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A TREATISE ON LOGIC

PUEE AND APPLIED

BY S. H. EMMEN8

AUTHOR OF " SELECTIONS FROM LOCKE ON THB HUMAN UNDERSTANDING '

introfouctixm anb

LONDON

CROSBY LOCKWOOD AND SON

7, STATIONERS' HALL COURT, LUDGATE HILL
1891

D. VAN NOSTRAND COMPANY,
NEW YORK.

VBRSITT

PEEFACE.

LITTLE more will be expected from a work of the
following description, than that it should contain an
intelligible and concise exposition of those facts and
principles which form, as it were, the groundwork of
logical science. Necessarily, therefore, it must be, for
the most part, a compilation of such views a^ have
obtained general acceptance, and can lay but little
claim to any high degree of originality.

At the same time, I may be permitted to state that
some features exist which serve to distinguish this
Treatise from its numerous predecessors, and which
will, I hope, prove of service to the student by inciting
him to examine for himself such theories and principles
as come under his notice. Those features to which I
more particularly allude, are the reference of all so-
called " Immediate Inferences " to the class of syllo-
gisms ; the grounds for an extended adoption of Aris-
totle's Dictum ; the refutation of the charge that every
syllogism involves a petitio prmcipii ; the explication
of the inductive theory in Applied Logic ; and, finally,

IV PREFACE.

the doctrine of classification, by which every detail and
branch of Logic is shown to exist in harmonious
unison. And as these views are, in a measure, opposed
to those contained in works of great repute, I have
appended to the body of this Treatise four Articles,
wherein are set forth such arguments as I think suffi-
cient to justify me in advancing the above-mentioned
doctrines.

I also deem it advisable to state that it has been my
endeavour to give this work as suggestive a character as
possible ; and, therefore, although it belongs to a rudi-
mentary series, professing to treat only upon the first
elements of Logic, I am yet not without hope that it
will be found a sufficient introduction to such compre-
hensive and elaborate treatises as those of Mr. Mill,
Professor De Morgan, and others. But while I have
thus been compelled to satisfy myself in many cases with
an enunciation rather than with a full investigation of
certain doctrines, I still trust that, in the following
pages, the student will find all that is really requisite
to give him a fair, practical knowledge of Logic.

The chapter on Applied Logic is, I am sensible, but
a mere sketch. As, however, to do justice to so vast a
subject would require a great extension of the present
limits, and would thus curtail the utility of this
Treatise by enhancing its price, I have contented
myself with directing the student's attention to such
points as are most important, both in theory and prac-
tice. For the same reason, nothing beyond the bare
outlines is given of such new doctrines as I have here

PREFACE.

adopted; all further development of them being de-
ferred to a future occasion.

I take this opportunity of acknowledging my many
and great obligations to those writers upon Logic
whose works I have consulted ; and although it may
seem invidious to particularise, yet as, for reasons
which will be found specified in their proper place, I
have expressly referred to Mr. John Stuart Mill, as
being the advocate of certain opinions which are com-
bated in the following pages, I think it only just that
I should here record my admiration for the profound
philosophy and great attainments which are so apparent
in the writings of that gentleman.

S. H. E.

London, January, 1865.

CONTENTS.

INTRODUCTION

CHAPTER I.

AN INQUIRY INTO THE VARIOUS MEMBERS OP AN ARGUMENT . . 7

CHAPTER II.
OF NOTIONS OR TERMS :

f 1. Simple-apprehension 14

2. Abstraction of Common -notions 16

3. Predicables, Extension, and Intension .,..,.. 18

4. Division of Common-notions 18

5. Positive, Negative, and Privative Terms 20

6. Definition 21

7. Names and their Divisions 22

8. Opposition of Terms 23

9. Structure of Terms 24

10. Conclusion and Recapitulation 24

CHAPTER III.

OF JUDGMENTS OR PROPOSITIONS :

1 . Formation of Judgments . . . . r .... 27

2. Categorical Propositions 28

3. Hypothetical or Conditional Propositions 29

4. Disjunctive or Alternative Propositions 29

5. Quantity of Propositions . 30

6. Quality of Propositions 30

7. Distribution of Terms 31

8. Relation of Terms . 32

CONTENTS. vii

Pajre

9. Systematic Classification of Propositions 33

10. Table of Possible Propositions 33

1 1 . Interpretation of the Copula 84

] 2. On some other Properties of Judgments 35

13. Concluding Remarks 35

CHAPTER IV.

OF REASONING OR ARGUMENT SYLLOGISMS:

$ 1. Reasoning in General 38

2. Syllogisms Inference 39

3. Opposition 41

4. Conversion 44

5. Coincident Junction 47

6. Mediate Inference formally expressed as such its Divisions 48

7. The Fundamental Law of Mediate Inference 49

8. Of Figure 54

9. Remarks upon the Four Figures 54

10. Of Mood or Mode 57

11. Table of Valid Syllogisms 58

12. Induction and Deduction 61

13. Extension and Intension 64

14. Denomination 66

\5. Syllogistic arrangement of Propositions 60

16. Conditional Syllogisms 6?

17. Disjunctive Syllogisms 72

18. The Dilemma 73

19. Incomplete Syllogisms 75

20. Complex Arguments, or Chains of Reasoning .... 76

21. Recapitulation 80

22. Conclusion 82

CHAPTER V.

OP FALLACIES:

1. Applied Logic in general 84

2. Classification of Fallacies 85

3. Formal Fallacies SS

4. Material Fallacies C^uarternio Terminorum 90

5. Material Fallacies Premiss unduly assumed 95

6. Material Fallacies Ignoratio Elenchi Ill

7. Conclusion 115

Viii CONTENTS.

CHAPTER VI.

Page
OF LOGIC AS PRACTICALLY APPLIED:

$ 1. Introductory Remarks ... 11?

2. Observation 119

3. Reflection

1. Of Laws and Causes 126

2. Of Induction 331

3. Of Deduction, Hypothesis, and Verification . . . 140

4. Of Analogy 143

5. Of Chance and Probability 345

6. Examples of Reflection

a. The Discovery of Neptune 148

b. Kirchhoff's Researches on the Solar Spectrum . 150

4. Conclusion 152

APPENDIX.

\ ON JUDGMENTS 155

B. ON THE SO-CALLED IMMEDIATE INFERENCES 159

C. ON THE DICTUM DE OMNI ET NULLO ] 63

D. ON THE SYLLOGISM CONSIDERED AS A Petitio Principii ... 166

Of THB

LOGIC.

INTRODUCTION.

LOGIC may be not inaptly described as the grammar of
thought ; that is to say, it reveals and explains the principles
according to which our judgments are formed, in much the
same manner as grammar analyses the laws which regulate
the expression of our thoughts by means of speech. It will,
therefore, be seen that Logic is a science of universal extent,
inasmuch as wherever any process of reasoning is carried
on, there will be found, in full operation, those mental laws
which it is the office of Logic to examine and systematise.
It does not, however, follow that every person who reasons is
a logician, for it is only when a process of judgment is carried
on in regular order, and according to the rules derived from
a study of the science, that such an appellation could be
justly bestowed. And, in like manner, it would be absurd to
suppose that there can be no correct reasoning without a good
knowledge of Logic; for, in order to perceive the error of such
a view, we have only to consider for a moment the mode in
which every science is formed. Take, for example, the science
of astronomy : the heavenly bodies had been urged through
space, by the operation of definite cosmical laws, for ages
previous to the discovery of those laws by human philosophers,
and it was the very fact of such motions being in progress,
which led to the investigation of the principles concerned.

Z INTRODUCTION.

Thus, too, with regard to Logic : men had thought and rea-
soned according to certain laws, long before Aristotle, by ob-
serving and reflecting upon the various judgments which
came under his notice, was able to enunciate the great funda-
mental truth upon which they were based. It is from con-
siderations such as these that we speak of scientific discoveries,
and not of scientific inventions ; for tLe latter term can only
be applied to some new method of accomplishing a specific
object, while the former is always used when we speak of any
fresh law or principle, which, previously existing, has been
brought to light by the exertions of the philosopher. Like,
then, as Newton discovered gravitation, so did Aristotle dis-
cover the syllogism ; and, therefore, the notion that the use of
the syllogism is merely one method of reasoning, is at once
shown to be altogether erroneous. The truth is, that there
can be no other process of forming a judgment, since every
conceivable example of reasoning may, by the application of
certain rules, be reduced to the syllogistic form.

From what has now been said, the true value of Logic will
be easily discerned, and as its subject is one which lies at the
root of all other sciences, its importance can hardly be over-
estimated. Its principal use is that it enables us to reason
correctly, by furnishing us with various rules and standards
wherewith to test the validity of any argument that may be
brought before us. And here it is requisite to guard against
a very prevalent misconception ; I allude to the idea, that,
by means of Logic, one may ascertain the truth or falsehood
of any statement. The source of this error is to be found in
the supposition that Logic is concerned with the subject of the
various statements (technically, propositions) whose relations
to each other it investigates ; whereas, in reality, it merely
considers their form. Thus, the two propositions, " Water
is a fluid," and, " Evil is good," would by a logician be con-
sidered as precisely similar, although one of them is false,

INTRODUCTION. 3

and the other true. Again, the following argument or
syllogism

All fluids are poisonous,

Water is a fluid ;
Therefore Water is poisonous,

is perfectly valid and correct, although the conclusion arrived
at is false. To render this point quite plain and intelligible,
let us adopt the following course : it was above stated that
Logic merely considers the form and not the subject (or
matter) of propositions ; accordingly, for all logical purposes,
we shall not alter the nature of the propositions employed, if
we substitute letters for the words we used to express the
substances or notions of which we spoke. Thus, instead of
" water is a fluid," let us say " A is B," and for " evil is good,"
let us put " is D : " we then see at once, that in both in-
stances we use exactly the same kind of proposition. Again,
let us similarly convert the syllogism : we have

All A's are B,

C is an A;
Therefore C is B ;

an argument which remains unalterable in form, no matter
what ideas are expressed by the letters.*

This it is which confers such rigorous accuracy upon all the
results and developments of Logic. Indeed, as Professor De
Morgan has said, Mathematics and Logic are the two exact
sciences. The primary doctrines of chemistry may require
alteration as new combinations of the elements are brought to
light ; the progressive theories of physiology are modified with
every advance of microscopical investigation ; the glorious
revelations of astronomy present an ever-changing aspect ;
but Logic, like Mathematics, abides, eternal and immutable.
The preceding remarks will probably have pointed out to
the reader that Logic is concerned with language as distin-

* For further information as to form and matter aae page 39 et seq.
B 2

INTRODUCTION.

guished from the ideas conveyed by the use of words ; but
in order that the student may be well grounded in the funda-
mental truths of the science before he proceeds to study its
details, I shall add some further observations upon this point.
Language in its ordinary sense, that is, speech, is useful as
a means of communication in two ways : it enables us to
minutely describe, or, in other words, to analyse, our various
ideas, and it also enables us to convey, by a single sound or
sign, the combined impression of many particulars. Take, for
example, this description :

" I gazed upon her form

Transcendent, and upon her face which gleamed
Pale through her tears, like some fair statue bathed
In the cold moonlight ; and I marked the mute,
Sad eloquence of that love-charged heart
Which quickly heaved its alabaster veil
In trembling fear."

Here gradually dawn upon us the many subjects of atten-
tion which exist in a single object, and it is only by means of
a protracted analysis such as the above, that we are able to
convey a complete idea of it. But then, again, we sometimes
wish to express the notion of a numerous class of objects, in
such a manner that the impression produced may serve for
any one of them. Thus, suppose the objects were men,
horses, cows, sheep, lions, &c. : we should merely confine our
attention to those points in which they resembled each other,
and should bestow a name upon this group of qualities, such
as '' animal/' by the use of which we might attain the desired
end. This process is the reverse of the first, but at the same
time is in a measure dependent upon it, for in order to ascer-
tain the points of resemblance between various objects, a partial
analysis is at all events necessary. Accordingly, Logic takes
cognizance of both operations, and investigates the relations
which subsist between them and the act of reasoning itself.

INTRODUCTION.

It has been said above that language enables us to convey
by a single sound or sign, the combined impression of many
particulars. Now it is our ability to do this, which alone
enables us to conduct a process of reasoning ; or otherwise we
should find it impossible to judge of the relations between two
ideas or objects a condition which is evidently essential to an
argument. One of the most curious proofs of this is afforded
by deaf-and-dumb persons, who, when they have once been
taught to speak by means of their fingers, are observed to
use this means of recording their impressions, even when
thinking alone. And it has been asserted, that " it will be
found by any one who will question a deaf-mute who has
been taught language after having grown up, that no such
thing as a train of reasoning had ever passed through his
mind before he was taught."*

We have hitherto considered Logic purely as a Science,
but it is very frequently regarded as an Art, and perhaps it
is this mode of viewing it which holds out the strongest in-
centive to the student. For it can only be the few who will
voluntarily engage in the study of principles which, complete
in themselves, give promise of no result beyond that delight
which naturally arises from the consideration of organic
symmetry and perfection ; the great majority being altogether
occupied with the hope of turning their knowledge to some
useful purpose. Therefore, in the following pages I shall
endeavour to give as practical an effect as possible to the
various laws of thought which we shall investigate ; and the
student will thus find that Logic, instead of being merely an
" ingenious recreation," is in reality a powerful aid to the pro-
secution of all other studies. Not that reasoning alone will
suffice for the discovery of truth, as to do this an extended
observation of facts is indispensable ; but when we have col-
lected a sufficient quantity of facts, we shall find that an

* Whately's "Logic," p. 13.

D INTRODUCTION.

acquaintance with Logic will greatly assist us in deducing a
correct inference.

I now trust that a tolerably clear notion has been gained
of the nature and extent of Logic ; and in the next place I
shall briefly describe the method of proceeding which I intend
to adopt in my explanation of the science. First, then, it will
be advisable to select some example of pure reasoning, and,
having dissected it, to point out the various members of which
it is composed, together with the principles which form, as it
were, the framework of the structure. We shall thus obtain
a bird's-eye view of the country before us, and we shall be
able to advance without doubt or hesitation to the end of our
journey. Accordingly, it will next become our duty to examine
each branch separately and in detail, which being done, we
shall proceed to the consideration of the various combinations
formed by these branches, and so at length we shall be enabled
to construct, or to analyse at pleasure, any train of argument,
however extensive it may be. Here, strictly speaking, the
study of Logic as such should terminate ; but in order that
the utility of this treatise may be increased, I shall devote a
chapter to the discussion of the several fallacies which are of
most frequent occurrence, giving such rules for their treat-
ment as have been found most effectual. The concluding por-
tion of the work will consist of some remarks upon the proper
application of Logic, with various illustrative examples.

Such is the course which I propose to take, and if the
student be not dismayed by the shadowy anticipation of tech-
nical difficulties which have no real existence, he will find an
ample reward for all his labours. A systematic regulation
of his intellect; a probe wherewith to examine the most
mysterious doctrines of philosophy ; a wand before whose
potent touch the stately fabric of deceit and fraud will dis-
appear ; these are but a few of the benefits to be obtained by
a study of Logical science.

TKM

[JJ1TIVER3ITT

A TREATISE ON LOGIC.

CHAPTER I.

AN INQU.RY INTO THE VARIOUS MEMBERS OF AN ARGUMENT.

IT has already been stated that our first step towards a right
understanding of Logic must be a strict examination of some
definite argument. Now, as we are not all concerned with
the subject of the reasoning, it will be the best plan for us to
choose some example which shall present us with the fe west
and most simple ideas, so that we may devote our whole at-
tention to the reasoning process, and not be led aside by any
extraneous matters. Accordingly, let us take for the subject
of our investigation, the proof of Euclid's first proposition,
which may be thus stated in arguments or syllogisms.

1. The radii of the same circle are ;> *.

equal to one another, / ./ \.

A and A B are radii of the f> A* ^ E ;

same circle BOD;
.-. A is equal to A B. -^-LJluX. .-'''

2. The radii of the same circle are equal to one another,

B C and A B are radii of the same circle ACE;
.-. B C is equal to A B.

3. Things which are equal to the same thing are equal

to one another,

A C and B C are equal to the same thing (viz. A B) ;
/. A is equal to B C.

Taking any one of the above syllogisms, we see that it is
composed of three statements, among which this relation sub-
sists ; that if we admit the truth of the first two, we cannot

8 AN INQUIRY INTO THE

avoid admitting the truth of the last. This last statement IB
termed the conclusion ; the other two being called the pre-
mises. And here the question comes why is it, that, having
admitted the premises, we are compelled to admit the conclu-
sion ? To answer this we must examine the constitution
of each premiss, and ascertain whatever is implied thereby.
Thus, in the first of the syllogisms given above, w r e find
as a commencement, the following assertion or proposition :
" radii of the same circle are equal to one another :"
where a certain property, viz., " equality," is asserted, or,
in logical language, predicated, of a group or class of objects,
viz., " radii of the same circle." That is to say, " equality "
is a property common to every individual comprehended in
the class. The second proposition is to this effect : " A
and A B are radii of the same circle ;" that is, we assert A
and A B to be individuals of that very class, concerning
which we admitted that " equality " was common to every
one of its members. Consequently we are compelled to
admit that A and A B possess the property of " equality,"
and this admission forms the conclusion.

Our mode of procedure has therefore been as follows : we
first predicate something of a certain class of objects ; we
then assert that certain individuals belong to that class ; and
lastly, we predicate the same thing of the individuals which
we had predicated of the class.

Now suppose the syllogism had stood thus : " Radii of the
same circle are not equal to one another ; A and A B are
radii of the same circle ; therefore A C is not equal to A B :"
it would still be perfectly valid, for, having denied that a
certain property is enjoyed by a class of objects among which
we admit certain individuals to be, we must necessarily deny
that those individuals possess the property in question.

We thus arrive at this axiom or law : " Whatever is affirmed
or denied altogether of any whole, may in like manner be
affirmed or denied of any individual part belonging to, or
comprehended in, that whole." Aristotle was the first who
distinctly enunciated this great truth, and it is commonly
known as " Aristotle's Dictum," or the " dictum de omni et
nullo"

VARIOUS MEMBERS OF AN ARGUMENT. 9

It may at first seem strange that a statement so simple and
obvious should be characterised as a great truth ; but a very
little reflection will soon convince us that any law which is of
universal extent and application, must be the more valuable
according as it is the more simple ; and therefore it is with
justice that Aristotle is honoured for having enabled us to
explain the formation and examine the validity of any argu-
ment whatever, in so plain and satisfactory a manner. Another
fact also which will appear improbable, is that the dictum may
be universally applied ; that is to say, no syllogism can be
valid or admissible unless it strictly complies with the require-
ments of the dictum, and in a later portion of this work rules
will be found by means of w 7 hich it is possible to bring every
specimen of reasoning to this test. Indeed, if we would
become thoroughly acquainted with the principles of logical
science, we must invariably bear in mind the dependence of
every train of thought upon the dictum of Aristotle.

But it is now time that we should revert again to our
example of reasoning, and continue the division of each
syllogism into its component parts. We have already seen
that a syllogism consists of three propositions divided into
the two premises and the conclusion ; we will now examine
the propositions themselves more closely. In the statement
" radii of the same circle are equal to one another," we
see three distinct portions : first, the subject of which we
are speaking, and of which something is predicated (that
is, asserted or denied) ; secondly, the attribute or condition
which is predicated of the subject ; and thirdly, the sign of
affirmation or negation. The technical names for these are,
the subject, the predicate, and the copula.

In the proposition above quoted it will be observed that
the whole of the subject is spoken of; for when we say " radii
of the same circle," we evidently mean every radius that
could possibly be drawn. Accordingly, such a proposition is
termed universal, as the predicate is universally applied to
every part of the subject. But if we had spoken of a portion
only of the subject, and had said " some of the radii of the
same circle are equal to one another," we should have what
is called a particular proposition inasmuch as the predicate

B 3

10 AN INQUIRY INTO THE

is affirmed of some particular part of the subject, and not of
the whole. Thus we see that propositions may be always
divided into universal and particular, and this distribution is
said to be made according to quantity.

Again, " equality " is predicated affirmatively of " radii of
the same circle ;" the sentence is therefore termed an affirma-
tive proposition : while if the predicate had been denied of
the subject, thus, " radii of the same circle are not equal to
one another," it would have been a negative proposition.
We have, therefore, another system, by means of which to
classify every possible proposition, and this distribution is
called a division according to quality.

And here we have introduced to our notice a very im-
portant branch of Logic, namely, division ; by means of
which mental process we may at all times obtain a distinct
grasp of any subject which occupies our attention. Indeed,
this faculty would seem to be an inherent principle of our
nature, for whatever may be the science, an attempt has
always been made from the commencement, to properly
classify and arrange its various subdivisions ; the best ex-
amples of such a course being found in such studies as Natural
History, Comparative Anatomy, &c. Accordingly, as Logic
instructs us concerning the principles upon which alone a
perfect division can be performed, it is an additional proof of
the necessity which exists for an intimate acquaintance with
that science.

We have now glanced quickly, but I trust intelligibly, at
the structure of a syllogism and its component propositions.
It remains that we should consider the nature of the materials
of which the propositions are formed, having already discussed
the mode of framing them together. The subject of the first
proposition is, " radii of the same circle ;" and in saying this
we speak of a class, the individuals of which, though they
may differ among themselves in many respects, yet have some
features common to all. Thus, one radius of a circle will be
unlike its fellows as regards position, but it will be exactly
similar with respect to magnitude. So, when speaking of a
given circle we mention its " radius," we employ a name
that may be applied to any straight line whatever that is

VARIOUS MEMBERS OP AN ARGUMENT. 11

drawn from the centre to the circumference. Such a word
is called by logicians, a common-name or common-term,
because, as just stated, it is enjoyed in common by a multi-
tude of objects. But if we proceed to the subject of the
second proposition, we are met by terms which differ entirely
from the preceding, viz., " AC and A B," the names given
to individual radii. These of course can only be applied to
a single object, and are consequently known as singular-
terms, thus serving to distinguish the various members of
a common-term.

Let us here pause for a moment to consider the results at
which we have now arrived, and let us fully comprehend
the purport of common and singular terms. We see that
a common -term when applied to an object, merely indicates
that it possesses certain properties which are shared in like
manner b;y all the other constituents of a specified group.
It is, therefore, evident that such a term or name belongs
in reality not to an individual, but to a definite combina-
tion of qualities which are found in it. And the mode in
which a common-term is obtained, is by comparing a number
of separate objects, observing the points wherein they agree,
combining these points of agreement into one idea, and then
giving this combination a name, so that at any future time
we may be able to recall the idea without having the trouble
to go through the same operations again. Thus, for ex-
ample, men observed the properties of many natural bodies,
and finding that a certain number refused more or less to
alter their volume or shape, the name of solidity was con-
ferred upon this property ; and, accordingly, whenever we
hear the term " solid " applied to anything, we at once know
that the body spoken of will resist a change either as to
volume or shape. This process of combining various pro-
perties into one idea is called abstraction, and is the reverse
of that previously described, namely division ; for while the
latter is al ogether occupied in discovering the points of
difference between various notions, the former exclusively
deals with the points of resemblance.

A singular -term is on the contrary employed to designate
individuals instead of classes, and therefore is a mere arbi-

12 AN INQUIRY INTO THE

trary sign which conveys the notion of one single object.
Such are all names of persons, rivers, cities, &c., and even
common-terms may be converted into singular-terms by the
employment of the demonstrative pronouns, as " this book,"
" that house," &c. &c.

There is yet another distinction of the members of a pro-
position, which it will be needful to notice. We have hitherto
spoken of the subject and predicate together with the copula ;
now the two former are called the terms, as when a proposi-
tion is expressed in logical order they will form its respective
boundaries or terminations, the copula occupying an interme-
diate position.

Of these terms it will be observed that there are three in
each syllogism ; two forming the subject and predicate of the
conclusion, while the other is confined to the premises, in
both of which it occurs. From these positions it is, that the
names of the respective terms are derived ; thus, the pre-
dicate of the conclusion is called the major-term, the sub-
ject of the conclusion is known as the minor-term, and the
remaining term is characterised as being the middle-term.
These names, too, are used to distinguish the premises, for
that proposition which contains the major-term is called the
major premiss, while the other, for a similar reason, is styled
the minor premiss.

We are now in a condition to perceive clearly the full force
of the train of reasoning which we chose in the first place as
the subject of our analysis. In the first syllogism, we see
that a middle -term, " radii of the same circle," is chosen, with
which are respectively compared the major-term, " mutual
equality," and the minor term, " A and A B ;" the result of
this comparison being, that a certain relation, viz., " mutual
equality," may be predicated of A C and A B. In the second
syllogism, we have precisely the same major and middle terms,
but a different minor-term, which, however, is found to bear
a similar relation towards " mutual equality," as did the other
minor, "AC and A B." The object then sought to be at-
tained, is to show the equality of certain portions of the two
minor-terms, and this is done by employing a fresh middle-
term to serve as a means of connecting the idea of " equality "

VARIOUS MEMBERS OF AN ARGUMENT. 13

with the notion u A C and B 0." This middle-term is " things
which are equal to the same thing," and when it has been
properly applied, as in the third syllogism, we attain the de-
sired result, viz., "AC and B are equal to one another," or
" A is equal to B 0."

Finally, let us recapitulate the information which we have
acquired from our rapid survey of the extent of Logic. We
.find that it will be necessary to investigate, first the subject
of notions or terms ; next, the comparison of terms, or pro-
positions ; and finally, the deducing a conclusion from the
juxtaposition of two propositions, or in other words, the
nature and construction of syllogisms.

Necessarily this preliminary chapter has been somewhat
discursive, and has but briefly sketched the more salient prin-
ciples and branches of Logic. This glimpse of the path
before him, however, as stated in the Introduction, will pro-
bably prove of great assistance to the student, for he will now
proceed to a more detailed examination of the science, with a
good notion of what he may expect to meet ; a course which
is surely preferable to that too often followed, whereby the
learner is introduced at once to tedious technicalities, without
the slightest idea as to where he will find himself at the end
of his study.

CHAPTER II.

OP NOTIONS OR TERMS.

THE student is now about to descend into the plain, and to
enter upon that road whose various windings and ultimate
end he has recently sun 'eyed from an eminence. Conse-
quently he will for awhile lose sight of the goal, but as he is
in a great measure acquainted with the general features of
his course, he will not be dismayed if the path should not
immediately appear to tend in the desired direction. And
here I may mention that at first we shall proceed through
a region abounding in hard names ; but as the principal
technicalities of the science have been already introduced,
together with the principles upon which they are based,
no difficulty will, I apprehend, be experienced in conquering
what might otherwise prove a rather formidable array.

Our immediate subject is, of course, notions or terms ; for
we must obviously possess a certain number of ideas (logically,
terms), before it would be possible for us to make any attempt
whatever at a train of thought or reasoning. Accordingly,
it might be considered necessary that I should in the first
place examine the question as to whether ideas are coeval
with the mind itself, or whether they are the results of ex-
perience : but, were I to do this, I should quit the domains
of Logic for those of metaphysics. Suffice it, therefore, if I
describe the manner in which we obtain certainly many of
our ideas, and possibly all.

1. Simple -apprehension.

Yv r hen any object is presented to the mind, and the atten-
tion is directed to it, a certain mental impression is produced,
unintelligible indeed as to its nature, but the result of which

OF NOTIONS OR TERMS. 15

is that the object is recognised when again observed. That
is to say, an idea is formed in the mind of that combination
of properties and appearances which revealed itself to the
senses upon inspection. Such an idea is termed an intuition,
or singular -representation, and evidently can only refer to an
individual object. It is also necessary for purposes of inter-
communication, that names should be given to these several
intuitions, and these names are called singular -terms ; such,
for example, are, " London, France, Charles, Bucephalus."

Now it is evident that if a separate personal name were to
be bestowed upon each object, great confusion would result ;
and as in the majority of cases it is by no means essential
that, when speaking of an object, reference should be made
to some particular individual, it would speedily be found
necessary to assign certain class-names, under which a number
of similar objects might be grouped. This, accordingly, is
done in the following manner.

Suppose a great many individual books had come under
our notice, and we wished to be able to recall at pleasure the
general idea produced by any one of them, without, however,
mentioning it by name. In the first place we should com-
pare several together, and ascertain the points in which they
resembled, and differed from each other ; thus, we should
perceive that some were illustrated and others not ; that one
related to biography, another to history, and a third to mathe-
matics ; that there were many gradations of size and bulk ;
that they were bound in various styles; but also that every
one of them agreed in possessing certain definite propertiers.
These properties we should then proceed to abstract or
separate from those qualities wherein the volumes differed ;
and, combining the former into one idea, we should be able
to conceive of a class of things, each member of which
would contain in itself all those marks or attributes which
we had selected as essential to the idea in question. Finally,
we should apply some name, in the present case '* book," to
the class thus imagined, and in this manner we should ac-
complish the object with which we had set out.

The process which has here been described is that of ab-
straction ; it will be seen to consist of five steps, viz., com-

16 OF NOTIONS OR TERMS.

parison, or placing several objects together in order to judge
of their resemblance ; reflection, by which we decide upon
the properties in which they agreo or differ ; abstraction,
which enables us to form the points of resemblance into one
idea complete in itself; generalisation, or the conception of a
class whose members shall each contain (inter alia) this com-
pound idea; and denomination, by means of which we im-
pose a name for the purpose of recalling to our remembrance
both the class and the idea ; the names thus imposed, being
known as common terms ; e.g., " sea, river, mountain."

Into these two classes, then, viz., singular and common re-
presentations, may all our notions be divided ; and as that
action of the mind which merely consists of forming an idea
is termed simple-apprehension, so it is said to be incomplex-
apprehension when we receive a notion of individuals with-
out observing any relation between them, or complex -appre-
hension, when we perceive the existence of a class.

2. Abstraction of Common-notions

The faculty of abstraction is possibly the most active and
powerful with which the human mind is endowed ; far from
remaining quiescent when it has succeeded in forming a
common -notion (or conception as distinguished from intuition)
by the comparison of separate individuals, it instantly pro-
ceeds to repeat the process on a larger scale. This is done
by treating a number of classes as so many individuals, and
then when their points of resemblance have been noted
and combined into one idea forming a higher class, which
will include amongst its members all the former classes.
Nor need we stop even here, for it is evident that no limit
exists to the number of repetitions of such a proceeding,
unless indeed there be a limit to the exercise of imagination
itself.

Now r every science arranges the subjects upon which it
treats, in a perfectly similar manner, this being based upon
the results of abstraction : accordingly, logicians have devised
a certain scheme of names for this system, which we shall
now explain.

OF NOTIONS OR TERMS. 17

A single object is called an individual, and comprehends
within itself two distinct sets of marks or attributes ; these
are; first, that combination of qualities which we abstracted
to form the idea of a class, and, secondly, such attributes as
remain. Each of the former is termed a property, whilst
the latter are called accidents or differences ; the class of
which the individual is a member being known as a species.
This species, which is merely composed of individuals, is
culled the lowest or infima species, and the next higher class,
being founded upon a consideration of infima species, is
termed a genus : the latter name, however, is only applied
when we contrast the higher class with the lower, for in the
next stage of our conceptions we come to a yet wider genus,
of which the previous genus is only a species. Thus we go
on until we arrive at the most comprehensive class of all,
which is accordingly named the highest or summum genus,
and this, of course, can never be a species, for there is no
higher class to include it. Every other genus is called a
sifoaltern genus, being alternately a species and a genus.

An example of the above method of arrangement may be
given as follows :

Individual .... Iron.

Intima species . . . Metal.

SuDaitern genus . . Elementary substance.

-. Summum genus . . Matter.

Accordingly, we can say that iron is a kind of metal ; that
a metal is a species of elementary substance ; that an elemen-
tary substance is a genus of which metals are a species, or
that an elementary substance is a species of matter.

It is, of course, quite clear that the precise details of the
system, such as the question of what are to be considered as
individuals, or where abstraction is to cease, must be left to
the arbitrary regulations of each science : the only point here
insisted upon being the fact that this system is employed in
every pursuit which engages the human mind, thus showing
decisively that thought proceeds according to certain fixed
laws ; which laws it is the province of Logic to explain.

18 OF NOTIONS OR TERMS.

3. Predicables, Extension, and Intension.

We have already stated that "predication" is the affirming
or denying one thing of another; thus, when I say "A is B,"
I am said to predicate B affirmatively of A, but were I to
state that " A is not B," I should predicate B negatively of
A. Now those notions or terms which may be predicated
affirmatively of others are called "predicables" and must neces-
sarily include a greater number of objects than the subjects of
which they are predicated.* Thus, a species may always be
predicated of an individual, or a genus of a species ; and there-
fore, in accordance with the above-given example, we may say
" iron is a metal," or " metals are elementary substances," but
not " metals are iron," or " elementary substances are metals."

It will here be seen that in legitimate propositions, the
subject contains within itself not only the whole of the marks
or attributes which collectively form the predicate, but also
an additional series of qualities. For instance, " iron " con-
tains the common-notion of a " metal," together with those
peculiar marks which enable us to distinguish it from other
metals : accordingly, there is a greater number of marks or
attributes in the subject than in the predicate, and this kind
of comprehensiveness is called the intension of a term. But,
on the other hand, we see that the predicate embraces a
much larger number of objects than the subject, as a "metal"
not only includes everything that is " iron," but multitudes
of other things besides, such as " gold, silver," &c. ; and this
species of capacity is known as the extension of a term. Con-
sequently, a term used in extension comprises only the specific
properties of a body ; and as it is, therefore, more general and
less distinctive, it may always be predicated of a term used in
intension, which consists both of properties and of accidents.f

4:. Division of a Common -notion.

If we are desirous of completely understanding any sub-
ject, it is very necessary for us to examine it closely, and the

* Here, of course, I allude to common-terms, for a singular-term can
never bo predicated of anything but itself; e.g., we can say * ; John is
John," but not " a man (i.e., every man) is John."

f See page 17.

OF NOTIONS OR TERMS. 19

mental process by which we perform this is what I shall now
consider. It is, in logical language, termed division, and
consists in viewing every general idea as composed of two
main sections, viz., the several members or parts of the idea,
and the tie which connects them together. We then place
the various parts in regular symmetrical order, such as is
best adapted to their mode of union, and thus we are enabled
to study each object separately, both as regards its own indi-
vidual features, and its relations to the other members of the
system.

Now the " tie " or " mode of union " which has been here
alluded to, is altogether arbitrary, and depends upon the
purpose which w r e have in view when entering upon the
study of any subject. Take, for example, the science of
natural history : Aristotle, looking upon the blood as the
grand basis of the phenomena of life, divided all animals into
two great classes, one possessing colourless and the other red
blood, which done, he proceeded to describe the individuals
forming these classes ; Cuvier, on the contrary, adopted the
bony skeleton as his guide in the arrangement of the various
forms of life ; while Rymer Jones, Vogt, and Siebold have
respectively chosen the nervous system, the phenomena of
development, and the relative complexity of organisation, as
keys wherewith to unlock the vast storehouse of nature.

But when we have in this manner set apart some portion
of the subject as a general principle to which we must con-
stantly adhere, it becomes necessary to separate the subject
into as many parts as may be convenient. This is done by
observing the marks in which one group or class of objects
differs from another, and thus dividing the whole of the sub-
ject into a certain number of genera : each of these genera is
then examined and similarly divided into lower genera ; and
BO we go on until we can no longer discover any smaller
groups in a class, but are compelled to enumerate the indi-
viduals of which it consists. Thus we arrive at a regular
system of summum genus, subaltern genera, infima species,
and individuals.

In order, however, that this process may be properly per-
formed, logicians have laid down the following rules :

20 OF NOTIONS OR TERMS.

1. The whole subject must be divided : that is to say, the

various parts taken together must exactly equal the
genus divided.

2. The division must be conducted according to some

single, definite principle.

3. The parts must be quite distinct ; no two containing

any common object.

Thus, if we were studying architecture, and wished to ob-
tain a correct idea of the class of objects which are termed
buildings, we must discuss the whole of the subject, and not
confine our attention to a few species, such as palaces and
temples only. And then when commencing the division, we
must proceed according to some settled principle, such as, for
instance, " application," consistently with which we should form
the different species of " private-dwelling-houses," " factories,"
" warehouses," " churches," &c., and therefore no confusion
would result, for the third rule given above would remain
uninfringed. But if we were to pursue a different plan, and
to divide buildings indiscriminately into " palaces," " Doric,"
" Gothic," " prisons," &c., we should violate both of the latter
rules, having employed two principles of division, viz., " style"
and " application," in consequence of which the various classes
would be intermingled, and no true division would be per-
formed ; for it is evident that some palaces might be Doric
and others Gothic, &c. This error is termed cross -division,
and is one of the most frequent sources of confusion and per-
plexity in discussion and argument.

5. Positive, Negative, and Privative Terms.

In order to test a division as to whether it be perfect, logi-
cians are accustomed to take each part separately, and ex-
amine the possibility of dividing the whole subject into
positive and privative portions with reference to the selected
part. Thus, suppose the subject " man " be divided according
to the principle of " colour :" we should have the four species
of" white-men," "black-men," "red-men," and "yellow-men."
We tli en see that it is possible to also divide " man " into the
two ideas or conceptions of " whitemen " and "non-whitemen,"
for black, red, and yellow may all be described as non-white.

