Elementary lessons in logic : deductive and inductive

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JEVONS # ELEMENTARY LESSONS IN

LOGIC

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I,

LEMENTARY LESSONS
IN LOGIC:

DEDUCTIVE AND INDUCTIVE.
'TH COPIOUS QUESTIONS AND EXAMPLES,

AND

A VOCABULARY OF LOGICAL TERMS.

BY

W. STANLEY JEVONS,

LL.D. (EDINB.), M-A. (LOND.), F.R.S.

SontJon :
MACMILLAN AND CO.

A2TB NEW YOBK.
1893

\The Bight of Translation is reserved.]

First Edition i 1870.

Reprinted 1871, 1872, 1S74, 1875, 1877, 1878, 1880,

1881, 1882, 1883, 1884, 1885, 1886, 1889,

i8go, 1893.

PREFACE.

In preparing these Lessons I have attempted to
show that Logic, even in its traditional form, can be
made a highly useful subject of study, and a powerful
means of mental exercise. With this view I have
avoided the use of superfluous technical terms, and
have abstained from entering into questions of a
purely speculative or metaphysical character. For
the puerile illustrations too often found in works on
Logic I have generally substituted examples drawn
from the distinct objects and ideas treated in the
latural and experimental sciences; and in this and
; other respects have aimed at rendering these Lessons
, a suitable companion to a series of science school-
books.

vi PRE FA CE.

Logic is not only an exact science, but is the
most simple and elementary of all sciences ; it ought
therefore undoubtedly to find some place in every
course of education. The relations of propositions
and the forms of argument present as precise a sub-
ject of instruction and as vigorous an exercise of
thought, as the properties of geometrical figures, or
t(ic rules of Algebra. Yet every school-boy is made
to learn mathematical problems which he will never
employ in after life, and is left in total ignorance of
those simple principles and forms of reasoning which
will enter into the thoughts of every hour. Logic
should no longer be considered an elegant and learn-
ed accomplishment; it should take its place as an
indispensable study for every well-informed person.
These Lessons I trust will introduce to the science
many who have not leisure or inclination to read more
elaborate treatises, and many who would not be at-
tracted by the numerous but somewhat dry and brief
compendiums published in past years.

It is desirable that Lessons in Logic should be
made the basis of many exercises, and for this pur-
pose I have supplied abundance of questions and
examples at the end of the book, some of which are
selected from the examination papers of the Oxford,

. PREFACE. vii

^ T.ondon, and Edinburgh Universities. In my own
classes T have constantly found that the working and
solution of logical questions, the examination of argu-
ments and the detection of fallacies, is a not less

* practicable and useful exercise of mind than is the
performance of calculations, and the solution of pro-
blems in a mathematical class.

Except in a few places, where special notice is
given, I have abstained from putting forward any
views not commonly accepted by teachers of logic ;
and I have throughout devoted more attention to

* describing clearly and simply the doctrines in which
t logicians generally agree, than discussing the points

in which there is a difference of opinion. The recent
logical discoveries of Sir W. Hamilton, Mr George
Bentham, Prof de Morgan, and especially the late
Prof Boole, cannot yet be fully adopted in an ele-
mentary work, but I have attempted to give a clear
notion of the results to which they inevitably lead.

In the latter Lessons which treat of Induction I

have generally followed Sir John Herschel, Dr WTiewell

and Mr J. S. Mill, as the recognised authorities on the

; subject. These Lessons in fact may be regarded as

^ an easy introduction to some of the m.ost important

parts of Mr Mill's treatise on Logic.

viii PREFACE.

At the end of almost every Lesson will be found
references to the works in which the student will most
profitably continue his reading of the subject treated,
so that this little volume may serve as a guide to a
more extended course of study. ^

Hampstead,

November^ 1876.

*

TABLE OF CONTENTS.

LESSON PAGE

I. Definition and Sphere of the Science i

II. The Three Parts of Logical Doctrine 9

TERMS.

III. Terms, and their various Kinds i6

IV. Of the Ambiguity of Terms 27

V. Of the twofold meaning of terms — in Extension

and Intension 37

VI. The Growth of Language 44

VII. Leibnitz on Knowledge 53

PROPOSITIONS.

Kinds of Propositions 60

The Opposition of Propositions 71

Conversion of Propositions, and Immediate In-
ference 81

Logical Analysis of Sentences 88

The Predicables, Division, and Definition 98

Pascal and Descartes on Method jw

X TABLE OF CONTENTS.

SYLLOGISM. {

LESSON >AGK J

XIV. The Laws of Thought 117

XV. The Rules of the Syllogism 126

XVI. The Moods and Figures of the Syllogism 135

XVIL Reduction of the Imperfect Figures 144

XVIII. Irregular and Compound Syllogisms 152 /

XIX. Of Conditional Arguments 160

FALLACIES.

XX. Logical Fallacies 169 .

XXI. Material Fallacies 176

n

RECENT LOGICAL VIEWS.

XXII. The Quantification of the Predicate 183

XXIII. Boole's System of Logic 191 '

METHOD.

XXIV. Of Method, Analysis, and Synthesis 201

v.

INDUCTION. ^

• /
XXV. Perfect Induction and the Inductive Syllogism 210

XXVI. Geometrical and Mathematical Induction, Ana-

logy, and Example 210.

XXVII. Observation and Experiment 228,

XXVIII. Methods of Induction 239J

XXIX. Methods of Quantitative Induction 24; [

TABLE OF CONTENTS. xi

LESSON PAGE

XXX. Empirical and Deductive Methods 255

XXXI, Explanation, Tendency, Hypothesis, Tlieory

and Fact 264

SUBSIDIARIES OF INDUCTION.

XXXII. Classification, and Abstraction 276

XXXIII. Requisites of a Philosophical Language 287

Questions and Exercises 296

Examples of Terms 297 — 299

Examples of Propositions 303

Examples of Arguments 312, 315

Index ,. 332

> t*W.^\ > ^ N*>^?^S . ^ 5:A ^v

L^^ixJ" a^Mi.^ (L<^ikZ^cc<<

INTRODUCTION.

LESSON I.
DEFINITION AND SPHERE OF THE SCIENCE.

' Logic may be most briefly defined as the Science of
Reasoning. It is more commonly defined, however, as the

" Science of the Laws of Thought, and some logicians think
it desirable to specify still more accurately that it is the
Science of the Formal, or of the Necessary Laws of
Thought. Before these definitions can be of any real

"^use to us we must come to a clear understanding as to
the meaning of the expressions ; and it will probably
appear that there is no great difference between them.

