then conclude indirectly, or mediately, that Some P is S. But in




THE HAMILTONIAN ANALYSIS.          243
the other Figures, there are two indifferent Conclusions,
neither of which is more direct or immediate than the
others. If A is B and C is B, we may conclude, with
equal propriety and directness, either that A is C, or
C is A; for there is nothing in the Premises to indicate
whether A includes, or is included under, C. And in like
manner in the Third Figure; if B is A and B is C, the
two Conclusions, A is C and C is A, are equally competent and equally immediate.  Of course, what has been
called the Fourth Figure is merely the First, with its indirect Conclusion enounced as if it were direct or immediate; it is a hybrid reasoning, with its two Premises in
one Quantity, and its Conclusion in the other. Hence
the Fourth Figure is properly abolished.
In fact, all difference of Figure is unessential,- a mere
accident of form. As it is demonstrated in the Hamiltonian analysis, that a Judgment is a mere equation of its
twD Terms, it makes no difference which is stated first, —
which is Subject or which is Predicate; A = B and B - A
are the same equation. Quantify the Predicate throughout, and this becomes evident. As all Conversion is then
reduced to Simzple Conversion, we have only to convert
simply (retaining the subordination of the Terms) the
Major Premise of the First Figure in Extension, in order
to produce the Second Figure; convert its Minor Premise,
and we have the Third. In Intension, this is merely reversed; convert the Minor for the Second, and the Major
for the Third.
To make the Syllogistic process depend upon the mere
position, either of the two Terms as Subject or Predicate,
or of the two Premises as enounced first or second, or of
the Conclusion as expressed first or last, is to reduce Reasoning to a mere accident of expression, and cause it to
vary with the genius of different languages, or even with
the mental peculiarities of individuals.  Reasoning is a




244         MEDIATE INFERENCE OR SYLLOGISM.
process of Thought, not of language. It depends solely
upon the relations of inclusion and exclusion, of subordination and superordination, of "Intension and Extension, existing between two Concepts and a Third; and it
must be regulated by universal laws, irrespective of differences of language and peculiarities of mental habit. The
order of enouncement is a convenient, though conventional, mode of indicating these relations to other persons,
and even a safeguard against confusion and error in the
successive elaboration of them in our own minds.  But the
actual inference, the mental process as such, is entirely
independent of this order.
To show further the unessential character of variation by
Figure, Hamilton pointed out the manner of abolishing the
distinction of Subject and Predicate, and thereby reducing
all Mediate Inference to what he calls the Unfigured Syllogism. Any Syllogisms whatever may find adequate,
though awkward, expresion under this form. The two following instances will suffice.
Fig. I. Darii,  reduced to an   Unfigured Syllogism.
All patriots are brave;   All patriots and some brave men
are equall;
Some persecuted men are    Some persecuted and some papatriots;                  triots are equal;.'. Some persecuted men are.-. Some persecuted and some brave
brave.                    men are equal.
Fig. II. Camestres.
All animals are sentient;    All animals and some sentient
things are equal;
Nothing unorganized is    Any unorganized and any sensentient;                 tient are not equal;..Nothing  unorganized is.. Any unorganized and any ananimal.                   imal are not equal.
In this Unfigured Syllogism, as Hamilton remarks, " the




THE HAMILTONIAN ANALYSIS.,           245
dependency of Extension and Intension does not subsist,
and accordingly the order of the Premises is wholly arbitrary.  This form has been overlooked by the logicians,
though equally worthy of development as any other; in
fact, it affords a key to the whole mystery of Syllogism.
And what is curious, the Canon by which this Syllogism is
regulated (what may be called that of logical Analogy or
Proportion) has, for above five centuries, been commonly
stated as the one principle of reasoning, whilst the form of
reasoning itself, to which it properly applies, has never been
generalized. This Canon, which has been often erroneously, and never adequately enounced, in rules four, three,
two, or one, is as follows: - In as far as two notions
(notions proper or individuals) either both agree, or one
agreeing the other does not, with a common third notion; in
so far these notions do or do not agree with each other. This
Canon thus excludes, — 1. an undistributed Middle Term,
as then no common notion; -2, two negative Premises,
as then no agreement of either of the other notions therewith."
A convenient, though somewhat mechanical, rule for
drawing the correct Conclusion from any pair of Premises
is* the following, which was first stated by Ploucquet, and
after him by Mr. De Morgan. Erase the symbols of the
Middle Term, the remaining symbols show the inference.
-Deleatur in prcemissis medius; id quod restat indicat conclusionem. Thus, in the two Syllogisms just given and reduced to the Unfigured form, strike out from the Premises, what I have italicized, all that relates to the Middle
Term, and what remains of the Premises is the Conclusion. But it should be mentioned that this Rule, though
valid for all the Aristotelic moods, does not hold good, as.we shall see, for all the moods recognized under the Hamiltonian system.
Perhaps the most striking, and certainly the most con



246        MEDIATE INFERENCE OR SYLLOGISM.
venient, improvement which Sir William Hamilton has
made upon the labors of former logicians, is his system of
notation, -a masterpiece of ingenuity in symbolization as
respects perspicuity, completeness, and simplicity. It is
valid for any system, and it manifests, at once, nearly all
the alterations and improvements which he has made in
the Aristotelic doctrine. It shows at a glance the equivalent Syllogisms in the different Figures, the convertible
Syllogisms in the same Figure, and points out the two
meanings which can be given to every Syllogism as interpreted according to its Extension or its Intension, in reference to the logical or the metaphysical whole. Even as a
mnemonic contrivance, it is second in ingenuity and usefulness only to the famous quatrain of hexameters, which
contains the whole doctrine of the Reduction of the Moods
of the lower Figures to the first Figure.
The purpose of any system of notation is to manifest, by
the differences and relations of geometrical quantities (lines
or figures), the differences and relations of logical forms.
A Proposition or Judgment is here indicated by a straight
horizontal line, its two Terms or Extremes being placed at
the extremities of that line, and represented, as usual, by
letters.
If, as in the Unfigured Syllogism, there is no distinction
of Subject and Predicate, this line is made of equal thickness throughout.  But if this distinction is introduced,
then, as it is possible to read the Judgment in two ways,
according to the Extension or the Intension of its Terms,
(the Subject, in the latter case, including the Predicate,
and in the former, being included under it,) the line is
made wedge-shaped. Its broad end then represents the
Subject of Extension or Breadth, and the thin end, that of
Intension or Depth. A line gradually diminishing or increasing from end to end aptly indicates the relation between two Quantities which are always co-existent, and in




THE HAMILTONIAN ANALYSIS.          247
inverse ratio to each other. As the employment of letters
following upon each other in the same alphabet might suggest that one was invariably subordinated to the other,
instead of being its subordinate in one Quantity and its
superordinate in the other, Hamilton uses for the Extremes
the Latin C and Greek F, each being the third letter in
its own alphabet; as usual, M stands for the Middle Term.
Thus: -
is read,         C and r are equal.
C = —-  F
may be read in two ways; Extensively, C is included
under F; Intensively, F is included in C: -or, in the
usual manner, C is F, and I is C, merely remembering,
without saying so, that Extension is signified in the former
case, and Intension in the latter.
Negation is indicated by a perpendicular stroke drawn
through the line, thus: —.  The line without this stroke
may be regarded as the Affirmative Copula; with the
stroke, as the Negative Copula. A colon (:) annexed to a
Term shows that it is distributed, or taken universally; a
comma (,) so annexed, that it is undistributed or Particular. When a Middle Term has a colon on the right, and a
comma on the left, it is understood that it is distributed
when coupled in a Judgment with the Term on the right,
and undistributed when coupled with the other.
A line drawn beneath or above three Terms indicates
the Conclusion (or the Copula of the Conclusion) deduced
from the two Premises which those Terms constitute. In
the Second and Third Figures, since there may be two
equally direct or immediate Conclusions, they are represented by two such lines, the one above, and the other
below the Premises. Thus: —
_       _.a —------ -  This is a Syllogism in the Second
C, —, M: -,     Figure, which may be read in
either of the following ways.




248        MEDIATE INFERENCE OR SYLLOGISM.
Extensively.             Intensively.
Some C is some 1IM;     All M is some F; 
Some r is all M;         Some M is some C;
e-. Some r is some C; or.'. Some C is some r; or.'. Some C is some r..'. Some F is some C.
C,, M: -+-   F   This is a Negative Syllogism in
the First Figure, which may be
read in  either of the following
ways; but in either way, it has only one direct or immediate Conclusion, though a Second Conclusion may be obtained from it indirectly, by converting simply the proper
or direct Conclusion.
Extensively.             Intensively.
Some M is some C;       No M is any r;
No r is any/V);         Some C is some M;
No r is some C; or,     Some C is not any F; or,
indirectly,             indirectly,
Some C is not any r.    Not any r is some C.
The following diagram presents the whole Hamiltonian
doctrine of Figure, together with the distinction between
the Analytic and the Synthetic order of enouncement.
After the explanations which have been given, it will be
easily understood.
As a Judgment has been designated by a line, a Syllogism, which is a union of three Judgments, is appropriately
typified by a triangle, a union of three lines, of which the
base represents the Conclusion, and the other two lines,
the Premises.  As the direction of the arrows indicates,
we may proceed either in the usual or Synthetic order,
from the Premises to the Conclusion, or in the reverse
order, which is Analytic, from the Conclusion to the Premises., As there is no valid reason for always placing the
Major Premise first in order, tile diagram shows that either
Premise may have precedence in this respect, so that what
has been called the Fourth Figure is here identified with
the Indirect Moods of the First.




THE HAMILTONIAN ANALYSIS.          249
y (
The Unfigured Syllogism is properly represented as including all the others, as any Syllogism of either Figure
may be easily expressed in this form. In like manner, tlhe
triangle representing the First Figure is made to include
the two typifying respectively the Second and Third, as
either of the latter may be readily reduced to the former.
And again, the essential unity of the Syllogistic process,
and the unessential nature of variation by Figure, are appropriately signified by a single triangle comprehending all
the varieties of form.
"The double Conclusions, both equally direct, in the
Second and Third Figures, are shown in the crossing of
two counter and corresponding lines. The Direct and
Indirect Conclusions in the First Figure are distinctly
typified by a common and by a broken line; the broken
line is placed immediately under the other, and may thus
indicate that it represents only a reflex of- a consequence
11*




250        MEDIATE INFERENCE OR SYLLOGISM.
through —the other (Kar' da'vcXaa-,, reflexim,  per reflexionem).  The diagram therefore can show, that the
Indirect Moods of the First Figure, as well as all the Moods
of the Fourth, ought to be reduced to merely mediate inferences;- that is, to Conclusions from Conclusions of the
conjugations or Premises of the First Figure."
If we have the two Premises, All C is some M, and All
HJI is some P, and consider that some JM is a Mark of (or,
is included in) all C, and some r a Mark of all M, then
we are reasoning in the Quantity of Intension; and, according to the Axiom that a Mark of a Mark is also a Mark of
the thing itself, the proper and direct Conclusion is, All C is
some P. But if we conclude that Some r is all C, according to the Fourth Figure or the Indirect Moods of the
First, Some 1P does not appear as a Mark of all C, but as
included under it, - as a Subject of Extension; the Premises, then, would be represented in one Quantity, and the
Conclusion in the other. "But though always coexistent,
and consequently always, to some amount, potentially inferring each other, still we cannot, without the intervention of an actual inference, at once jump from the one
Quantity to the other,, —change, per salturm, Predicate
into Subject and Subject into Predicate. We must proceed gradatim.   We cannot arbitrarily commute the
Quantities, in passing from the Quvasitum to the Premises, or in our transition from the Premises to the Conclusion. When this is apparently done, the procedure is
not only unnatural, but virtually complex and mediate,
the mediacy being concealed by the concealment of the mental
inference which really precedes ";- indicated by the broken
line in the diagram.
One other species of Hamiltonian notation should be
noticed, as it brings to light very clearly the virtual equivalence of those Moods in the several Figures which are indicated, in the old mnemonic hexameters, by names begin



THE HAMILTONIAN ANALYSIS.                251
ning with the same capital letter. Four straight lines are
all that is needed for such a notation. Three of these are
horizontal, to represent the Terms; and one perpendicular,
or the want of it, at the beginning of the comparison, to
express the Quality of Affirmation or Negation.  " Quantity is marked by the relative length of a terminal line
within, or its indefinite excursion before, the limit of comparison. This notation can represent equally total and
ultratotal distribution, in simple Syllogism and in Sorites;
and it shows at a glance the competence or incompetence
of any Conclusion."
C                         C
M                         M
r                              r
6' Of these, the former, with its converse, includes Darii,
Dabitis, Datisi, Disamis, Dimaris, &c.; whilst the latter,
with its converse, includes Celarent, Cesare, Celanes, Camestres, Cameles, &c.  But of these, those which are represented by the same diagram  are, though in different
Figures, formally the same Mood."  "In  all the other
geometrical schemes hitherto proposed, whether by lines,
angles, triangles, squares, or circles, the same complex
diagram is necessarily employed to represent an indefinite
plurality of Moods."
The application of Hamilton's doctrine of the thoroughgoing quantification of the Predicate to the explication of
the Syllogistic theory produces, as might have been expected, a great enlargement of the number of Moods. If
there are butfour fundamental Judgments, the number of
conceivable Moods that can be framed from them, by taking
them three and three, is sixty-four *; excluding from these
* The computation is easily made. The four letters A, E, I, O, give
us four different Major Premises; each of these may have four different
Minor Premises; — hence there will be sixteen pairs of Premises. But
each of these pairs may be conceived to have four different Conclusions;
whence, 16 X 4 _ 64 conceivable Moods.




252         MEDIATE INFERENCE OR SYLLOGISM.
the invalid Moods, as offending against one or more of
the general Rules of the Syllogistic process, there remain
only fourteen as valid in some one of the first three Figures; - nineteen, if we admit the Fourth Figure; - twentyfour, if we include also the anonymous indirect Moods.
But under the Hamiltonian doctrine of eight fundamental
Judgments, we have five hundred and twelve * conceivable
Moods.  Excluding from these all that offend against the
General Canon, (as by having an undistributed Middle,
two Negative Premises, or collecting more in the Conclusion than was distributed in the Premises,) there remain
thirty-six valid Moods, of which twelve are Affirmative and
twenty-four Negative.  On this doctrine, each Affirmative
Mood yields two Negative ones, as each of its Premises
may be successively negatived. Figure now appears in its
true character, as an unessential variation; but as each of
these valid Moods can, if we please, be thrown into either
of the three Figures, there are 36 X 3 =108 valid Moods,
reckoning as such all the modifications of statement of
which they are susceptible. But to show how trifling are
the changes thus effected by carrying what is really one
Mood through each of the three Figures, I borrow a concrete example from Mr. Baynes.
FIG. I.                      FIG. II.
All man is some animal;       Some animal is all man;
Every Celt is some man;       Every Celt is some man;.'. Every Celt is some animal..'. Every Celt is some animal,
FIG. III.
All man is some animal;
Some man is every Celt;.X. Every Celt is some animal.
* Computing as before, from eight Judgments we have eight different
Major Premises, each of which may have eight different Minor Premises,
whence 8 X 8 = 64 pairs of Premises; and as each of these may have
eight different Conclusions, there are 64 X 8 = 512 triplets of Judgments,
or conceivable Syllogisms.




THE HAMILTONIAN ANALYSIS.          253
Hamilton's General Canon has already been enounced
in the mode of statement in which it is directly applicable
to the Unfigured Syllogism. As applied to the Figured
Syllogism, wherein we have to consider the two counter
Quantities of Extension and Intension, it should be thus
expressed: —" What worse relation of Subject and Predicate subsists between either of two Terms and a common
Third Term, with which one at least is positively [affirmatively] related, that relation subsists between the two
Terms themselves." As already stated, this Canon is
only a succinct statement of the six general Rules which
have been laid down as fulfilled in every valid case of
Mediate Inference; and it is, also, only a restatement of
the two Primary Axioms of Pure Thought, the laws of
Identity and Non-Contradiction, with the necessary conditions and limitations which determine their application.
As these Rules and Axioms were found to hold good under
the Aristotelic doctrine of four fundamental Judgments,
they are also valid under the system which increases the
number of these Judgments to eight. No Syllogism can
be invalid which accords throughout with this Canon, and
every illegitimate process, either directly or indirectly,
openly or covertly, violates it.
But we must accurately determine which is the " worse
relation " of Subject and Predicate that can subsist between either of two Terms and a common Third Term.
When there are but four Judgments, the corresponding
principle, that the Conclusion follows the'" weaker part,"
admits of easy interpretation; Particular Quantity is
weaker than Universal, Negative Quality is weaker than
Affirmation. But with eight Judgments, the various degrees of better or worse, stronger or weaker, must be
more precisely ascertained. Always considering Negation
as weaker than Affirmation, we now say that the best
(strongest) Quantity of Affirmation is the worst (weakest)




254        MEDIATE INFERENCE OR SYLLOGISM.
Quantity of Negation. In other words, we affirm best when
we affirm all, and affirm worst when we affirm only some; on
the contrary, we deny best when we deny only some, and
deny worst when we deny all. On account of this inverse
relation of the two Quantities, an Affirmative Mood with a
Particular Conclusion may be changed, by merely negativing one of its Premises, into a Negative Mood with a
Universal Conclusion. But though the Quantity is thus
altered from Particular to Universal, this is not a change
from worse to better, but firom worst to worst; for though
a Particular stands lowest in the scale of Affirmation, a
Universal stands lowest in the scale of Negation. The
seeming exception only confirms the rule, and proves that
the Canon is universally applicable. Take the following
instance:
C: -— on, M:- I:r          Some M is all C;,All r is all M;.'. Some I is all C.
Some blacks are all slaves;
All of African descent are all blacks;.'. Some of African descent are all slaves.
Now, if we negative this Syllogism by negativing the
Minor Premise, the Conclusion changes from Particular to
Universal, thus -
Some M is all C;
No r is any M;
No r is any C.
Some blacks are all slaves;
No Caucasian is any black;. No Caucasian is any slave.
This change, though from Particular to Universal, is
really from the worst of Affirmation to the worst of Negation. But such changes are infrequent, as, in the inter



THE HAMILTONIAN ANALYSIS.           255
mediate relations, the commutation is only from equal to
equal, and the predesignations of Quantity, in their inverse signification, remain externally the same. Out of
the twenty-four valid Negative Moods, only four cases are
found of a Particular quantification disappearing in the
Negative Conclusion. Hamilton gives the following arrangement of the eight Judgments in the order proceeding
from best to worst.
Best.          1. Afa.  All are all.
2. Afi.  All are some.
-3. Ifa.   Some are all.,-4. Ifi.   Some are some.
I —5. Ini.  Some are not some.
— 6. Ina.  Some are not any.
-- 7. Ani.  Not any is some.
Worst.         8. Ana. Not any is any.
With these explanations, the following list of the twelve
valid Affirmative Moods in each of the three Figures, and
the 24 valid Negative Moods in the First Figure, all expressed in the Hamiltonian notation, will be found intelligible.
In this Table, the Quantity of the Conclusion is marked
only in the cases already considered, wherein the Terms
obtain a different Quantity from that which they held in
the Premises; accordingly, when not marked, the quantification of the Premises is held as repeated in the Conclusion. The symbol -,  placed beneath a Conclusion,
indicates that, when the Premises are converted, the Syllogism remains in the same Mood; > shows that the two
Moods between which it stands are convertible into each
other by converting their Premises. The Middle Term is
said to be balanced, when it is Universal in both Premises.
The Extremes, or Terms of the Conclusion, are balanced,
when both alike are distributed; unbalanced, when one is,
and the other is not, distributed.  Accordingly, of the




256        MEDIATE INFERENCE OR SYLLOGISM.
SCHEtME OF NOTATION -
TABLE OF SYLLOA. AFFIRMATIYE MOODS.
F:. 1. FIG. I.         FIG. II.
i. C:-:M:M: -     r    C: —-:M:          x:r
A (
t ii. C,_  ~:  r  C,-  M: 
M.,r        C       M:
B ii, C: —~I   -N  M: -.B     P C -   My
X                       X
ix. C: —-- N: - -, P, r    C:w. —-N —i,
Xii. C:,, M: -,  r     C, —, m: -— cM,r
vi. C::M,r,      C: m —: M,,r
vi. C,:, M: —— ~, r      C,_ —-, M: _ —-=:,r
ii. C:  M,:    r  c: —m —:,r
><                       X
iii C:,_ M: _: r         C,: —-  M:  _:r
} -      _
X. C:     M,,r C'.   —:M,,: r
xii. C:,,M::       r    C, —,M:          r
]ionO..- a. i and ii. are Balaned. B. The other moods are Unbalanced.  Of these,




THE HAMILTONIAN ANALYSIS.          257
FIGURED SYLLOGISM.
GISTIC MOODS.
A. AFFIRMATIVE MOODS.           B. NEGATIVE MOODS.
FIG. III.                      FIG. I.
_         _ t- MaC: —:..r.
C::M: -:r                  i. t M.__=......__             (b   C:_-.:M:     r
( aC,:-~+:M: -, r, 
C,_(: M:  C-,r           ii.           M         
--    -r                   CM
><_______ —+ M__'               C
b   C: —-— a rs~P ----
_                              C,-:' —,m, i   r
c,-~e: M, x,_r          iii.
__-__                 b C,-~: M ~ ~,   r
C:-   a, M:                                D r-P
C,_,M_,   _                   b C: M: -,r.__   _               a_ _  C:, M: -M —-==,   r
(bC: a,M:,r
Q- ------                          ---- {.r  b  aM, r
C,- - ~~M, wYi. — -r.
C,_,-~a: M:    xr            b C,_:,   Ib
)(~<~p —-               11  a  c,-+.:  M: -—, r
b C:-:   M::  r
~-_/                  i a C:r —9.~ ~ M: ],: —-a,m: na-  x      b C, —— ~:.; —m-:   r
_C:i M, and.r.. aubC:rbc:M, op: t r,'a(bC:_:M,  ~:r
--— =  - {- a'C:,M: —-~: r
C:,M': r - —: b C:,M: -:r
baC,: —], M:,-_: r
iii. and iv. are unbalanced  in terms only, not in propositions; the rest in both~




258        MEDIATE INFERENCE OR SYLLOGISM.
Moods in the Table, numbers I. and II. are balanced as
respects both Terms and Propositions; in III. and IV.,
only the Terms are unbalanced; in the remainder, both
Terms and Propositions are unbalanced.
"If we apply the Moods to any Matter, however abstract, say letters, there will emerge forty-two Syllogisms;
for the formal identity of the balanced Moods will then be
distinguished by a material difference." Thus, numbers I.
and II., with the four Negative Moods formed from them
by successively negativing each of their Premises, will,
when thus treated, yield six additional Syllogisms, making
forty-two in all. Take for instance, number I., Affirmative; when each of its Judgments is converted, it is still
in the same Mood.
Converting each Judgment.
I. All rational are all risible;    All risible are all rational;
All men are all rational;  All rational are all men;.-. All men are all risible..'. All risible are all men.'6 On the contrary, if we regard the mere formal equivalence of the Moods, these will be reduced to twenty-one
reasonings, - seven Affirmative and fourteen Negative."
For, of the unbalanced Moods, every odd number is converted into the even number immediately following; and
thus, if each Mood is regarded as formally equivalent to its
converse, (and numbers I. and II. are so regarded in the
Table,) numbers IV., VI., VIII, X., and XII. must be
struck out of the enumeration, and only seven valid Affirmative Moods remain. In like manner, in Negatives,
the first and second Moods (a, 6) of the pair corresponding to the even number which was struck out, are reduced
from or to the second and first Moods (b, a) of the odd
number which was retained. Five pairs being thus eliminated, only seven pairs - fourteen valid Negative moods
- remain.
Under the Aristotelic doctrine, as we have seen, logi



THE HAMILTONIAN ANALYSIS.           259
clans found that the six general Rules, which they had
enounced as governing all Mediate Inference, did not suffice to determine which of the Moods were valid, and
which invalid, in each of the four Figures. The variations
of Figure depend upon the relative position of the Middle
Term, as Subject or Predicate to each of the two Terms
of the Conclusion; and special Rules were necessary to
prevent these variations from  conflicting with the two
principles which, according to the Aristotelians, determine
the implicit quantification of the Predicate.  These principles are, —1. That in all Affirmative Judgments the
Predicate is Particular; and, 2. That in all Negative Judgments the Predicate is Universal., Now, in the Second
Figure, the Middle Term being Predicate in both Premises, the logicians were compelled, ini;order to prevent the
infringement of the General Rule, that the Middle Term
m.ust be distributed in at least one of the Premises, to enact
the Special Rule, that, in this Figure, one of the Premises,
and consequently the Conclusion also, must be Negative.
But under the Hamiltonian system of the thorough-going
quantification of the Predicate, since the Middle Term can
be distributed when it is the Predicate of an Affirmative,
just as well as when it is the Predicate of a Negative
Judgment, this Special Rule is both useless and false.
And so with all the other Special Rules for each of the
Figures. They are needless, because they were formed
only on the supposition that the Predicate could be but
partially quantified; they are false, because the thoroughgoing quantification of the Predicate brings to light many
valid forms of Syllogism which violate each of these rules.
The following demonstration of the falsity of these Special Rules is borrowed in part from Mr. Baynes's "New
Analytic of Logical Forms."
The Rules of the First Figure are, — 1. That the Sumption must be Universal; 2. That the Subsumption must




260         MEDIATE INFERENCE OR SYLLOGISM.
be Affirmative. Quantify the Predicate, and neither of
these holds good.
First Rule falsified.
Some men are     some fleet-footed,  
All rational is all man;-.'. Some rationalis some fleet-footed.
Second Rulefalsified.
--- Al idealists are some philosophers;
No sensualist is any idealist;.... No sensualist is some philosopher.
The Rules of the Second Figure are, -  1. That one of'
the Premises must be Negative; 2. That the Sumption
must be Universal.  Both are abrogated by a quantified
Predicate, thus:First Rule falsified.
All risible is all man;
All philosophers are some men;. All philosophers are some risible.
Second Rule falsified.
Some mortal is all man;
All rational is all man;. All rational is some mortal.
The Rules of the Third Figure are,- 1. That the Subsumption must be Affirmative; 2. That the Conclusion
must be Particular.
First Rule falsified.
-.-All free agents are all responsible;..No free agent is any brute;.-.No brute is anyyresponsible.)
Second Rule falsified.'All triangles are halves of parallelograms;
All triangles are all trilaterals;. All trilaterals are halves of parallelograms.
All the Special Rules being thus abrogated, the unity




THE HAMILTONIAN ANALYSIS.          261
and simplicity of the Syllogistic process become manifest.
Hamilton's Supreme Canon, which is a mere compend of
the six General Rules, appears as the universal and allsufficient law of Mediate Inference, and the science of
Logic is freed from the encumbrance of a mass of needless
distinctions and superfluous details. As Figure is demonstrated to be an unessential variation, all the Rules for
Reduction are swept away. In fact, the process of Reduction is so far simplified by allowing all Judgments to be
converted simply, that, if we still need to have recourse to
it in order that the reasoning may appear in its most obvious and natural form, the requisite changes suggest themselves, and the work may be performed without the aid of
rules.
Some observations are necessary, however, in respect to
the applicability of the different Figures to those two directions of the reasoning process which are called Deductive and Inductive. This subject has, been so well explained by Mr. Baynes, that I borrow his language. We
have seen that the characteristic of reasoning in Intension
-or Comprehension, as it is more frequently called — is,
that the Predicate is contained in the Subject; of reasoning in Extension, that the Subject is contained under the
Predicate.  "This being remembered," says Mr. Baynes,
"it will appear that in the Second Figure, where the Middle Term as Predicate contains both the Subjects under it,
Extension will predominate. In the Third, where the Middle Term as Subject is contained under, and therefore eomprehends in it both the Predicates, Comprehension will prevail. In the First Figure, again, where the Middle Term
is both Subject and Predicate, Extension and Comprehension balance each other. The First Figure is indifferently
competent to either.
"Reasoning, however, proceeds not only in different
wholes, but in different aspects of the same whole. We




262        MEDIATE INFERENCE OR SYLLOGISM.
may, it is evident, regard any whole, considered as the
complement of its parts, in either of two ways; for we
may, on the one hand, look from the whole to the parts,
and reason  accordingly downwards; or, on the other
hand, look from the parts to the whole they constitute,
and reason accordingly upwards.  The former of these
~reasonings is called Deductive, the latter Inductive.  DeWuctive reasoning is founded on the maxim,' What belongs to the containing whole belongs also to the contained parts'; Induction, on the contrary maxim,'What
belongs to the constituent parts belongs also to the constituted whole.' Thus, in Deductive reasoning, the whole
is stated first, and what is affirmed of it is affirmed of the
parts it contains; in other words, a general law is laid
down, and predicated of the particular instances to which
it applies. In Inductive reasoning, the parts are first stated,
and what is predicated of them is also predicated of the
whole they constitute; in other words, the particular instances are first stated as facts, and then the law they constitute is evolved.
"' This being the nature of these counter and correlative
reasonings, it appears to us, that, though each kind is competent in either whole (Extension or Comprehension), yet
the reasoning in the whole of Extension is more naturally
allied to the Deductive, and that in Comprehension to the
Inductive.  For, in the whole of Extension, the reasoning proceeds from the general to the special, - from the
abstract to the concrete, - from general laws to the particular instances which are contained under them; while
in that of Comprehension, on the other hand, the reasoning
proceeds from the special to the general, -from the concrete to the abstract,- from the particular instances to the
general laws, whose operation they exemplif.
"6 Considering these kinds of reasoning in relation to the
Figures, it will appear, then, that since Extension prevails




THE HAMILTONIAN ANALYSIS.,          263
in the Second, that will be so far more suitable for Deductive reasoning; and since Comprehension prevails in the
Third, that Figure will so far be more adapted for Inductive reasoning; while, since Extension and Comprehension
prevail equally in the First, that Figure will be equally
fitted for either kind of reasoning.
"The relation of the Figures to these different kinds of
reasoning will be best illustrated by an example. We will
take first the Second Figure:FIG. II.
Deductive Reasoning: Quantity of Extension.
Endowed with reason is all man.
European, Asiatic, African, American, are all man.
European, Asiatic, African, American, are endowed with reason.
"Here the reasoning is -Deductive, for the law is first
enounced, the individual instances are next brought under
it, and it is then affirmed of them; it is Extensive, for it
proceeds from the wider notion through the narrower to
the individual. Let us now take the same Terms and treat
them Inductively, beginning with the individuals. The
reasoning will then be in the whole of Comprehension, and
will naturally appear in the form of the Third Figure:FiG. II.
Inductive Reasoning: Quantity of Comprehension.
European, Asiatic, African, American, are all man.
European, Asiatic, African, American, are endowed with reason.
Endowed with reason is all man.
"Here the reasoning is Inductive, for, beginning with the
individuals in the Premises, we arrive at the law (with
which we started in the previous Syllogism) in the Conclusion; it is Comprehensive or Intensive, for it proceeds from
thie concrete to the abstract, from a greater totality of attribute to a less. In other words, in either Quantity (Extensive or Intensive), we reason front the greatest whole; but




264        MEDIATE INFERENCE OR SYLLOGISM.
in the Quantity of Extension, the greatest whole is the most
abstract notion (i. e. the widest law), whereas in that of
Comprehension, the greatest whole is the most concrete
notion (i. e. the individual instance).  But proceeding
thus from the widest law, the reasoning is necessarily
Deductive, while on the other hand, proceeding from the
individual instance, it is as necessarily Inductive.
"We may give the same example in the First Figure, to
illustrate (what will now be quite obvious) that it is indifferently competent to either reasoning: -
FIG. I.
Deductive Reasoning: Quantity of Extension.
All man is endowed with reason.
European, Asiatic, African, American, are all man.
European, Asiatic, African, American, are endowed with reason.
Inductive Reasoning: Quantity of Comprehension.
European, Asiatic, African, American, are all man.
All man is endowed with reason.
European, Asiatic, African, American, are endowed with reason.
"The Second and Third Figures are indeed naturally
respectively connected with Deductive and Inductive reasoning; for in the Second, we judge the likeness or unlikeness of two parts, as they are contained or not contained by
a common whole; while in the Third, we judge the likeness
or unlikeness of two wholes, as they severally contain or
do not contain common parts."
In respect to Hypothetical and Disjunctive reasoning,
Hamilton has followed Kant in declaring that all Mediate
Inference is one, - that which has been denominated Categorical; all the so-called Conditional Syllogisms are reducible to Immediate Inferences. Their characteristic feature
is, that they have no Middle Termn; the agreement or disagreement of the two Terms of the Conclusion with each
other is ascertained, not by comparing each of them separately with a third Term, which is a mediate process, but




THE HAMILTONIAN ANALYSIS.           265
directly, from a single Premise, here incorrectly styled a
Major Premise. This Premise consists, not of two Terms
merely, but of two Judgments, called respectively the Antecedent and the Consequent; a relation of mutual dependence is affirmed to exist between these, by virtue of which
the Axiom of Reason and Consequent becomes applicable
to the case. This Axiom, as has been shown (page 54),
is directly explicated into the two Laws, - 1. That to affirm
the Reason or the Condition is also to affirm the Consequent;
and, 2. That to deny the Consequent is also to deny the
Reason. A ratione ad rationatum, a negatione rationati ad:negationem rationis, valet consequentia.  The single Premise affirming that this relation of Reason and Consequent
exists between the Judgments which are its two parts, this
Axiom compels us to infer immediately, or without the aid
of a third Term, both that the Consequent follows when
the Antecedent is posited, and that the Antecedent is denied when the Consequent is sublated.
The reduction of a Hypothetical Judgment to a Categorical shows very clearly the Immediacy of the reasoning
in what is called a Hypothetical Syllogism. Thus, If A is
B, C is D, is equivalent to
All cases of A is B are cases of C is D.
Some cases of A is B are cases ofCiD
This case of A is B is a case of
In such reasoning, as Kant remarks, the Premise does
not afford a proof of the Conclusion, but a ground or manner of proving it; it is then only an explication of the
meaning of the Premise, when we say that the Consequent
holds good when the ground or Reason exists, and that the
Reason does not exist if the Consequent does not hold
good. Hence, this kind of reasoning may properly be
referred to the doctrine of Exponibles. All the Matter
which we are reasoning about is embraced in the one complex proposition that is here called the Premise; and all
12




266        MEDIATE INFERENCE OR SYLLOGISM.
that the reasoner has to do is to explicate or interpret this
ijroposition. Considered as an Exponible, the Conditional
Judgment, If A is B, C is -D, may be interpreted in two
ways, — 1. as a Restrictive; 2. as an Exclusive.  The
first of these interpretations yields, by the Immediate Inference of Subalternation, what is called the Modus ponens
of Conditional Reasoning; the second yields, also Immediately, the Modus tollens.
1. Thus, Restrictively, in affirming that, if A is B, C is
-D, we do not say, C is always D, but only, "All C, when
A is B, is D," the italicized clause being the Restriction,
and answering to a limiting adjective,- say, yellow: All
yellow C is -D.  Then, by Subalternation,
Some yellow C } is D.
This yellow C
Again, the same Judgment, If A is B, C is -D, yields, by
the Immediate Inference of Contraposition, If C is not D,
A is not B. This is an Exclusive; it affirms that
A ls B only when C is D; then, Immediately,
A is not B when C is not -D.
In fact, all reasoning is hypothetical; the Syllogism, as
such, does not affirm its Conclusion absolutely, but only its
dependence on the Premises. If the Premises are true,
the Conclusion follows. Any Immediate Inference, also,
may be stated hypothetically. Take that by Subalternation, for instance:
All A is B;,'. Some A is B.
Stated hypothetically thus: —
If all A is B, some A is B;,. Some A, or this A, is B.
It is unnecessary to consider separately the case of Disjunctive reasoning; for it has already been proved (page
131) that Disjunctives are only complex Hypotheticals.




OF FALLACIES.                267
CHAPTER IX.
OF FALLACIES.
FALLACY  is any instance of unsound or invalid
reasoning which has a deceptive appearance of correctness and truth. If it be such that the writer or speaker
is himself deceived by it, it is called a Paralogism; if
framed by him for the purpose of deceiving others, while
he is himself aware of its unsoundness, it is a Sophism.
Those of the former class are what we have most to dread;
for on account of the necessary dependence of Thought on
Language, we. often commit them in our silent meditations,
while we are attempting to discover the truth or to disintricate it from error. The danger is greatly enhanced
by the symbolic or algebraic use of Language, whereby
we employ words for the moment as mere signs, without
spreading out their signification before the mind, and thus
are often deceived by their ambiguity and vagueness.
Sophisms are comparatively of rare occurrence, as one
who wishes to deceive can do so more easily and effectually by false statements than by false reasonings. It is
more difficult to weave invalid but specious arguments,
knowing their incorrectness, than to reason correctly from
wrong premises.  Formerly it was otherwise; the great
use of disputation by the ancient sophists and the Schoolmen, as a logical exercise and a means of education, tended
to create a special art of sophistry, and has left on record a
multitude of logical puzzles for the amusement of later
times.  Dexterity in framing and solving these sophisms




268                 OF FALLACIES.
was reckoned a scholarly accomplishment, and one of the
special fruits of a university education.  Nowadays this
species of mental gymnastics has fallen into entire disrepute, as men prefer to sharpen their wits on graver matters
and subjects of more immediate interest.
The purpose of the doctrine of Fallacies, as it is now
taught, is to familiarize the mind with those instances of
erroneous reasoning which are most likely to lead our own
thoughts astray in the search after truth and the elimination of error.  For this end, a classification of Fallacies is
desirable. The earliest attempt, of which we have any
distinct knowledge, thus to reduce them to system, was
that of Aristotle; and the chief endeavor of later logicians
has been to ascertain, develop, and illustrate his meaning.
Even the phraseology which he employed became consecrated, as it were, by long use in the Schools; and the
chief dispute among modern writers has been, whether a
particular Fallacy is rightly designated by this or that technical name. A more unprofitable logomachy can hardly
be imagined. Our business is to teach Logic, and not to
write a commentary upon Aristotle. The classification
framed by him, though a marvellous work for the time,
evincing the prodigious acuteness and comprehensiveness
of view for which his intellect was so remarkable, must
still, if viewed under the lights of modern science, be regarded as crude and imperfect. A better arrangement can
be effected, not by laying aside his phraseology altogether,
but by employing his technical terms, when they are convenient, under the conventional meaning which has long
been assigned to them, and by striking out many of his distinctions, and introducing others in their place which have
been suggested by later experience. The use of classification, it must be remembered, is merely subsidiary; the
main purpose is to become familiar with the characteristics of those forms of erroneous reasoning which most




OF FALLACIES.                 269
frequently occur in practice; and this can be best accomplished by dividing them into species, and discriminating
these species from each other.
It should be observed that, strictly speaking, the consideration of Fallacies is extralogical. We have already laid
down the Rules of correct or valid Inference; any argumentation which violates one or more of these Rules is invalid. But an open violation of one of them, as, from its
very obviousness, it is not likely to deceive anybody, is not
usually called a Fallacy. A classification of what are properly denominated Fallacies would depend on an enumeration of those circumstances which are most likely to deceive
us —to cover up the violation of a Rule —in the formation of our Judgments and Inferences; and a disquisition
on these circumstances would form a valuable chapter of
Psychology, or in a Treatise on the practical Conduct of
the Understanding. The chief source of these errors is
the ambiguity of language, both as respects the meaning
of single words (cequivocatio) and the construction of
sentences (amphibolia).  Then the ultimate remedy for
them is to be found in the study of language; it would be
a part of the doctrine of iermeneutics, or the science of
Interpretation. But as certain prominent classes of them
frequently perplex and vitiate our reasonings, a description
of such is not entirely out of place as an appendage to the
science of Logic.
We observe in the first place, then, that Aristotle was
wrong, and his authority has misled most of the later logicians, in forming a distinct class of the Fallacies of language.
His first distinction is between those in dictione, which
arise merely from the improper use of words as arbitrary
signs of thought, and which, therefore, generally disappear
when the proposition is translated into another language,
and those extra dictionem, which are in the Thought itself,
whether in its Matter or its Form, and therefore adhere to




270                 OF FALLACIES.
the Thought, however it may be expressed. He enumerates six classes or subdivisions of the former; but the
division is a faulty one, as the six can be reduced to two,
namely, the ambiguity of single words, or the ambiguous
construction of sentences. But we object generally, that
the erroneous use of language is of no logical import whatever, if it be not employed to hide some defect in the reasoning. The ambiguity of words may cloak; but does not
constitute, the sophism. If the suspected Syllogism does
not contain an undistributed Middle, or four Terms instead
of three, or an Illicit Process, or some other violation of
logical Rule, it is a sound Inference, however faulty may
be the language in which it is expressed. Accordingly, it
will be found, that all the instances given in the books to
illustrate the six classes of what may be briefly termed
Verbal Fallacies, resolve themselves, when the ambiguity
is detected, into logical quadrupeds, as Syllogisms with four
Terms have been derisively called, or some other form of
violating one or more of the Canons of Pure Logic. Take
the following illustration, from Mr. De Morgan, of the Fallacy of ambiguous words, Aristotle's first subdivision.
All criminal actions ought to be punished by law;
Prosecutions for theft are criminal actions;
Therefore, prosecutions for theft ought to be punished by law.
Here the Middle Term, criminal actions, is ambiguous; in
the Sumption, it means immoral deeds; in the Subsumption, it is a technical phrase for a particular class of legal
proceedings.  Substitute these definitions for the phrase
defined, and it is apparent that the pretended Syllogism is
a quadruped.
Take the following as an instance of Aristotle's second
subdivision, - ambiguous construction.
All that glitters is not gold;
Tinsel glitters;
Then, tinsel is not gold.