OF NOTIONS OR TERMS. 21

In the same manner " man " may be divided into " black " and
"non -black," "red" and "non-red," "yellow" and " non-
yellow," and so at length we see that none of the classes in-
termingle with each other.

The term " white-men " is called positive, because it denotes
that a certain view (white) is taken of the object (men), while
the term " non-whitemen " is said to be privative, in conse-
quence of its implying that such a view might be, and yet
is not taken. If, on the other hand, it were impossible to
form a certain notion of a subject, the term which implies
this, such as, for instance, a " non-white negro," would be
styled negative.

6. Definition.

In the process of logical division it is evidently necessary
that we should employ some means of precisely determining,
first, the full extent of the subject to be divided, and then
the respective capacities of the various parts or species : this
we are enabled to do by the use of definitions, that is, certain
expressions which describe an object or notion in such a
manner that we are enabled to distinguish it from all others.

Now the act of forming these expressions is termed the
process of definition, and consists in an enumeration of the
various attributes composing a notion. As a notion, how-
ever, may be either singular or common, we are obliged to
use two kinds of definition, one of which, accidental definition,
is applied to individuals, and consists of the specific name
together with the accidents ; while the other, essential -defini-
tion, being applied to classes, consists of the generic name,
together with the specific difference. Thus, the Thames
might be defined as " a river which flows through London,"
where " a river " is the name of the species, and " flowing
through London " the accident which distinguishes the
Thames from other rivers. Again, we may define light as
" a species of motion affecting the optic nerves in such and
such a manner," the genus being " motion," and " affecting
the optic nerves" the difference which distinguishes light
from other species of motion.

This latter kind of definition, consisting of the genus and

OF NOTIONS OR TERMS.

specific difference, is also termed logical-definition, in opposi-
tion to physical -definition, which enumerates such parts of the
object as are actually separable : e.g., the boiler, mechanism.
&c., of a steam-engine. Some writers also include physical-
definitions under the head of essential-definitions.

Various rules have from time to time been given by
logicians for the purpose of securing correct definitions, and
may be summed up as follows.

1. The definition must be of exactly the same extent as
the object defined : that is to say, it must not be of too
narrow or too wide an application. Thus, to define "gravity"
as " a force which attracts bodies to the earth " would be too
narrow, as not including the celestial attractions, and being
only applicable to terrestrial gravity : to define it as " a
force which attracts one body to another," would be too
wide, in consequence of its including magnetic attraction, &c.

2. The definition must not contain anything beyond what
is absolutely essential to the subject. For instance, it would
be incorrect to say that a " man" is "an animal endowed
with the faculty of speech and with life" as it might then be
supposed that the existence of an animal with speech, but
lifeless, was possible.

3. The definition must be plainer than its subject, and must
not be a repetition of the same term : e.g., the explana-
tion that " a metal " is " a metallic substance," would be no
definition at all, while to assert that it is " a product of
Plutonic action " is equally unsatisfactory.

7. Names and their Divisions.

We have already seen that when an idea or conception is
gained of any object or class of objects, some name is imme-
diately attached to it, for the purpose of recalling the impres-
sion at any future time. It now remains to describe the
various species into which these names are divided for logical
purposes.

1. Making a division according to logical quality, we find
that all names or terms may be divided into positive, privative,
and negative, which have been described above. Positive
terms, however, are also called definite t from their distinctly

OF NOTIONS OR TERMS. 23

defining an object ; while for the reverse reason privative and
negative terms are styled indefinite.

2. Names, as regards the method of using them, are either
univocal, equivocal, or analogous ; that is to say, some have
only one meaning, such as " book," "sofa ;" others have several
meanings, such as " light," which signifies either the contrary
of " heavy," or a physical force ; while others, again, are ex-
tended from one object to another in consequence of some
similarity thus, " tongue " may be applied either to the body
or to a piece of land.

3. Viewed as to their mutual dependence, terms are absolute
or relative. The former appellation is bestowed upon those
terms which are considered by themselves as a whole ; the
latter belongs to those which form part of a more complex
idea. For example, the term " man " would be absolute ;
while plaintiff would be relative, as being a portion only of
the idea plaintiff-and-defendant. It will therefore be seen
that relative terms exist in pairs, and cannot be applied to
the same object, as then they would be what is called opposite,
to distinguish them from compatible terms, as those are
named which may be so applied.

Correlatives is a name given to each pair of relative terms,
and implies their mutual connection.

4. Terms are either concrete or abstract, according as they
imply a notion together with the object furnishing the notion,
01 the notion by itself. Thus " fluid " is a concrete, "fluidity''
an abstract term.

Also when the terms employed are common terms, or the
names of classes, a further distinction will be observed. Take,
for example, the concrete term "fluid;" it is evident that there
is here implied a substance possessing certain attributes ; ac-
cordingly, such a term is called attributive, or connotativc,
because it connotes some attributes together with the object.
Again, the abstract term " fluidity " is, in like manner, named
absolute, or non-connotative, from its merely denoting ail
attribute and nothing beyond.

8. Opposition of Terms.
There is said to be a contradiction in terms, or two terms

24: OF NOTIONS OR TERMS.

are said to be in contradictory opposition to one another, when
the only difference between them consists in the respective
presence and absence of a negative particle ; this difference
enabling us to apply them universally. Thus, everything
must be either "living" or "not living," "red" or "not
red," &c.

When, however, two terms differing as to the same idea
cannot be both applied to the same object, and yet there are
some objects to which neither can be applied, such terms are
said to be in contrary opposition to one another : e.g., a man
is not at the same time " walking " and " running," but a tree
does neither,

9. Structure of Terms.

An idea or term is expressed by a word or words ; thus,
14 man," " horse," " steam-engine," " the Emperor of Russia/'
and such words as can be used alone to represent a term, are
called categorematic ; while all others are denominated syn-
categorematic. Sometimes, however, we meet with a single
word apparently filling the place of a term, but for which it
is necessary to substitute some other expression before its
fnll import is conveyed. Take, for example, the sentence
" He loves ;" this, if reduced to logical form, would be " He is
a person who loves."

10. Conclusion and Recapitulation.

\Ve have now reached the end of our investigation into
the first great division of Logic, and before we proceed any
further, it will be well for us to cast a brief glance backwards,
and fully comprehend the connection which exists between
the subjects just discussed, and those to come.

The course, then, of our investigations has been first to
analyse the method in which we gain and record the im-
pressions or ideas produced by the various objects which
attract our attention : iD doing this we found that all our
ideas are either of individuals or of classes, the former
being the result of incomplex-apprehension, the latter of
complex-apprehension, which consists of the five processes of
comparison, reflection, abstraction, generalisation, and deno-

OF NOTIONS OR TERMS. 25

miiiation. In the next place we examined the mode of
arranging and classifying our ideas by the abstraction and
division of conceptions (common-notions) : this led us to per-
ceive that the subject of a proposition embraces more marks
or attributes than the predicate, while the predicate compre-
hends a greater number of objects ; that is to say, the subject
has the greater intension, the predicate the greater exten-
sion. We then showed how a logical division might be
tested by the use of positive and privative terms, which done,
it became our duty to describe the process of definition, and
to explain the various rules which have been laid down for
the purpose of securing correct results. Finally, we enu-
merated the divisions of the various names which have been
bestowed upon ideas, and concluded by noticing the opposi-
tion and structure of terms.

It will of course be understood that in order to form an
idea, it is not necessary that a tangible, corporeal object
should be presented to the senses, for we have many notions
to which there exists no corresponding reality : such, for ex-
ample, are our ideas of justice, honesty, &c. In fact it may
be said that no common-notion whatever has any existence
out of our own minds ; the conception of "man'' for instance
being merely that of a combination of marks or attributes
which are never found separately by themselves, but are
always united to other objects. Thus it is certainly true that
the idea " man " has no isolated existence, but still it cannot
be denied to exist, simply because it does so in conjunction
\yith something else.

This question, here touched upon, is the celebrated bone
of contention between the schools of the nominalists and the
realists, the former following Abelard, and denying that
common-notions (or universals) are anything more than mere
names, while the latter, under the guidance of Plato, strongly
affirmed the reality of their existence. The days of the
schoolmen was the time when this controversy grew most
warm, and such was the importance attached to the subject,
that kings and popes did not scruple to exert their utmost
power in the attempt to secure the triumph of the sect which
they respectively patronised. But this by the way.

26 OF NOTION L OR TERMS.

Now when the mind has once become supplied with ideas,
it is enabled to reflect, the result of which is the formation of
certain judgments. These judgments, when formally stated,
are termed in logical language propositions; and, accordingly,
the subject of our next chapter will be an examination of
their origin and nature.

CHAPTER III.

OP JUDGMENTS OR PROPOSITIONS.

1. Formation of Judgments.

Judgment is the act of determining by comparison whether
one idea is or is not included within another ; that is to say,
it ascertains whether an individual belongs to a certain
species, or a species to some genus. Archbishop Thomson
has defined it as " an attempt to reduce to unity two cogni-
tions." He says, "When one decides that * Socrates is wise/
it is that hereafter one may, by combining the two notions,
think of ' the wise Socrates.' " Now it is by no means evident
that the two cognitions are here attempted to be reduced to
unity, for no person would surely expect to render them so
inseparable, that whenever the idea of " wisdom " presented
itself to his mind it should be invariably accompanied by the
notion of " Socrates." In fact the judgment that " Socrates
is wise/' is merely an assertion that " Socrates belongs to the
class or species of wise men," or " Socrates possesses wisdom,"
thus enabling us to fix his place more exactly in our system
of ideas.*

Accordingly, it will be seen that judgment is the result of
that mental faculty which so strongly impels us to classify and
arrange the various notions with which our senses provide
us, so that we may the more clearly comprehend the various
dependencies and relations by which they are connected to-
gether into one harmonious whole. We have already con-
sidered three portions of this faculty, viz., abstraction, division,
and definition ; it now remains to consider judgment, without
which none of these processes could be conducted.

* For further information upon this point, see Appendix A.

28 OF JUDGMENTS OR PROPOSITIONS.

And here it might well be asked whether, if the formation
of common-notions is the result of judgment, a judgment also
in its turn is not the result of reasoning for we have already
seen that the conclusion of a syllogism is a judgment or pro-
position. This question, however, belonging as it does to
metaphysics, cannot be satisfactorily answered in the present
place ; and, therefore, I shall at once proceed to discuss the
nature and proximate origin of propositions, without minutely
investigating their remote ancestry.

2. Categorical Propositions.

A categorical judgment or proposition is an assertion that
one idea agrees or disagrees with another, and consists of
three parts the subject or idea under examination ; the
predicate, or idea to which the subject is referred ; and the
copula, which determines the relation between them. Thus,
in the proposition " lions are animals," the subject is " lions,"
and is connected to the predicate " animals," by the copula
" are," which implies that " lions " form a species of the genus
" animal." This judgment results from our having compared
the two ideas with a view to ascertain whether the attributes
of " animal " were contained in " lion."

The subject and predicate of a proposition, may of course
be infinitely varied, since there is no limit to the number of
ideas ; but the copula always remains the same, being either
" is," or " is not," or their equivalents. And here it may be
remarked that the word " is " signifies, when employed in a
proposition, the identicality of the subject and predicate, such
identicality being, however, limited by the form of the propo-
sition. The subject and predicate are also called the terms of
the proposition, as they form its boundaries or terminations.

Categorical propositions are divided into pure and modal
the former being cases where the subject is directly asserted
to agree or disagree with the predicate ; the latter where the
subject is said to agree or disagree with the predicate in some
particular manner. For instance, " The sea is rough ;" " He
addressed the people ;" are both pure, but "The sea is terribly
rough ;" " He addressed the people good humouredly ;" are
modal. This distinction is, however, of no use for logical pur-

OF JUDGMENTS OR PROPOSITIONS^

poses, since we may always treat modal propositions as being
pure, by simply attaching the mode to either the subject or the
predicate : thus, in the example above given, " terribly rough "
must be taken for the predicate.

3. Hypothetical or Conditional Propositions.

All judgments are not formed by a comparison of existing
notions, for it is possible to decide upon the mutual relation
of two assumed conditions of things. Accordingly, we meet
with a class of propositions termed hypothetical, or conditional,
whose assertions are subject to a certain condition : of this
kind are such sentences as the following " If the results of
geological science are trustworthy, the earth has existed for
countless ages." " If you do this well, you shall be rewarded."

Hypothetical propositions are not, however, to be considered
as different in nature from categoricals, for both species of
judgment result from precisely the same operation of the
mind. This will be clearly seen if we examine one of the
instances given above, and ascertain what it is that we really
assert. Taking the first example, it is evident that we decide
nothing as to the results of geological science, or as to the
earth, but we say that the assuming those results to be trust-
worthy would necessitate our granting the earth to be of the
age stated. This judgment, then, may be expressed as
follows, viz., " The case or supposition of the results of geolo-
gical science being trustworthy, is a case or supposition of
the earth having existed for countless ages" where the
subject, copula, and predicate of a categorical proposition will
be at once recognised.

4:. Disjunctive or Alternative Propositions.

There is yet another form which our judgments may
assume, this being the statement of some alternative, such as,
" Either Tyndall is wrong, or mechanical force produces
heat ;" which, accordingly, is known as a disjunctive or alter-
native proposition. To show its harmony with the forms
already discussed, we have only to remark that it may be
converted at will into a hypothetical, as, " If Tyndall is not

30 OF JUDGMENTS OR PROPOSITIONS.

wrong, mechanical force produces heat ;" or into a categori-
cal, thus : k< The case of Tyndall being wrong, and the case of
mechanical force producing heat, are all the cases possible."

As regards hypothetical and disjunctives considered apart
from categoricals, we shall have more to say when we come
to discuss the treatment of arguments where they occur ; at
present, however, we are concerned altogether with pure cate-
goricals, having shown that all propositions whatever may be
regarded as such.

5, Quantity of Propositions.

As we have no ideas beyond those of individuals and of
classes, our judgments must always be concerning intuitions
(singular-notions), or conceptions (common-notions). Now a
singular-notion being indivisible, we must invariably treat of
the whole of it ; but as regards common-notions, we are able
to discuss either a part or the whole. This distinction has
enabled logicians to divide all propositions according to
quantity ; that is to say, according to the extent of their
subjects : and, therefore, whenever the subject is a singular-
notion, as, " John is rich," or the whole of a common-notion,
as, " All metals are conductors of heat," the proposition is
called universal ; but if only part of a common -notion be
employed for a subject, as, "Some metals are lighter than
water," then it is termed particular.

6. Quality of Propositions.

Another division of propositions is according to the signi-
fication of the copula, which is termed the quality of a judg-
ment, and as this must be either affirmation or negation
(' is " or " is not "), so propositions are styled affirmative or
negative, according as they respectively express the agree-
ment or disagreement of subject and predicate. Thus, " The
whale is a mammifer " is an affirmative proposition ; while
" No alloy of ammonium is stable " is negative.

It must here be remarked that a negative sign may occur
in a proposition, and yet not belong to the copula ; in such a
case the proposition is affirmative. Take, for example, this

OF JUDGMENTS OR PROPOSITIONS. 31

judgment, "Not to accept the offer is great folly," and we see
that the " non-acceptance " and " great folly " are declared to
agree with each other.

7. Distribution of Terms.

Whenever in a judgment a term is used in its full sense
that is to say, as comprehending every single object that it
could possibly include it is said to be distributed: accord-
ingly, every universal proposition distributes its subject, but
particulars do not. When, however, we examine into the
distribution or non-distribution of the predicate, we find that
this depends not on the quantity, but upon the quality of the
proposition. Thus in negative judgments it will be seen
that the whole of the predicate is declared to disagree with
the subject ; as, for instance, in the following proposition, " No
negro kingdom is civilised," where the entire idea of " civili-
sation " is pronounced to be incompatible with the idea of
" negro kingdoms." But in affirmative judgments the case is
different, as we can only infer from the form of the expression,
that a, part of the predicate is implied. Thus, knowing that
one portion of the genus "animal" is composed of "horses,"
or in other words, that the attributes forming the idea of
" animal " is to be found in every horse, we can say correctly
that " horses are animals." Here, then, the predicate is not
distributed.

Consequently, we arrive at these two rules :

1. The subject is distributed in universal, but not in

particular propositions.

2. The predicate is distributed in negative, but not in

affirmative propositions.

The latter rule is, however, subject to three exceptions ;
first, when in an affirmative proposition the predicate is a
singular notion and is consequently distributed, for we can-
not think of a part only of an intuition ; secondly, when some
expression is employed which indicates that the whole of the
common-notion forming the predicate is compared with the
subject. Thus, in both of the propositions, " Davy was the
discoverer of potassium," and " These fragments are all that

32 OF JUDGMENTS OR PROPOSITIONS.

remain," the predicate is distributed. The third exception
is to bo found in negative propositions, where the predicate
is qualified in such a manner as to indicate that part only of
its signification is employed. This will be observed in such
sentences as " Steam-engines are not some machines ;" " No
men are some created beings;" which import respectively
that some machines are not steam-engines, and that some
created beings are not men. These latter propositions are
termed partial-negatives, those to which the rule applies
being styled total-negatives.

8. Relation of Terms.

We have already stated that judgment is the act of deter-
mining by comparison, whether one idea is or is not included
within another. In doing this we find some cases where the
notions are of equal extent, such as the various intuitions
produced by the same object under different circumstances,
or those conceptions which comprise the same individuals.
This fact we express in the form of the proposition, which
consequently indicates that it is the result as it were of two
judgments, the one having ascertained that the subject of
thought belonged to a certain class, while the other deter-
mined that it was co-extensive with the class. Such propo-
sitions are those mentioned above as constituting exceptions
to the rule which declares that no affirmative proposition dis-
tributes the predicate.

Now in consequence of this relation, it follows that we may
indifferently affirm the predicate of the subject, or the subject
of the predicate. Thus it matters not whether we say
" Davy was the discoverer of potassium," or " The discoverer
of potassium was Davy ;" or again, whether we say, " These
fragments are all (the fragments) that remain," or " All the
fragments that remain are these (fragments)." Accordingly,
such propositions are termed substitutive, from our being able
to employ subject and predicate as substitutes for each other.

All other affirmative propositions have their predicates
non-dietributed, and merely import that these may be attri-
buted to, and not substituted for, the subjects. On this
account thev are stvled attributive.

OP JUDGMENTS OR PROPOSITIONS. 3?

9. Systematic Classification of Propositions.

Having now given a full description of the various divisions
and subdivisions of propositions, it will be well to give a short
summary of the system. This is best done by the use of a
" scheme," as follows :

Propositions

regarded logically, i.e. with reference to their form,
are divided according to

1 1

Quantity, Quality,
into into

I 1

1 1 !

Universal. Particular. Affirmative :
these being sub-
divided as regards
the relative extent
of subject and
predicate,
into

Negative :
these being sub-
divided as regards
the distribution or
non-distribution of
the predicate,
into

.1 i

Substitutive. Attributive.

1 !

Total. Partial

10. Table of Possible Propositions.

We see by the above scheme, that propositions are of
four great classes, affirm ative-substitutive, affirmative -attri-
butive, total -negative, and partial-negative. Each of these
may be again subdivided into universal and particular, so
that altogether there are eight possible kinds of judgment or
predication. The names of these propositions, however, being
too long and cumbersome for constant repetition, logicians
have adopted certain letters to serve as symbols for these
names, and in the following table will be found a list of all
possible propositions, together with their respective symbols,
and illustrative judgments ; the subject and predicate in each
being represented by the letters X and Y.

34 OF JUDGMENTS OR PROPOSITIONS.

Name. Example. Symbol.

Univ. Affirm. Substi. All X is all Y. * U.

Univ. Affirm. Attrib. All X is some Y. A.

Univ. Total Neg. No X is Y. E.

Univ. Partial Neg. No X is some Y. rj.

Part. Affirm. Substi. Some X is all Y. Y.

Part. Affirm. Attrib. Some X is some Y. I.

Part. Total Neg. Some X is no Y. O.

Part. Partial Neg. Some X is not some Y. w .

In this table there are two propositions which, as being of
little practical importance, we may leave out of our future
consideration. I allude to those whose symbols are rj arid u ;
the reason of their inutility being as follows. When we say
" no men are some animals " (rj), we mean " some animals are
not men " (0), which latter, being a much more forcible and
convenient mode of expression, is usually adopted. Also
when we say " some men are not some animals " (w), the
power of negation is still less, for there is nothing to prevent
us saying at the same time " some men are some animals."

Accordingly, I shall confine my future remarks to the six
kinds of judgment, U, A, E, Y, I, and 0, and when the
student is able to treat arguments involving these, he will
find very little difficulty in disposing of those rare cases in
which r) and w may occur.

11. Interpretation of the Copula.

The copula, as already stated ( 2), signifies a certain
identically of the subject and predicate. This identically,
however, may be considered from several points of view, ac-
cording to the purpose we have in hand. Thus, if we were
engaged in determining the intension of the notion " fluids,"
i.e. in ascertaining what were its marks or attributes, and we
were to form this judgment, "All fluids are compressible," we
should mean that fluids were contained in the class of com-
pressible substances, in virtue of one of their attributes being
compressibility. But if we were chiefly desirous to fix the
relative extent of the terms, i.e. to determine their extension,
we should only care to imply by the above expression that
the class of compressible substances included amongst other
things the class of fluids.

OF JUDGMENTS OR PROPOSITIONS. 35

It will, however, be observed that these are not two different
meanings of the proposition, but merely two different modes of
regarding the same meaning.

Another method of interpreting the copula, or connection
between subject and predicate, has been suggested. This
consists in viewing the judgment as regards its denomination,
i.e. in considering it as implying that the predicate may be
given as a name to each of the objects contained in the
subject. The example stated above, if interpreted in this
manner, would be held to imply that the name " compres-
sible " might be given to every fluid.

12. On some other Properties of Judgments.

It is impossible for us to form a complete idea of any object,
as we are unable ever to ascertain the whole of its various
marks or attributes. Accordingly, we observe continually
some new feature, and this it is which causes us to make so
many fresh judgments. At the same time there always exists
a certain set of marks which are almost inseparably connected
in our minds with respective ideas; so that it is scarcely
possible to recall these ideas without at the same time recall-
ing those attributes. Take, for example, the case of material
bodies ; we cannot think of any, without also thinking of
shape and extension, two properties of matter.

Upon these considerations, metaphysicians, and after them,
logicians, are occasionally accustomed to consider judgments
with reference to their bearing upon our knowledge of the
subject. If they increase our information, such as those
which result from our discovery of some new attribute, they
are termed ampliative. If they add nothing to what we
really know 7 , they are called explicative when they are in a
measure explanatory of the subject by predicating some-
closely-connected attribute; or tautologous, when the predicate
is identical with the subject, such as, " A man's a man."

13. Concluding Remarks.

In the present chapter we have taken the subject of
"judgments," for logical investigation, and the result of our
studies may be summarised as fellows.

3fi OF JUDGMENTS OR PROPOSITIONS.

Judgment is the act of determining the agreement or dis-
agreement of two notions, and when its result is expressed in
words, it forms a sentence which is termed a proposition.
Propositions may be stated categorically, such as " A is B," or
" A is probably B," the former being pure, the latter modal :
hypothetically, such as " if A is B, C is D :" or disjunctively,
such as " either A is B, or C is D." All propositions may,
however, be reduced at pleasure to a pure categorical form.
Accordingly, in a systematic account of judgments, reference
is made exclusively to pure categoricals, concerning which
there are four great doctrines. The first is of quantity, and
divides all propositions into universal or particular, according
to the respective extent of their subjects. The second is of
quality, and divides all propositions into affirmative or nega-
tive, according to the import of their copulae. The third is
of distribution, and determines in what cases the various
terms are employed as wholes or parts, i.e., whether they are
distributed or non-distributed. The fourth is of relation,
and arranges all propositions according to the extent of their
predicates ; affirmatives being divided into substitutives and
attributives, and negatives into total and partial. From this
classification it results that there are eight different kinds of
propositions, each being for the convenience of logicians
distinguished by an arbitrary symbol. Two, however, of
these species may be dispensed with as being of little prac-
tical importance ; and, therefore, only the remaining six need
be dwelt upon in future. Judgments may also be viewed as
regards the significance of their import, which varies with
the method of interpretation. Thus, they may be considered
with reference to their intension, or attributes of the subject;
extension or relative capacity of the predicate ; denomina-
tion, or applying the predicate as a name to each member
of the subject ; or, finally, with reference to their bearing
upon our knowledge, according to which they are ampliative,
or informing ; explicative, or explanatory ; tautologous, or
useless.

We are, therefore, now in a position to enter upon the in-
vestigation of a most important and interesting topic the
formation of new judgments from a consideration of some

OF JUDGMENTS OR PROPOSITIONS. S

already existent. This process, termed reasoning, is as it
were, the very climax of logical science, and illustrates the
use of our preceding reflections upon terms and judgments.
Its study is, however, far from being difficult when orderly
arranged, and is calculated to induce the most pleasing emo-
tions in the mind of any person who has attentively pursued
it, and has observed the singular simplicity and harmony
with which the mind works. In fact, we have already had
some remarkable instances of this, for we have discovered
that the vast, nay infinite world of ideas than which nothing
can be more varied and diverse may be referred to a few
simple processes of the intellect, and may be grouped together
into a system of surprising lucidity. The same thing occurs
with our innumerable judgments, which, though outwardly
dissimilar and confused, are found to be all constructed on
the same plan, and to be capable of arrangement in orderly
sequence and regularity.

Accordingly, to him who zealously strives after a complete
understanding of these facts, there accrues an elevation of
the mind such as cannot otherwise be attained. That grand
principle of systematic grouping which underlies all his
capacities of acquiring knowledge, is roused into vigorous
and healthy exercise ; his powers of observation, or rather,
his capabilities of impression by outward objects, are greatly
increased ; and, while he is charmed by the stately vista of
theoretical truth which reveals itself before him, he is at the
same time conscious that his toils have not been unfruitful in
practical results.

CHAPTER IV.

OF REASONING OR ARGUMENT. SYLLOGISMS.

1. Reasoning in General.

THE desire of the mind for knowledge admits of no satiety :
vast though its acquisitions may be, the pursuit is in nowise
slackened ; and the regions of infinity itself oft yield rich
spoils to some aspiring intellect, which, thirsting for new
worlds to conquer, has striven to investigate the most mys-
terious recesses of the universe. This fact is proclaimed in
every page of the world's history : the speculations of the
philosopher, the actions of the statesman, the harmonious
breathings of the poet, all alike bear witness that the watch-
word " progress " is stamped indelibly upon the human mind.
If, then, we consider that in our souls- there is implanted a
faculty which irresistibly carries us forward to the acquire-
ment of new truths, we shall not be surprised when we
discover that there are also implanted certain natural laws,
which serve to control and guide that faculty in the manner
best adapted for the attainment of its ends. Accordingly,
since these laws exist, and are the same in all minds, it results
that the method of acquirirfg knowledge is identical in every
case.

Now, information may be obtained in three different ways :
by the presentment to our minds of the various objects of
thought, thus inducing the formation of ideas ; by the com-
parison of ideas, which enables us to make judgments ; and
by the comparison of judgments for the purpose of arriving
at some new truth. The two former of these processes have
hitherto engaged our attention exclusively ; we have there-
fore now to investigate the latter, which, of all the mind's

OF REASONING OR ARGUMENT. SYLLOGISMS. 39

actions, challenges our observation in the most marked
manner.

Beasonmg, then, consists in arriving at some new truth,
from a consideration of other truths already established.
These truths it is evident may be expressed in numberless
ways, as also may the truth to be inferred ; but whenever
an act of reasoning is put into words, it will always be
found possible to separate it into two portions, one expressing
some admitted truths, the other some truth resulting from
them. Thus the mere arrangement of the argument (as an
act of reasoning when expressed in words is termed) matters
nothing with regard to the principles involved ; and, conse-
quently, in spite of these principles being, as above stated,
universal, we everywhere find that reasoning is expressed in
whatever manner may be suggested by the circumstances of
the case. This it is, which has led to such erroneous opinions
as to the true office and nature of Logic ; men, distinguished
in other respects for their prodigious intellectual power (e.g.
Locke), having imagined that because Logic alters the loose,
popular arrangement of arguments, into a form better adapted
for elucidating the principles concerned, it therefore is oc-
cupied in teaching some particular method of reasoning, the
laws of which are different to those employed by such as have
not studied the science.

2. Syllogisms. Inference.

From the preceding remarks it will have been gathered
that before entering upon a logical investigation of any act
of reasoning, it is necessary that this should be expressed in
a certain regular form. Such forms are termed syllogisms,
and are so constructed as to show the validity of the argument,
without any reference to its matter, i.e., to the subjects of
which it treats : that is to say, the mere manner of expression
is such that the new truth, or conclusion, is at once seen to
be legitimately deduced from the truths already granted, viz.,
the premises.

The act of thus deducing the conclusion from the premises
is termed inference, and consists in ascertaining the full pur-
port of the premises. Thus, ascertaining that chlorine is a

OF REASONING OR ARGUMENT.

gas, and knowing that all gases are elastic, I infer, or conclude
that chlorine is elastic. If expressed in logical form, the
argument would run thus : " All gases are elastic ; chlorine
Is a gas ; therefore chlorine is elastic." It is not, however,
always the case that we commence our reflections with the
premises, for we frequently first consider the conclusion,
under the guise of a question or problem. For instance,
suppose in the above case that we wished to know whether
chlorine was elastic or not : we might ascertain the truth by
examining the substance ; and, finding it to be a gas, we
should be certain that it was elastic, as previous investiga-
tions had decided that all gases were so. Here we see that
there are two terms, " chlorine," and " elastic," the agreement
or disagreement of which, we were enabled to decide upon
by finding some third term, " gas," wherewith they might be
respectively compared. This third term is called the middle
term, and is the very essence of the syllogism ; the inference
connected with it being accordingly termed syllogistic, or
mediate inference.

We now arrive at a somewhat interesting question, viz.,
whether there can be any kind of reasoning other than
mediate inference ; that is to say, can we from one judgment
or truth only, directly infer some other ? Some writers have
contended that such a thing is possible, and have accordingly
described a species of reasoning which they term immediate
inference. Others have denied the possibility of this, and
assert that in the examples adduced by their opponents, there
is no inference or reasoning whatever.

Now the truth would appear to be that the disputed cases
are in reality certain examples of mediate inference, which
possess such strongly marked peculiarities as to distinguish
them from all other instances of reasoning, and to lead to the
belief that the laws upon which they are constructed differ
from those of the regular syllogism.

It will, therefore, be well to consider these arguments apart
from the great bulk of reasonings, more especially as owing
to the above mentioned views being adopted, logicians have
devised rules for the treatment of such cases, to which rules
both parties agree. The arguments themselves may be

SYLLOGISMS.

classed under three great heads or doctrines, viz., opposition,
conversion, and coincident junction : these I shall now pro-
ceed to investigate, showing in each case the real nature of
the argument.

3. Opposition.

The relation which exists between any two propositions
differing in form, but identical in matter, is termed opposi-
tion. Thus, the judgments "All fishes swim," and " No fishes
swim," agree as regards their matter, i.e., their subjects and
predicates are respectively formed by the same notions ; but
they differ with respect to form, one being A, or universal-
affirmative-attributive, while the other is E, or universal -total -
negative : they are accordingly said to be opposed. And
here it should be remarked, that in order for opposition to
exist, the respective subjects and predicates must, in both
propositions, be considered with reference to the same ideas,
time, and circumstances. Thus, I might say, " This man is
happy," and " This man is not happy," with perfect truth,
providing I were alluding to his condition at separate times ;
but otherwise, the judgments would be opposed to each
other.

The doctrine of opposition is based upon an examination
of the various forms of propositions, and declares the natural
laws which regulate their mutual relations. Take, for ex-
ample, a proposition in E, " No metals are vaporisable." On
analysing this, we arrive at the following results: that the
proposition asserts the total exclusion of the class " metals "
from the class of " vaporisable substances;" that since from the
nature of things we know there must always be either a total
exclusion, or partial inclusion at least of one class in another
accordingly, if the proposition be true, any judgment which
asserted an inclusion (even if only partial) of " metals" within
" vaporisable substances," would be false ; while if the proposi-
tion were not true, a judgment of partial inclusion, at any rate,
must be correct. The rule, then, that we should deduce from
such an examination would be, " Either E or I must be true ;"
this, when required for formal use, being converted into ita
equivalent categorical propositions, " The case of E being
false, is a case of I being true ;" and "the case of I being false,

4:2 OF REASONING OR ARGUMENT.

is a case of E being true." Taking the example given above,
we have for the complete syllogism,

The case of E being false is a case of I being true,
The present is a case of E (" no metals are vaporisable ")
being false ;

/. The present is a case of I (" Some metals are vaporis-
able ") being true.

In logical language, when we assert the truth of any pro-
position, we are said to posit it ; when we deny its truth, we
remove it. Consequently the above rule is thus technically
expressed, " From the position of E we may infer the removal
of I ; from the removal of E we may infer the position of I -,
and, in both cases, vice versa" The relation thus declared to
subsist between E and I, is called contradictory-opposition,
and E and I are termed the contradictories of each other.

I have now I trust shown, once for all, that the inference
which obtains in cases of opposition, is mediate, and may be
regularly expressed in the syllogistic form. I shall, therefore,
in recounting the remaining kinds of opposition, merely give
the usual logical rules for the position and removal of propo-
sitions, without discussing their bases, as the student will be
able to do this for himself, by following the method of proce-
dure adopted above.*

There are four kinds of opposition : contradictor) 7 , contrary,
subaltern, and subcontrary.

Contradictory opposition exists only between E and I,
although those writers who do not recognise U and Y, describe
it as also existing between A and 0. The rule of this oppo-
sition is, " The position of a judgment infers the removal of its
contradictory ; the removal of a judgment infers the position
of its contradictory." It has been fully explained above.

Contrary opposition exists between those pairs of judgments
which may be false together, but cannot at the same time be
true. These are A and E, A and U, A and 0, A and Y,
U and Y, U and 0, E and U, and E and Y. The rule is,
'The position of a judgment infers the removal of its con-
trary." Nothing, however, follows from the removal of a
judgment. Thus, " All whales are warm-blooded," and " Somo

* For further remarks upon this subject see Appendix B.

SYLLOGISMS. 43

whales are not warm-blooded," are contraries (A and 0) : if
we admit the former, we must deny the latter, but if we
deny the latter, we are in doubt whether to say, " All whales
are all the warm-blooded (things) " (U), or, " All whales are
(some) warm-blooded " (A).

Subaltern opposition exists between certain pairs of judg-
ments which may be true or false together, viz., A and I,
U and I, Y and I, E and 0, and Y and 0. In these cases,
that judgment which has most distribution in its terms is
called the subatiernant, its opposite being styled the subal-
ternate. Thus I is subalternate to A, U, and Y, while is
so to E and Y. The rule here is that, " The position of the
subalternant infers the position of the subalternate."

Subcontrary opposition exists between I and 0, which may
be true, but cannot be false together ; accordingly, the rule in
this case is, " The removal of a judgment infers the position
of its subcontrary." Y and have been termed subcontraries
by Dr. Thomson, but they would rather appear to come
under the head of subaltern opposition, where it will be ob-
served that I have placed them.

It is proper to remark here that the word opposition does
not in logical language imply an incongruity of two judgments,
for we have just seen that there are some cases where opposed
propositions may both be true at the same time ; it is merely
a name given to a certain relation existing between the various
forms of judgments, such relation differentiating as the forms
themselves differentiate. Therefore, when Sir William
Hamilton states* that " there is no opposition between sub-
contraries," and that to say so " is a mistake," he appears to
have been misled by grafting the ordinary sense of the word
;< opposition " upon its logical signification ; for at a short
distance previously we find him declaring opposition to be a
relation existing between two judgments which are " opposed
or conflictive" It is, however, somewhat strange that he
should omit to take any notice of subaltern opposition as such,
and content himself with merely mentioning it as a relation oil
subordination. He, it will thus be seen, admits of only two
kinds of opposition contradiction and contrariety.

* " Lectures on Logic," vol. i. p. 261.

4"i OF REASONING OR ARGUMENT.

It is generally the practice in logical works to give a figure
or " scheme " of opposition ; and, as this plan is useful in
many respects, I subjoin the following, which shows at a
glance the relations that have been described above as exist-
ing between the various forms of propositions.

(All X is all Y) U - Contrary - Y (Some X is all Y)

^L CO

(All X is some Y) A/ Subaltern - 1 (Some X is some Y)

(No X is Y) E - Subaltern - O (Some X is not Y)

V "3

(All X is all Y) U Contrary Y (Some X is all Y)

4-. Conversion.