^ By a Law of Thought we mean a certain uniformity or
agreement which exists and must exist in the modes in

, which all persons think and reason, so long as they do not
make what we call mistakes, or fall into self-contradiction

-,and fallacy. The laws of thought are natural laws with
which we have no power to interfere, and which are of

' course not to be in anyway confused with the artificial laws
of a country, which are invented by men and can be altered

• by them. Every science is occupied in detecting and
describing the natural laws which are inflexibly observed

* I

2 DEFINITION AND SPHERE [less.

by the objects treated in the Science. The science of
astronomy investigates the uniform or similar way in
which the heavenly bodies, and in fact all material sub-
stances, tend to fall towards each other as a stone falls
towards the earth, or to move round each other under ^
the influence of this tendency. The universal law of
gravitation is thus the natural law or uniformity treated
in physical astronomy.

In chemistry the law of equivalent proportions de- ,
scribes the well ascertained fact that each chemical
substance enters into combination with every other che- ;
mical substance only in certain definite proportions ; as
when exactly eight parts by weight of oxygen unite with -
one part of hydrogen to form water, or sixteen parts of
oxygen and six parts of carbon unite to form carbonic
acid in the ordinary burning of a flame or fire. When-
ever we can detect uniformities or similarities we so far
create science and arrive at natural laws. But there may
be, and are, many things so fickle, complicated, and "
— tmcertain, that we can never be sure we have detected
laws that they will uniformly obey; in such cases no
science, in the proper sense of the word, is possible.
There is no such thing, for instance, as a real science of
human character, because the human mind is too variable ^
and complicated a subject of investigation. There are
no two persons so much alike that you may be sure of ;•
one acting in all circumstances as the other would; it
thus becomes impossible to arrange persons in classes so >
that all who are in the same class shall act uniformly in
the same manner in any given circumstances. '^

But there is a science of human reason or thought
apart from the many other acts of mind which belong to *
human character, because there are modes in which all
persons do uniformly think and reason, and must think ^
and reason. Thus if two things are identical with a third

I.] OF THE SCIENCE. 3

common thing they are identical with each other. This
is a law of thought of a very simple and obvious charac-
ter, and we may observe concerning it, —

1. That all people think in accordance with it, and
agree that they do so as soon as they understand its
meaning.

2. That they think in accordance with it whatever
may be the subject about which they are thinking.

Thus if the things considered are —

London,

The Metropohs,

The most populous city in Great Britain,
since "the Metropolis is identical with London," and
" London is identical with the most populous city in
Great Britain," it follows necessarily in all minds that
" the metropolis is identical with the most populous city
in Great Britain."

Again, if we compare the three following things —

Iron,

The most useful metal.

The cheapest metal, —
and it be allowed that " The most useful metal is Iron,"
and " Iron is the cheapest metal," it follows necessarily
in all minds that "the most useful metal is the cheapest."
We here have two examples of the general truth that
things identical with the same thing are identical with
each other ; and this we may say is a general or necessary
form of thought and reasoning.

Compare, again, the following three things, —

The earth,

Planets,

Bodies revolving in elliptic orbits.
We cannot say, as before, that "the earth is identical
with the planets;" it is identical only with one of the

I — 2

4 DEFINITION AND SPHERE [less.

/ planets, and we therefore say that " it is a planet." Simi-
larly we may say that " the planets are bodies revolving
in elliptic orbits," but only a part of the whole number
so revolving. Nevertheless it follows that if the earth is
among the planets, and the planets among bodies re- '
volving in elliptic orbits, then the earth is among the
latter.

A very elementary knowledge of chemistry enables us
to argue similarly concerning the following ; —

/ Iron,
: Metals,

Elementary substances.

Iron is one of the metals, and metals are elements or
simple undecomposable substances, in the sense of being
among them or a part of them, but not as composing the •
whole. It follows necessarily that " Iron is one of the
elementary substances." We have had then two exam- >
pies of a fixed and necessary form of thought which is
necessary and true whatever the things may be to which -
it is applied. The form of argument may be expressed in
several different ways, and we shall have to consider it \
minutely in the lessons on the syllogism ; we may express
it, for instance, by saying that "part of a part is part
of the whole." Iron is part of the class of metals, which
is part of the class of elements: hence iron is part of
the class of elements.

If I now introduce another definition of Logic and '
say that it is "the science of the necessary forms of
thought," the reader will I hope clearly apprehend the
meaning of the expression " necessary forms of thought."
A form is something which may remain uniform and
unaltered, while the matter thrown into that form may be ^
varied. Medals struck from the same dies' have exactly
the same form, but they may be of various matter, as

I.] OF THE SCIENCE. 5

bronze, copper, gold or silver. A building of exactly the
same form might be constructed either of stone or bricks ;
furniture of exactly similar shape may be made of oak,
mahogany, walnut wood, etc. Just as we thus familiarly
recognize the difference of form and substance in common
tangible things, so we may observe in Logic, that the
form of an argument is one thing, quite distinct from the
various subjects or matter which may be treated in that
form. We may almost exhibit to the eye the form of
reasoning to which belong ojarjtwo latter arguments, as
follows : — -

/ (Y) •, .

' (X) is (Z) ^

If within the three pairs of brackets, marked respect-
ively X, Y and Z we place three names, such that the
one in place of X may be said to come under that in F,
and that in Y under that in Z, then it necessarily follows
that the first {X) comes under the last (Z).

Logic, then, is the science occupied in ascertaining
and describing all the general forms of thought which we
must employ so long as we reason validly. These forms
are very numerous, although the principles on which they
are constructed are few and simple. It will hence appear
that logic is the most general of all the sciences. Its
aid must be more often required than the aid of any other
science, because all the particular sciences treat portions
only of existing things, and create very different and
often unconnected branches of knowledge. But logic
treats of those principles and forms of thought which
must be employed in every branch of knowledge. It
treats of the very origin and foundations of knowledge
itself ; and though it is true that the logical method em-
ployed in one science may differ somewhat from that em-

/

6 DEFINITION AND SPHERE [less.

ployed in another science, yet whatever the particular
form may be, it must be logical, and must conform to the
laws of thought. There is in short something in which
- all sciences must be similar ; to which they must con-
form so long as they maintain what is true and self-
consistent ; and the work of logic is to explain this
common basis of all science.