OF FALLACIES.                  271
Here, in the Sumption, tile Middle Term  is apparently
distributed by the predesignation all; but it is not so in
reality, as the negative particle ought to be construed as
qualifying all, and not all means some are not.  But if we
read, Some things that glitter are not gold, the Middle is not
distributed in either Premise.
The class of Verbal Fallacies, then, should be abolished,
as all instances of invalid. or erroneous reasoning, being
either an open or a concealed violation of the Laws of
Thought, are necessarily extra dictionem, or independent of
language.  Then the most general division of them will be
into Formal and Material Fallacies, "according as the
source of deception lies in the act of Thought itself, or in
the object upon which, or the circumstances under which,
it is exercised." This distinction may be well expressed
by saying that, in every Fallacy, the Conclusion either
does, or does not, follow from the Premises.  If it does not so
follow, it is clear that the fault is in the reasoning, and in
that alone; the error concerns only the Form of Thought,
so that these alone are Logical Fallacies strictly so called.
If the Conclusion does follow from the Premises, we must
search for the deception in the Matter of the Thought;
that is, we must consider what we are reasoning about,
and what is the Conclusion which we wish to establish.
Such consideration is properly extralogical; but as the purpose of examining both classes of these Fallacies is the
same, namely, to guard the mind against error in its own
processes, and as the consideration of only one class of Fallacies would very imperfectly answer this end, we subordinate strict method to convenience, and take into view all
cases of defective and sophistical argumentation.  While
considering both of these classes of Fallacies, the ambiguities of language which hide them, and which originally
led the reasoner astray, will incidentally come into notice,
and the exposure of them thus effected will be, in a prac



272                  OF FALLACIES.
tical point of view, the most valuable result of the discussion.
The subdivision of Fallacies in the Form of Thought,
the Conclusion being illogically drawn, is easily effected,
as it must have reference to the six General Rules, which
are all embodied in Hamilton's one Supreme Canon of
Mediate Inference.  But the classification thus made is not
easily adhered to, as it will often be found that the same
Fallacy involves a violation of two or more of these General Rules. The subject being once properly distributed
into parts, however, the question is of little moment
whether a particular case is rightly assigned to this or that
class, if it may fairly be placed under either. The Rules
most frequently violated are those which require, -1. That
a Syllogism should consist of only three Terms; 2. That
the Middle Term should be distributed in at least one of
the Premises; 3. That neither Term can be distributed in
the Conclusion, if it was not taken universally in the Premises; 4. That the Conclusion must be Negative, if either
Premise is Negative; 5. That at least one Premise must
be Affirmative.  Besides the five kinds of Fallacies arising
from violations of these Rules, two others should be mentioned, being the two invalid Moods of Hypothetical Inference: — 6. From denying the Antecedent, or, 7. From
affirming the Consequent, no Conclusion can be drawn. A
number of other classes might be framed, arising from violation of the various Rules of Immediate Inference, — the
Laws of Conversion, Opposition, Infinitation, for instance.
But as such errors are neither frequent nor insidious, they
need not be considered here.
1. To the class of Syllogisms which are invalid because
they consist of more than three Terms may be referred all
the cases which are usually placed under the head of ambiguous Mliiddle. If an ambiguous word or phrase is employed
as the Middle Term in the Major Premise in one of its




OF FALLACIES.'               273
significations, and in the Minor Premise in a different signification, it is evident that it does not afford us any means
of ascertaining the relation of the Extremes to each other.
Having only compared A with M, and B with N, we cannot tell whether A is, or is not, B. Cases of this Fallacy
are more numerous, and more apt to deceive, than those
of any other class. They are the more insidious, because
terms in frequent use, and which are constantly employed
by the vulgar in ordinary conversation, are precisely those
which are most apt to become ambiguous; but on account
of their familiarity, we fancy that we are perfectly acquainted with them, and therefore never suspect that they
are leading us astray.
Most political Fallacies are of this order. That very
common phrase, the government, means both " the system
of laws under which we live and the machinery by which
these are administered," and "the members of the administration for the time being, whose duty it is to carry
out this system and to work this machinery "; or it may
mean certain measures, or a favorite policy, of these administrators. Hence what Jeremy Bentham calls "' the official
malefactor's screen"; - "; Attack us, you attack the government." It may well happen that we best manifest our
attachment to the government in the former sense, by a
vehement opposition to it in the second meaning; or, if the
administrators are really able and well disposed, but are
pursuing a mistaken policy in one respect, that we best
show our regard for them personally, by laboring to convince them of their error.
Still more ambiguous is that which is so much talked and
written about, — the Church.  How many controversies
might have been spared, and how many volumes remained
unwritten, had it been remembered that, at least in all
countries where a religious establishment exists supported
by law, "the Church" may have these six different
12*                           i




274                  OF FALLACIES.
meanings:- 1. a place of meeting for worship; 2. all the
people engaged as worshippers; 3. only the faithful who, in
in every age, since the advent of the Redeemer, have
constituted the mystical Body of Christ; 4. the inferior
clergy by whom the ceremonies of worship are conducted;
5. the superior clergy, who may be regarded as the heads
of the Church; 6. rules and customs respecting the modes
of worship. As Bentham remarks, church is often made to
mean churchmen, and law to signify lawyers, by the easy
device of "substituting for men's proper official denomination the name of some fictitious entity, to whom, by
customary language, and hence opinion, the attribute of
excellence has been attached."
If it were allowable to make a new use of one of Bacon's
technical appellations, another large class of these sophisms
might be called Fallacies of the Forum. These relate
chiefly to money, currency, prices, interest, profits, and
other terms of frequent use in commercial and financial
transactions. Money may mean either specie, or bank-notes,
or currency consisting of a mixture of these two, or credit,
or capital, or that portion of capital which is offeredfor loan.
An individual merchant is said to be in want of money
wherewith to pay his debts, when his only real lack is of
credit, capital, or merchandise, money serving no other
purpose in the affair than that of the carts by which the
merchandise is transported.  Again, interest is usually
spoken of as if it were the interest of money; whereas a
little reflection will satisfy any one, that money (if the
name be applied, as it usually is, to specie, to bank-notes,
or to a combination of the two) yields neither profit nor
interest; whether it is in the hands of an individual or a
corporation, whether in the pocket or in a safe, it is a part
of the owner's dead capital, and therefore he usually aims
to get along with the use of as little of it as possible.
Again, money is usually considered as the measure of




OF FALLACIES.                  275
wealth; and then, by a very common metonomy, the measure is confounded with the thing measured.  Hence the
following sophism, which may be said to have directed the
commercial legislation of all civilized countries, down, at
least, to the time of Adam Smith.
Any increase of the money in a country is an equivalent enlargement of its wealth.
taws to protect native manufactures against foreign competition
tend to increase the money in the country.
Therefore, such laws tend to increase the nation's wealth.
But Adam Smith demonstrated that laws directed solely to
keeping specie at home, only tend to make the country
poorer; and his arguments being at last generally admitted
to be conclusive, there arose the opposite Fallacy of universal Free Trade, which now controls the legislation of
England, and is gaining ground in many other quarters.
Laws which do not increase the quantity of money in the country are at best useless.
A Protective System does not increase this quantity.
Therefore, a Protective System is useless.
Of course, the answer to this argument is, that measures
which do not prevent specie from going abroad may yet
make the people more wealthy and prosperous, by enabling them, in their foreign trade, to exchange manufactures
for raw material, - that is, the products of skilled labor
for those of rude labor, -that is, again, the fruits of the
industry of one man for those of the industry of three or
four men. And it is precisely this system, - fostering the
growth of native manufactures and allowing the production of raw material to take care of itself, - and not the
prevalence of the doctrine of Free Trade, which has been
the great source of England's prosperity.
Another frequent source of this Fallacy -the introduction, through the ambiguity of language, of four Terms into




276                 OF FALLACIES.
a Syllogism -is the doctrine that the primary or etymo.logical meaning of a word is its only proper signification, or
that it is the standard to which modern usage ought to conform. This sophism is the more frequent, as it affords an
opportunity for a little display of erudition; numerous
instances of it can be found in what is otherwise an ingenious and excellent work, Tooke's 1" Diversions of Purley."
Thus, right comes from rectus, and that from rego, - to
rule or govern; hence an alleged confirmation of the doctrine of Hobbes, that right is only a creature of positive
law, another unfounded assumption being then allowed to
slip in, that the only kind of law is human, not divine.
Again, most of the words which are now significant of the
operations of Mind were originally applied to some of the
forms or changes of Matter; and this fact has heen held to
countenance the doctrine of materialism. But that spirit
once signified breath, and animus, "aveuog, air, does not
afford even a presumption that such is their present meaning. The secondary or usual sense- of a word has often
travelled so far away from its primitive application as to
have lost sight of it altogether, though we may be able to
point out the stopping-places in its long journey.
I cannot help thinking that Sir William Hamilton has
unconsciously glided into a Fallacy of this sort in his criticism of Dr. Reid's definition of memory. Reid says,
"Memory is an immediate knowledge of things past";
meaning thereby, as it seems to me, a present knowledge
of the past. This, at any rate, is a very common use of
the word; an action is said to be immediate which takes
place now, at once, or without delay. But immediate is
also the opposite of mediate or vicarious; we are said to
lhave an immediate knowledge of a thing when we know it
directly or in itself, in contradistinction from knowing it
vicariously, or through the medium of an image or representation of itself. In this sense, Hamilton argues very




OF FALLACIES.                 277
properly that an immediate knowledge of the past is impossible; and Reid, I think, would have agreed with him;
while Hamilton would not have denied that memory is
present knowledge, or knowledge which exists at the present
time.
Another source of ambiguity, which is well exposed by
WVhately, is the supposition that paronymous or conjugate
words —as the substantive, verb, adjective, and adverb
formed from the same root —necessarily agree in meaning; whereas, they often depart widely from each other in
signification.  Thus, what is imaginary is unreal; but an
image, as formed from wood or stone, is a reality. To apprehend ~is to lay hold of, or to come to a knowledge of;
while apprehension often signifies fear, dread.
What Aristotle calls the Fallacy of Accent (he should
have explained it as an ambiguity which may be resolved
by accent) may be illustrated by the difference between
gal'lant and gallant'; the former means brave, high-spirited;
the latter, courteous or devoted to women. It is more difficult to resolve by accent the curious ambiguity of the
phrase,' not the least, where the two meanings are opposites
of each other.  Thus, "'not the least difference" may
mean either " no difference at all," or, "6 a very considerable, perhaps the greatest, difference."  In the former
case, the phrase is elliptical, standing for "not any, not
even the least, difference."  The least is excluded or negatived, as in the phrase ".not the least," both by nothing
and by the greatest.
As De Morgan remarks, " a statement of what was said,
with the suppression of such tone as was meant to accompany it, is the fallacia accentus. Gesture and manner often
make the difference between irony or sarcasm and ordinary assertion. A person who quotes another, omitting
anything which serves to show the animus of the meaning;
or one who without notice puts any word of the author he




278                  OF FALLACIES.
cites in Italics, so as to alter its emphasis; or one who
atteinpts to heighten his own assertions, so as to make
them imply more than he would openly say, by Italics, or
notes of exclamation, or otherwise, is guilty of the faUlacia
accentus."
2. The Fallacy of Undistributed Middle does not occur
so frequently, and is not so insidious, as that of Ambiguous
Middle.  We may fall into it unawares by overlooking
the difference between the Collective meaning of the word
all==' all taken together," and its Distributive meaning,
in which all signifies "each and every."  Thus, all the
Senators (taken collectively) try impeachments; all the
Senators (i. e. each and every Senator) are chosen by the
State legislatures.
All these exercises will fatigue me;
This performance is one of them;
Therefore, this performance will fatigue me.
Another ambiguity, which may serve to cloak this logical
fault, is passing friom the Composite to the Divisive, or from
the Divisive to the Composite, meaning of a proposition.
If we take together those members of the sentence which
ought to have been taken separately, it is called the sophism of Composition; if we take separately what is true of
all only when they are united, it is the sophism of Division.
A ludicrous instance of the latter is found in most of the
old text-books on Logic.
Two and three (taken compositely) are five;
Two and three (taken divisively) are odd and even;
Therefore, five is odd and even.
An instance of the former is what may be called the
Spendthrift's Fallacy.
All of these contemplated expenditures (taken separately) are
of trifling amount;
Therefore all of them may be incurred (together) without ruining me.




OF FALLACIES.                   279
The lazy person reasons in the same manner, in respect
to the waste of an hour or two of time, or to missing this
or that favorable opportunity. It behooves such persons
to remember, that the predesignation any one is not the
equivalent of all taken collectively.
This is the nature of the famous old Fallacy called
ropows, a heap, whence the name Sorites applied to a different and legitimate argument.  Does one grain of corn
make a heap? No. Do two grains make a heap? Nd.
Do three grains? No. And in like manner, we may ask
a series of questions, successively adding unity to the number, till the respondent is at last obliged to contradict himself, and confess what he has just denied, that a single
grain of corn makes the only difference between what is
not, and what is, a heap.  The same sophism was denominated by the old logicians the CaZvus, because illustrated
by a series of questions beginning with the inquiry, whether
pulling one hair out of a man's head made him bald.
Horace used it to ridicule the fashion of valuing ancient
authors simply on account of the antiquity of their productions., Iste quidem veteres inter ponetur honeste,
Qui vel mente brevi vel toto est junior anno,
Utor permisso, caudmeque pilos ut equinme
Paulatim vello, et demo unum, demo etiam unum,
Dum cadat elusus ratione ruentis acervi,
Qui redit ad fastos, et virtutem mestimat annis,
Miraturque nihil nisi quod Libitina sacravit."
But while laughing at an old sophism, we may be found
ridiculing a modern paralogism. I have recently heard
this very argument gravely reproduced in a learned Academy, during a debate on an important question of science.
The answer to it is obvious; - not one alone, but one added
to the previous 999, constitutes a heap.
The Fallacy of the Composite and Divisive sense is apt
to be repeated by the incautious in estimating the proba



280                  OF FALLACIES.
bility of two events happening conjointly. Though each
of them, taken separately, is more likely than not to
happen, the probability of their occurrence together is
of a very inferior character. Thus, the probability of the
first being represented by 3, and that of the sepond by -,
that of their joint occurrence is the product of these two
fractions, or 7-, or much less than a, which represents
an even chance. So we are often misled by the use of
the word tendency.  We rightly say that a given result
tends to happen only when there is more than an even
chance of its occurrence; if there is less than an even
chance, it tends not to happen.  This is the form of a common blunder in the doctrine of means or averages. Thus,
all persons who have attained the -age of twenty-four survive on an average till they are sixty-two years old. But
no one person, now aged twenty-four, has a right to expect
that this average will be exemplified in his particular case.
On the contrary, his chance of attaining the precise age of
sixty-two, no more and no less, is very much less than his
chance of dying at some other age. All (collectively) tend
to the average; but no one tends to the average. This is
no paradox; for the average is only a compensation of
errors, and therefore remains the same whether the errors
are great or small, provided only that they are equally distributed on all sides of the average; and such equality of
distribution is the direct consequence of the fact, that no
one error has any tendency to be on one side of the average
rather than on any other side. No one tends to the average, but tends equally, or indifferently, to depart from it.
Mr. Darwin, in his theory of " the Origin of Species by
Natural Selection," is guilty of both of these forms of the
Fallacy. He first argues, that the specific Marks of Species, both in the animal and vegetable kingdoms, tend to
vary, because, perhaps in one case out of ten thousand, a
child is born with six fingers on one hand, or a cat with




OF FALLACIES.                281
blue eyes, or a flower grows out of the middle of another
flower. Collecting many instances of such sports of nature
or monstrosities, he bases his whole theory upon them, forgetting that the vastly larger number of normal growths
and developments proves that the tendency is to non-variation. Then, secondly, because perhaps one out of a hundred of these abnormal Marks is transmitted by inheritance,
he assumes that these freaks of nature tend to perpetuate
themselves in a distinct race, and thus to become permanent Marks of distinct species. Thirdly, as either of the two
preceding points, taken singly, affords no basis whatever
for his doctrine, he assumes that their joint occurrence
is probable, because he has made out what is, in truth, a
very faint probability that each may separately happen.
But if the chance of a variation in the first instance is only
one out of a thousand, and that of the anomaly being
handed down by descent is one out of a hundred, the
probability of a variation established by inheritance is but
one out of a hundred thousand. As the theory further
requires the cumulation of an indefinite number of such
variations one upon another, the formation of a new species
by the Darwinian process may be safely pronounced to be
incredible.
3. The third class of Fallacies, those which arise from a
violation of the Rule that neither Term must be distributed
in the Conclusion if it was not distributed in the Premise,
are frequent enough, but will deceive no one if they are
not ambiguously expressed. If it is the Predicate of the
Conclusion which is illogically distributed, the error is
called an Illicit Process of the Major Term; if the Subject, an Illicit Process of the Minor Term. Of these, the
former is more common and insidious; for as the Quantity
of the Predicate is not expressed in the ordinary use of
language, we are apt to forget that, in a Negative proposition, it is always presumed to be Universal, and in an




282.                  OF FALLACIES.
Affirmative, if nothing be said to the contrary, it is usually
Particular.  In what the Aristotelians call Indefinite propositions, the Quantity of neither Term is expressed; but if
Affirmative, both Terms are commonly understood to be
distributed; for most propositions of this sort are either
Definitions, or statements of a general law; and in both of
these cases, the Universal quantification of each Term is
easily supplied in thought. Thus, Falsehood is wilfiul deception, is easily and properly construed to mean, Allfalsehoods
areall wilful deceptions; and Matter gravitates, to-mean, All
matter is all that gravitates.  But statements of a general
law must be carefully distinguished from statements of the
application of such a law to a particular class of cases;
thus, Stones gravitate, means only, "All stones are some
gravitating substances."
All birds are winged;
The bat is not a bird;
Then the bat is not winged.!
Here, the Conclusion is logically false, for it contains an
Illicit Process of the Major Term. The Sumption is understood to mean only that " All birds are some winged.
things"; the bat, therefore, though not a bird, may be
(as here it happens actually to be) one of the other some
winged things, while the illogical Conclusion declares it to
be not (any) winged thing.
No slave has his rights;
All slaves are persons of African descent;
Therefore no person of African descent has his rights.
The Illicit Process is here of the Minor Term; for the
Conclusion denies of any, what the Premises authorize us
to deny only of some Africans.
In both these cases, the Fallacy is so obvious that it cannot deceive any one who thinks clearly.  But the ambiguities of language may so cloak the deception as to render
its exposure difficult.  Most insidious in this -respect is the




OF FALLACIES.                   283
ambiguity between what is true absolutely, and what is
true only in some respect, To d7r\XJ iX,  darX-,.  From
this confusion of language two modes of false reasoning
result, the first of which is denominated by the Aristotelians the fallacia a dieto secundum quid ad dictum simpliciter.  It consists in inferring something as true of the
subject simply, or without limitation, which is true of it only
in some respect.  Thus, Man is immortal (in respect to his
soul); therefore, man is immortal (absolutely, both as to
soul and body). The second has been called the fallacia
accidentis, because it confounds an accidental attribute with
what is essential or principally intended. But as it is the
exact converse of the former, it should rather be called the
fallacia a dicto sirnpliciter ad dictum secundum quid. Thus,
to take the converse of the former instance, Man is mortal
(mwan being here understood, as usual, to be a living organism); therefore, man is mortal (as respects his soul).
Aristotle gives the following illustration, which is puerile,
though it might well puzzle a beginner:Socrates is not Coriscus (in any sense);
But Coriscus is a man (this being one of his characteristics);
Therefore, Socrates is not a man.
The most difficult cases to be resolved are those in
which giving the name of the genus, to which the subject
belongs, is confounded with giving the name of its species.
Thus,
He who calls you a man speaks truly;
He who calls you a knave calls you a man;
Then he who calls you a knave speaks truly.
A ludicrous instance of the former mode of the Fallacy is
found in most of the text-books:
What you bought yesterday you eat to-day;
But you bought raw meat-yesterday;
Then you eat raw meat to-day.
Perhaps both forms of this Fallacy are best resolved by




284                 OF FALLACIES.
considering that the ambiguity resides in the Copula.
When one thing is predicated of another, it is seldom understood that the Predicate is thereby entirely identified
with the Subject, as the proposition would then be merely
tautologous, A is A. But unless it is so identified, we cannot affirm of the Predicate all that might be affirmed of the
Subject. The logical rule as usually enounced, that no
Term must be distributed in the Conclusion if it was not
distributed in the Premises, is defective; for it only insures
that the Quantity shall be the same. The sense ought also
to be the same throughout, whether absolute or relative,
whether in one respect or in many, whether essentially or
accidentally. An adequate enouncement of the rule would
be, that no more and no less, in any respect, must be collected
in the Conclusion than was given out in the Premises. In
order to know how much was so given out, we must consider
the meaning of the Copula, is, in each separate case. Mr.
De Morgan says: " The most common uses of the verb
are, -1. absolute identity, as in'the thing he sold you
is the one I sold him,' —this is the dictum simpliciter;
2. agreement in a certain particular or particulars understood," dictum secundum quid, " as in' he is a negro,' said
of a European in reference to his color; 3. possession of a
quality, as in' the rose is red'; 4. reference of a species to
its genus, as in'man is an animal.' All these uses are
independent of the use of the verb alone, denoting existence, as in'man is [i. e. exists].'"  In most cases, these
meanings are not interchangeable; and whenever they are
not, a Fallacy may be founded upon the difference between
any two of them.
But the enumeration is imperfect; several additions may
be made to it, by observing, what has been already remarked in treating of Contradiction, " that two Judgments
properly contradict each other only when that which is
affirmed by the one is denied by the other,-1. in the




OF FALLACIES.                 285
same respect; 2. in the same manner; 3. in the same
degree; 4. at the same time."  Thus, Mr. De Morgan's
instance of absolute identity is unhappily chosen; for if the
limitation of time is taken into account, " the horse which
he sold you," being ten years old, is not absolutely the same
horse which I sold him, as that was only six years old.
All Fallacies of this class may be easily resolved by merely
completing in expression what was previously only implied
in thought. We thereby prevent any more or less stress
being laid upon an accident, or upon any view of the subject, in the Conclusion, than was done in the Premises.
The use of wine is destructive to the health;
Therefore its use ought to be forbidden.
As stated, this Enthymeme may seem indisputable; but
there can be no practical application of it, unless it is understood to mean that any use of wine is pernicious, and hence
that it ought always to be forbidden. This is the fallacy
of arguing against the use of a thing merely from its liability to abuse. The proper caution is, that no change whatever in the Terms employed must take place during the
process of inference.
In ordinary language, few terms are so loosely used, or
so often improperly applied, as the same, all, always, &c.
Hence the logicians were obliged to form a separate class
of Fallacies, which they called those fictce universalitatis.
People say the same, when they mean similar; all, when
they mean only most; and always signifies to them the
same as frequently. They do not even mention the excuse
which the Psalmist alleges when conscious of his exaggeration,-" I said in my haste, All men are liars."  It was
once considered a difficult question, whether a stocking,
which had been so much darned that not a thread of the
original fabric remained, was, or was not, the same stocking.
But it can present no difficulty to one who considers that
sameness or identity is an absolute term, which can neither




286                  OF FALLACIES.
be affirmed nor denied except in an unqualified sense; and
that all which can be truly predicated of what comes short
of sameness is similarity.
"We might suppose that most persons have no idea of a
universal proposition; but use the language, never intending all to mean more than most. And in the same manner,
principles are stated broadly and generally, which the
assertor is afterwards at liberty to deny, under the phrase
that he does not carry them so far as the instance named.
It would not do to avow that the principle is not always
true; so it is stated to be always true, but not capable of
being carried more than a certain length. Are not many
persons under some confusion about the meaning of the
word general?  In science, it always has the meaning of
universal; and the same in old English.  Thus the Catechism of the Church of England asserts that there are two
sacraments which are generally [universally] necessary to
salvation, -meaning, necessary for all of the genus in question, be it man, Christian, member of the Church, or any
other.  But in modern and vernacular English, general
means only usual, and generally means usually." *
An opposite error, but one proceeding from the same
source, viz. from confounding the Universal with the Particular, is committed by many Americans and some Englishmen in respect to the word quite. Its proper meaning
is completely, entirely, as " quite contrary principles "; but
it is often used inl the sense of very, as "quite warm,"
"quite cold," " quite recent."
The word same, in ordinary parlance, is applied to all
objects for which a single description will serve, or which
are included under one Concept. Thus we say, 1" This
writing is on the same paper with that," meaning the
same kind of paper; " This erroneous reasoning is the same
Fallacy with the other," meaning the same kind of Fallacy.
* De Morgan's Formal Logic, p. 272.




OF FALLACIES.                    287
A description or Concept, as we have seen, is an imperfect
enumeration of the qualities of a whole class of objects;
and it is only because the enumeration is imperfect that
many can be ranked under one class.  A perfect enumeration, if such were possible,- a list of all the qualities, -
would cause each Individual (if this were not a contradiction in terms) to constitute a class by itself.
" Nothing, perhaps," says Dr. WVhately, "has contributed
more to the error of Realism, than inattention to this ambiguity.  When several persons are said to have one and the
same opinion, thought, or idea, many men, overlooking the
true, simple statement of the case, which is, that they are
all thinking alike [or similarly], look for something more
abstruse and mystical, and imagine there must be some one
thing, in the primary sense, though not an Individual,
which is present at once in the mind of each of these persons; and thence readily sprung Plato's theory of Ideas,
each of which was, according to him, one real, eternal
object, existing entire and complete in each of the Individual objects that are known by one name.*  Itence, first
in poetical mythology, and ultimately, perhaps, in popular
belief, Fortune, Liberty, Prudence (Minerva), a Boundary
(Terminus), and even the Mildew of Corn (Rubigo), became personified, deified, and represented by statues;
somewhat according to the process which is described by
Swift, in his humorous manner, in speaking of Zeal, in the'Tale of a Tub,'' how  from  a notion it became a word,
and thence, in a hot summer, ripened into a tangible substance.'"
But Dr. Whately seems to depart from his own prin* "When abstract truth is contemplated," asks Dr. Price, " is not the
very object itself present to the mind? When millions of intellects contemplate the equality of every angle in a semicircle to a right angle, have they
not all the same object in view? Is this object nothing? Or is it only an
image or kind of shadow 2 These inquiries carry our thoughts high."




288                 OF FALLACIES.
ciples, when he proceeds to remark, that'" Sameness, in
the primary sense, does not even necessarily imply Similarity; for if we say of any man that he is greatly altered
since such a time, we understand, and indeed imply by
thle very expression, that he is one person, though different
in several qualities; else it would not be he."  Surely,
what we mean by Personal Identity is sameness of substance under great differences of phenomenal manifestation.
Sameness here does not imply Similarity, merely because
it implies a great deal more; —namely, absolute oneness
of substance, under the greatest diversity of outward appearance. The Person is not different at different times,
but his attributes and actions are.  But perhaps this is
what Dr. Whately really means, though it is not the obvious construction of his language. He seems to consider
the Person, and his outward character or manifestation, as
one.
The Fallacy of over-hasty generalization is very frequent,
as Bentham remarks, in political reasoning. It consists in
attributing to an individual person or thing certain attributes which appear in many or most others which have
been loosely ranked in the same class with the object in
question, and thereby designated by the same name. Thus,
a pamphlet entitled " The Crimes of Kings" was published
in Paris in 1792, in order to prove that Louis XVI. ought
to be put to death. In like manner, "The Cruelties of
Catholics " was the title of a book published in England as
all argument against Catholic Emancipation. Most political harangues abound in arguments of the like character;
but they are evidently addressed to the passions rather
than the intellect, as they cannot deceive any one who is
cool enough to be able to think.
To the ambiguity between what is true absolutely, and
what is true only in some respect, may be referred the
famous sophism of Eubulides, called Yev8gpero,, the Liar.




OF FALLACIES.                    289
According to Diogenes Laertius, Chrysippus the Stoic wrote
six different treatises upon this logical puzzle, and Philetas
of Cos studied himself to death in the vain attempt to solve
it. "' If you say that you lie, and say so truly, then you
do lie; but if you say so falsely, then you speak the truth.
In either case, therefore, the same assertion is both true
and false."  But if any onie says, " I lie," his assertion is
not a dictum simpliciter; for a lie is only possible secundum
quid.  He who lies must lie about something, in some particular affirmation or denial; otherwise, his assertion is as
meaningless as the remark that "6 something is very like."
Like what? *  If he means only, "I have lied in some
former assertion," there is no contradiction; if he means,
4' I lie now, in saying that' I lie,' " he really makes two
affirmations, of which the one, the oratio obliqua, is vague
and meaningless, and the other, the oratio directa, improperly characterizes this one as a falsehood, - improperly, for
that which has no significance cannot be either true or
false.
This sophism  has been stated in a different and inferior
form, as follows:4' All the Cretans are liars."
But Epimenides, who says this, is himself a Cretan.
Therefore, as he is a liar, this saying is not true.
But if the saying is not true, Epimenides may have spoken the
truth.
Then the saying is true; —and so on, as before.
But here the Major Premise does not support the Conclusion, unless it is construed to mean that the Cretans are
always liars, -that they cannot speak the truth.  And
even if this were true, one who is himself a Cretan could
not say so, for then he would speak truly, and so contradict himself. Of a similar nature is the following puzzle.
* Mansel's Notes to Aldrich, p. 145.
13




290                  OF FALLACIES.
"No rule holds true without some exceptions."
But this very remark is a rule.
Then it has exceptions.
Then there are rules without exceptions.
Here the reasoning, as such, is correct, and the absurdity to which it leads demonstrates what has been properly
called the Fallacy of universal scepticism.  As Sir James
Mackintosh remarks,'" universal scepticism involves a contradiction in terms; it is a belief that there can be no
belief." He who denies every assertion thereby denies his
own denial, and so contradicts himself.  The Major Premise in this very puzzle is such a self-contradictory assertion; I cannot make a true general remark, that all general
remarks are false; or, what is the same thing, that they
"have exceptions."
4 & 5. Little need be said to illustrate the remaining
classes of Fallacies, as they are of infrequent occurrence,
and are easy to be detected unless cloaked by some of the
ambiguities of language which have already been exposed.
Those which respect the Quality of the reasoning may well
be considered together.  The two Rules are, that at least
one of the Premises must be Affirmative, and that the Conclusion must be Negative if either Premise is Negative.
These Rules may be-violated in appearance, when they are
not so in reality. For instance: —
No one is rich who has not enough;
No miser has enough;
Therefore no miser is rich.
Here, both Premises are seemingly negative; but they
are not really so, for the negation of having enough is a
part of the Predicate, and therefore does not affect the
Quality of the Judgment, which depends on the Copula.
Instead of not having enough, substitute the equivalent
phrase, wanting more, and the seeming incorrectness is
removed~




OF FALLACIES.                  291
No one who wants more is rich;
Every miser wants more;
Therefore no miser is rich.
As has been shown in treating of Exponibles, the Exclusive proposition, "'None but Whites are civilized," is
really complex; it contains one direct assertion, respecting
all non- Whites, that they are not civilized, and one implied
assertion, that some Whites are civilized. Then the following syllogism is valid, though each of its three Judgments
appears to be negative.
None but Whites are civilized; = No non-White is civilized;
The Hindoos are not Whites; —  The Hindoos are non-Whites;
The Hindoos are not civilized.
Two ludicrous instances, which have often been repeated
in the books, are enough to illustrate the Fallacy which
arises from a violation of the fifth Rule, though both of
them can be referred also to one of the other classes which
have been already considered.
Nothing is heavier than platinum;
Feathers are heavier than nothing;
Therefore, feathers are heavier than platinum.
This sophism cannot puzzle even a beginner, and is of
the same character in the following.
No cat has two tails;
Every cat has one tail more than no cat,;
Therefore, every cat has three tails.
The Fallacy pluriumr interrogationum, as it was called,
may be brought under this head by being referred to the
ambiguous construction of sentences.  It is a mere trick,
which consists in asking two or more questions as if they
were one; then the respondent is entrapped whether he
answers in the Affirmative or the Negative, as either will
be inappropriate to one or the other of the two interrogatories. Of course, the Fallacy is solved by dividing the




292                 OF FALLACIES.
questions and answering them separately. The standard
illustration is asking a man "whether he has ceased beating
his father."  Lawyers are often guilty of this sophism
while examining a witness in court, by insisting that he
shall give what they call "a categorical answer "; - that
is, that he shall say either Yes or No. But to the question
as they propound it, either Yes or No will be a false
answer. A question often involves a real duplicity under
a seeming unity, as the uncertainty may regard, not the
meaning, but the extension, of the Terms employed; and the
same ambiguity may lurk in a categorical proposition, or in
the answer to an interrogatory.  The distinction between
Contraries and Contradictories, and the relation between
Sub-Contraries, must be kept in view. He who denies
that all are lost, does not thereby deny that some, perhaps
many, even all but one, have perished. Some are not may
mean perhaps all are not, or some certainly are. To assert
or deny a particular motive for an action, is still to leave the
question undecided as to the concurrence of many motives,
and to say nothing about their comparative strength.
Most of our actions proceed from a mixture of motives,
and the agent himself may not be able to say which was
the principal.  Men easily deceive themselves in this
respect, as their memory, their vanity, or even their remorse, may mislead them; and the mistake is especially
frequent when conscientious or religious motives are in
question.
Those who made it their business to invent logical puzzles, and to entrap an opponent in disputation, often secured
their Premises beforehand, by requiring their interlocutor
to answer a series of questions. Socrates was a great master of this eristic art; but though it may fairly and profitably be employed in the communications of a teacher with
his pupils, a free use of it may reduce an opponent to silence
without convincing him. In Plato's Dialogues, Socrates




OF FALLACIES.                 293
often appears in no better light than a satirical disputant
quibbling about the meaning of words. The following
instance of the Fallacy plurium interrogationum, which I
borrow from Fries, would not puzzle any one if it were not
stated in the form of questions and answers.
Is it not true that you must have lost that which you once had,
but which you have no longer? Yes.
Did you not have ten counters when you commenced the game?
Yes.
Have you ten counters now? No.
Then you have lost ten counters.
But he still had eight, having lost only two; to deny
possession of the whole is not necessarily to deny that you
have a part.  But if obliged to answer simply Yes or No,
the respondent could not avail himself of this distinction.
6 & 7. From Dr. Whately's convenient collection of
"examples for the exercise of learners," to which I have
been indebted for several of the preceding illustrations, I
borrow the following instances of violation of the Canons
of hypothetical reasoning.
If penal laws against Papists were enforced, they would be aggrieved;
But they are not enforced;
Therefore, the Papists are not aggrieved.
Though this argument was often gravely repeated in
Parliament, and elsewhere, during the debates on Catholic
Emancipation, it is, of course, entirely invalid by the rules
of Logic; for from denying the Antecedent in a Hypothetical Judgment, no Conclusion follows, since the Consequent may still be true from some other reason than the
one here specified.  In this case, though the penal laws
were not enforced, the Catholics had a right to feel aggrieved that these laws should be permitted to remain in
the statute-book, as this was an insult to them personally,
and to their faith.