Conversion is the technical name applied to the operation of
forming one judgment from another in such a manner that
the subject and predicate of the original proposition (the con-
vertend) shall be respectively the predicate and subject of the
new one (the converse). Thus, " Some men of great imagina-
tion are all the good poets," is said to be the converse of " All
good poets are men of great imagination."

Now it is evident that a process of inference takes place
here :* let us, therefore, inquire into its nature.

The import of our first judgment is that the class of
" good poets " is included, amongst other things, in the class

* See Appendix B.

SYLLOGISMS. 45

of " men of great imagination ;" and as we know from the
natural laws of extension that when one thing is included
in another, a part of the object including is equal to the
whole of the object included, we therefore see that in the
present case it will be allowable to predicate the entire class
of good poets," of " some men of great imagination." Accord-
ingly, we frame a general judgment which may be applicable
to all cases, and which runs thus, " A case of A is the case of
the same subject and predicate being reversed and thrown into
the form of Y."

The syllogism, then, will be as follows :

A case of A is a case of Y containing the same terms as

A, but reversed in position,
The present case (" all good poets," &c.) is a case of A ;

/. The present case is a case of " some men of great
imagination are all good poets."

The general practice, however, with regard to conversion is
the same as that pursued in reference to opposition : instead
of framing a syllogism every time we wish to convert a pro-
position, we employ certain rules which enable us to perform
the operation in a more speedy manner. These rules are :

1. The quality of the converse must be the same as that

of the convertend.

2. No terms must be distributed in the converse, but

such as are distributed in the convertend.
If the above rules be adhered to, no difficulty need be ex-
perienced in converting any proposition whatever ; but as a
means of facilitating the process still more, the following table
will be found useful.

U may be converted into U
A Y

E , E

Y
I

, o

One peculiarity of this table will be at once noticed by the
student : I allude to the employment of the form rj. This
is necessitated by the consideration that if we follow the rules

4.G OF REASONING OR ARGUMENT.

just given, we can only convert into r? ; it is, ho7> r ever,
a conversion which is never likely to be made, for, as stated
in a former part of this work (p. 34), is " a much more
forcible and convenient mode of expression" than ?/.

The above method of conversion may be termed simple-
conversion, although this name is usually limited to the con-
version of E and I ; that of A being called conversion per
accidens, or by limitation, in consequence of a particular pro-
position being educed from a universal ; while is treated as
inconvertible.*

There is another process which is sometimes considered as
a species of conversion, and which may well be examined in
the present place. It is variously termed conversion by
equipollence, by contraposition, by negation,^ by double nega-
tion,"^ and immediate inference by means of privative concep-
tions ; the name which I shall employ will be privative-con-
version, as this both indicates the nature of the process, and
is harmoniously opposed to the term simple conversion.

The modus operandi of privative-conversion consists in
changing the quality of the convertend, and altering its
predicate into a corresponding positive or privative concep-
tion, according as the case may be. The reasoning pro-
cess which forms the foundation of the doctrine is as follows.
Take some proposition in A, as, " All intellectual men are
amiable," and let us think what it is that we know about its
terms : the judgment itself makes us aware that " intellectual
men " are in the class of " amiable men," but gives us no
further information regarding the latter class ; we know, how-
ever,^" that it is possible to form a conception which shall in-
clude every man not comprised under " amiable men," and
that then we may deny the latter of the former : this we pro-
ceed to do, and say, " No amiable men are unamiable " a
judgment which supplies us with the desired premiss, and
enables us to form a complete syllogism ; thus :

* Here it will be seen that I allude to those writers who only admit
A, E, I, and ().

f Whately's " Elements," Book ii. chap. ii. 4.

j Hamilton's " Logic," vol. ii. Appendix V. c. p. 267.

Thomson's " Outlines," 86. ^f Supra, p. 20.

SYLLOGISMS. 47

No amiable men are un amiable,
All intellectual men are amiable ;
.*. No intellectual men are unamiable.
This conclusion is the converse required, and is seen to
fulfil all the conditions of privative-conversion ; that is, its
quality is changed, and its predicate is replaced by a cor-
responding privative -conception.

5. Coincident Junction.

When one class is said to be comprised in another we
mean that all the members of the former are also members
of the latter. Accordingly, these members may be considered
as objects which (inter alia) are composed of two sets of ideas
inseparably connected. We cannot, therefore, add anything to
one idea and not at the same time add it to the other: nor for
the same reason can we add one of the ideas to anything, with-
out also adding the other. These considerations supply the
general principles of what may be termed the doctrine of coin-
cident-junction, and which is thus expressed : " From any
judgment we may form another by adding some marks equally
to the subject and to the predicate ; or we may add the sub-
ject and predicate as marks to some fresh conception." Thus
if " a metal is a solid " be true, we may also infer that " a
red metal is a red solid ;" or if we admit that " Logic is
the science of the laws of thought," we must equally admit
that "the study of Logic is the study of the science of the
laws of thought." The former of these inferences has been
termed " immediate inference by added determinants ;" the
latter, " immediate inference by complex conceptions." It will,
however, be readily seen from the above investigation of the
principles involved, that these reasonings may be exhibited in
the syllogistic form, as easily as any of the others.

This concludes the discussion of those arguments which are
commonly styled immediate inferences ; and, accordingly,
whenever we have occasion to employ them in any future
portion of this work, they will be considered as falling under
their own special rules, and not as regular syllogisms. Such
a course will be the more convenient as it will be more familiar
to the student ; for the general laws which constitute the third

18 OF REASONING OR ARGUMENT.

propositions of such syllogisms as have been already con-
sidered, are so firmly fixed in our minds, that we are scarcely
conscious of their existence, until our attention is specially
directed to them ; and, consequently, it may almost be said
that they are never overtly employed in the eduction of so-
called immediate inferences.

It will of course be understood that these arguments are
not limited to a single operation ; for it is possible to start
with a judgment and successively employ the three processes
of opposition, conversion, and coincident -junction, until we
arrive at some other proposition which may satisfy our re-
quirements. Such a proceeding is sometimes said to be merely
a determination of a proposition's full signification ; but this
may be said in effect of all reasoning whatever, for " an ex-
tension of any science through Logic is absolutely impos-
sible ; as 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."*

6. Mediate Inference formally expressed as such. Its
Divisions.

When an act of reasoning is fully expressed in words, i.e.,
if the three judgments be articulately stated, we have what is
termed a syllogism. But as we saw, when treating upon pro-
positions, that these are of three kinds, categorical, condi-
tional, and disjunctive ; so in like manner are syllogisms
divided, according as they contain these respectively. Thus
the syllogism, " All A is B ; C is A ; therefore is B," is cate-
gorical ; " If A is B, C is D ; A is B ; therefore C is D," is
conditional ; and, " Either A is B, or C is D ; A is not B ;
therefore is D," is disjunctive.

Now the two latter species of syllogisms may always be re-
duced to the former when occasion requires, and therefore an
examination of the necessary laws of reasoning, together with
the systematic arrangement induced by these laws, will best
find place under the head of categorical syllogisms. Accord-
ingly, in the following analysis, I shall speak simply of the
* Hamilton's " Logic," Lect. iii. p. 44.

SYLLOGISMS. 4:9

arguments so denominated ; this plan being consonant with
that pursued when judgments were discussed.

7. The Fundamental Law of Mediate Inference.

" Thought," says Sir W. Hamilton, " is the cogniH'm of
any mental object by another in which it is considered ao n-
cluded ; in other words, thought is the knowledge of things
under conceptions." This accords with what I have already
stated concerning the grand principle of classification which
underlies our faculties of acquiring knowledge ; and prepares
us to appreciate the fundamental law of mediate inference,
which is as follows : " Whatever belongs or does not belong to
the containing whole, belongs or does not belong to each and all
of the contained parts."* This law, commonly called the
" dictum de omni et nullo" we owe to the commanding genius
of Aristotle, who first placed Logic upon a sound and durable
basis. It is not, however, to be understood that this dictum is
directly applicable to every case of reasoning ; the assertion
merely being that the validity of any argument is ultimately
referable thereto.')'

For practical purposes men seldom ascend to general and
fundamental truths, but devise a system of rules which, being
immediately applicable, may obviate much of the inconvenience
and delay that would otherwise ensue. Hence it is that logi-
cians have developed Aristotle's dictum into the following
proximate canon. " If two notions agree either wholly or in
part with one and the same third, they agree with each other ;
but if one of them is agreed and the other disagreed with the
same third, they disagree with each other." This canon is,
however, differentiated still further, thus :

1. A syllogism must contain three, and only three, terms, con-
stituting three, and only three, propositions. The force of this
rule is at once evident when we consider that the object sought
to be attained by syllogising, is to determine the agreement
or disagreement of two notions by respectively comparing

* Hamilton's " Logic," Lect. xvii. p. 321.

f Some objections having been raised by Mr. Mill and others to this
account of the fundamental law of mediate inference, I have discussed the
question at greater length in article C of the Appendix.

^^^-^^

>> 0* THK

50 OF REASONING OR ARGUMENT.

them with a third. This, of course, could not be done if we
employed more or less than the three terms, or formed more
or less than the three judgments.

The names of these terms depend upon their position in the
syllogism. The predicate of the conclusion is called the major
term : the subject of the conclusion is called the minor term ;
while the third notion with which the two former are each
compared is styled the middle term. In like manner are
the premises named, that in which the major term is com-
pared with the middle being the major premiss ; the other,
the minor premiss.

Much objection has been taken to this employment of
the words major and minor on account of their ordinary sig-
nification being respectively " greater " and k< smaller,*' whereas
it sometimes happens that the minor term is in reality greater
than the major term, or that we are unable to compare them
together as regards their extent. There is no doubt that
these names were originally imposed from their representing
the facts of the case in one particular form of syllogism which
was considered the most perfect ; but as they have continued
to be used by numerous logicians who were well aware of how
the matter stood, it must be inferred that" major" and " minor,"
when used logically, have merely a technical meaning as dis-
tinguishing the terms of the conclusion, and not as implying
any relative degree of amplitude. A parallel case is to be
found in the use of the word " opposition " (see p. 41). In
consequence of such objections, the premises of a syllogism
have been variously re-named, the appellations of proposition,
lemma, and sumption, being bestowed upon the major premiss,
while the minor is known as the assumption, subsumption, or
hijpolemma.

2. The premises must not both be 'negative. This follows
from the consideration that a term can only show the relation
of agreement or disagreement subsisting between two others,
in so far as it is applicable to one of them at least. If, for in-
stance, we were first to say, "No mathematician is a good moral
reasoner," and then that " Shakspeare was not a mathema-
tician," these statements would give us no grounds of com-
parison between the notions of " Shakspeare " and " good

STLLOGISMS. 51

moral reasoner." We should still be uncertain as to whether
the latter might or might not be predicated of the former.

3. If either of the premises be negative, the conclusion must also
be negative; for this is precisely the case stated in the second
portion of the proximate canon above laid down, viz., " If one
notion is agreed and another disagreed with one and the same
third, they disagree with each other." Thus, from the pre-
mises, "no matter is imponderable," and " all gases are matter,"
we can only conclude that " no gases are imponderable ;" for
the attribute of imponderability was totally denied of matter,
which contains, inter alia, all gases.

4. When the 'premises are affirmative, if either of them be
attributive, the conclusion must also be attributive. Since a
substitutive premiss implies a total identicality in extent of
the middle term with one of the terms of the conclusion,
and an attributive premiss implies only a partial identicality
of like nature, it follows that between the terms of the con-
clusion a partial identicality of extent is all that can be in-
ferred. An example of this will be found in the following
syllogism :

Compounds are all bodies which may be resolved into

simpler forms (U),
Sugar is a compound (A) ;
/. Sugar is a body which may be resolved into a simpler

form (A).

5. The middle term must be more than distributed in the
premises, both taken together. For if this were not the case
we should have no real inference whatever ; as witness this
apparent syllogism

Some beautiful objects are pictures,
Some hideous objects are pictures ;
/. Some hideous objects are beautiful.
Here the two premises are in the form I, which we know
does not distribute the predicate, this, in the present case,
being the middle term " pictures." Accordingly, the major and
minor terms may, for anything the form of expression can tell
us, be compared with different portions of the same thing ;
and this, being equivalent to employing two middle terms,
would violate the first rule, which prohibits the appearance of

D 2

52 OP REASONING OR ARGUMENT.

more than three terms altogether. Of course it might so
happen that when premises of the above nature were used, we
arrived at a true conclusion, as in the following case :
Some beautiful objects are pictures,
Some valuable objects are pictures ;
.*. Some valuable objects are beautiful.
This conclusion would, however, still be considered as invalid,
that is, as not following directly and inevitably from the pre-
mises ; for Logic, it will be remembered, regards not the matter,
but merely the form of reasoning.

Usually the middle term is distributed in one of the pre-
mises at least; we can then tell at a glance that the rule
now under discussion is not violated. Take, for example, the
syllogism

All the metamorphic rocks have been subjected to the

action of heat,

Gneiss is a metamorphic rock ;
.*. Gneiss has been subjected to the action of heat.
The major premiss being A, distributes the middle term ;
and as this must be again mentioned in the minor premiss, it
will necessarily be more than distributed, and will not affect
the validity of the conclusion.

Sometimes, however, we meet with a syllogism whose pre-
mises contain the middle term in such a manner as to show
that the portions employed in each, if added together, would
give more than the whole ; e.g.

Twenty per cent, of these knives are bad,
Ninety per cent, of them are apparently well-made ;
/. Some of these apparently well-made knives are bad.
In this case suppose that the notion " bad " coincides with
the entire portion of " these knives," with which " apparently
well-made " does not ; such portion being only ten per cent,
would still leave a further extent of ten per cent, to be ac-
counted for, and this it is evident must come out of the
" ninety per cent. ;" so that we are sure that the notions
" apparently well-made," and " bad," must correspond to
the extent of ten per cent, at least : this is asserted in the
conclusion.

It will in this place be opportune to remark that much con-

SYLLOGISMS. 53

fusion frequently results from the use of an ambiguous middle
term, thus :

Capes are articles of clothing,

Some tracts of land are capes ;
/. Some tracts of land are articles of clothing.
This syllogism is logically correct, that is, in form ; but if
we examine its matter, we shall see that it contains two middle
terms, for in the major premiss one kind of "cape" is spoken of,
while in the minor, another kind is alluded to. The discussion
of such cases will be further conducted when we come to
examine the subject of fallacies.

6. In the conclusion no term must be distributed, unless it
has also been distributed in one of the premises. The terms
of the conclusion only agreeing or disagreeing with each other
in so far as they respectively agree or disagree with the
middle term ; they can merely be compared with each other
by means of those portions which were found to coincide in
any way with the middle term.

All trees are organised beings (A),

Men are not trees (E) ;
.*. Men are not organised beings (E) ;
And again

Diamonds are combustible (A),

Some precious stones are diamonds (I) ;
.*. All precious stones are combustible (A).
In the former of these syllogisms we have an illicit process
of the major ; that is, the major term is distributed in the con-
clusion without being so in its premiss : in the latter there is,
in like manner, an illicit process of the minor. The valid con-
clusions which might be inferred would respectively be " men
are not some organised beings " (*/), and " some precious stones
are combustible " (I).

By the six foregoing rules may all syllogisms be tested to
ascertain whether they are real or only apparent, whether the
reasoning is correct, or incorrect. They are of great practical
importance, as they enable us to dispense with the reduction
of many syllogisms into a form where the dictum of Aristotle
might be directly applied ; but, as already stated, they must
only be considered as proximate differentiations of one fun-
damental truth.

54: OP REASONING OR ARGUMENT.

8. Of Figure.

In order to facilitate a full examination of syllogistic argu-
ments, that is, of arguments formally expressed, logicians have
investigated the number of positions which the middle term may
assume in the premises, and in accordance thereto, have formed
four classes, under which all possible syllogisms may be ranged.
These classes they call figures, the form of which may be
represented as follows ; employing P to signify the major term
(predicate of conclusion), S the minor (subject of conclusion),
and M the middle.

1st Fig.
MP
SM
.'. SP

2nd Fig.

SM
.'. SP

3rd Fig.
MP
MS
/. SP

4th Fig.
PM

.-. SP

Thus when the middle term is the subject of the major
premiss, and the predicate of the minor, we have the first
figure ; when it is the predicate of both, the second ; when it
is the subject of both, the third ; and finally, when it is the
predicate of the major, and subject of the minor, there results
a syllogism of the fourth figure.

9. Remarks upon the four Figures.

1. The first figure is the most natural and obvious form into
which an act of reasoning can fall ; the cause of this apparently
being that it is the only one in which the Aristotelian dictum
will at once and immediately apply. Thus, to give a concrete
example

The rushing of particles to a nucleus causes the body so

formed to rotate,

The earth was formed in this manner ;
.-. The earth rotates.

This argument, which is employed by the author of
" Vestiges of Creation," I have expressed in popular language,
but the student will find no difficulty in arranging it according
to the model ; " All M is P ; S is M ; therefore S is P."

2. The second figure, though a somewhat distorted method
of stating an argument, is yet very useful and ready in certain

SYLLOGISMS. 55

cases, where we desire to prove that some distinction exists
between two notions, so as to prevent one of them including
the other. Suppose, for instance, we wished to prove that a
certain substance did not contain the metal sodium ; we might
employ such a syllogism as the following :

Any substance containing sodium would give, when

burnt, two yellow bands in its spectrum (U),
This substance when burnt does not do so ;

/. This substance does not contain sodium.

Here the middle term forms the predicate of both premises ;
consequently, the syllogism is of the second figure. If, how-
ever, we wished to apply the Aristotelian dictum, it would be
necessary to arrange this argument according to the first
figure, such an operation being termed reduction. It consists
in a skilful application of the doctrines of opposition, conver-
sion, and coincident junction. In the present case all that
we have to do is to substitute for the major premiss its simple
converse, thus

Any substance which when burnt gives two yellow

bands in its spectrum, contains sodium,
This substance when burnt does not do so ;

.*. This substance does not contain sodium ;
a syllogism most manifestly of the first figure.

It has been held that in every case the rnind unconsciously
performs the process of reduction, and that therefore the
second, third, and fourth figures are merely elliptical expres-
sions of trains of reasoning, the first figure alone being an
adequate representation of a single mediate inference. This
statement, as implying a more direct influence than is usually
imagined of the dictum upon our minds, is not unworthy of
attention ; but since a full examination of the question would
occupy more space than could be conveniently devoted to the
purpose, I shall remain satisfied with having shown that any
argument may be overtly expressed in such a manner as to
evince its dependence upon the great fundamental law of
reasoning.

3. The third figure is of use when we wish to disprove a
theory by instancing some example to the contrary. If we
wished to combat the assertion that " no bodies except water

56 OF REASONING OR ARGUMENT.

ever expand when cooling," we might do so in this manner :
Bismuth sometimes expands when cooling,*
Bismuth is a body other than water ;
/. Some other body than water occasionally expands when

cooling.

The conclusion thus obtained is the contradictory (I) of
the theory to be disproved (E), and accordingly our purpose
is accomplished. In order to reduce this syllogism to the
first figure, we must simply convert the minor premiss, when
the whole will run thus

Bismuth sometimes expands when cooling,
Some other body than water is bismuth ;
.*. Some other body than water occasionally expands when

cooling.

4. The fourth figure is chiefly remarkable for the offence
which it has given to many logicians, who accordingly have
been neither sparing nor gentle in their attacks upon it :
"tortuous," "unnatural," "perverse," "hybrid," "useless,"
" clumsy," " a monster," and " a caprice " may be taken as
samples of the objections raised to its reception. It will,
therefore, be advisable to examine the nature of some syllogism
in this figure : take, for instance, De Quincey'sf explanation
of the non-existence of duelling among the ancient Greeks
and Romans, which is as follows :

No duelling can exist wherever unlimited license of

tongue is allowed to anger (E),
Unlimited license of tongue was allowed to anger among

the ancient Greeks and Romans (U) ;
.'. Among the ancient Greeks and Romans duelling could

not exist (E).

Here it is objected that the mind naturally expects the
converse of the conclusion, in accordance with the tendency
of the argument this leading from " no duelling can exist
where certain license is allowed," to " this license was allowed
among the Greeks and Romans," and then in all symmetry
to " no duelling could exist among the Greeks and Romans."
Now the answer to this is, that the figure of a syllogism

* It invariably expands at the point of solidification.
f Works. Author's Edition. Vol. vii. p. 281.

SYLLOGISMS 57

depending entirely upon the position of the middle term in
the premises, it will not be affected by a change in the rela-
tive positions of conclusion and premises. We have, therefore,
only to state the conclusion first, and then give the premised
as our reasons for forming it, when we shall at once obtain a
smooth and naturally proceeding argument. Thus, we can
say " Among the ancient Greeks and Romans duelling could
not exist ; for this is impossible where unlimited license of
tongue is allowed to anger, which was the case in Greece
and Rome ;" than which a more harmonious expression could
not easily be found.

In like manner, if we take mere arbitrary symbols to repre-
sent the three terms, we shall still have a perfectly clear
syllogism, e.g.

No S is P (conclusion) ;
for No P is M (major premiss),
and M is all S (minor premiss) ;

the meaning of which is, that none of the objects comprised
by S are included by P, since the latter is totally excluded
from M, which contains the same objects as S.

At the same time, however, that the fourth figure is thus
shown to be perfectly legitimate and unforced, it may be
readily conceded that it is but seldom used, as from the same
premises and the converted conclusion we can form a syllo-
gism of the first figure : thus, " M is all S ; no P is M ;
therefore no P is S ;" which being, as it were, more familiar
to the mind, is oftener suggested.

The formal reduction of syllogisms like the above to the first
figure, is effected by simply converting both premises ; e.g.
No M is P,
All S is M ;
.-. No S is P

10. Of Mood or Mode.

The arrangement of the propositions of a syllogism with
reference to their quantity, quality, and relation, is termed
the mood or mode of the syllogism ; and as we are in posses-
sion of symbols which fully express the form of a proposition,
we can at all times represent the mood by the arrangement

i) 3

REASONING OR ARGUMENT.

of these letters : the conclusion, it is well to remark, being
always placed last.

Now as there are eight kinds of propositions, viz. U, A,
E, rj, Y, I, 0, and M, it follows that five hundred and twelve
forms of syllogisms or moods may be made. Most of these,
however, do not constitute valid arguments, and therefore we
must reject them ; e.g. A A has an affirmative conclusion,
though one of its premises is negative ; EGO has both pre-
mises negative j III has either the middle undistributed or
else an illicit process; and so on in numerous other cases. In
like manner some moods are admissible in one figure, but
not in another ; thus, A 1 1 is valid in each of the first and
third figures, but in the second and fourth the middle term
would be undistributed.

11. Table of Valid Syllogisms in each Figure.
From the foregoing considerations it will be evident that
a table may be constructed which will show all the valid syl-
logisms falling under each figure ; and as such a table is of
great practical use, I have drawn up the following :

TABLE OF MODES.

Fig. I.

Fig. II.

Fig. III.

Fig. IV.

Aff. Neg.

A AA . E AE

AU Y . AEE

A A I . E A O

A AI .AEE

All . EIO

AYY . AGO

All .EIO

AUA . E AO

AUA . EUE

. . . E AE

AUA . E UE

AUY .EIO

A YI . EYO

. . . EIO

A YA . EYE

. . .EUE

EUE

%. Tf V f~\

...EYE
"u 1 v r\

IUI . QUO

^ E Y XL
IUI . . .

I AI . O AO

I AI

I YI . OYO

IYI . . .

IUI . OUO

IUI

U A A . U E E

UA A . UEE

UAY .UEE

UAY . UEE

UII . UOO

UII .UOO

UII . . .

UII .UOO

U U U . . .

UUU . . .

UUU. . .

UUU

UY Y . . .

UYY . . .

UYA. . .

UYA

UYY

YUY . YEE

YAA . . .

Y AY . YEE

YII

YY Y . YOO

YII . . .

YUY . . .

YUA

Y YI

SYLLOGISMS. 60

The above table is arranged alphabetically, so as to facili-
tate reference, and enables us at once to determine the
validity or invalidity of any syllogism whose figure is known ;
for if legitimate, it will be found in its proper position, while
if inadmissible, it will be absent.

The propositions rj and w have been omitted from this
table on account of their small importance (see p. 34). It
may also be proper to remind the student that in most of the
older treatises on Logic he will find tables of judgments which
differ materially from the one above given, inasmuch as they
only recognise the four propositions A, E, I, and 0. The
usual form in which such a table is given consists of the
following four mnemonic Latin verses :

Fig. I. Barbara, Celarent, Darii, Ferioque, prioris

Fig. II. Cesare, Camestres, Festino, Baroko, secundce ;

Fig. III. Tertia, Darapti, Disarms, Datisi, Felapton, Bo
kardo, Feriso habet : quarta insuper addit

Fig. IV. Bramantip, Camenes, Dimaris, Fesapo, Fresison.

These lines, or rather the first three, were the invention of
Pope John XXII., whose work upon Logic, under his name
of Petrus Hispanus, enjoyed great celebrity. To each of the
four figures it will be observed that a verse is appropriated,
consisting chiefly of a number of names distinguished by
capital letters,* and containing three vowels ; the vowels thus
employed serve to indicate the mood of the respective syllo-
gisms. For instance, the syllogism " all M is P; all S is M ;
therefore all S is P," is said to be in the mood barlara,
which signifies A A A in Fig. I. The consonants of the
various moods are intended to assist the process of reduction ;
the initial letters show that each mood must be reduced to
that mood in the first figure which is similarly characterised :
s indicates that the proposition immediately preceding is to
be simply converted (in its old acceptation ; see p. 46) ; p
that it is to be converted per accidens, except in the mood
bramantip, where it denotes that the conclusion (I) will, when
the syllogism is reduced, become A ; m that the premises are
to be transposed ; and k that the contradictory of the con-

* Tertia, in the third verse, is merely employed for the sense of the
expression, and is not a mood.

60 OF REASONING OR ARGUMENT.

elusion is to be substituted for the immediately preceding
proposition. The two moods, however, in which k occurs
(baroko and bokarko) may be more simply reduced by em-
ploying the process of privative conversion ; they will then
become ferio and darii respectively.

An example will perhaps assist in rendering the above
description intelligible. Let us take a syllogism in disamis ;
thus,

Some rocks have been formed by the action of water (I),
All rocks are solid (A) ;

.-. Some solid things have been formed by the action of
water (I).

Here the ra indicates that the premises must be transposed,
the major and conclusion being simply converted in accordance
with the requirements of s and s. When this is done, we
obtain the following :

All rocks are solid (A),

Some things which have been formed by the action of
water are rocks (I) ;

.'. Some things which have been formed by the action of

water are solid (I) ;

which is a syllogism in darii, that mood of the first figure
which was indicated by D, the initial letter of disamis.

I have thought it advisable to enter at some little length
upon this subject, as these ancient names of moods are not
confined to logical works, but are often to be met with in old
authors ; in addition to which, it might be expected that in a
work like the present, of professedly a practical character,
some notice would be taken of a method so universally fol-
lowed. In fact, the perfect adaptation of the above quoted
lines to their purpose, would alone render them deserving of
mention; for, as Sir William Hamilton observes, " it must be
confessed that, taking these verses on their own ground,
there are few human inventions which display a higher
ingenuity."

It must also be observed that so far from the method just
described being out of date and obsolete, it may still be
applied in many cases ; the only difference between it and
the table of judgments given in the present volume, being

SYLLOGISMS. 61

that the latter is much more complete, containing not only
all that the A, E, I and system includes, but many other
tjyllogisms in addition.

12. Induction and Deduction.

We have now seen that all acts of mediate inference when
formally expressed, i.e. all syllogisms, may be systematically
arranged and discussed under the two heads of mood and
figure. There are, however, some further divisions of syllo-
gisms which require our attention ; the first of these being
that into inductive and deductive.

The distinction between these two methods of reasoning
may be thus expressed : induction is the process of forming
a general law ; deduction, that of applying a law so made to
some particular case or cases. Or, in other words, induction
consists in reasoning from the parts to the whole ; deduction,
in reasoning from the whole to the parts. In formal Logic,
however, this distinction is comparatively unimportant, as
will be seen from the following considerations.

Take some inductive syllogism, as follows :
Oxygen, chlorine, and steam are elastic (A),
Oxygen, chlorine, and steam are all gases (U) ;

.*. All gases are elastic (A).

Here we see that from predicating "elastic" of the various
parts *'' oxygen, chlorine, and steam," we are enabled to pre-
dicate it also of the whole thus constituted, viz., " gases." It
is, therefore, evident that the general law or truth upon which
the validity of such a syllogism depends, may be thus ex-
pressed : " That which belongs, or does not belong, to each
and every one of the parts, also belongs, or does not belong,
to the whole." This law has been declared to differ from the
dictum de omni et nullo, which, the student will remember, is
to the following effect : " That which belongs, or does not be-
long, to the whole, also belongs, or does not belong, to each
and every one of the parts." Now if we admit the difference
thus asserted that is to say, if we admit that these two laws
are " equally necessary and independent " * then we must, in

* Hamilton's " Logic," vol. i. p. 321. The italics are my own.

62 OF REASONING OR ARGUMENT.

addition, admit that the division into inductive and deductive
syllogisms is imperatively called for, since each species of
reasoning will have been shown to rest upon separate funda-
mental* laws.

That this independence, however, does not exist, may be
shown by a few reflections based upon the nature of what we
understand by the notion of a " whole." In the case under
examination the " whole " of which we speak is the conception
" gas." This, as the student will recollect from what was
said in a previous chapter, is the result of our comparing
various bodies together, and ascertaining those attributes in
which they are all agreed ; the set of attributes so obtained
being then abstracted to form the idea, and receive the name
of " gas." Consequently, when we say " gases," we think of a
class whose members are, not various individual objects, but
various similar sets of attributes existing in separate bodies or
objects, viz., "oxygen, chlorine, and steam;" and when we
say that what may be predicated of the class " gases," may also
be predicated of each of its members, w r e mean that the attri-
bute " elasticity," for instance, may be predicated of oxygen,
chlorine, and steam, not as individual objects, but as separate
and similar sets of attributes ; or, in other words, we imply
that each set of attributes must be capable of forming the
idea "gas" in our minds, and must, consequently, be of
similar constitution with the remainder. In like manner,
when we say that whatever may be predicated of each member
may be predicated of the class " gases," we mean that what-
ever attribute is common to oxygen, chlorine, and steam must
form part of that set of attributes which is called " gas ;'' that
is, we imply that oxygen, chlorine, and steam, considered as
definite sets of attributes, are of similar constitution, and must
consequently each be capable of forming the same idea, " gas,"
in our minds. Now these two expressions, which are thus
seen to have almost identical meanings, are the self-same
laws which have been spoken of as independent of each other,
this statement, therefore, is seen to be incorrect, and, accord-

* As regards the use of the word fundamental in tins place, see
Appendix C.

SYLLOGISMS. 63

ingly, we need not consider the distinction between the pro-
cesses of induction and deduction as more than a logical
trifle.

It must here be rigidly borne in mind, that the above
remarks only apply to induction and deduction when con-
sidered as divisions of pure Logic ; for when we come to treat
upon applied Logic, it will be found that another kind of
induction exists, which necessitates a particular mention, and
which is of very great importance. The difference between
these two kinds of induction is closely connected with a fact
which the student has doubtless observed, viz., that the minor
premiss of our inductive syllogism is obviously incorrect, for
so far from oxygen, chlorine, and steam being all gases, they
only constitute an exceedingly small portion of the class.
This brings us to the consideration that in formal Logic we
have nothing at all to do with truth or falsehood we can only
ascertain whether a conclusion legitimately follows from pre-
mises already granted. Accordingly, we merely look upon
the minor premiss with reference to its form, i.e., its quantity,
quality, and relation, and not as regarding its matter, viz.,
the reality and nature of the notions composing the subject
and predicate : thus, for all purely logical purposes, the pro-
position might be replaced by " X, Y, and Z, are all S "
without in the least interfering with the reasoning process.
Applied Logic, on the contrary, takes into account the relative
natures of the objects furnishing notions, and would construct
the syllogism in the following manner :

Oxygen, chlorine, and steam are elastic (A),
Oxygen, chlorine, and steam are gases (A) ;

/. All gases are elastic (A).

Here it will be seen that the minor premiss is indeed true,
but then there is an illicit process of the minor term, so that
the syllogism cannot be admitted as formally valid.

The deductive syllogism corresponding to our inductivo
example would be as follows :

All gases are elastic,
Oxygen is a gas ;
.*. Oxygen is elastic
where the general law is applied to a particular case.

OF REASONING OR ARGUMENT.

13. Extension and Intension.

In a former chapter it was explained that a proposition
might have its meaning regarded from different points of
view, according as the subject and predicate were regarded
intensively or extensively. Thus, when we say, " All fluids
are compressible," we mean not only that the attributes of
" compressibility " are among the attributes of every " fluid "
(intension), but, also, that the class of " compressible sub-
stances " numbers in its ranks all " fluids " (extension). This
differentiation of meaning, in like manner, finds place among
arguments, and thence has arisen a distinction of syllogisms
into extensive and comprehensive (intensive). An extensive
syllogism is of this nature

Motion is immaterial,
Heat is motion ;
/. Heat is immaterial,
and would be thus interpreted :

Motions are contained in the class of immaterial objects,
Heat is contained in the class of motions ;
/. Heat is contained in the class of immaterial objects.
The same syllogism, if stated comprehensively, or inten-
sively, would run as follows :

Heat is motion,
Motion is immaterial ;
/. Heat is immaterial ;

and its meaning, when broadly stated, would be this :
Heat comprehends in it the attributes of motion,
Motion comprehends among its attributes those of im-
materiality ;

/. Heat comprehends the attributes of immateriality.
An examination of these four syllogisms will reveal their
dependence upon each other ; all of them being evidently the
same result of the same process of reasoning. This is rendered
clear by a brief analysis of the import which attaches to pre-
dication. We say, for instance, that " motion is immaterial,"
and in doing so we state that a certain relation of congruity
exists between two compound ideas : " motion" which con-
sists of two sets of attributes, viz., the generic feature " imma-
teriality ' and certain specific differences ; and " immaterial

SYLLOGISMS. 65

objects" which likewise is duplicate, containing the notion
" immateriality " per se, and the notion of " immateriality "
indefinitely repeated, as existing in combination with various
sets of specific differences. It therefore results that the rela-
tion implied by our predication is also compounded, its con-
stituents being, that motion is an immateriality united with
certain distinguishing marks ; and that motion is capable of
producing on the mind, together with other impressions, the
same idea that immateriality per se would do. These two
relations it will easily be seen are those of extension and
intension. But another fact remains to be noticed : that
although the two ideas and relations are thus shown to be
compound, yet the union of their respective parts is so inti-
mate that they cannot be separated. We are unable to
resolve the idea "motion" into its two sets of attributes,
" immateriality " and " specific differences," so as to think of
these separately, and at different times : we are also unable
to divide the idea " immaterial objects " into " immateriality "
per se, and " immaterialities " respectively combined with
distinguishing attributes ; and, finally, we are unable to think
of one of the relations above described without also thinking
of the other. The utmost we can do is to bring one portion
of the compound idea, or relation, into greater prominence
than its fellow, by concentrating our attention as much as pos-
sible upon the chosen part ; it being remembered that we can-
not so concentrate the whole of our attention, and, therefore,
we must always, in some measure, be impressed by the less
important constituent.

These observations, if taken in conjunction with those con-
tained in the section upon induction and deduction, will, it is
hoped, afford an intelligible and clear view of the manner in
which the mind acts when comparing notions and judgments ;
and as the operation is always identical, being, though com-
plex, yet irresoluble, it follows that the only useful, or, strictly
speaking, admissible division of judgments and reasonings,
is that which merely refers to their form. Hence, in formal
Logic the distinction between the processes of extension and
comprehension must, like that between induction and deduc-
tion, be considered as of trifling consequence.

66 OF REASONING OR ARGUMENT.

14. Denomination.

When speaking of the interpretation of the copula, I men-
tioned that another mode of doing so had been suggested, in
addition to those connected with the doctrines of extension
and intension. This was the interpretation of denomination,
and is as applicable to arguments as to propositions : for ex-
ample, the syllogism

All planets are stars,
Mercury is a planet ;
/. Mercury is a star,
may be thus translated :

Planets may be called stars,
Mercury is a planet ;
.*. Mercury may be called a star.

This interpretation is, of course, merely verbally significant,
and is not intended to imply any approach to a radical, or
even formal difference between the syllogisms. The doctrine,
if doctrine it may be called, must, therefore, be received as
nothing more than a practical hint for turning a syllogism to
some special account, and as such belongs properly to applied
Logic. Former usage, however, is my excuse for placing it
here.

15. Syllogistic Arrangement of Propositions.

Before concluding the subject of pure-categorical syllo-
gisms, it will be advisable to mention a matter about which
the student might otherwise entertain an erroneous opinion.
I allude to the order of the three propositions constituting a
syllogism. It will have been observed that the usual course
pursued is to place the major premiss first, the minor next,
and the conclusion last ; and it may consequently be thought
that this order is the one most in accordance with natural
laws. Such, however, is not the case ; the arrangement in
question being merely an arbitrary practice adopted by
logicians in order to facilitate their expositions of the science.