One name which has been given to Logic, namely the
Science of Sciences, ver}' aptly describes the all extensive
power of logical principles. The cultivators of special
branches of knowledge appear to have been fully aware
of the allegiance they owe to the highest of the sciences,
for they have usually given names implying this allegi-
ance. The very name of logic occurs as part of nearly
all the names recently adopted for the sciences, which are
often vulgarly called the "ologies," but are really the
"logics," the "o" being only a connecting vowel or part
of the previous word. Thus geology is logic applied to
explain the formation of the earth's crust ; biology is logic
applied to the phenomena of life ; psychology is logic
applied to the nature of the mind ; and the same is the
case with physiology, entomology, zoology, teratology,
morphology, anthropology, theology, ecclesiology, thalat-
tology, and the rest*. Each science is thus distinctly
confessed to be a special logic. The name of logic itself
is derived from the common Greek word Xoyop, which
usually means word, or the sign and outward manifesta-
tion of any inward thought. But the same word was also
used to denote the inward thought or reasoning of which
words are the expression, and it is thus probably that later ,
Greek writers on reasoning were led to call their science

* Except Philology, which is differently formed, and means
the love or study of words ; the name of this science, if formed
upon the same plan, would be logology.

I.] OF THE SCIENCE. 7

enia-Tri^r] XoyiKi], or logical Science ; also rex^r] XoytKi^, or
logical art The adjective Xoyt<7, being used alone, soon
came to be the name of the science, just as Mathematic,
Rhetoric, and other names ending in "ic" were ori-
ginally adjectives but have been converted into substan-
tives.

Much discussion of a somewhat trifling character has
arisen upon the question whether Logic should be con-
sidered a science only, an art only, or both at the same
time. Sir W. Hamilton has even taken the trouble to
classify almost all the writers on logic according as they
held one opinion or the other. But it seems substan-
tially correct and sufficient to say, that logic is a science
in so far as it merely investigates the necessary princi-
ples and forms of thought, and thus teaches us to under-
stand in what correct thinking consists; but that it be-
comes an art when it is occupied in framing rules to assist
persons in detecting false reasoning. A science teaches us^
to know and an art to do, and all the more perfect sciences
lead to the creation of corresponding useful arts. As-
tronomy is the foundation of the art of navigation on the
ocean, as well as of the arrangement of the calendar and
chronology. Physiology is the basis of the art of medi-
cine, and chemistry is the tasis of many useful arts.
Logic has similarly been considered as the basis of an art
of correct reasoning or investigation which should teach
the true method to be observed in all sciences. The cele-
brated British logician Duns Scotus, who lived in the 13th
century, and called logic the Science of Sciences, called it
also the Art of Arts, expressing fully its preeminence.
Others have thus definCvd it — " Logic is the art of direct-
ing the reason aright in acquiring the knowledge of
things, for the instruction both of ourselves and others."
Dr Isaac Watts, adopting tiiis view of logic, called his
well-known work "the Art of Thinking."

8 DEFINITION AND SPHERE [less.

It may be fairly said however that Logic has more
the form of a science than an art for this reason — all
persons necessarily acquire the faculty and habit of rea-
soning long before they even know the name of logic.
This they do by the natural exertion of the powers of
mind, or by constant but unconscious imitation of others.
They thus observe correctly but unconsciously the prin-
ciples of the science in all very simple cases ; but the con-
tradictory opinions and absurd fallacies which are put
forth by uneducated persons shew that this unaided ex-
ercise of mind is not to be trusted when the subject of
discussion presents any difficulty or complexity. The
study of logic then cannot be useless. It not only
explains the principles on which every one has often
reasoned correctly before, but points out the dangers
which exist of erroneous argument. The reasoner thus
becomes consciously a correct reasoner and learns con-
sciously to avoid the snares of fallacy. To say that
men can reason well without logical science is about as
true as to say that they can live healthily without medi-
cine. So they can — as long as they are healthy ; and so
can reasoners do without the science of reasoning — as long ^
as they do reason correctly; but how many are there that
can do so ? As well migh - a man claim to be immortal
in his body as infallible in his mind.

And if it be requisite to say a few words in defence of
Logic as an art, because circumstances in the past his-
tory of the science have given rise to misapprehension,
can it be necessary to say anything in its praise as a
science "i Whatever there is that is great in science or in
art or in literature, it is the work of intellect. In bodily
form man is kindred with the brutes, and ;in his perish-
able part he is but matter. It is the possession of con- .
scious intellect, the power of reasoning by general notions
that raises him above all else upon the earth ; and who

II.] OF THE SCIENCE. 9

can say that the nature and procedure of this intellect is
not almost the highest and most interesting subject of
study in which we can engage? In vain would any
one deny the truth of the favourite aphorism of Sir W.
Hamilton —

In the world there is nothing great but man.
In man there is nothing great but mind.

LESSON II.

THE THREE PARTS OF LOGICAL DOCTRINE.

It has been explained in the previous lesson that Logic
is the Science of Reasoning, or the Science of those Ne-
cessary Laws of Thought which must be observed if we
are to argue consistently with ourselves and avoid self-
contradiction. Argument or reasoning therefore is the
stiictly proper subject before us. But the most conve-
nient and usual mode of studying logic is to consider first
the component parts of which any argument must be
made up. Just as an architect must be acquainted with
the materials of a building, or a mechanic with the ma-
terials of a machine, before he can pretend to be ac-
quainted with its construction, so the materials and in-
struments with which we must operate in reasoning are
suitably described before we proceed to the actual forms
of argument.

If we examine a simple argument such as that given
in the last lesson, thus —

Iron is a metal,

Every metal is an element,

Therefore Iron is an element, —

lo THE THREE PARTS OF [less.

we see that it is made up of three statements or asser-
tions, and that each of these contains, besides minor
words, two nouns substantive or names of things, and the
verb " is." In short, two names, or terms, when connected
by a verb, make up an assertion or proposition; and
three such propositions make up an argument, called in
this case a syllogism. Hence it is natural and conve-
nient first to describe terms, as the simplest parts ; next
to proceed to the nature and varieties of propositions
constructed out of them, and then we shall be in a posi-
tion to treat of the syllogism as a whole. Such accord-
ingly are the three parts of logical doctrine.