294                  OF FALLACIES.
We ought to give one day in seven to religious duties, if the
Fotlrth Commandment is obligatory on us;
But we are bound to set apart one day in seven for religion;
Therefore, the Fourth Commandment is obligatory on us.
The Canon here violated is, that from affirming the
Consequent no Conclusion can be drawn, since the Consequent may have resulted from some other reason than that
specified in the Antecedent. A little attempt is here made
to cloak the Fallacy, by inverting the natural position of
the Antecedent and the Consequent in the Major Premise.
We pass now to a consideration of those fallacious reasonings which are correct in Form, since the Conclusion is
logically drawn, but are faulty in Matter, either from some
error or undue assumption in the Premises, or some mistake as to the point to which the argumentation ought to
be directed. An exhaustive classification of Material Fallacies is not to be expected, as they are numerous and
varied in form, and derive their characteristics chiefly from
the particular Matter of the special sciences which first
suggested them. The only proper classes of them which
have been separately considered by logicians are those
which, ever since Aristotle's time, have been technically
designated as the petitio principii, the ignoratio elenchi, and
the non-causa pro causa; to which may be added several
miscellaneous sophisms of so puzzling a character that the
old logicians called them the Inexplicables.
1. The vulgar equivalent for petitio prineipii is begging
the question; and the common explanation of it is, that it
consists in assuming, in the course of the argument, the
-very point which ought to be proved.  Its most deceptive
application is what is called reasoning in ctairele, in which
Premises are first assumed, and subsequently proved by
means of the very Conclusions which they had been used
to establish.' This error is more difficult of detection in
proportion as the circle is more extended, or as more Syl



OF FALLACIES.                 295
logisms are employed before the reasoner comes round to
the very point that he started from. As Krug remarks,
"4 to the Circle there are properly required two probations,
which are so reciprocally related that the Antecedent in
the one is proved by its own Consequent in the other.
The proposition A  is true because the proposition B is
true; and the proposition B is true because the proposition
A is true. A Circle so palpable as this would, indeed, be
committed by no one. The vice is usually concealed by
the interpolation of intermediate propositions, or by a
change in the expression." "s Thus," says Hamilton, " Plato, in his Phcedo, demonstrates the immortality of the soul
from its simplicity; and, in the Republic, he demonstrates
its simplicity from  its immortality."   Theologians, also,
sometimes fall into this error, by first proving the authority
of the Church from the testimony of the Scriptures, and
then seeking to establish the authenticity of the Scriptures
by the testimony of the Church; and the Fallacy escapes
notice, because one branch of it is found, perhaps, in a
polemic tract on Church government, and the other half in
a treatise on the Evidences.
Strictly speaking, all valid reasoning proceeds ex concessis. Two Premises must be assumed, or taken for
granted; and these two, taken in conjunction, necessarily
involve the Conclusion.  Thus much must be conceded to
those who claim that every Syllogism presupposes the truth
of what it is brought forward to establish. But then it is
presumed that there is no undue assumption; — that the
two Premises, which we now posit, either have been already proved, or that they are universally admitted truths,
or that they have just been conceded, pro hac vice, by the
opponent. As Mr. Mansel remarks, " the petitio principii is
a material, not a formal Fallacy, and consists in assuming,
in demonstration, a non-axiomatic principle as axiomatic,
or in dialectic disputation, a non-probable principle as prob



296                 OF FALLACIES.
able."  It consists not in mere assumption, tthen, for that
is necessary, but in undue assumption. That branch of it
which is called reasoning in a circle is, from the nature of
the case, not a vice which can be committed in a single
Syllogism, but only in a series of Syllogisms constituting a
chain of proof. That which vitiates a single Syllogism is
reasoning from Premises, one, if not both, of which either
is in more need of proof than the very proposition which
we seek to prove by it, or it is that proposition itself
only veiled in other words, or it assumes two Terms to
be mere equivalents of each other, when they really have
not the same meaning.  We must not reason like the
physician in Moligre, who accounts for opium producing
sleep by saying that it has a soporific virtue. The argument that locomotion is not an attribute of all animals, since
sponges cannot change their place, contains the undue assumption that sponges are animals. Indeed, the Fallacy
in this case becomes obvious when the argument is explicated into a regular Syllogism. And this is usually so in
what is popularly called begging the question; the argument
is stated as an Enthymeme, and the suppressed Premise is
that which contains the undue assumption.
A petitio princriii is involved in every case of reasoning
which depends upon an Imperfect Disjunction, though such
cases might also be properly referred to other kinds of
Fallacy. A Disjunction must be assumed to be perfect, or
the Dilemma which is founded upon it is obviously invalid.
Of this character is the famous sophism of Diodorus Cronus, which professes to demonstrate the impossibility of
motion, and which has probably occasioned more discussion than any other logical puzzle on record. It occupies
a high place among those which were formerly called the
Inexplicables.  Dr. Whately seems tacitly to admit that it
is insoluble; for, though he justly criticises an attempted
explanation of it by Aldrich, he proposes nothing to take
its place. The sophism may be thus stated.




OF FALLACIES.                  297
If motion is possible, a body must move either in the place where
it is, or in a place where it is not.
But a body cannot move in the place where it is; and of course,
it cannot move where it is not.
Therefore, motion is impossible.
It is hazardous to differ from Mr. Mansel upon any logical question; but the solution of this sophism which he has
adopted and improved seems to me unsatisfactory. He
says, "The true solution is, that the disjunctive premise is
false.'The place where a body is,' is contradictory of'the place where a body is not'; as' Englishmen' is contradictory of'not-Englishmen'; but'moving in the place
where it is,' is no more contradictory of'moving in the
place where it is not,' than'I an army composed of Englishmen' is contradictory of'an army composed of not-Englishmen.' As it would be false to say,' Every army must
be composed of Englishmen or not-Englishmen,' to the exclusion of the third possibility of a mixed force, so it is
false to say,' Every body must move in the place where
it is, or in the place where it is not,' to the exclusion of
the third possibility of moving partly in the one and partly
in the other.  This solution is substantially given  by
Hobbes." *
Hobbes even gives a diagram  to prove that a body —
quantulumcunque sit, however small it may be -  " cannot,
all at once, so leave the whole of its former place that a
part of it shall not be in that portion which is common to
the two places, namely, the one which is left and the other
which is reached."  But the difficulty cannot be thus
evaded. A part of a body cannot be in two places at once,
any more than the whole. For suppose that which moves
to be a mathematical point, as in the geometer's conception
of the generation of a line. Such a point, of course, being
indivisible, cannot be'" partly in the one and partly in the
X Mansel's Notes to Aldrich, p. 144.
13*s




298                  OF FALLACIES.
other " place. A whole cannot move unless every point in
it moves also. Every individual must be, as Mr. Mansel
acknowledges, either an Englishman or a not-Englishnian.
Reduce the army to a single soldier, and the difficulty of
moving him, according to this sophism, is still insuperable.
The following solution, I believe, has not before appeared in print. The Major Premise of the sophism is not
true except with a proviso or limitation, which is improperly
suppressed; so that the Fallacy may properly be referred
to the class a dicto secundum quid ad dictum simpliciter.
A  moving body, at any one indivisible moment, must be
either where it is, -or where it is not."  When the proviso
here italicized is expressed, the proposition is true, the
reasoning is sound, and the conclusion is correct. In any
one indivisible moment, motion is impossible; for motion requires time as well as space.  The Axiom of Excluded
Middle, that a thing must be, or not be, in a certain place,
does apply to a body; but it does not apply to a moving
body, and this is what covers up the Fallacy. For in order
to be moving, it must, at the second indivisible instant, be
where it was not at the first instant.  Hence, we do not
violate the Axiom when we deny the Major Premise as
originally stated; for " a moving body " is that which has
been where it now is not. The difference of tense (time)
makes it possible for the same thing to be and not to be.
The law of Excluded Middle itself, as we have seen, is true
only when the qualification at the same time is understood.
A solution which is substantially similar to the one here
given is proposed by Mr. De Morgan.  Movement is
change, and so requires two places; a body is not moved in
a place, but from one place to another.
2. Ignoratio elenchi is what we should now call answering to the wrong point. It is proving something which
does not really controvert your antagonist's position, though
it is assumed to do so. An Elenchus is a Syllogism which




OF FALLACIES.                299
will confute the argument of your opponent; and ignoratio
elenchi is ignorance of what will so confute him, — ignorance of the fact that your Conclusion, even if it were
established, would not contradict his Conclusion. This
error in reasoning is so common, that special precautions
have, in some cases, been adopted in order to obviate it.
Thus, in Law, the only object of what is called special
pleading is, to ascertain the precise point at issue, or to
prevent irrelevancy of evidence and argument by binding
both parties in the suit to address themselves to what is
really the sole point in controversy. A -Demurrer has been
happily explained to be equivalent to the remark, "' Well,
what of that?"  Even granting the facts stated in the
declaration to be true, it may be insisted that these facts
give the plaintiff no ground of action; and hence, that it
was an ignoratio elenchi to state them at all.
As the Port Royal logicians remark, the passions of men
afford the reason why this sophism is so common in controversy.  "We dispute with warmth, and often without
understanding one another. Passion or bad faith leads us
to attribute to our adversary that which is very far from
his meaning, in order to carry on the contest with greater
advantage; or to impute to him consequences which we
imagine may be derived from his doctrine, although he
disavows and denies them. All this may be reduced to
this kind of sophism, which an honest and good man ought
to avoid above all things."
Logicians have distinguished and described certain kinds
of argument which are valid, and may fairly enough be
used, provided that it is clearly seen and admitted that they
have no bearing upon the main question.  The Fallacy
consists in referring such arguments to a wrong Conclusion,
in. urging them as if they established the real point of controversy, whereas they actually tend only to direct censure
or laughter against those who hold the opposite opinion, or




300                 OF FALLACIES.
to some other equally irrelevant object. Let the reasoning
which tends directly to prove the main point at issue be
called the argumentum ad rem. Then the argumentum ad
hominem is- that which convicts your opponent of inconsistency, ignorance, bad faith, or illogical reasoning. Any or
all these charges may be well founded, but they are aside
firom the purpose; for the doctrine which is in dispute may
be well founded, though its supporter is deficient in all the
qualities of a good reasoner.  The argumentum ad verecundiam appeals to our reverence for some high authority,
or some venerable institution, as a means of silencing an
opponent, but not of convincing him that he is mistaken
in opinion.  The argumentum ad populum is a similar
appeal to the passions or prejudices of common people; it
is a fair inference that proper arguments are wanting, when
such appeals are permitted.
To these must be added the argumentum ad ignorantiam,
which is asserting that your own position is correct, unless
your opponent can show some valid reason to the contrary. This mistake is often committed with reference to
alleged occurrences which appear to us strange and improbable, or which we may even believe to be impossible. The
Fallacy consists in denying that the thing is so, merely because we do not know how it is so. But if this reasoning
were correct, we ought to deny that the human will has
any control over a single movement of our animal organism, or even that the grass grows; for, certainly, no one
can tell how a mere volition moves the arm, or how the
green herb in the spring-time absorbs inorganic matter and
assimilates it to itself. But our ignorance of one thing, the
modus operandi, is no disproof of a very different thing, the
opus operaturn.  The king of Siam was illogical in denying
that water could become ice, merely because, within his
experience, a liquid had never become solid. The inconceivable is no sure indication of the impossible. Sir Wil



OF FALLACIES.                301
liam Hamilton even undertakes to show, that all which is
conceivable in thought lies between two extremes, both of
which are inconceivable, but of which, as they are contradictories of each other, one must be true.
But lest this exposition should seem to favor credulity
and superstition, it should be observed, that the paralogism
here exposed is usually met by a counter argument just as
untenable as the one which it is brought forward to confute. Because neither I nor you know how a certain
phenomenon is produced, I am not justified in arbitrarily
assigning it to a certain cause, whether natural or supernatural, and then calling upon. you to accept this explanation for want of a better. This also would be an appeal
to ignorance, - an attempt to found knowledge upon ignorance. To take an instance from the reputed wonders
of animal magnetism;- perhaps I do not know how the
table tips; but you are not therefore to assume that spirits
from the other world are tipping it. It is an ignoratio
elenchi to argue, that your hypothesis must be well founded
because I am not able to invent a better. Your business
is to support your own Conclusion by valid reasoning, not
to rest it merely on my inability to prove the opposite.
This Fallacy pervades all the speculations of those whom
Dr. Whewell calls the uniformitarian school of geologists.
They argue that the geological phenomena now visible,
many of which are of stupendous magnitude, can be accounted for by the ordinary working of physical causes
now in operation, if we only assign a sufficient lapse of time
for the cumulation of their results. It is unnecessary, they
say, to suppose that there was any cataclasm, any violent
disruption of what is the usual course of nature in our own
days, in order to account for the elevation of vast mountain
chains, the sinking of continents, or the dislocation of strata
many miles in thickness; the same causes, which are now
altering the level of a continent at the rate of an inch in a




302                 OF FALLACIES.
century, can have piled up the Andes or the Himalayas, if
you give them time enough. Perhaps so; and yet it may
be questioned which is the more violent supposition, the
sudden and irresistible outbreak of a power whose operations, at least on so grand a scale, have never since been
witnessed, or the undisturbed lapse of those countless millions of ages on which the imaginations of geologists love to
dwell. But this is not the real question. Their ignoratio
elenchi consists in multiplying proofs that slow-working
causes might have effected all these stupendous results,
and then jumping at the Conclusion that these causes
did so produce them. They propound this Dilemma: -
Accept this solution of the problem, or propose a better
one. We may logically decline to do either. An ingenious mechanic, witnessing for the first time the uniform
motion of the hands over the dial-plate of a clock, if challenged to explain, without inspecting the works, how this
equable and long-continued motion could be produced,
might easily invent a combination of springs, wheels, and
pinions, which would be adequate for the purpose; but it
would be extravagant for him to assume that the machinery thus invented by himself was an exact copy of the
works which he had not been allowed to examine. He
could only say, the results in question might be brought
about by my apparatus; but I cannot tell how they are
actually produced. Science does not rest on hypothesis,
and is not content with possible explanations of phenomena.
The well-known rule in controversy, that the burden of
proof rests on him who maintains the affirmative, because
it is difficult, or impossible, to prove a negative, rests on
the considerations here alleged. In order to prove a negative, it must be demonstrated that not one out of many
different contingencies admits the positive. Thus a survey
of the whole field is necessary, and the exclusion of the
opposite hypothesis from every point in it must be made




OF FALLACIES.                 303
certain.  On the other hand, the proof of the positive is
established at a single point; no wide range of search is
requisite. To borrow an illustration, it is easy to demonstrate that the book is in the room; we have only to produce it. But to prove that it is not there, "it must be
made certain, first, that every book in the room has been
found and examined, secondly, that it has been correctly
examined. No one, in fact, can prove more than that he
cannot find the book; whether the book be there or not, is
another question, to be settled by our opinion of the vigilance and competency of the searcher." The geologists
say their opponents cannot find any proof that the ordinary
working of Nature's laws could not, in an indefinite lapse
of years, produce the effects in question. What is that to
the purpose? Our inability to find a needle in a hay-mow
is no proof that the needle is not there.
Indirectly, indeed, many negatives are established by a
single positive; it is thus that an accused person in court
makes a triumphant defence by proving what the lawyers
call an alibi; direct testimony that he was in Manchester,
on the night in question, is an indirect demonstration that
he was not in any part of Birmingham, where the crime
must have been committed. Here, the testimony required
is positive in character, though it tends indirectly to a negative result; hence, it is easily obtained.  Sometimes, indeed, when there are but few possible cases, so that the
field for search is very limited, we may be required to
prove a negative directly. This is the nature of the geometer's demonstration per impossibile, as it is called. Failing to obtain direct proof that the angle A is equal to the
angle B, we remember that only three suppositions are possible; and then, by demonstrating that it cannot be either
greater or'less, we indirectly prove that it must be equal.
In like manner, after it has been proved that the accused
person committed a homicide, it is a presucmption in law




304                  OF FALLACIES.
that the act was done "with malice prepense"'; in other
words, the law puts upon the accused the burden of proof
that he did not do it maliciously. But this seemingly harsh
presumption of law rests, as Mr. De Morgan remarks, upon
the fact, that there are so few alternatives to the supposition of wilful murder; in order to disprove malice, the
accused is only required to make out either mishap, insanity, or heat of blood. He is not put to hunting for a needle
in a hay-mow, under penalty of being hanged if he fails;
but, out of four possible cases, he is obliged to disprove the
single fatal supposition by direct evidence that his case is
some one of the three others.
Most rhetorical artifices may be referred to the class of
the ignoratio elenchi.  Thus, says Dr. Whately, "when
the occasion or object in question is not such as calls for, or
as is likely to excite in those particular readers or hearers,
the emotions required, it is a common rhetorical artifice to
turn their attention to some object which will call forth
these feelings; and when they are too much excited to be
capable of judging calmly, it will not be difficult to turn
their passions, once roused, in the direction required, and
to make them view tile case before them in a very different
light. When the metal is heated, it may easily be moulded
into the desired form. Thus, vehement indignation against
some crime may be directed against a person who has not
been proved guilty of it; and vague declamations against
corruption, oppression, &c., or against the mischiefs of
anarchy, with high-flown panegyrics on liberty, rights of
man, &c., or on social order, justice, the constitution, law,
religion, &c., will gradually lead the hearers to take for
granted, without proof, that the measure proposed will lead
to these evils, or to these advantages; and it will in consequence become the object of groundless abhorrence or
admiration."
Under this class of Fallacies also may be ranked the




OF FALLACIES.                 305
error of adopting an argument which proves either too little
or too much. In one of these cases, however, the error is
by no means so serious as in the other. The reasoning
which proves too little may be good as far as it goes; it
conduces to the end in view, and, taken in conjunction
with another argument also partial in its effect, it may
establish the whole doctrine in question. But the argument which proves too much is invalid throughout; Palsus
in uno, falsus in omnibus, is a sound logical maxim.  If
any portion of the Conclusion is evidently false, the reasoning which led to it, considered in itself alone, must
be essentially and altogether vicious; since from correct
premises, and by valid inference, no error whatever can
possibly be deduced.
When the main purpose is to disprove a particular doctrine, it is not enough to refute one or more arguments
that have been alleged in its support; this is merely confuting your opponent, and not the proposition which he
maintains, and which may be supported by better reasons
than he has been able to adduce. In like manner, to state
objections, though they may be perfectly valid ones, to a
specific plan of action, is insufficient to prove that this plan
ought to be rejected; for it may well be that some action
is unavoidable, and yet that strong objections may be urged
against every mode of action that can be devised. When
the Necessitarian says that the doctrine of the freedom of
the human will is inconceivable, Sir William  Hamilton
justly replies, that the argument proves too little; for it is
at least equally inconceivable that the will should not be
free. Unbelievers, says Dr. Whately, ",may find numerous objections against various parts of Scripture, to some
of which no satisfactory answer can be given; and the
incautious hearer is apt, while his attention is fixed on
these, to forget that there are infinitely more and stronger
objections against the supposition that the Christian religion
Ta




306                   OF FALLACIES.
is of human origin; and tlat, where we cannot answer all
objections, we are bound in reason and in candor to adopt
the hypothesis which labors under the least."
3. A full illustration of the Fallacy, non causa pro causa,
would carry us too far into the domain of the physical
sciences, and therefore would be more in place as a chapter
of Applied Logic. Only the more frequent and obvious
errors of this class can hbe noticed here.  Prominent among
these are the common blunders of reasoning post hoe, ergo
propter hoc; of mistaking physical laws for efficient causes;
and of applying the doctrine of the Necessitarian or Fatalist
as a motive of action, or rather of inaction, in our ordinary
concerns.
An invariable antecedent is a sign, but often it is indisputably not a cause, of the phenomenon which it precedes.
As that which leads the mind to expect a certain event, it
may be regarded as a causa cognoscendi; but this is very
different from the causa essendi, which is the ordinary signification of the word cause.  Cicero states this distinction
very clearly: — Causa autem ea est quce id efficit cujus est
causa.  Non sic causa intelligi debet, ut, quod cuique antecedat, id ei causa sit, sed quod cuique efficienter antecedat.
In this sense, deliberation is certainly not the cause of the
action which follows it, nor is one beat of the pulse the
cause of the subsequent beats.  In fact, two successive
states of the same substance are seldom regarded even by
the vulgar as cause and effect. But since we necessarily
think a cause as immediately preceding its effect, or as
simultaneous with it, the mind is prone, especially in the
case of obscure and anomalous phenomena, of which the
true cause cannot easily be discovered, to consider any antecedent event as such a cause. This is the origin of the
belief in omens, and many other superstitions of the vulgar.
An accidental conjunction in time between some private
or public calamity, and the appearance of a meteor or a




OF FALLACIES.                  307'
comet, or the occurrence of an earth uake, is regarded as
indicating a causal union of the two events. The science
of medicine, at least in that branch of it which is called
therapeutics, is little else than an application of the maxim,
Post hoc, ergo propter hoc.  The wisest physician cannot
tell, in any one case, whether the recovery of the patient
took place because he swallowed the drugs, or in spite of
them, or whether they were powerless in respect either to
good or evil.  A harsh application of this fallacious rule
consists in judging the wisdom of a man's conduct by its
consequences, or the uprightness of his intentions by the
immediate results of his action upon the happiness or
misery of'those around him. A brave and able commander is not always successful in battle, and a conscientious and kind-hearted man may be compelled by a
sense of duty to inflict suffering and death.  Practical
men, as they are called, who profess to be guided only by
experience, and to rely upon facts instead of theories, are
especially liable to this class of errors.  In their. eyes, the
disorders and other evils which follow some long-delayed
reform are attributable to the reform itself, and not to its
undue postponement.
Forming an induction from too small a class of cases,
and disregarding,negative instances, are  the  frequent
source of this confusion between an antecedent phenomenon and an efficient cause. The most common of all the
superstitions of the vulgar, the belief that Friday is an
unlucky day for beginning any new enterprise, may be
traced to this origin. And it should not be forgotten, that
the prognostications of evil thus formed very often bring
about their own fulfilment; fearful and dispirited men
can make little effectual effort to avert danger.  The
belief in the hereditary transmission of diseases of mind
and body, at least in the unreasonable extent to which it
new prevails, is formned in this manner, and tends in this




308                  OF FALLACIES.
way to verify itself. Gout and insanity run in families
where a perpetual apprehension of them exists, and where,
perchance, habits of life are actually transmitted firom
father to son which are likely to induce and foster such
diseases. But even in these cases, a careful enumeration
might satisfy one that, of all who are within the unlucky
circle, at least as many escape the dreaded calamity as
those who suffer from it. Were it otherwise, indeed, the
circle would continue to enlarge itself in successive generations, till few could hope to escape the hereditary taint.
As Dr. Johnson remarks, the one prophetic dream which
comes to pass is remembered and spoken of, while the
ninety and nine which fail of accomplishment are forgotten.
" In minds not habituated to accurate thinking," says
Mr. Mill, "' there is often a confused notion that the general laws are the causes of the partial ones; that the law
of general gravitation, for example, causes the phenomenon
of the fall of bodies to the earth. But to assert this would
be a misuse of the word cause; terrestrial gravity is not
an effect of general gravitation, but a case of it; that is,
one kind of the particular instances in which that general
law obtains." A Law of Nature is only a general fact, or,
rather, a general statement comprehending under it many
similar individual facts. Hence, such a Law does not account for, or explain, the phenomena of Nature; it only
describes them. Thus, it is not a Law of Hydrostatics
which causes water to remain at the same level in the two
arms of a bent tube; but the fact that water stands at this
level is ranked among many other facts, which are comprehended under the general statement called a Law of
Hydrostatics.
The process of Thought by which we pass from a Physical Law to an individual case happening under it is one
of Deduction, and is therefore governed by the dictum de




OF FALLACIES.                  309
omni.  Because all bodies tend to fall towards the common
centre of gravity, therefore this body thus tends to fall.
Hence, the statement of the Law is that which makes us
believe that the individual event will happen; and this, by
a very natural confusion of Thought, is mistaken for the
cause which makes the event happen.  But the relation in
the former case is that between Premises and Conclusion;
in the latter, between Cause and Effect; the former is a
law of Thought, the latter is a law of things; the one is
the causa cognoseendi, the other, the causa essendi.
The Fallacy here exposed is one of much interest, as it
is that which lies at the bottom of every scheme of Materialism, - every attempt to account for the origin of species,
and the general phenomena of the universe, without bringing in any other agency than that of mere Physical Laws,
or what it was once the fashion to call " Second Causes."
Such a theory is not only insufficient, or unsupported by
the requisite evidence; it is founded upon a mere confusion
of Thought, and is illogical and absurd. There is no such
thing as the agency or action of a Law; except as a figure
of speech, we might as well predicate locomotion of an idea,
or speak of bilateral triangles. "; Second Causes " are no
causes at all; they are mere fictions of the intellect, and
exist only in Thought. A cause in the proper sense of the
word, that is, an efficient cause, as original and direct in its
action, must be a First cause; that through which its action is transmitted is not a cause, but a portion of the
effect, - as it does not act, but is acted upon.
The Ignava Ratio, or do-nothing argument, is a fallacious application of the Necessitarian theory. According
to this theory, all occurrences whatever have their environment of circumstances, with which they stand in necessary and fixed relations by an absolute law; and the state
of the universe at any one moment, in all its parts, from
the creation of a world to the stirring of an aspen-leaf, could




310                  OF FALLACIES.
not possibly have been different from what is. Every occurrence has its cause, of which it is the necessary result,
and to which it is necessarily proportioned, even in the
minutest respects. Every event, of course, is surrounded
by other events, and must be considered as being at the
same time both antecedent and consequent, -as necessarily resulting from those which preceded it, and necessarily followed by those which come after it, - and thus
as forming one link in an adamantine chain which extends
from  eternity to eternity. As Mr. Mill himself, an enlightened and consistent advocate of this theory, remarks,
" there is no Thing produced, no event happening, in the
known universe, which is not connected by a uniformity,
or invariable sequence, with some one or more of the
phenomena which preceded it; insomuch that it will happen again as often as these phenomena occur again, and
as no other phenomenon having the character of a counteracting cause shall coexist.  These antecedent phenomena,
again, were connected in a similar manner with some that
preceded them; and so on, until we reach, as the ultimate
step attainable by us, either the properties of some one
primeval cause, or the conjunction of several. The state
of the whole universe at any instant we believe to be the
consequent of its state at the previous instant; insomuch
that one who knew all the agents which exist at the present moment, their collocation in space, and their properties,
- in other words, the laws of their agency, - could predict the whole subsequent history of the universe, at least
unless some new volition of a power capable of controlling
the universe should supervene." *
The confutation of this astounding theory is the business
of the metaphysician or the theologian; we have no concern with it here, except to point out the Fallacy of regarding it as justifying inaction, or as demonstrating the
* Mill's Logic, 3d ed., Vol. I. p. 358.




OF FALLACIES.                  311
hopelessness of any endeavor on our part to control the
course of natural events.  The Ignava -Ratio is thus stated
by Cicero, in the form of an argument against taking any
measures for the restoration of one's health.
If it is fated that you shall recover from the present disease, then
you will recover whether you call in a physician or not.
If it is fated that you shall not recover, then, with or without a physician, you will not recover.
But either the one or the other of these two contradictories is
fated.
Therefore, it will be of no use to call in a doctor.
As Cicero remarks, if this reasoning were correct, our
whole life would be reduced to a state of hopeless inactivity; as it would prove the inutility of any endeavor to
bring about a desirable result, or to avert a threatened
calamity. The Turks, who are fatalists, so understand it,
and reduce it to practice by refusing to take any precautions against a pestilence, or to remove a lighted match
from its dangerous proximity to a powder-magazine.  But
they only show thereby that they are incapable of following out correctly the logical consequences of their own doctrine. Calling in medical aid furnishes a new antecedent,
and thus presents a new case for the determination of Fate.
It may also be fated that I should send for a physician, and,
with his aid, that I should recover; or it may be fated that
he should not be called in, and, as a consequence of this
neglect, and not as a necessary result of the disease alone,
that I should die.  Fate is only a concurrence of causes
and an assemblage of conditions; supply a new cause, take
away one of the necessary conditions, and the result will
be different, though it will still be a fated or necessary
result. Zeno aptly confuted this Fallacy, when he was
whipping a slave, who called out, in excuse for his fault,
that it was fated for him to steal; " And so it is for me to
whip you," was the reply.




312                   OF FALLACIES.
Most of the sophisms once called Inexplicable have been
already resolved in treating of the different classes of Fallacies to which they were respectively referred. It is only
necessary to consider here the famous argument, called the
Achilles, proposed by Zeno the Eleatic, as Mr. Mansel says,
" to support the leading tenet of Parmenides, of the unity
of all things, by showing that the identity of rest and motion is a necessary result from the contrary opinion." It
might more aptly be adduced to prove that extension is not
infinitely divisible, for if it were so, according to this argument, motion would be impossible. The sophism is thus
stated.
The swiftest runner can never overtake the slowest, if
the latter has ever so little the start. Suppose, for instance,
that Achilles runs ten times as fast as a tortoise, and that
the tortoise is one mile in advance at the outset.  While
Achilles is traversing this mile, the tortoise has advanced
y-[oth of a mile farther; before his pursuer has passed over
this ~th, the tortoise has advanced 1 ith, and then, again,.1-th, and so on forever, always being some fraction,
however small, of a mile in advance.
Dr. Whately seems to have been entirely puzzled by
this sophism, as he does not attempt a solution of it, but
merely remarks that it "furnishes a confirmation of the
utility of an acquaintance with the Syllogistic form, in
which form the pretended demonstration cannot possibly
be expressed." But this confession, as Mr. Mansel observes, " is in fact a surrender of the Syllogistic criterion,
as a means of discriminating between sound and unsound
reasoning. On the contrary, nothing is easier than to exhibit the reasoning in a Syllogism, and to show thereby
that the fallacy does not lie in the Form, but the Matter.
Thus, representing the whole space to be traversed by a,
a     a      a'Any space equal to0 + 100 +  1000' &c. is infinite (being the
sum of an infinite series).




OF FALLACIES.                  3813'The space to be passed before Achilles overtakes the tortoise is
equal to this sum.'Therefore, it is infinite.'
"' The whole logical mystery of this famous Fallacy lies
in this, that the major premise is false.  The sum  of an
infinite series may be, and in this case is, finite.  This
premise is equally false, whether space is, or is not, divisible ad infinitum." *
Fries remarks that the sophistry is here covered up by
the mode of stating the problem.  The question rqally
asked is, when will Achilles have passed over the particular
extent of ground which the tortoise, at any one moment, has
already left behind him; and this question, on account of
the infinite divisibility of space and time, may be repeated
ad infinitum. The true question, at what point will Achilles overtake the tortoise, is not allowed to come into view.
The space between the two parties, however small, is, in
thought, though not in reality, infinitely divisible; and the
series of constantly diminishing terms into which it is
mentally broken up, though infinite in number, is finite in
amount, the sum of the series being equal, of course, only
to the small space originally divided. Any finite quantity
may be broken up into an infinite number of terms, if these
terms become infinitely small.  The confusion of thought
consists in mistaking the sum of the terms of such a descending series, composed of infinitesimals, for the sum of
an infinite series the terms of which are not infinitely small.
It is only this latter sum which is necessarily an infinite
quantity.
* Mansel's Notes to Aldrich, pp. 141, 142.
14




314                APPLIED LOGIC.
CHAPTER X.
APPLIED LOGIC.
kPPLIED Logic, as it will be here understood, includes
both what has usually been called the Doctrine of
Method, and what Sir William Hamilton terms Modified
Logic. Its object is the proper regulation of the Thinking
Faculty, not only in forming individual cognitions, but in
the more complex processes required for the construction
and advancement of Science.  Pure Logic, as we have
seen, is concerned only with the Forms of Thought; it
considers these as given, or already formed, and regards
only the necessary and fundamental laws, emanating from
the mind itself, which have concurred in their formation
and which regulate their use. Applied Logic has regard
also to the Matter of Thought, - to the infinitely numerous and diversified objects' of cognition which Nature furnishes us, - and considers by what general processes these
are brought within the grasp of mind, or are made intelligibleg or, what is the same thing, are put under the Forms
of Thought. The laws which govern these processes are
not universal and necessary, as in the former case, but are
contingent and varied, depending, in part, on the diverse
and multiform characteristics of the objects of cognition,
and, in part, on the powers and limitations of the human
mind itself. To avoid the vagueness and perplexity which
result from attempting to grasp too much, Applied Logic
treats directly only of the latter, - that is, of the formation
of Science so far as this depends on the nature of the human




APPLIED LOGIC.                315&
intellect, leaving to the special sciences the duty of adapting their own procedures to the nature of the peculiar
objects of study with which they are immediately concerned.
This division, however, like many others in Science, cannot be always accurately preserved. The processes through
which the mind acts can be exemplified only in their application to -various classes of objects, and as varying somewhat with the nature of those objects. The practical distinction will be, that Applied Logic regards the peculiarities
of what we are thinking about only so far as these illustrate,
and in some measure direct, the processes of thinking.  It
considers primarily how the mind acts, and only secondarily
what it is acting upon.
Science is a body of truths relating to any well-defined
object or class of objects, so arranged as to be easily comprehended and retained, and conveniently used. The merits at which it aims are Completeness, Thoroughness, and
Method. Its objects are the numberless things cwhich Nature furnishes us for study.
What we call Nature is an assemblage of objects and, a
succession of events.  The mind, on account of the limitation of its faculties, and the endless number and variety of
these objects and events, cannot grasp and consider them
all at once. Neither can it undertake to study successively
each individual thing by itself; for a lifetime might be so
spent, before we could obtain even a small fraction of the
knowledge which is requisite for the proper guidance of life.
The first necessity, then, which is imposed upon us by the
constitution of the mind itself, is to break up the infinite
wealth of Nature into groups and classes of things, with
reference to their resemblances and affinities, and thus to
enlarge the grasp of our mental faculties, even at the expense of sacrificing the minuteness of information which
can be acquired only by studying objects in detail. The




316                 APPLIED LOGIC.
first efforts in the pursuit of knowledge, then, must be
directed to the business of Classification.  Perhaps it will
be found in the sequel, that Classification is not only the
beginning, but the culmination and the end, of human
knowledge.
We will first consider the mental processes through which
we gain a knowledge of real Objects, - that is, of Objects
which coexist in space, leaving for subsequent inquiry the
question, how far these processes must be modified in constructing a science of Events which succeed each other in
time.
It has already been remarked, that the beginning of all
knowledge is in single acts of the Perceptive or Acquisitive
Faculty, which operates either through the external senses,
thus constituting External Perception, or through that notice which the mind takes of what is passing within itself,
this being denominated Consciousness, or Internal Perception. In either case, one indivisible act of the Perceptive
Faculty gives us to know only one phenomenon.  A succession of such acts relating to one Object furnishes a number of cognitions of the qualities or attributes of that Object; and these qualities we unite together, and bind up
into one whole, through the conception, which the mind
furnishes, of Substance, or that in which the qualities inhere.
Thus, suppose the Object presented is an apple; the eye
tells me that it is red; the touch, that it is spherical and
moderately hard; the muscular sense, that it has weight;
the taste, that it is subacid, &c.; and these qualities I unite
into one whole by the conception of one substance in which
they all inhere, and call the aggregate thus formed apple.
The reason why just these qualities, and no others, are
united into the whole is, that they all are, or may be,
received at one time, under the same circumstances, and
appear to proceed firom one Object, as they are referred by
me to one definite locality in space.




APPLIED LOGIC.                 317
Take another instance from Internal Perception. I am
conscious, either at once or in succession, of joy or pain, of
a thought, reminiscence, or volition, of a sensation of hunger, coldness, &c.; and these separate Intuitions I put
together into one whole through the Intuition, which enters
into each of them, that they are mine, or that they all belong to the one person which I call myself. Here, the Intuition of Self is the unifying principle, or that through which
the aggregation of many into one is accomplished, just as,
in the former case, it was the conception of Substance.
Manifestly, then, the first step towards the formation of
science is a Synthesis, a putting together of the Matter of
several Intuitions into that one whole which we call an
Individual Object. This Object itself, though called an Individual, as if it were one thing, has in trfth only a virtual
unity; it is really complex, consisting of many parts and
many qualities, which were at first separately perceived;
but having often been perceived together, or in combination, they become so firmly united that the perception of a
few, perhaps of only one, of its parts or qualities immediately calls up the imagination of all the others, that is, of
the whole. Thus, I am said to perceive the apple, when,
in fact, I perceive only its shape and color; but this shape
and color immediately suggest all its other qualities, and
the complex Intuition thus formed, partly perceived and
partly imagined, is what is called, though improperly, a
single perception of one thing. The wholes thus formed
are of all degrees of complexity, either having as many
parts, qualities, and uses as a house or an intricate machine,
or as few as a spot of purple cloud in the sky. They may
be either real or factitious, the conception and belief of
actual existence being one of the parts or elements of the
former, but not of the latter.  Each of these wholes is, or
might be, designated by a Proper Name, belonging to this
one thing and to nothing else.