In fact, it frequently happens that the conclusion occurs
to the mind as a problem or thesis, which requires certain
judgments (premises) to be formed, in order that its validity

SYLLOGISMS. 67

may be apparent. Thus, I might suspect a certain gas to
be hydrochloric acid, but in order to be sure it would be
necessary for me to find some proof of this. Accordingly,
knowing the general law that ammonia produces white fumes
only when brought into contact with hydrochloric acid, I
should proceed to test the suspected gas in this manner ; and,
the anticipated result following, I should be enabled to con-
struct the syllogism :

This gas is hydrochloric acid ;
Because, It produces white fumes with ammonia,
And, Everything which does that must be hydro-
chloric acid.

Hero the premises and conclusion are reversed. Again,
some fact comes under our notice, such as, " This metal takes
fire upon touching water ;" we make inquiries, and find that
" The only metal behaving in such a manner is potassium ;"
hence we draw the conclusion that " This metal is potassium."
An argument so expressed is a syllogism of the first figure,
but with the premises reversed. Accordingly, it thus appears
that there is no natural and definite order of judgments; it
cannot, therefore, be said that any arrangement is incorrect,
or alone correct, the disputes between logicians upholding
different models being so many lost words, we can scarcely
say arguments.

16. Conditional Syllogisms.

We have now to consider the case of syllogisms whcse con-
stituent propositions are not all pure-categoricals ; and first
we will examine those in which one or more conditional*
judgments appear, the argument being then termed a con-
ditional syllogism.

Now these reasonings may be treated in two ways prac-
tically, and theoretically ; that is to say, their own special
canons or proximate rules may be applied to them as they
stand ; or they may be reduced to categorical syllogisms,
when, of course, they immediately fall under the law r s which

* I omit modal propositions, as these cannot be treated otherwise than
as pure-categoricals. See p. 28.

68 OF REASONING OR ARGUMENT.

have been analysed in the foregoing pages. And, first, as
they stand.

Every conditional proposition consists of two parts the
antecedent and the consequent between which a certain rela-
tion is asserted to exist. These parts are both distinct judg-
ments, the relation being that the consequent depejids upon the
antecedent in such a manner as to necessitate the inference of
the former if the latter be granted ; e.g., " If the anchor holds
out, the ship will be saved," where " If the anchor holds out "
. is the antecedent, " the ship will be saved" is the consequent,
and the relation asserted is, that if we admit that the anchor
will hold out, then we must also admit that the ship will be
saved. A complete syllogism having such a proposition for
a premiss, would be of the following form :

If the anchor will hold out, the ship will be saved,
The anchor will hold out ;

.*. The ship will be saved.

In cases where both the premises are conditional, then the
conclusion must be conditional also, e.g.

If the anchor will hold out, the ship will be saved,

If the storm does not increase, the anchor will hold out ;

.*. If the storm does not increase, the ship will be saved.

Now, from a consideration of the relation subsisting between
the antecedent and consequent of a conditional proposition,
logicians have devised two practical rules, which suffice to
determine the validity of any conditional syllogism without
reducing it to a categorical form. These are :

1. If the antecedent be granted, the consequent may be in-
ferred; for this is merely to state the nature of the assertion
made by the form of the proposition. Nothing, however,
follows from granting the consequent : thus, in the proposi-
tion " If he is truly wise, he will be happy," we must infer
that he will be happy, if we admit that he is truly wise ; but
admitting him to be happy will not prove him to be wise, as
it is possible for an ignorant person to enjoy himself.

2. If the consequent be denied, the antecedent may also be
denied. This follows from the consideration that the truth
of the consequent is necessitated by that of the antecedent,
o that if the latter were true, the former would be so too.

SYLLOGISMS. 69

If, for example, we deny the consequent of this proposition,
" If he be shot through the heart, he is dead," and say that
he is not dead, we may evidently infer that he is not shot
through the heart; but to deny the antecedent would not
enable us to say that he is not dead, because he may have
been killed by many other causes.

These two laws have given occasion to a division of con-
ditional syllogisms into two moods, viz., the ponent, wherein
the antecedent is granted, and the tollent, where the conse-
quent is denied. These moods are reciprocally convertible,
as may be seen from the following example :

If the moon is not shining, the night is dark,
The moon is not shining ;
.*. The night is dark.

This is in the ponent mood ; but if we wish to make it
tollent, we may do so by reversing the hypothetical, and duly
negating, thus :

If the night is not dark, the moon is shining,
The moon is not shining ;
/. The night is dark.

These moods are also termed constructive and destructive,
answering respectively to ponent and tollent.

The second method of treating conditional -syllogisms is,
by reducing them to categoricals. Such a proceeding has,
indeed, been condemned by high authority* on the ground
of its being unnecessary and not always possible. I venture,
however, in common with many logicians,")* to think that this
condemnation is erroneous, as both of the objections urged
may be thus disposed of. The reduction is necessary, as, by
this means, conditional-reasoning being brought under the
same proximate la\vs with categorical arguments, is shown to
be of exactly the same nature, and so the unity of the reasoning
process is maintained ; at the same time, however, I do not
contend that it is necessary for practical purposes, as then the
rules above explained would become inept. Again, that the

* Krug's " Logik," p. 258. Bachmann's " Logik," 89, Anm. 2.
Sir W. Hamilton's " Logic," vol. i. p. 342.

f Esser's "Logik," 99; Wolfs " Philos. Rat.." 412; Whately'a
" Elements," book ii. chap, iv., 6; Thomson's <% Outlines/' 73.

70 OF REASONING OR ARGUMENT.

reduction is never impossible, may be seen from the very case
adduced as presenting insuperable difficulties, viz., " If A is
C, B is D ; but A is ; therefore, B is D ;" where we have
only to say, "The case of A being C is a case of B being D ;
the present case is a case of A being C ; therefore, the present
case is a case of B being D" and ihe obstacle is surmounted,
the resulting syllogism being a categorical in A A A, Fig. I.,
or, as the old logicians would say, in Barbara. The re-
spective terms are here distinguished by being printed in
italics.

That these objections should have been brought against
the reducing process as applied to conditional syllogisms, is
apparently owing, first, to the acceptance of the principle,
" Infer nothing without a ground or reason " as a necessary
and primary law of thought ; and, secondly, to its being lost
sight of that a term may be composed of more than one
conception. With regard to the first of these causes, it may
be observed, that the law there mentioned, called the law of
reason and consequent, has been a subject of much discussion
among metaphysicians and logicians, but should properly be
referred to the former alone. By it the antecedent is ex-
plained as being " the complement of all, without which
something else would not be," and the consequent as being
" the complement of all that is determined to be by the
existence of something else." This, which is Sir William
Hamilton's explication, given with especial reference to con-
ditional propositions, is, however, too wide and general for
application in such cases ; since, were we to admit that the
consequent " could not be " without the antecedent, we must
also admit, that by denying the antecedent we may deny
the consequent, which is contrary to the second rule above
given. It is likewise too wide and general to be considered
as a separate law, for if the antecedent be the " complement
of all, without which something else would not be," it must
necessarily be that " something else " itself. Now, a thing
cannot be something else ; and, therefore, in order to attach
any admissible meaning to the definition under question, we
must interpret it thus : " The antecedent is the same thing as
the consequent, but from a different point of view," a state-

SYLLOGISMS.

ment much the same as " a thing is itself," and answering
to another primary law, viz., " whatever is, is." * Indeed,
Sir William Hamilton's latest views would appear to have
been in accordance with those advocated here, as we find
him saying, that the law of reason and consequent " should
be excluded from logic." (

The second source of objection which led to the statement
that some conditionals could not be reduced, probably arose,
as stated above, from an incomplete view of the structure of
terms. Thus, in the syllogism, " If A is B, is D ; but A
is B ; therefore, C is D ;" it was hastily concluded that there
are four terms, A, B, 0, and D ; but, in so doing, it is as-
sumed that the reasoning process concerns these simple
notions ; whereas, in fact, it is occupied with the more com-
plex ideas, " A is B " and " C is D." Accordingly, instead
of four terms, which of course would be incompatible with a
categorical syllogism, we have only two, and require a third,
viz., " the present case," before we can draw a conclusion.
This third term is implied in the second premiss, when we
say "A is B."

During the course of the preceding remarks, the student
will doubtless have observed the technical method of reduc-
tion employed in these cases. It may be articulately enounced
as follows : " Each conditional proposition is to be considered
as a universal-affirmative-attributive categorical, with the
antecedent for a subject, and the consequent for a predicate."
Thus, the syllogism here stated,

If a body is struck, heat is generated,

But if a meteorite falls into the sun. a body is struck ;

.-. If a meteorite falls into the sun, heat is generated,
may be reduced in the following manner :

All cases of " a body is struck," are cases of " heat is

generated" (A),

All cases of " a meteorite falls into the nun," are cases
of " a body is struck " (A) ;

. . All cases of " a meteorite falls into the sun," are cases
of " heat is generated."

* As regards the primary laws of thought, see Appendix C.
f " Discussions," p. 603.

72 OF REASONING OR ARGUMENT.

In this way, or by using equivalent expressions, any condi-
tional syllogism may be thrown into the form best adapted
for displaying its real import aa an act of reasoning.

17. Disjunctive Syllogisms.

A disjunctive syllogism is an argument in which there is
one, or more than one, disjunctive proposition, and may be
represented by these formulae : 1. " A is either C or D ; B
is neither nor D ; therefore, B is not A." 2. "A must be
either or D ; but it is not C ; therefore, it is D." 3. "A is
either C, D, or E ; but it is not C ; therefore, A is either D
or E." 4. " Either A is B, or C is D ; but A is not B ;
therefore, C is D," &c. &c.

The import of the disjunctive propositions in all these syl-
logisms is, that the cases enumerated are the only possible
ones, and that they are mutually exclusive ; a perfect logical
division has in fact been performed. Accordingly, the prac-
tical rules which result are

1. Prom the assertion of one alternative, we may deny all
the others ; e.g., if in the proposition, " All men must be
either white, black, red, or yellow," we were to affirm, " These
men are red," we might infer that " they are neither white,
black, nor yellow."

2. From the disjunctive assertion of more alternatives than
one, we may deny the rest. Thus, in the above example, if we
were to say, for our second premiss, that " these men are
either white or black," we should then conclude that " they
are neither red nor yellow."

3. From the denial of one, or more than one alternative, we
may assert such as remain ; directly, if one, disjunctively, if
more. Accordingly, the following syllogism would be
valid :

All poems are either epic, lyrical, or didactic,
The poem of Paradise Lost is neither lyrical nor
dadactic ;

/. Paradise Lost is an epic.

The reduction of disjunctive syllogisms to categoricals is
similar to that of conditionals. Take, for instance, the syllogism
just quoted it will become :

SYLLOGISMS. 73

Poems which are neither lyrical nor didactic, are epics,
Paradise Lost is a poem which is neither lyrical nor

didactic ;

.'. Paradise Lost is an epic.

And here it must be stated, that in order to have a true
conditional or disjunctive syllogism, it is necessary that the
reasoning should hinge upon the consequence in the one case,
and on the alternative in the other ; for it is possible for a
conditional or disjunctive proposition to exist in a categorical
syllogism; thus,

All simple forms of matter are indestructible as such,
If the caloric theory be correct, heat is a simple form of

matter ;
.*. If the caloric theory be correct, heat is indestructible as

such.

In this case, " If the caloric theory be correct, heat " must
be considered as the minor term, for it is evident that the
reasoning is merely a comparison of this, and the major term
" indestructible as such," with the middle " simple forms of
matter ;" leaving the consequence of the conditional proposi-
tion altogether untouched.

18. The Dilemma.

If in a syllogism there be a conditional premiss, whose ante-
cedent or consequent is composed of a disjunctive proposi-
tion, such an argument is termed a dilemirtaTorhypothetico-
disjunctive syllogism. Take, for example, the following :
If the army were defeated, it must either have sur-
rendered or retreated,
But it did neither of these ;

/. It was not defeated^

The rules upon which the validity of such syllogisms
depend, are compounded of those referring to both condi-
tionals and disjunctives ; thus, 1. The antecedent being
affirmed, either disjunctively or not, as the case may be, the con-
sequent is also admitted ; and 2. The consequent being denied,
either disjunctively or not, as the case may be, the antecedent is
also denied.

An argument of the above description is termed a dilemma

74: OF REASONING OR ARGUMENT.

in consequence of its having two disjunctive members in the
consequent of the major premiss: that is to say, it contains
a double lemma, or double supposition. If there are three
such members, it is a trilemma ; if four, a tetrakmma, and
so on ; but the name polylemma is usually applied to those
containing more than four. Any one of these would, how-
ever, be loosely called a dilemma.

Such is the account commonly given of those arguments
to which the name of dilemma is applied ; but it is incom-
plete, as it does not refer to a class of syllogisms which, if
anything, would fall more properly under that denomination.
I allude to those in which several antecedents and consequents
are disjunctively affirmed or denied ; e.g.

If he leaps out of the window, he will severely injure
himself; if he does not do so, he will be burned,
But he must do either the one or the other ;
/. He must either severely injure himself, or be burned.
Or again

If this man were happy, he would not be angry ; and
if he retained his self-command, he would not be
excited,

But he is either angry or excited ;
/. He is either unhappy, or has lost his self-command.
In these syllogisms, we see that the major premiss (so to
speak) is composed of two distinct conditional propositions,
thus being a truer di-lemma than the cases previously con-
sidered.

All hypothetico-disjunctive arguments may be reduced,
either to conditionals or categoricals at pleasure. There is
no difficulty in the process, it being merely a judicious com-
bination of the methods already studied, and as a general
model, the following formula will be all that is needed. It-
shows the categorical reduction of a complex-dilemma, that
is, where the major premiss is composed of two distinct
conditionals.
Syllogism :

If A is, B is ; and if C is, D is,
But either A is, or C is ;
/. Either B is, or D is.

SYLLOGISMS. 75

Reduction :

1. Take for a major premiss the categorical equivalent of
the given minor ; and for a minor term, the denial of the
consequent in the first conditional of the given major premiss :
complete the syllogism, thus

All non-A's are C's,
All non-B's are non-A's ;
.*. All non-B's are C's.

2. Take for a major premiss, the categorical equivalent of
the second conditional in the given major ; and for a minor
premiss, the conclusion of the syllogism last formed : the
conclusion resulting from these premises, will be the cate-
gorical equivalent of the disjunctive conclusion in the syl-
logism given for conversion : e.g
All C's are D's,
All non-B's are C's ;
.*. All non-B's are D's ;

or
Either B is, or D is.

19. Incomplete Syllogisms.

When any one of the propositions forming a syllogism is
not overtly enounced, such an argument is termed an Enihy-
meme. It will be evident that there is no difference in the
reasoning process between enthymemes and formal syllogisms,
as the premises and conclusion are in both cases the same :
the distinction merely consists in the number of judgments
that may be actually expressed in words. Accordingly,
since there are three propositions in every syllogism, enthy-
memes are divided into three orders, w 7 hich respectively
suppress the major premiss, the minor premiss, and the con-
clusion. Examples of them may be thus given :
The formal syllogism :

All women are inquisitive,
Julia is a woman ;
.'. Julia is inqusitive.
Enthymeme of the first order (the major suppressed) :

Julia is a woman ;
.*. Julia is inquisitive.

76 OF REASONING OR ARGUMENT.

Enthymeme of the second order (the minor suppressed) :

All women are inquisitive ;
.*. Julia is inquisitive.
Enthymemeof the third order (the conclusion suppressed):

All women are inquisitive,

And Julia is a woman.

Into one or other of these three forms, nearly all argu-
ments, as popularly expressed, fall ; for it is seldom that a
person takes the trouble to state a syllogism in full. This
elliptical method of overt inference, is most strikingly de-
veloped in those arguments which were discussed under the
heads of Opposition, Conversion , and Coincident- Junction .
where not only is a premiss not expressed, but it is almost
unconsciously thought ; so much so. indeed, that it requires
a searching investigation to become convinced of its exis-
tence. We need not wonder, therefore, at their being often
termed immediate inferences. Conditional judgments too,
are frequently of an enthymematic nature, such as, for in-
stance, " If Pegasus be a horse, it must be a quadruped,"
which manifestly proceeds upon the assumption that " all
horses are quadrupeds."

20. Complex Arguments, or Chains of Reasoning.

It often happens that we arrive at a conclusion through a
string of correlative syllogisms, and when this is the case we
have what is termed a chain of reasoning. These arguments
are, however, generally of an enthymematic form, and are
divided according as they suppress the conclusion, .or one of
the premises, in each syllogism.

Those chains of reasoning, where all conclusions but the
one desired are suppressed, must necessarily consist of pre-
mises, and this form is known as a sorites. It may be of two
kinds first, where the predicate of each premiss is the sub-
ject of the next succeeding one, and where the conclusion is
the last predicate affirmed of the first subject ; this is termed
the ascending, regressive, or Aristotelian sorites: and secondly,
where the subject of each premiss is the predicate of the next,
and where the conclusion is the first predicate affirmed of

SYLLOGISMS. 77

the last subject ; this is styled the descending, progressive, or
Goclenian sorites. The formulae of these are :

Aristotelian. Goclenian.

A is B, D is E,

BisC, CisD,

C is D, B is C,

D is E ; A is B ;

.'. AisE. /. AisE.

Or, concrete examples may be given, as follows :
Aristotelian :

Red is a colour,
A colour is a kind of light,
All light is a kind of motion ;
.*. Red is a kind of motion.
Goclenian :

All light is a kind of motion,
A colour is a kind of light,
Red is a colour ;
.*. Red is a kind of motion.

It will have been observed, that the formulae are entirely
affirmative ; this arises from the rule that we can draw no con-
clusion from negative premises. We may, however, have the
last premiss of the series negative, but then the conclusion
must be negative also, thus :
Red is a colour,
A colour is a kind of light,
All light is a kind of motion,
No motion is material ;
.'. Red is not material.

A sorites containing premises of the above description,
may have its validity directly tested by this modification of
the dictum : " Whatever belongs, or does not belong, to a
given whole, belongs, or does not belong, to each and every
one of the parts constituting any whole contained in the
given whole." If, however, the premises are of different forms
(I, U, <fec.), and the reasoning, in consequence, rather com-
plicated, we may readily ascertain the legitimacy of the
porites by a process of dissection ; that is, by resolving it

78 OF REASONING OR ARGUMENT.

into its constituent syllogisms. The formulae for this pur-
pose are the following :

Aristotelian. Goclenian.

A is B, Minor, D is E, Major,

B is C ; Major, C is D ; Minor,

Minor, (.'. A isC), Conclusion. M^ior, (.'. C is E), Conclusion.

Major, C is D ; Minor, B is C ;
Conclusion. (/. A is D), Minor, Conclusion. (.'. B is E), Major,

D is E ; Major, A is B. Minor,

/. A is E. Conclusion. /. A is E. Conclusion.

From this diagram, it will be seen that each suppressed
conclusion forms the minor premiss of the succeeding syllog-
ism in the Aristotelian sorites, and the major in the Goclenian.
Accordingly, if we detect any false mood among the syllog-
isms, all its successors will be invalid, as depending upon an
erroneous premiss.

A chain of reasoning, wherein one, or more than one
premiss is suppressed, is termed an epicheirema, and may be
of three orders ; first, where the major premiss of the main
syllogism is the conclusion of another syllogism, with but
one premiss expressed ; secondly, where the minor premiss
is similarly characterised ; and lastly, where the conclusion
forms the sole expressed premiss of a succeeding syllogism,
a second conclusion thus resulting. The epicheirema may
also be single, double, or treble, according as it is a combi-
nation of one, two, or three orders.

The nature of these arguments will be evident from an
inspection of the following examples :

Single epicheirema of the first order (the major a conclu-
sion) :

All planets are attracted by the sun ; for they revolve

about him as a centre,
The earth is a planet ;
.'. The earth is attracted by the sun.
Single epicheirema of the second order (the minor a con-
clusion) :

All birds are oviparous,

The condor is a bird ; for it has wings, feathers, and a

heart ;
/. The condor is oviparous.

SYLLOGISMS. 7S

Single epicheirema of the third order (the conclusion a
premiss :

Matter is imperishable,
Gold is matter ;
/. Gold is imperishable,

and

.'. Gold is eternal.

Treble epicheirema of the conjoint orders :
He who is truly wise is just ; for he is virtuous,
Aristides is truly wise ; for he is led astray by no

passions ;
.'. Aristides is just,

and

/. Aristides is happy within himself.

By symbolising, the last epicheirema may be thus extended
into complete syllogisms; the propositions in parentheses being
those which were suppressed :

t f (All C's are B's) major.
Conclusion.-A is B j A is .... minor.

( (All E's are A's) major.
Conclusion.-!) is A j D is E . . . . minor .

.*. D is B minor.

(All B's are F's) major.
/. D is F conclusion.

The two syllogisms whose conclusions form the premises
of the main argument, are called prosyllogisms, while the
syllogism which takes the main conclusion for a premiss is
termed an episyllogism.

In the strictest view of the science, pure Logic would take
no cognisance whatever of incomplete or complex arguments;
as in them the inference is not necessitated by the mere form
of the expression. Since, however, all practical reasoning is
of this nature, it would not be advisable to omit its consider-
ation, as one of our objects is to show the universal extent of
pure Logic, and also how its laws and principles pervade the
whole universe of thought. We cannot, therefore, condemn
the practice of logicians, who almost invariably have dis-
cussed these reasonings when treating upon the doctrines of
logical elements.

80 OF REASONING OR ARGUMENT.

21. Recapitulation.

We have now concluded our investigation of the principles
upon which the reasoning process is based, and of its various
products. I shall, therefore, in accordance with my previous
practice, briefly recapitulate the principal results at which
we have arrived.

Reasoning in general is the eduction of a truth from some
truths already established, but of whose full import we are
not aware. It, therefore, cannot be an instrument for the
extension of science, which would involve the discovery of
fresh facts, but is of use in the due comprehension and orderly
arrangement of our knowledge. It also follows that any pro-
cesss of reasoning (termed a syllogism) is composed of two
parts the antecedent, or established truths, and the conclu-
sion, or truth educed from them. Now the antecedent inva-
riably consists of two judgments termed premises, but both
of these are not always articulately enounced. This gives
rise to a division of arguments into two classes; the one com-
prising certain syllogisms whose major premiss is always sup-
pressed ; the other comprising all that remain. The first of
these classes is divided under three great heads, viz., opposition,
or the relation subsisting between propositions which differ
in form, but are identical in matter, such relation being either
contradictory, contrary, subaltern, or subcontrary ; conversion,
or the transposition of the subject and predicate in a judg-
ment, which may be of two kinds, simple and privative ; and
coincident-junction, or the inseparable union of the attributes
in a conception. The second class, composed of formal syl-
logisms, requires as an essential preliminary of its treatment,
the determination of a fundamental law which may decide
the validity of all arguments. This law is found to be as
follows : " Whatever belongs, or does not belong, to the con-
taining whole, belongs, or does not belong, to each and all of
the contained parts;" but, for proximate application, it is
developed into this canon, "If two notions agree, either
wholly or in part, with one and the same third, they agree
with each other ; but if one of them is agreed, and the other
disagreed with the same third, they disagree with each other,"

SYLLOGISMS. 81

which, variously differentiated for particular purposes, enables
us to test the legitimacy of any syllogism. This canon formed,
we find that all syllogisms whatever are susceptible of two
methods of classification ; first, with reference to the position
of the middle term in the premises, whereby arguments are
arranged into four figures ; and, secondly, with reference to
the form of the constituent propositions, the symbols repre-
senting these being grouped in threes, and termed moods.
This distinction of figure and mood is sufficient as regards the
form of syllogisms to determine their validity ; but some
other divisions respecting the import of arguments have a
claim upon our notice. The doctrines of induction and de-
duction come first, and apparently depend upon different
principles, for induction reasons from the parts to the whole ;
deduction from the whole to the parts. A close examination,
however, shows that, as far as pure Logic is concerned, they
may be regarded as almost identical. Then follow compre-
hension (intension) and extension, which respectively interpret
syllogisms as predicating an attribute of a notion, and a genus
of a species ; but this distinction also fades into obscurity
when we reflect upon the irresoluble complexity of our ideas.
Lastly, we have denomination, which identifies the reasoning
process as one of naming ; the significance of this interpre-
tation being merely verbal. Having thus obtained a clear
notion of the syllogistic theory, by confining our attention to
arguments composed of categorical propositions, we proceed
to the consideration of those cases wherein we meet with con-
ditional judgments ; and, by analysis, we find that they may
all be referred to these two rules 1. " The antecedent being
granted, the consequent may be granted;" and 2. "The
consequent being denied, the antecedent may be denied.'*
Next, taking the syllogisms which depend upon disjunctive
judgments, we find that the principles involved are those of
a perfect logical division ; while those arguments which fall
under the name of dilemma may be treated by a combination
of the rules applicable to each of the two former classes.
Lastly, we have to examine the popular method of stating
arguments, and find that they either assume the form of enthij-
memes, or syllogisms with one proposition suppressed ; or

E 3

82 OF REASONING OR ARGUMENT.

else that they are expressed as chains of reasoning, these
being of two kinds a sorites, or string of premises with one
conclusion ; and an epicheirema, or syllogism whose premises
are the conclusions of prosyllogisms, and whose conclusion is
the premiss of an episyllogism.

22. Conclusion.

Here, as stated in the introduction, the province of pure
Logic terminates ; and if the student has closely followed the
foregoing analysis of its principles, he will be in a position to
rightly appreciate its nature and end. Whatever may be the
ulterior object for which the mind is cultivated, every person
" must have thoughts to arrange, knowledge to transplant,
and facts to record;" and the more effectually these can be
done, the greater will be the progress. Now, the three great
instruments for the above-mentioned processes are,first, Logic;
secondly, languages ; and lastly, the arts of memory.* Thus
the superiority and precedence of Logic in point of utility is
apparent : it prepares a sure and solid foundation ; it arranges
the materials as they arrive in regular courses ; and, finally,
completes the majestic edifice of a well-ordered mind Here,
of course, I allude to the science of Logic ; that is to say, the
knowledge of the formal laws of thought as applied to the
treatment of acquired information ; consequently, we must
not suppose that pure Logic will furnish us with powers of
observation, or with facts to observe ; its sphere being limited
to the invigoration of those mental abilities with which we
are respectively endowed, and to the elucidation of those
truths which have already attracted our attention. It is but
the few whom Nature has endowed with great intellectual
power ; and no amount of Logic, or of mental training, will
supply the original deficiency. A Bacon or an Aristotle is
born, not made. At the same time, however, the most com-
manding genius is capable of being raised to a still loftier

* Compare De Quincey, " Works," vol. xiii. p. 25, who advocates
these views in a series of Letters, respecting which one can scarce tell
whether most to admire their purity of style, their elegance of diction,
their cogency of argument, or their subtle play of humour.

SYLLOGISMS.

elevation ; as much so as is the weakest mind. We are not,
therefore, surprised to discover that the names of the most
sedulous cultivators of Logic are those of the greatest philo-
sophers that have ever lived. From Socrates, Plato, and
Aristotle to Bacon ; from Kanaka and Gotama to Kant ;
whether among the academic groves of ancient Athens, the
busy haunts of British industry, the tropical luxuriance of
eastern climes, or the ponderous reflections of learned Ger-
many, there has ever been a bright succession of eminent
men who have devoted their efforts to the investigation of
the human mind, its thoughts, their principles, and laws.
These principles they have employed, not only as regulators
of the intellect, but also as guides and restraints in their
search after truth, both moral and physical such a dispo-
sition of the science being what is termed applied Logic,
which will form our next subject of study.

CHAPTEK V.

OF FALLACIES.

1. Applied Logic in' General.

WE have now left behind us the sterile, but grand and im-
pressive realms of theory, and are entered upon the luxuriant
regions of practice, where there is everything to interest and
to delight, but whose green and smiling soil too often hides a
treacherous morass. Here, then, is the opportunity afforded
to us of putting our experience to the test, and of deter-
mining in what way the rules, which we have been acquiring,
may. be of service to us.

Now, the ultimate end of all thinking, is the attainment of
truth, and therefore, when we have ascertained what are the
necessary laws of thought, we should not remain satisfied
with this speculative knowledge, but should actively employ
it as a means of advancement towards that higher object for
which those laws were implanted. This operation it is,
which forms the province of applied Logic, and which we are
now about to consider, although the limits of our space must
necessarily preclude any attempt to do more than take a cur-
sory but I trust, instructive view of so vast a subject.

I have said that our object now is, to examine into the
employment of the formal laws of thought as thought, for
the purpose of attaining truth ; and since we continually
make use of one fact as a means of arriving at another, it
follows that the practical application and operation of in-
ference, must occupy much of our attention. Inference,
however, may be examined from two points of view, positive
and negative ; for we must either reason correctly or in-

OF FALLACIES. 85

correctly : it follows, therefore, that the spheres of investigation
which present themselves are first, the essential conditions of,
and inducements to, a legitimate inference ; and secondly, the
causes and nature of an illegitimate inference. The question
now comes, which of these subjects shall we first examine ?
and the ratio decidendi must be the end which we propose to
ourselves : this is the acquirement of truth, and can only be
attained by a proper understanding of what constitutes cor-
rect inference. But, in order to properly understand what a
thing is, we should first ascertain what it is not ; for, as Bacon
says, " Inductio quse ad inventionem et demonstrationem
Scientiarum et Artium erit utilis, Naturam separare debet, per
rejectiones et exclusiones debitas ; ac deinde post negativas tot
quot sufficiunt, super affirmativas concludere." Accordingly,
our immediate duty must be to investigate the conditions
and concomitants of incorrect inference, or " bad reasoning,"
as it is generally termed.

Every argument consists in drawing a conclusion from
certain evidence which has been adduced, and if this evidence
be such as to warrant the conclusion, we are said to reason
legitimately ; if not, the reverse. Now, as no man ever
assents to a judgment unless he deems its evidence conclusive,
a case of false reasoning can only occur where the evidence,
though seemingly just and sufficient, is, in reality, fallacious
and deceptive ; such an argument is called & fallacy.

2. Classification of Fallacies.

The true way of comprehending any subject is as we
discovered when treating upon pure Logic to arrange it in
a system constructed upon the principles of logical division
and classification. It, therefore, behoves us, if we would
make a practical use of the science, to at once arrange the
various fallacies under their respective heads, before proceed-
ing to discuss them in detail.

Every syllogism consists of two parts, form and matter :
this enables us to divide all fallacies into two great classes, viz.,
those whose inference is erroneous, through being informally

86 OF FALLACIES.

expressed ; and those where the premises legitimately imply
the conclusion, if the/orm of the syllogism be alone regarded,
but where an examination of the matter will show the reason-
ing to be invalid.

Formal fallacies are those which violate the syllogistic
canons, and may be subdivided into as many co-ordinate
species as there are proximate rules. It will only be neces-
sary, however, for our purposes, to regard the faults of un-
distributed middle and illicit process.

Material fallacies may be erroneous, either as regards
their terms, their premises, or their conclusion, and are con-
sequently subdivided into these three subaltern genera, viz.,
quaternio terminorum } or syllogisms with four terms ; syllo-
gisms with a premiss unduly assumed and ignoratio elenchi,
or syllogisms which do not prove the required conclusion.

The species of these subaltern genera, may be arranged
in accordance with the following considerations :

1. Quaternio terminorum. This fallacy may arise from
the ambiguity of the middle term, so that in the major pre-
miss one sense of the word is used, in the minor, another.
Or, for any one of the terms, two words may be employed
which are supposed to imply the same meaning, but do not.
Or, again, a term may consist of several notions, these being
taken together in one judgment, and separately in the other.
Or, lastly, a term may be used absolutely in one judgment,
and relatively in the other.

2. A premiss unduly assumed. The causes of this may
be, considering certain truths as self-evident which are not
so ; forming a judgment from some pre-conceived opinion,
false analogy, or false generalisation ; over-estimating the
weight of probabilities; reasoning in a circle; or, taking
for a premiss some proposition which is the same as, or im-
plies, the conclusion.

3. Ignoratio elenchi. This occurs whenever appeals are
made to the passions, prejudices &c., of men ; when a part is
proved instead of the whole ; &c., &c.

The foregoing division may be exhibited in a " scheme,"
as follows :

OP FALLACIES.

Fallacies
are

/ , / Undistributed middle.
Formal j Illicit process.

Material (

Quaternio
terminorum

Premiss
unduly j

Ambiguous middle.
Fallacia figures dictionis.
Fallacia sensus compo \H
et divirt.
Fallacia a dicto secun-
dum, &c.

A priori fallacies.
Fallacies from pre-con-
ceived opinions.
From false analogies.
From false generalisa-
tions.

assumed

Ignoratio
elenchi

False estimation of pro-
babilities.
Reasoning in a circle.
Petitio principii ("beg-
ging the question.")

iArqumenta ad hominem,
&e.
Part for whole,
Ac. <fec.

Before we commence the discussion of each of the above
fallacies in its order, it may be well to remark that the above
division could only be logically perfect, provided we were
allowed to make arbitrary distinctions between individual
examples of false reasoning ; for there are some fallacies
which belong to one species equally as much as they do to
another. This, in many cases, arises from the enthymematic
mode of expression which obtains so universally : were a man,
for example, in maintaining the efficacy of imprisonments for
life, to argue that " capital punishment is improper," because
" it does not tend to make the criminal a better member of
society, " we must either suppose him to hold that " all proper
punishments are for the purpose of reformation, as regards
the criminal's social behaviour," or that some are. In the
former case, the complete syllogism would run thus :

All proper punishments are intended for the criminal's

social reformation,
Capital punishment is not so intended ;

.*. Capital punishment is improper.

Here the formal reasoning is perfectly valid, but when
the matter is examined, we see that the major premiss is un-
duly assumed ; for, obviously, imprisonment for life is not
intended to make the criminal a better member of society, as
it starts with the condition that he shall never mix with his
fellow-creatures again.

OP FALLACIES.

If wo adopt the latter of the suppositions stated above, the
argument will be as follows :

Some proper punishments are intended for tho criminal's

social reformation,
Capital punishment is not so intended ;

/. Capital punishment is improper ;

where there is an illicit process of the major term, and, con-
sequently, a formal fallacy.

In cases similar to the foregoing, it must always remain
doubtful as to which class thej 7 belong ; and, therefore, the
division adopted must be considered as only approximatively
correct. This state of things, however, obtains in every
science, and arises from the necessary imperfection of our
knowledge : in chemistry, for instance, it is a moot point as
to whether arsenic should be included amongst the metallic
or non-metallic elements; while, in biology, it is almost im-
possible to draw the line between animal and vegetable life.
At the same time, most classifications are correct enough
for all practical purposes, if not in strict accordance with the
rigorous requirements of theoretical truth. Thus much pre-
mised, we shall now enter upon a detailed account of the
various species of fallacies.

3. Formal Fallacies.

These, as already stated, consist of such syllogisms as
violate the canons which have been laid down for the purpose
of determining the validity of an argument from its form.
The principal species are Undistributed middle, and Illicit
process. Examples may bo thus given :
Undistributed middle:

Negroes are men,
Hindoos are men ;
/. Hindoos are negroes.
Illicit process :

All planets revolve round the sun,
All planets are stars ;
/. All stars revolve round the sun.

The subject of form has been so fully discussed in the pre-
ceding chapter, that it will not be necessary to add anything

OF FALLACIES. 8 ( J

further upon this point. The following observations, how-
ever, taken from Archbishop Whately's " Elements," are of
great importance.

" To the present class [formal fallacies] we may the most
conveniently refer those fallacies, so common in practice, of
supposing the conclusion false because the premiss is false, or
because the argument is unsound ; and of inferring the truth
of the premiss from that of the conclusion, e.g., if any
one argues for the existence of a God, from its being uni-
versally believed, a man might, perhaps, be able to refute the
argument by producing an instance of some nation destitute
of such belief; the argument ought then to go for nothing :
but many would go further, and think that this refutation
had disproved- the existence of a God ; in which they would
be guilty of an illicit process of the major term : viz., ' What-
ever is universally believed must be true ; the existence of a
God is not universally believed ; therefore, it is not true.'
Others again, from being convinced of the truth of the con-
clusion, would infer that of the premises, which would
amount to the fallacy of an undistributed middle : viz.,
' What is universally believed is true ; the existence of a God
is true ; therefore, it is universally believed.' Or, these
fallacies might be stated in the hypothetical form ; since the
one evidently proceeds from the denial of the antecedent, to
the denial of the consequent ; and the other, from the estab-
lishing of the consequent, to the inferring of the antecedent ;
which two fallacies will usually be found to correspond re-
spectively with those of Illicit process of the major, and
Undistributed Middle.