But though we may say that the three parts of logic
are concerned with terms, propositions, and syllogisms,
it may be said with equal or greater truth that the acts of
mind indicated by those forms of language are the real
subject of our consideration. The opinions, or rather
perhaps the expressions, of logicians have varied on this
point. Archbishop Whately says distinctly that logic is
entirely conversant about language ; Sir W. Hamilton, Mr
Mansel, and most other logicians treat it as concerned
with the acts or states of mind indicated by the words ;
while Mr J. S. Mill goes back to the things themselves
concerning which we argue. Is the subject of logic, then,
language, thought, or objects.? The simplest and truest
answer is to say that it treats in a certain sense of all
three. Inasmuch as no reasoning process can be ex-
plained or communicated to another person without
words, we are practically limited to such reasoning as is
reduced to the form of language. Hence we shall always
be concerned with words, but only so far as they are the
instruments for recording and referring to our thoughts.
The grammarian also treats of language, but he treats it
as language merely, and his science terminates with the
description and explanation of the forms, varieties, and

II.] LOGICAL DOCTRINE. ii

relations of words. Logic also treats of language, but
' only as the necessary index to the action of mind.

Again, so long as we think correctly we must think of
' things as they are; the state of mind within us must
_ correspond with the state of thmgs without us whenever
an opportunity arises for comparing them. It is im-
possible and inconceivable that iron should prove not to
be an elementary substance, if it be a metal, and every
metal be an element We cannot suppose, and there is
no reason to suppose, that by the constitution of the
mind we are obliged to think of things differently from
the manner in which they are. If then we may assume
' that things really agree or differ according as by correct
logical thought we are induced to believe they will, it
does not seem that the views of the logicians named are
irreconcileable. We treat of things so far as they are the
objects of thought, and we treat of language so far as it is
the embodiment of thought. If the reader will bear this
explanation in mind, he will be saved from some per-
plexity when he proceeds to read different works on logic,
and finds them to vary exceedingly in the mode of treat-
ment, or at least of expression.

If, when reduced to language, there be three parts of
logic, terms, propositions, and syllogisms, there must be
as many different kinds of thought or operations of mind.
These are usually called —

1. Simple apprehension.

2. Judgment

3. Reasoning or discourse.

s The first of these, Simple Apprehension, is the act of
mind by which we merely become aware of something,
or have a notion, idea, or impression of it brought into
the mind. The adjective simple means apart from other
things, and apprehettsion the taking hold by the mind.
Thus the name or term Iron instantaneously makes the

12 THE THREE PARTS OF [less.

mind think of a strong and very useful metal, but does
not tell us anything about it, or compare it with any thing
else. The words sun, Jupiter, Sirius, St PauVs Cathe-
dral, are also terms which call up into the mind certain
well-known objects, which dwell in our recollection even
when they are not present to our senses. In fact, the use
of a term, such as those given as examples, is merely as a
substitute for the exhibition of the actual things named.

Judgment is a different action of mind, and consists in
comparing together two notions or ideas of objects de-
rived from simple apprehension, so as to ascertain whe-
ther they agree or differ. It is evident, therefore, that we
cannot judge or compare unless we are conscious of two
things or have the notions of two things in the mind at
the same time. Thus if I compare Jupiter and Sirius I
first simply apprehend each of them ; but bringing them
into comparison I observe that they agree in being small,
bright, shining bodies, which rise and set and move
round the heavens with apparently equal speed. By
minute examination, however, I notice that Sirius gives
a twinkling or intermittent light, whereas Jupiter shines
steadily. More prolonged observation shews that Ju-
piter and Sirius do not really move with equal and
regular speed, but that the former changes its position
upon the heavens from night to night in no very simple
manner. If the comparison be extended to others of the
heavenly bodies which are apprehended or seen at the
same time, I shall find that there are a multitude of stars
which agree with Sirius in giving a twinkling light and
in remaining perfectly fixed in relative position to each
other, whereas two or three other bodies may be seen
which resemble Jupiter in giving a steady light, and also
in changing their place from night to night among the
fixed stars. I have now by the action of judgment
formed in my mind the general notion oi Jixed stars^ by

II.] LOGICAL DOCTRINE. 13

bringing together mentally a number of objects which
agree ; while from several other objects I have formed the
general notion oi planets. Comparing the two general
notions together, I find that they do not possess the same
qualities or appearances, which I state in the proposition,
" Planets are not fixed stars."

I have introduced the expression "General Notion" as
if the reader were fully acquainted with it. But though
philosophers have for more than two thousand years con-
stantly used the expressions, general notion, idea, con-
ception, concept, &c., they have never succeeded in
agreeing exactly as to the meaning of the terms. One
class of philosophers called Nominalists say that it is all a
matter of names, and that when we join together Jupiter,
Mars, Saturn, Venus, &c., and call them planets, the
common name is the bond between them in our minds.
Others, called Realists, have asserted that besides these
particular planets there really is something which com-
bines the properties common to them all without any of
the differences of size, colour, or motion which distin-
guish them. Every one allows in the present day how-
ever that nothing can physically exist corresponding to a
general notion, because it must exist here or there, of this
size or of that size, and therefore it would be one particu-
lar planet, and not any planet whatever. The Nominal-
ists, too, seem equally wrong, because language, to be of
any use, must denote something, and must correspond, as
we have seen, to acts of mind. If then proper names
raise up in our minds the images of particular things, like
the sun, Jupiter, &c., general names should raise up
general notions.

The true opinion seems to be that of the philoso-
phers called Conceptualists, who say that the general no-
tion is the knowledge in the mind of the common pro-
perties or resemblances of the things embraced under

14 THE THREE PARTS OF [less.

the notion. Thus the notion planet really means the
consciousness in anybody's mind that there are certain
heavenly bodies which agree in giving a steady light
and in moving about the heavens differently from the
fixed stars. It should be added, however, that there are
many, including Sir \V. Hamilton, who would be counted
as Nominalists and who yet hold that with the general
name is associated a consciousness of the resemblance
existing between the things denoted by it. Between this
form of the doctrine and conceptualism it is not easy to
draw a precise distinction, and the subject is of too de-
batable a character to be pursued in this work.

It will appear in the course of these lessons that the
whole of logic and the whole of any science consists in so
arranging the individual things we meet in general no-
tions or classes, and in giving them appropriate general
names or terms, that our knowledge of them may be
made as simple and general as possible. Every general
notion that is properly formed admits of the statement of
general laws or truths ; thus of the planets we may affirm
that they move in elliptic orbits round the sun from west
to east; that they shine with the reflected light of the '
sun ; and so on. Of the fixed stars we may affirm that
they shine with their own proper light; that they are
incomparably more distant than the planets ; and so on.
The whole of reasoning will be found to arise from this
faculty of judgment, which enables us to discover and ,.
affirm that a large number of objects have similar pro-
perties, so that whatever is known of some may be in-
ferred and asserted of others.