318                 APPLIED LOGIC.
But as the number of such Objects and Names would be
endless, we seek, as has been said, to bring them within
the grasp of the mind by throwing them into groups and
classes. The first step of the process directed to this end
is the reverse of the former one; we must now begin by
Analysis. The many complex wholes, called Individual
Objects, which we have previously formed by a procedure
so easy and so frequently repeated that we are almost unconscious of it, must now be resolved into their constituent
parts and properties, in order that, by an abstraction of
their dissimilar elements and restricting the attention to
those which are similar, classes may be formed, all the
members of which have some like or equivalent attributes.
The process of Classification, then, is an Analysis immediately followed lT a Synthesis into groups, this Synthesis
being directed by the Comparative or Elaborative Faculty
of the mind, the chief function of which is the perception
of relations, and especially the relations of likeness and
unlikeness. Having formed one set of classes, called the
Infime Species, because they are composed of Individuals
only, we then proceed, in an exactly similar way, to group
these groups into Genera; and so on, erecting a hierarchy
of Concepts, until we at least approximate a Summum
Genus, or that thought which embraces all conceivable
things. The highest generalization usually attempted is
that which arranges all existence, whether actual or potential, under the three heads, Man, the Universe, and God
who is Absolute Being and Absolute Cause.
Evidently, then, the universal procedure of Science is
an Analysis followed by a Synthesis, the result of the
whole being a more or less complete Classification. All
the problems which Science has to solve may be reduced
to these two questions: What Classes ought to be formed?
and, Does this or that Object possess the special attribute or
attributes which entitle it to be ranked under a certain




APPLIED LOGIC.                319
Class?  Isolated cognitions  the knowledge, for instance,
that this particular attribute does, or does not, belong to
this particular thing-are not entitled to be called Science, until they are arranged in some Class, or subsumed
under some comprehensive Law.
There is a confusion in the application of the terms Analysis and Synthesis, which may be best resolved by borrowing a passage from  Sir William  Hamilton.  "6 It is
manifest, in general, from the meaning of the words, that
the term Analysis can only be applied to the separation of
a whole into its parts; and that the term  Synthesis can
only be applied to the collection of parts into a whole. So
far, no ambiguity is possible, - no room is left for abuse.
But there are different kinds of whole and parts; some of
the wholes, like the whole of Comprehension (called also
the _/Metaphysical), and the whole of Extension (called also
the Logical), are in the inverse ratio of each other; so
that what in the one is a part, is necessarily in the other a
whole. It is evident, then, that the counter processes of
Analysis and Synthesis, as applied to these counter wholes
and parts, should fall into one, or correspond; inasmuch as
each in the one quantity should be diametrically opposite to
itself in the bther. Thus, Analysis, as applied to Comprehension, is the reverse process of Analysis as applied to
Extension, but a corresponding process with Synthesis;
and vice versa.  Now, should it happen that the existence
and opposition of the two quantities are not considered, -
that men, viewing the whole of Extension or the whole of
Comprehension, each to the exclusion of the other, must
define Analysis and Synthesis with reference to that single quantity which they exclusively take into account;on this supposition, I say, it is manifest that, if different
philosophers regard different wholes or quantities, we may
have the terms Analysis and Synthesis absolutely used by
different philosophers in a contrary or reverse sense. And




320                 APPLIED LOGIC.
this has actually happened.  The ancients, in general,
looking only to the whole of Extension, use the terms
Analysis and Synthesis simply to denote a division of the
Genus into Species, - of the Species into Individuals; the
moderns, on the other hand, in general, looking only at the
whole of Comprehension, employ these terms to express a
resolution of the Individual into its various attributes."
The words analytic and synthetic, Hamilton further observes, "are, like most of our logical terms, taken from
Geometry "; and the applications of them in this science
are thus admirably illustrated by Dr. Whewell. In discursive processes of reasoning, he remarks, " we obtain our
conclusions, not by looking at our conceptions steadily
in one view, which is intuition, but by passing from one
view to another, like those who run from place to place
(diseursus). Thus, a straight line may be, at the same
time, a side of a triangle and a radius of a circle; and in
the first proposition of Euclid, a line is considered first in
one of these relations, and then in the other, and thus the
sides of a certain triangle are proved to be equal. And by
this'discourse of reason,' as by our older writers it was
termed, we set forth from those axioms which we perceive
by intuition, travel securely over a vast and varied region,
and become possessed of a copious store of mathematical
truths." In such geometrical reasoning, he continues, " we
introduce at every step some new consideration; and it is
by combining all these considerations that we arrive at the
conclusion, that is, the demonstration of the proposition.
Each step tends to the final result, by exhibiting some part
of the figure under a new relation.  To what we have
already proved, is added something more; and hence this
process is called Synthesis, or putting together.  The proof
flows on, receiving at every turn new contributions from
different quarters; like a river fed and augmented by
many tributary streams.  And each of these tributaries




APPLIED LOGIC.                321
flows from some definition or axiom as its fountain, or is
itself formed by the union of smaller rivulets which have
sources of this kind. In descending along its course, the
synthetical proof gathers all these accessions into one common trunk, the proposition finally proved.
" But we may proceed in a different manner. We may
begin from  the formed river, and ascend to its sources.
We may take the proposition of which we require a proof,
and may examine what the supposition of its truth implies.
If this be true, then something else may be seen to be
true; and from this, something else, and so on. We may
often, in this way, discover of what simpler propositions our
theorem or solution is compounded, and may resolve these
in succession, till we come to some proposition which is
obvious. This is geometrical Analysis. Having succeeded
in this analytical process, we may invert it; and may descend again, from the simple and known propositions, to the
proof of a theorem, or the solution of a problem, which was
ootr starting-place." *
We have said that an Individual Object, as thought, is a
Synthesis of parts and attributes. But it is not an arbitrary Synthesis, - not a' putting together of any elements
whatever, such as mere caprice may have induced us to
select. Imaginary Objects, it is true, may be thus built up
at pleasure; mere fancy may construct a centaur, a griffin,
or any other imaginative creation, recognizing it at the moment to be unreal.  But if actual existence is one of the
elements of the combination, that is, if the Object thus
thought is understood to be a real Object, our conception of
it must be a Synthesis of such parts and properties only as
we know it actually possesses. Truth may be defined to
be the conformity of our mental representations to the
things which they are intended to represent; and in Applied Logic, where we are concerned not only with the
* Philosophy of the Inductive Sciences, Vol. I. p. 144.
14~                            o U




322                 APPLIED LOGIC.
Form, but with the Matter, of Thoughlt, truth is the chief
object in view, - the first requisite of Science. The Synthesis in thought is true only when it corresponds to the
combination which exists in nature.
In like manner, the Classification which is to serve the
purposes of Science cannot be arbitrary.  In the construction of Science, the first, and perhaps the most difficult,
question which we have to answer is, What classes ought
to be formed.  " The power of framing classes," says Mr.
iVIill, " is unlimited, as long as there is any (even the
smallest) difference to found a distinction upon. Take
any attribute whatever, and if some things have it and
others have it not, we may ground upon this attribute a
division of all things into two classes; and we actually do
so, the moment we create a name which connotes the
attribute"; - as the class of white things, and that of
things not-white.  "The number of possible classes, therefore, is boundless; and there are as many actual classes
(either of real or imaginary things) as there are general
names, positive and negative together."
The relations and connections of the various attributes
with each other must guide us in selecting those upon
which the Classification is to be founded. The purpose of
the arrangement is, that all the individual objects included
in any one class shall have as many common or similar
elements as possible;-that they shall resemble each other
in numerous and important respects. Now it is found that
certain attributes always carry along with them, or are
constantly found in company with, many other attributes;
-not merely those which are necessarily thus connected
as derivative from them by necessary inference, but many
others, of which we can only say that nature always puts
them  together.  On the other hand, certain attributes
have no such regular companionship, but are found indifferently in connection with entirely different sets of ele



APPLIED. LOGIC.                323
mernts.  Among inorganic bodies, for example, the metallic
property is an instance of the former class; among animals,
the possession of a vertebrated column or backbone. There
is good reason, then, for forming a class of Metals, and a
class of Vertebrates, because we are sure that each of these
classes will have many common properties, besides the single one from which their name is derived. On the contrary, the same color or the same magnitude is not found in
constant companionship with many other qualities, so that
it would be comparatively useless to form a class of white
objects, or a class of animals three feet high. Such classes
would be found to include the most dissimilar and heterogeneous members.
it is evident even from  these few examples, that the
quality selected as a principle of Classification is not usually an obvious or conspicuous trait. The casual observer
would generally think that it was small and insignificant.
Thus, the Botanist, disregarding the size, shape, and color
of trunk, branches, and leaves, founds an important classification of plants upon the minute and rudimentary cotyledons, or seed-coverings. All the Monocotyledons are Endogens, and therefore have in common all the numerous
traits of that great tribe or family; while the Dicotyledons
are all Exogens. On the other hand, the number and
relative position of the stamens and pistils, on which Linnaeus founded -his artificial system, are not found to be
invariably joined with any important features in the organization of the vegetable kingdom. It should be observed,
however, that classifications are framed for different uses;
and the peculiar nature of the purpose in view may justify
an arrangement that would be otherwise indefensible.
Thus, the alphabetical order is the only convenient one for
a dictionary; but only such classifications of words are
properly scientific as are found in Logic and Grammar.
In order to carry on the Classification, and erect a hie



324                 APPLIED LOGIC.
rarchy of Concepts of many ascending steps, it is absolutely
essential that the Infima Species, or class first formed,
should embrace only those individuals which have, at least,
several common attributes.  There must be, at least, as
many of these attributes as will furnish a Specific Difference for each step in the ascending scale.
Passing now from the science of coexistent objects to
that of events which succeed one another in time, we come
upon a totally different principle of connection. In the
former case, it was the Concept of substance; in the present one, it is that of causation.  It belongs to Metaphysics
rather than to Logic to explain the peculiar nature of the
relation of Cause and Effect. Here it is enough to say,
that the connection between thetm is conceived to be absolute or necessary; where the Cause exists, the Effect must
follow, and the presence of the Effect is inconceivable unless the Cause immediately precedes it. But causation, as
well as substance, is incognizable through the perceptions of
sense. In the outward world, at least, we never can perceive the nexus, the bond of union which compels the Effect
to follow. We believe that it exists, and that the connection is a necessary one; but we are compelled to infer its
existence from the invariableness of the sequence in time
between the two events. If heat is applied to wax, the
wax always melts; if poison in sufficient quantity is taken
into the stomach, the man invariably dies. Hence we are
led to believe that the heat causes the melting, and the
poison causes the death; or, in other words, that the subsequent event is the necessary result of some poower or force
in the antecedent, which, though it cannot be perceived by
us, inevitably produces this phenomenon. If heat be a true
Cause, the melting of the wax must follow; but as far as
our experience, and, if human testimony may be believed,
as far as all human experience has gone, the melting always
does follow; therefore, the heat is the Cause. On such




APPLIED LOGIC.                 325
reasoning as this, all our evidence of physical causation -
i. e. of Causation in the material universe - depends. But
it is obvious that the reasoning is illogical and the evidence
is insufficient. Human experience is limited; it extends
only to a certain number of cases,- no matter to how
many, as the number is certainly finite. Any number of
instances of actual measurement would never satisfy the
geometer that the three angles of a triangle must equal two
right angles. It is conceivable - nay, the case has actually happened - that, after one hundred millions of favorable instances occurring in uninterrupted succession, the
hundred-million-and-first instance should be an exception,
or one of an opposite character. Mr. Babbage tells us that
his Calculating Machine may be so adjusted that, when put
in regular motion by the descent of a weight, it will present to the eye successively the series of natural numbers,
1, 2, 3, 4, 5, &c.; that, if we should have patience and time
to watch it long enough, we should find that it would
present this series in one unbroken chain from 1 up to
100,000,000, each term exceeding its antecedent by unity.
Now an induction extending successively to 100,000,000
terms, without a single inconformable instance being discovered, would be regarded by most persons as equivalent
to a demonstration that the law of the series was universal
or absolute.  But in fact, the next number presented,
after 100,000,001, instead of being 100,000,002 would be
100,010,002, and the next term would be 100,030,003.
Human experience, then, as it is limited to a finite number
of cases, can never establish an absolute law, or prove that
a certain result is necessary. As the very idea of Efficient
Causation involves that of the necessary consequence of the
Effect, it follows that the range of human experience in
the material universe does not extend to the discovery of
Causes properly so called.
In all the Physical Sciences, then, causation should be




326                 APPLIED LOGIC.
understood to mean only constant conjunction in time. We
cannot even declare that this conjunction is absolutely
invariable; all that can be said is, that it has been invariable so far as human observation has extended, and we
may firmly believe that no instance will ever be found to
the contrary. But this is not a necessary belief; its contradictory neither violates, any Law of Thought, nor any of
the primitive and ineradicable laws of human belief.  The
assumed invariability of what are called " the laws of nature" rests upon no foundation whatever but uniform experience, and is absolutely certain, therefore, only to the
extent of that experience. That a Law of Nature may hereafter be violated, or be altogether changed, is not merely
conceivable; we say as much as that of any Judgment
which does not contradict one of the Axioms of Pure
Thought. Such a violation or change must be pronounced
to be possible, though not probable. Our only reason, for
instance, for believing that sugar always will be soluble in
water, and that powdered chalk, under the same circumstances, will always be insoluble, is, that, though a vast
number of experiments have been tried, we have not, as
yet, known or heard of one instance to the contrary.
But in the strict meaning of the Word cause, - that is,
efficient cause, -what is called the Law of Causation is
absolute; it is, in the strictest meaning of the term, impossible that any event should take place without a true
Cause. I do not say that the contradictory of this Law
would violate any Axiom of Pure Thought; for as we are
now concerned, not with the Form, but with the Matter,
of Thought, these Axioms are inapplicable. But it may
be said that the Law of Causation is held to be inviolable
by what I have here called " the primitive and ineradicable
laws of human belief." It is, for instance, just as impossible for us to believe that an event should take place without a Cause, as it is to believe that any particular space




APPLIED LOGIC.                327
should be annihilated, or that what I am now conscious of
does not really exist as a mental phenomenon. He who
can believe that space has limits or boundaries beyond
which there is no space, or that he himself does not exist
as a thinking being, may also believe that a physical event
can take place without a Cause; no sane person is capable
of crediting either of these propositions.
The distinction here established would seem to authorize
some change of the phraseology usually employed in Physical Science. What has hitherto been denominated, not
only by physicists, but by people generally, a cause, might
more properly be called a constant conditino., of the phenomenon. What the physical inquirer is really in search of,
when he is inquiring after what he calls the cause of any
event, is a constant antecedent of it, which, being discovered,
will ever afterwards enable him, should not the sequence
of antecedent and consequent be altered, (and of this he
justly entertains no fears whatever,) to predict the recurrence of the phenomenon. To him, the Law of Causation, to adopt Mr. J. S. Mill's language, means only this:
" For every event, there exists some combination of events,
some given concurrence of circumstances, positive and negative, the occurrence of which will always be followed by
that phenomenon." Under this view, the so-called Laws
of Nature might more properly be denominated General
Facts, as the word " law 9 generally implies what is absolute or necessary. But as any sweeping change of scientific phraseology is hardly to be expected, the language
heretofore in use must continue to be employed, though
under protest from those who understand the impropriety
of its application. There may be Laws of Nature which
are absolutely invariable; but it is certain that none such
have been, or ever can be, discovered. Human science is
merely able to establish certain General Facts, which are
indisputably true only to the extent of our experience.




328                  APPLIED LOGIC.
We shall hereafter examine some of the reasons which
have caused a higher degree of certainty and generality
to be attributed to these Facts than they actually deserve.
It is manifest from what has been said, that Science is
made up of two sorts of cognitions, - those in which the
objects are given as contingent phenomena, and those in
which the objects are given as necessary facts or laws.
The former are called empirical, as they are derived from
experience, and are true only to the extent of that experience. Their origin is also said to be a posteriori, because
they are subsequent to experience.  The latter are said to
be a priori in origin, for although first manifested on occasion of experience, they are truly prior to it; for if they
had not previously existed, as native to the mind and inwrought into its very constitution, experience itself would
not have been possible. We have already had examples
of such, in our notions of substance, cause, space, time, &c.
These may be expressed, as here, each by a single term
which is significant of one act of the mind, - an indivisible
Intuition or Thought; or they may be resolved into one
or more Judgments, as statements of necessary laws. Thus,
the cognition of substance may be resolved into this Law,
that every real attribute or quality presupposes some substance in which it inheres.  Cause, as already mentioned,
furnishes the universal and absolute Law of Causation, that
every physical event or change must have a cause. The Intuition of space yields many necessary Judgments, thus:
Every physical object must exist in'space; Space is indestructible, even in Thought, as a whole, or in any of its parts;
Space is boundless; &c. The notion of Time also is resolved into several necessary laws, thus-: Every event must
take place at some determinate point in time; Time necessarily flows on in one continuous lapse; Time is boundless
both before and after, or, as the Schoolmen say, both a
parte ante and a parte post; &c.




APPLIED LOGIC.                329
These necessary Laws must be regarded as mere explications of their respective a priori cognitions; they are
not inferences from such cognitions, but are involved in
them, so that it is impossible to have a full and adequate
conception of the one- that is, to fully understand the
meaning of the term —without the other.  In neither
form, as one conception nor as a judgment, can they be derived from experience; for experience can only tell me of
what is true in certain cases, - namely, those cases which
I or other persons have actually witnessed; while these
Laws are known to be absolutely true for all cases past,
present, and future. All the maxims of experience are
reversible in thought; that is, I can conceive that their
opposites or contraries should be true; —I can conceive,
for instance, that fire should not burn, that water should
not drown, that stones should fall upwards instead of downwards, that "when the brains were out, the man should
not die."  But these necessary cognitions a priori are not
reversible in thought; I cannot conceive that an attribute
should exist without a substance, or that space should be
annihilated, or have limits affixed to it, or that a physical
event should take place without a Cause. Moreover, as
has been said, these cognitions are prerequisites of experience, without which experience itself would not be possible.
As no body can exist without space, no quality without a
substance, I could not have my first experience of either,
- that is, I could not know body to be body, or quality to
be quality, - unless these cognitions were already present
to the mind, although then first drawn out and made distinct to consciousness. As the capacity of being exploded
must be conceived to exist in the gunpowder before the
actual explosion can take place, although this capacity was
latent up to that moment, so the cognition of space must
have been in the mind before we could have a conception
of body, and the cognition of time, before we could have
that of an event, since every event must be in time.




330                 APPLIED LOGIC.
And yet these cognitions are not, like the Axioms which
we formerly considered, mere Laws of thought; for they are
necessarily apprehended as actual and immutable Laws of
real things. It is true, that the attribution of these Laws to
actual phenomena is an act of thought; so is all cognition,
whether of external events and things, or of abstract universal principles. Berkeley and other Idealists, then, who
hold that what we call external realities exist only in
the mind, may consistently maintain that these a priori
cognitions are merely necessities of thinking thus and so.
But the Realist, who believes in the objective validity of
our external perceptions, who holds that things are what
they seem to be, cannot consistently deny the objective
reality of those Forms and Laws without which any external
existence would be impossible,- which are, in fact, necessary conditions of the reality of such existence.  Hence I
cannot but regard Kant's elaborate attempt to reduce these
cognitions to mere Laws of Thought as inconsistent with his
own doctrine. He affirms that we have no knowledge of
external realities, and are, therefore, incompetent to pronounce whether they do, or do not, possess certain attributes; and yet he declares that'" things in themselves "
have a real existence apart from our thoughts. He admits
the distinction between noumena and phenomena, between
things as they are and things as they appear, and asserts
the reality of the former, though they are wholly incognizable to our minds. But if they are absolutely incognizable,
how does he know that they do not exist under the Laws of
space, time, and Cause; and if they are real, how can they
exist except under those Laws which are the conditions of
all reality? To deny the objective validity of these Laws
is to contradict the primitive testimony of consciousness,
and to cut away the foundations of all philosophy, whether
dogmatic, critical, or sceptical, by impeaching the correctness of those principles and arguments by which the sceptic




APPLIED LOGIC.                331
himself attempts to show the reasonableness of his doubts,
I have no better and no other reason for affirming that two
straight lines cannot enclose a space, than for pronouncing
that space itself exists in some other manner than as a
mere law of the perceptive faculty.  The doctrine of the
Idealists is at least intelligible; for I can imagine the annihilation or non-existence of objects in space; but the
non-existence of space itself is literally unthinkable. It is
a mere paradox to assert the reality of the objects, whose
existence is contingent, and deny that of space, which
exists by necessity. And the argument is worse than the
doctrine which it is offered to support; since the only reason alleged for believing space and time to be unreal, is the
impossibility of thinking that they are unreal.
In conformity with what has been said, it might seem
that the doctrine of the formation of Science would properly fall into two great divisions; the one relating to the
acquisition of contingent knowledge by means of experience, and  the other to the attainment of necessary
knowledge by the development and application of those
primitive truths which are revealed to usin the very constitution of our minds. And, in a certain sense, this division exists. Geometry and Arithmetic, as the sciences of
continuous and discrete quantity, are applied most directly,
and in their purest form, to the conceptions of space and
time, in which these two modes of quantity are most
clearly manifested, not being modified or confused by the
presence of other attributes.  The lapse of time cannot be
conceived or expressed except by the idea of number, or
discrete quantity; and the extent of space, in like manner,
is necessarily conceived as continuous quantity. And in
both cases, our conception of pure quantity is most distinct,
because there are so few other attributes of space and time
with which it might become confused.  But these two
sciences are not restricted to the consideration of pure




332                 APPLIED LOGIC.
space and time, and do not exhaust our conceptions of
them.  They relate to space and time only so far as
these are magnitudes, or things to be measured; and they
relate to everything else, so far forth as any other thing is
susceptible of measurement.  Mathematics itself is the
science of relative magnitude. Thus, Algebra, which is
the highest form of mathematical generalization, is the
science of pure magnitude, or quantity in the abstract, and
thus includes both Geometry and Arithmetic, since its
principles and formulas are alike and indiscriminately applicable both to space and time. Thus the expression for
the square of the sum of two quantities, (a + b)2 = a2 +
2ab +- b2, holds true alike for continuous and discrete
quantity, for space and time; since it is equally an expression of the truth, that the square erected upon the sum of
two lines. may always be resolved into two smaller squares
and two rectangles, corresponding to the formula; and also
of that which is only another aspect of the same truth,
viz. that the arithmetical expression for the square of the
sum of two numbers may be resolved in precisely the same
manner.
It does not appear, then, that what are called the demonstrative sciences owe their attribute of logical certainty
to the peculiar nature of the subjects about which they are
conversant. It is not because space and time are at once
necessary conceptions of the intellect and immutable laws
of real things, that the mathematician is able to build up
his vast fabric of pure truths, which are absolutely certain
and are independent of any verification by experience.
The science of pure quantity, which seems to me the only
proper definition of mathematics, is also the science of real
things, but so far only as these are affected by quantity
and thus subject to measurement, and so far only as this
measurement is executed with that ideal precision and
accuracy which are presupposed in every mathematical




APPLIED LOGIC.                333
investigation. The necessary and a priori cognitions of
the human mind do not constitute a department of science
by themselves, but are interwoven with the empirical elements of our knowledge. Their office is not constitutive,
but regulative. They determine the limits of the understanding, prescribe its functions, and regulate its belief.
Whatever is apprehended under the relations.of Quantity,
is subject to the immutable laws of Quantity. Whatever is
known as an event or change, is governed by the necessary
laws of Causality and Time. Attributes or qualities are
apprehended under the law of Substance, which determines
the mode of their existence. It is only by abstraction, or
disjoining in thought what cannot be separated in reality,
that a separate science can be created of necessary cognitions a priori, as in that branch of Metaphysics which is
called Ontology.
Going back to the physicist's conception of Cause, that
is, Invariable Antecedence, we observe that the method of
distinguishing invariable sequences from accidental ones is
by analysis. Every event has many antecedents and a
crowd of concomitant circumstances. We seek to ascertain
which of these are necessary conditions of the phenomenon
by analyzing them; that is, by trying the experiment over
again, leaving out each time one or more of the attendant
circumstances; if the same result still follows, the circumstances thus left out are not the causes which we are in
search of, but were only accidental concomitants, that did
not at all affect the issue. Proceeding in this manner,
step by step, we come at last to some of the original antecedents, which being omitted, the event no longer takes
place. Then, in common parlance, we are said to have
discovered the cause of the phenomenon; strictly speaking, it is only, so far as we know, its invariable antecedent,
or a condition of its existence, - perhaps only a condition
of our knowing that it exists. The whole method is ten



334                 APPLIED LOGIC.
tative, and is evidently exposed to error, as it is only an
application of that fallacious mode of reasoning which has
been exposed as the sophism post hoe, ergo propter hoe.
Hence, the conclusion is not held to be established for the
purposes of science, until the experiment has been tried, or
the observation repeated, under every possible variety of
circumstances. But a large experience, especially if confirmed by some analogy between this phenomenon and
others that are known to follow similar antecedents, may
establish the conclusion beyond all reasonable doubt.
As our knowledge of the phenomena of succession increases, the Concepts which we form of individual objects
and classes of objects become larger and more complex.
Our conception of any corporeal thing must include not
only those obvious qualities, such as shape, color, specific
gravity, texture, &c., which it manifests on nearly all
occasions, but the changes to which these are subject when
it is brought in contact with other substances under different circumstances, and also those changes in other bodies
of which its presence may be a constant antecedent.
"The ideas," says John Locke, "that make up our complex notions of corporeal substances are of these three
sorts. First, the ideas of the primary qualities of things,
which are discovered by our senses, and are in them even
when we perceive them  not; such are the bulk, figure,
number, situation, and motions of the parts of bodies, which
are really in them, whether we take notice of them or no.
Secondly, the sensible secondary qualities, which, depending on these, are nothing but the powers those substances
have to produce several ideas in us by our senses; which
ideas are not in the things themselves, otherwise than as
anything is in its Cause. Thirdly, the aptness we consider
in any substance to give or receive such alterations of
primary qualities as that the substance so, altered should
produce in us different ideas from what it did before; these




APPLIED LOGIC.                335
are called active and passive powers; all which powers, so
far as we have any notice or notion of them, terminate
onfly in sensible simple ideas. For whatever alteration a
loadstone has the power to make in the minute particles of
iron, we should have no notion of any power it had at all
to operate on iron, did not its sensible motion discover it;
and I doubt not but there are a thousand changes, that
bodies we daily handle have a power to cause in one
another, which we never suspect, because they never appear in sensible effects."
"' Powers therefore justly make a great part of our complex ideas of substances. He that will examine his complex idea of gold, will find several of its ideas that make it
up to be only powers; as the power of being melted, but
of not spending itself in the fire, of being dissolved in aqua
regia, are ideas as necessary to make up our complex idea
of gold, as its color and weight; which, if duly considered,
are also nothing but different powers. For to speak truly,
yellowness is not actually in gold, but is a power in gold
to produce that idea in us by our eyes, when placed in a
due light; and the heat which we cannot leave out of our
idea of the sun is no more really in the sun, than'the
white color it introduces into.wax. These are both equally
powers in the sun, operating, by the motion and figure of
its sensible parts, so on a man, as to make him have the
idea of heat, and so on wax, as to make it capable to produce in a man the idea of white." *
A fourth class of the elements that form our Concepts of
individual objects consists of the Relations in which these
objects stand to other things. These, of course, are numberless, and therefore are a great source of the indistinctness
land imperfection of this sort of knowledge. Every object
may be compared with every other object in nature, and
with every Concept which the mind has previously formed;
* Essay on Human Understanding, Book II. Chap. 23, ~~ 9 and 10.




836                 APPLIED LOGIC.
and of the countless Relations thus brought to our notice,
many are essential to an adequate knowledge of the related
object. Most of Aristotle's Categories are an imperfect
attempt to classify these Relations, and place them under
their summa genera.  Some of them, such as those of
Quantity, Place, and Time, are definite and admit of accurate determination; as such, they are the objects of the
Exact Sciences. Others, like those of Quality, Posture,
and Modes of Being, Doing, and Suffering, are wholly
indeterminate, at least in this respect, that their various
sorts and degrees are shaded into each other imperceptibly,
or without any natural lines of demarcation. These, of
course, can be grouped into classes only in some rough
and arbitrary way, the divisions not being marked out by
nature. As our knowledge of them is thus vague and
incomplete, our conclusions or inferences concerning them
must be uncertain, and the Sciences under which they fall
may be said to be occupied with Contingent Matter.
In Applied Logic, the test of the adequacy of a Concept
is its more or less complete enumeration of the essential
qualities of the real thing, or class of things, which it denotes. Any attempt to ascertain and enumerate all of
these empirically, or by successive observations and experiments, is hopeless; a lifetime would not suffice to accumulate more than a small fraction of such knowledge of a
single object.  Thus, its active and passive powers, as
they are termed, or, more properly, the fixed Relations of
antecedence and consequence which subsist between the
changes affecting it and those affecting all other substances,
could be ascertained only by placing it in juxtaposition with
every other thing singly, and with every conceivable combination of other things. Apply heat or water to some one
substance taken separately, and only two or three series of
changes would be observed, such as its greater or less fusi-.
bility, solubility, absorption of heat or fluid, capability of




APPLIED LOGIC.                337
being oxidized, &c. But apply the same agents to it in
combination with one or more other substances, and series
of very different phenomena may be manifested. By reason of the endless number and variety of such possible
observations and experiments, the results of them in a vast
majority of cases being individual truths of no special interest or importance, no one can think of engaging in them by
detail, or with a view of exhausting the round of possible
inquiry and trial; and hence our knowledge must always
fall infinitely short of the truth of things. The most important single facts of this character now known to man
were accidentally discovered; they are the fruits, not of
study and research, but of mere chance. Hence we seldom know the history of such discoveries, or the person
who made them. Centuries after the attractive power of
magnetic iron had been known, some one, we know not
who, happened to observe its polarity, or quality of pointing constantly to the north; and the result was the invention of the mariner's compass. The ancients were familiar
with the obvious qualities of nitre, sulphur, and charcoal;
but some obscure alchemist, some time in the fourteenth
century,.happened to mix them together in the right proportions, and the explosion Which ensued taught the world
the secret of gunpowder.  The art of printing was hit
upon by a similar lucky chance. Yet " these three things,"
says Lord Bacon, "to wit, Printing, Gunpowder, and the
Mariner's Compass, have changed the whole face and state
of things throughout the world; the first in literature, the
second in warfare, the third in navigation; whence have
followed innumerable changes; insomuch that no empire,
no sect, no star, seems to have.exerted greater power and
influence in human affairs than these mechanical discoveries."
But as much the greater number of casual observations
of individual things reveal only unimportant relations and
15                           v




338                 APPLIED LOGIC.
qualities, there is no encouragement to pursue and record
them  methodically, in the hope of hitting at last upon
some one of interest and value.  Yet Lord Bacon, misled
by a few brilliant examples, such as those just cited, seems
to have required, as the first step towards carrying out his
new system of inductive research, a "' Natural and Experimental History, sufficient and good, as the foundation of
all."  This " History"'was to be a complete record of
individual observations and experiments, omitting nothing
on account of its seeming triviality and obviousness, to be
subsequently digested into " Tables and Arrangements of
Instances, in such method and order that the understanding may be able to deal with them." * Upon this vast
store of crude material, towards furnishing which he himself made a respectable beginning in his WTistoria Naturalis
et Experimentalis ad condendam Philosophiam, and his Sylva Sylvarum, or a Natural History, all the subsequent processes of his Inductive Method were to be expended.
"' Since there is so great a number and army of particulars,'.' he observes, " and that army so scattered and dispersed as to distract and confound the understanding, little
is to be hoped for from the skirmishings and slight attacks
and desultory movements of the intellect, unless all the
particulars which pertain to the subject of inquiry shall,
by means of Tables of Discovery, apt, well arranged, and
as it were animate, be drawn up and marshalled; and the
mind be set to work upon the helps duly prepared and
digested which these Tables supply." t
Bacon failed to observe that the minds of all men naturally and inevitably proceed in great part by this method, as
is evinced by the construction of language. As we have
seen, all words properly so called are only the General
Names of the groups and classes into which we marshal
and digest our individual observations; —yet with this
* Novurn Organon, Book II. Aph. x.  I Id. Book I. Aph. cii.




APPLIED LOGIC.                339
improvement uplon the system that Bacon recommends,
that thie Concepts thus framed include only the original
and essential attributes, the others being left out as of no
account, and needlessly burdening the memory by their
vast number.  If experiment or casual observation should
hereafter determine that one of these omitted elements is
really of interest and importance, it will then henceforward
constitute an integral part of the Concept. Every one's
notion of the magnet now includes its attribute of polarity.
Derivative attributes, it has been mentioned, are not
expressly included in the Intension of a Concept, because
they are implied and virtually contained in their primaries.
Thus, the numberless properties of every geometric figure
are reduced, in the Concept which bears the Name of that
figure, to the two or three qualities, constituting its Definition, from which they may all be derived by necessary inference a priori, or without the aid of actual observation and
experiment.  Down to the time of the Baconian reform in
the processes of physical science, it seems to have been
imagined that individual substances or bodies, like geometric figures, had each its one or two essential properties,
which being known, all the others could be immediately
deduced from them by a purely logical process, without
any aid from experience. This, in fact, was the meaning of
the word essence, that internal constitution of a body which
makes it what it is, or from which all its attributes necessarily flow.  Change the essence of the body, then, and you
thereby change all its properties. To the eye of Omniscience, doubtless, there is such an essence; but it must
ever remain unknown to man's finite capacities, on account
of the endless number of unknown attributes with which
it is intermingled.  Those qualities alone appear to us
essential which are known to be constantly associated with
a few others, either because these others can be deduced
from them by necessary inference, or because they have




340                 APPLIED LOGIC.
always been found together in a large experience. In the
latter case, of course, the conclusion is contingent or uncertain, being necessarily true only to the extent of our
previous observation.  In the former case, the conclusion
is absolute, if, by the hypothesis, all other qualities are
excluded from the Concept except those which are certainly known. In geometry, for instance, the Concept or
definition of any solid body includes only its shape and
magnitude, and supposes that these are accurately determined; abstraction is made of all its other qualities, because these are not susceptible of perfect determination,
and we know only from experience how far they associated
with each other.
If the Matter of Thought, then, includes real existences,
or such objects and events as are actually presented to us
in nature, our conclusions respecting them, being derived
only from  experience, must always be subject to doubt.
As we know them only imperfectly, our inferences respecting them can never be logically certain. But if the Concepts are limited to imaginary. objects, consisting only of a
few perfectly determinate qualities, our conclusions respecting them will be absolute, though they will be applicable
only in the realm of pure abstractions. Bacon was right,
then, in maintaining that the Physical Sciences, so far as
they extend to the knowledge of real objects, are dependent
solely upon observation and experiment.  "Man, being
the servant and interpreter of Nature, can do and understand so much only as he has observed, either in fact or in
thought, of the course of Nature; beyond this, he cannot
understand or do anything."
We can now see what are the preliminary classifications
upon the formation of which all Science depends, and can
point out the principles which regulate this formation.
1. We forim classes of real things or Natural Objects,
arranging them according to the similarity of their attri



APPLIED LOGIC.                  341
butes, and selecting by preference, as the basis of the classification, those qualities which are invariably found conjoined with the greatest number of other uniform qualities;
as the presence of one of these constant elements enables
us to infer, in anticipation of experience, that it will be
found in conjunction with those others. The- science of
Natural History, in its various departments, consists exclusively of such classifications, together with such descriptions
and definitions as are subsidiary to them.
2. We classify the  qualities themselves, according to
their similarities, irrespective of the real objects in which
they inhere. Thus, we form classes of colors, sounds,
shape, and dimension, degrees of consistency, specific gravity, &c.  Sometimes a single set of these arrangements is
found important enough to be made the basis of a distinct
science, as in the case of Acoustics and Optics; more frequently, several sets of them  are grouped together for
scientific consideration, as is the case with the chemical
qualities of substances.
3. We classify events according to the uniformity of
their succession in time. These, if regarded as mere sequences of phenomena, may be referred to the subsequent
head of Relations; if regarded as the active or passive
powers of bodies, they may be placed under the preceding
head of Qualities. A constant order of succession is often
erroneously supposed to be a necessary sequence, because
the mind superadds in such cases its pure conception of the
necessary relations of Cause and Effect; and hence sciences
based upon such classifications are improperly termed
sciences of causation.  Several departments of Physics,
such as the sciences of Mechanics and Hydrostatics, and
some divisions of the moral sciences, such as Politics and
Civil History, are made up chiefly of classifications of this
sort.
4. We classify the relations of things, irrespective of the




842                 APPLIED LOGIC.
other Qualities and differences of the things related. Thus,
Geography is, in the main, a classification of the Relations
of the different portions of the earth's surface to each other;
Astronomy takes a similar view of the Relations between
the different members of the solar and stellar systems. A
large portion of the sciences of Law and Politics has regard
to the different Relations which subsist between human
beings, such as those of husband and wife, parent and
child, rulers and subjects, countrymen and aliens, &c.
The mind takes special cognizance only of a very few of
the countless Relations which comparison and reflection
bring to light. We select those only which happen to be
of special interest to us, through the guidance which they
afford for our future conduct, the wonder and curiosity
which they excite, or the bearing which they may have in
any way upon our welfare.
It is not meant that each one of the Classes and Sciences
which we form consists exclusively of one or the other of
the four species here enumerated. Indeed, the division
itself is a very imperfect one, for the Dividing Members,
as we have intimated, do not exclude each other; a Concept of Real Things includes a view of their Qualities, their
active and passive Powers, and their Relations; and the
two latter may be comprised under the name of Qualities.
But these four, sometimes separately and sometimes in
combination, are the elements which we group together
into classes, out of which those higher classes, or hierarchies of Concepts, which we call Sciences, are subsequently
erected. In every case, the classifying principle is similarity, or uniformity of succession, those Objects and Qualities being united which resemble each other in certain
respects, and those events being reduced to the same head
which uniformly follow one another under similar circumstances.  The education of every human being consists in
the gradual acquisition of a large stock of these elementary




APPLIED LOGIC.                 343
Concepts, which are taught to him in learning the use of
his mother-tongue, while exercising at the same. time his
powers of observation and reflection.
The advancement of Science depends on the success of
the attempts which man is constantly making to enlarge
and improve the classifications which are the bases of these
Concepts.  By detecting hitherto unobserved similarities
and conjunctions in time, we extend the generalizations
and reduce the number of classes, thereby bringing. the
infinitude of objects and events which nature offers us
more nearly within the grasp of the human intellect.
Sometimes the principle itself, or the Ground of Division,
which determines the classification of a whole set of phenomena, is altered; as we find a greater number of the
attributes of these phenomena to be in constant companionship with some one or more traits hitherto disregarded as
of little account, a differently constituted hierarchy of Concepts, founded upon these traits, is adopted. This may be
called an improvement in the Method, rather than air
actual enlargement of the domain, of Science.  Thus the
Natural System was substituted for the Linnman classification of plants, and an improvement almost equally extensive was made by Cuvier in the arrangement of the animal kingdom.  But most of the questions and problems
which Science encounters in its progress relate to successive improvements and extensions of the classification
which, in all its main features, was long since formed, and
not to the substitution of an entirely different one in its
place.  The fixedness of language, which stereotypes, as it
were, the names and phraseology appropriated to the old
division, is a great obstacle to the introduction of a new
one, which would require a new set of words.  The principal object of the researches of Science is to determine
whether this or that object, or class of objects, has the
special characteristics which entitle it to be placed in a




844                 APPLIED LOGIC.
certain class, and therefore to be called by the name of
that class. For instance: - Is the lightning to be placed
in the class of electrical phenomena? Can the revolution
of the planets be reduced to the phenomena of falling
bodies?  Is light the undulatory movement of an ether?
Are the processes of digestion and assimilation reducible
to the ordinary action of chemical affinities?  Ought the
relation of a motive to a volition to be classed with the
relations of cause and effect, or with those of mere antecedence and consequence?
Such questions relate, for tile most part, not to some one
object or event, but to whole classes of phenomena, and
therefore presuppose a classification already formed. Sometimes, indeed, one particular phenomenon of an anomalous
character may now be observed for the first time; and
then the purpose of the inquiry is, to refer it to its proper
class, and call it by its right name. But such inquiries belong usually to the education of a child, who has not yet
acquired the amount of knowledge long since possessed by
his elders, and embodied by them in language through the
appropriation of names to the different Concepts.  But
Science advances almost exclusively by the resolution of
problems which concern whole classes of objects, and a
single phenomenon is observed and experimented upon
only as a typical specimen of its class, and therefore, as
leading to conclusions which affect all that are called by
the same name.  Thus, Franklin experimented with his
kite upon a particular thunder-cloud, but only because this
one represented to his mind the whole class of meteorological phenomena whose characteristics he was investigating. This, indeed, is the difference between the intellect of a common man and that of a philosopher.  The
latter flies at once to generalities; the former wonders at
the individual case, and seldom goes beyond it.
6" From the moment an isolated fact is discovered," says




APPLIED LOGIC.                345
Hamilton, c" we endeavor to refer it to other facts which it
resembles. Until this be accomplished, we do not view it
as understood. This is the case, for example, with sulphur,
which, in a certain degree of temperature, melts like other
bodies; but at a higher degree of heat, instead of evaporating, again consolidates."   Another example may be
taken from the General Fact, which some will call a Law
of Nature, that all bodies give out heat on passing from a
gaseous to a liquid, or from a liquid to a solid, state; in
other words, that contraction of bulk is attended or occasioned by loss of heat, and expansion of bulk by addition
or absorption of heat. Yet clay is known to contract from
the application of heat; and though water contracts in bulk
when it is cooling down to as low a temperature as 40~, yet
as it falls below that point it expands again, and in the
act of congelation there is a sudden and considerable increase of bulk. Our natural love of unity, or disposition
to reduce corresponding phenomena to one class or Law,
does not allow us to rest in the consideration that such
cases are anomalous, or isolated exceptions. We seek
either for a new expression of the Law, which shall cover
also these apparent exceptions, or for the discovery of
some attribute of these now isolated cases which shall
harmonize them with the Law as already expressed.'When
the facts are thus generalized, or brought together under
one Concept and name, " our discontent is quieted," Hamilton continues, " and we consider the generality itself as
tantamount to an explanation. Why does this apple fall
to the ground? Because all bodies gravitate towards each
other. Arrived at this General Fact, we inquire no more,
although ignorant now, as previously, of the cause of gi-avitation; for gravitation is nothing more than a name for a
General Fact, the why of which we know not. A mystery,
if recognized as universal, would no longer appear mysterious."
15*




346                 APPLIED LOGIC.
We now see how it is that the successive discoveries,
and consequent enlarged and improved generalizations, of
Science are embodied, as fast as they are made, in language, so that we learn them through the simple mode of
gradually acquiring the use of our mother tongue. This is
done to some extent by the actual introduction of new
words and names, these being necessary to designate the
new groups and Concepts which the improved classification
requires. But it is effected still more largely by modifying
and enlarging the connotation of worids already in use.
For a time, these new elements of phraseology are in current use only among a small circle of scientific inquirers,
whose labors have made them necessary. But gradually
they creep out into the ordinary dialect of the market, the
parlor, and the newspaper, and are naturalized there, and
taught to children as fast as children learn to speak. How
much more knowledge is now necessarily acquired in learning the use of the English language, than was gained from
such learning only one or two centuries ago!
The same considerations of interest and convenience, of
immediate relation to the curiosity or the physical wants
of men, which determine us to classify and name some
of our individual observations and experiences, to the exclusion of many others, also guide us in the selection of
those groups of Concepts which we enlarge, develop, and
methodize into distinct Sciences. As many objects and
events do not need to be classified because they are not
worth remembrance, so the classification of many others
needs not to be extended beyond the first and most elementary stage, because a Science elaborated out of them
would neither interest us nor minister to our necessities.
We do not chronicle petty occurrences, we do not study
out and subsequently generalize the insignificant relations
of unimportant objects to each other. But as circumstances change and knowledge is enlarged, what formerly