" Fallacies of this class are very much kept out of sight,
being seldom perceived even by those who employ them ; but
of their practical importance there can be no doubt, since it
is notorious that a weak argument is always, in practice,
detrimental; and that there is no absurdity so gross which
men will not readily admit, if it appears to lead to a con-
clusion of which they are already convinced. Even a candid
and sensible writer is not unlikely to be, by this means, mis-
led, when he is seeking for arguments to support a conclusion
which he has long been fully convinced of himseL

rnr THS

OF FALLACIES.

will often use such arguments as would never have convinced
himself, and are not likely to convince others, but rather (by
the operation of the converse Fallacy) to confirm, in their dis-
sent, those who before disagreed with him."

4. Material Fallacies : Quaternio Terminorum.

1. Ambiguous middle. This occurs whenever one sense
of the middle term is employed in the major premiss, and
another in the minor, thus

Whoever is nervous is timid,
Hercules was nervous ;
/. Hercules was timid.

The word nervous is here used in two senses, viz., " timid "
and " strong," and, consequently, the syllogism contains four
terms, which, of course, renders it invalid. I have given an
example in which the error may be easily perceived, but it
must not be supposed from this, that all cases of ambiguous
middle are of such a simple character. Indeed, there are
many words of common use, which continually give rise to
mistaken ideas in consequence of their ambiguity. Thus, the
impression is very general, that the " men of old " were
superior in wisdom and experience to those of modern times ;
this notion arising from the natural reverence which we feel
for the opinions of " old men" in consequence of their longer
life having enabled them to form a better judgment of the
world's course than younger men can do. Of course, when
the syllogism is fulty expressed " Old men are worthy of
reverence; these men are men of old; therefore, these men are
worthy of reverence" we see at once that the word old is
used at one time in the sense of aged, and at another, as
signifying removed from us by length of time; and that,
accordingly, the reasoning is inconsequent; but then we
must remember that arguments, in practice, are elliptical,
the premises being oftener hinted at, than articulately stated.
A skilful sophist, therefore, will avoid anything like a defini-
tion of the terms he employs, or a full expression of his in-
ference ; trusting to the various associations, traditions, and
prejudices of his hearers to supply such ideas as may be best

OF FALLACIES. 91

calculated to lead them to the desired conclusion. And iw
like manner, it follows that the most effectual remedy against
fallacies of this description, is to insist upon a precise expla-
nation of the sense in which each term is used. That this
caution is not unnecessary, will easily be seen if we reflect
upon the great number of words which are susceptible of
duplicate, triplicate, (fee., interpretations ; e. g., law may mean
either a command for persons to obey, or a general expression
for a group of physical facts ; same implies identicality, and
also great similarity ; may and can, sometimes signify liberty,
and sometimes possibility, (fee., (fee.

2. Fallacia figurce dictionis. It frequently happens that
paronymous words, i.e., those which have a grammatical
relation to each other in consequence of their springing
from the same root, differ considerably in meaning, but yet
in the haste of an argument are assumed to be of similar
import. This produces what the old logicians have termed
the fallacia figurce dictionis, and is dangerous on account
of the many variations which may be, and commonly are,
given to a term in the course of a chain of reasoning, with-
out infringing the validity of the conclusion. Thus, it
would be perfectly allowable to say, " Wherever a lighted
candle maintains great luminosity, the atmosphere is respir-
able ; in this well a lighted candle continues to be very lumi-
nous ; therefore, here the atmosphere is respirable ;" for the
expressions " to maintain luminosity " and "to continue lumi-
nous " are justly treated as equipollent : but were we to sa} ,
" No designing persons are honest ; all sculptors design ;
therefore no sculptor is honest," we should in reality employ
four terms ; " designing " meaning scheming or plotting, while
" to design " implies the conception of some idea to be executed
by an artist.

The proper method of combating this fallacy consists in an
explanation of the different senses attaching to the parony-
mous words.

3. Fallacia sensus compositi et divisi. This, which is also
termed the fallacy of composition and division, is produced
whenever a term is used in one judgment collectively, aix!
in the other distributively . A simple example is as follows :

92 OF FALLACIES.

" Five and two are odd and even ; seven is five and two ;
therefore, seven is odd and even." Here "five and two"
means in the major premiss, those numbers alluded to
distinctly and respectively ; in the minor, the same taken
together ; accordingly, there is a case of quaternio termi-
norum.

Perhaps the most frequent method of employing fallacies of
this description, is when a truth which has been separately
established concerning many individual notions is sought to
be inferred of them all collectively. Thus it is occasionally
argued, that because the ordinary alterations of temperature
produce comparatively little effect upon the physical configura-
tion of the earth's surface, and because the same thing may
be asserted of each of the natural disintegrating and abrading
powers, such as tides, rivers, rain, glaciers, &c., therefore the
combined operation of all together would not do more, and,
consequently, that we must assume some grand cataclysm as
the cause of such great changes as may be apparent.

In all cases of probability there is often a tendency to fall
into the error now under consideration, and this tendency is
in opposite directions. Suppose we are told that it is an even
chance whether the disease upon reaching a certain stage will
kill the sufferer or not ; and, also, that it is an even chance
whether the disease will reach that stage ; we are apt to con-
clude that an even chance results of the person dying or not
dying; whereas the chances are three to one against his
dying. This is rendered evident as follows : the chance of
the disease reaching a certain point is one-half of all the pos-
sible changes which may supervene ; but the chance of dying
is only one-half of these, i.e., one-quarter of the possible cases ;
therefore the chance of not dying is three-quarters, or in the
"ratio of three to one. Here the probability was over-esti-
mated, but in many instances the reverse is the case : thus,
if we were to argue, that because it is improbable that the
whole of Newton's discoveries were the results of fortunate
coincidences, it is, therefore, improbable that any one of them
was so, we should commit this error.

Archbishop Whately under this head describes what he
terms the thaumatrope fallacy ; this consists in presenting

OF FALLACIES. 93

several incompatible notions to the mind in quick succession,
so as to induce the belief that they might exist together.
After the Crimean war, for example, a statement was pub-
lished showing the several objects which the money spent
might have separately accomplished. Now, in all probability,
many persons on reading the long list, and finding that this,
that, and the other thing might have been done, left off with
the idea that all of these objects together were capable of
realisation.

4. Fallacia a dicto secunditm, &c. These fallacies arise
when we conclude absolutely of a notion what is true of il
only under certain circumstances ; and when we conclude
relatively what is only true when absolute ; the latter is
sometimes termed fallacia accidentis.

Persons occasionally fall into this error when arguing
against capital punishment, forming their syllogism thus :
To return evil for evil is wrong,
Capital punishment is returning evil for evil ;
.'. Capital punishment is wrong.

Here the major premiss is only true under certain qualifica-
tions ; that is to say, a revengeful animus is supposed in com-
bination with returning evil for evil ; whereas in the minor,
the action is considered in the abstract, and without any such
attendant circumstance.

Again, uneducated people are greatly astonished upon
being told that the earth is nearer to the sun in winter than
in summer, for their thoughts immediately run in this fashion ;
" the nearer we are to a hot body the warmer we must be,
and therefore the earth ought to become warmer instead of
colder on approaching the sun." The mistake, of course,
lies in their ignorance of the fact that we only get warmer
upon approaching a hot body provided that the rays of heat
continue to strike us at the same, or at a more favourable
angle.

Fallacies of this nature are very difficult to detect, in con-
sequence of the readiness which exists to lose sight of the
limitations which alone render a general law capable of being
applied to some particular case. The best method of treatment
is to require a rigid proof of both premises, which wil always

: OF FALLACIES.

exhibit whether the inference is legitimated by the circum-
stances of the case.

The false reasonings which have been described above
are the principal fallacies belonging to the genus of quatemio
terminorum ; but there are many various ways of sophistica-
tion by means of ambiguity in expression, which, though
not syllogistic, are often employed. Such is the practice of
asking a question that may be susceptible of various interpre-
tations according to the answer given ; e.g., an opponent of
free-will might ask, "Am I free to do as I please?" and,
being answered in the affirmative, would reply, " Then I am
at liberty to kill you and half-a-dozen more if I so please."
If answered in the negative, he would at once say, " Then I
am controlled by necessity, and am not a free-agent." In
this instance the ambiguous word is " free," which in one
case is held to mean " free as regards nature ;" in the other,
" free as regards the laws of society." The student will have
no difficulty in forming the corresponding syllogisms.

Perhaps, however, the most celebrated fallacy depending
upon the ambiguity of a word, is the sophistical puzzle of
Achilles and the tortoise. Its enunciation and solution are
given by Mr. Mill as follows :

" The argument is, let Achilles run ten times as fast as the
tortoise, yet if the tortoise has the start, Achilles will never
overtake him. For suppose them to be at first separated by
an interval of a thousand feet : when Achilles has run these
thousand feet, the tortoise will have got on a hundred ; when
Achilles has run those hundred, the tortoise will have run
ten ; therefore, Achilles may run for ever without overtaking
the tortoise.

"Now, the 'for ever' in the conclusion, means, for any
length of time that can be supposed; but in the premises 'ever'
does not mean any length of time : it means any number of
subdivisions of time. It means that we may divide a thou-
sand feet by ten, and that quotient again by ten, and so on as
often as we please ; that there never needs be an end to the
subdivisions of the distance, nor, consequently, to those of
the time in which it is performed. But an unlimited number
of subdivisions may be made of that which is itself limited,

OF FALLACIES. 95

The argument proves no other infinity of duration than may
be embraced within five minutes. As long as the five
minutes are not expired, what remains of them may be divided
by ten, and again by ten, as often as we like, which is per-
fectly compatible with their being only five minutes alto-
gether. It proves, in short, that to pass through this finite
space requires a time which is infinitely divisible, but not
an infinite time."

Another example of the same fallacy may be thus given :
If at present we look forward into eternity we see that the
duration yet to come is infinite ; but the same state of things
will obtain a hundred years hence, and as two infinite dura-
tions must be equal to each other, the futurity then, and the
futurity now cannot differ ; therefore the hundred years con-
stitute no lapse of time whatever, as otherwise there would
be a difference of so much between the periods in question.
Thrown into a syllogistic form the argument would stand
as follows :

Two infinite durations are equal to each other,
The present futurity, and the present futurity less a
hundred years, are two infinite durations ;

.'. The present futurity is equal to the same, less a hundred
years.

Here the major premiss involves a contradiction in terms,
for it implies that two incommensurable things (i.e., two dif-
ferent infinities) are commensurable j it is, therefore, inadmis-
sible. Or the solution might pass were we to say that the
middle term is ambiguous, meaning in the major premiss, "two
infinite durations starting from the same point" and in the
minor, " two infinite durations starting from different points."

5. Material Fallacies : Premiss unduly assumed.

1. A priori fallacies. We have now to consider those
errors which arise from the assumption of a premiss, either
without any proof at all, or without such proof as would be
considered sufficient by both parties, if they were equally
apprised of the questions at issue. And first, of those cases
wh^re there is no proof whatever of the assumed premiss.

6 OF FALLACIES.

As an essential preliminary, it must be remarked that there
are some truths which we do not attain by any reasoning
process,* and which, therefore, are not susceptible of proof.
Thus, when a piece of brass engages my attention, I am con-
scious of some change which takes place in my mind, and
this change I call the sensation of yellow, applying the name
yellow- to those attributes of the brass which produced the
sensation ; therefore, when I say, " This brass is yellow," I
cannot abstractedly prove the statement, as I am merely
asserting a subjective fact, of whose existence I alone can
judge, and which is only granted by my opponent in con-
sequence of his being affected by similar sensations. Accord-
ingly, such truths are termed self-evident, and must form the
foundation of all reasoning.

This consideration is the clue which guides us to the source
of the particular class of sophisms at present under investiga-
tion. Men, rinding that certain of their sensations corre-
spond with outward facts, go further, and imagine that
whenever any subjective state of consciousness is ascertained,
there must always exist a correlative condition of the objects
about which thought is concerned. Thus, Philolaus and
the Pythagoreans, imagining that the nature of fire was
more incomprehensible than that of earth, and feeling that
whatever they could least comprehend impressed their minds
with the greatest sensations of awe, concluded that fire
in itself was more capable of majesty than earth, and in the
disposition of the universe would occupy the most worthy
place. Accordingly, they conceived that there existed in
the centre of the universe a mass of fire termed the " Altar
of Nature," and that, at distances varying with the dif-
ferent degrees of fiery composition, were ranged the heaven
containing the fixed stars, the planets, and all other cosmical
bodies.

Perhaps the most prevalent class of a priori fallacies is that
\vhich results from an inspection of the imaginative powers,
it being assumed that objective existence is dependent upon

* A practical view. Compare with this the section upon Obser-
vation.

OF FALLACIES. 97

the possibility or impossibility of its being conceived by us.
Dr. Clarke, for instance, in a correspondence with Bishop
Butler, makes use of the following expression, " The suppos-
ing anything possibly to exist alone, so as not necessarily to
include the pre-supposal of some other thing, proves demon-
strably that that other thing is not necessarily existing ;
because whatever has necessity of existence cannot possibly,
in any conception whatsoever, be supposed away." Here the
statement is implied that because we cannot conceive it, there-
fore, no necessary existence can be apart from or indepen-
dent of any other existence ; this, of course, being an arbi-
trary assumption that the laws of our minds regulate the
facts of nature.

Again, one of the most celebrated modern systems of phi-
losophy was based upon this error; viz., that of Descartes,
concerning whom Mr. Mill speaks thus : " His favourite
device for arriving at truth, even in regard to outward things,
was by looking into his own mind for it. ' Credidi me,' says
his celebrated maxim, ' pro regul& generali sumere posse
omne id quod valde dilucide et distincte concipiebam, verum
esse :' whatever can be very clearly conceived must certainly
exist ; that is, as he afterwards explains it, if the idea includes
existence. And on this ground he infers that geometrical
figures really exist, because they can be distinctly conceived.
Whenever existence is ' involved in an idea,' a thing con-
formable to the idea must really exist which is as much as
to say, whatever the idea contains must have its equivalent in
the thing ; and what we are not able to leave out of the idea
cannot be absent from the reality. This assumption pervades
the philosophy not only of Descartes, but of all the thinkers
who received their impulse mainly from him, in particular
the two most remarkable among them, Spinosa and Leibnitz,
from whom the modern German metaphysical philosophy is
essentially an emanation."*

Locke, too, founds his proof of the existence of a God upon
the considerations, that as (self-evidently) nothing cannot
produce any real being, something must have existed from all

* " Logic," book v. chap. iii. 3.

98 OF FALLACIES.

eternity ; and that this something must be a cogitative being,
because it is as impossible to conceive that every bare incogi-
tative matter should produce a thinking intelligent being,
as that nothing should of itself produce matter. This reason-
ing hinges upon the supposition that " what is inconceivable
is impossible," a proposition which is continually being dis-
proved as knowledge advances, and our means of investigation
become greater. In fact, that great truth which is ever
present with us the action of mind upon matter should of
itself suffice to overthrow all reliance upon a-ny necessary con-
nection between subjective and objective existences.

An ordinary case of the operation of the above fallacy is to
be found in the reception accorded to any account of won-
derful events. Take, for example, the case of mesmerism, or
spirit-rapping. One person cannot conceive the possibility
of the facts being produced by ordinary means, and, therefore,
assumes that they must be the results of supernatural agency ;
while another, not being able to imagine that immortal beings
would, or that mortals could, give rise to such events, con-
cludes that these cannot have occurred. In each extreme
an erroneous inference takes place, founded upon a premiss
unduly assumed.

Another duplicate group of errors is based upon the sup-
positions that nothing can be true unless some reason can be
assigned for it, and that everything must be true if there
exist no reason against its being so. To the former may be
referred the usual objection of " cui bone ?" which assumes
that an objective fact does not exist if its practical uses arc
not immediately observable. To the latter belong most of
the a priori demonstrations of physical truths, one of the best
known being Duchayla's proof of the composition of forces,
which rests upon the axiomatic statement that " the resultant
of two forces meeting at a point, must bisect the angle
between them." This is said to be self-evident, " because we
can assign wo reason why the resultant should incline to one
force rather than to the other." Here, as all a priori reason-
ing is necessarily anterior to experimental knowledge, we
cannot be certain but that something may exist in the natural
action of two forces upon each other, which shall invariably

OF FALLACIES. 99

incline their resultant to the right or to the left ; nor can
any reason be assigned for the resultant bisecting the angle,
rather than inclining to one of the forces. The first step,
therefore, of the proof being unfounded, the remaining por-
tions are untenable ; and, indeed, it would appear generally
true, that the only valid reasoning with reference to physical
facts is such as may be deduced from experiment, i.e., such
as is a posteriori.

A very ancient example of the fallacy which we have just
considered is to be found in the astronomical doctrines of
Anaximander, who flourished at the commencement of the
sixth century, B.C. He held that the earth was suspended
immovably in space, because * " being equidistant from the
containing heaven in every direction, there was no reason
why it should move in one direction rather than in another."

There remains but one more species of a priori fallacies to
which I shall allude, viz., those arguments which rest upon
the suppositions that an effect has but one cause, and that
causes must resemble their effects. Thus, Plato,* in one of
his dialogues, makes Socrates give an account of an investi-
gation into the causes of things, which results in the conclu-
sion that every phenomenon has its own single and separate
cause a substance being red, because a certain abstract
"redness" dwells in it; large, because an abstract " magni-
tude" is present; small, on account of " littleness;" and so
on. This opinion pervaded all philosophy until the days of
Bacon, who, by his advocacy of experiment, led the way
towards the admission that the same effects may be produced
by different causes. At the same time, however, it is to be
remarked that even Bacon himself was not altogether free
from these errors, inasmuch as in his celebrated inquiry con-
cerning the " form," or nature of heat, he assumes that the
sensation of heat is always caused by the same set of condi-
tions or attributes, whereas we now know that intense cold
(and other causes) will produce a similar effect as far as cur
feelings are concerned. He also imagines that there must be

* Sir G. C. Lewis's " Astronomy of the Ancients,** chap. ii. 5.
f " Phado," ^ 103.

F 2

100 OF FALLACIES.

a resemblance between causes and effects, for we find him
tpeaking as follows :* " Heat is a motion of expansion, not
uniformly of the whole body together, but in the smaller parts
of it; and at the same time checked, repelled, and beaten
back, so that the body acquires a motion alternative, per-
petually quivering, striving and struggling, and irritated by
repercussion, whence springs the fury of fire and heat."
Hence it is that, although very near the mark, he has yet
failed to obtain a clear and comprehensive notion of heat, for
he says,f " Again, it [that heat is a motion of constituent
atoms, not of constituted bodies] is shown in this, that when
the air is expanded in a calender glass, without impediment
or repulsion, that is to say, uniformably or equably, there is
no perceptible heat. Also, when wind escapes from confine-
ment, although it burst forth with the greatest violence, there
is no very great heat perceptible, because the motion is of
the whole, without a motion alternating in the particles."
Here, from the assumption that the sensation of heat must
always be produced by heat, he concludes the absence of the
latter in cases where we know it is really present. The rea-
son, then, of Bacon's failure would appear to be that he con-
fined himself to the investigation of the nature of that set of
conditions which are capable of producing the sensation of
heat ; whereas he should have endeavoured to ascertain the
number of different effects which might be produced by the
action of heat : "the power of artificially producing an effect,"
as Mr. Mill says,:): " implying a previous knowledge of, at least,
one of its causes. If we discover the causes of effects, it is
generally by having previously discovered the effects of causes."

I have considered these a priori fallacies at some length,
in consequence of their universal influence, and small liability
of detection. The remedy is to deny the self-evidence of the
assumed principle, and require a proof.

2. Fallacies from pre-conceived opinions. It often hap-
pens that men are content to accept, as established truths,
assertions whose only foundations are derived from their

* " Nov. Org.," book ii. A ph. 20. Spedding's Trans. f Ibl '<*.

J ;< Logic," book v. chap. iii. 7. Compare with preceding remarks.

OF FALLACIES. 101

consonance with some pre-conceived opinion, or from a hasty
inspection of the facts involved. And in cases where an
intentional piece of sophistry is employed, the most suc-
cessful plan is to mention the premiss as something wonderful
and surprising ; the effect of which is that our attention is
no longer directed to the question of the proposition's truth
or falsity, but rather to the best method of accounting for the
fact.* Thus, the Royal Society were, for a long time, puzzled
by King Charles II.'s inquiry, as to the reason why a dead
fish will not add to the weight of a vessel of water, although
a live fish will ; and it was not until after many vain attempts
to discover a solution of this marvel, that the philosophers
remembered that there might be a doubt as to whether it
existed at all.

Most cases of superstitions may be referred to this head ;
that is to say, most instances of superstitious belief producing
any effect upon the mind. How many reputed supernatural
appearances would have been investigated, and their real
nature detected, if the prevalent belief that such events were
of frequent occurrence, had not precluded the necessary ex-
amination! And even to the present day, there are persons
to be found in provincial districts, who will attribute any
sudden misfortune to the operation of witchcraft, simply be-
cause they have always understood that this power was the
usual cause of similar events ; never deeming it necessary to
ascertain the truth of the tradition.

Indeed, there would seem to exist some faculty in the
mind which renders us disposed to accept whatever is handed
down in the shape of tradition, the more especially if it be
of prodigious and marvellous import Possibly the fact is,
that the majority have a great disinclination to exert their
mental powers more than is absolutely required for the proxi-
mate objects of their pursuits ; and, consequently, they regard
with disfavour any attempt to disabuse them of erroneous
opinions, as such a course would necessarily involve the
exertion of accustoming themselves to new methods of belief.

3. Fallacies from false analogies. Analogy is, properly

* Compare Whately's " Logic," book iii. 14.

102

OF FALLACIES.

speaking, a " resemblance of relations ;" and when " we argue
from analogy," we assert that two objects which resemble
each other in one point, will also resemble each other in
another point, which depends in both cases, by a similar
relation upon the first. Thus, we conclude that ammonium
is a metal, because it resembles other metals in its forma-
tion of an amalgam with mercury ; that is to say, the rela-
tion between the constituents of each amalgam, being pre-
cisely similar, we infer that they are severally composed of
mercury, in combination with a metal. But were we to infer
that sulphur is a metal, because heat vaporises it as well as all
metallic substances, we should be employing a false analogy,
because the relation of vaporisation does not necessarily
determine the presence of a metal in conjunction with heat.

Accordingly, a fallacy of false analogy may be considered
to exist wherever from a resemblance in one point is inferred
a resemblance in another, without, at the same time, its being
shown that there exists a similarity of relations between the
two points.

Professor De Morgan notices the following prominent in-
stances of tli is fallacy* : " All the makers of systems, who
arrange the universe, square the circle, and so forth, not only
comfort themselves by thinking of the neglect which Coper-
nicus, and other real discoverers, met with for a time, but
sometimes succeed in making followers. These last forget
that for every true improvement, which has been for some
time unregarded, a thousand absurdities have met that fate
permanently. It is not wise to toss up for a chance of being
in advance of the age, by taking up at hazard, one of the
things which the age passes over. As little will it do to
despise the usual track for attaining an object, because
(as always happens) there are some who are gifted with
energies to make a road for themselves. Dr. Johnson tells a
story of a lady who seriously meditated leaving out the classics
in her son's education, because she had heard Shakspeare
knew little of them. Telford is a standing proof (it is sup-
posed by some) that special training is not essential for an
engineer."

* " Formal Logic," p. 276.

OF FALLACIES. 103

In Plato's " Dialogue upon the Immortality of the Soul,"
Simmias objects that, according to Socrates' account, the
soul is a harmony of the body, and that therefore, it will be
destroyed when the body is, in the same manner as the har-
mony of a lyre ceases when the lyre is broken. But Socrates
shows the fallacy of this argument, by pointing out that the
same relation does not obtain between the soul and body, as
between the lyre and its harmony ; for, as had been pre-
viously granted, the soul exists before the body, and is, there-
fore, independent of it, while the harmony of any particular
lyre cannot exist until the instrument is constructed, and
accordingly perishes when it is destroyed.

The records of ancient astronomy abound with examples
of fallacious analogies. The Pythagoreans, for instance, are
reported by Aristotle, to have conceived that ten was the
only perfect number, and, therefore, the number of bodies
revolving round the central fire must also be ten. But nine
only were visible to them ; viz., the sun, the moon, the earth,
the five planets, and the sphere of fixed stars ; accordingly,
they imagined another, which they termed the antichthon,
and declared to be invisible from the earth, as it was upon
tho opposite side to the inhabited portion. In like manner,
the distances of the several orbits were assumed to increase
constantly, in the ratio of three to one, a calculation which
made the sun's distance from the centre 729 : this number
being both a square and a cube, the sun also was said to be a
square and a cube. " Finding that the distances of the
planets bore, or seemed to bear to one another, a proportion
not varying much from that of the divisions of the mono-
chord, they inferred from it the existence of an inaudible
music, that of the spheres : as if the music of a harp had
depended solely on the numerical proportions, and not on the
material, nor even on the existence of any material any
strings at all. It has been similarly imagined that certain
combinations of numbers, which were found to prevail in
some natural phenomena, must run through the whole of
nature : as that there must be four elements, because there
are four possible combinations of hot and cold, wet and dry ;
that there must be seven planets, because there were seven

104: OF FALLACIES.

me tab, and even because there were seven days of the week.
Kepler, himself, thought there could be only six planets,
because there were only five regular solids."* Nor must it
be imagined that these fantasies are confined to the olden
times, for I, myself, have heard a clergyman seriously main-
tain, from the pulpit, that the number seven must be sacred
in its nature, because it is composed of three and four ; the
former representing the Holy Trinity ; the latter, man and
nature, all of whose attributes and members are regulated by
twos and fours.

" Another example is the not uncommon dictum, that
bodies politic have youth, maturity, old age, and death, like
bodies natural that after a certain duration of prosperity
they tend spontaneously to decay. This also, is a false an-
alogy, because the decay of the vital powers in an animated
body, can be distinctly traced to the natural progress of those
very changes of structure, which, in their earlier stages, con-
stitute its growth to maturity ; while in the body politic, the
progress of those changes cannot, generally speaking, have
any effect but the still further continuance of growth : it is
the stoppage of that progress, and the commencement of re-
trogression, that alone would constitute decay. Bodies politic
die, but it is of disease, or violent death : they have no old
age."f

Fallacies of false analogy may be shown to be erroneous,
by proving that there is no causative connection between
the resemblance observed and the resemblance inferred ; or,
in other words, that it does not necessarily follow that they
must always co -exist.

4. Fallacies from false generalisations. Numerous causes
exist, which lead us to infer universal propositions where
only particular ones are warranted by the facts of the case.
Memory itself is an active agent in promoting this error ; as,
for instance, in the case of predictions being verified, marvel -
loiu coincidences, and the like, we only remember those
occurrences where the prediction was fulfilled, or where some
result followed the coincidence, and entirely forget those of

* Mill's " Logic," book v. chap. v. 6.
f Mill's " Logic," book v. chap. v. 6.

OF FALLACIES. ''"V Ip5

the contrary nature. We then enumerate the remembered
cases, and conclude that the prophet is a true one, and that
the coincidence is an example of cause and effect.

This fallacy often assumes a dilemmatic form, and was in
constant use among the ancient Greek logicians, when en-
gaged in their disputative tournaments. A celebrated in-
stance is the following, which endeavours to show, from the
argument of necessity, that it is of no use to strive against
any occurrence, fortunate or unfortunate.

If I ought to exert myself to effect a certain event, this

event either must take place or it must not ;
If it must take place, my exertion is superfluous ; if it
must not, my exertion is of no avail ;

/. On either alternative, my exertion is useless.

Here, in the major premiss, it is assumed that for the
event to take place necessarily, and for it not to do so, are all
the cases possible. But this enumeration is imperfect, as the
event taking place may depend upon my own exertions ; and
therefore, the alternative member of the premiss should be,
" This event must either take place through my own exer-
tions, or through some other cause, or not at all."

Occasionally, the answer to a dilemma is to " retort " it ;
i.e., to propose one which shall be correlative and reciprocal.
The best known of these cases is called the litigiosus. Sir
William Hamilton's account is as follows : " It relates to "
an action between Protagoras, the prince of the sophists,
and Euathlus, a young man, his disciple. The disciple had
covenanted to give his master a large sum to accomplish
him as a legal rhetorician ; the one half of the sum was
paid down, and the other was to be paid on the day when
Euathlus should plead and gain his first cause. But when
the scholar, after the due course of preparatory instruction,
was not in the same hurry to commence pleader, as the master
to obtain the remainder of his fee, Protagoras brought
Euathlus into court, and addressed his opponent in the fol-
lowing reasoning : ' Learn, most foolish of young men, that
however matters may turn up (whether the decision to-day
be in your favour or against you), pay me my demand you

106 OF FALLACIES.

must. For, if the judgment be against you, I shall obtain
the fee by decree of the court, and if in your favour, I shall
obtain it in terms of the compact, by which it became due
on the very day you gained your first cause. You thus
must fail, either by judgment or by stipulation.' To this
Euathlus rejoined : * Most sapient of masters, learn from
your own argument, that whatever may be the finding of the
court, absolved I must be, from any claim by you. For, if
the decision be favourable, I pay nothing by the sentence of
the judges, but if unfavourable, I pay nothing in virtue of
the compact, because, though pleading, I shall not have
gained my cause.' * The judges,' says Gellius, ' unable to
find a ratio decidendi, adjourned the case to an indefinite day,
and ultimately left it undetermined.'"

The "horned" dilemma is also a much-renowned fallacy.
It consists of the question, " Have you cast your horns ?" to
which, if you answer " No," I reply, " Then you have them
still :" if you answer " Yes," I reply, "Then you have had
horns." The error here is the assumption that you must
either have had horns and cast them, or have had them
and retained them ; whereas, another case is possible, viz.,
the fact that you have never had them.

Another example is the fallacy of continuous questioning,
to which the name of sorites is often applied. It is thus em-
ployed : The sophist asks whether a man with so many
thousand hairs on his head is bald. You answer, " No ; "
and are next asked whether if he had one hair less he would
be bald. The same reply being given, a further diminution
of one hair takes place, and so on, until you are either forced
to admit that you cannot distinguish between bald and not-
bald, or that they differ by a single hair. The reasoning is
based upon the supposition that a man must either be bald
or not-bald, whereas he may be both : and this refutation
does not involve a contradiction in terms, as at first it would
seem to do, for " bald " and " not-bald" being relative terms,
may, when their correlatives differ, be both applied to the
same object. Of course, an exact method of evading the
sophism would be to regard " bald " as meaning entire desti-
tution of hair; in which case there would be no absurdity in

OF FALLACIES. 107

maintaining that a single hair constituted the difference be-
tween bald and not-bald.

These will serve as a specimen of the fallacies invented by
the Greeks for purposes of recreation. We will now consider
the practical forms in which false generalisation appears
among the ordinary reasoning processes of philosophy and
common life.

The non causa pro causa is an error of very wide extent,
and consists in imagining a causal relation between two facts
which happen to occur either at the same time, or within
some short interval of one another. Thus, the ancients
imagined that anything which apparently moved of itself
was animated, since they had observed voluntary motion to be
accompanied by life in many cases : accordingly, they assumed
that the stars were animated. Here, from observing a co-
incidence, they inferred a causal relation, and so laid down a
general law which, false in itself, was the parent of many
kindred errors when applied to scientific speculations. So,
too, from the fact that wars or pestilences have happened
soon after the appearance of a comet, it has been held that
heavenly bodies of like description are the causes, or at least
precursors of great calamity. In this case, a sequence was
considered as a relation of antecedent and consequent; the
technical name for such a fallacy being post hoc, ergo propter
hoc, while the former is called cum hoc, ergo propter hoc.

It is not, however, to be supposed that all examples of this
fallacy are of such a simple description. Thus, a country is
often said to be prosperous because it is rich, whereas in fact,
it is rich because it is prosperous : or the government and
constitution must be praiseworthy, because under them the
country has flourished, the truth being that it has flourished
in spite of them.

The want of sufficient investigation frequently leads to
false generalisation : iron, for instance, was supposed to be
rusted whenever it came into contact with water ; recent ex-
periments have, however, determined that air, and probably
carbonic acid, are also necessary to the production of this
effect. Oxygen, as is imported by its name, was considered
the active principle of all acids, merely because it was a

108 OF FALLACIES.

constituent of such as were then known analytically : the
doctrine was but short-lived, owing to the discovery that many
acids contained no oxygen whatever. And this will always
be the case, where efforts are alone directed to discover the
points of similarity between various bodies, instead of the
attempt being made to ascertain the properties wherein they
differ.

" Experience " has also much to account for as an erroneous
guide : no public vehicle had been made to run at more than
ten or twelve miles the hour ; therefore, to travel quicker by
railway could never take place. A certain law has hitherto
worked well ; therefore, it will never require alteration : the
swans that had been seen before the discovery of Australia
were white ; therefore, there were no black ones. No person
had met with birds without wings ; consequently, until the
apteryx was found in New Zealand, the notion obtained that
all birds were thus provided ; and so on, the love of dogma-
tising from truths within our observation to facts beyond it,
being irresistible.

Of a similar nature is the employment of general pro-
positions as such, which are only the result of a majority of
cases : estimates of national character, for instance, when ap-
plied to an individual case, cannot give a correct inference,
although, of course, the conclusion may possibly be true.
When I say the Hindoos are Pagans, I mean only that most
of them are so; and, therefore, were I to declare that this
man is a Pagan because he is a Hindoo, my syllogism would
either be invalid, the middle being undistributed, or the major
premiss would be unduly assumed.

5. Fallacies from a False Estimation of Probabilities.
A premiss which in itself is only probable, is not uncom-
monly assumed as certain ; or, should it be just possible, it is
taken as probable. The degrees of probability are also un-
duly increased in many arguments, more especially where
the reasoning takes the form of a sorites or epicheirema.
Thus, if we were to argue that since earthquakes are possibly
caused by sudden formations of steam within the earth, and
since the intrusion of fused rocks and other highly heated
matter into cavities filled with water would probably occasion

OF FALLACIES. 109

such bursts of steam, therefore, the probable existence of in-
ternal lakes may be inferred, we should vastly over-estimate
the chances involved. So, " one of the great fallacies of
evidence is the disposition to dv&ell on the actual possibility
of its being false ; a possibility which must exist when it is
not demonstrative. Counsel can bewilder juries in this way
until they almost doubt their own senses. A man is shot,
and another man, with a recently discharged pistol in his
hand, is found hiding within fifty yards of the spot, and ten
minutes of the time. It does not follow that the man so found
committed the murder ; and cases have happened, in which
it has turned out that a person convicted upon evidence as
strong as the above, has been afterwards found to be inno-
cent. An astute defender makes these cases his prominent
ones ; he omits to mention that it is not one in a thousand
against whom such evidence exists, except when guilty." *

The chance of deception in such cases must depend, in a
great measure, upon the capacity of the parties to decide
upon the proper weight to be given to each probability. If
numerical values can be assigned to the various statements,
the conclusion is merely a matter of arithmetical computation,
but it w r ould seldom be feasible to obtain the consent of an
opponent to such a course. Accordingly, the best plan is to
require that each proposition shall be expressed in one of
these forms " A is more likely than not, to be D," or, "A
is less likely than not, to be D :" it is a simple matter then
to arrive at a satisfactory result.

6. Fallacy of Reasoning in a Circle. This fallacy arises
whenever one of the premises is the same in sense with
the conclusion, and it is scarcely necessary to point out that
its unfairness consists in the fact of assuming as already
proved (i.e. as a premiss) the very thing which you are
about to prove, viz., the conclusion. An argument might,
for example, be maintained in the following manner :
" Light is certainly material, for it adds to the weight of any
body which absorbs it, although in so slight a degree as to
escape perception by our most exact means of investigation.

* De Morgan's " Formal Logic," pp. 275-6.

110 OF FALLACIES.

And that it does so add to the weight results from the con-
siderations that all matter is ponderable to some extent at
least, and that when any substance is absorbed by another,
the ponderosity of the former is necessarily added to that of
the latter." If this train of reasoning were extended by a
judicious introduction of illustrative examples of each state-
ment, with elaborate analyses of the various principles in-
volved, it might very possibly escape the observation of many
readers, that to mention in such connection the case of one
substance being absorbed by another, is, in reality, to assume
the conclusion, i.e., that light is material.
"" 7. Petitio Principii is a modification of the foregoing,
and occurs when the faulty premiss is " proved from the
conclusion, or is such as the persons you are addressing are
not likely to know, or to admit, except as an inference from
it, as e.g., if any one should infer the authenticity of a certain
history, from its recording such and such facts, the reality
of which rests on the evidence of that history." *

This fallacy is more dangerous than that of reasoning in a
circle, from the circumstance that the premiss merely depends
upon, and does not explicitly state the conclusion ; conse-
quently, it often requires a minute and searching investiga-
tion to detect the error. Hence we cannot be surprised upon
discovering that many philosophers whose acuteness and
intellectual power stand almost unrivalled, have yet fallen
into the snare of petitio prmcipii, or, in other words, have
" begged the question " at issue. " Plato, in the " Sophietes,"
attempts to prove that things may exist which are incorporeal
by the argument that justice and wisdom are incorporeal, and
justice and wisdom must be something. Here, if by some-
thing be meant, as Plato did in fact mean, a thing capable of
existing in and by itself, and not as a quality of some other
thing, he begs the question in asserting that justice and
wisdom must be something/' f

It has, indeed, been urged that every syllogism is a case
of the petitio principal, since the truth of the major premiss

* Whately'e " Logic," book iii. 1C.
f Mill's " Logic,' ' book v. chap. vii. 2.