It is in the application of such knowledge that we ;
employ the third act of mind called discourse or reason-
ing, by which from certain judgments we are enabled, ,
without any new reference to the real objects, to form a
iiew judgment. If we know that iron comes under the

II.] LOGICAL DOCTRINE. 15

general notion of metal, and that this notion comes under
the still wider notion of element, then without further
examination of iron we know that it is a simple unde-
composable substance called by chemists an element. Or
if from one source of information we learn that Neptune
is a planet, and from another that planets move in ellip-
tic orbits, we can join these two portions of knowledge
together in the mind, so as to elicit the truth that Nep-
tune moves in an elliptic orbit.

Reasoning or Discourse, then, may be defined as the
progress of the mind from one or more given propositions
to a proposition different from those given. Those pro-
positions from which we argue are called Premises, and
that which is drawn from them is called the Conclusion.
The latter is said to follow, to be concluded, inferred or col-
lected from them ; and the premises are so called because
they are put forward or at the beginning (Latin prcB^ be-
fore, and mitio, I send or put). The essence of the pro-
cess consists in gathering the truth that is contained in
the premises when joined together, and carrying it with
us into the conclusion, where it is embodied in a new
proposition or assertion. We extract out of the pre-
mises all the information which is useful for the purpose
in view — and this is the whole which reasoning accom-
plishes.

I have now pointed out the three parts of logical doc-
trine. Terms, Propositions, and Reasoning or Syllogism,
into which the subject is conveniently divided. To the
consideration of these parts we shall proceed. But it
may be mentioned that a fourth part has often been
added, called Method, which is concerned with the ar-
rangement of the parts of any composition.

It is sometimes said that what proposition is to term,
and what syllogism is to proposition, such is method to
syllogism, and that a fourth division is necessary to com-

i6 TERMS, AND THEIR [less.

plete the doctrine of Logic. It is at any rate certain
however that this fourth part is much inferior in import-
ance and distinctness to the preceding three ; and all that
will be said of it is to be found in Lesson xxiv.

LESSON III.
TERMS, AND THEIR VARIOUS KINDS.

It has been explained in the preceding lesson that every
assertion or statement expresses the agreement or dif-
ference of two things, or of two general notions. In
putting the assertion or statement into words, we must
accordingly have words suitable for drawing the attention
of the mind to the things which are compared, as well as
words indicating the result of the comparison, that is to
say, the fact whether they agree or differ. The words by
which we point out the things or classes of things in
question are called Terms, and the words denoting the
comparison are said to form the Copula. Hence a com-
plete assertion or statement consists of two terms and a
copula, and when thus expressed it forms a Proposition.
Thus in the proposition " Dictionaries are useful books," *
the two terms are dictionaries and useful books; the co-
pula is the verb are, and expresses a certain agreement of
the class dictionaries with the class of useful books con-
sisting in the fact that the class of dictionaries fonns part '
of the class of useful books. In this case each term con-
sists of only one or two words, but any number of words
may be required to describe the notions or classes com-

III.] VARIOUS KINDS. 17

pared together. In the proposition "the angles at the
base of an isosceles triangle are equal to each other," the
first term requires nine words for its expression, and the
second term, four words (equal to each other) ; and there
is no limit to the number of words which may be em-
ployed in the formation of a term.

A term is so called because it forms one end (Latin,
termitius) of a proposition, and strictly speaking it is a
term only so long as it stands in the- proposition. But
we commonly speak of a term or a name meaning any
noun, substantive or adjective, or any combination of
words denoting an object of thought, whether that be, as
we shall shortly see, an individual thing, a group of things,
a quality of things, or a group of qualities. It would be
impossible to define a name or term better than has been
done by Hobbes : " A name is a word taken at pleasure
to serve for a mark, which may raise in our mind a
thought like to some thought which we had before, and
which, being pronounced to others, may be to them a
sign of what thought the speaker had before in his mind."

Though every term or name consists of words it is
not every word which can form a name by itself. We
cannot properly say "Not is agreeable" or "Probably is
not true ;" nothing can be asserted of a preposition, an
adverb, and certain other parts of speech, except indeed
that they are prepositions, adverbs, &:c. No part of
speech except a nouii substantive, or a group of words
used as a noun substantive, can form the subject or first
term of a proposition, and nothing but a noun substan-
tive, an adjective, the equivalent of an adjective, or a
verb, can form the second term or predicate of a propo-
sition. It may indeed be questioned whether an adjec-
tive can ever form a term alone; thus in "Dictionaries
are useful," it may be said that the substantive things or
books is understood in the predicate , the complete sen-

2

i8 TERMS, AND THEIR [less.

tence being " Dictionaries are useful books f but as this
is a disputed point we will assume that words are divided
into two kinds in the following manner : —

Words which stand, or appear to stand alone as com-
plete terms, namely the substantive and adjectivej^.and ^
certain parts of a verb, are called categorematic words,
from the Greek word Kar-qyopea), to assert or predicate.

Those parts of speech, on the other hand, such as
prepositions, adverbs, conjunctions, &c., which can only-
form parts of names or terms are called syncategorematic
words, because they must be used wi^/i other words in
order to compose terms (Greek a-vv, with, and Karrjyopea)).
Of syncategorematic words we need not take further
notice except so far as they form part of categorematic
terms.

We have now to consider the various kinds and pecu-
liarities of terms, so as to gain a clear idea of what they
mean. Terms are first of all distinguished into singidar
or individual, and gejieral or common terms, this being a
very obvious division, but one of much importance. A
Singular term is one which can denote only a single ob-
ject, so long at least as it is used in exactly the samei
meaning ; thus the Emperor of the French, the Atlantic
Ocean, St Paul's, William Shakspeare, the most pre-
cious of the metals, are singular terms. All proper names
belong to this class ; for though John Jones is the name
of many men, yet it is used not as meaning any of these
men, but some single man — it has, in short, a different
meaning in each case, just as London, the name of our
capital, has no connexion in meaning with London in
Canada.

General terms, on the contrary, are applicable in the
same sense equally to any one of an indefinite number of
objects which resemble each other in certain qualities.
Thus metal is a general name because it may be applied

V- ^ c5 . <^ . /?> ,

III.] VARIOUS KINDS. 19

indifferently to gold, silver, copper, tin, aluminium, or any
of about fifty known substances. It is not the name of
any one of these more than any other, and it is in fact
applied to any substance which possesses metallic lustre,
which cannot be decomposed, and which has certain
other qualities easily recognised by chemists. Nor is the
number of substances in the class restricted; for as new
kinds of metal are from time to time discovered they are
added to the class. Again, while IMars, Jupiter, Saturn,
&c., are singular terms, since each can denote only a
single planet, the term planet is a general one, being
applicable to as many bodies as may be discovered tq
revolve round the sun as the earth does.