APPLIED LOGIC.               347
seemed trivial often assumes a new dignity and interest,
or is unexpectedly found to be subservient to some great
purpose. A new Science, or department of Science, is thus
formed, perhaps to be carried up by subsequent discoveries
and generalizations highler than any of those formerly cultivated. How many new departments of study and research have thus been opened within the last few generations! The Sciences of Geology, Ethnology, Comparative
Philology, and Political Economy are hardly more than a
century old. The moderns know more than the ancients,
not so much because they know the same things more perfectly, as because their investigations are extended over a
larger range of objects.
Hence it is easy to see why the numerous attempts that
have been made to classify the Sciences, and thereby to
reduce them  into one complete and orderly system  of
human knowledge, have not been more successful. The
Sciences have not been formed on any predetermined and
systematic plan, with a view of covering the whole ground
of inquiry; but they have grown by a natural and irregular
development, corresponding both to the ever increasing
wants and stimulated curiosity of those who prosecute
them, to the different aptitudes of the various classes of
objects to be digested into system and divided by obvious
lines of demarcation, and especially to ithe facility with
which our conclusions respecting these objects may be
drawn without the aid of observation and experience.
Such a survey of all that is possible to be known, compared with all that is actually known, as Bacon attempted
to make in his treatise on the "' Advancement of the Sciences," must always disclose, as it did to him, many lacunce,
or gaps which it is necessary to fill, before man can be said
even to have entered upon all the avenues which lead to
truth.  Divisions of the Sciences, like those which have
been devised by Bacon, Locke, Ampere, Comte, Wilson,




348                 APPLIED LOGIC.
and  themrs, must always be imperfect, or, if they approxi -
mate completeness, must always indicate at least as many
blanks as there are departments already occupied. Whether
we try to distribute the various branches of knowledge, as
Bacon did, according to the different faculties of the mind
which they respectively call into play; or, with Locke,
according to the several ends in view; or, with Descartes,
as followed by Comte, according to the order of their development, as determined by their degrees of simplicity;some Sciences will appear redundant, others as defective,
and many as having an equally good title to be ranked
under two or three different heads.
As one of the best specimens of these attempts at
classification, we may take Dr. Thomson's account of the
arrangement proposed by Comte, on the basis of Descartes's
aphorism, that knowledge should advance from the simpler
to the more complex phenomena.
" Mathematics, or the science of quantities, is at once the
most simple in its elements and the most general in its application, entering, more or less, into all the sciences of Nature, and constituting almost the whole of that which comes
next it in the order of dependence. Astronomy, or the
science of the heavenly bodies, is the application of mathematical truths to the laws of matter and motion; matter
and the motions of material bodies being the new conceptions which belong to this science. Physics, being the
science, or rather group of sciences, which is conversant
with the general laws of the world, so far as they relate to
beings without life or organization, would come next; and
it imports, in addition to the conceptions of Astronomy,
those of light, of heat, of sound, of electricity, of magnetism,
and many others. Chemistry would rank next, which is
the science of the decomposition and combinations of the
various substances that compose and surround the earth.
Next in order of complexity would rank Physiology, founded




APPLIED LOGIC.                349
on the additional conception of vegetable,and animal life.
To this would succeed Anthropology, or the science of
man's nature; and to this, Social Science, which ascertains
the laws that govern men when combined in cities and nations. Each of these departments may be divided into
many branches; as Physics into Acoustics, Optics, Electricity, and the like; or Social Science into Morals, Politics, Political Economy, Law, and the like.
"On comparing scientific works, differences in the mode
of teaching the same subject become apparent. In one,
the pure theory of Astronomy is presented; in another, the
striking features of its historical progress as a science, with
speculations on the historical sequence of the phenomena
themselves; in a third, the practical applications of which
the Science admits in respect to the comfort and progress of
mankind. This threefold mode of treatment runs through
all the Sciences, and in a table of them might well be expressed. The classification would thus embody all that is
valuable of another system of classes, that according to the
purpose towards which the Science was directed.
" A classification which advances on Descartes's principle,
from the more simple to the more complex subjects, which
commences from the notions of extension and quantity,
and proceeds through material things up to living, intelligent, and moral agents, ought to coincide with the order
in which the sciences themselves have reached maturity.
And this it certainly does. Mathematics had made good
its ground when Astronomy was yet in its infancy; Physics
began to obtain a sure footing later than either; whilst the
Sciences which relate to Life are still very immature; and
some of the main problems of Social Science are yet matter of controversy even in our own days."
It is an obvious imperfection of this scheme, that it takes
no notice of the numerous branches of that Science, Natural History, which, as it depends solely upon observation,




350                 APPLIED LOGIC.
and thus gives us our first knowledge of all the objects of
study, would seem to constitute the basis of all the other
Sciences. In explanation of this defect, Comte remarks,
"we must distinguish between the two classes of Natural
Science; — the abstract or general, which have for their
object the discovery of the Laws which regulate phenomena
in all conceivable cases; and the concrete, particular, or
descriptive, which are sometimes called Natural Sciences
in a restricted sense, whose function it is to apply these
Laws to the actual history of existing beings. The first
are fundamental; and our business is with them alone, as
the second are derived, and, however important, not rising
into the rank of our subjects of contemplation. We shall
treat of Physiology, but not of Botany and Zoology, which
are derived from it. We shall treat of Chemistry, but not
of Mineralogy, which is secondary to it." But this remark
is inconsistent with the previous assertion, that this order
of classification " coincides with the order in which the
Sciences themselves have reached maturity."  In the order
of time, certainly, Zoology and Botany had been cultivated
to a considerable extent before men had obtained more
than the crudest notions of the physiological processes of
animal and vegetable life; just as Civil History, the basis
of another department, had been very filly treated before it
first suggested the idea of Social Science. In what may
be called the logical order, or the order of ideas, however,
it is true that the Sciences which embody principles and
general results talie precedence of those which afford only
the material of knowledge.




DEMONSTRATIVE REASONING.           351
CHAPTER XI.
DEMONSTRATIVE REASONING AND DEDUCTIVE EVIDENCE.
W-~V E have already said, that the principal object of the
researches of Science is, to determine whether this
or that object, or class of objects, has the special characteristics which entitle it to be placed in a certain class, and
called by a certain name.
Most of such questions, if they relate only to one thing,
or to a very few things, are answered directly, and without difficulty, by observation or intuition. We answer one
of them, in fact, whenever we perceive any object and call
it by its appropriate Common Name. For instance; — this
thing which I now hold in my hand I call a pen, a rose, or
an apple, because I perceive that it has the attributes which
are the Marks connoted by that name. In like manner, I
pronounce the animals now before me to be dogs, horses, or
cows, according as I recognize their distinctive qualities.
Writers like Dr. Brown, Mr. J. S. Mill, and Mr. Bailey,
who have laboriously attempted to restrict the range and
depreciate the utility of the Syllogistic process, have seemingly failed to notice the fact, that we must reason syllogistically whenever we use language with any perception of
its meaning, - that is, when we call anything by its appropriate name. If I had not already spread out before my
mind the Marks which constitute the Intension of the
Concept apple, or rose, I could not designate the object
now presented to me by that appellation. This process of
reasoning, which we are performing almost every moment




252           DEMONSTRATIVE REASONING
of our lives, and therefore so quickly and easily that its
several steps are taken almost unconsciously, is thus spread
out into the formal process.
The Concept or Class-notion apple has, as Marks, a
nearly spherical shape, a red color, a moderate hardness,
and a certain smell;
This object has all these Marks;
Therefore, this object is an apple.
This is what Hamilton calls Reasoning in Intension, for,
in each of the Premises, the Predicate is contained in the
Subject. Moreover, the Reasoning is not only logical, -
i. e. valid in Form, but it is also Demonstrative, -i. e. absolutely certain in respect to its Matter. It is Demonstrative,
because the Major Term, which is here the Subject of the
Major Premise, is a Concept or Class-notion, which, being
a-mere creation of the mind, cannot have any other Marlks
or qualities than those which we voluntarily attribute to it.
As we know by Intuition, that the object has all the Marks
which we included in the Concept, it is certain that it
should be designated by the name of that Concept, - that
is, that it should be included under its Extension.
On the other hand, if the Reasoning is made to concern,
not a mere Concept in the mind, but a class of real things,
which, as we have seen, always have an unknown and unknowable number of qualities and relations, then I cannot
be sure that the object in question possesses all these qualities, but can only doubtfully infer that it has all, because I
know that it possesses some, of the more important of them.
An element of uncertainty is introduced; the Reasoning
ceases to be Demonstrative, and becomes merely Probable
or contingent. For instance; -if, in the Major Premise
of the preceding Syllogism, we say, not " the Concept or
Class-notion apple," but "All apples" - i. e. All the
actual objects which we have been accustomed to call apples-" have a nearly spherical shape, a red color, a mod



AND DEDUCTIVE EVIDENCE.            353
erate hardness, and a certain smell "; then, though ", this
object has all these Marks," I cannot be sure that " it is an
apple."  It may be only a wax counterfeit, and the deception would instantly be detected by the taste, which quality
was not included in the enumeration. The Reasoning is
still valid in Form, but the Major Premise is false; it covers up the Fallacy fitcte universalitatis. In order to be
sure that an object is properly ranked under a given class,
we must be certain that it contains all the original and
essential qualities of the objects denoted by the class-name;
and this certainty, in the case of real things, is unattainable. In our conception, we may arbitrarily restrict the
meaning of the word apple, so as to exclude the quality of
taste; and in this sense, the wax counterfeit is properly
called an apple.  But in speaking to others, the word
would be understood to signify all the qualities possessed
by the real things, viz. this sort of fruit; and in this meaning, the wax substitute is not an apple.
We can now see why tile Reasonings of the mathematician are Demonstrative, while those of the zoologist, the
botanist, and other naturalists who deal only with real
things, are merely Probable or contingent. The Form is
always the same; Reasoning, as such, must always be
Syllogistic; and when the rules of Pure Logic are duly
observed, the Consequence, or the mere deduction of the
Conclusion from the Premises, must be absolutely certain. The difference, then, concerns the Premises only,
the truth of which, as we have seen, is not guaranteed by
the principles of Logic. The universal rule, that the Middle Term  must always be distributed, requires that the
predesignation all, or none, should appear in at least one
of the Premises. Now, our knowledge of real things is
derived solely from experience; and experience, as has
been mentioned, must be restricted, from its very nature,
to a limited number of examples. In respect to real obo
w




354            DEMONSTRATIVE REASONING
jects and events, it can never extend either to the inclusion or the exclusion of all; it can never pronounce with
certainty either upon all, or none. Only with reference to
a certain class arbitrarily formed by the Understanding,
to the very things which I am now thinking of, or which
I have actually observed, and to none others, — to the
things which are included under this Definition, and to
these only, — can the finite understanding of man, so far
as it is enlightened only by experience, safely pronounce
upon all or none. Without such limitations, naturalists,
and all others who seek to educe Science from mere experience, can never speak of all or none, without falling into
the Fallacy fictce universalitatis.
The mathematician deals only with certain Concepts of
Quantity, whether continuous or discrete, which are precisely limited and determined by the Definitions that he
employs.  The propositions which he establishes do not
concern circular objects and triangular objects, which are
real things, but circles and triangles, which are imaginary
things as conceived by the Understanding, and which are
restricted by their Definitions to the possession of those
qualities only which Thought voluntarily attributes to
them. Hence, the conclusions which the mathematician
forms respecting them are not liable to be vitiated by the
intrusion of any unexpected and counteracting elements.
Any theorem, therefore, which is proved of one, must hold
good of all; any property which cannot belong to one, can
be possessed by none, of the class thus defined.  The same
measure of certainty which the student of nature obtains
by Intuition respecting a single real object, the mathematician acquires respecting a whole class of imaginary
objects, because the latter has the assurance, which the former can never attain, that the single object, which he is
contemplating in Thought, is a perfect representative of its
whole class; he has this assurance, because the whole class




AND DEDUCTIVE EVIDENCE.            355
exists only in Thought, and are therefore all actually before
him, or present to consciousness. For example; this bit
of iron, I find by direct observation, melts at a certain
temperature; but it may well happen that another piece
of iron, quite similar to it in external appearance, may be
fusible only at a much higher temperature, owing to the
unsuspected presence with it of a little more, or a little less,
carbon in composition. But if the angles at the basis of
this triangle are equal to each other, I know that a corresponding equality must exist in the case of every other
figure which conforms to the Definition of an isosceles
triangle; for that Definition excludes every disturbing element. The conclusion in this latter case, then, is Universal, while in the former, it can be only Singular or Particular.
Conclusions which are demonstratively certain and absolutely universal can be obtained only when we are reasoning about abstract conceptions.  In the case of natural
objects and events, which can be known only through experience, we approximate universality and certainty in reasoning only by the aid of Induction and Analogy.  The
lack of certainty is a consequence of the lack of universality. No doubt affects the few instances which I am
now actually observing, or which are present to sense or
consciousness. Of these, I am as certain as of any conclusions in arithmetic or geometry.  The doubt comes in only
when I attempt to extend the conclusion from some, which
I have examined, to all others, of which I know nothing,
except from testimony, Induction, or Analogy. And this
doubt is inevitable; no matter how many cases have been
examined, experience can never extend to all. The fact
that all matter gravitates, or has weight, is a truth which
rests upon as large a testimony from experience as has ever
been collected. Yet the chemist will readily admit that it
is not only conceivable, but we may almost say probable,




356            DEMONSTRATIVE REASONING
that some of the imponderable agents, as they are called, —
heat, light, electricity, &c., - may at last be found to be
material; and the astronomer has not yet proved entirely
to his satisfaction, that the law of gravitation is universal
throughout the stellar system.  From the nature of the case,
he would say, the fact does not admit of absolute proof.
It appears, then, that the range of Deductive reasoning
and Demonstrative proof is not confined to pure Mathematics. Whenever the objects about which we reason are
pure Concepts, or mere creations of the intellect, strictly
limited by Definition, and thus guarded against reference
to things actually existent in Nature, our conclusions respecting them, if obtained in strict uniformity with logical
rules, are as absolute as the truths of the multiplicationtable.  But Mathematics, it must be admitted, afford vastly
the larger number.of conclusions of this class; in no other
science is Demonstrative reasoning either carried so far, or
so fruitful in results.  This peculiarity seems to be due
to the nature of those Concepts, quantity, space, and number, with which the mathematician deals.  Two of these,
quantity and number, are universal attributes, as they belong
to all things, both to objects of sense and consciousness; and
the third, space or extension, is an attribute of all external
things. They are suggested to us on a greater variety of
occasions than any other qualities, and thus are more frequent objects of contemplation, and more filly determined.
"Propositions concerning numbers," as Mr. Mill observes,
"have this remarkable peculiarity, that they are propositions concerning all things whatever, - all objects, all existences of every kind, known to our experience.  All
things possess quantity; consist of parts which can be numbered; and, in that character, possess all the properties
which are called properties of numbers."
Again, the various modes, properties, and relations of
quantity, space, and number admit of being more accurately




AND DEDUCTIVE EVIDENCE.            357
defined and clearly determined than those of any other
class of ideas; they are separable from each other by lines
of demarcation that cannot be overlooked or mistaken.
Differences of degree, with which we are chiefly concerned
in the case of all other qualities, are not by any means so
definite, as they are shaded into each other by imperceptible gradations; their minute differences are inappreciable
either by the senses or by the understanding.  But the
difference between two quantities, whether of number or
extension, may be reduced as low as we please, and still
remain as distinct to our apprehension as if it were worldwide.
But the chief peculiarity of these three Concepts, which
causes them to afford so broad and fruitful a field for Demonstrative reasoning, is the measureless variety of accurately determinable relations in which all their modes stand
to each other. Any one quantity stands in a perfectly conceivable ratio- whether it can be exactly expressed in
numbers or not - to every other quantity, and also has a
countless number of peculiar relations in which it stands to
many at once. Attempt to enumerate, for instance, the
properties of the number 9; —that it is the square of 3,
the square-root of 81, the double of 41, the half of 18,
&c.,- and we soon abandon the undertaking in despair.
And when we come to think of the relations of these relations, as in the doctrine of proportions, it becomes evident
that the properties of quantity are too great to be numbered. The field of investigation is infinite.
These innumerable and perfectly definite relations, which
subsist between distinct quantities, furnish an inexhaustible
number of Midcle Terms, through which we obtain, by
Mediate Inference, such Conclusions as are not apparent at
a glance, or by direct Intuition.  When the geometer, for
instance, cannot determine directly the distance from one
point to another, he constructs a triangle, the base of which,




358            DEMONSTRATIVE REASONING
with its adjacent angles, as accessible, can be easily measured; and he can then deduce the required distance, or
the height of the triangle, from the known relations which
exist between it and the quantities which he has thus directly determined.  In like manner, the value of one or
more unknown quantities, symbolically represented in an
algebraic equation, is deduced from some of the given relations which subsist between them  and the known quantities, with which they are taken in connection. Indeed,
the peculiar function of algebraic science is to determine
general relations between different groups and classes of
magnitudes, these general ratios, proportions, and' analyses
being subsequently applied by the geometer and the arithmetician to the solution of particular problems.  The mere
construction of a geometrical diagram enables us to see the
use which is made of one or two known relations between
several quantities, as means of determining indirectly other
relations between them which cannot be directly measured.  The diagram is only a means of making clear to
our apprehension the fact, that the same straight line, or
length already determined, is at once the base of a triangle,
the radius of a circle, the side of a square, &c.; then this
line may be used as a Middle Term, or means of proving
syllogistically what the other properties and dimensions,
hitherto unascertained, of this triangle, circle, and square'must be. Thus to ascertain a new property of a former
object of Thought is to advance a step in the classifications
which the mind is continually forming, enabling us to refer
this object, perhaps hitherto anomalous, to its proper class.
The diagram, indeed, is a Singular instance; but what it
enables us to discover is a General Truth; for, as already
remarked, we know that this one instance is a perfect representative of its whole class, since that class exists only in
our Thought, and is therefore perfectly known.  The little
triangle which I am contemplating as drawn on paper cor



AND DEDUCTIVE EVIDENCE.             359
responds perfectly, in all particulars that can be essential for
the Reasoning, to the magnificent one, having as its base
line the diameter of the earth's orbit, which the astronomler, when he would determine the distance of a fixed star,
imagines to be erected in the heavens.
These considerations appear to me to evince very clearly,
that the peculiar cogency and fruitfulness of mathematical
reasoning do not arise, as Kant maintains, from the fact
that it concerns nothing but Space and Time, and that
Space and Time exist only in our minds.  The sole object
of this sort of reasoning seems to be quantity in its, various
forms; and reasoning would be equally Demonstrative, if
it related to any other single attribute of things considered
abstractly, or as we conceive it apart from all other properties- with which it is united in the actual constitution of
things. The fact that Quantity is a universal attribute, belonging to all objects of Thought whatever, explains the
broad scope and general applicability of mathematical reasoning; while its peculiar fruitfulness, or the vast number
of truths which it brings to light, appears to proceed from
the countless number and definite character of the relations
which subsist between different quantities. No other attribute presents itself so universally, or in modes at once so
numerous and so distinct, capable alike of indefinite augmentation and diminution.  The field is boundless, and we
advance over any portion of it with the precision and certainty in every movement which admit neither error nor
doubt.
The views which have now been presented enable us to
refute the doctrine, originally proposed, as Mr. Stewart
thinks, by Leibnitz, that the certainty of mathematical
reasoning depends upon the fact, that all the evidence on
which it is supported may be resolved, in the last analysis,
into the perception of identity; -" the innumerable variety of propositions which have been discovered, or which




360            DEMONSTRATIVE REASONING
remain to be discovered in the science, being only diversified expressions of the simple formula, a= a."  It is true
that this theory correctly presents the form, not only of
mathematical reasoning, but of all reasoning whatever;
for we have shown that every Affirmative Judgment, in a
certain sense, or with reference to the denotation of the
Concepts which it concerns, is an equation of its two
Terms.  The formula, A is B, to which all conceivable
Affirmative Judgments may be reduced, is resolvable, in
this sense, as B equals A, into A =- A. But the peculiar
cogency of mathematical evidence cannot be explained by
the possession of an attribute which does not distinguish it
from  Moral Reasoning.  In reference to the connotation
of its Terms, a Judgment does not express an equation,
but the inclusion of an object in a class, and the consequent possession by that object of the peculiar attributes.of that class. In this sense, the signification is, not that
the Subject equals the Predicate, but that it possesses one
or more of the attributes of the Predicate, or possesses the
Predicate itself as one of its own attributes. The doctrine
which we are considering owes its plausibility to a confusion of the significance of these two very' different words,
identity and equivalence.  When the geometer proves the
area of a circle to be equal to that of a triangle having the
circumference for its base and the radius for its altitude,
he certainly does not mean that it is identical with such a
triangle, but only that it is equivalent to it in a single respect, -viz. in magnitude; they are not identical, for, in
shape, they are wholly unlike. Take even a simpler case,
which seems more nearly resolvable into an expression of
identity: 4 =2 + 2. Even here, the meaning is not that
the two members of the equation are identical, but only
that the Concept or group four is equivalent in one respect
- viz. the possession of an equal number of units - to
the two groups two and two. It is plain that one group




AND DEDUCTIVE EVIDENCE.             361
cannot be identical with two groups, or that two distinct
acts of the mind, each conceiving or grasping together two
units, cannot be literally the same thing as one mental act
conceiving four.
The essential distinction between Pure and Applied
Mathematics consists in this, that, in the former, our
thoughts never go beyond the conception of pure quantity, or magnitude in the abstract, considered in either of
its two modes, space or number; while in the latter, the
additional qualities of weight, attraction, impenetrability,
elasticity, density, and many others, are brought in, not
merely as they are conceived in the mind, but as they
actually exist, or are manifested, in real things.  These
qualities also, so far as they are viewed in the former light,
that is, abstractly, as mere Concepts strictly limited by
Definition, may be reasoned about demonstratively; though
it is only in respect to their quantity that the reasoning will
have any wide range, or be fruitful in' conclusions, since
they have not the numerous and distinctly conceived relations which subsist between the innumerable degrees of
Quantity. But if viewed as actual qualities of real things,
our knowledge of them is derived merely from experience,
and must therefore be subject to all the limitations and imperfections of knowledge so derived. No Judgments concerning them can be absolute or universal; they are objects
only'of Probable Reasoning.  Previous to experience, we
could not attribute wei1ght to any material substance, much
less to all such substances; that every particle of matter
should attract, would seem no more probable than that it
should repel, every other particle. This is the source of
Dr. Whewell's error; because weight, attraction, impenetrability, &c. can be conceived abstractly, and therefore
be strictly limited by Definitions, and so reasoned about
demonstratively, he maintains that the Physical Laws of
Motion are necessary truths, and "' capable of demonstra16




362           DEMONSTRATIVE REASONING
tion, like the truths of Geometry." So they are, if viewed
as mere Concepts, not necessarily having anything corresponding to them in the outward universe. But if regarded as Physical Laiws, expressing the actual phenomena of real things, they are mere educts from experience,
can be reasoned about only Inductively,. and rest solely
upon Probable evidence.
-Deduction is not a happily chosen word to indicate the
characteristic feature of reasoning from Universals to Particulars, as contradistinguished from Induction, whereby we
reason from  Particulars to Generals.  In the Syllogism
which expresses the Form of the latter process, the Conclusion is as much a deduction from the Premises, as in
the former case. We may speak of a Law, or general rule,
as deduced from several individual facts, with just as much
propriety as of facts as deduced from the Law. In either
case, the Conclusion may be said to depend upon the Premises in this sense, that the latter authorize us to proceed to
the former. But it is a mere figure of speech, and not a
very happy one, to speak of the Conclusion as so involved
in the Premises, that the one can be drawn out of, or deduced, from the other. The process is rather an explication of what was previously in the mind, whereby two acts
of Thought are brought into harmony with each other.
The Subsumption either includes one or more individuals
in a class, or excludes them from it; and the Conclusion
then states explicitly what is virtually or implicitly thought
in that act of inclusion or exclusion. The process of reasoning is not so much a mode of evolving a new truth, as
it is of establishing or proving an old one, by showing how
much was admitted in the concession of the two Premises
taken together, or what follows from the act of bringing
them into harmony.  The Conclusion is not authorized by
either of them taken singly.
Hence it is a still graver mistake, and one which has




AND DEDUCTIVE EVIDENCE.            363
given rise~ to much misunderstanding, to speak of the Conclusion as deduced from one of its antecedents, from the
Major Premise only. A Sumption or General Rule is a
necessary part of every Syllogism; but it does not by any
means follow, that this Rule alone implicitly contains all
the particular Conclusions which are ordinarily said to be
drawn out of it. The Conclusion is drawn in accordance
with the Rule, and the latter may, in one sense, be said to
afford a proof of the former, inasmuch as it evinces that
the Conclusion, if the truth of the Minor Premise or Subsumption is granted, cannot be denied without overthrowing a general principle the truth of which is presupposed,
as resting upon the evidence either of Intuition, or of a
Primary Law of Thought, or of previous Demonstration.
In one sort of Immediate Inference, that of Subalternation, the Premise luay be rightly viewed as containing the
Conclusion, as a whole contains one of its parts, and the
latter may therefore be held to be deduced from the former. But the relation between the Subalternans and the
Subalternate is very different from that which subsists between the Sumption and the Conclusion in a case of Mediate
Inference. In the latter case, the gist of the reasoning
does not depend upon any Maxim or First Principle, but
upon the discovery of a Middle Term, with which both
Terms of the Conclusion are separately compared. This
Middle Term is the name of a Class, and the new truth
which is developed by the reasoning consists in the Subsumption of the Subject of the Conclusion into that Class,
and the consequent discovery that it possesses all the attributes or properties which are connoted by its Name. For
example:- the geometer, wishing to ascertain the size of
a certain angle, finds that it is one of the angles of an equilateral triangle;. this is the Subsumption, and when it is
accomplished, the discovery is really made and the problem
solved, for the Conclusion that the angle measures 60~ im-p




364           DEMONSTRATIVE REASONING
mediately follows, in accordance with the General Truths
already demonstrated, that the three angles of an equilateral triangle are equal to each other, and that their sum is
180~. But no manipulation, no analysis, of these Truths
previously demonstrated would enable him to evolve from
them, without the aid of the classification given in the
Minor Premise, the measure of this particular angle.
When the Sumption, instead of being, as in this case, a
General Theorem previously demonstrated, happens to be
one of those Maxims which are called Axioms in Geometry, it is still more evident that it is a meagre and barren
Rule, from which no fruitful and significant Conclusion
can properly be deduced.
I accept, then, to its full extent, the doctrine originally
propounded by John Locke, and adopted and defended in
our own day by Dugald Stewart, that the Axioms of Geometry, and the other very general maxims which are
usually considered as First Principles in our researches,
" are not the foundations on which any of the Sciences are
built, nor at all useful in helping men forward to the discovery of unknown truths." If Reasoning were an organon
of discovery, a means for the advancement of truth, its characteristic feature would appear in the Subsumption, which
places the Subject of inquiry, hitherto anomalous, or of
uncertain classification, under a Concept, or, what is the
same thing, in a class, the attributes of which are known;
and the proof that it possesses one or more of the attributes
of that class then appears by citing the General Rule,
which is the Major Premise. In other words, each of the
two Premises in a Syllogism has its own appropriate function; the Minor announces a discovery, a new truth, which
is always a truth of classification, and the Major cites an
Axiom, or some other general rule, previously well known,
which proves some consequence of this new truth, or enables us to acquiesce, with more or less confidence, in the




AND DEDUCTIVE EVIDENCE.              365
announcement of this consequence.  If the Major is an
Axiom properly so called, or a truth previously demonstrated, - in either case, having absolute universality and
certainty, - then the Conclusion, if the Subsumption is
correct, is demonstrated; but if it is merely a general rule
obtained by Induction or Analogy, the Conclusion is merely
probable.
The correctness of this analysis will appear, I think,
from an examination of either of the following Syllogisms.
1. All electricity may be silently drawn off from any charged
body, by bringing near to it a sharp-pointed rod.
Lightning is electricity... Lightning may be so discharged.
2. The nervous fluid will not travel along a tied nerve.
Electricity will travel along a tied nerve... Electricity is not the nervous fluid.
3. All alternate angles made by one straight line cutting two
parallel lines are equal.
A B C and B C E are alternate angles..'. A B C and B C E are equal.
4. Things which are equal to the same thing are equal to each
other.
A B and B C are each equal to C D... A B and B C are equal.
5. Happiness is desirable.
Virtue is happiness..'. Virtue is desirable.
It is evident that no one of the General Rules which
form the Major Premises of these Syllogisms can be " at
all useful in helping men forward to the discovery of unknown truths." The real discovery is announced in the
Minor Premise, and the connection of the two Premises in
one act of reasoning is the means of proving the Conclusion, and of assuming it into its proper place under the
General Rule. It does not appear, then, that Reasoning




g366          DEMONSTRATIVE REASONING
as such, or as an act of Pure Thought, is a means for the
advancement of knowledge. This doctrine, indeed, follows
immediately from the principles that have been already
laid down. Reasoning as such is one of the processes of
pure Thought which determine the Porm, but not the Matter, of our knowledge.  The Matter of Thought is obtained by Intuition, - by observation through the senses or
through consciousness. The fact or truth thus discovered
is announced in the Subsumption, not as first made known
by it, or as deduced from what was previously known, but
in order to be proved through the Reasoning process; that
is, to be brought into harmony with our previous knowledge
as stated in the Miajor Premise, and that the same consequences may be attributed to it which are already known to
follow from all the cases included under that general statemrent.
Accordingly, what Hamilton remarks of the whole doctrine of Logic may be applied to the theory of Reasoning,
which is but one of the departments of this science. We
cite again, in reference to one of the parts, what has been
already quoted in reference to the whole. "An extension
of any science through [pure Reasoning] is absolutely impossible; for, by conforming to the logical canons, we acquire no knowledge, - receive nothing new, but are only
enabled to render what is already obtained more intelligible by analysis and arrangement.  [Reasoning] is only the
negative condition of truth.  To attempt by mere [Reasoning] to amplify a science, is an absurdity as great as if we
should attempt, by a knowledge of the grammatical laws of
a language; to discover what is written in this language,
without a perusal of the several writings themselves. But
though [Reasoning] cannot extend, cannot amplify, a science by the discovery of new facts, it is not to be supposed
that it does not contribute to the progress of science. The
progress of the sciences consists not merely in the accumn



AND DEDUCTIVE EVIDENCE.             367
lation of new matter, but likewise in the detection of the
relations subsisting among the materials accumulated; and
the reflective abstraction by which this is effected" must
follow the laws of Reasoning.
We are now prepared to understand and appreciate
Locke's doctrine, which has been accepted and ably supported by Mr. Bailey and Mr. J. S. Mill, that " the immediate object of all our reasoning and knowledge is nothing
but particulars."  Locke argues that "the perception of
the agreement or disagreement of our particular ideas is
the whole and utmost of all our knowledge.  Universality
is but accidental- to it, and consists only in this, that the
particular ideas about which it is are such as more than
one particular thing can correspond with and be represented by. But the perception of the agreement or disagreement of any two ideas is equally clear and certain,
whether either, or both, or neither, of those ideas be capable of representing more real beings than onle, or no." *
fr. Mill says: W66  e much oftener conclude from particulars to particulars directly, than through the intermediate
agency of any general proposition.  We are constantly
reasoning from ourselves to other people, or from one person to another, without giving ourselves the trouble to
erect our observations into general maxims of human or
external nature." t
The only question here concerns the proper use of words.
The process of comparing one individual object or event
with another, and thereby ascertaining some relation between them, is unquestionably the first step to knowledge,
and the only means of enlarging our stock of knowledge.
But the particular fact thus learned is a fact of observation,
not of reasoning.  Certainly I do not need to reason, nor,
in the strict and technical sense, to think, in order to per* Essay on Human Understanding, Book IV. Chap. 17, ~ 8.
t System of Logic, Book II. Chap. 3, ~ 3.




368            DEMONSTRATIVE REASONING
ceive that John is taller than William. A brute perceives
this fact as well as I do, and acts upon it, as in distinguishing his master. Even if we carry the process one step
further, and form a Judgment, by subsuming the individual
object of intuition under a class, through perceiving that it
affects our senses just as some other objects ranked under
that class have done, still we are engaged only in enlarging
and generalizing our knowledge, and not in reasoning properly so called. But when we take one step more, and proceed to -attribute certain qualities to that individual thing,
which are not now directly perceived in it, but are sup-s
posed to exist in it, because we have noticed them in other
objects of the same class, we are properly said to reason;
the act is one of Mediate Inference.  But this act does not
properly enlarge our knowledge, but only explicates it, by
bringing out explicitly into Thought what was already virtually contained in it. By putting an object into a class,
we have already virtually attributed to it all the qualities
which belong to that class.
This doctrine is not inconsistent with what has already
been maintained, that an act of Reasoning is necessary to
enable us to call anything by its appropriate Common
Name.  Mere observation cannot teach us what is the
proper appellation of any object which is now for the first
time perceived; its name is not stamped upon it, - is not
one of its qualities directly perceptible either by sense or
consciousness. But by the joint action of our faculties of
perception and comparison, we are made aware that the
new object resembles a certain class of previously known
objects in all the particulars which are connoted by the
name of that class, and therefore, that the object may be
properly subsumed into that class, and called by its name.
The doctrine of Locke and Mill, then, appears true to
this extent; -that we certainly compare one individual
thing with another, and only by such comparison can dis.




AND DEDUCTIVE EVIDENCE.            369
coveries be made and knowledge advanced. But that simple comparison, and the consequent perception of a relation
of likeness or unlikeness, is not an act of reasoning. We
do not, in the technical sense of the term, " conclude from
particulars to particulars." Before this particular discovery can be made available for the purposes of Science, -
before it can be brought into union and harmony with out
previous stock of knowledge, an act of Pure Thought
of Mediate Inference, or Reasoning properly so called
- is necessary. We must become aware that at least one
of the two Individuals which were compared together is a
typical specimen or representative of a whole Class, and
the corresponding Conclusion must be reached, that the
other Individual possesses some one or more of the essential attributes of that Class. To advance to this Conclusion is, in one sense, an unimportant step; for it contains
nothing new, - it does not increase our knowledge. Having learned the individual fact, that "A and B are both
equal to C," we do not really make any progress, except in
the way of systematizing our knowledge, when we add the
very obvious corollary, that " they are equal to each other,"
since this is but one instance under the General Rule, that
" all which are equal to the same thing are equal to each
other." Butbin another respect, this step is far from being
unimportant. Though we have already virtually attributed
all the qualities of the class to the individual when we have
included that individual in the class, so that the technical
Conclusion only draws out explicitly what was already implicitly thought, a new act of classification is thus completed, and the memory is disburdened of particulars by an
act of arranging and harmonizing our knowledge. First
to bring out into distinct consciousness the truths which
are already, so to speak, within our reach, but in a confused and undeveloped state, and then to place them under
their appropriate heads or classes in a methodized system
16 *                          x




870           DEMONSTRATIVE REASONING
of knowledge, is the peculiar office of Reasoning. The
Conclusion, when once drawn, is obvious enough; otherwise it could not be said to be demonstratively proved.
But far the greater part of our knowledge exists in this
half latent semi-developed state; only by an act of Reasoning can it be drawn forth, proved, and made available
for, use in further inquiry. In respect to utility, it matters
little whether our stores are positively enlarged, or our
previous acquisitions are developed, systematized, and rendered more efficient. I believe that no- ndw truth was
ever discovered by a direct process of pure Reasoning;
and, on the other hand, that, without the aids and appliances furnished by such Reasoning, no progress beyond
the most elementary steps of Science would have been
practicable. Good observers discover new facts, but good
reasoners do most to educate and instruct mankind.
Of course, the fact of observation on which the Reasoning is based, and which it is the office of the Reasoning to
develop, is not necessarily one perceptible by sense. The
mere thinker, who, by some lucky chance or by dint of
patient reflection, hits upon some relation, hitherto unobserved, between two abstract ideas, is just as much a discoverer, as the chemist who first finds that a metal is the
basis of an alkali; otherwise, no progress could be made
in pure mathematics or any other abstract science. The
naked fact, that the square upon the hypothenuse of a
right-angled triangle is equal to the sum of the squares
on the two other sides, was observed and known long before Pythagoras first succeeded in proving it, by showing,
through a series of Middle Terms, that it is really involved
in and harmonizes with some elementary principles, the
whole compass and meaning of which had not before been
duly developed. The fact was first made known by reflective observation, - perhaps by sensible experiment; but it
did not become a step in the progress of Science till it had




AND DEDUCTIVE EVIDENCE.           371
been proved, or subsumed under some broader principles,
and thus assigned its due place in a system of knowledge,
by an act of pure Reasoning.
To those who have fully considered the doctrine which
was laid down at the commencement, that Logic is not an
organon for the discovery of truth, and that it is exclusively concerned with the Form, and not the Matter, of
Thought, this discussion may seem to have been needlessly
prolonged. But it has so long been supposed that the
admission of the inapplicability of the Syllogistic process
to the discovery of truth was tantamount to a confession
of the entire inutility of the science, that it seemed worth
while, even at the expense of some repetition, to prove
that this supposition was wholly groundless, and to show
precisely what is the utility of the ends to which mere
Reasoning is subservient. When Mr. Locke says, " I am
apt to think that he who should employ all the force of his
reason only in brandishing of Syllogisms will discover very
little of that mass of knowledge which lies concealed in the
secret recesses of nature," we have a right to answer, in
the words of an acute logician, Mr. J. Walker, of Dublin,
that "he expresses himself with needless caution. Such a
man will certainly not discover any of it. And if any imagined that the mere brandishing of Syllogisms could increase their knowledge, as some of the Schoolmen seemed
to think, they were indeed very absurd." But to those
who consider how limited the range'of human knowledge
would be, if it were confined to isolated facts of observation
resulting from the comparison of one individual thing with
another, having no connection with each other, often seemingly at variance, not systematized, not summed up into
general truths, and hence incapable of communication by
language, it will be evident that, without the capacity and
the constant exercise of Reasoning, mankind would haveadvanced but little beyond the condition of the brutes.