OF FALLACIES. Ill

depends upon the truth of the conclusion. Thus, in this
argument

All horses are quadrupedal,
Bucephalus is a horse ;
/. Bucephalus is quadrupedal :

it is objected that before we can assert all horses to be
quadrupedal, it must be true that Bucephalus is so. To dis-
cuss the question involved would here, however, be out of
place; but those students who may wish for any further in-
formation upon the subject will find such in the Appendix,
Article D.

A common method of expressing the petitio principii is to
employ words, which, although synonymous, are yet of dif-
ferent etymology and derivation. A happily -chosen example
is thus given by Archbishop Whately : " To allow every
man an unbounded freedom of speech must always be, on the
whole, advantageous to the state ; for it is highly conducive
to the interests of the community, that each individual should
enjoy a liberty perfectly unlimited, of expressing his senti-
ments."

The remedy for the last-mentioned fallacies consists in
cutting down the chains of reasoning as much as possible, so
as to bring the erroneous premiss and the conclusion into
close juxtaposition, when it will not be a matter of any difficulty
to discern their relation and inter-dependence.

6. Material Fallacies. Ignoratio Elenclii.

1. Argumenta ad hominem, &c. The passions and pre-
judices of men having an enormous influence over their
reasoning powers, a skilful sophist will often, by appealing
to some particular bias, convince his hearers that such and
such a proposition is perfectly correct, and then maintain that
being so it must be received as universally true. Now, in
doing this he has merely proved the conclusion partially,
i.e., in so far only as his hearers are concerned ; whereas
he should have proved it generally, and as applicable to all
classes. Accordingly, he is guilty of an ignorance or evasion
of the required proof (elenchus), this being the distinguish-

112 OF FALLACIES.

ing characteristic of the class of errors at present under
examination.

There are three principal heads contained under the first
division of this class, viz., the Argumentum ad hominem, the
Argumentum ad verecundiam, and the Argumentum ad pop u-
lum. Of these, the first consists in unfairly appealing to the
opinions, &c., of the individual addressed ; the second, in
similarly addressing the reverence entertained for old institu-
tions and the like ; the third, in apparently determining the
question by exciting the passions and fancies of the populace.
Thus, I might go to one man whom I knew to be a disbeliever
in the results of geological science, and compel him to admit
that coal could not have required vast ages for its production,
by arguing that the world itself had only existed for six
thousand years ; this would be an appeal ad hominem. Again,
I might go to another, and succeed in establishing the same
conviction, by reminding him that surely he would never
think of setting his opinion up against what had been main-
tained by men of such learning and genius as so and so, and
so and so; here I should address my argument ad verecun-
diam. Or, I might carry this point with a mob, by telling
them that the contrary opinion was only upheld by those men
who were always endeavouring to deceive the poor, and to
take the bread out of the labourer's mouth by new-fangled
inventions, which would be an argumentum ad popnlum.

2. Substituting a Part for the Whole. When a universal
proposition cannot be established, it often gains admittance
by the proof of its corresponding particulars. Thus, with
regard to the various sciences it is frequently urged that none
of the principles are trustworthy, because there has always
been a difference of opinion as to facts and theory between
even the most renowned philosophers. Here the assertion ia
true in a measure, for some facts and theories have undoubtedly
given rise to continual discussion ; but, then, we must not lose
eight of the fact that investigators of all parties and shades of
opinion are in perfect agreement as regards the major portion
of the respective sciences. And this form of ignoratio elenchi
has a still commoner modification, viz., the assumption which
persons frequently make, that upon their own preconceived

OF FALLACIES. 113

opinions, men of science are at variance, because controversy
exists as to other doctrines; this being, not an inference of the
whole from a part, but of one part from another. As might
be expected from its recent development, the science of geo-
logy is greatly exposed to these mistaken notions ; and in
reference thereto, Sir Roderick Murchison has made the fol-
lowing valuable observations: " In all the grand leading data
on which the history of geology is based, we [himself and
Sir C. Lyell] are completely united; whether it be in record-
ing the regular succession of formations from the oldest to
the youngest, the progression from lower to higher types of
life, the enormously long periods which must have elapsed in
the formation of deposits, and their frequent change into
crystalline conditions by that metamorphism which he has so
skilfully expounded ; or, lastly, in the evidences he has brought
together to show that man must have coexisted with some of
the great fossil mammalia. On all these subjects I hold the
same opinions as himself; and I have ventured to make this
explanation because it seems to me essential that the public
should not run away with the idea that because geologists occa-
sionally disagree on points of theory , that there exists among them
any divergence of opinion as to the great foundation stones
on which their science has been reared"

In the refutation of an argument we frequently meet
with examples of this fallacy : the objector shows that his
opponent is mistaken upon one point, and thence concludes
that the whole of his reasoning is unsound even though it
may in nowise depend upon the erroneous statement. " Hence
the danger of ever advancing more than can be well main-
tained, since the refutation of that will often quash the whole.
.... Thus, also, a guilty person may often escape by having
too much laid to his charge ; so he may also, by having too
much evidence against him, i.e., some that is not in itself
satisfactory. Accordingly, a prisoner may sometimes obtain
acquittal by showing that one of the witnesses against him
is an infamous informer and spy ; though, perhaps, if that part
of the evidence had been omitted, the rest would have been
tfufficient for conviction."*

* Whately's " Logic," book iii. 18.

114: OF FALLACIES.

There may often be a combination of the ignoratio elenchi
with other kinds of fallacies. Thus, instead of proving the
impossibility of space being finite, philosophers are accus-
tomed to prove its inconceivability ; and the same thing occurs
with regard to any limit of duration : both of these errors
arising from the a priori belief that the conclusion proved,
and the conclusion required, were in each case of equivalent
import. So, too, if a supposed cause can be shown as suffi-
cient to produce a certain effect, its existence is inferred,
when the real question is, have we any grounds to warrant the
supposition itself. Until, for example, Torricelli had suc-
ceeded in producing the vacuum to which his name is given,
men of science were all agreed upon the statement that
" Nature abhors a vacuum," a supposition which was suffi-
cient to account for the difficulty they experienced in making
a void space. The illustrious Newton himself adopted the
opinion that an interstellar ether existed, not on account of
those facts which have led modern philosophers to the same
belief, such as the variation observable in the course of comets,
and similar reasons ; but because he conceived that the effects
of gravity might be explained by such an assumption. In
the same manner he was obliged to suppose various arbitrary
properties of different kinds of matter, in order that his pre-
conceived theory of light should be accordant with the
respective phenomena of colour ; but yet it must not be ima-
gined that hypotheses are not often of very great service in
scientific investigations ; for when cautiously applied, and
only admitted as provisional, until a more extended know-
ledge is attained, they form a most valuable instrument of
reflection and observation. That such is the case will be at
once apparent upon a mere mention of the atomic theory,
which found chemistry a scattered, disjointed collection of
isolated facts, and gathering the members into one organic
whole, left it endowed with vitality, self-impulsive, and pos-
sessed of unfathomable power.

The fallacy of " shifting ground " should properly be ranked
under this head, and occurs whenever a fresh point is raised
before the former one is decided. This is also called " beating
about the bush;" it chiefly happens in conversational argu-

OF FALLACIES. 115

ments, and some very good examples may be found in the
" Dialogues " of Plato. For instance, in the following passage
from the " Gorgias " an ignoratio elenchi is finely exposed by
Socrates ; the question being what name should be applied
to Gorgias, the famous orator of Leontium :

Chce. But now, since he is skilled in a certain art, what can we pro-
perly call him ?

Pol. Chaerephon, there are many arts among men by experience expe-
rimentally discovered; for experience causes our life to proceed according
to art, but inexperience according to chance. Of each of these, different
persons partake of different arts in different manners ; but the best of the
best ; in the number of whom is Gorgias here, who possesses the finest of
the arts.

Soc. Polus appears, Gorgias, to be very well prepared for speaking ;
but he does not do what he promised Chserephon.

Gor. How so, Socrates ?

Soc. He does not appear to me to answer the question that was asked.

Gor. Do you, then, if you please, ask him.

Soc. No, but if yourself would be willing to answer me, I would much
rather ask you. For it is evident to me that Polus, from what he has
said, has studied more what is called rhetoric than conversation.

Gor. Why so, Socrates ?

Soc. Because, Polus, when Chaerephion asked you in what art Gor-
gias was skilled, you praised his art as if some one had blamed it, but
you did not say what the art itself is.

In all these cases the only plan of arriving at a satisfactory
result is to come to a distinct understanding with regard to
the question under debate : and if every proposition admitted
or proved be closely compared with the conclusion required,
it will be found that very little danger exists of sophistry
proving successful.

7. Conclusion.

Here, then, terminates our investigation of the several
fallacies which most frequently occur ; and by a careful study
of their various natures, together with the import of the rules
laid down for their treatment, we shall find ourselves in a
great measure secure against the common forms of error at
least ; but it will easily be understood that much depends

116 OF FALLACIES.

upon the extent of individual ability, for however perfect an
instrument may be, it yet requires a directing intelligence in
order to perform its work, and the more ably it is guided
the better it will act. Logic can offer no panacea against
the spread of deception.

The preceding analysis has then enabled us, as far as rules
go, to discover whether a given argument be fallacious or
the reverse. Accordingly, we are now in a position to under-
stand what true reasoning is, since we know what it is not ;
and we may proceed with some certainty to the considera-
tion of the various processes which are employed in the dis-
covery of truth. In speaking of these processes, I of course
allude to those operations which form the especial province of
Logic, for although the formal laws of thought must be
obeyed in every possible case of observation and reflection,
yet there are certain actions of the mind in which they are
more particularly concerned. These will form the subject of
our next chapter.

117

CHAPTER VI.

OF LOGIC AS PRACTICALLY APPLIED.

1. Introductory Remarks.

THE object of all science is the acquisition of truth, a subject
which has as yet occupied but little of our attention ; indeed,
it would have been impossible to have arrived at any accu-
rate results respecting the laws of thinking, if we had not
abstracted from these the matter upon which they operate.
Now, however, that we have obtained, as I trust, clear and
accurate notions of the mode in which the natural constitu-
tion of our minds influences the operation of all thought, we
shall be quite prepared to investigate the results of such in-
fluence, and to ascertain its practical effects. To do this suc-
cessfully we must continually bear in mind the various prin-
ciples which have been enounced during our survey of formal
Logic : these relate to the three processes of apprehension,
judgment, and inference, teaching us first, that our objects of
thought must be either the ideas of individuals or of classes ;
secondly, that any assertion concerning these ideas must take
the form of a quantitative comparison ; and, thirdly, that no
reasoning is correct which does not conform to the syllogistic
rules, which are proximate applications of the inherent mental
canon. But the most transcendent product of our researches
has been the firm establishment of the fact that the greatest
instrument by which the mind works is system; it invariably
strives to arrange the facts which it gathers, and to erect
them into some connected structure ; the peculiar office of
Logic as a science being to secure the symmetrical adjust-
ment of parts which compose the fabric. This truth, I make
bold to say, is the indispensable key to a proper understand-

118 OF LOGIC AS PRACTICALLY APPLIED.

ing of the nature and working of the reflective faculties ; it
may be seen to underlie each separate step of our inquiries
hitherto ; and no explanation of the mysteries involved in the
mind's search after truth can be complete unless it enters as
an essential element.

Thus much premised, it will readily be imagined that un-
less our researches conform strictly to the natural laws of the
intellect, we can only arrive at confusion and contradiction,
instead of at truth ; for, although we must always in some
degree be regulated by the inherent forms of thinking, yet in
many cases a considerable deviation takes place, in conse-
quence of an imperfect acquaintance with, and analysis of
the principles which should be universally prevalent. This it
is which occasions the necessity for an applied Logic ; that
is to say, a science which shall point out the proper method
of interweaving the laws developed by formal Logic, with
the web of facts that constantly come under our notice, in
such a manner that we may attain to the most perfect and
correct knowledge of them. And hence it will be apparent
that in so doing these laws will require various modifications,
in order that they may be accommodated to the respective
circumstances of the case ; for it must not be forgotten that
in treating upon the formal aspect of thought no account was
taken of the phases into which reflection would fall when
concerned with the truth and falsity of propositions. So, too,
with the mathematical sciences ; the principles involved are
analysed upon a partial consideration only of the facts to
which they are ultimately applied. In geometry, for instance,
points are regarded as possessing no magnitude, lines as
without breadth, circles as perfectly uniform ; although for
any practical purposes we must always make allowance for
the many departures from theoretical supposition, which
must invariably occur. And, paradoxical as it may seem, it
is this very disregard of actual truth which confers upon
mathematics and Logic the rigid exactness attending all their
investigations ; the reason being, that by removing all dis-
turbing influences, the attention is concentrated upon such
points alone as are of vital importance to the laws which
regulate the existence of the science.

OF LOGIC AS PRACTICALLY APPLIED. 119

Accordingly, we shall find that there is not that precise
distinction between the several branches of applied Logic
which we found to exist in the subjects about which formal
Logic is conversant. The operations run, as it were, hand
in hand, presenting such an appearance of simultaneity, that
it is often a matter of considerable difficulty to ascertain the
exact nature of their mutual dependence and relation. They
may, however, be grouped under two heads, Observation and
Reflection ; the first of these being amenable to the laws of
conception and judgment ; the second, to those of inference ;
while connecting them is the motive power of classification,
concerning which I have so often spoken. At the same time,
it will be impossible, within the present limits, to do more than
indicate the best method of studying the vast subject of
applied Logic ; which, comprehending as it does, the generic
features of all the sciences existent and to come, has required
the combined efforts of the world's greatest philosophers to
attain its present development ; and which gives such promise
of future progress as to warrant our most sanguine anticipa-
tions of results which shall excel by far all that has hitherto
been accomplished.

2. Observation.

The process of observation naturally presents itself before
us as having the prior claim upon our attention ; for it is
evident that it must always precede reflection, as without
objects to think about there would be no thought. And
here it behoves us to determine more explicitly than hereto-
fore the import which attaches to the phrase " objects of
thought ;" as otherwise some ambiguity of expression would
be likely to occur in consequence of the idea generally attached
to the word " object." This, in ordinary parlance, is held to
imply some substance or existence which produces an impres-
sion upon our minds, but, when used philosophically, may also
signify the impression itself. If, for instance, I say, " Heat
is a most mysterious thing," I may either mean the sensation
of heat, or the cause of that sensation ; and it is with words
of this description that confusion commonly arises. Thus, iii
Mr. Mill's elaborate and masterly " System of Logic," from

. 120 OF LOGIC AS PRACTICALLY APPLIED.

which I have often had occasion to quote, there is the follow-
ing passage : " But from these and similar generalisations
countenance and currency have been given to attempts to
resolve, not motion into motion, but heat into motion, light
into motion, sensation itself into motion;" where "heat" and
"light" would appear to mean the outward causes of the respec-
tive sensations, and not the sensations themselves ; for other-
wise there needs to be no distinction draw 7 n between " heat,"
"light," and "sensation; but yet, a few lines further on, we
read, " All I insist upon ... is, that it shall not be supposed
that by proving these things [i.e., " that certain motions in
the particles of bodies are among the conditions of the pro-
duction of heat or light "] one step would be made towards
a real explanation of heat, light, or sensation. . . . Let it be
shown, for instance, that the most complex series of physical
causes and effects succeed one another in the eye and in the
brain to produce a sensation of colour ; . . . still, at the end
of these motions, there is something which is not motion,
there is a feeling or sensation of colour." Here, indisputably,
Mr. Mill is combating the supposition that the sensation of
heat, light, &c., is motion, a proceeding, however, altogether
irrelevant to the question in hand (as at first stated), viz.,
whether motion is the cause (or " among the conditions ") of
such sensations. An example of this nature is the more in-
structive, as it will be easily supposed that when so acute
and profound a philosopher is led into a confusion of expression
(for one cannot imagine that there is any confusion of thought)
by the ambiguity above-mentioned, multitudes of inferior
writers will continually mistake the point to be proved, and
will involve their arguments accordingly.

Now the word " phenomena " would appear to be better
adapted than any other for expressing the notion intended to
be conveyed by the phrase "objects of thought;" it being
seldom used but in a strictly philosophical sense. We shall,
therefore, in the first place, ascertain the nature of those phe-
nomena concerning which our thoughts are occupied, having
in view the determination between such as are, and such as
are not, the subjects of direct observation.

Every phenomenon is either subjective or objective ; either

OF LOGIC AS PRACTICALLY APPLIED. 121

a condition or state of our mind, or a condition of something
apart from our mind. Any knowledge that we may possess
of the former must obviously be the result of intuition or im-
mediate perception ; but as regards the latter, the operation
is by no means so simple, even in the most familiar and, appa-
rently, incomplex cases. Thus, when I touch a piece of
iron and say, " This iron is hot," the train of thought from
which the judgment results is of the following character :
I look in a certain direction, and am immediately impressed
with those sensations of sight, which, from prior experience, I
have concluded to be always produced by a series of pheno-
mena termed " iron." I extend my hand in the same
direction, and receive two sets of sensations, one consisting of
" hardness," &c., thus corroborating the evidence of my eyes
as to the existence of 4< iron," and the other reminding me of
sensations similar to those antecedently produced by cases of
" heat." I, therefore, feel certain that a series of phenomena
exists before me, which resembles a large class of other series in
its capacity of raising up a particular sensation, known by the
name of "heat;" a conviction which I express by saying, "This
iron is hot." Here, then, a process which would be com-
monly called an act of observation, is seen to consist of two
Bteps: first, the perception of certain sensations, and secondly,
an inference based upon the existence of these sensations ;
consequently, the truth of the statement must depend upon
the correctness of the reasoning. Nor is this analysis by any
means unimportant, for it frequently happens that a supposed,
but non-existent, fact is taken for granted, merely because it
has been observed; whereas the truth is that it was inferred.
There is, for example, a beautiful experiment in optics, where
a revolving wheel is rendered visible by means of flashes of
light, so adjusted that the wheel is once illuminated during
each revolution ; the effect of this being that although the
wheel revolves at the rate of several hundred times a minute,
it yet appears to be standing perfectly still ; and so perfect is
the illusion, that even to imagine it as such is almost impos-
sible. The explanation of this is, that the means employed
in the experiment produce sensations which are indistinguish-
able from those produced by a wheel standing perfectly still,

122 OF LOGIC AS PRACTICALLY APPLIED.

and this latter phenomenon we accordingly infer to be the
case ; an instance of fallacious a priori reasoning, where the
supposition that an effect has but one cause is unduly assumed.

Accordingly, we find that the only phenomena which can
be the subject of direct observation, and concerning which
we may arrive at truth by means of direct observation, are
subjective ; that is to say, the existence of certain sensations is
the only thing of which we can be sure when the observing
faculties are alone employed. At the same time, it would
serve no useful end if we were to push this doctrine to its
extreme limits, and more especially in a treatise like the
present, which cannot enter very minutely into the ultimate
processes of thought ; suffice it, therefore, to have called the
attention of the student to a point so interesting and essential,
as by so doing it may be reasonably hoped that he will have
been put sufficiently on his guard to prevent any chance of
error arising from this cause. In future, then, I shall not
care to be rigidly precise when making use of expressions
which involve the process of observation ; but I shall still
hope to be philosophically exact, for, as we formerly saw when
treating upon the parallel case of the so-called immediate
reasoning compared with syllogistic inference, a preliminary
examination and subsequent neglect of some mental operations
is by no means incompatible with a correct exposition of
logical science.

Assuming, then, that a comparatively loose sense may be
attached to the notion of observation, we have next to inquire
into the nature of the process as logically required for the
purposes of science ; and, as science is merely concerned with
the acquirement of truth, it follows that the end of logical ob-
servation should be the formation of correct conceptions with
reference to those phenomena which are the objects of thought.

Now, the first requisite is that our notions should be clear ;
that is to say, that they should be determinedly fixed; and
as the method of arriving at general conceptions, or, in other
words, the process of abstraction, has already been described
as regards its formal aspect, it now remains to introduce the
element of material truth. The main feature of the process
consists in comparing together a number of individual objocts

OP LOGIC AS PRACTICALLY APPLIED. 123

with a view to ascertain their points of resemblance, and
then conceiving a class composed of any number of objects
which might happen to possess those points ; and this dupli-
cate operation can only be correctly performed by attending to
the following considerations. Let us endeavour, for example,
to trace the formation of the conception " metals." We
meet with certain individual objects, say gold, silver, and tin,
and we wish to obtain such a general notion as may enable
us to remember the sensations produced equally by each one
of them, and by no other thing. We accordingly analyse
the complex impression of each individual, i.e., we concen-
trate our attention successively upon each separate ^e of the
sensations, and note those which were produced indifferently
by gold, silver, or tin. Extending our language a little, we
may describe ourselves when so doing as observing the attri-
butes which were possessed in common by the three objects,
gold, silver, and tin. Suppose us, therefore, to remark that
they all possess weight and hardness ; we might here pause
and give the name of " metal " to the combination of those
two attributes, but were we to do so, we should find that such
an idea was not complex enough to distinguish gold, silver,
and tin from many other objects, such as stone, wood, &c. ;
that is to say, we should not have formed a clear and distinct
idea of a metal. We, consequently, resort to observation
again and again, until we have abstracted such a combination
of attributes, that gold, silver, and tin are the only objects
which we know to possess it ; we can then dearly recall the
sensations produced by a " metal." This capability, however,
would only belong to ourselves, who had performed the above
process ; and were we to employ the name in communicating
with other persons, it would be necessary for us, in the first
place, to define exactly what we mean by the term, as other-
wise they might attach a different signification to it, and
might include the notions of things totally different from gold,
silver, and tin. Here, then, we have two sources of obscurity,
imperfect abstraction, and imperfect definition ; the remedy
for the former being renewed observation ; for the latter, those
rules which were laid down when treating upon definition iu
the second chapter of this work.

a 2

. -.- .-.-' r ' -. i

124 OF LOGIC AS PRACTICALLY APPLIED.

The second requisite for correct conception is that our
notions should be appropriate; that is to say, that they should
have a proper relation to the question in hand. There can,
of course, be no general rule laid down as to what this rela-
tion must be in every case, for that can only be settled by
the specific end which we propose to ourselves ; but yet it
may be remarked that the attributes observed should all have
some distinct reference to the principle of division adopted in
the particular science under investigation. Thus, in the ex-
ample chosen above, our notion of " metal " would include
such marks as hardness, weight, ductility, and malleability, if
we were occupied with mechanical researches ; to these would
be added the capability of forming a base by union with
oxygen, if chemistry were our object ; while the study of
physics would necessitate the inclusion of " great conductive
powers" among the metallic attributes.

If, therefore, we take care that our conceptions are clear
and appropriate, ascertaining at the same time that our senses
do not deceive us as to the real existence of the properties
observed, we shall so far be in the possession of truth, and our
consequent reflections will rest upon a sound basis. This is
all that can be done by observation, and as the nature, con-
ditions, and end of this process have now been described, it
would appear that nothing further remains to be added :
before, however, I quit this portion of my subject, it may be
advisable to offer a few remarks upon the mode of observing.

We have already seen that, strictly speaking, subjective
facts only can be directly observed ; but that no inaccuracy
need result if we admit the application of the process to cer-
tain objective phenomena. It is these latter which will now
be considered. And, first, we must note that observation
may be direct or indirect ; that is to say, we may either
employ our unaided senses, or we may make use of instru-
ments to assist us. In the former case, the chief truths at
which we arrive are those of quality ; in the latter, of quantity.
Thus, by making use of the eye alone, we can form an approx-
imate notion as regards the height of an object, and this will
be nearer to the truth according as our practical experience
is greater ; but to know it exactly, we must employ some

OF LOGIC AS PRACTICALLY APPLIED. 125

measure. Here, in one case, we could merely be sure that
the object possessed some height ; in the other, we could tell
the exact amount. Or again, a ray of light appears to ordi-
nary observation as perfectly homogeneous and white; Saturn,
too, is a mere luminous point ; but the application of a prism
reveals the existence of various colours in the sunbeam, while
a telescope discloses the vision of a far-off world encircled
with a glittering belt ; and with the perfection of the instru-
ment advances, pari passu, our powers of observation. In the
solar spectrum, for instance, Fraunhofer was just able to
ascertain the duplex nature of the line D, but, recently,
Mr. Gassiot, with his magnificent spectroscope, has resolved
it into at least sixteen distinctly defined lines. And the same
thing took place with regard to Saturn ; the employment of
a higher telescopic power showed that what at first seemed
to be but one belt, was in reality two. It will thus be seen
that when the capability of exact admeasurement by means
of instruments is asserted, all that can be strictly understood
is our power of fixing definite limits in one direction at least ;
and hence we gather that the best method of forming correct
conceptions is by observing as precisely as possible, both the
nature and amount of the properties wherein bodies resemble
or differ from each other. We must, however, bear in mind
the fact that although two attributes differ very much in
quantity, yet, if they are alike in quality, they will produce
exactly the same kind of sensation, although varying in degree ;
consequently, we must place them together in the same class.
In our example of " metals," gold, silver, and tin all possess
the mark of " weight," but in very different quantities, this
difference being one of their distinguishing characters as
individuals ; and, therefore, if we were to meet with some
other object, such as lead, and were to recognise in it the
existence of the same kind of attributes as those which we
abstracted from gold, silver, and tin, to constitute the notion
of a metal, we should at once refer it to that class, although
each mark might present a totally different appearance as
regarded its amount.

Experiment may also be considered as an act of observa-
tion ; for although usually the result of reflection, yet in itself

126 OP LOGIC AS PRACTICALLY APPLIED.

it differs not from the ascertainment of attributes or properties
by means of an instrument. In the present place, therefore,
we shall merely consider it from the latter point of view, and
shall defer all inquiry into the motives for its performance
until we come to treat upon the processes of which it is a
necessary accompaniment. A clear notion then can only be
obtained from experiment, by closely observing the nature and
amount of the difference between the respective state of things
before the commencement, and after the termination of the
act ; while as to what is an appropriate notion, must be wholly
determined by the particular object for which we performed
the experiment. Thus, if I wished to ascertain the mechanical
effects of heat upon red glass, I should notice that the latter
became plastic when very hot; but were I investigating
its optical properties, I should confine my attention to the
fact that its colour had changed from red to green.

And here it may be remarked that Logic can no more
make men good observers than she can make them good
reasoners, except in so far as the adherence to rules laid
down in strict accordance with mental laws will tend to a
healthy exercise and invigorating discipline of the intellect.
It is a just saying that " practice makes perfect," but all the
watering and attendance possible will never produce an oak
from a thistle-seed ; and so the most that can be done is to
cultivate to the best advantage whatever has been originally
implanted. Accordingly, the end of observation i.e., the
attainment of correct notions will be greatly promoted by
the habitual exercise of the faculty in accordance with the sug-
gestions given above ; but it is necessary that a good observer
should also possess a retentive memory and wide experience,
as otherwise his ideas would soon become confused, or they
would not accord so closely with actual truth as to be of much
avail for practical purposes.

3. Reflection.

1. Of Laws and Causes. As yet our attention has been
confined to the ascertainment of what amount of truth may
be acquired by the employment of observation alone. \Ve

OP LOGIC AS PRACTICALLY APPLIED. 127

have found that even when the widest latitude is allowed,
the results so obtained are merely a collection of separate
ideas, these ideas being composed of various resemblances
and differences. But, numerous as such notions may be, they
constitute a very small portion indeed of existent truth.
We have certainly coasted along the shore, and surveyed its
general features ; the vast interior, however, still remains un-
explored. That is to say, having collected the facts, we must
now examine into their connection, and in so doing we shall
perceive that the laws of inference are alone adequate to the
task : therefore, without a previous knowledge of them, our
labours would but terminate in confusion and disappointment.

The bare existence of phenomena has hitherto been the
subject of our analysis ; we must now endeavour to justly
appreciate the modes in which they exist ; and as the order
of time is here alluded to, it will at once be seen that a list
of these modes may be easily made ; in fact, there are but
two coexistence and sequence, for phenomena must either
occur together, or in succession. Which order obtains in any
particular case is, of course, determined by observation ; the
right understanding of such order is the office of reflection.

Now, in our sphere of thought, we cannot but observe that
a certain principle of uniformity prevails, more or less, in
every occurrence which comes under our notice. Thus, a
heavy body if unsupported falls to the ground ; a pressure,
when not sufficiently opposed, is followed by motion in the
object pressed ; death invariably succeeds the infliction of
certain wounds ; the explosion of gunpowder is always accom-
panied by the extrication of heat and light. All these facts
must impress themselves strongly upon our, attention. But in
other cases the uniformity is by no means so general ; it is
only some men, for instance, who have black hair ; it is only
occasionally that we meet with natural springs whose waters
are more highly heated than the surrounding earth ; it is not
always that a west wind is accompanied by rain. These con-
siderations lead us to a distinction between uniformities,
which we accordingly regard as necessary, or casual ; as
invariably occurring, or happening, as it were, by chance.
The grounds upon which this distinction may be correctly

128 OF LOGIC AS PRACTICALLY APPLIED.

made will shortly be explained ; at present we are concerned
simply with the fact as it stands.

The impression produced upon our minds by the regula-
rity with which many phenomena recur is that nature works
according to some uniform necessity, this being termed a law ;
and, consequently, we speak of certain uniformities as being
laws of nature. Thus, we say that for matter to possess
weight as one of its attributes is a natural law; that the
orderly constitution of nature renders it necessary for water
to tend to find its level; that motion unopposed must con-
tinue for ever. It is, however, only to truths of this ultimate
description that the term "laws of nature" is applied; many
uniformities which at first sight might appear of the same
description, being in reality results of the former. Thus,
that the moon should revolve about the earth as a centre,
would, from the perfect uniformity of the revolution, seem to
be a natural law ; but closer investigation shows that the
motion takes place in obedience to three separate laws applied
under certain circumstances. In fact, we might predict a
priori such an effect as resulting from given conditions, but
we could not predict the conditions themselves antecedently
to experience.

And this leads us to a cognate consideration of great im-
portance ; the determination of what is implied by the expres-
sion " resulting." Here, of course, the cases are limited to
uniformities of sequence that is to say, those phenomena
which we always observe to occur in regular succession. The
names usually applied to any duplicate set of this description
are cause and effect; reference being made to a law of nature,
which must now be explained, viz., the law of universal caus-
ation. Some idea of the mode in which we arrive at this
law may be thus given : we observe throughout nature that
whenever anything occurs there have always existed some
antecedent conditions ; and we also observe that certain con-
ditions are invariably followed by definite consequents. If I
feel unwell I know that some abnormal state of my body has.
previously supervened ; if I thrust my hand into the fire I
know that sharp pain will immediately succeed ; when rain
falls we feel certain that the suspension of water in the air

OF LOGIC AS PRACTICALLY APPLIED. 129

preceded the storm ; or, should we pass a strong current of
electricity through a piece of thin platinum wire, we are
assured that the latter will speedily become red-hot. Expe-
rience of this nature leads us to the conclusion that if any-
thing have a beginning it has also a cause ; that is to say,
some condition, or group of conditions, must have previously
existed, in virtue of which existence the phenomenon in
question was produced.

But we must not suppose that all uniformities of sequence,
how universal soever they may be, are cases in which the
law of causation operates ; for it will have been observed that
the name of cause is only applied to those conditions in virtue
of whose existence the effect necessarily follows to those phe-
nomena without which other phenomena would not occur,
but which being once posited the other mmt spring into
being* Therefore, when the sequence is merely casual, and
there is no connection of necessity between the events, we
cannot refer them to the law of causation : for example,
when summer invariably follows spring ; autumn, summer ;
and winter, autumn ; it could not be said that one season waa
the cause of the next, for then the two requisites of cause and
effect would be violated ; it being possible for a perpetual
summer to exist, or for winter to immediately succeed summer
without the intervention of autumn, in consequence of some
change taking place in the earth's position with regard to the
sun, or in the present physical configuration of the earth.

Nor must any mere arbitrary limit be placed upon the
signification of " cause ; " we must not make a selection from
the conditions upon which an event depends. It is true that
this is almost invariably done, as when the prick of a needle
is said to 'be the cause of the pain which I feel ; or when iron
is said to be dissolved because sulphuric acid is poured on it ;
or, again, when the metamorphism of certain rocks is said
to be produced by the action of fire. In all these cases there
is an omission of necessary particulars. Thus, in the first
I should not feel pain from the prick unless I were alive, and
possessed a certain organisation, &c. ; in the second, the iron
would not be dissolved if, in addition to the mere presence o
the acid, there did not exist a certain attraction between

a 3

130 OF LOGIC AS PRACTICALLY APPLIED.

oxygen and iron, oxide of iron and sulphuric acid ; while in
the third, some physical properties of matter, such as polarity,
&c., are equally essential with heat to the production of the
effect. Also, in every case there must necessarily exist a
negative condition, besides those which are positive; this
being the absence of counteracting causes, that is, those con-
ditions which tend to produce a contrary effect. Thus, in
the present state of the solar system, the earth keeps at a cer-
tain distance from the sun ; but were the latter body and his
attendant planets in their common motion through space to
enter some resisting medium, the earth, although acted upon
by all its former influences, would yet fall into the sun by reason
of the new condition preventing the old causes from producing
their wonted effects.

Accordingly, the vulgar sense of the word cause does not
express its philosophical import ; and this ambiguity it will
be necessary to bear in mind, as, from the convenience attach-
ing to limited notions, it is often expedient for the attainment
of the purpose in hand to consider that the cause, which
really is but a portion of the conditions requisite for the pro-
duction of the effect. For instance, when heat is said to
cause the expansion of a bar of iron, we mean that heat is
the condition whose introduction amongst other conditions
gives rise to the change in volume ; or, in the example given
above, the resisting medium would be said to cause the earth's
fall into the sun, not because it could produce such an effect
when acting alone, but on account of its enabling gravitation
to act under less opposition from centrifugal force.

It will now be seen that a law of nature is nothing more
nor less than the expression of the relation existing between
any single cause and its effect. By applying this doctrine to
the truths first cited as natural laws, we may obtain a clear
notion of its application. That matter possesses weight, then,
means that wherever the entity termed matter exists it will
possess the attribute of weight ; but it may be said that
matter would not be matter without possessing weight, and
that, therefore, weight would be simultaneous in its existence
with matter. This, of course, opens up the question as to
all cases of cause and effect, for who can say that the conse-

OF LOGIC AS PRACTICALLY APPLIED. 131

quent does not commence to exist at the selfsame moment
that its conditioning antecedents are complete ; so that the
argument, if valid, would show that there is no such thing as
sequence in any case of causation. Now I am very far from
denying the cogency of such reasoning, hut this I do say, that
for all practical purposes we may safely admit the notion of
succession. As, therefore, "weight" is but the attraction
subsisting between material bodies, we may assume that were
some new matter to be created it would have no weight until
it attracted, and had been attracted by other matter; this
operation taking place by virtue of a natural law that renders
its occurrence a matter of necessity. And so with the second
and third laws ; whenever a gravitating fluid exists there
results an equal pressure in all directions, this fact being ex-
pressed by the statement that water tends to find its own level ;
or, lastly, whenever motion exists alone, it continues for ever.
In all these cases the antecedents are the causes, the conse-
quents are the effects, and the necessary connections between
the respective pairs of phenomena are the laws.

2. Of Induction. When speaking of observation, I had
occasion to remark, that the existence of objective facts was a
matter of inference based upon our " experience " of subjective
phenomena ; and again, in the preceding division, we found
that the distinction between necessary and casual uniformities.
was also originated by the accumulations of observation, i.e.,
by " experience." What is the meaning of this phrase must
now, therefore, be discussed.

We have just synonymised " experience " by the expression
"accumulation of observations;" but when we eay that a
certain proposition is warranted by experience, we do not
mean that our inference rests upon the whole mass of observa-
tions which we have ever made, but that a consideration of
such observations as relate to the fact in question, has disposed
us to infer, as a general truth, the uniformity which constitutes
the judgment. That is to say, by reflecting upon certain
separate observations, we are induced to believe in the exist-
ence of some law. The operation of the mind by which this
result is produced, has been named Induction, and may be
defined as the process of assigning causes for effects.

1S2 OF LOGIC AS PRACTICALLY APPLIED.

Now, as it is by induction that we arrive at laws and
causes, which, as shown above, constitute by far the major
portion of existent truth, it follows that in an exposition of
applied Logic this operation of the mind must occupy the
most important position. And, accordingly, it will be advisable
to treat as fully as our limits of space will allow, upon the
nature and method of correct induction ; or, in other words,
upon the mental laws which impel us to generalise from
experience, and upon the quantity and quality of that ex-
perience, which these laws render necessary for the establish-
ment of a correct inference.