We must carefully avoid any confusion between ge?
neral and collective terms. By a collective term we
mean the name of a number of things when all joined
together as one whole ; like the soldiers of a regiment,
the men of a jury, the crew of a vessel : thus a collective
term is the name of all, but not of each. A general term,
on the other hand, is the name of a number of things,
but of each of them separately, or, to use the technical
expression, distributively. Soldier, jurj'man, sailor, are
the general names which may belong to John Jones,
Thomas Brown, &c., but we cannot say that John Jones
is a regiment, Thomas Brown a jury, and so on. The
distinction is exceedingly obvious when thus pointed out,
but it nf^y present itself in more obscure forms, and is
then likely to produce erroneous reasoning, as will be
pointed out in Lesson xx. It is easy to see that we must
not divide terms into those which are general and those
which are collective, because it will often happen that
the same term is both general and collective, according
as it is regarded. Thus, library is collective as regards
the books in it, but is general as regards the great num-
ber of different hbraries, private or public, which exist.

2 — 2

20 TERMS, AND THEIR [less.

Regiment is a collective term as regards the soldiers
which compose it, but general as regards the hundred
different regiments, the Coldstream Guards, the High-
land regiment, the Welsh Fusiliers, and the rest, which
compose the British standing army. Army, again, is a
collective whole, as being composed of a number of regi-
ments organized together. Year is collective as regards
the months, weeks, or days of which it consists, but is
general as being the name either of 1869 or 1870, or any
period marked by a revolution of the earth round the sun.

We have not always in the English language suffi-
cient means of distinguishing conveniently between the
general and collective use of terms. In Latin this dis'
tinctive use was exactly expressed by oviiies^ meaning all
distributively, and aincti meaning all taken together, a
contracted form of conjiincti (joined together). In English
all men may mean a7iy jnan or all men together. Even
the more exact word every is sometimes misused, as in
the old proverb, ' Every little makes a mickle,' where it is
obvious that every little portion cannot by itself make
much, but only when joined to other httle portions.

A second important distinction between terms is that
of concrete terms and abstract terms ; and it cannot be
better described than in the words of Mr Mill, by saying
that a concrete name is the name of a thing, the abstract
name is the name of a quality, attribute, or circumstance
of a thing. Thus red house is the name of a physically-
existing thing, and is concrete; redfiess is the name of
one quality of the house, and is abstract. The word
abstract means drawn from (Latin, abstractus, from abs-
trahere, to draw away from), and indicates that the quality
redness is thought of in the mind apart from all the other
qualities which belong to the red house, or other red
object. But though we can think of a quality by itself,
we cannot suppose that the quality can exist physically

III.] VARIOUS KINDS. 21

apart from the matter in which it is manifest to us. Red-
ness means either a notion in the mind, or it means that
in red objects which excites the notion.

The reader shnnld rarpfnHy n^gpryp that adiectlves
are concrete^ not abstract. If we say that a book is use-
ful, iris to the book we apply the adjective useful, and
usefulness is the abstract noun which denotes the quahty ;
similarly, the adjectives eqtial, grateful, reverent, ratio-
nal, are the names of things, and the corresponding abs-
tract nouns are equality, g7'atitude, reve7'e7ice, rationality.
This distinction will become more apparent in reading
Lesson v.

It is a good exercise to try and discover pairs of cor-
responding concrete and abstract names ; thus animal
has animality ; miser, miserliness ; old, agedness, or old
age ; substance, substantiality ; soap, soapiness ; shrub,
shrubbiness ; and so on. But it by no means follows that
an abstract word exists for each concrete ; table hardly has
an abstract tabularity ; and though ink has inkiness, we
should not find the abstract of pen. It is by the accidents
of the history of language that we do or do not possess
abstract names ; and there is a constant tendency to in-
vent new abstract words in the progress of time and
science.

Unfortunately concrete and abstract names are fre-
quently confused, and it is by no means always easy to
distinguish the meanings. Thus relation properly is the
abstract name for the position of two people or things to
each other, and those people are properly called relatives
(Latin, relativus, one who is related). But we constantly
speak now of relations, meaning the persons themselves ;
and when we want to indicate the abstract relation
they have to each other we have to invent a new abstract
name relationship. Nation has long been a concrete
term, though from its form it was probably abstract at

22 TERMS, AND THEIR [LESS.

first ; but so far does the abuse of language now go,
especially in newspaper writing, that we hear of a tiation-
ality meaning a nation, although of course if nation is
the concrete, nationality ought to be the abstract, mean-
ing the quality of being a nation. Similarly, action,
mtentiojt, exteftsion, conception, and a multitude of other
properly abstract names, are used confusedly for the corre-
sponding concrete, namely, act, intent, extent, concept, &c.
Production is properly the condition or state of a person
who is producing or drawing something forth ; but it has
now become confused with that which is produced, so
that we constantly talk of the productions of a country,
meaning the products. The logical terms, Proposition,
Deduction, Induction, Syllogism, are all properly abstract
words, but are used concretely for a Proposition, a De-
duction, an Induction, a Syllogism ; and it must be al-
lowed that logicians are nearly as bad as other people in
confusing abstract and concrete terms. Much injury is
done to language by this abuse.

Another very obvious division of terms is between
those which are positive, and those which are negative.
The difference is usually described by saying that posi-
tive terms signify the existence or possession of a quality,
as in grateful, metallic, organic, etc., while the correspond-
ing negatives signify the absence of the same qualities
as in ungrateful, non-metallic, inorganic. The negative
terms may be adjectives as above, or substantives, con-
crete or abstract ; thus ingratitude, inequality, incon-
venience are abstract negative terms; and individuals,
unequals, &c. are concrete negatives. We usually consider
as negative terms any which have a negative prefix such
as not, non, un, in, &c. ; but there are a great many terms
which serve as negatives without possessing any mark of
their negative character. Darkness is the negative of
light or lightness, since it means the absence of light;

III.] VARIOUS KINDS. 23

compound is the negative of element, since we should
give the name of compound to whatever can be deconi'
posed, and element is what cannot be decomposed ; theo-
retically speaking every term has its corresponding nega-
tive, but it by no means follows that language furnishes
the term ready-made. Thus table has the corresponding
adjective tabular, but there is no similar negative tnitahi-
larj one man may be called a bookworm, but there is no
negative for those who are not bookworms, because no
need of the expression has been felt. A constant process
of invention of new negative terms goes on more rapidly
perhaps than is desirable, for when an idea is not often
referred to it is better to express it by a phrase than add
to the length of the dictionary by a new-created word.