372            DEMONSTRATIVE REASONING
It may be useful to enumerate the different classes of
General Rules which are the Major Premises of all Syllogisms, and, as such, are not so much the First Principles
whence all our Conclusions are derived, as they are the
Ultimate Truths in which all Reasoning terminates.
1. The first of these classes consists of the Primary
Laws of Pure Thought, and those secondary or derivative
maxims into which, in different sciences and for differeit
purposes, these Primary Laws are explicated. In Logic,
as we have seen, both the supreme Canons of Mediate Inference, such as the -Dictum de omni et nullo, and the special Rules of various sorts of Syllogisms, are all resolvable,
in the last analysis, into these Laws of Thought. In like
manner, the Axioms properly so called of Geometry, that
"i' f equals are added to equals, the wholes are equal," "if
equals are subtracted from equals, the remainders are
equal," &c., are only varied expressions, explications, or
immediate consequences, of the Laws of Identity and Noncontradiction.
2. The foregoing maxims are merely analytic or explicative. The next class consists of synthetic or ampliative
Judgments.  These are necessary intuitions of pure reason, or universal truths known a priori, as resulting from
the constitution of the mind itself. Such are the Judgments,
that every event must have a cause, that space is infinite,
that substance underlies all material attributes, &c. With
these I am inclined to rank what have been called Axioms
-more properly, Assumptions —of geometrical science,
as they are propositions which the geometer must assume
to be true, though they cannot be demonstrated; for example, - two straight lines cannot enclose a space; a
straight line is the shortest distance between two points;
two straight lines cut by a third line at equal angles, if
produced, will never meet.
3. We also reason demonstratively from Definitions, that




AND DEDUCTIVE EVIDENCE.            373
is, from explications of the Intension of any Concepts which
we see fit to frame. Of course, such Judgments are purely
analytic, and if they contain no unfounded assumption,
that the signification thus assigned to the Names of the
Concepts is that which is usually affixed to them in the
common use of language, or that the Marks enumerated
are all the original and essential qualities of the real things
which these Names denote, the Conclusions at which we
arrive must be demonstratively certain.
4. The laws, or positive precepts, which emanate from
any sufficient authority, whether human or divine. These
are not Judgments, but commands, and, as they are to be
obeyed at all hazards, and on all occasions, the only question which can arise respecting them concerns their interpretation. Of this nature are the injunctions of conscience,
the laws of the land, and the commands of God, as made
known in his revealed word. Apart from any doubt which
may arise concerning the signification of the terms in which
they are expressed, any Conclusion legitimately deduced
from such commands must be absolutely valid, since universality is of the very nature of law.
5. Universal propositions previously demonstrated.
6. Truths of generalization, based upon observation and
Induction or Analogy. These are true only to the extent
of our experience, which, as we have seen, never extends
to all or none. Consequently, these propositions rest only
upon probable evidence; and though such evidence be sufficient for moral certainty, they are not available for Demonstration strictly so called.  We may assume them to
be universally true, and upon such assumptions may rest
perfectly valid syllogisms; but the Conclusion in such
cases will have no other or higher certainty than belongs
to the Major Premise.
It should be observed, however, that, when we thus
speak of merely probable evidence, the epithet is used only




374            DEMONSTRATIVE REASONING
in its technical sense, and it is not meant that we have
necessarily less confidence in it than in mathematical Demonstration.  "The word probable, when thus used," says
Dugald Stewart, "does not imply any deficiency in the
proof, but only marks the peculiar nature of that proof as
contradistinguished from another species of evidence. It
is opposed, not to what is certain, but to what admits of
being demonstrated after the manner of mathematicians.
This differs widely from the meaning annexed to the same
word in popular discourse; according to which, whatever
event is said to be probable is understood to be expected
with some degree of doubt." Perhaps the clearest distinction between Demonstrative and Probable evidence consists
in the fact, that the former does not admit of degrees, as a
proposition is either demonstrated absolutely, or not at all;
while the latter may exist in any degree, from the faintest
shade of probability up to moral certainty.
This seems the proper place for the explanation of
the technical terms, or Second Intentions of Judgments,
that are used in the construction of Science.  Most of
these, however, are of infrequent occurrence, except in the
mathematical sciences. All propositions are either Theoretical or Practical; — tlhe former are purely speculative,
the truths which they enounnce being merely objects of contemplation by the mind, as having no reference to action
or conduct; the latter have regard to something which is
to be done or omitted, to some performance or mode of
procedure. Propositions are also said to be demonstrable,
if they require or admit of proof; they are indemonstrable,
if they are self-evident, or intuitively known.
An indemnonstrable judgment, if theoretical, is called an
Axiom; if practical, it is styled a Postulate.  A demonstrable judgment, or one which is announced as needing
proof, if theoretical, is called a Theorem; if practical, it is
a Problem.  A Thesis coincides very nearly with a Theo



AND DEDUCTIVE EVIDENCE.            375
rem; it is a judgment proposed for discussion and proof.
A Corollary is a truth announced as an immediate consequence or collateral result of another judgment that has
just been proved, and therefore as not needing any separate proof for itself. A Judgment which does not properly
belong to the science in which it appears, but is borrowed
from some other, is called a Lemma; one which merely
illustrates the science, but is not an integral part of it, is a
Scholion. An ]Hypothesis is a judgment not known to be
true, but accepted for the time as a provisional explanation
of some phenomena, and as liable to be modified or rejected
altogether on the production of further evidence. A Theory, sometimes incorrectly used as a synonyme for Hypothesis, is a comprehensive and methodical arrangement of
some large group of phenomena under their supposed
Causes and Laws, offered as at least a provisional account
of them and mode of reducing them to system.  " Theoriarum vires," says Bacon, " arcta et quasi se mnutuo sustinente
partium adaptatione, qud quasi in orbem cohcerent, Jirmantur."




376            INDUCTION AND ANALOGY.
CHAPTER  XII.
INDUCTION AND ANALOGY.
A   NY act of Reasoning strictly so called presupposes the
universality of its Sumption or Major Premise. If I
am not absolutely certain that all A are B, then, though
the Subsumption that C is A be undoubtedly true, I cannot be sure that C is B.
Now it has been repeatedly proved, that universal Judgments cannot be derived from mere experience, which is
competent to pronounce upon some, or many, but never
upon all, or none. But as we cannot have any knowledge
of real things, or actual existences, except by means of
experience, it follows that such things are not objects of
Reasoning in the proper sense of the term, - that is,
of Demonstrative Reasoning, in which the Conclusion is
accepted with absolute certainty. From the enumeration
which has just been made, it appears that, with the unimportant exceptions of legal precepts and a few truths known
a priori, all Major Premises must be either mere analytic
judgments obtained by explicating our own abstract conceptions, or general rules that are true only to the extent
of our experience. We may assume such rules to be universally true, and the Reasoning will then become perfect
or Demonstrative in Form; but as the Conclusion can
never be purged from the shade of uncertainty thrown
upon it by the imperfect evidence of the universality of
its Major Premise, such Reasoning is rightly considered as
merely probable or contingent. We may suppose, also, that




INDUCTION AND ANALOGY.              377
the real existences perfectly correspond to the abstract conceptions that we have formed of them, and, in this way,
may seem to obtain absolute Conclusions about matters of
fact. This is commonly said to be reasoning from hypotheses; but just so far as such reasoning is Demonstrative, it
concerns only the Concept, which cannot be more than an
imperfect representation of the reality.
For illustration, I borrow from Mr. Bailey's " Theory
of Reasoning," page 2, the following examples of Probable
or contingent Reasoning.
1. " I am walking, I will suppose, on the sea-shore, and, perceiving a quantity of sea-weed lying on the beach, while the
water is at the moment a quarter of a mile from it, I conclude that the tide has ebbed, and left the weed where I
perceive it lying."
2. " I notice the print of a small foot on the sand, and I feel
pretty sure that it was made by a child."
Each of these instances may be resolved into the Form
of perfect or Demonstrative Reasoning, and it will then be
seen that the uncertainty which attaches to the Conclusion
arises solely from the doubt, which experience, however
often repeated, is incompetent to remo~ve, as to the absolute universality of the Major Premise.
1. All sea-weed found within the space usually covered by the
sea at high water must have been left there by the ebbing
of the tide;
This bunch of sea-weed was so found; therefore, &c.
2. No small foot-shaped imprint on the sand can have been left.
by anything else than the foot of a child;
This is a small foot-shaped imprint on the sand; therefore, &c.
" In these several cases," says Mr. Bailey, " my mind is
determined by the sight of present phenomena, conjoined
with knowledge previously acquired, to believe something
which I do not actually perceive through the organs of




378           INDUCTION AND ANALOGY.
sense; —something past, something future, or something
distant; or, in other words, to believe that some event has
happened, will happen, or is happening, although beyond
the sphere of my observation."  In short, it is an attempt
to make the Thinking faculty do the work of the Perceptive faculty; to gain a knowledge of an external fact by a
mere process of Thought, instead of acquiring it by observation through the senses. Such an attempt can have but
imperfect success; its result is not properly denominated
knowledge, but belief, or opinion. The inference is rightly
said to rest upon anoral, or probable, evidence.
It is contended by some, that the mind actually rests
such inferences upon the amount -of evidence which has
really been collected, though conscious that it is incomplete, and does not go through the Form of assuming a
Major Premise which is absolutely universal, and which,
if we were only sure that it was well founded, would render the Conclusion certain. Thus, to recur to one of the
instances just cited, Mr. Bailey argues that the Premise
from which the mind actually draws the inference is what
he terms the Collective Eact, viz. that, in all the cases which
I have ever observed or hzeard of, all sea-weed so found has
been left by the tide,- -and not the General Law, announced without this limitation, which affirms as much absolutely of all sea-weed so found. He maintains that the
General Law itself, just as much as the particular case in
question, is an inference from the Collective Fact. To
rest the inference respecting the individual case upon the
General Law, does not make the Conclusion a whit more
probable, than to rest it upon the Collective Fact on which
this General Law itself is founded.
Perhaps the question is one which does not merit much
discussion. Obviously it matters not whether the mind, in
seeking for competent proof of this particular inference,
proceeds by throwing what evidence it possesses into the




INDUCTION AND ANALOGY.              379
Form of perfect or Demonstrative reasoning, through the
assumption of a Major Premise which is not free firom
doubt; or whether it forbears any undue assumption in the
Premises, and adopts a process of inference which is confessedly imperfect even in Form. Taking a doubtful assertion for a Premise, it thus preserves the Form of valid
reasoning.
All men are fallible;
The author of this book is a man;
Therefore the author of this book is fallible.
Restrict the statement in the Major Premise, so that it
shall express no more than what is known to be true, and
the Reasoning thus becomes invalid through an undistributed Middle.
All men, so far as observation has extended, have been fallible;
Therefore this author is fallible.
As a fact, however, I believe the first of these forms is
much more frequently in use. For proof in any particular
case, we usually refer to a Law of Nature, the universality of which is expressed with as little hesitation as if it
were a Law of Thought. The usual form of Enthymerme
employed is the following: —This bit of iron will melt,
because all iron is fusible; This water will boil at 212~,
because water always boils at that temperature; These
men must die, for all human beings are mortal. In truth,
with the exception of those who have made a special study
of the theory of Reasoning, nobody thinks of restricting
the universality of such statements by the qualifying clause,
"so far as has been observed," or " according to all known
experience."  And it is not mere carelessness in the use
of language, or the proneness to exaggeration which has
already been pointed out for censure, that causes such
statements to be made without their proper limitations.
Very few are conscious, even after reflection, that there




380            INDUCTION AND ANALOGY.
is any exaggeration in the case; and there is none, except
what is implied by adopting the Form, without the substance, of Demonstrative Reasoning.
Induction and Analogy are the two processes of thought
by which we endeavor to make our Judgments about whole
classes of real objects, or actual existences, approximate the
absolute certainty and universality of our Judgments about
abstract conceptions. Hence they are, what Pure Reasoning is not, organa for the discovery of truth and the actual
advancement of knowledge. But just so far as they are
means to these ends, they lose the character of Pure or
Demonstrative Reasoning; the Syllogisms to which they
are reducible are faulty either in Matter, as having a
Major Premise the universality of which is merely probable, or in Form, as containing an undistributed Middle.
The question whether they are entitled to be called Reasoning is hardly worth discussing here, as it concerns only
the use of words. Logical or Demonstrative Reasoning
they are not; but they may be denominated Probable
Reasoning, or Philosophical Presumptions.
It should be mentioned, however, that what may be
termed Logical Induction, the plena enumeratio of the
logicians, which deduces a General Rule from what is
known to be true of every individual in the class, belongs
to Pure Reasoning strictly so called. Conclusions drawn
from such Premises as the following, are Demonstrative or
absolutely certain; but these only generalize our knowledge, or alter its expression; they do not enlarge it.
Mercury, Venus, the Earth, &c. are all the Planets.
Peter, James, John, Matthew, &c. are all the Apostles.
This mode of Reasoning has already been analyzed; but
it is not what is understood by Induction in the processes
of Science. Logical Induction concludes from each one to
all; Induction properly so called concerns the Matter of
Thought, and concludes from some to all.




INDUCTION AND ANALOGY.            381
The difference between Induction and Analogy has been
clearly stated and illustrated by Kant. In order to enlarge
our knowledge beyond the bounds of experience, we must
either conclude from many things to all others of the same
Species, which is Induction; or we must conclude from
the known agreement of two things in several qualities,
that they agree also in some other quality which is not
directly known. In our progress from tfhe Particular to
the General, Induction proceeds upon the principle, that
what certainly belongs to many Individuals of the same kind,
also probably belongs to all the other Individuals of that kind;
the principle of Analogy is, that, if two things agree in many
respects, they probably agree also in some other respect. Because some one quality exists in many things, therefore it
exists in all of the same kind; this is Induction. Because
many qualities in this are the same as in that, therefore one
other quality in this resembles that; this is Analogy. In
other words, Induction concludes fiom one in many to the
others, by way of Extension; Analogy, from many in one
to the others, by way of Intension.
The following are instances of Induction: —
1. In many cases in which water has been analyzed, it
has been found to consist solely of oxygen and hydrogen;
therefore, all water is made up from these two elements.
2. Very many animals have been examined, and these,
without a single exception, have been found to possess a
nervous system; therefore, all animals have a nervous
system.
3. Most bodies expand in bulk, if heated; therefore,
heat always produces expansion, if it be not counteracted
by some other cause.
The following are instances of Analogy: —
1. The planets Venus and Mars resemble the earth in
many respects, as in size, density, time of rotation on the
axis, distance from the sun, receiving light and heat from




382           INDUCTION AND ANALOGY.
it, &c.; therefore, they probably resemble it in one othler
respect, in being inhabited by living beings.
2. Fossil skeletons that are found in the rocks bear a
close resemblance in very many respects to the skeletons
which, as we know, once belonged to recently living animals; therefore, they resemble them in one other respect,
in that these fossils are the remains of animals which were
formerly living'upon the earth.
3. In many respects, as in complexity of parts, nice adjustment and mutual dependence of these parts one upon
another, delicacy of finish, symmetry, and adaptation to
many useful ends, the human hand resembles some ingenious machines, which we know to have been contrived and
fashioned by the exercise of mind; therefore the hand was
so contrived and fashioned.
4. The argument of Origen an(l Bishop Butler is, that
if the Scriptures and the constitution of Nature are alike in
this respect, that they proceeded from the same Author,
we may well expect to find the same difficulties in the former as are found in the latter.
It is plain that what is here called Analogy is the same
mental process which is described and analyzed by Aristotle as " reasoning from Example."  He gives the following as an instance of this sort of argument. If we would
prove that it is not expedient for the Athenians to make
war upon the Thebans, who are their neighbors, we may
reason from the analogous case, that the war against the
Phoceans, who were their neighbors, was fatal to the Thebans. He says that Example is not founded, like Syllogism, upon the relation of the whole to its parts, nor, like
Induction, upon the relation of the parts to the whole, but
upon the relation of one part to another, because the one
is more perfectly known than that other. The Aristotelic
Induction proceeds from all the individual cases, nTwhile Example is founded.only upon some of them, perhaps, as
above, upon a single instance.




INDUCTION AND ANALOGY.             383
Comparatively little need be said of Analogy, as the Conclusions to which it leads are evidently not Demonstrative,
but merely Probable. Strictly speaking, there is no proof
whatever, because two, things resemble each other, however nearly, or in however many respects, that tile resenmblance extends to a single point other than what has been
actually observed. The existence of one quality, it is true,
may be necessarily implied in that of another, either by the
Laws of Thought, or by the a priori laws of the human
mind; as one geometrical property of a body may be deduced from another, or as its divisibility may be inferred
from its extension. This is Demonstrative Reasoning, but it
is merely explicating our knowledge, and not directly adding to it; and certainly it is not reasoning from Analogy,
which proceeds from similarity in some respects to similarity in one other, or in many others. Analogical conclusions may have any degree of probability, varying from a
merely permissible hypothesis up to what may fairly be
called moral certainty. Because this kind of inference is
often greatly abused, for some degree of resemblance may
often be detected between two things apparently most dissimilar, - skill in such detection, when the inference is
ludicrously improbable, constituting wit,- I am inclined
to think that the force of which it is susceptible is generally
underrated.  Slight Analogies are worth nothing, except
to show that the coexistence of two or more qualities is
barely possible, no belief whatever being justly created that
it-is _probable. On the other hand, the Analogy may be
so perfect that the Conclusion founded upon it may be accepted with as full faith as if it rested upon an extensive
and cautious Induction, with which, indeed, it is frequently
confounded.
To recur to the instances just cited. The supposition
that the other planets are inhabited rests upon an Analogy
which is so faint and imperfect, that it does not afford suffi



384            INDUCTION AND ANALOGY.
cient ground for making up any opinion on the subject,
either for or against the hypothesis. The resemblance is
but slight, even in the few particulars that are cited; and
we have no evidence that there is any similarity whatever
in a vast number of other respects, many of which are
essential to the existence of life under any of the forms
with which we are acquainted.  On the other hand, the
Analogy between the skeletons that exist only in a fossil
state, and those of animals now living, is so broad and perfect, that a man's sanity or sincerity would be questioned
who should affect to doubt that the former also once walked
the earth or swam in the seas. These fossils do not differ
more from  the extant types than many of the latter do
from each other, while in the numberless points of Analogy
the resemblance is perfect. And the conclusion in the
third case, founded upon the Analogy between the human
hand and a contrivance of man's device, is still more indisputable. If, without the aid of mind, without foresight or
design, the mere fortuitous concourse of atoms, in the lapse
of a past eternity, could have formed a living tree, fish, or
elephant, then, we say, that same rudderless and purposeless crowd of primeval atoms, in the lapse of a past eternity, could have formed, what is much easier, afossil tree,
fish, or elephant. We are here pointing out the analogous
character of two arguments, each founded upon Analogy,
but pointing to different Conclusions; and we find the resemblance between them so perfect, that it is impossible to
maintain the validity of the Conclusion in the former case,
and deny it in the latter.
The definition which is ordinarily given of Analogy, that
it means proportion, or a similarity of relations, does not
differ from the one here propounded. Thus, it is said,
when we affirm the relation of the fins of a fish to the
water to be the same [similar] to that of the wings of a
bird to the air, that we are judging from Analogy. So we




INDUCTION AND ANALOGY.             385
are; we are pointing out what is perhaps an unexpected
resemblance amid apparent diversity.  However unlike
fins are to wings, we still pronounce that they agree in this,
thle adaptation of the former to the anirmal's motion through
the water being very similar to the fitness of the latter to
effect motion through the air. From this equality of fitness for corresponding purposes, we reason analogically that,
if one was contrived by intelligence, the other was also.
Induction, says Mr. Mill, "may be summarily defined as
Generalization from  Experience.  It consists in inferring
from some individual instances in which a phenomenon is
observed to occur, that it occurs in all instances of a certain class; namely, in all which resemble the former in
what are regarded as the material circumstances."  This
last qualification is an important one, and has not received
sufficient notice from those who have speculated upon the
theory of Induction. The process would be invalid and
nugatory, /f we did not presuppose the correctness of the preceding Classifications that have been formed of the objects of
Science. A conclusion from some to all would not hold,
would not have even the slightest shade of probability, if it
were applied to a Class formed of the objects now contained
in this room, or of those embraced within my present field
of vision, or of things having no common attribute except
that they are of the same color, or the same size. But
such a conclusion becomes extremely probable, even mor,
ally certain, when applied to a Class, like that of metals
or stars, having many common characteristics which are
definite and peculiar.  Thus, having ascertained of only
two metals, iron and copper, that they are conductors of
electricity, it would be a tolerably safe Induction, that
all metals are such conductors. Having found that one
thunder-cloud was electrical, Franklin at once safely leaped
to the conclusion, that all such clouds had that property.
We have already seen that the Classifications formed of the
17                            T




386            INDUCTION AND ANALOGY.
innumerable objects of thought cannot be arbitrary, but
must be framed to embrace as many common or similar
elements as possible.  The numberless properties of a
geometric figure can be deduced by necessary inference
from the one or two leading properties of it which are
selected to form its Definition. And the hope always is,
in forming a Classification of real objects or events in Nature, to hit upon some attribute as the basis of the arrangement with which all the other qualities of it are connected
by some necessary, though to us invisible, tie.
This appears to afford the solution of a problem which
has puzzled many inquirers;- how it is, that we often
safely frame an Induction from a single instance, while, in
other cases, the conclusion is precarious, though supported
by a multitude of affirmative examples. Thus, the chemist, having discovered a new metal, ascertains by a single
experiment its specific gravity, degree of hardness, toughness, &c., and then safely concludes that every other specimen of the metal, which may afterwards be obtained, will
be found to possess these qualities in the same degree. On
the other hand, a multitude of instances of recovery from a
specific disease after the administration of a particular drug
are insufficient to establish the universal efficacy of the medicine in what appear to be similar cases. In Meteorology,
also, and in the several branches of Natural History, though
the Induction may be very extensive, and conducted with
all possible caution, the general conclusions have only that
low degree of probability which is indicated by calling
them empirical laws.  The reason of this difference evidently is, that the Classifications in the science of Chemistry
approach very nearly to perfection, the qualities determninable by chemical analysis being definite, strongly marked,.
and constant in their forms of combination with each other;
while Medicine, Meteorology, and.Natural History are,
and probably must ever remain, sciences very imperfect in




INDUCTION AND ANALOGY.               387
Classification, as the objects with which they are cdncerned
have an indefinite multitude of ill-determined attributes,
shaded into each other by imperceptible degrees, and combined in the most irregular manier. -The lines, and even
the principles, of division of the objects of these sciences are
merely provisional, and are frequently changed, so as to
adapt them  to the progress of observation, or in the hope
of hitting upon some qualities which may be found in more
constant relations with the other leading properties than
those which have hitherto formed the basis of the Classification.  Of course, the Induction becomes extremely precarious, when we are not sure that the instances over which
it extends agree with each other in all material circumstances.
It is evident, moreover, that the smaller the Class is, or
the nearer that it comes to an Infima Species, the stronger
is our assurance that, in reference to this Class, the conclusion from some to all will hold good. The Induction is
safer, for instance, from some to all lumps of iron, than
from some to all metals; and it is still more certain in reference to all specimens of one kind of iron, wrought or
malleable, than with respect to all sorts of that metal. As
the Extension and Intension of the Class-name are in inverse ratio to each other, that is, as the number of attributes connoted is greater in proportion as the number of
objects denoted is less, the similarity of the members of the
Class to each other is increased as the number of those
members is diminished; and the greater the similarity, the
safer the Induction, because it is then more probable that
the resemblance extends to the material or essential circumstances.  As the Intension is greater, the Induction is
founded upon a larger number of qualities, that is, upon a
more perfect resemblance; and as the Extension is less,
the Induction extends to fewer objects, and is therefore
more likely to be well founded. The gap between some




388           INDUCTION AND ANALOGY.
and all is not so great, when even all denotes only a few.
We cannot safely reason, from the process of treatment
which has been effectual in one case of fever, to the efficiency of the same treatment in any other instance, merely
because the symptoms of no one fever-stricken patient have
anything more than a general resemblance to those of another; and the internal peculiarities of the malady, of
which the outward symptoms are only the faint and easily
mistakable indications, are still more unlike.
Thus much, however, is certain, that if the Classification
is correct, if the cases brought together are really parallel
in all the essential circumstances, - and we must presuppose as much as this before we can reason from Induction
at all,- then we firmly believe, and assume it even as an
axiomatic truth, that " the course of nature is uniform,"
that " natural events are governed by constant general
laws," that " what has been will be," and that C" what has
been even in one instance has been in all other instances."
These are only different modes of expressing one and the
same Universal Truth, — one invincible conviction of the
human mind. This Truth is the ultimate Major Premise,
upon which all reasoning from Induction depends, or which
is taken for granted in all such reasoning. The simplest
and most indisputable case of such reasoning depends upon
this Maxim, just as much as the latest and broadest general
conclusion that has been propounded in physical science,
though this conclusion may be so questionable that it is
propounded only as an hypothesis. I could not be sure, for
instance, that the identical piece of coin now in my hand
still possesses the same weight, malleability, hardness, purity, &c., which I ascertained from actual observation that
it had only five minutes ago, if it were not for this irresistible belief in the uniformity of nature's laws. Whatever
doubts may perplex or weaken the inference from some to
all, these doubts do not concern the Primary Truth upon




INDUCTION AND ANALOGY.             389
which all such inferences are based, but relate solely to the
correctness of the Classification over which the inference
extends.  Is it certain that we have classified rightly?
that the cases brought together are really parallel in all
essential respects? If so, one instance is just as good to
base an Induction upon as ten thousand; for we have an
irresistible conviction that, as the law thus operates in one
case, it must so operate in all. What is the ground of our
assumption of this General Truth?  How came we to be
convinced thus absolutely that nature's course is uniform?
He who can answer this question has solved the great
problem in the philosophy of Induction.
Dr. Reid, Mr. Stewart, and most of the other Scotch
philosophers, attempt to resolve our assumption of this
Maxim into an ultimate fact, into an original and instinctive law of the human mind. Experience is constantly
tending to confirm it, but they hold that we believe in it
previously to all experience. They do not identify it with
the principle of Causation, - with the law that every event
must have a Cause, - but maintain that it is a distinct and
independent Axiom. Dr. Brown even goes so far as to attempt to resolve the law of Causality itself into this Axiom.
He asserts that we are obliged to refer every event, every
beginning to be, to some Cause, because we have an instinctive anticipation of the uniformity of nature's laws. My
own opinion, as will be seen hereafter, is exactly the reverse of Brown's theory. It seems to me that our irresistible conviction of the truth of this Maxim, that nature's
course is uniform, is resolvable into our necessary belief
of the law of Causality; that the latter is the primitive
judgment a priori, and the former is secondary and derivative; that a process of Thought, an act of Reasoning,
if not an appeal to experience, always precedes, and is
used to confirm or prove, our assertion that nature's course
is uniform, while we affirm at once, antecedently to all exs.




890             INDUCTION AND ANALOGY.
perience, and without any attempt at proof, that every
event must have a Cause.
But however this may be, the doctrine in which Brown
agrees with Reid and Stewart, that we have an instinctive
and a priori conviction that nature's laws are unchangeable, appears plainly indefensible.  _Entia non sunt mnultiplicanda Gprceter necessitatemn; it is a cardinal" maxim in
philosophy, that no principle can be admitted as an ultimate fact until it is clearly shown that it cannot be explained as derivative. Indirectly, therefore, this doctrine
is refuted by the proof, which will subsequently be attempted, that this principle is resolvable into the law of
Causality. But still further: — any conviction, which is a
priori in its origin and character, must be universal, necessary, and immediate. Now without going so far as Comte
and Mill, who maintain, with respect to this principle, that
"far from being the first Induction we make, it is one of
the last," that "it was only acquired gradually, and extended itself, as observation advanced, from one order of
phenomena to another," and that "there are cases, in
which we reckon with the most unfailing confidence upon
uniformity, and other cases in which we do not count upon
it at all"; —without adopting these assertions, I say, it
may safely be pronounced,- that we do not accept this principle at first, or in all cases, unless it is justified by some
reflection or experience; that is, until we have satisfied
ourselves that it is a necessary consequence of some intuitive and imperative belief, or have verified it by subsequent
observations. Through the law of the Association of Ideas,
it is true, the recurrence of any phenomenon suggests all
the circumstances by which it was originally accompanied;
it may even incline us to believe that these circumstances,
also, will recur in the same order as before. Even the dog
cowers at the sight of the whip which has once or twice
been used to punish him.  But this is very far from an




INDUCTION AND ANALOGY.            391
immediate and necessary conviction that any of these former concomitants nmust so recur. We stop to analyze the
case and make distinctions; we separate the conjunctions
that are believed to be invariable from those that are
merely casual, and accept the former only because we
recognize one of the events either as a Cause, or what is
believed to be the regular concomitant of a Cause, of the
other.
6 Every person's consciousness," says Mr. Mill, "' assures
him that he does not always expect uniformity in the course
of events; he does not always believe that the unknown
will be similar to the known, that the future will resemble
the past. Nobody believes that the succession of rain and
fine weather will be the same in every future year as in
the present. Nobody expects to have the same dreams
repeated every night. On the contrary, everybody mentions it as something extraordinary, if the course of nature
is constant, and resembles itself, in these particulars. To
look for constancy where constancy is not to be expected,
as, for instance, that a day which has once brought good
fortune will always be a fortunate day, is justly accounted
superstition. The course of nature, in truth, is not only
uniform, it is also infinitely capricious. Some phenomena
are always seen to recur in the very same combinations in
which we met with them at first; others seem altogether
capricious."
On the other hand, the doctrine of Comte and Mill, that
our conviction of the uniformity of nature's laws, which is
the ground or principle upon which all Induction rests, is
itself obtained by Induction, appears to be an evident begging of the question. How can any mental operation be
used as a means of discovering and verifying a principle
which must be taken for granted before that operation itself can be performed? To obtain a number of Conclusions
by adopting a certain Maxim as a Major Premise, and then




392           INDUCTION AND ANALOGY.
to use those very Conclusions as a means of proving that
Maxim, is evidently reasoning in a circle. Mr. Mill is perfectly aware of this objection to his doctrine, and frankly
states it in the strongest terms.  "Can we prove a proposition," he asks, "by an argument which takes it for
granted? And if not so proved, on what evidence does it
rest?"
But though aware of the objection, it does not appear
that Mr. Mill has been successful in his endeavors to obviate it. He rather augments the difficulty, by admitting
that the Maxim "' was not, of course, derived from rigid
Induction, but from the loose and uncertain mode of Induction per enumerationem  simplicem."  Then the Premise
rests upon less satisfactory evidence than the Conclusion,
and yet the latter is based exclusively upon the former.
Is not this a contradiction?  How can the superstructure
be more stable than the very foundation on which it rests?
Induction by simple enumeration "consists in ascribing
the character of general truths to all propositions which are
true in every instance that we happen to know of." Thus,
we say that "All ruminating animals divide the hoof,"
merely because no instance to the contrary has, as yet,
been discovered.  But " to Europeans, not many years
ago, the proposition,'All swans are white,' appeared an
equally unequivocal instance of uniformity in the course
of nature. Further experience has proved that they.were
mistaken."  Then the presumption in favor of what is still
the accepted rule, in the present state of our knowledge,
that all ruminating animals divide the hoof, would not be
held to outweigh the testimony of one unimpeachable witness, who should declare that, in some hitherto imperfectly
explored region, he had discovered a solid-hoofed ruminating animal. How can the evidence of these merely provisional truths, which are liable to be overturned at any
moment, be the same with that which supports the validity




INDUCTION AND ANALOGY.            393
of the Maxim upon which the most rigorous Inductions depend?
Mr. Mill answers, that even this precarious Induction,
that something is universally true because we have never
known any instance to the contrary, may become a valid
ground of belief when it is preceded by the assurance, that,
" if there were in nature any instances to the contrary, we
should have known of them." An empirical law, he argues,
" of which the truth is exemplified at every moment of
time, and in every variety of place or circumstance, has an
evidence which surpasses that of the most rigid Induction,
even if the foundation of scientific Induction were not itself
laid, as we have seen that it is, in a generalization of this
very description." As to the admissions made in the passage which has just been quoted from Mr. Mill, that we do
"not always expect uniformity in the course of events,"
and that " the course of nature, in truth, is not only Imiform, it is also infinitely capricious," it is claimed that the
progress of Inductive Science has already explained away
these apparent exceptions.  This progress has been so
great, it is argued, that we now know directly that the
Maxim holds good of far the greater number of phenomena, "the utmost that can be said being that of some we
cannot positively, from direct evidence, affirm its truth;
while phenomenon after phenomenon, as they become better known to us, is constantly passing from the latter class
into the former; and in all cases in which that transition
has not yet taken place, the absence of direct proof is accounted for by the rarity or the obscurity of the phenomena,
or our deficient means of observing them, or the logical difficulties arising from the complication of the circumstances
in which they occur."
But even when the doctrine is thus limited and explained, it does not appear to be relieved from the two fundamental objections which have been urged against it, first,
-17*




394           INDUCTION AND ANALOGY.
that it founds tile principle of Induction upon Induction
itself, which is reasoning in a circle, and secondly, that it
bases a stronger conviction upon a weaker one, a higher
probability upon a lower one. Granted, if you will, that
Induction itself, a rude Induction, gradually leads us to believe in rigorous scientific Induction; this may explain the
genesis of the phenomenon, or how it was that we were
first led to employ this organon of discovery. But before
we can accept the fruit of the Induction with the strong
and unhesitating conviction which we now accord to any
well-established Law of Nature, we must not only know
how we were first induced to believe that such a Law
exists, but we must find some valid principle which may
fairly be accounted a proof of its existence. Certainly such
proof cannot be obtained by reasoning in a circle. Mill
and Comte would have us believe, that our invincible conviction of the universality of the Law of Gravitation rests
upon no firmer basis than the opinion, which, indeed, is
daily gaining ground, and which the progress of mere Physical Science evidently tends to confirm, that everything in
nature is subject to law, so that it takes place by a physical necessity, and might be predicted with unerring confidence, if we had a perfect knowledge of its antecedents.
"Every event has some invariable and unconditional antecedent";- if we hesitate to admit this proposition in all its
generality, Mr. Mill thinks we cannot consistently believe
that all matter gravitates, that oxygen is necessary for the
support of animal life, or even that fire will burn and water
drown. We maintain that the latter propositions are incontestable, while the former, the principle of the universality of law, is merely a hypothetical conclusion, though
an extremely probable one. Accordingly, to base the latter upon the former is to make the superstructure stronger
than its own foundation.  Mr. Mill himself is compelled to
admit, with respect to one very large class of phenomena,




INDUCTION AND ANALOGY.            395
those of the human will, that at least one half of the speculative world, even in our own day, do not believe in the
universality of law, or that every event is necessarily determined by its antecedents. And with regard even to
physical events, a large and increasing number of philosophers, among whom are ranked Bishop Berkeley, Dr.
Samuel Clarke, and Dugald Stewart, hold that none of
them are subject to law, in the sense of being absolutely
determined by their physical antecedents, but are the results of volition, which is free to modify them at any moment. But without adopting this theory, he is a bold
advocate of the perfectibility of Physical Science who will
maintain that the probability of ultimately discovering that
phenomena still so apparently irregular and inconstant as
those of the weather, of health and disease, the countless
peculiarities of individual plants and animals, and the
equally numerous idiosyncrasies of human intellect and
character, are subject to fixed and definite laws, is so great,
that we may safely rest upon it all our confidence fin the
physical laws that have already been established; —that
this probability is the measure and the test of all the certainty that has hitherto been obtained in Physical Science.
Let us examine, then, the only remaining theory, which
is, that the ultimate Ground of Induction is the Law of
Causality, or the judgment that every event must have a
Cause,- not merely a constant physical antecedent, but an
eficient Cause. It is only necessary to show, that the Law
of Causality is readily and naturally explicated into the
Maxim that nature's course is uniform, so that the absolute and imperative conviction, which belongs to the formner as an a priori cognition of the human mind, is transferred, by an easy association of ideas, to the latter, though
not logically belonging to it.
Take the simplest case of Induction, by which we are
led to expect that any physical object will always continue




896             INDUCTION AND ANALOGY~
to manifest the same qualities that have hitherto been otserved in it, unless it is exposed to some new influences, or
a new antecedent is brought in. Here the assumption evidently is, that the qualities of the same thing are permanent, unless some Cause intervenes to change them; and
this assumption is logically certain, for it is an Immediate
Inference from the Law of Causality, that no change whatever can take place in anything without a Cause. The
coin must retain the same attributes which it was recently
observed to possess, if there has not been some Cause of alteration.  This proviso is the source of doubt which must
always arise when an unquestionable abstract truth is applied to real objects or actual events.  We never can be
sure that such a Cause of change has not intervened; but
we are morally certain that it has not, if there has been no
apparent alteration of the circumstances of the case, no
seeming exposure to new influences. To this extent, then,
we can safely reason from the past to the future, or from
some to all, when satisfied that the Classification is correct,
-that is, that no new occurrence or Efficient Cause has
destroyed the resemblance of the observed instances to the
expected ones, or of some to the others.
The next sort of Induction, though a little more complicated, is easily resolved into the same Law of Causality. It
has already been shown that among the other properties
of any particular substance must be ranked its active and
passive powers, that is, the changes in other bodies of
which its proximity has been a constant antecedent, or the
changes to which it is itself subject when brought into relation with other substances under different circumstances.
These active and passive powers, regarded as mere sequences of phenomena, may properly be reduced to the
preceding head of qualities; they form, as we have seen,
one class of the attributes of every substance, and, as such,
enter into the Intension of the Concept which denotes that




INDUCTION AND ANALOGY.             397
substance. In truth, what are called secondary qualities
are only the powers which bodies possess to excite certain
sensations in us, when brought into relation with our organs of sense. And in like manner, the capacity of gold
to be melted on the application of a sufficient degree of
heat is an integral part of our complex notion of this substance. Powers being nothing but qualities, then, the Law
of Causality is applicable just as in the former case; these
powers must be fixed or constant in their operation, if a
new Cause has not supervened to alter them. The general
maxim is one of absolute certainty, but in its application to
a given case we never can be sure that the proviso in it
has been rigidly fulfilled. This doubt must always remain,
and is usually more serious, and less capable of being reduced by further observation and experiment, as regards
the powers, than with respect to the other qualities, of bodies. The circumstances to be observed in order to prevent
the intrusion of a new antecedent are more numerous and
complex; we cannot so easily be assured that the cases are
strictly parallel. The unexpected presence of a little more
or less carbon may have diminished the fusibility of the
metal; if a large mass of iron be near, the action of the
magnetic needle is disturbed.
Still further;- it is now known that the merely physical antecedents and other circumstances are not the Efficient Cause of the phenomenon, but are believed to be its
regular concomitants only because their presence, thus far,
has been invariably followed by the effect. Accordingly,
whatever assurance we may possess that the outward circumstances are unchanged, it is still possible that the real
Cause may be so far modified that the expected result will
no longer be produced. The doubt which thus rests upon
the case cannot be dispelled by any precautions whatsoever.
The cases may be strictly parallel in every visible respect,
as tested by the nicest observations; but if the physical




398           INDUCTION AND ANALOGY.
antecedent was only the occasion, and not the. Cause, the
phenomenon may not be repeated, as it is always possible
that the true Cause may now for the first time exist under
different combinations.  To recur to the illustration taken
from Mr. Babbage's machine; — though, in countless instances, each number presented has been greater than its
immediate predecessor by unity, yet as this constant precursor was not the- true Cause which determined the number that was to come after it, it is always conceivable that
the next presentation should be of an entirely novel character.
We can now see why it is that the Maxim which is the
Ground of Induction, and on the assumption of which the
validity of all our reasoning about real objects and actual
events depends, appears so unquestionably true that we
regard it as an Axiom. To say that nature's course is
uniform, and that all events are subject to law, is only to
assert our intuitive conviction, that every phenomenon must
have an Efficient Cause, -that, while the Cause remains
the same, the effect must be constant and proportional to it,
and hence, that, whenever the true Cause is discovered, we
are enabled to predict unerringly the recurrence of the
effect. The relation between a true Cause - that is, an
efficient Cause- and its effect, is radically unlike that between a physical antecedent and its physical consequent.
No absolute conviction, no law of the human mind, manifesting itself anterior to all experience, and thereby first'
rendering experience possible, asserts any connection between antecedent and consequent like that which exists
between Cause and effect. The relation between the two
former, that of mere succession in time, is contingent, resting solely upon experience, and liable to be overturned at
any moment by subsequent experience; between the two
latter, it is a Causal relation, and, as such, is absolute and
unchangeable, for it is irreversible even in thought. What