Let us, then, in the first place, retrace the steps by which
we have arrived at any proposition, and endeavour to ascer-
tain upon what fundamental ground they all rest. Suppose
we take this judgment, " The earth is a globe ;" the question
then comes, what are the premises from which such a conclu-
sion was derived ? These we know to be " every body which
in certain positions would cast such and such a shadow upon
the moon, and which could be circumnavigated, &c., is a
globe " (U) for the major, and " the earth possesses these
attributes " for a minor ; and as the latter is the direct pro-
duct of observation (loosely), it remains to be considered how
the former was obtained that is to say, we must next
examine our grounds for stating that all globes possess the
properties in question. This judgment cannot, of course, be
the direct product of observation, for even had we been able
to examine every globe at present existing, the proposition
directly resulting would not be equivalent to the one above
stated, which, being universal, must apply to all globes which
have ever existed, or will exist henceforth, in addition to
those of present entity. It must, consequently, depend upon
reflection, i.e., upon a process of reasoning from observed
facts ; and as we have seen in formal Logic, that all reasoning
whatever may be reduced to syllogisms, it results that the
judgment, " all globes possess such and such properties," is
a conclusion drawn from previously established premises. Of
these Observation gives one, viz., " This, that, and the other
globe, have been found to possess the attributes above men-
tioned ;" and, therefore, since the syllogism is valid, the other

OF LOGIC AS PRACTICALLY APPLIED. 133

must be to this effect, " Whatever may be predicated of this,
tiiat, and the other globe, may be predicated of all globes ;"
which means, " Whatever attributes are found to accompany
this, that, and the other globe, will be found to equally accom-
pany every other globe." Pursuing a similar course, we next
arrive at the following syllogism :

A case of a certain particular uniformity is a case of the

corresponding general uniformity,
The case of this, that, and the other globe being found

to possess the attributes in question, is such a case of

particular uniformity ;
.*. The case of this, that, and the other globe being found

to possess certain attributes, is a case of all globes

being similarly marked.

Now beyond this we cannot go ; that is to say, we cannot
assign any premises which would necessitate as a conclusion
the last-mentioned major-premiss. Accordingly, for all pur-
poses of Logic, we must assume the principle thus stated to
be a fundamental law of the mind, by which, from ascertaining
one truth, we are compelled to believe another. Its enuncia-
tion in the above syllogism is manifestly of a very partial
character, as a due comprehension of its import would neces-
sitate a complete explication of the phrase, "a, certain particular
uniformity ;" but this is the province of inductive method, and
is foreign to our immediate purpose, viz., the treatment of
inductive elements. To firmly establish these, we must next
show that the law at which we have just arrived, is really of
the nature claimed for it, i.e., fundamental. At the same
time, it will not be necessary to proceed any further with an
investigation of the mind's ultimate constitution, as to do this
would be to intrench upon the domain of metaphysics. But
we must rather endeavour to show, that all other principles
of reasoning, or axioms, are merely differentiations of the
foregoing law. And as so wide a subject could not be
entirely discussed in our limited space, it will be sufficient if
we confine our attention to the axiomatic " law of causation,'*
and to any one of the mathematical principles ; say, " if equals
be added to equals, the wholes are equal."

We have already taken occasion to remark that the first of

134: OF LOGIC AS PRACTICALLY APPLIED.

these axioms is the result of experience, that it is our
observation of some cases of antecedence which induces us
to believe that all events are the effects of causes. But
unless there existed some necessary mental law to legitimatize
this inference, we shoald obviously be unable to rely upon its
correctness, as then the only conclusion that could possibly
be trustworthy, would be that resulting from an inductive
syllogism of the kind mentioned in Formal Logic ; in other
words, we should be unable to proceed beyond the limits of
our actual experience. Consequently, our observations of
various instances of cause and effect require the aid of the
inductive law before we can deduce any such general state-
ment as that under consideration, and which is often termed
" the assertion of nature's uniformity."

The second axiom, although usually considered funda-
mental, is, strictly speaking, of more complex derivation than
. the law of causation ; for the latter is but one step removed
from the inductive principle, while the former is separated by
two syllogisms. These may be thus expressed :
1. Certain particular uniformities legitimatize the inference

of the corresponding general uniformities,
Some cases of equal magnitudes being the same number
of coincident magnitudes, constitute the required
particular uniformity ;
. It is true that " all equal magnitudes are all coincident

magnitudes."
2. All equal magnitudes are coincident (U),

All sums of equals are coincident ;
/. All sums of equals are equal.
I Irave stated the second argument as a simple syllogism,
although it would be posoible to show that it is of an epi-
cheirematic nature, the minor premiss being a conclusion
based upon the major. But this matters not in the present
place, where we are only concerned with proving that the
canon, " if equals be added to equals, the wholes are equal :"
or, as otherwise expressed, " the sums of equals are equal,'-'
is dependent for its adoption upon the inductive law, and has
per se no locus standi. An inspection of the above reasoning
will show that we have effected our purpose, and that the

OF LOGIC AS PRACTICALLY APPLIED. 135

fundamental grounds of the mathematical axioms are observa-
tion conjoined with reflection ; the knowledge acquired by
experience being developed and increased by the laws which
regulate our minds.*

It will be remembered that when treating upon syllogistic
inference, we found the fundamental law of that process to be
directly inapplicable to many forms of reasoning, insomuch
that for practical purposes it was developed into a series of
proximate rules, which were sufficient to test the validity of
all arguments, without our being at the trouble of effecting a
reduction to syllogisms of the first figure. The same thing
occurs in Applied Logic. We must differentiate the law of
induction to such an extent, that the proximate canons thus
obtained may enable us to judge correctly as to the truth of
the propositions at which we arrive, and may render any
reference to original principles unnecessary. But since such
a differentiation can only be accomplished by completely ap-
preciating the meaning of the inductive law ; it follows that
the doctrine of inductive method will next claim our attention.

Now, the truths at which we arrive by means of induction,
are of two kinds : either the statement of general laws,
i.e., an assertion of natural uniformities, without any exact
discrimination of cause and effect, such as mathematical
axioms, &c. ; or the knowledge of special laws, which consists in
the assignment of definite causes for definite effects, and vice
versa, as, for instance, the truths of astronomy or chemistry.
And, first, we will inquire as to what kind of experience
warrants us in concluding the latter class of truths.

The cause of any effect is, as already stated, the whole of
the conditions which unite in producing it ; but this definition
being too wide for my present purpose, I shall in the fol-
lowing remarks understand by a cause " that circumstance
which produces some definite change in a set of antecedent
conditions :" thus, a bell while sounding remains in exactly
the same state as when it was silent, with the exception that
its particles are vibrating : this vibration, then, is termed the

* Some additional exposition of this subject will be found in Ap-
pendix D.

136 OF LOGIC AS PRACTICALLY APPLIED.

cause of the sound. So much being premised, I shall now
investigate the mode in which we may determine the cause
of any phenomenon.

It will of course be evident, that the cause must exist
amongst the conditions which compose the phenomenon in
its totality ; for otherwise, there would not be that connection
of necessity which we have seen is essential in every case of
a sequence obeying a law. If, therefore, we have two or
more instances of the effect which differ from each other in
some things, but all agree in certain conditions, these latter
are the only things which exist in every instance of the effect,
and, accordingly, in them the cause must be sought. We
thus obtain the canon of Agreement, which runs as follows :

1 Q . The cause will be found among the circumstances in
which two or more instances of the effect agree.

Or,

A uniformity which is observed in two or more instances,
may be considered as invariable and necessary.

If, for example, we found that gold and silver both con-
ducted heat, we might say that the cause of such a power
was included in the possession of metallic attributes, since
that would be the sole circumstance in which the instances
agreed ; or, in accordance with the above variation of the
canon, it would be allowable to hold that every metal is
capable of conducting heat. We can, however, only infer
absolute laws, whether the observed effects be relative or
absolute ; thus, from gold and silver being heavier than
water, we cannot conclude that all metals are so, as the phe-
nomenon investigated was not precisely the same in each
case, i.e., the two metals differed in the amount by which
they were heavier than water. But since they definitely
agreed in possessing weight, we may affirm that property of
all metals ; indeed, it forms one of the purely metallic
attributes.

The information acquired by means of the above canon is
seldom satisfactory, as we are only able to ascertain the pre-
cise cause in those very rare cases where the phenomena
agree but in one point ; so that although truth is acquired,
yet it is so vague and indefinite as to be oftentimes prac-

OP LOGIC AS PRACTICALLY APPLIED. 157

tically worthless. In the example just given, all that we can
be sure of is, that the power of conducting heat is in some
manner connected with the possession of metallic attributes.
If, therefore, we would arrive at a clearer notion of causes,
we must seek for some method of singling out the desired
conditions from among the set which have been presented to
us by the canon of agreement.

Now, as an effect necessarily follows from its cause, except
where there is a counteracting cause (which would be a new
condition), we may conclude, that when, of two cases, one
contains the phenomenon under investigation, and the other
does not, the cause is not to be sought among the conditions
common to both. If, therefore, we observe a case which
does not exhibit the phenomenon, but all of whose conditions
are contained in the set pointed out by the canon of agree-
ment, we shall be enabled to eliminate these conditions from
the number among which the cause is to be found, and thus
our limits of search will be much narrowed. A sufficient
repetition of this process will eventually point out with defini-
tion and certainty the law which we are endeavouring to
discover; and thus it may be seen that in this we possess a
method of complete efficacy, in all cases susceptible of its
application. The canon which regulates the operation, and
which is termed the canon of Difference, may be enunciated
in the following manner :

2. The cause will be found among the circumstances in
which an instance, composed of a portion of the con-
ditions set apart by the canon of agreement, but not
containing the effect, differs from an instance which is
composed of all such conditions.

The example chosen for exhibiting the method of agree-
ment is not adapted to illustrate that of difference, for we are
unable to select any body which is totally destitute of conduc-
tive powers as regards heat ; we must consequently make use
of some other instance, and leave this to be dealt with here-
after. Suppose we wished to discover the conditions upon
which our hearing the sound of a bell depends : we should
learn by the method of agreement that all bells, however they
might differ in shape, size, tone, &c., yet, when sounding,

138 OF LOGIC AS PRACTICALLY APPLIED.

agreed in vibrating and in being placed in the atmosphere.
Next, we should endeavour to obtain an instance of a bell
being struck, and thus thrown into vibration, but under dif-
ferent circumstances, which might result in the sound being
no longer heard. This would be effected by striking the bell
in the exhausted receiver of an air-pump, when we should be
unable to hear any sound ; and the condition in which the
instances differed, i.e., the presence of an atmosphere, would
consequently be the cause of sound being audible.

We have just seen, however, that the method of difference
is always inapplicable when no instance of the phenomenon's
non-occurrence can be obtained ; a circumstance which would
be a great hindrance towards the acquirement of truth, were
we unable to find any remedy. But this is not impossible,
for although the canon of difference is much more powerful
than that of agreement, yet it is similarly restricted, as, by its
means, we can only discover absolute laws, without any
reference to quantity. Accordingly, we must now endeavour
to obtain some knowledge of the means whereby the latter
object may be accomplished.

Among the uniformities of invariable sequence which
come within our observation, we cannot fail to remark the
existence in most cases of a certain ratio between cause and
effect ; between antecedent and consequent. Thus, a small
dose of arsenic produces no visible effect upon a man's con-
stitution ; a larger dose makes him ill ; and a still greater
quantity kills him ; while beyond this limit no extension of
its deadly effect can occur. Or, in blasting rocks, the work
done is altogether dependent upon the weight of gunpowder
used ; assuming, of course, that the modus operandi remains the
same. We are, consequently, led to the conclusion that the
effect is always directly proportional to the cause, and that a
variation in one is attendant on, or followed by, a correspond-
ing variation in the other. But in one of the examples men-
tioned above, this law does not appear at first sight to be
universally true, for we have said that however large the
quantity of arsenic may be, it can do no more than produce
death ; and this leads us to the consideration that, for prac-
tical purposes, apparent limits are often assigned to the law

OF LOGIC AS PRACTICALLY APPLIED. 130

in question, a cause being still regarded as the same with
reference to the effect, although some condition has disap-
peared. In the case alluded to, it is evident that the com-
plete antecedent of death is composed of the poison capable
of acting upon some organism, together with the organism
itself in a state of life ; but it is equally evident that when
death has supervened, the conditions existing are such as not
to be capable of producing a similar effect, for the object to
be destroyed no longer exists. The law is, therefore, seen to
be universal, when we adopt the strict signification of " cause"
as formerly explained ; but at present we may safely assign
those limits which are rendered necessary by our immediate
apprehension of " invariable sequence."

The canon then of Proportional Variation runs thus :

3. Whenever a phenomenon varies proportionately to the
variation of some condition, there exists a uniformity
of necessary sequence between them.

The employment of this doctrine will enable us to arrive
at truths which would otherwise be inaccessible. Take, for
instance, the determination of the properties which cause
metals to conduct heat. We find that no two possess equal
conductive powers, and, also, that no two possess simitar mo-
lecular constitution ; in like manner we ascertain that any
variation in the arrangement of the particles in a single metal
occasions a corresponding variation of its conductive power ;
but as our means of observation do not at present enable us
to assign any distinct ratio between the variations of each
separate mode of constitution, and the induced variations of
conductivity, we can only conclude that some uniformity of
dependence exists, without attempting to fix its precise law.
I have purposely chosen an example of this extreme nature,
as by it is shown that the canons of induction will at all
times suffice to assure us of the right path to pursue, even in
cases where the imperfect state of science precludes our
attaining any immediate proximity to ultimate truth.

We have now discussed the three principal canons of induc-
tion ; there are, however, various practical corollaries and
rules which spring from them, and as it would be impossible
to consider each of these separately in a treatise like the

liO OF LOGIC AS PRACTICALLY APPLIED.

present, I think it best to proceed at once to the investi-
gation of the other processes employed in the attainment of
truth, and then to give an account of some scientific dis-
coveries which will exhibit in a concrete form the develop-
ment and application of such doctrines as we have examined.

3. Of Deduction, Hypothesis, and Verification. By induc-
tion we are enabled to arrive at general truths. When these
are employed for the ascertainment of any particular truth
not previously established we are said to deduce. Thus,
induction has taught us that all beings which possess the attri-
butes of humanity are mortal ; therefore, when a fresh nation
is discovered in Central Africa, we may with certainty predict
that they are subject to death. Or, from the laws which have
been found to regulate the respective motions of the bodies
forming the solar system, astronomers can accurately foretell
eclipses and other results of the changes that continually take
place in the relative positions of the sun and its attendant
planets. These judgments are the product of deduction based
upon prior induction, and it is, therefore, commonly main-
tained that the sole and ultimate foundation for all our know-
ledge of truth is experience, i.e., our observation of particular
facts. This view, however, we have shown to be but par-
tially correct, as the primary operation to which we traced
the process of induction, consisted of a deduction from obser-
vation referred to a general principle of a syllogism, in fact,
and, as such, amenable to the laws of mediate inference. Formal
Logic, therefore, is the ultimate judge of all the mental ope-
rations with which thought is concerned ; and deduction is
the first step made in our search after truth. Consequently,
the title of the present division of Reflection must be held to
refer to a secondary and derivative process of deduction, em-
ployed for the purpose of utilising the laws determined by
the original deductive operation which, on account of its
strongly marked and distinguishing features, has received the
name of Induction.

In all scientific inquiries it is seldom found that single
causes are in operation ; but as the inductive method is better
adapted for the ascertainment of individual than of general
laws, it usually makee u& alone conversant with the relation

OF LOGIC AS PRACTICALLY APPLIED. 141

subsisting between solitary cases of antecedents and conse-
quents. Here, then, we have the special province of dedac-
tion pointed out, viz., the determining of the effects neces-
sarily resulting from a combination of causes. And as this
is done by a series of syllogistic reasonings, it will not require
analysis in the present place, as we have already considered
these at full length in the chapter upon syllogisms. I may, how-
ever, remark that the finest examples of the deductive method
will be found in the mathematical sciences, such as geometry
and algebra, where the vast body of general truths are all
derived from a proper union of a few simple laws.

I have said that by induction we usually arrive at indivi-
dual laws, i.e., at laws which are applicable to single or to
few phenomena. By this I would be understood to mean,
that the laws thus acquired will, in general, merely suffice to
explain the sequence in the cases under direct consideration,
or in cases essentially similar, being quite unserviceable when
we attempt to extend their sphere. Thus, the phenomena of
falling bodies led at first to the inference that it was the
nature of most terrestrial matter to move downwards ; and a
consideration of the planetary motions resulted in the con-
clusion that orbits were circular, because of the perfection
supposed to inhere in that species of curve. And even when
more correct notions prevailed, laws were for long enter-
tained, which assumed different sequences of causation as
existing between celestial and terrestrial motions, it being
reserved for Sir Isaac Newton to point out by a process of
deduction, that the one law of gravitation was the regulating
principle of the solar system, extending its influence from the
determination of the cosmical cycles, to the least important of
the movements taking place upon the earth's surface.

It is not, however, always possible at the first blush to
obtain such laws by induction, as may suffice when developed
by the deductive method, for the full appreciation of the phe-
nomena under investigation. In such cases the resort of the
philosopher is hypothesis, which, when properly employed,
will often suggest those observations that are capable of
affording the grounds required by induction ; but as regards
the formation of hypotheses, all rules are of little avail, for

14:2 OF LOGIC AS PRACTICALLY APPLIED.

success must entirely depend upon that natural sagacity, the
possession of which is in a great measure the characteristic of
genius. At the same time, it is quite possible to indicate the
manner in which a hypothesis should be treated, and to point
out the purposes it will best serve.

A hypothesis, then, is the supposition of some law which shall
serve to explain such sequences as have become the objects of
observation. It is, therefore, employed when the cases in
question are incapable of the particular collation required by
the inductive canons, or their corollaries ; that is to say, when
the facts cannot of themselves lead to any determined truth ;
and when once the hypothesis has been framed it should be
used deductively ; first, with a view to ascertain if the results
thence arising correspond with the actual instances observed ;
and in the next place, to infer the existence of new phenomena,
which may then be sought for, and which, if discovered, will
render probable the truth of the supposition. This duplicate
process is termed verification, but, as just described, cannot
be considered complete ; the hypothesis being spoken of, as
thereby shown to be " probably," not " certainly," true. In
many cases, however, an extension of verification may
amount to a perfect induction, for if we first prove that the
supposed law is of such a nature as to account for the pheno-
mena already observed, and to predict the occurrence of fresh
examples ; and, then, in addition, show that no other suppo-
sition could offer a similar explanation, we shall satisfy the
requirements of the canons of agreement and difference, thus
establishing the hypothesis as a true law.

It will also be seen that in verification we have a most
important adjunct of deduction, for when the latter process
has, from the. results of induction, arranged a system of laws,
we may test the accuracy of these by employing them to
explain observed phenomena, and to foretell facts that yet
remain to be discovered ; and if in this manner we are led
to satisfactory conclusions, we shall be enabled to strengthen
the primary induction by means of the additional evidence
thus obtained. Experiment is perhaps the most common
method of verification, and deals exclusively with the pre-
diction of sequences ; in fact, every operation of practical life

OP LOGIC AS PRACTICALLY APPLIED. 14:3

is an experiment by which we confirm afresh the laws de-
duced hy the various sciences. Our ships and buildings arc
all constructed in accordance with the principles of mechanics ;
the art of agriculture is successful proportionately as it con-
forms to chemical laws ; the safety of every sailor depends
upon a special application of mathematics ; and thus we
continually become more and more convinced of our ability
to attain truth by means of a strict adherence to those
mental laws which it is the office of Logic to discover and
explain.

4:. Of Analogy. The framing of any hypothesis is never
a work of chance, i.e., a mere guess, in the strictest sense of
the word, but is usually suggested by some circumstances of
the observed phenomenon. Of these circumstances, the only
one which it will be necessary to mention here, is analogy,
which, it will be borne in mind, has already required our
attention, when we were discussing the subject of fallacies.
It was then described as the similarity of relations, and argu-
ments both false and true were noticed as being founded
thereupon. We must not, however, suppose that complete
certainty may be attained by analogical reasoning ; as at the
best, one can only infer a very strong degree of probability for
the law deduced ; this being treated hypothetically, i.e., as a
provisional principle, until fully verified, when it of course
assumes the position of an established truth. It will, there-
fore, be obvious, that the cogency of any argument from
analogy must depend altogether upon the special features of
the case ; and, accordingly, I shall not attempt to give an
exposition of the various analogical methods. The student
may, however, gain a very good idea of analogy in general,
by carefully considering the following resume of a celebrated
problem, viz., whether the planets are inhabited.

In the first place, it is requisite that we should be put in
possession of a certain number of facts, upon the basis of
which we may found our argument. And, for reasons which
will shortly appear, these facts should consist of similarities
observed to exist between the earth and the other planets.
Accordingly, a judicious use of the telescope has enabled us
to accumulate the truths which follow. We find that Mercury,

14:4: OF LOGIC AS PRACTICALLY APPLIED.

Venus, and Mars, are each provided with an atmosphere ; and
so distinctly is this visible, that we can clearly perceive the
morning and evening twilight on Venus ; we find, too, that
clouds exist in these atmospheres, thus showing the existence
of meteorological phenomena, such as rain, hail, snow, winds,
&c., upon the respective planets. Again, it is ascertained
that Mercury, Venus, and Mars revolve upon their axes,
giving rise to the regular production of night and day, the
respective lengths of these differing only by a few minutes
from that which obtains upon the earth ; and, as the axis of
Mars is inclined to the plane of his orbit at an angle very
similar to the obliquity of the terrestrial ecliptic, it follows
that as far as the sun is concerned, the seasons in both planets
do not vary to any great extent, while very good reasons
exist for supposing the same thing to occur in Mercury and
Venus also. Nor does much variety obtain in the supply of
light and heat to the four bodies of which we are speaking,
whether reference be made to its uniformity or intensity ;
and, as regards the effect of gravity, it is found that the
weights of bodies upon the surface of Venus are very similar
to those upon the earth, and that weights upon Mercury and
Mars are about half as heavy. Lastly, the existence of con-
tinents and seas has been observed upon Mars ; his polar
regions being eternally covered with snow, the limits of
which extend in winter and contract in summer.

Having thus found that certain similarities exist between
the earth and its neighbouring planet, we must, in the next
place, ascertain what bearing these conditions have upon the
phenomena of life. Nor does this require a lengthened
investigation, for it will be immediately apparent, that on the
earth all life is exactly adapted to, and depends upon, such
physical circumstances as the existence of light, heat, air,
water, night, day, the succession of the seasons, the surface
configuration of land and sea, &c., &c. Now, in their relation
to life such as ours, the physical conditions of Mercury, Venus,
and Mars, may be considered as identical with those of the
earth, and, accordingly, we form the following syllogism
based upon analogy, or, in other words, upon a similarity of
relations :

OP LOGIC AS PRACTICALLY APPLIED. 14:6

Terrestrial phenomena are accompanied by life (A),
Terrestrial phenomena are the phenomena of Mercury,
Venus, and Mars (U) ;

/. The phenomena of Mercury, Venus, and Mars, are ac-
companied by life (A).

If the premises are here granted, the argument is perfectly
true, for A U A is a valid mood, and the proper method of
refuting the syllogism would be to show the falsity of the
minor premiss, which asserts, that as far as the present argu-
ment is concerned, the physical phenomena of Mars, Venus,
and Mercury are the same as those of the earth.

With reference to Jupiter, Saturn, Uranus, and Neptune,
the argument is of less force, as although they possess atmo-
spheres, alternations of day, night, and the seasons, together
with water, &c., yet a consideration of their bulk, and other
reflections, show that if life does exist upon them, it must
differ considerably from terrestrial being : at the same time,
it may be proved that there need be no greater variation
between the life upon those planets and that upon the earth,
than exists between the inhabitants of our torrid and frigid
zones. Accordingly, the analogical relation is much weaker,
thus casting greater doubt upon the admissibility of the minor
premiss.

5. Of Chance and Probability. In the preceding remarks
occasion has been taken to introduce the subject of proba-
bility ; and as absolute certainty is of very rare occurrence in
practice, it would not be advisable to close this notice of the
reflective processes, without adding a few words upon the
amount of belief which may be attached to certain judgments.

This leads us to consider a certain restriction which attends
the application of the canon of agreement. Its enunciation,
it will be remembered, is as follows : " A uniformity which
is observed in two or more instances, may be considered as
invariable and necessary ;" this referring to a law of causation
existing between the common antecedent and consequent ot
the instances in question. Now it is evident that, for any-
thing we can tell to the contrary, it may be necessary for tht
whole of such antecedent to exist before the phenomenon can
be produced ; and therefore, at the best, we can only generalise

14.6 OF LOGIC AS PRACTICALLY APPLIED.

as to cases precisely similar in every respect to the observed
instances. The law thus induced is termed an empirical law,
and is of no use for the explanation of phenomena. But then
again, it may happen that an effect is capable of being pro-
duced by a variety of causes ; that is to say, that the common
conditions of the instances may co-operate successively with
the respective points of difference in giving rise to the same
effect, assuming, of course, that we know of no connection
between the various instances, all of them being equally inde-
pendent. In such a case the effect would be termed the
result of chance, as distinguished from law ; this meaning
that we see no reason why the common conditions should be
joined to any particular antecedent, or why, if so joined, the
phenomenon should occur.

It, therefore, becomes a matter of some interest to discover
under what circumstances we are entitled to infer a causal
instead of a casual uniformity, when the canon of agreement
is alone used, and when, consequently, we are ignorant of
any relation subsisting between the instances except such as
are by this means discovered. These circumstances are
usually determined in the following manner :

Suppose a series of instances among which we know none
of the causes in operation, nor any necessary connection what-
ever ; as for instance, the case of a box containing balls similar
in every respect but colour, these being drawn out separately
by a person blindfolded. The question comes as to what
probability there is for any one colour to be drawn rather than
another. Now the supposition being that any one ball is
as likely to be drawn as any other, it follows that if there
were only two, black and white, the chances would be equal;
and so, in like manner, would it be if there were two of each
colour, or three, or four, or, in fact, any number. But sup-
pose there were two white to one black, then it is evident
that of all the drawings possible, two would be in favour of
white, and only one in favour of black, so that the " chances "
are two to one against black ; and in general it will be found
that, as far as mere casualty is concerned, the probability of any
event occurring may be measured by the proportion of the
number of cases in favour of such event to the total number

OP LOGIC AS PRACTICALLY APPLIED. 147

possible ; thus, in the first of our examples the probability of
white was one -half, or one out of two ; in the second it was
two-thirds, or two out of three.

By similar investigations mathematicians have determined
that the chance against any particular casual event recurring a
given number of times in succession, is as the number of pos-
sible events raised to a corresponding power to unity. Thus,
four to one are the odds that heads will not be thrown twice
in succession when a coin is tossed ; nine to one that heads
will not occur three times successively, and so on. Also it
has been shown that the chance of an event already observed
again occurring may be represented by a fraction whose
numerator is composed of the instances observed, increased
by one, and whose denominator is the same number increased
by two ; the chance against recurrence being that fraction,
which, together with the chance for, would amount to unity.
If, for example, I knew nothing of astronomy, and were to
observe a comet appear for six successive nights in a certain
portion of the sky, I might reasonably conclude that the
chances for the phenomenon being again apparent on the
next night were as seven-eighths to one-eighth, i.e., as seven
to one.

Thus it will be seen that every increase in the number of
times of observing the uniformity under similar conditions
lends a vast amount of additional weight to the belief that
there is some law concerned, and that the phenomenon is not
a product of chance ; accordingly, it is considered generally
requisite that before an empirical law can be laid down as
such there must have been a sufficient number of instances
observed to have eliminated chance ; that is to say, the uni-
formity must have occurred a greater number of times than
can be accounted for by the operation of chance.

The importance of these considerations will be at once
evident, when we reflect that the law of causation and all
axiomatic principles .are the products of the canon of agree-
ment alone, and are, so far, but empirical laws. As, however,
their limits of space and time comprehend all that we, as
human beings, are concerned with, we may act upon them
with a perfect assurance of their certitude.

H 2

HS OF LOGIC AS PRACTICALLY APPLIED.

6. Examples of Reflection, a. The Discovery of Neptune.
I shall take for my first concrete illustration of the reflective
process that most stupendous achievement of modern astro-
nomy, the discovery of the planet Neptune, which, present-
ing as it does one of the completest triumphs of the human
intellect, is pre-eminently calculated to display the vast acces-
sion of power which original sagacity acquires by the proper
development of the reasoning faculties.

The process of verification first led to the above-mentioned
discovery, and in the following manner. The Newtonian
law of gravity, together with the laws of motion, had been
found sufficient for the explanation and prediction of plane-
tary movements until, in 1781, Uranus was discovered by
Sir W. Herschel. This afforded a fresh test of those laws,
and astronomers were not slow in availing themselves of the
opportunity ; for not only did they compute tables, and con-
struct ephemerides by which the future places of Uranus
might be predicted, but they also calculated the positions which
it had occupied in past times, and so were enabled to identify
it with a supposed fixed star that had previously been observed
at various periods by Flamsteed, Bradley, Mayer, and Lemon -
nier. At the same time, however, it was found that the
planet had not occupied the exact positions which were
deduced from the above-mentioned laws, as its observed
places deviated sensibly from the calculated ones ; it, therefore,
became a matter of importance to ascertain the cause of such
deviations ; and for this there were two hypotheses open
either the deviations were caused by chance, such as errors
of observation, or by the operation of some definite and
regular law. Accordingly, it was not until about 1840 that a
sufficient number of observations had been accumulated so as
to eliminate chance, and then the facts stood as follows. The
planet was known to move in obedience to three causes the
laws of motion, the attraction of the sun, and the perturbations
induced by the proximity of Jupiter and Saturn ; but a de-
duction from these failed to explain the whole of Uranus's
movements, for from 1795 to 1822 the observed placet* con-
tinued, year by year to be in advance of those calculated,
while from 1822 to IP 30-1 a regression took place until the

OF LOGIC AS PRACTICALLY APPLIED.

tabular and observed positions agreed ; and this regression
uniformly continued in the years succeeding 1830-1, so that
the hypothesis of some regular disturbing cause was the
only one tenable, chance being eliminated, and the planetary
deviations being too small to cast any doubt upon the validity
of the gravitative and dynamical laws. At this point it was
that Messrs. Le Verrier and Adams took up the question
simultaneously, each, strangely enough, being in complete
ignorance of the other's investigations ; and their first resort
was to analogy ; for, knowing that the irregularities in the
orbital movements of other planets were referable to the per-
turbing effects of mutual attraction, they concluded that the
same thing obtained with regard to Uranus ; that is to say,
they inferred that all those disturbances which could not be
accounted for by the influence of Jupiter and Saturn were
caused by some planet hitherto unknown. But this was by
no means sufficient, as mathematical considerations proved
that any one of an infinite number of planets, varying in
mass, distance, &C M would be capable of producing the devi-
ations in question, so that the problem admitted of number-
less solutions. It, therefore, became necessary still further
to limit the question before any hope of arriving at a satis-
factory answer could be entertained ; and this was done by a
wider application of analogy. It was assumed that the un-
known planet resembled those already discovered, in the
plane of its orbit being nearly the same, in the direction of
its motion being similar, in its orbit being an ellipse differing
but little from a circle, and in its mean distance from the sun
agreeing with Bode's law of progression. Also, as it was
assumed to be a planet of the solar system, it was supposed to
move in accordance with Kepler's laws, and from all these
hypothetical conditions, the mass of the planet sought, together
with the elements of its orbit, could be calculated very pre-
cisely. This was accordingly done, and the results possessed
a very high degree of probability, in consequence of the
cogent analogical reasoning upon which they were based ; so
much so, indeed, that until something further could be ob-
tarned, the deduction might be assumed as true for all prac-
tical purposes. But it will at once be evident that the ques-

150 OF LOGIC AS PRACTICALLY APPLIED.

tion was susceptible of a complete settlement, as it was only
necessary to calculate the position which the supposed planet
would occupy on any given night, and then to look for it in
that place, when, if the hypothesis were correct, the planet
would be immediately seen. Consequently, " on the 23rd of
September, 1846, Dr. Galle, one of the astronomers of the
Royal Observatory at Berlin, received a letter from M. Le
Verrier, announcing to him that the longitude of the sought
planet must then be 326, and requesting him to look for it.
Dr. Galle, assisted by Professor Encke, accordingly did ' look
for it, 1 and found it that very night. It appeared as a star
of the eighth magnitude, having the longitude of 326 52',
and consequently only 52' from the place assigned by M. Le
Verrier. The calculations of Mr. Adams, reduced to the
same date, give for its apparent place 329 19', being 2 27'
from the place where it was actually found." Thus the eli-
mination of chance, combined with analogy, suggested a
hypothesis, which assumed the rank of an established truth
when the deductions from it received a complete verification.
b. Kirclihoff's Researches on the Solar Spectrum. In this
case the phenomenon observed was the occurrence of various
dark lines in the spectrum of a sunbeam, and to discover the
*iause of these constituted the question at issue. The method
of Difference was first employed by showing that solid or
liquid bodies, when heated to incandescence, emit rays which
produce spectra differing only from the solar spectrum in the
absence of dark lines : the inference drawn from this fact
being that the cause of such lines must be sought among the
conditions in which the two cases differed. Now it was
evident that both kinds of rays proceeded from incandescent
bodies, and also passed through the terrestrial atmosphere,
but the solar rays, in addition to this, had to pass through
the sun's atmosphere, and, therefore, in this latter condition
the sought cause should be found ; a conclusion which received
additional strength from the analogical arguments of Sir David
Brewster and Dr. Gladstone. In the next place, it had been
found by experience that all transparent bodies emit, when
incandescent, only those rays which they absorb when cold ;
thus, red glass if strongly heated appears green, yellow glass

OF LOGIC AS PRACTICALLY APPLIED. 151

appears purple, &c. It was also known that the spectra of
incandescent vapours consisted simply of bright lines upon a
dark ground ; so, combining the two facts together, Kirch -
hoff conjectured that vapours comparatively cold would absorb
the rays corresponding to such bright lines. Accordingly,
he tried the experiment by causing the rays from a solid
luminous body to pass through the vapour of sodium, and
obtained a spectrum similar in every respect to that produced
when no vapour was interposed, with the exception of two
dark lines ; these were found to be identical in position with
the two yellow lines composing the spectrum of luminous
sodium vapour. But, on examining the solar spectrum, two
dark lines were therein perceived w T hich corresponded exactly
with those resulting from the absorptive power of vapourised
sodium, and, therefore, it was evident that the presence of
such a body was one of the conditions of the solar atmo-
sphere. In a similar manner it has been ascertained that iron,
nickel, calcium, magnesium, barium, copper, &c., all sur-
round the sun in a state of vapour, and thus produce those
dark lines which formed the subject of investigation. The
argument may be thus thrown into a train of syllogistic
inference :

1. The facts observed being the production of uniform
spectra by incandescent solids, and spectra with dark lines by
the solar rays, we have the inductive syllogism, U U U :

The difference of conditions is the cause of the difference
of phenomena,

The solar atmosphere is the difference of conditions ;
/. The solar atmosphere causes the difference of the phe-
nomena, viz., the dark lines.

2. A deduction from a law previously established, A A A :
All transparent bodies when cold will absorb those rays

which they emit when incandescent,
Sodium vapour is a transparent body ;
/. Sodium vapour when cold absorbs those rays which it
emits when luminous.

3. This last conclusion is verified by experiment, and the
facts now observed being the presence of two dark lines, both
in the spectra from solar rays, and in those from incandescent

152 OF LOGIC AS PRACTICALLY APPLIED.

solids surrounded with sodium vapour, we construct a deduc-
tive syllogism in A A I, Fig. 3, based upon the two former :
The cause of the two dark lines is sodium vapour,
The cause of the two dark lines is the solar atmosphere ;

/. Some portion of the solar atmosphere is sodium vapour.

I may mention that I have here purposely abstained from
the consideration of more causes than one being capable of
producing the same effect, as, otherwise, the argument would
become too perplexed for my present intention, viz., to give
an example of simple logical processes when practically
applied.

It would be easy to adduce many more instances of scien-
tific discoveries, but the above, if thoroughly studied with a
due recollection of the principles discussed in this treatise,
will suffice to exhibit the method of analysing a complex
argument into its logical elements ; and the student will be
able to select for himself such other events in the history of
philosophy as are well adapted for this purpose, thus putting
his knowledge of mental laws to the test, and discovering what
those particulars are which will be most advantageous for
his individual pursuits.

4. Conclusion.

Having now reached the end of our subject, it may not be
amiss if we briefly consider the results which ought to flow
from the study of a dissertation upon Logic. In the first
place, we should be able to grasp the science as an organic
whole, distinctly apprehending the nature of those inherent
principles which compel the mind to think in one uniform
manner, and forming a clear notion of the dependence which
exists between them and our every act of acquiring know-
ledge. Secondly, we should have become accustomed to
concentrate our attention upon the process of thought, without
any reference to the matters about which it is employed.
And, lastly, we should have learnt so to apply the practical
principles which are deduced from a consideration of the
primary mental laws, that without yielding to the blandish-
ments of error, we may certainly attain the great temple of
truth.