It would seem that in many cases a negative term
implies the presence of some distinct quality or fact.
Thus incoiivenience doubtless implies the absence of
conveniejice, but also the presence of positive trouble or
pain occasioned thereby. Unhappiness is a negative
term, but precisely the same notion is expressed by the
positive term misery. The negative of healthy is un-
healthy, but the positive term sickly serves equally well.
It thus appears to be more a matter of accident than
anything else whether a positive or negative term is used
to express any particular notion. All that we can really
say is that every positive term necessarily implies the
possibihty of a corresponding negative term, which is
the name of all those things to which the positive name
cannot be applied. Whether this term has been invented
or not is an accident of language: its existence may be
assumed in logic.

The reader may be cautioned against supposing that
every term appearing to be of a negative character on
account of possessing a negative prefix is really so. The
participle unloosed certainly appears to be the negative of

24 TERMS, AND THEIR [LESS.

loosed; but the two words mean exactly the same thing,
the prefix ini not being really the negative ; invaluable,
again, means not what is devoid of value, but what is so
valuable that the value cannot be measured; and a
shameless action can equally be called by the positive

\ term, a shameficl action. Other instances might no

' doubt be found.

Great care should be taken to avoid confusing terms
which express the presence or absence of a quality with
those which describe its degree. Less is not the negative
oi greater because there is a third alternative, equal. The
true negative di greater is not-greater, and this is equiva-
lent to either equal or less. So it may be said that dis-
agreeable is not the simple negative of agreeable, because
there may be things which are neither one nor the other,
but are indifferent to us. It would not be easy to say
offhand whether every action which is not honest is dis-
honest, or whether there may not be actions of an inter-
mediate character. The rule is that wherever the question
is one of degree or quantity a medium is possible, and
the subject belongs rather to the science of quantity
than to simple logic ; where the question is one of the
presence or absence of a quality, there cannot be more
than two alternatives, according to one of the Primary
Laws of Thought, which we will consider in Lesson XIV.

,In the case of quantity we may call the extreme terms

;opposites; thus less is the opposite of greater, disagreeable
of agreeable ; in the case of mere negation we may call
the terms negatives or contradictories, and it is really
indifferent in a logical point of view which of a pair of
contradictory terms we regard as the positive and which
as the negative. Each is the negative of the other.

Logicians have distinguished from simple negative
terms a class of terms called privative, such as blind,
dead, S^c. Such terms express that a thing has been

III.] VARIOUS KINDS, 25

deprived of a quality which it before possessed, or was
capable of possessing, or usually does possess. A man
may be born blind, so that he never did see, but he pos-
sesses the organs which would have enabled him to see

, except for some accident. A stone or a tree could not ,
have had the faculty of seeing under any circumstances.
No mineral substance can properly be said to die or to
be dead, because it was incapable of life ; but it may be

► called uncrystallized because it might have been in the
form of a crystal. Hence we apply a privative term to
anything which has not a quality which it was capable of
having ; we apply a negative term to anything which has
not and could not have the quality. It is doubtful however
whether this distinction can be properly carried out, and
it is not of very much importance.

It is further usual to divide terms according as they
are relative or absolute, that is, non-relative. The adjective

^ absolute means whatever is " loosed from connection
with anything else" (Latin ab, from, and solutus, loosed);
whereas relative means that which is carried in thought,
at least, into connection with something else. Hence a

, relative term denotes an object which cannot be thought
of without reference to some other object, or as part of a
larger whole. A father cannot be thought of but in rela-
tion to a child, a monarch in relation to a subject, a shep-

■• herd in relation to a flock ; thus father, monarch, and /
shepherd are relative terms, while child, subject, and /
flock are the correlatives (Latin con, with, and relativus), '
or those objects which are necessarily joined in thought
with the original objects. The very meaning, in fact, of
father is that he has a child, of monarch that he has
subjects, and of shepherd that he has a flock. As ex-

^ amples of terms which have no apparent relation to any-
thing else, I may mention water, gas, tree. There does
not seem to me to be anything so habitually associated

26 TERMS, AND THEIR [less.

with water that we must think of it as part of the same
idea, and gas, tree, and a multitude of other terms, also
denote objects which have no remarkable or permanent
relations such as would entitle the terms to be called rela-
tives. They may therefore be considered absolute or
non-relative terms.

The fact, however, is that everything must really have
relations to something else, the water to the elements of
which it is composed, the gas to the coal from which it is
manufactured, the tree to the soil in which it is rooted.
By the very laws of thought, again, no thing or class of
things can be thought of but by separating them from
other existing things from which they differ. I cannot use
the term mortal without at once separating all existing
or conceivable things into the two groups mortal and
immortal; metal, element, organic substance, and every
other term that could be mentioned, would necessarily
imply the existence of a correlative negative term, non-
metallic, compound, inorganic substance, and in this
respect therefore every term is undoubtedly relative.
Logicians, however, have been content to consider as;
relative terms those only which imply some peculiar and
striking kind of relation arising from position in time 6r
space, from connexion of cause and effect, &c. ; and it
is in this special sense therefore the student must use the
distinction.

The most important varieties of terms having been
explained, it is desirable that the reader should acquire a
complete familiarity with them by employing the exercises
at the end of the book. The reader is to determine con-
cerning each of the terms there given : —

i. Whether it is a categorematic or syncategore-
matic term.

2. Whether it is a general or a singular term.

3- Whether it is collective or distributive.

III.] VARIOUS KINDS. 27

4. Whether it is concrete or abstract.

5. Whether it is positive, or negative, or privative.

6. Whether it is relative or absolute.

It will be fully pointed out in the next lesson that
most terms have more than one meaning; and as the one
meaning may be general and the other singular, the one
concrete and the other abstract, and so on, it is absolute-
ly necessary that the reader should first of all choose
one precise meaning of the term which he is examining.
And in answering the questions proposed it is desirable
he should specify the way in which he regards it. Taking
the word sovereign, we may first select the meaning in
which it is equivalent to monarch; this is a general term
in so far as it is the name of any one of many monarchs
living or dead, but it is singular as regards the inhabit-
ants of any one country. It is clearly categorematic,
concrete, and positive, and obviously relative to the sub-
jects of the monarch.

Read Mr Mill's chapter on Names, System of Logic
Book I. chap. 2.