INDUCTION AND ANALOGY.            399
do we mean when, as a ground of reasoning from some to
all, we assert that nature acts uniformly, or that all physical events are subject to law? Not, surely, that a given
antecedent must always be followed by that particular phenomenon which, according to all experience thus far, has
been its invariable consequent. This is the only conclusion which mere Induction aims to establish; but it is not
competent to serve as the Ground of Induction itself, or as
that Premise which must be taken for granted before reasoning by Induction is possible. But we mean only that
the sequence in question is necessary, if the antecedent is
the Efficient Cause (or the invariable concomitant, sign, or
precursor of such Cause) of the consequent. We mean
only to assert the existence of an irreversible law, and not
necessarily that such law has already been discovered.
Comte and all his followers will tell us that no event, however extraordinary and unexpected, is to be deemed a
miracle, - that is, a violation of law, - because the presumption is, that farther research will either reveal a new
law, or an improved expression of an old one, under which
the occurrence, however strange and marvellous, may naturally be subsumed. He will say, -to adopt a well-worn
illustration, - that the conversion of water into a solid was
a miracle to the King of Siam; but with our larger experience, it is no miracle to us, for we have even discovered
-the law,- that is, the constant antecedent, - under which
the formation of ice takes place. What is this but to assert
that our conviction of the universality and permanence of
-law, so far from being derived from experience, so far from
resting on that very process of Induction of which it is the
sole support, is strong enough to contradict all experience,
and to maintain its place as an Axiom, though contradicted
by the largest and most cautious Induction which human
science has ever framed?  Not even the resurrection of a
dead man, says the Positivist, would be a violation of




400            INDUCTION AND ANALOGY.
law;- then his conviction of the permanence of nature's
laws overrides all the evidence of experience, and contradicts the whole tenor of modern Inductive science.
What is called physical necessity is nothing but a conviction that the relation of an Efficient Cause to its effect is
unalterable, coupled with the assumption, which is a natural
one, but still illogical, either that the particular antecedent
or concomitant phenomenon is itself the Cause, or is so
closely connected with it that its presence must always be
followed by the recurrence of the effect. The only ground
of this assumption is the invariability of the succession in
time, or the fact that, so far as our experience, or as all
human experience, has extended, the one phenomenon has
always been the immediate consequent of the other. That
this ground is insufficient to justify us in calling the succession a necessary one has already been abundantly proved.
The Positivists, in their desire to eliminate the notion of
cause altogether, although they are compelled to retain the
word and all the associations connected with it, refuse to
attribute the phenomenon to any single antecedent. The
invariable sequence, they say, exists between a consequent
and the sum of its several antecedents, all of which must
concur before we can be sure of the presence of the effect.
In other words, what they call a cause is only an assemblage of the conditions, all of which must be fulfilled before
the phenomenon can be reproduced.  "The real Cause,"
says Mr. Mill, "is the whole of these antecedents; and we
have, philosophically speaking, no right to give the name
of cause to one of them, exclusively Qf the others." And
again, " the Cause is the sum total of the Conditions, positive and negative, taken together; the whole of the contingencies of every description, which, being realized, the
consequent invariably follows." Among these " negative "
conditions, or rather, as the sum of them, he ranks "the
absence of preventing or counteracting Causes."  In con



INDUCTION AND ANALOGY.             401
formity with this view, the distinction between agent and
vatient, between something which acts and some other
thing which is acted upon, is formally abolished, as it is
denied that there is any action in the case. An inevitable
corollary of this doctrine is, that there is no power or efficieney in any one of the antecedents the exertion of which
necessarily creates the effect. Yet the denial of any such
causal agency entirely refutes the hypothesis that there
is any necessary connection between the two events, and
leaves their union merely a contingent one, liable to be
dissolved or contradicted by subsequent experience.  By
rejecting the doctrine of Efficient Causation, the Positivist
theory throws away all evidence of the permanence and
universality of nature's laws.
This conclusion will appear still more obvious when it is
demonstrated, as can very easily be done, that every process of Inductive Reasoning, however rigidly conducted,
and however verified by subsequent observations, is still resolvable, in the last analysis, into the despised'" Induction
by simple enumeration," which Lord Bacon calls mera palpatio, or groping in the dark. The best evidence which
physical science has been able to collect in support of the
most generally recognized Laws of Nature amounts only to
this, that they are found to be true in every instance that
we happen to know of. Mr. Mill admits that Induction
necessarily commences with this very imperfect evidence;
and he should have added, that it also proceeds and ends
with it, finding no other or stronger basis on which to rest
its conclusions.
Nearly all the additional evidence which the advancement of science procures for those conclusions which were
at first avowedly accepted as inferences from Induction by
simple enumeration, (perhaps from an enumeration only of
a few instances, or even from a single case,) arises either
from extended observation and experiment, from an imz




402            INDUCTION AND ANALOGY.
proved classification of the objects about which we reason,
or from what Dr. Whewell calls, by a happily invented
phrase, the consilience of several Inductions. The process
of Induction, when considered as an operation of mind, or
as a sort of inference, is essentially one and the same, and
perfectly determinate in character.  There are not several
kinds of it, though there are various degrees of caution,
precision, and thoroughness with which it is carried out.
It is always employed with reference to a class of objects,
qualities, or events, whether that class be well or ill formed,
that is, whether the members of it do, or do not, agree
with each other in all material respects; and it always proceeds from some to all of that class, whether the conclusion
thus formed does, or does not, coincide or harmonize with
other conclusions obtained by a perfectly similar process,
though from other data, and with a different purpose in
view. The village matron, undertaking to prescribe for
tile illness of her neighbor's child from what she judges to
be the similar cases that have happened in her own family,
and Sir Humphry Davy, anticipating that his mode of
analyzing potash into the oxide of a new metal would not
only hold good of all other lumps of potash besides the
very one he was experimenting upon, but would be found
practicable, and would lead to similar results, in the case
of other alkalis and earths, are both alike reasoning from
Induction by simple enumeration. The only difference is,
that the diseases which affect the human frame are very
numerous, and, as they have but few recognizable symptoms, can be but imperfectly classified at best, and a village
matron would probably classify them very ill, so that her
inference from  some to all would be wrong; while the
alkalis are few in number, and have determinable and
strongly marked common qualities, so that the corresponding inference in their case was entirely safe.
Attempts -have been made at various times to frame what




INDUCTION AND ANALOGY.            403
may be called a " Logic of Induction," or a full analysis
and description of the operations by which we proceed to
the discovery of physical laws. Lord Bacon, who made
the earliest and most remarkable endeavor of this sort,
hoped to furnish a method of scientific investigation which
should be so complete and accurate as to constitute an organon of discovery, and reduce all intellects to a level,
making success in the search after truth a matter merely
of time and labor. Taught by experience that discoveries
cannot be thus made by rule, but are generally the results
of a tentative process many times repeated, and a happy
combination of circumstances, the later followers of Lord
Bacon have attempted merely to analyze and describe the
process by which discoveries have been made, without hoping to indicate any sure method of adding to their number.
But even this endeavor, though aided by all the lights of
modern physical science, and prosecuted by such eminent
thinkers as Sir John Herschel, Dr. Whewell, and Mr. J.
S. Mill, has had but very limited success. The results do
not agree; though the same compound phenomena are presented for examination, they are analyzed by these three inquirers into very different elements and processes of thought.
These theorists do not even hold the same opinion as to
the nature of the process which they have to separate into
its elements, or, in other words, as to what constitutes Induction. Dr. Whewell, fearful of resting the whole certainty of physical science upon so narrow and unstable a
basis as reasoning in respect merely to all the cases that we
happen to know of, boldly restricts the name of Induction
to what seems to be a mere generalization of the facts
already observed, but as now seen under a new light because succinctly comprehended in one general formula;.and appears to lose sight altogether of the necessity, if
science is to fulfil its office of anticipation and prediction,
of extending the generalization to all the objects and events




404           INDUCTION AND ANALOGY.
of a given class, whether they have yet been observed or
not. Mr. J. S. Mill, who has more confidence in the precautions and the means of verification by which men of
science test and confirm the rude Inductions of the vulgar,
justly asserts that Dr. Whewell's mere " Colligation of
Facts," far from being the type of Induction generally,
"is not Induction at all," but only a new description of
the phenomena. He undertakes to analyze and reduce to
system these precautions and means of subsequent verification, and to show that, when they are duly observed
and practised, scientific Induction differs in kind, and not
merely in degree, from Induction by simple enumeration,
and, though based merely on experience, establishes its
conclusions with the highest certainty of which the human
mind is capable. But experience, from its very nature,
cannot extend beyond a limited number of cases; and as
even the most cautious and rigorous Induction avowedly
has no other foundation than experience, either the absolute universality of the Laws of Nature is not scientifically
established, or it must be deduced from a priori considerations respecting the relation of an Efficient Cause to its
effects. The consilience of several Inductions merely extends the enumeration to a larger number of cases; but
any such extension, of course, cannot include future instances, nor in any way enlarge the domain of possible experience. In fact, most of the scientific processes, which
are ably analyzed by Mr. Mill, have reference to the use of
Induction as an organon of discovery, and not as a medium
of proof; they point out the inferences which we ought to
make, but they do not render any more stable the foundation by which all such inferences are supported. And any
improvements in the modes of observation, or in the classification of the things observed, are merely preparatory to
the process of Induction, and do not in any way affect the
essential nature of that process.




INDUCTION AND ANALOGY.            405
Putting aside the terminology invented by Dr. Whewell,
and also that recommended by Mr. Mill, as not even their
authority has sufficed to bring either into common use, it
may be said that there are but three phrases generally employed to designate those results of Induction which constitute the highest generalizations of science. These are
a General Fact, a Law of Nature, and a Cause, this last
being now usually understood to mean nothing more than
an Invariable Antecedent. Unfortunately, even these three
phrases are so wavering and uncertain in their signification, that they are often employed as synonymes, while
hardly any scientific person is consistent in the use which
he makes of them, and no two writers upon the philosophy
of the physical sciences agree with each other in the attempt to limit and define their meaning.
The first of the number, a General Fact, though employed with somewhat more precision and consistency than
the other two, is yet of narrow and indeterminate range,
and is grudgingly used, because it is modest in pretension,
and does not feed the pride of science, or gratify the vanity of the inquirer into the secrets of nature. It coincides
with what Mr. Mill calls an Empirical Law, or the result
of an Induction by simple enumeration. Thus, it is properly a General Fact that all horned animals are ruminant,
that all quadrupeds are viviparous, that every living thing
is produced from an egg, that opium and alcohol intoxicate,
&c. But the phrase is sparingly used, because we are not
content simply to point out a new characteristic of a whole
class of objects, or to form a new class of facts by tracing
their hitherto unsuspected agreement with each other, so.
far as our observation has extended, in some latent attribute. We aspire to the much higher praise of determining a new "Law of Nature," which must hold true on all
occasions, whether observed or not, and the discovery of
which is therefore equivalent to a revelation of another of




406            INDUCTION AND ANALOGY.
the immutable purposes of the Almighty.  The General
EFact is admitted to be true only so far as our observation
has extended, or at any rate to afford comparatively but a
slight presumption that it will be found to hold good in
cases as yet unobserved.  But as already remarked, the
narrower and the more definitethe class, the stronger is
this presumption. Thus, that every antelope is ruminant,
is a far more probable conclusion than that all horned animals are ruminant; we admit very readily that all the
mammalia are produced -from eggs, but not so readily that
the whole animal kingdom are thus produced.
A Law of Nature, in its more definite signification, is
employed to designate a group or series of General Facts,
relating to the same subject or class of subjects, and differing from each other by some mode of proportional variation, so that the place of every member of the series may
be easily deduced from one numerical formula. Such are
Kepler's laws of the planetary motions, the law of definite,
reciprocal, and multiple proportions in Chemistry, and of
phyllotaxis in Botany. The General Facts may be known,
long before their relation to each other, or their law of
proportional variation, is discovered. Thus, the General
Fact that the leaves of the apple-tree are disposed in cycles
of fives, and so that the spiral line connecting their points
of insertion passes twice round the stem for each cycle,
their arrangement being thus conveniently denoted by the
fraction 2, was ascertained, and a corresponding General
Fact for many other species of plants was equally well
known, before the " Law " was discovered, that the resulting fractions fall into a series, any one of which has for its
numerator the sum of the two preceding numerators, and
for its denominator the sum of the two preceding denominators. So, also, the General Facts in Optics, that'the
angle of refraction, measured from  the perpendicular to
the surface of any medium heavier than air, is always less




INDUCTION AND ANALOGY.            407
than the angle of incidence, and is not proportional to it,
were commonly known, and even Tables had been laboriously formed, giving experimental measures of refraction
for the various angles of incidence, and for different media,
many centuries before Snell, in 1621, superseded the use
of many of these Tables by discovering the simple Law
of Nature, that the ratio of the sines of the angles of
incidence and those of refraction is constant for the
same medium. Every measurement of refraction as formerly given in those Tables was a General Fact, including every case of a ray of light falling upon the given
medium at the given angle; and this Fact was obtained,
of course, by reasoning Inductively, that as the refraction
for this angle of incidence and this medium had been actually observed to be of this magnitude in some cases,
(namely, in all that had been observed,) it would be
found of the same magnitude in all such cases. Snell's
discovery of the "Law" took the place of an immense
number of such Facts, by summing them all up in one
general proposition or formula, thereby rendering any detailed mention of them unnecessary.
Such a discovery as this by Snell is what Dr. Whewell,
by a happily selected phrase, calls a " Colligation of Facts";
and the process by which it is arrived at -the method, if
there be one, of making such a discovery -is what he denominates Induction. Mr. Mill very properly objects, that
it is not Induction at all. It is an act of generalization,
founded on direct intuition of the relations which the cases
actually before us bear to each other, and not professing to
extend beyond these cases. Consequently, it does not enlarge our knowledge, as Induction always does, but only
grasps up together into one Concept the knowledge which
we already possessed; and it accomplishes this through
perceiving that this group of General Facts, instead of
being entirely heterogeneous, as they at first appeared,




408           INDUCTION AND ANALOGY.
are really linked together by some common relation, the
expression of which reduces them to unity in the Understanding, and so renders them more easy to be remembered and more convenient to be used.
It is true, as Mr. Mill remarks, that a real act of Induction usually goes along with the Colligation, as subsidiary
to it. In this case, Snell not only took for granted the
previous Inductions, which, as we have seen, are expressed
in the separate General Facts that he grouped together in
his formula, but also, having ascertained by actual observation that this formula held true for refraction in some media,
he reasoned Inductively that it would hold true for all
media, or, in other words, that it was the universal Law
of refraction.
It ought also to be remarked, that the discovery of the
Law which colligates the General Facts does not change
the nature of the evidence on which those Facts depends,
or raise them out of the rank of Probable, into that of Demonstrative, judgments. These Facts are still nothing but
truths of Induction, just as much after the discovery of the
Law as they were before it. The discovery, it is true,
makes the previous Inductions somewhat more probable
than they were before; but it does not by any means demonstrate them. The degree of probability is increased
through the discovered consilience of the Inductions, as this
consilience amounts to increasing the basis of enumeration on which each of them rests. A number of conclusions affecting a group of kindred subjects are mutually
strengthened, when it is found that the separate Induction
leading to each one of them harmonizes in one respect,
or in several respects, with the Inductions leading to all
the others; for such harmony is precisely what we expect,
in view of the Maxim on which all Inductive reasoning
depends, that nature's course is uniform. Each Induction
stands more firmly, when it not only rests on its own fount




INDUCTION AND ANALOGY.             409
dation, but is indirectly supported by the foundations of its
neighbors.
According to the view here given,. a Law of Nature is a
generalization of the second order; in some respects, it
bears the same relation to General Facts, that a General
Fact bears to Individual Facts. I say "in some respects";
for this statement does not convey the whole truth. A
Law of Nature is not a mere truth of classification; it is
not merely a Genus of which the several General Facts are
the Species. If it were, then the tabulated measures of
refraction, or any other mere collection of General Facts
relating to the same class of subjects, might be called a
Law.  But it is not so; a Law may be contained in such
a Table, but it is concealed there, and when discovered,
the Table itself becomes useless. The discovery, as I have
said, consists in a perception of the truth, that the group
of General Facts fualls naturally into a series, in which the
place or power of any term is easily deduced from a single
brief formula.  The effort of mind by which such a discovery is made is rather an Intuition, or a happy conjectare, than an Induction. The kind of conviction which
attends the discovery, when made, is not mere probability,
but certainty. With reference to the General Facts actually before us, we know that the Law is there, for we see it
just as soon as we have learned where to look for it. But
the universality of the Law, the extension of it to all other
General Facts, not now observed, of the same class, is the
result of an Induction; and the establishment of the Law
zalso takes for granted the validity of the preceding Inductions on which each separate General Fact depends. Here,
as elsewhere, whenever we attempt to extend our knowledge beyond what is actually observed, our only guide is
Induction by simple enumeration.
The process of hunting for a Law of Nature amid a
group of General Facts is essentially tentative, resembling
is




410            INDUCTION AND ANALOGY.
an attempt to find the meaning of a riddle; we try one
guess after another, and at last stumble upon the right one
when we least expected it. Success is usually obtained,
not by trying to extend the survey, or to contemplate the
largest possible number of cases, but by restricting the
field of search to a few well-chosen instances, and attempting to find a pattern or construction which these few will
precisely fit. To take an example from a quarter where
we should least expect to find one, —from pure mathenatics; Newton discovered the Binomial Theorem, which
is a true Law of Nature according to our definition, probably by simple inspection of a, few of the lower powers of
binomials, the law of the exponents being obvious enough,
and that of the coefficients offering but little difficulty to
his marvellous insight.  He certainly discovered and used
the Theorem long before he endeavored to demonstrate it,
or to trace it to its true mathematical principles. There
is reason to believe that not a few of the general theorems
of the higher mathematics have been discovered in a precisely similar manner.
Why the Law should be suddenly revealed to a single
happy glance, when it had previously escaped the most
laborious research, is a curious problem, which perhaps
admits of no complete solution, though the process may
be elucidated in a few particulars. The essential characteristic of such a Law is a series proceeding by some uniform gradation, the relation between two or more consecutive terms in any part of it being the same as that existing
between the corresponding terms in any other part. This
relation may be simple or complex, recondite or obvious.
Each term may be an increment of its predecessor by the
addition of a constant quantity, or may be a simple multiple of it, or may be related to it through some of the periodic magnitudes connected with a varying angle, such as
the sine, tangent, secant, &c.;'or the law of progression




INDUCTION AND ANALOGY.             411
may be covered up, as it were, by a constant quantity
added to each of the terms; or the numbers, as we have
them, may be the complex results of two or more independent series multiplied into each other, in which case there
are two or more independent Laws to be discovered. Two
difficulties, then, are to be overcome, either one of which
would seem to be insuperable if the other had not been
previously mastered; we must properly arrange the terms
of the series before the Law of it can be discovered, but a
knowledge of the Law is indispensable before we can with
certainty make such an arrangement.  In a contest with
so many and so serious difficulties, it is not surprising that
success at last should often seem attributable quite as much
to accident, as to sagacity and dogged perseverance.
Kepler has furnished an instructive narrative of his successive attempts to reduce to Law the astronomical observations of Tycho, constructing many formulae by hypothesis,
finding that one after another would not fit, and, after each
disappointment, trying again with unwearied patience. At
last, his perseverance was rewarded with the discovery of
the great Laws which deservedly bear his name, as they
are the foundations of the whole modern science of astronomy, for they sum up in three sentences all recorded astronomical observations.  He also attempted, in a similar
way, to detect the Law concealed in the measured angles
of refraction, by comparing them with the angles of incidence through a variety of constructions by triangles, conic
sections, &c.; but all without success.  Where he failed,
Snell succeeded, twenty years later, merely by turning his
attention from the direct measures of the angles to the ratio
of their sines. The law was then manifest at a glance.
Such instances are needed to remind us, that the wellknown fable of Columbus and the egg is not a caricature,
but a faithful representation, of many of the greatest discoyeries in science.  What Dr. Whewell happily calls




412           -INDUCTION AND ANALOGY.
c" the ex-post-facto obviousness of discoveries, is a delusion
to which we are liable with regard to many of the most
important discoveries."
The validity of a Law of Nature thus discovered, as it
were, by a happy casualty, is regarded as sufficiently established by comparison with but very few of the observed
data from which it was educed. Thus, Dalton's magnificent generalization, coextensive with all matter, and now
verified by almost countless analyses, that chemical elements combine only in definite, reciprocal, and multiple
proportions, was first suggested to him during his examination of only two compounds; "and was asserted generally," says Dr. Whewell, " on the strength of a few facts,
being, as it were, irresistibly recommended by the clearness and simplicity which the notion possessed." What is
the ground of this bold anticipation of the universality of a
Law as yet verified only by a very few examples, when, in
the case of a General Fact, as already shown, a very extensive Induction may still leave us in doubt whether the
supposed truth may not be contradicted by the next instance that arises?  In general terms, the answer is obvious. Simple uniformities, such as are comprehended in a
General Fact, may be merely accidental; to recur to an
instance already cited, all ruminating animals now known
divide the hoof; but as the number of such animals is not
very great, this simple coincidence of two properties may
be as casual as tile experience of an individual observer
who has never happened to see a squint-eyed person that
had not also brown hair. But complex uniformities, such
as are marshalled into the symmetrical series called Laws
of Nature, and thus expressed in one formula, cannot be
regarded as accidental. As the number of individual facts
comprehended in one of these series is very great, it is incredible that mere chance should throw even a portion of
them into symmetrical groups, bearing a constant ratio to




INDUCTION AND ANALOGY.             413
each other.  Hence, if we can detect but a portion, even a
fragment, of such a series, we feel assured that it will prove
to be continuous, that the Law will not change, that the
uniformity will be carried out to the end.  Only the action
of a permanent and unvarying Cause, it is assumed, could
so harmonize results. Nay, so strong is our assurance of
the universality of the principle thus discovered, though it
seems as yet very imperfectly verified, that, when an anomalous or inconformable instance actually arises, we seek at
once for the means of eliminating it, or explaining it away,
instead of allowing it to wrest the inchoate discovery out
of our grasp and send us to the work of research again.
We class the exception immediately among those apparent
exceptions which really confirm the rule; -just as we
now see that the rising of a balloon in the atmosphere does
not contradict, but actually verifies, the Law of gravitation.
We come, then, to the conception of a physical Cause, as
indicating the third or highest stage in the generalizations
of science, and therefore as bearing the same relation to a
Law of Nature, that such a Law bears to a General Fact.
As thus understood, a Cause is simply a higher Law, under which several inferior Laws are subsumed; it appears
as the original principle, of which these lower Laws are
the derivatives by immediate and necessary consequence.
Thus, the theory of gravitation, or the doctrine that every
body attracts every other body with a force which is directly as its mass and inversely as the square of its distance, is the statement of a universal principle, under which
not only Kepler's Laws of the planetary motions, but the
Laws of falling bodies, of the equilibrium of fluids, &c., are
subsumed in this sense; — that if we take for granted the
existence of the force or physical Cause, termed Gravity,
which this theory assumes, then these inferior Laws may
all be deduced from it by Demonstrative Reasoning. That




414           INDUCTION AND ANALOGY.
such Deduction is possible, is the only proof we have that
such a force or Cause exists. The hypothetical force, for it
is nothing more, represents the inferior Laws that are subsumed under it, merely because it is an expression of them
in a single formula. It may well happen that two or more
such formulas may be devised, differing essentially from
each other,, yet answering equally well all the conditions
of the case, as the given Laws may logically be deduced
from either of them. For instance:- all, or the greater
part, of tile Laws of vision and light may be explained with
equal precision and accuracy either on the doctrine of emission, or on the undulatory theory. Two such hypotheses
correspond to two very dissimilar engines, which different
mechanics might invent, in order to cause the hands of a
clock to make the required movements over the dial-plate,
or the little balls in an orrery to counterfeit the motions of
the solar system. It is no more necessary to suppose that
such an attractive force as Gravity, or such a luminiferous
ether as the undulatory theory treats of, actually exists,
than it is to believe that a set of wheels and pinions, like
that which moves an orrery, really produces the motion of
the planets. All that the theory does for us is to represent
~the phenomena correctly; no one who understands the
subject supposes that the hypothetical force or Cause, which
is merely a convenient supposition for the theorist, actually
produces those phenomena.
It is evident that such Causes as we are now speaking
of are merely the highest generalizations of Physical Science, and that the invention of them - for they are rather
invented than discovered -affords not the slightest additional evidence of the universality of those Laws of Nature
which they represent, or which are subsumed under them.
The proof, indeed, proceeds in the opposite direction; the
only evidence we have that the right Cause has been assigned is, that it correctly represents the Laws which are




INDUCTION AND ANALOGY.             415
placed under it. When it is demonstrated that the Law
may be deduced from such a Cause, the real course of the
argument is, from the admitted validity of the Conclusion
to infer the soundness of the Premise.  Gravity does not
cause heavy bodies to fall to the ground, nor does it bind
the planets to their orbits; but Gravity is rightly considered as a "4 physical Cause," in the technical sense of that
phrase, because its hypothetical existence enables us correctly to represent in a single formula the phenomena of
falling bodies and of the planetary motions.
The higher generalizations, then, depend exclusively, for
proof of their correctness, on the validity of those which are
next below them. When the proper Law of Nature is
provisionally assumed, certain consequences can be demonstrated to follow which agree with the General Facts that
were previously established on Inductive evidence; when
the proper physical Cause is assumed, we can logically
make certain Deductions from it which harmonize with the
Laws of Nature which this Cause was invented to express.
Neither the Law nor the Cause brings any additional evidence of its own, but both alike depend for proof, in the
last analysis, on the validity of the Induction by simple
enumeration by which we first collected their common
basis, the General Facts.  The process of verifying both
consists in enlarging the Induction, but not in altering its
character; both the Law and the Cause being assumed to
be universally true, we make further Deductions from
them, and still find these to coincide with the observed
Facts. In other words, we first reason Inductively from
some to all, and then, assuming provisionally that the principle holds true of al, we reason from it Deductively to
other some, and find that these also are confirmed by observation, so that they reflect evidence upon the Law or the
Cause of which they are the logical consequences. Turn
the matter as we may, Induction by simple enumeration is




416            INDUCTION AND ANALOGY,
still the basis of the whole procedure, and the discovery, or
invention of Laws of Nature, or physical Causes, only supplies names and formulas of expression for the successive
steps of generalization, as we form one after another the
proper hierarchy of Concepts.
We can now see more plainly than before the correctness of the doctrine already advanced, that the strong and
unhesitating belief which we accord to any well-established
Law of Nature, and which we indicate by saying that an
event happening under it takes place by a phAysical necessity, is not due to the strength of the Induction through
which the Law was discovered, but to our absolute a priori
conviction of the fixedness of the relation which connects
every effect with its efficient Cause. The Law is discovered
by Induction; but it is proved by a different process, - by
bringing it under a necessary a priori conception of the
human mind, that of Efficient Cause, and thereby subjecting it to the principle of' Causality, that every event must
have a Cause, and must be proportional to that Cause.
In speaking of the use which is sometimes made of Inductive reasoning in pure mathematics, as in the case of
Newton's discovery of the Binomial Theorem, Mr. Mill
maintains that the process of thought in such cases is not
an Induction properly so called, but is governed by certain
"a priori considerations (which might be exhibited in the
form of demonstration), that the mode of formation of the
subsequent terms, each from that which preceded it, mzust
be similar to the formation of the terms which have been
already calculated." But it was certainly Inductive in this
respect, that the observed regular formation of the first few
terms of the series originally led NeWton to anticipate that
all the other terms must be formed in the same manner,
and to act upon this anticipation, - that is, confidently to
use the Theorem for a long time, - without giving himself
the trouble to work out a demonstration of it. Undoubt,



INDUCTION AND ANALOGY.             417
edly he had a strong belief that such a demonstration was
practicable; and this belief prompted him to acquiesce with
greater confidence in the result of the Induction.  For this
very reason, this instance appears to be a typical and instructive case of Inductive reasoning. Pure Induction is
exclusively an organon of discovery, a clew for anticipating
facts not yet observed and truths not yet proved. The
Ground of the Induction, that is, the proof, if it may be
called such, or the source of the confidence with which we
accept its conclusions, is an indistinct assurance, derived
from a priori considerations, that the results might be demonstrated, if we were acquainted with all the circumstances
of the case. Newton's assurance was founded on his indistinct anticipation of the truth, that the formation of the coefficients of the series must depend in some manner on the
laws of the permutation and combination of numbers, —
an anticipation which he did not stop to work out and
verify.  The physicist's assurance is based primarily, as
we have seen, on his necessary conviction that every event
or change must have an efficient Cause, a truth which
is readily explicated into the maxim that Nature's course
is uniform; and secondarily, upon his belief that the proportional variation of the successive terms in such a series as is called a Law of Nature is another consequence
of the axiomatic principle of Causality, that effects must be
proportional to their Causes.  The physicist's anticipation
cannot be verified, because, in the physical universe, Efficient Causes lie beyond the reach of human insight.  We
can discover nothing but Invariable Antecedents. But so
strong is the bias which leads us to identify an Invariable
Antecedent with an Efficient Cause, that the phraseology
of Causation is still employed throughout our investigations,
though it has been demonstrated over and over again, that
constancy of sequence is no certain indication of causal
efficiency.  We still speak of physical Causes, of acgents
18 *.AA.




418            INDUCTION AND ANALOGY.
and their action, of forces and powers, although it is now,
admitted on all hands that we mean nothing by such
language, when employed with reference to the material
universe, except "constant relations of succession or of
similarity." The very persistency of this inappropriate
phraseology indicates quite clearly the source of our conviction that Nature's course is uniform, and her Laws unchangeable, except by Him whose infinite wisdom first
established them, and whose unvarying purposes and modes
of action they express.




SOURCES OF EVIDENCE AND CAUSES OF ERROR.   419
CHAPTER XIII.
THE SOURCES OF EVIDENCE AND THE CAUSES OF ERROR.
INTUITION is not only the source in which all our
- knowledge originates, but it is the universal basis of
certainty, or the sole ground of the confidence with which
we accept any facts or truths as known. What we directly
or immediately perceive, whether by the external senses
or by consciousness, that we know. What is not thus directly perceived is entitled to be called knowledge only in a
secondary or derivative sense; properly speaking, it is only
an inference from our knowledge, and however legitimate
this Inference may be, it is worth nothing if the truth of
one or more Intuitions, on which it depends, be not previously taken for granted. Take even Demonstrative Reasoning, for instance, in which it is rightly said that the
Conclusion is a necessary inference from the Premises.
Still, before we can accept this Conclusion as certain, we
must assume that both the Premises are true. Now, whatever be the nature of the Major Premnise, the Subsumption
must express, either directly or indirectly, a truth of Intuition. We can knowingly assert that a given object possesses a certain attribute, or bears a certain relation of likeness or unlikeness to some other object, only through our
direct perception of this fact either by sense or consciousness; and such an assertion must enter into every act of
Reasoning, as one of the grounds on which the Conclusion
rests. Any Reasoning, then, by which we might attempt
to doubt or deny the validity of our Intuitions, would be




420           THE SOURCES OF EVIDENCE
self-destructive; for in such Reasoning, the truthfulness of
our Intuitive faculties must be presupposed, or taken for
granted. We should, by such scepticism, deny the legitimacy of our dwn denial.
Intuition, therefore, is the highest source of evidence,
and the ultimate foundation of all certainty. If we cannot accept, as absolutely true, what we immediately perceive, or are conscious of, then we can know nothing; we
cannot even know that we do not know. But before we
place this absolute reliance upon Intuition or Perception,
we must carefully distinguish what it is that we really perceive, or, in other words, what that is of. which we have
an Intuition. In ordinary mental action, Inferences are so
quickly and habitually drawn from Intuitions, and thereby
so closely blended with them, acts of comparison and generalization also entering into the compound result, that it
becomes extremely difficult to separate the pure Matter of
Intuition, of which we are absolutely certain, from the
heterogeneous ingredients which are thus united with it,
and of which we are not by any means equally sure.
Hence it is often said that our senses deceive us, when
the truth is, that we are mistaken only in the Inferences
which we have incorrectly drawn from the data actually
furnished by the senses. Thus we are often deceived into
accepting a counterfeit as a good coin; but the mental act
which thus leads us into a mistaken belief is really compound, embracing an act of memory, one of generalization, and one of Reasoning. The little object placed in
our hands for examination is perceived to have a certain
color, weight, shape, stamp, &c.; and it is impossible that
these qualities should be, to us, in any respect different from
what they are perceived to be. But when we proceed to
compare these qualities with others which we remember to
have perceived at some other time in good coins, and to
infer from their similarity that this supposed coin is not a




AND TEE CAUSES OF ERROR.            421
counterfeit, it is evident that we are exposed to many
sources of error. Even if we go so far only as to designate one of these qualities by its Common Name, - to say,
for instance, that this coin is yellow, — we go beyond the
Intuition, and, so far, become liable to mistake; it may well
be that we have but an imperfect recollection and imagination of the color which is usually so called, and therefore
may be mistaken in supposing that this color is so similar
to it as to merit the same name. In like manner, any
other comparison, as of the weight, shape, or stamp, as it
requires either memory, if both objects be not actually before us, or a decision as to the degree of similarity, if they
are both present to sense, must involve an element of uncertainty.
The question has been raised, whether external objects
are directly perceived by us as external, or whether their
externality is an Inference subsequently drawn from this
-perception as combined with others, and as governed by
the necessary and a priori convictions of the mind. In
other words, is the externality of the object, or the fact
that it is something different from myself, that it is not-me,
a constituent part of the Intuition, or only an Inference
from it? If the former supposition be true, then I know
that the external world exists, and any Reasoning upon the
case, either for or against this knowledge, is superfluous,
and even illogical; for as Reasoning must involve and depend upon Intuition, it cannot contradict Intuition. But
if the latter supposition be correct, then the reality of the
outward universe is not, strictly speaking, known, but only
inferred through an act of the understanding, which, as it
purports to relate to real objects, and not to a mere conception of the mind, certainly may be a mistaken one.
The question is an important one, but the full discussion
of it belongs to Metaphysics, and not to Logic. We can
only consider here the nature and the relevancy of the evi



422           THE SOURCES OF EVIDENCE
dence adduced, regarded as illustrating the general laws of
evidence. Thus much, I think, must be admitted, that
the mind, in its adult state, is immediately conscious of the
affections of its own bodily organism as such, - that is, as
affections of the body, which is foreign to itself, or a part
of the not-me; for we localize these affections, or refer them
instantly, and without an act of reasoning, to the affected
parts.  Thus; I am immediately conscious of a pain, not
merely as a pain, but as a pain in the foot, in the hand, or
in the head, the Intuition extending to the locality, just as
much as to the severity, of the affection.  But it is said
that the pain, being a sensation, can exist only in the sentient mind, and not in the unsentient matter of the body.
Very true; but the question then arises, Where is the mind?
You have no right to confine it to a certain part of the
body, - to the brain, for instance. I say, that the mind is
wherever it feels; for its feeling- its state of consciousness
-is the only evidence that we have of its existence. It
is present, at least, to the whole nervous organism. As we
certainly feel at the tips of our fingers, it is little more.than
tautology to assert, that that which feels is existent at the
tips of the fingers.  It is admitted that this doctrine of the
ubiquity of the mind to the body is incomprehensible; we
cannot see how it is thatthe thinking being should be " all
in every part" of its extended nervous organism.  In like
manner, many physical facts, especially those of electricity
and magnetism, and whatever involves the action of what
are called Polar Forces, are inconceivable; but this is no
reason for doubting their reality, when they are evidenced
by Intuition. But if the mind immediately localizes its
sensations, if it. perceives that the pain is here, and not
there, then it is immediately conscious of its own body as
extended, and therefore of space and externality.
This is a mere outline of Sir William Hamilton's doctrine of our immediate perception, or consciousness, of the




AND THE CAUSES OF ERROR.            423
external world. It appears to disprove very satisfactorily
Kant's counter assertion, that space is wholly subjective,
-a mere law of our perceptive faculty, which imposes
the modes of its own being upon the constitution of the
objects which it perceives.  But while the Hamiltonian
doctrine seems to hold good of the adult mind, it is not so
clear that it would apply to the perceptions of an infant.
It may be questioned whether, at the dawn of our existence, our sensations are distinctly referred.to outward
things, or that the perceptions by which they are accompanied appear to be anything else than states of our own
consciousness. An infant's world, it may be suspected,
lies entirely within himself; and if so, the subsequent
reference of these perceptions to external realities must
be produced, or aided, by experience and an act of Reasoning, and the knowledge or belief thus gained is no longer
exclusively Intuitive.
Passing over this metaphysical question, however, it is to
be observed that Memory, as a source of evidence, stands
next in extent and importance to Intuition. In many cases,
the two are so closely interwoven with each other, as we
-have just seen, that facts are often loosely said to be Intuitively known, when we have no better evidence of their
existence than is afforded by Memory. Intuition, as such,
is always present, relating only to what exists now and
here; past Intuitions can, be now known to us only by an
act of remembrance; and as the strength of a chain is the
strength of its weakest link, that which we did know Intuitively, can be now accepted only on the strength of our belief that we remember rightly.- In like manner, when we
are judging of Individual Objects by comparison, or are
ascertaining their relations to each other, or to a class of
cognate Objects, the results of the observation will not be
Intuitively certain, unless all the related objects are present, at one and the same moment, either to sense or con



424            THE SOURCES OF EVIDENCE
sciousness; if all are not thus present, then, to the extent
of this deficiency, objects actually observed must be compared with those which are merely remembered.  Moreover, as Locke and Dugald Stewart have remarked, even
in mathematical demonstration, we have not, at every step,
the immediate evidence of Intuition, but only that of
Memory.  The whole science of geometry hangs together
by a continued chain of Intuitive judgments; but in the
case of any advanced theorem, it is not to be supposed that
we can carry in mind, as simultaneously present to consciousness, all the truths, previously established, which must
concur in order to support this particular demonstration.
In by far the greater number of instances, we trust entirely
to judgments resting on the evidence of Memory. At the
close, before we can accept the Conclusion as demonstrated,
we must remember tile whole chain so perfectly as to be
sure that nothing has been left out; we must recollect not
only that we have proved, but how we proved, each point.
Practically, then, the truths of geometry, and all other*
Conclusions dependent on a chain of Demonstrative Reasoning consisting of more than two or three links, must be
accepted on the evidence of Memory quite as much as on
that of Intuition. Of course, the Inductive Sciences, including, as they do, a vast collection of facts, are dependent,
to a still greater extent, upon this source of evidence.
But the edifice of Science, when it is thus shown to be
largely dependent upon individual recollections, would seem
to rest on a very insecure basis. The defects of Memory,
as every one is aware, are both numerous and grave. It
is capricious, it often fails us when we most need its aid,
and it exists in very different degrees in different persons.
We might be tempted, at the first glance, to pronounce it
one of the most untrustworthy of all our faculties. But on
closer observation, it will appear that the faults with which
it is chargeable are not so serious as we might at first sup