OF LOGIC AS PRACTICALLY APPLIED. 153

But I shall have written to very little purpose, if the reader
be not in a position to recognise that great fact, the unity of
philosophy, which, when once fully understood, lends a signi-
ficance to all scientific truths, such as they otherwise would
not possess ; for it is the office of Logic to show that every
ramification of our knowledge, however diverse, may ulti-
mately be traced back to one parent stem ; and, so far from
the various sciences differing as regards their nature, it be-
comes a question as to whether the subjects concerning which
they treat have any more than an apparent incompatibility.
Therefore, he who would act in a truly philosophical spirit,
must not remain satisfied with a crude, empirical acquaint-
ance with isolated groups of facts, but should endeavour to
obtain such general principles as may embrace them all; for
then, not only would he obtain a more perfect knowledge of
those facts themselves, but he would be enabled to gather
many new truths, which, by any other method, must be lost
for ever. And this may be observed in all the branches of
learning : while the various facts are looked at in themselves,
and by themselves, no great progress can be made ; but im-
mediately that laws, even of a comparatively limited nature,
are discovered and borne in mind, then a vast impulse is
given, the effects of which will speedily become apparent.
At the same time, we should remember the intimate connec-
tion of reflection with observation, and endeavour not to culti-
vate one at the expense of the other.

Logic, then, may be considered as abstract philosophy,
that system of which all other sciences are but the concrete
manifestations ; and, therefore, he alone can be justly termed
a philosopher who has made himself acquainted with the
laws that regulate the working of his own thoughts. But a
mere acquaintance, in the ordinary sense of the word, will
by no means suffice ; for, as Archbishop Thomson observes,
* philosophy does not exist until the mind of the student
begins to work for itself with the principles it receives histo-
rically ; to decompose and to compose anew, to criticise the
arguments employed, to essay at least to push the confines o f
truth farther into the wilds of error and ignorance, and to
leave her a wider territory." In other words, we should not

H 3

154: OF LOGIC AS PRACTICALLY APPLIED.

become accustomed to acquiesce is a matter of course in the
assertions with which we meet, nor to imagine that the sub-
ject is capable of no further development; but, by actively
applying the powers of om own minds to the elucidation of
the question, we should endeavour to ascertain the precise
amount of truth which inheres in the principles laid down,
and to add something however small, to the previously
accumulated store of knowledge.

The end, accordingly, at which all should aim who desire
the proper cultivation of their intellects, is rectification and
progression the correct adjustment of opinions already en-
tertained, and the establishment of views more wide and lofty ;
for. as this can only be done by a recourse to the latent powers
of their own understandings, it will assuredly result both in
a surprising accession of vigour to the individual mind, and
in great benefits to the world at large. Nor can it be doubted
that the practice of thought, when duly controlled by the
regular operation of its formal laws, must highly conduce in
the promotion of mental calmness and sobriety : no longer led
astray by the influence of passion, or deceived by the repre-
sentations of the senses, the well-ordered intellect, secure and
undisturbed, reviews by the light of necessary truth those
facts which come under its notice, and delivers judgment in
strict accordance with the immutable laws of nature.

In conclusion, I would remark that by far the noblest subject
of human investigation is the human mind. The science of
astronomy may give rise to emotions of awe and sublimity as
we contemplate the vast infinitude of space, with its myriads
of worlds and systems of worlds ; geology may astonish us
with its record of the marvellous forms of life which have
successively inhabited the earth ; the physical sciences may
endue us with power so prodigious, as to become almost
miraculous ; but yet, the fascination which attends every
inquiry into the nature of our own being, must always cause
the study of mental philosophy to take its place as the most
mysterious and attractive object of all our speculations.

APPENDIX.

ON JUDGMENTS.

IN the body of this treatise, I have (p. 27) described judg-
ment as " the act of determining by comparison, whether one
idea is or is not included within another," and have referred
it to the motive faculty of classification. But as the subject is
one of great importance, and has much influence upon a due
appreciation of logical science, I deem it advisable to append
some further observations which shall enable the student to
form a completer notion of the import which attaches to pre-
dication.

Now the most useful manner of introducing such remarks
will be to criticise the most important objections which have
been made to the above views ; and for this purpose I shall
select the following passage from Mr. Mill's " System of
Logic," (vol. i. p. 104). " This theory appears to me a signal
example of a logical error very often committed in logic, that
of vtTTepov nportpor, or explaining a thing by something
which presupposes it. When I say that snow is white, I
may and ought to be thinking of snow as a class, because
I am asserting a proposition as true of all snow : 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.
When, indeed, I have judged or assented to the propositions,
that snow is white, and that several other things are also
white, I gradually begin to think of white objects as a class,
including snow and those other things. But this is a con-
ception which followed, not preceded, those judgments, and

156 APPENDIX.

therefore cannot be given as an explanation of them. Instead
of explaining the effect by the cause, this doctrine explains
the cause by the effect, and is, I conceive, founded on a latent
misconception of the nature of classification."

In the expression " when I say that snow is white," Mr.
Mill evidently alludes to the formation of such a judgment
before the conception of a class of white objects, for he says
shortly after, " This [white objects as a class] is a conception
which followed " the establishment of similar propositions ;
and as this is the ground upon which he charges the classifi-
catory doctrine of judgment with error, his argument will be
sufficiently refuted by showing that it is impossible to form
the proposition " snow is white," before recognising white
objects as a class.

And first, let Mr. Mill himself be brought forward as a
witness : he says (vol. i. p. 30), " "When we say snow is white,
milk is white, linen is white, we do not mean it to be under-
stood, that snow, or linen, or milk, is a colour. We mean that
they are things having the colour." Therefore the meaning of
the proposition is, so far, that snow is a white object. It must
next be shown that we cannot think of " a white object,"
by itself, but that we always think of " some (or all) white
objects," that is, of a class; and this may be done by a
reference to the process of abstraction. Eor, as was seen at
an early stage of our logical studies, it is necessary that such
a process should be completed before we are able to possess
any common notion or abstract term ; and, therefore, the idea
" white" is the result of comparison, reflection, abstraction,
generalisation, and denomination, the first four of these
being simultaneous, a fact which will become evident upon
pushing our analysis a little further. Thus, suppose we had
never obtained the idea of u white," or of any other common
notion, and that we met with the object " snow : " the
impression produced upon our senses would be a combination
of such sensations as solidity, granular structure, absence of
what is commonly termed colour, &c., but we should find
it altogether impossible to separate this compound idea into
its various parts; consequently, the only notion obtained
would be an intuition, and we should be unable to form any
other judgment than that "snow is snow." Immediately,
however, that we met with any other intuition, say "milk,"
we should receive an immense acquisition to our knowledge ;
we should instinctively, as it were, compare them, and thus

APPENDIX. 157

perceive that although the two objects resembled each other
in some respects, yet that they differed in others ; that, for
example, in one object a solution of molecular continuity was
easily observable, while in the other such a condition did not
obtain ; that snow offered some resistance to a change of shape,
while milk did not ; but also that the intuitions produced by
both were partly indistinguishable. This fact would compel
us to recognise that the idea (" snow ") which we had previ-
ously considered as simple, was in reality compound ; or, in
other words, that it was capable of division : for we should
have sensible evidence that a part of it could exist without
the remainder. Accordingly, we should see that snow and
milk were separate objects, but yet, as far as our minds were
concerned, partially identical ; that is to say, we should
recognise a class composed of two individuals. Now the whole
of the preceding mental action would take place in equal
progression, for with the commencement and advance of
comparison, would commence and advance, pari passu, reflec-
tion, abstraction, and generalisation. But after this was
concluded as far as would suit our more immediate purpose,
we should take some measure to prevent our forgetting its
results, and this would be the imposition of an abstract term,
together with its correlative concrete. In the present case we
should term that sensation in which both intuitions agreed,
" whiteness," and then we should form the proposition " snow
and milk are white objects ; " or, in more detail, we should
say, " snow is white, and milk is white." Therefore, it will
be evident that no judgment (excluding such as are tautologous)
can be formed without the conception of a class composed of
at least two individuals ; although, in most cases, a general
name cannot be imposed until after the comparison of many
objects, and the recognition of a proportionately larger class.
But it must here be borne in mind, that when once we have
gone beyond the idea of unity, there is no definite limit
which we can impose upon our powers of imagination ; and,
accordingly, no sooner is a general notion conceived, than we
regard the class as hypothetically infinite. This hint will,
I hope, prove sufficient to prevent the opinion being enter-
tained that classification is merely " an arrangement and
grouping of definite and known individuals ; " and that the
doctrine above stated implies the theory, "that when names
were imposed, mankind took into consideration all the indi-
vidual objects in the universe, distributed them into parcels

i58 APPENDIX.

or lists, and gave to the objects of each list a common name,
repeating this operation toties quoties, until they had invented
all the general names of which language consists. " (Mill' a
" Logic," vol. i. p. 105.)

It has now, I apprehend, been irrefragably demonstrated
that the classificatory doctrine of predication rests upon valid
grounds, and that the objections considered above are un-
tenable. Indeed, so simple and natural is the theory, that
even Mr. Mill himself, when not engaged in actual combat
therewith, implicitly sifords his support to it, as witness the
following passage : " A child learns the meaning of the words
man or white, by hearing them applied to a variety of individual
objects, and finding out, by a process of generalisation and
analysis of which he is but imperfectly conscious, what those
different objects have in common." (Vol. i. p. 39.) If
this mean that an abstract notion and its concrete can-
not be formed from the observation of a single object
and certainly neither from the passage itself, nor from the
context can I suppose any other signification intended then
the whole question at issue is granted, since the idea of a
class is merely the conception of two or more individuals
resembling each other in certain respects.**

I have already taken occasion to protest against Archbishop
Thomson's exposition of judgment, but my remarks must not
be held to refer to anything beyond the terminology employed,
as it is possible that the doctrine so ambiguously put forth,
may, in all essential points, be that of classification. Thus,
speaking of the proposition "All men are animals," Dr.
Thomson says, "We mean by our judgment, not that men
and animals are just the same things, but that men are
contained in [sic] the wider class animals." ("Outlines,"
p. 151.)

And as regards my own statement (p. 28) that the copula
of a proposition signifies "the identically of the subject and
predicate, such identicality being, however, limited by the
form of the proposition," I must refer the reader for a more
complete explication of its import, to the foregoing analysis
of the manner in which common terms are formed.

* It may be proper to observe that in the above quotations many of
the italics are my own.

APPENDIX.

ON THE SO-CALLED IMMEDIATE INFERENCES.

These are such arguments as were discussed under the
heads of opposition, conversion, and coincident j unction ;
and since a universal misconception appears to exist regarding
their real nature, it may be worth while to present the reader
with some additional information upon this point.

And first, it will he necessary to prove that an inference
takes place in these processes, for many logicians exclude
them altogether from the sphere of reasoning. Now, I can-
not do this better than by adopting the words of Archbishop
Thomson, a philosopher to whom the science of Logic is under
very great obligations ; and therefore, without further apology,
I proceed to quote the following remarks :

" Some logicians refuse the name of inference to this and
similar processes [those named above], on the ground that
' there is in the conclusion no new truth, nothing but what'
was already asserted in the premises, and obvious to whoever
apprehends them.' That the conclusion is virtually asserted
in the premises, is true not only of these immediate inferences
but of all syllogisms whatever; even in the inductive, the
mere consequence the act of concluding brings in nothing
which is not known potentially as soon as we have the whole
grounds before us. So that the objection proves too much; as
it would disqualify a set of inferences which no one thinks of
rejecting. If, however, there is absolutely nothing new if
the concession of the premiss is not only a virtual, but an
actual and express declaration of the conclusion, there is no
inference, but mere repetition. But who can say that ' no
unjust rulers are good ' is a bare repetition of ' all good rulers
are just ? ' In the one we affirm, in the other deny ; in the
one the subject of thought is * good rulers,' in the other,
' unjust rulers.' They are, in these two points at least, dis-
tinct judgments, and as the passing of the one makes it pos-
sible, without further observation or decision upon facts, to
r-ollect the other, there is an inference. In many such cases,
it is true, the inference is so obvious, so certain to occur upon
the first glance at the premiss, that it seems needless to draw
it out ; but all the inferences we are about to specify are used
from time to time, and this entitles them to our consideration."

160 APPENDIX.

The above passage will suffice for the establishment of the
arguments in question as inferences ; it now remains to prove
that they are mediate inferences. And here it may be re-
marked as somewhat singular, that so acute a thinker as
Dr. Thomson should have made such a near approach to the
whole truth, and yet should have grasped but a portion ; for
it will be observed that although he clearly perceives the con-
clusion to result from a process of reasoning, he still maintains
that it is dependent upon one premiss only ; a doctrine which
probably arises from the very fact that arrests his attention,
viz., the obviousness and transparency of the inference this
rendering him loth to suppose the existence of a syllogistic
deduction in so simple an operation, as, in like manner, it
prevented the older logicians from admitting the presence of
any reasoning whatever, no matter how supposedly direct it
might be.

I shall, accordingly, proceed to enunciate the several princi-
ples upon which the validity of the inferred propositions rests ;
and if they are obviously essential, the doctrine here advo-
'cated must be admitted as established.

1. Opposition:

a. Contradictory. Any two classes must be either mutually
and wholly exclusive or mutually and partially inclusive. This
canon is necessitated by the laws which regulate our thoughts,
and therefore, as far as Logic is concerned, must be considered
fundamental. Its meaning is that we cannot think of any
two classes, except in one of the manners stated ; and from
it are developed these judgments : " If E be true, I is false ; "
" If E be false, I is true ; " " If I be true, E is false ; " and
"If I be false, E is true;" which respectively serve as
major propositions in any particular case where this kind of
opposition may be employed, the judgment operated upon
serving as a minor. Thus, admitting the fact that " no men
have wings," we must also admit that the statement "some
men have wings " is false ; for,

If E be true, I is false,
E ("no men have wings ") is true ;
.. I (" some men have wings ") is false.

Now, a moment's inspection will show that unless the major

be here assumed, there can be no inference.

b. Contrary. Neither the mutual and total exclusion of two
classes, nor their mutual and partial inclusion, can be thought
at the same time with their mutual and total inclusion. By

APPENDIX. 161

development from this canon we obtain such majors as may
be required, varying with the form of the original proposi-
tion ; for example, if the position of A be employed as a
minor premiss we may conclude that E, U, 0, and Y are
false, by employing the major "If A be true, then E, TJ, 0,
and Y are all false."

c. Subaltern. Whatever relation exists "between two classes,
the same exists between any portions of those classes. Here
will be observed a modification of Aristotle's dictum; for
when we assert that the whole of one class is or is not con-
tained in another, we must also be able to assert that a
portion of it is similarly characterised ; and so on, to a full
exposition of the canon, with its resulting majors.

d. Subcontrary. Any two classes must be either mutually
and wholly exclusive (when, by the last canon, we may assert
them as mutually and partially exclusive), or they must be
mutually and partially inclusive. This canon is at once seen
to be a corollary from the first and third ; it can only refer to
cases of I and 0, the majors being respectively, "If I be
false, is true ; " and "If be false, I is true."

2. Conversion:

a. Simple. Those magnitudes which coincide are equal.
This canon, common both to geometry and logic, will hardly
be questioned. The explication of its present import is that
when two classes, or parts of classes, comprise the same
objects, or when two individuals comprise the same ideas,
they may at pleasure replace each other as subject and
predicate in any form of proposition. We are, therefore,
entitled to assume for majors, " If A be true, the correspond-
ing Yis," etc.

b. Privative. Every object of thought must be either a posi-
tive idea or its correlate privative. Now, since these ideas are
mutually and wholly exclusive, we are manifestly enabled to
infer the presence of one from the absence of the other, and
vice versa. From this development of the canon, we must
educe such majors as may be required from time to time;
thus

"No immaterialities are material,
All forces are immaterialities ;
.'. No force is material.

3. Coincident Junction :

The canon of this doctrine is, " Whatever is joined to one
of two or more inseparable ideas, is joined to all" That is to

162 APPENDIX.

say, if we must always think simultaneously of two objects,
and we think of one of these at the same time with a third,
the other must in like manner be conceived. Accordingly,
we may construct as many syllogisms as we please of the
following form :

Whatever may be added to the subject of an admitted
proposition may at the same time be added to its pre-
dicate,

" Bed " may be added to the subject of the admitted pro-
position, " metals are solids ; "

/.It may be added at the same time to the predicate e.g.,
" red metals are red solids."

Thus have I shown that every so-called immediate inference
is, in reality, of a syllogistic nature ; for let any of the above-
mentioned majors be denied, and the conclusion is no longer
valid. The object with which I set out is, therefore, attained ;
but ere I conclude, it will be useful to make a few brief obser-
vations upon some detached portions of the subject.

I have then to remark that as regards simple conversion, it
must not be thought of as only applicable to tautologous
judgments ; for, as shown by the table given in page 45, every
possible proposition may be simply converted. Nor must it
be held that the convertend and its converse are the expres-
sions of the same operations of thought ; for confessedly, the
respective subjects about which we think are different. There-
fore, when, speaking of conversion, Sir William Hamilton states
(" Logic," Appendix, Y. c.) that "it is of no consequence,
in a logical point of view, which of the notions collated " are
" subject or predicate," he would appear either to have been
bestowing too little attention upon the process of thinking, or
to have expressed himself ambiguously.

I may also mention that Mr. Mill, who repudiates the notion
of inference when applied to the above processes, has himself
made a remark which affords a key to the whole question.
He is alluding to " such considerations as these, that contrary
propositions may both be false, but cannot both be true ; that
subconcrary propositions may both be true, but cannot both
be false," etc., etc. ; which the reader will immediately recog-
nise as modifications of the canons above given ; and says
that "in this respect [i.e., as involving general principles],
these axioms of Logic are on a level with those of mathematics."
He also implicitly terms them "elementary generalisations,"
but yet does not see that any one operation of opposition, etc.,

APPENDIX. 163

is as regular a deduction from a " general truth. " as is any
reasoning of geometry or algebra, which, depends upon pre-
cisely similar axioms. (Compare Mill's " Logic," Book ii.
chap. 1, 2.)

ON THE DlCTTJM DE OMNI ET KtJLLO

This canon I have enunciated (p. 8) in the following terms :
" Whatever is affirmed or denied altogether of any whole,
may in like manner be affirmed or denied of any individual
part belonging to, or comprehended in that whole ; " and I
have here used the word " whole" (the customary term
being " class") in order that the principle might be more
obviously applicable to syllogisms having singular terms. It
will, however, be necessary to present in this place a more
explicit view of the dictum than I have hitherto done ; for
otherwise, the objections frequently urged against that law
might possibly be considered as unanswerable.

We have seen already (article A) that the notion of a class,
or a " common notion," is the complex idea of an indefinite
number of individual members all possessing the same cha-
racteristic, and also that the notion of an individual, or a
" singular notion," is the complex idea of an indefinite
number of attributes, most of them being class-characteristics,
and all possessing the same unity of connection. Therefore,
as a " class" and its " members" are, for all present pur-
poses, precisely equipollent with an " individual" and its
" attributes," I shall use the terms u whole " and " parts,"
which will serve equally well to represent either of the
former pairs.

"We are now able to perceive a fact which lies at the very
root of the question, viz., that a " whole " is not composed
merely of its " parts," but that it contains in addition the
" unity" which obtains among them. And also as was
shown in the sections of this treatise which discussed the
subjects of formal induction, deduction, extension and com-
prehension we know that it is possible to direct at pleasure
the major part of our attention upon either of the above con-

164: APPENDIX,

stituents of a " whole," upon the " unity," or upon the
" parts."

Thus much premised, I have next to point out a very
important distinction, viz., the relative powers of conceiving
the " unity" and the " parts." The " unity" is obviously
a single object of thought; the " parts" are, on the contrary,
not merely a numerous, but an indefinitely numerous collection
of such objects : therefore, while it is possible to form a clear
and precise notion of the "unity," we can only obtain a
vague and indefinite idea of the " parts." Hence it results
that we can always direct a greater portion of our attention
upon the " unity," than upon the " parts ; " for that which
we can perform more easily, we can perform better ; and as
a corollary, we see that the natural disposition of the mind
is to regard the " unity" as pre-eminent, the " parts" as
subordinate.

The dictum results from the facts thus proved : it asserts
that whatever is recognised as belonging to, or excluded from,
the " whole," when principally looked upon as the " unity,"
will be found to hold the same relation, not to the " parts "
in a body for they, although vaguely conceived, yet form an
essential constituent of the " whole," and are at least co-
extensive with " unity" but to any one of the " parts," no
matter whether it be already known as individually existing, or
whether it have yet to be rescued from the depths of inde-
finity. And as I have formerly shown that all judgments
are classifications (Appendix A), and that all reasoning what-
ever may be exhibited in syllogisms (passim) these doctrines,
taken in connection with the proof just now afforded, that the
dictum is a necessary law of thought, will, I apprehend, make
it evident that the Stagirite's canon is the organic principle of
all inference.

That the above remarks were not altogether uncalled for,
I shall show by quoting the following passage from Mr. Mill's
" Logic " (Book ii. chap. ii. 2); my reason for selecting
this author being that he is one of the ablest and best known
of the logicians adopting similar views :

" Now, however, when it is known that a class, an universal,
a genus or species, is not an entity per se, but neither more
nor less than the individual substances themselves which are
placed in the class, and that there is nothing real in the
matter except those objects, a common name given to them,
and common attributes indicated by the name j what, I should

APPENDIX. 165

be glad to know, do we learn by being told, that whatever can
be affirmed of a class, may be affirmed of every object contained
in the class? The class is nothing but the objects contained
in it ; and the dictum de omni merely amounts to the identical
proposition, that whatever is true of certain objects, is true of
each of those objects. If all ratiocination were no more than
the application of this maxim to particular cases, the syllogism
would indeed be what it has so often been declared to be,
solemn trifling. The dictum de omni is on a par with another
truth, which in its time was also reckoned of great importance,
' Whatever is, is. 7 To give any real meaning to the dictum
de omm, we must consider it not as an axiom, but as a defini-
tion ; we must look upon it as intended to explain, in a cir-
cuitous and paraphrastic manner, the meaning of the word
class." The italics here are Mr. Mill's.

In what points the above passage differs from the doctrine
previously advocated, and which view is supported by the
more weighty arguments, are questions that must be left for
each reader to decide for himself. Suffice it if a clear state-
ment of the facts involved has been put forward.

I have frequently spoken of Aristotle's dictum as being the
fundamental law of inference ; but I should here wish to
qualify thai expression by stating that I do not use the word
" fundamental " in its most explicit sense; that is to say, I
do not imply the non-existence of some more recondite and
general principle. My only meaning is, that for all logical
purposes, it will be sufficient to consider the dictum, i.e., the
practical law by which the motive faculty of classification
works, as the ultimate principle of thought as thought : to the
end that we may not be compelled to encroach upon metaphysical
ground.

In this connection it may be useful to mention that by
many writers the fundamental laws of thought have been
given as follows :

1. The Law of Identity. "A concept is equal to all its
characters," or, "A thing is equal to itself."

2. The Law of Contradiction. " What is contradictory is
unthinkable."

3. The Law of Exclusion. " Either a given judgment must
be true, or its contradictory ; there is no middle course."

4. The Law of Sufficient Reason. " Whatever exists or is
true, must have a sufficient reason why the thing or preposi-
tion should be as it is, and not otherwise."

1GG APPENDIX.

I shall content myself with having called the reader's
attention to these laws, and shall not attempt to discuss them
in the present place. I may, however, refer to Sir William
Hamilton's fifth and sixth lectures upon Logic, as containing
an ahle analysis of the principles in question.

ON THE SYLLOGISM CONSIDERED AS A PETITIO PEINCIPH.

The form which this objection to the syllogism generally
assumes is thus stated by Mr. Mill :

* l It must be granted that in every syllogism, considered as
an argument to prove the conclusion, there is &petitioprincipii.
"When we say,

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 pre-supposed
in the more general assumption, All men are mortal : that we
cannot be assured of the mortality of all men, unless we are
already 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 aliundb, 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 we cannot
infer any particulars, but those which the principle itself
assumes as known."

" This doctrine," Mr. Mill goes on to add, " appears to me
irrefragable," and the mode of issuing from the difficulty
which he adopts, is to deny that the syllogism as such is an

APPENDIX 167

inference. He asserts that the same evidence which enabled
us to infer the general truth "All men are mortal," would
equally enahle us to draw the particular conclusion " Socrates
is mortal ; " and that a true representation of the reasoning
process which takes place, would be to say that as Solon,
Lycurgus, Pisistratus, and other individuals possessed the
attribute mortality, and as Socrates resembles those indivi-
duals in his possession of the attribute humanity, he will
therefore resemble them in being mortal. This ' * type of
ratiocination," says Mr. Mill, "does not claim, like the
syllogism, to be conclusive from the mere form of expression ;

nor can it possibly be so Whether, from the attributes

in which Socrates resembles those men who have heretofore
died, it is allowable to infer that he resembles them also in
being mortal, is a question of induction; and is to be decided
by the principles or canons which we shall hereafter recognise
as tests of the correct performance of that great mental
operation."

It will thus be seen that in refusing the name of inference
(strictly speaking) to syllogistic reasoning, and in referring it
to induction, Mr. Mill evidently considers the latter as alto-
gether different in nature from the syllogism. It would not
be difficult to quote other passages to the same effect, thus
"This was induction, but bad induction; just as a vicious
syllogism is reasoning, but bad reasoning," where the processes
of induction and syllogism are contrasted. Consequently, the
theory of induction maintained in the body of this treatise, is
directly at variance with the views just stated ; for I have
endeavoured to show that the inductive process is merely a
peculiar species of deductive (syllogistic) inference, and
depends altogether upon reasonings which assume the form of
syllogisms. It is necessary, then, to produce some considera-
tions which shall serve to establish the fact that Mr. Mill
is mistaken in supposing induction to be independent of
syllogism.

Now this point may, I think, be proved by using Mr, Mill's
own words. Eirst, as regards inductions in general, I find
the following statement: "It hence appears that if we
throw the whole course of any inductive argument into a
series of syllogisms, we shall arrive, by more or fewer steps,
at an ultimate syllogism, which will have for its major
premiss the principle, or axiom, of the uniformity of the course
of nature." A passage like this might apparently be held as

168 APPENDIX.

an admission of all that I require to prove ; I shall, however,
push the matter a little further, and ask, TJpon what does Mr.
Mill rest his " ultimate major premiss ? " The answer I find
to be, " "We arrive at this universal law, by generalisation
from many laws of inferior generality." But here another
step presents itself, which leads us to inquire what it is that
gives validity to this last-mentioned " generalisation," which
is described in another place as being an "induction by
simple enumeration in other words, generalisation of an
observed fact from the mere absence of any known instance to
the contrary ; " or, to vary the expression, what makes us
certain that the conclusion to which this generalisation
conducts is true ? The only approach to a reply which Mr.
Mill gives, is as follows :

"The considerations which, as I apprehend, give, at the
present day, to the proof of the law of uniformity of succession,
as true of all phenomena without exception, this character of
completeness and conclusiveness, are the following : First,
that we now know it directly to be true of far the greatest
number of phenomena; that there are none of which we
know it not to be true, the utmost that can be said being that
of some we cannot positively from direct evidence affirm its
truth ; while phenomenon after phenomenon, as they become
better known to us, are constantly passing from the latter
class into the former ; and in all cases in which that transition
has not yet taken place, tbe absence of direct proof is accounted
for by the rarity or obscurity of the phenomena, our deficient
means of observing them, or the logical difficulties arising
from the complication of the circumstances in which they
occur ; insomuch that, notwithstanding as rigid a dependence
ou given conditions as exists in the case of any other pheno-
menon, it was not likely that we should be better acquainted
with those conditions than we are."

Accordingly, the observed ground for the conclusion that
all phenomena have a cause, is the fact that some have ; but
there is no reason assigned for such an inference being valid.
I can therefore only suppose that Mr. Mill implies the exist-
ence of some mental law which assures us of a particular
uniformity so characterised being sufficient to warrant the
truth of the corresponding general uniformity. And this
view is borne out by such statements as this "The un-
prompted tendency of the mind is to generalise its experience
provided this points all in one direction," which are to be

APPENDIX. ICO

frequently ir.et with in the work quoted. The result, th^n, at
which we finally arrive, is that the mind supplies a general
law, according to which, if certain facts are ascertained by
observation, a fixed conclusion must be obtained. Let us
state this mental law, the observed facts, and the conclusion
in the order named, thus :

A case of a certain particular uniformity is a case of the

corresponding general uniformity,
The case of some phenomena being caused is such a par-

ticular uniformity ;

.-. The case of some phenomena being caused is a case of
all phenomena being caused.

This evidently is nothing but a syllogism, and indeed is
precisely the same syllogism as that to which, in the body of
this treatise, I traced all induction. A comparison of the in-
vestigation then followed out, with that just concluded, will
thus show that Mr. Mill implicitly, and myself explicitly, are
agreed in considering induction as but a species of syllogistic
inference.

It now remains to prove that the syllogism is not obnoxious
to the charge of depending upon a petitio principii ; and this
may, I think, be done in two ways. First, making use of
the fact recently established, that all reasoning whatever is
syllogistic, it can fairly be maintained, that even if it were
impossible to directly point out any flaw in the argument
supporting the charge ; yet there must of necessity be one
somewhere, or otherwise no valid inference could ever exist.
But, secondly, the alleged fallacy may be disposed of, in the
following manner, by a reference to the simple processes of
thought.

Taking the example already used, i. e., "All men are
mortal, Socrates is a man ; therefore, Socrates is mortal," let
us consider whether or not the major premiss alone contains
the conclusion. The subject is the class " man " taken uni-
versally, that is, as a whole, and accordingly, the object which
occupies our thoughts is composed principally of the unity
"humanity." The predicate is the class "mortal things,"
considered mainly with reference to a portion of its " parts ; "
and the import of the entire judgment is that "humanity " is
one of the unities possessing " mortality," and that the parts
which are connected together by humanity form a complex
portion of the parts connected by mortality. Now the only
assertion which is here made respecting individual objects is

170 APPENDIX

that any case of " humanity " is a case of " mortality," and
therefore it is not implied that any intuition such as Socrates,
Plato, or Junius, is mortal, until such intuition has been ana-
lysed and found to contain " humanity." Then, indeed, I
grant, the major premiss implies the conclusion ; but then, it
must be borne in mind, we are also in possession of the minor
premiss, without which the conclusion would not be so implied.
Accordingly, the major tells us that the general notion " man "
forms a portion of the general notion " mortal things ; " the
minor, that the intuition Socrates forms a portion of the
general notion "man;" the conclusion, that the intuition
Socrates forms a portion of the general notion "mortal
things." And thus it will also be seen, that both the major
and minor premises separately contain the conclusion when
both are admitted ; but that, unless this be the case, neither
of them does. Therefore, as loth premises are essential to
the conclusion, there is no petitio principii.

The above is necessarily but a mere outline of the argu-
ment by which the syllogistic theory, as ordinarily, and I
apprehend, justly received, may be defended. The full details
cannot here be set forth, and therefore I must ask the reader
to supply them himself, a task which will be easy when once
he is in possession of the key to the whole question, viz.,
when he perceives the distinction which must be made
between an intuition as an intuition, and an intuition resolved
into its constituting general notions.

In this article, the work quoted from is Mr. Mill's " Logic,"
and I annex a list of the passages referred to, in the order of
their occurrence above.

Book ii. chap. iii. 2.

Do. do. 7.
Book iii. chap. iv. 3, note.

Do. chap. iii. 1.

Do. chap. xxi. 2.

Do. do. 4.

Do. chap. iii. 2.

INDEX.

Absolute terms, 23.

Abstraction, 16.

Abstract terms, 23.

Accident, 17.

Affirmative propositions, 30.

Alternative propositions, 29.

Ampliative propositions, 35.

Analogous terms, 23.

Analogy, 143.

Applied logic in general, 84; necessity

for, 118.

Attributive propositions, 32.
Attributive terms, 23.

Categorematic terms, 24.

Categorical propositions, 28.

Causes, 126.

Chance, 145.

Classification, doctrine of, 155, 163.

Coincident-junction, 47.

Common terms, 11, 16; abstraction of,

16.

Compatible terms, 23.
Complex arguments, 76.
Conceptions, 16.
Concrete terms, 23.
Conditional propositions, 29.
Conditional syllogisms, 67 ; reduction of,

69; Sir W. Hamilton's objections to

reduction of, refuted, 70.
Connotative terms, 23.
Conversion, 44 ; rules for, 45 ; simple and

privative, 46.

Copula, interpretation of, 34.
Correlative terms, 23.

Deduction, in applied logic, 140 ; in pure

logic, 61.

Definitive terms, 22.
Definition, 21 ; rules for, 22.
Denomination, 35, 66.
Dictum de omni et nullo, 8, 49, 163.
Differences, 17.

Dilemma, 73 ; reduction of, 74.
Disjunctive propositions, 29.
Disjunctive syllogisms, 72 ; redaction of,

ib.

Distribution of terms, 31.
Division, 18; rules for, 20.

Entliymeme, 75.

Epicheirema, 73 ; resolution of, 79.

Episyllogism, 79.
Equivocal terms, 23.
Explicative propositions, 35.
Extension, 18, 64.

Fallacies, 84 ; classification of, 85 ; formal,

88.
Fallacies, material: Quaternio termino-

rum, 90 ; premiss unduly assumed, 95 ;

Ignoratio Elenchi t 111.
Figure, 54.

Figures, the four, remarks upon, 54.
Form and subject (or matter), 2, 39.
Fundamental laws of thought, 62, 165.

Genus, 17; subaltern, 17; summum, 17.

Hypothetical propositions, 29.
Hypothesis, 141.

Incomplete syllogisms, 75.

Indefinite terms, 23.

Individuals, 17.

Induction, in applied logic, 131 ; in pure

logic, 61.
Inference, 39.
Inferences, immediate, so-called, 40

shown to be mediate, 159.
Inferences mediate, 40 ; canons of, 49 ;

divisions of, 48; fundamental law of,

49.
Intellectual cultivation, proper ends of,

154.

Intension, or comprehension, 18, 64.
Intuitions, 15.

Judgment, 27 ; Dr. Thomson's definition

of, 27.'
Judgments, examination of Mr. Mill's

remarks on, 155.

Language, useful in two ways, 4.
Laws, 126.

Logic, as abstract philosophy, 153 ; results
arising from the study of, 152.

Modal categoricals, 28.
Mood or mode, 57.

Negative terms, 20.
Negative propositions, 30.
Nominalists and realists, 25.

172

Notions or terms, 14.

Notions should be appropriate, 124 ;
should be clear, 122.

Object, 119.

Observation, 119.

Opposite terms, 23.

Opposition, 41; "scheme" of, 44; con-
tradictory, 42 ; contrary, 42 ; subaltern,
43 ; subcontrary, 43 ; Sir W. Hamilton'a
remarks upon subcontrary, 43.

Opposition of terms, 23, 24.

Partial-negative propositions, 32.

Particular propositions, 30.

Phenomena, 120.

Positive terms, 20.

Predicates, 18.

Premises, syllogistic arrangement of, 66.

Privative terms, 20.

Probability, 145.

Propositions, formation of, 27 ; classifica-
tion of, 33 ; table of possible, 33 ; quan-
tity of, 30 ; quality of, 30.

Propositions, affirmative and negative, 30 ;
alternative or disjunctive, 29 ; amplia-
tive, explicative, and tautologous, 35 ;
attributive and substitutive, 32 ; cate-
gorical, 28 ; conditional or hypothetical,
29 ; partial-negative and total-negative,
32 ; particular and universal, 30.

Prosyllogism, 79.

Pure categoricals, 28.

Quality, 30.
Quantity, 30.

Reasoning in general, 38.
Reduction, 55.

Reflection, 126 ; examples of 148, 150.
Relation, 32.
Relative terms, 23.

Science, its object, 117.

Simple-apprehension, 14.

Singular terms, 11, 15.

Sorites, Aristotelian, 76 ; G-oclenian, 77.

Species, 17 ; infima, 17.

Substitutive propositions, 32.

Syllogism, shown to be no petitto prtn-
cipii, 166.

Syllogisms, 39 ; valid, table of, 58 ; con-
ditional, 67; reduction of conditional,
69.

Sir W. Hamilton's objections to reduction
of conditional syllogisms refuted, 70.

Syllogisms, disjunctive, 72 ; reduction of,
72.

Syllogisms, incomplete, 75.

Syncategorematic terms, 24.

Tautologous propositions, 35.

Terms, distribution of, 31 ; relation of, 32 ;
absolute and relative, 23 ; abstract and
concrete, 23; attributive or connota-
tive, 23; categorematic and syncate-
gorematic, 24; common and singular,
11 ; compatible and opposite, 23; corre-
lative, 23 ; definite and indefinite, 22 ;
positive, privative, and negative, 20
univocal, equivocal, and analogous, 23.

Total-negative propositions, 32.

Universal propositions, 30.
Univocal terms, 23.

Verification, 142.

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