AND THE CAUSES OF ERROR.            425
pose, and, especially, that they do not much diminish its
usefulness, or the confidence which we place in it, as an
indispensable means for the progress of Science. In the
first place, its faults are rather negative than positive in
character; we often forget, but we are very seldom mistaken in what we think that we distinctly remember. In
truth, a remembrance, seemingly clear and distinct, of
what we have but recently observed, especially if the phenomenon be of a simple and definite character, must be
placed next to Intuition as a ground of certainty. The
distinction between a pure Intuition now present to the
mind, and a distinct recollection of a very recent one, experienced perhaps within the last hour, is theoretical rather
than practical. In the ordinary conduct of life, no one
would think of maintaining that the former was more trustworthy than the latter. Our judicial tribunals, in grave
matters involving property and life, will not allow the clear
and distinct recollections of a witness, though extending
over a much longer period, to be even called in question.
Still, the theoretical distinction exists; Intuition, as the
basis of-Demonstration, has absolute or logical certainty,
and does not admit of degrees; while Memory is confessedly subject to error, and therefore is a source only of
probable evidence, though, in its highest degree, it amounts
to what is called moral certainty.
And here another distinction must bedrawn.  We mutst
distinguish, as Hamilton has done, between the simple fact
that we do remember, or think that we remember, a certain phenomenon, and the truthfulness of this act of remembrance, or our belief in the former actual existence of
that phenomenon. The former is matter of direct Intuition, and therefore does not admit of doubt; the latter rests
merely upon probable evidence, and may be a mistaken belief. Memory may be compared to a witness giving testimony in a court of justice'; the judge and jury cannot




426            THE SOURCES OF EVIDENCE
doubt that he does testify to this or that occurrence, for
they have sensible - that is, Intuitive - evidence of the
fact; but they may well doubt whether he testifies truly,whether the occurence in question ever took place. It is
only in this last respect, the correctness of the representation of what we remember, that the faculty of Memory is
said to be a source of merely probable evidence.
It is to be observed that the art of writing is a most valuable auxiliary to the faculty of Memory, inasmuch as a
proper use of it may obviate, in great part, the uncertainty
that would otherwise attach to this source of evidence.
Remembrance is more perfect, that is, more clear and distinct, and thus more trustworthy, according as the Intuitions which it preserves and stores up are more recent.
But a written record of the observations, taken at the
time when they were made, or as soon afterwards as might
be, keeps the evidence as perfect as it would be if Memory were not liable to be impaired by the lapse of time.
The possession of such a record may enable even future
generations to accept the evidence of the occurrence with
as full confidence as if it had. been observed by their contemporaries only a few days, or a few hours, before. Of
course, the age and genuineness of the document must first
be proved, just as we must first establish, on satisfactory
grounds, the verapity and competency of the witnesses who
testify to contemporary events which we have not ourselves
observed. But this being done, and it is generally about
as easy to do in the one case as in the other, the evidence
remains as perfect after the lapse of centuries as it was at
the time when the record was made. Time is thus deprived of its power to wipe out by degrees the recollection
of events.  Many facts in history, though of very old date,
must be admitted to be now as firmly established as if they
had taken place within the lifetime of the present generation.  Thus, the fact that a deed of privileges, called the




AND THE CAUSES OF ERROR.            427
Great Charter, was granted by King John to the English
people, June 5, 1215, is even now as firmly established as
that of the passage of the Reform Bill in 1832; and the
precise nature and extent of the franchises granted are as
fully known in the former case as in the latter, for in both
cases the original parchment rolls, on which these titledeeds of freedom were first engrossed, and attested by the
seals and signatures of those who were parties to them, are
yet extant.
We dwell upon this point as one of some importance, because it has been wrongly maintained, in reference to what
may be called the historical part of Christianity, that as the
mere lapse of time slowly, but surely, wears away all historical evidence, the greatfacts on which our religious faith
depends must become subject in future centuries to so
much uncertainty as to be wholly unworthy of credit.
The proper answer to this assertion is, that nothing less
than a. general conflagration, which should burn up all the
written and printed records now in existence, could make
these facts, to any appreciable extent, less certain thousands
of years hence, than they are at the present day. Miracles
were needed for the first establishment of Christianity; but
only the ordinary course of God's providence is necessary
to preserve its blessings to any number of future generations.
The two faculties of Intuition and Memory are the
sources only of our individual experience.  But the experience of an individual —what I have myself observed
and remembered, or reduced to writing —is extremely
limited, when compared with the vast fund of information
that is opened to us by accepting the experience of our fellow-men, and combining it with our own. Not merely in
our labors for the advancement of Science, but in the ordinary management of our every-day concerns, we are
obliged to depend upon the Testimony and the Authority




428           THE SOURCES OF EVIDENCE
of others. Science grows by a combination of the labors
of many minds and a long succession of generations. The
lifetime of an individual might be spent in a vain endeavor
to review, and verify by personal observation, all the data
which support the conclusions in but one of its departments. Many of them, from the nature of the case, cannot be so verified; the occurrences of former times, and
even those in our own day that took place under a peculiar combination of circumstances, such as may never be
repeated, must be received on the Testimony of others, or
be left entirely out of account, together with all the conclusions that are founded upon them. We must continually accept on trust what others have observed, and even
the Inferences that they have drawn, without pretending
to verify them for ourselves, or we must sit down in ignorance. And this remark is applicable not merely to the
Inductive, but also to the Exact Sciences. In astronomical calculations, for example, very few of the data rest
upon the evidence of our own senses, and we compute by
the aid of a book of logarithms, the accuracy of which, at
the present day, no one thinks of verifying by independent
calculation.
Testimony and Authority ought to be sharply distinguished from each other, though they are often loosely used
as synonymous. Properly speaking, we accept Testimony
as to matters of fact, and yield to Authority in matters of
opinion. Our confidence in the former depends mainly on
our opinion of the veracity of our informant; in the latter
case, we rely chiefly on the soundness of his judgment, the
accuracy of his habits of reasoning, and the largeness of
his information.  We disbelieve Testimony, we reject Authority. The reason why these two sources of belief are
so frequently confounded is, that the provinces of observation and of reasoning are not kept sufficiently distinct;
the certainty of the Intuition is improperly extended to the




AND THE CAUSES OF ERROR.           429
Inference which is drawn from it, and drawn so quickly
and easily that it is mistaken for a part of the observation
itself. When Dr. Cullen remarked, with as much truth
as point, that " there are more false facts than there are
false theories in the world," he did not mean to impugn
the general disposition of men to tell the truth. He alluded to what are generally supposed to be facts, and
which go by that name, but are really nothing but loose
compounds of matters of opinion with those of observation. Probably what he had in mind was the insufficiency
of the evidence on which the members of his own profession, that of Medicine, are often obliged to act. Thus, it
is said that a patient is in a Consumption; this, if true,
would be a fact; but the only known fact is, that certain
symptoms were manifested from which it was inferred,
perhaps wrongly, that the case was one of Consumption.
Again, it is announced as a fact, that the use of a certain
medicine cured the disease; when the truth ig, that the'dose was administered, and the man got well, perhaps in
spite of the medicine. Men are so prone to confound their
own crude conjectures with what they have actually seen
or heard, that very few, except those who have been carefully trained to scientific habits of mind, can be trusted to
report their own observations, until they have undergone
a severe cross-examination. They do not intend to deceive others, but they have effectually deceived themselves. The reputed sciences of Phrenology and Animal
Magnetism rested exclusively, in the opinion of their admirers, on a basis of observed facts, and hence were to be
maintained, in spite of the arguments with which they
were assailed, because facts are admitted to be a better
test of truth than reasoning. But it became evident on
severe scrutiny, that this basis was made up, for the most
part, out of what Dr. Cullen calls "false facts."
On account of this frequent confusion of two very dis



430            THE SOURCES OF EVIDENCE
similar things, it is commonly said, and with good reason,
that before accepting Testimony, we ought to have satisfactory proof both of the veracity and the competency of
the witness. But if people generally could be trusted to
separate their Inferences from their observations, and toreport the latter unmixed, it would evidently be enough
to have assurance only upon the former point.  In respect
only to their quality or certainty, though -not with regard
to their extent or comprehensiveness, one man's Intuitions
are as good as another's.  The one, indeed, may see more
than the other, because he knows where to look and what
to observe. He will therefore have more to report, or, at
any rate, more that is pertinent and useful. But the Testimony of the other, as far as it goes, will be equally valid
and trustworthy, for it is equally a report of what has actually been observed, and the Intuitive faculty cannot deceive. The only doubt, then, which can properly affect
the reception of Testimony, or the admission of other people's experience as at least of equal value with our own, is
that which regards the disposition of the witness to tell the
truth.  Doubts respecting his competency as an observer
can be settled by sifting the report itself, better than by
inquiring into the abilities of him who made it.
The proper distinction to be- made is, that the claims of
Testimony to be accepted depend upon the evidence which
is offered as to the Veracity of the witness, while those of
Authority rest upon.the proofs which we possess of the
Competency of the person whose opinions we are invited
to follow. The rules for forming an estimate either of the
Veracity of an observer or the Competency of a judge are
too obvious to need mention here, except in very general
terms.  "In regard to the honesty of a witness," says
Esser, as translated by Hamilton, " this, though often
admitting of the highest probability, never admits of absolute certainty; for though, in many cases, we may know




AND THE CAUSES OF ERROR.            431
enough of the general character of the witness to rely with
perfect confidence on his Veracity, in no case can we look
into the heart, and observe the influence which motives
have actually had upon his volitions. We are, however,
compelled, in many of the most important concerns of our
existence, to depend on the Testimony, and consequently
to confide in the sincerity, of others. But, from the moral
constitution of human nature, we are warranted in presuming on the honesty of a witness; and this presumption is
enhanced in proportion as the following circumstances concur in its confirmation. In the first place, a witness is presumed to be veracious in this case, in proportion as his love
of truth is already established from others. In the second
place, a witness is to be presumed veracious, in proportion
as he has fewer and weaker motives to falsify his Testimony. In the third place, a witness is to be presumed
veracious, in proportion to the likelihood of contradiction
which his Testimony would encounter, if he deviated from
the truth."
In respect to the Competency of the person to whose
Authority we are requested to defer, the only important
principle which needs to be here laid down is contained in
the old adage, Cuique credendum est in sud arte,- Trust
each person in his own specialty. Eminence in one department of science, far from being an indication of superior
power of judgment and reasoning in other departments,
is often a disqualification for forming a correct opinion in
them.  The mind is prone to carry over the special forms
and processes which are appropriate to one science into
others, where they are out of place, and lead only to error.
To adopt Bacon's expressive metaphor, it imports into a
new sphere of research the rust and tarnish contracted in
the workshop wherein it has chiefly labored.  A  distinguished mathematician, other things being equal, is not so
competent to form an opinion upon some disputed point in




432           THE SOURCES OF EVIDENCE
the moral sciences, as one who is conversant with questions of this sort, though he has never gained distinction
in them, and may be ignorant of the first principles of
Algebra and the Calculus. " The merit of a mathematical invention," as Hamilton justly remarks, " consists in
the amount of thought which it supersedes"; and hence
it is matter of common remark, that those who are most
capable of making such inventions, and profiting by them,
are least fitted for reasoning by -Induction and Analogy.
Consequently, "Mathematics afford us no assistance either
in conquering the difficulties, or in avoiding the dangers,
which we encounter in the great field of _probabilities
wherein we live and move."
Hume's celebrated argument against the credibility of
miracles is a fallacy which results from losing sight of the
distinction between Testimony and Authority, between
Veracity and Competency. He argues, that it is contrary
to all experience that a Law of Nature should be broken,
but it is not contrary to experience that human testimony
should be false; and therefore we ought to believe that
any amount of Testimony is false, in preference to admitting the occurrence of a miracle, as this would be a violation of Law. We answer, that the miraculous character
of an event is not a matter of Intuition, but of Inference;
hence, it is not to be decided by Testimony, but by Reasoning from the probabilities of the case, the only question
being whether, in view of all the circumstances, the Conclusion is competent that the occurrence was supernatural.
The Testimony relates only to the happening of the event
considered merely as an external phenomenon; the question respecting the nature of this event, whether it is, or is
not, a violation of Physical Law, whether it is an effect
of this or that Efficient Cause, cannot be determined by
Intuition and Testimony, but is a matter for Judgment
founded on Reasoning, in view of all the circumstances of




AND THE CAUSES OF ERROR.           433
the case. If doubtful of our own Competency to form a
correct opinion on this point, we may defer to the Authority of another, who is familiar with the kind of Reasoning
by which such questions are settled. Now we have abundant evidence from experience, that no event whatever,
regarded simply as an external phenomenon, can be so
strange and marvellous that sufficien-t Testimony will not
convince us of the reality of its occurrence. To the contemporaries of our Saviour, not even bringing a dead man
to life would have appeared so incredible as the transmission of a written message five thousand miles, without
error, within a minute of time. Yet this feat has been
accomplished by the Magnetic Telegraph. Why do we
decide, then, that the raising of Lazarus was, and the
transmission of intelligence by telegraph is not, a miracle?  Evidently not by Intuition, but by reasoning from
the very different circumstances of the two cases. The
fact, that the eyes of the blind were opened, or a storm was
reduced to a calm, or the dead were raised, is established
by Intuition and Testimony, which have established many
other facts quite as wonderful; the character of this fact,
whether miraculous or not, is to be settled in a very different manner. We say, then, that Hume's argument,
which is based exclusively upon an appeal to experience
and Testimony, is totally inapplicable to the question respecting the credibility of a miracle. Testimony has nothing to do with the correct inference of a Conclusion from
its Premises.
We can touch only very briefly on the Criticism of recorded Testimony, and of writings in general. As we must
avail ourselves, in the construction of Science, of the experience of former generations, in respect to which the
Testimony of eye- and ear-witnesses is no longer directly
accejsible, we are obliged to consider the credibility of
this, Testimony as affected by the channels of transmission
19                          BEB




434           THE SOURCES OF EVIDENCE
through which it has been passed. There are but two such
channels, Tradition and Ancient Writings.  The former
of these may be left out of account; for if the lapse of time
has been considerable, the probability that the Testimony,
if transmitted merely by word of mouth, has been materially altered or falsified, is so great, that the report can be
received only with extreme caution. But it has already
been mentioned; that the invention of the art of writing has
rendered it possible for the experience of a former generation to be handed down, through an indefinite lapse of centuries, in as perfect a state as that in which it was first
communicated to those who were the contemporaries of
the events narrated. This is possible, we say; the question whether it has been actually so transmitted is what we
have to consider in the Criticism of Ancient Writings.
When a documnent purporting to be the recorded Testimony of certain individuals of a former generation is presented to us, we have first to inquire whether it is actually
the handwriting, or the composition as taken down by dictation, or a faithful report, made at the time, of the substance of the evidence of the individuals whose names it
bears, or to whom it is attributed.  The establishment of
either of these three points is the proof of what is called
the Genuineness of the writing.  It is comparatively unimportant which of the three is proved, as either of them
gives us assurance that the document is a faithful record
of the Testimony of the persons whose evidence is to be
weighed. Thus, even if we were sure that the Testimony
of the Evangelists was originally written out by their own
hands, we certainly do not possess their autograph copies;
still, the Gospels are Genuine, if we have sufficient evidence that they are faithful records, made at the time, (or
correct transcripts of such records,) of what the Evangelists said.
But a-second question must be answered before we can




AND THE CAUSES OF ERROR.            435
accept the evidence furnished by the document. We must
be satisfied, not only that the Testimony is Genuine,-that
it was actually given by those from whom it purports to
come, but that it is Authentic, -that this Testimony is
a true and faithful narrative of what actually happened.
Proofs of the Genuineness of the writing amount, at the
utmost, only to bringing the witnesses into court and establishing their identity; proofs of the Authenticity must be
found by sifting their evidence, and applying to it all the
tests and means of verification which we possess, in order
to ascertain whether they are telling the truth.  If not
Genuine, the document is said to be Spurious; if not
Authentic, it is false.
As most of the tests and proofs of the Genuineness and
Authenticity of a writing are such as readily suggest themselves to the inquirer, it is unnecessary to consider them
here at any length. Generally, they may be divided into
two classes, called respectively the External and the Internal Evidences of the point to be proved. The External
Evidences of Genuineness are to be found either in other
and admitted writings of the supposed author, or in the
works of writers who were either his contemporaries, or
nearly of the same antiquity; and the evidence is either
direct, if the disputed writing is therein explicitly attributed
to him, or indirect, if these works quote as his production
passages which are found in the document. This indirect
testimony has the greater force, for on account of its casual
or incidental character there is less reason to suspect that it
has been forged. The External Evidences of the Authenticity of the writing, considered as a narrative of facts, are
too numerous to mention. They are found in allusions to
the same facts, or to incidents obviously connected with
them, by contemporary authors; in customs, traditions, and
institutions, which have come down to later times, and the
origin of which cannot be accounted for, except on the sup



436            THE SOURCES OF EVIDENCE
position that the reported events actually took place; in
coins, medals, and inscriptions, belonging to the same age,
or one immediately subsequent, and connected by equally
close relations with the alleged facts; in the notoriety
which such incidents must have obtained, the interest which
must have been felt in them, and the consequent probability that falsifications and forgeries respecting them would
never have been attempted, or would have been detected
and disproved at the time.
Of the Internal Evidence, it has been justly remarked,
that it is weak to establish either Genuineness or Authenticity, but powerful to disprove both. As Hamilton remarks,
c" We can easily conceive that an able and learned forger
may accommodate his fabrications both to all the general
circumstances of time, place, people, and language under
which it is supposed to have been written, and even to all
the particular circumstances of the style, habit of thought,
personal relations, &c. of the supposed author." On the
-other hand, a single anachronism, well made out, in respect
either to events, institutions, customs, or even the use of
language, is as fatal to the document's claim to antiquity, as
a well-established alibi is to the success of a criminal prosecution. Bentley's Dissertation upon the Epistles of Phalaris might have been limited to pointing out two or three of
the numerous anachronisms which he detected in them, if
his only object in writing it had been to prove that these
alleged Epistles were an impudent forgery. In respect to
the Authenticity of a narrative, it is to be observed, that
the credibility of certain facts is one thing, and the proof
of their actual occurrence is another. For establishing the
former, Internal Evidence is sufficient; for the latter, it is
powerless, being entirely inapplicable. By saying that a
narrative of certain events bears with it Internal Evidence
of its truth, we mean only that the events are possible,
that they are consistent with each other, - that they har



AND THE CAUSES OF ERROR.            437
monize with what we know from other sources concerning
the men of that country and that age, - that they are conformable to the ordinary course of things. All this may be
true of an avowed fiction. Some of Shakespeare's plays,
most of Scott's novels, have as much Internal Evidence of
truth as any testimony given in a court of justice. They
may have even more; for it is a common proverb that truth
is often stranger than fiction. If we disregard all extraneous circumstances, and look only at the face of the narrative, Robinson Crusoe appears as true a story as Cook's
Voyages, and Richardson the novelist is as faithful an historian as Hume.
As the evidence from the several sources that have now
been mentioned may be of various degrees of strength, and
as opinion is often drawn in opposite directions by conflicting testimony, we are naturally led to inquire whether
there is any measure of probability, or any means of accurately estimating the amount of belief which ought to be
accorded under different circumstances. This brings us at
once to the Theory of Probabilities, or, as the mathematicians sometimes call it, the Doctrine of Chances. Only
the outlines, or first principles, of the subject can be considered here, as the details are exclusively mathematical,
and so do not come within our province.
It is first to be observed, that, in the calculation of
Chances, as in every other department of pure mathematics, since the reasoning employed is Demonstrative in
character, the correctness of the results obtained depends
upon the truth of certain assumptions made in the outset;
and the applicability of one of these results to any given
case, or actual instance, turns upon the answer to the question whether this instance is exactly comprehended within
the Definition of the Concept upon which the whole calculation is based. Thus, in calculating the probability of any
one out of a given number of events, it is assumed that all




438            THE SOURCES OF EVIDENCE
the events considered are equally possible, —that no one
has any advantage which would render it more likely to
happen than the others.  Practically, this supposition is
never fulfilled. In illustrating their conclusions, the mathematicians have shown much ingenuity in selecting cases
where the chances would seem to be equally balanced; but
it is easy to show that they have never entirely succeeded.
Their favorite case is that of putting a number of balls,
equal in size, but different in color, into an urn, and then
considering the probability of a blindfolded person drawing
one of a certain color after a given number of trials. But
suppose the number of balls is considerable, that all the
white ones are first thrown in together, and then all the
black ones; in such case, the chance of drawing a black
ball at the first trial is obviously much greater than that of
a white one. A dozen other suppositions might be made,
depending on the size and shape of the urn, and the manner
of throwing in the balls, any one of which would be fatal to
a precise agreement of the actual with the calculated result.
Another favorite case is that of throwing up a half-penny,
to determine whether it will give head or tail; but here it
is assumed that the two sides of the coin just balance each
other, which, on account of the different imprints that they
bear, is never the case. Even in the better chosen illustrations, then, the calculated result will be only an approximation to the truth. In ordinary cases in which the Doctrine of Chances is applied, as in gambling, it will be but a
rude approximation; most of what are called games of
chance are, at least in some faint degree, games of skill;
and in the long run, though not necessarily in a few trials,
skill will tell.
In most cases of the practical application of the Doctrine
of Chances, the existence of numerous causes of error is
admitted; but as we know nothing of the character of these
causes, and do not see any reason why more of them should




AND THE CAUSES OF ERROR.           439
operate on one side than on the other, it is assumed that, in
the long run, they will compensate each other, so that the
result will agree with the calculation. But this is only the
argument ad ignorantiam, the fallacy of which has already
been noticed; because we do not know any reason why there
should not be as many and as heavy errors on one side as
on the other, it does not follow that there is no such reason. It was for a long time supposed, that the arithmetical
mean of several distinct observations of the same astronomical phenomenon would afford the nearest approximation
to a correct result, as there was no known reason why different observers should not err as much on one side as on
the other. But it is now known that each observer has a
constant tendency, distinctly appreciable in amount, to err
in one direction; and if allowance is not made for this
"1 personal equation," as it is called, the arithmetical mean
is not the nearest attainable approximation to the truth.
What is called "c the Method of Least Squares " has been
adopted as a mode of finding the most probable result, since
it was ascertained that the arithmetical mean is not the best
mean of a number of observed quantities. This Method
proceeds upon the assumption that all errors are not equally
probable, but that small errors are- more probable than large
ones. An easy corollary from this assumption is, that the
most probable conclusion can be obtained by making, not
the errors themselves, but the sum of the squares of these
errors; of the smallest possible amount. To borrow an instance from Dr. Whewell:- Let the observed numbers be
4, 12, 14; and suppose it known that these numbers must
be erroneous, as they ought to form an arithmetical progression.  The question is, what arithmetical progression
do they most probably represent.  The following table
shows that there are three such progressions which approximate the observed series, and also indicates which one of
them, according to the Method of Least Squares, is the
most probable.




440            THE SOURCES OF EVIDENCE
Errors.  Sums of Sums of squares
errors.  of errors.
Observed Series 4, 12, 14
1st Progression  4, 9, 14    0, 3, 0    3      9
2d     "       6, 10, 14    2, 2, 0    4       8
3d     "       5, 10, 15    1, 2, 1    4       6
We here see, although the first progression gives the
least sum of errors, the third shows the least sum of the
squares of the errors; and therefore, according to this
Method, the third is the most probable of the three.
These remarks were necessary in order to obviate the
inference which too many are inclined to draw, that, because the calculations in the Doctrine of Chances are made
on strict mathematical principles, the calculated probability
of an event, in any actual application of this Doctrine,
must therefore be mathematically exact and absolutely
certain. On the contrary, in any such application of the
principles, the result is only a rough approximation to the
truth.
It is also important to remember, that the application of
the Theory of Probabilities only shows us what we ought
to expect, or what, as rational beings, we are bound to believe, and does not reveal any Cause or Law that actually
determines the occurrence. To speak technically, the calculated probability is subjective, and not objective; it reveals what may be called a law of thought, but not a law
of things.  "The subject-matter of calculations in the
Theory of Probabilities," says Professor Donkin, " is quantity of belief. In every problem, a certain number of hypotheses are presented to the mind, along with a certain
quantity of information relating to them; the question is, -
In what way ought belief to be distributed among them? "
The calculation of the chances does not assume to increase
this " quantity of information," or to reveal any new data
on which our judgment ought to be based; but only how
we ought to judge and to act on the data that we already




AND THE CAUSES OF ERROR.           441
possess. The doctrine does not even assure us that the
calculated result will be verified at the first trial, or at any
subsequent trial; but it only shows us how we ought to
expect the actual results to be distributed in the course of
an infinite number of trials. The calculation does not relate merely to future events, the occurrence of which is
still contingent; it may be applied also to the past, to determine the probability that the event did, or did not, take
place. In cases of the latter sort, it is sufficiently obvious
that the application of the Theory of Probabilities does not
in any wise affect the event itself, which is already irrevocably determined either one way or the other; but only
assumes, in our ignorance of what the actual result has
been, to determine what we ought to believe respecting it.
Keeping this distinction in mind, we can explain the
seeming paradox, that an event should be sure to happen
at the first trial, though the chances were indefinitely great
against its occurrence. Put into an urn any number of
balls numbered consecutively from  one upwards, -say
1,000. Of course, there are 999 chances to 1 against a
blindfolded person drawing, at the first trial, tile particular
ball marked with any one of these numbers; and yet some
one ball so marked must be drawn. But this is no violation of the law regulating what we ought to expect; for
we ought not to expect any particular. number to come at
the first trial, though we are certain that some — we know
not what -number must so come.
It is assumed in the Doctrine of Chances, that the various degrees of belief may be represented by numbers.
An impossible event, as it has no probability whatever in
its favor, is appropriately represented by zero. An event
which is sure to happen, as tile expectation of its occurrence is not broken or divided by any chance of failure,
might be represented by any integral number; its most
convenient, because the simplest, symbol is unity. Then
19*




442            THE SOURCES OF EVIDENCE
all the degrees of probability between impossibility and
certainty will be denoted by the fractions that may be interpolated between 0 and 1.
The first- principle of the Doctrine of Chances is, that
the probability of an uncertain event is represented by the,number of chances favorable to its occurrence, divided by the
total number of chances whether favorable or unfavorable.
Thus, as a pack contains 52 cards, divided into four equal
suits, into 12 pictured and 40 plain cards, and into 26 red
and 26 black cards, the chance of drawing a heart at the
first trial is -  or -1;. of a pictured card, 12- or 3; of a red
card, 2 or 1. This last case represents an event which is
entirely uncertain, the chances being equal for and against
its occurrence. We may get rid of the fractional form by
expressing the probability of an event in that mode which
is called " the odds "; that is, we may take the numerator
to express the chances for, and the difference between the
numerator and the denominator to signify the chances
against, the occurrence. This rule is an immediate corollary from the first principle as just stated, since the numerator gives the number of favorable chances, and the denominator the total number of them both favorable and
unfavorable. Thus, the chance of drawing a pictured-card
is represented fractionally, as above, by -4A, or by the odds
as 3 to 10; of a red card, as 2-, or 26 to 26,- even
chance.
The improbability of an occurrence is denoted by the
complement of the fraction which expresses its 2'obability;
that is, the odds are reversed. Thus, as there are six faces
to a die, all of which are supposed to be equally likely to
come uppermost, the probability of throwing six is 1 or 1
to 5; the improbability of it is 1- 1 - 5, or 5 to 1. The
reason of this rule is obvious; the improbability of one
event must be the sum of the probabilities of all the other
possible occurrences; and as the total of all the chances,




AND THE CAUSES OF ERROR.            443
which represents what is sure to happen, is unity, the sum
of the probabilities of all the others is found by subtracting the probability of this one from unity.  Thus, some
one of the six faces must come uppermost; this certainty
is denoted as 1. Then, as the probability of a six is -3, the
chance of some one out of the other five faces, (in other
words, the improbability of a six,) is 1 -  -- -.  As each
of the five other faces has a probability of -, the sum of
their chances, or the improbability of the remaining one, is
evidently -.
The probability of a compound event - that is, of two
independent uncertainties happening conjointly - is ascertained by multiplying the separate chances of the two together.  Thus, the chance of throwing six with one die
being I-, and of throwing the same with another die being
-, the chance of obtaining sixes at once with the two dice
is  X 6-  3 I.  This rule, again, is a direct corollary from
the first principle as already enounced; for as the number
of possible throws with two dice is 6 X 6 _  36, (since
each face of the one might be combined with either of the
six faces of the other,) and as only one of these is favorable, the odds are evidently as 1 to 35.  To take another
instance:- the chance of drawing a pictured card out of
a pack being -3-, and of a red card, 1-, the probability of
having a red pictured card is 13 X ---  3 —'or -;6-, as there
are six red pictured cards out of the 52 in the pack.
According to this rule, the chance of drawing a red card
four times in succession, the card being replaced after each
trial, so that the number in the pack shall always be 52,
will be   XX  X    X 1 -  1 or only 1 to 15. But ganlblers often deceive themselves in respect to the application
of this rule. As it is so unlikely that a red card will turn
up several times in succession, they imagine that, after it
has thrice thus turned up, the chance of obtaining a black
card at the fourth trial is much greater than it was at first.




444           THE SOURCES OF EVIDENCE
But it is not so; if the card drawn is always immediately
replaced, the probability of drawing a black card after we
have drawn a red one at three, or even at a thousand, successive trials, is precisely what it was before the first experiment, -namely, 1-. The number of cards being always
the same, 26 red and 26 black, the probability of obtaining
a red one is always the same, whatever previous experiments
may have been made with the same pack. The three experiments already tried have reduced so many uncertainties
to certainties, — that is, have thrown them out of the calculation in the Doctrine of Chances, which deals only with
uncertain events. Before any trial was made, the chance
of a red card turning up four times in succession was only
T-,  each of the four results being then uncertain; after
three trials, but one event is still an uncertainty, and the
probability of its occurrence is 1. We see, then, the folly
of the gambler's expectation that his luck must soon turn,
because he has had a long series of ill-luck. But all his
past trials having been reduced to certainties, his chance
of good fortune is now precisely what it was when he began. His only chance of success, after he has had a long
series of misfortunes, is to stop playing altogether; and this
is also the best thing he can do, if fortune has smiled upon
him.
The development of these principles must be left to the
mathematician; but a further caution in respect to the
application to be made of them by the gambler may be
borrowed from Buffon. C" If two men," he asks, " were to
determine to play for their whole property, what would be
the effect of this agreement?  The one would only double
his fortune, and the other reduce his to naught. What
proportion is there between the loss and the gain? The
same that there is between all and nothing. The gain of
the one is but a moderate sum; the loss of the other is
numerically infinite, and morally go great that the labor of




AND THE CAUSES OF ERROR.            445
his whole life may not, perhaps, suffice to restore his property."  But the fascination of gambling is so great, and
the habit of it, when once formed, is so incontrollable, that
every one who even begins to play may be regarded as
staking his whole fortune upon the issue, and thus as voluntarily subjecting himself to these tremendous odds.
The principal intellectual Causes of Error have been already indirectly considered, inasmuch as they consist in any
violation of the rules and methods which have been laid
down for the attainment of truth.  But the moral Causes
which blind our perceptions, warp our judgments, and lead
us to accept illusions in the place of truths, deserve some
separate notice.  Most of these are modifications or consequences of self-love, or rather of that short-sighted selfishness which has more regard for present ease and enjoyment,
however trifling, than for future good, however great, if
the latter be attainable only by effort and self-denial. Such
are prejudices, pride, undue desires, precipitancy, and sloth.
All of these are faults of character rather than of intellect;
yet they are more frequent sources of delusion, and more
formidable obstacles to our mental progress, than can be
found in the original weakness and limited range of our
faculties, or in the insufficiency of the aids and incitements
which nature furnishes for the pursuit of truth.  We approach the study of a subject, not as prepared to accept any
conclusions to which our researches might naturally lead,
but with minds stuffed with preconceived opinions, which
pride prevents us from relinquishing after they have been
once avowed, or with a bias in favor of some startling consequences of the inquiry, the announcement of which may
feed our vanity or establish our reputation.  Pride also
leads us astray, by inducing us to over-estimate the extent
and importance of the acquisitions that we have already
made, or to adopt too easily the conclusion that the investigation has reached its limit, and that we already know as




446            THE SOURCES OF EVIDENCE
much as is capable of being known. I know of no error
which is more fatal to progress than the idea that there is
no progress to be made, -of no opinion which is more detrimental to improvement than the belief that no improvement is possible. It is true that a low estimate of the extent of our knowledge does not amount to the Christian
virtue of humility in the largest sense. It may be, it frequently is, accompanied with a very lofty opinion of the
extent of our powers, or the excellence of our natural endowments. But a conceit of ability, bad as it is, is not so
injurious to progress as a conceit of knowledge. The one
encourages a person to study, by leading him to believe that
he can grapple with any subject; the other disposes him to
sit down in idleness, under the belief that he has already
mastered that subject.  Seneca says, _lultos potuisse cad
sapientiam pervenire, nisi putassent se pervenisse, - Many
might have obtained wisdom, if they had not supposed that
they had already got it.
Moderation in our personal desires, and that earnestness
of inquiring purpose which leads not so much to an abnegation as to the entire forgetfulness of self, are more important elements of success in the pursuit of truth than is
commonly supposed. The brilliant results of Dr. Franklin's scientific career seem attributable, in a great degree,
to his generous disregard of his own fame and standing in
the eyes of the public. A lively curiosity, an eye quick at
observation, great sagacity in detecting the more occult relations of facts and bearings of experiments, and a mind of
incessant and intense activity, were not the only means
that enabled him to accomplish so much in science. His
attention was not diverted from the object of investigation
by any regard for what the world might think of the importance of that object, or of his own merit in obtaining it.
The necessary experiments were instituted, not to convince
others, but to satisfy himself. The most brilliant results at




AND THE CAUSES OF ERROR.           447
which he arrived were communicated only in private letters to a few friends, to whom he left the care of publishing
them or not, as they saw fit. His theories sat loosely upon
him, and he modified or abandoned them, when further observations made it necessary, without dreading the charge
of inconsistency, and without shame at confessing a mistake. He was never seduced, by the accidental brilliancy
or novelty of one object of inquiry, to pay more attention
to it than to another, apparently of a more homely character, but really of equal interest to a philosophical mind.
He studied the means of remedying smoky chimneys with
as much ardor and industry as he showed in penetrating
the secrets of the clouds, and robbing the thunderbolt of its
terrors. He formed theories of the earth, and projects for
cleaning and lighting the streets of Philadelphia, with equal
zeal; and having communicated the former in a private
letter to a friend, and urged upon his fellow-citizens the
adoption of the latter, he dismissed both from his mind, and
pursued with fresh interest a wholly different set of investigations.
The most frequent cause of failure in any pursuit is the
lack of earnestness. Habit may impart a kind of mechanical facility in the performance of a given task; but there
will' be little vigor or energy in the work, if the feelings
be not deeply interested in it, so that the result shall be
awaited with eager expectation or trembling anxiety. Longcontinued labor easily degenerates into mere routine; and
then, even though the specific object in view should be obtained,  though a science should be learned or a livelihood got, — there will be no strain of the faculties, and
consequently no development of them, -no correction of
errors, and therefore no discipline of mind. This is the
secret of the great force displayed, and the large results
that are often accomplished, by those who are opprobri-.
ously termed " men of one idea," - persons who have con



448           THE SOURCES OF EVIDENCE
centrated their attention upon one object, and who pursue
it, regardless of everything else, with all the strength and
the bitterness of fanaticism. Half an hour of strenuous
exertion is worth a week of mechanical and desultory labor. Too often we dawdle over the business of life, instead
of taking it up with eagerness, and prosecuting it to the end
as a work of love. There is all the difference in the world
between an active mind and a passive one; between earnestly hunting after truth, and only swallowing knowledge
inertly, as it is poured into the memory by a teacher or a
book, and just as quickly washed out again. We are made
what we are, experts or dolts, much more by our acquired
habits than by success or failure in the attainment of knowledge. Aim not so much to be learned, as to be able to
learn; one truly wise man is worth a hundred erudite pedants. The study of Logic itself will do little to cultivate
our power of reasoning, or to improve our habits of thought,
except indirectly, by the effort which is necessary for the
mastery of its principles, and by the endeavor to verify or
correct them in the course of our subsequent researches.
What we really need to attain is Logical power, and a
knowledge of the science of Logic is useffal so far only
as it is conducive to such attainment.
Among the occasions for the use of this power, that to
which the gravest responsibility is attached is the formation
of our opinions. Properly speaking, we must all begin life
without any opinions which we can call our own by any
better right than that of passive inheritance or unconscious
inoculation. We have probably imbibed most of them just
as we took the measles or the whooping-cough in infancy,
from accidental contact with others. We are Whig, Democrat, or Republican, conservative or radical, - we go to
the Episcopal, Presbyterian, or Congregationalist church,
simply because parents alid friends thought so, or did so,
formerly. Now, in one respect, this is all right and just as




AND THE CAUSES OF ERROR.            449
it should be. It is fortunate, both for ourselves and the
world, that we begin life with a set of provisional opinions
already formed, not by us, but for us. This vis inertice of
opinion, this tendency of the human mind to move in the
ruts where others have preceded it, is the great conservative principle of society, all that keeps us from intellectual
and social anarchy. Without it, all the wise men who
have been before us would have lived in vain, and society
would drift along helplessly, without keel or rudder. If
we were not willing to accept opinions before we are able
to form them  for ourselves,-ay, and to cling to them
with the fondness which early association imparts, — half of
the time we should act at random, and the other half extravagantly and foolishly.
But we cannot pass through life merely as docile children; and our first duty as men-at any rate, as educated
and thinking men  is to begin the great work of fashioning our own creeds in politics, religion, philosophy, and social economy. When we have attained our majority, we
have become as' accountable for our opinions as for our conduct. A wise man, however, might hesitate before going
as far as Descartes, who urges us to begin by doubting
everything; his advice is, to take up every question, as it
were, de novo, with a determination not to accept any answer to it the correctness of which is not made out by evidence satisfactory to our own minds, and elicited by our own
inquiries. A safer course, as it seems to me, is to begin,
not by discarding all our previous opinions, but by examining the foundations on which they rest. There is just as
much of prejudice and rashness in presuming that they are
all false, as in believing, previous to inquiry, that they are
all true. Do not ask, Why may it not be otherwise? but
rather, Why is it so? The presumption is in favor of the
received doctrines in any science, until good reasons are
made to appear for doubting or denying them. But the
cc




450   SOURCES OF EVIDENCE AND CAUSES OF ERROR.
duty of inquiry, in order to ascertain whether there are
such reasons, is one which always exists, and which opens
the largest and fairest field for the exercise and development of our powers of thought. Only by such exercise
can we hope to perfect our knowledge of the principles of
Logic, and to make that knowledge of use to ourselves and
others. 66 We employ reason," said the Port-Royalist logicians, " as an instrument for acquiring the sciences, whereas
we ought to use the sciences as a means of perfecting our
reason, correctness of judgment and accuracy of thought
being infinitely more valuable than all the speculative
knowledge which we can obtain from the best-established
sciences.  Wise men, therefore, ought to engage in the
study of the sciences only so far as they conduce to this
end, and to make them only the training-ground, and
not the field for the regular employment, of their mental
powers.'"
THE END.
Cambridge: Stereotyped and Printed by Welch, Bigelow, & Co.