LESSON IV.

OF THE AMBIGUITY OF TERMS.

There is no part of Logic which is more really useful
than that which treats of the ambiguity of terms, that is
of the uncertainty and variety of meanings belonging to
words. Nothing indeed can be of more importance to
the attainment of correct habits of thinking and reason-
ing than a thorough acquaintance with the great imper-
fections of language. Comparatively few terms have one

28 OF THE AMBIGUITY [less.

sinj^le clear meaning and one meaning only, and when-
ever two or more meanings are unconsciously confused
together, we inevitably commit a logical fallacy. If, for
instance, a person should argue that " punishment is an
evil," and according to the principles of morality "no
evil is to be allowed even with the purpose of doing
good," we might not at the first moment see how to avoid
the conclusion that " no punishments should be allowed,"
because they cause evil. A little reflection will show that
the word evil is here used in two totally different senses ;
in the first case it means physical evil or pain ; in the
second moral evil, and because moral evil is never to be
committed, it does not follow that physical evils are never
to be inflicted, for they are often the very means of pre-
venting moral evil.

Another very plausible fallacy which has often been
put forth in various forms is as follows : " A thoroughly
benevolent man cannot possibly refuse to relieve the poor,
and since a person who cannot possibly act otherwise
than he does can claim no merit for his actions, it follows
that a thoroughly benevolent man can claim no merit for
his actions." According to this kind of argument a man
would have less merit in proportion as he was more
virtuous, so as to feel greater and greater difficulty in
acting wrongly. That the conclusion is fallacious every
one must feel certain, but the cause of the fallacy can
only be detected by observing that the words cannot
possibly have a double meaning, in the first case referring
to the influence of moral motives or good character, and
in the second to circumstances entirely beyond a person's
control ; as, for instance, the compulsion of the laws, the
want of money, the absence of personal liberty. The
more a person studies the subtle variations in the mean-
ing of common words, the more he will be convinced of
the dangerous nature of the tools he has to use in all

IV.] OF TERMS. 29

communications and arguments. Hence I must ask
much attention to the contents of this Lesson.

Terms are said to be univocal when they can suggest
to the mind no more than one single definite meaning.
They are called equivocal or ambiguous when they have
two or more diiTerent meanings. It will be observed,
however, that a term is not equivocal because it can be
apphed to many objects when it is applied in the same
sense or meaning to those different objects. Thus cathe-
dral is the name of St Paul's, the York Minster, and the
principal churches of Salisbury, Wells, Lincoln and a
number of other cities, but it is not ambiguous, because
all these are only various instances of the same meaning ;
they are all objects of the same description or kind.
The word cathedral is probably univocal or of one logical
meaning only. The word church, on the other hand, is
equivocal, because it sometimes means the building in
which religious worship is performed, sometimes the body
of persons who belong to one sect or persuasion, and
assemble in churches. Sometimes also the church
means the body of the clergy as distinguished from the
laity; hence there is a clear difference in the sense or
meaning with which the word is used at different times.

Instances of univocal terms are to be found chiefly in
technical and scientific language. Steam-engine, gas-
ometer, railway train, permanent way, and multitudes of
such technical names denoting distinct common objects,
are sufficiently univoca]. In common life the names
penny, mantelpiece, teacup, bread and butter, have a suf-
ficiently definite and single meaning. So also in chemistry^
oxygen, hydrogen, sulphate of copper, alumina, lithia,
and thousands of other terms, are very precise, the words
themselves having often been invented in very recent
years, and the meanings exactly fixed and maintained
invariable. Every science has or ought to have a series

30 OF THE AMBIGUITY [less.

of terms equally precise and certain in meaning. (See
Lesson XXXIII.) The names of individual objects, build-
ings, events, or persons, again, are usually quite certain
and clear, as in Julius Caesar, William the Conqueror, the
first Napoleon, Saint Peter's, Westminster Abbey, the ^
Great Exhibition of 185 1, and so on.

But however numerous may be the univocal terms
which can be adduced, still the equivocal terms are asto-
nishingly common. They include most of the nouns and ,
adjectives which are in habitual use in the ordinary
intercourse of life. They are called ambiguous from the
Latin verb ambigo, to wander, hesitate, or be in doubt; or
again homoiiyniotis, from the Greek o\xoi^ same, and ovofia,
name. Whenever a person uses equivocal words in such
a way as to confuse the different meanings and fall into
error, he may be said to commit the fallacy of Equivoca-
tion in the logical meaning of the name (see Lesson XX.) ;
but in common life a person is not said to equivocate -
unless he uses words consciously and deceitfully in a
manner calculated to produce a confusion of the true and
apparent meanings.

I will now describe the various kinds and causes of i
ambiguity of words, following to some extent the inter-
esting chapters on the subject in Dr Watts' Logic. In
the first place we may distinguish three classes of equi-
vocal words, according as they are — ^'

1. Equivocal in sound only.

2. Equivocal in spelling only.

3. Equivocal both in sound and spelling.

The first two classes are comparatively speaking of very
slight importance, and do not often give rise to serious
error. They produce what we should call trivial mis- .
takes. Thus we may confuse, when spoken only, the ^
words right, wright and rite (ceremony) ; also the words
rein, rain and reign, might and mite, &c. Owing partly

IV.] OF TERMS. 31

to defects of pronunciation mistakes are not unknown
between the four words air^ hair, hare and heir.

Words equivocal in spelling but not in sound are such
as tear (a drop), and tear pronounced tare, meaning a
rent in cloth ; or lead, the metal, and lead, as in follow-
ing the lead of another person. As little more than mo-
mentary misapprehension, however, can arise from such
resemblance of words, we shall pass at once to the class
of words equivocal both in sound and spelling. These I
shall separate into three groups according as the equivo-
cation arises —

1. From the accidental confusion of different words.

2. From the transfer of meaning by the association of

ideas.

3. From the logical transfer of meaning to analogous

objects.

I. Under the first class we place a certain number
of curious but hardly important cases in which ambi-
guity has arisen from the confusion of entirely different
words, derived from different languages or from differ-
ent roots of the same language, but which have in
the course of time assumed the same sound and spell-
ing. Thus the word mean denotes either that which
is mcdiiuii or mediocre, from the French vioyen and
the Latin mediiis, connected with the Anglo-Saxon
viid^ or middle J or it denotes what is low-minded and
base, being then derived from the Anglo-Saxon Gem(e?te,
which means " that belonging to the moene or many,"
whatever in short is vulgar. The verb to 7nea7i. can
hardly be confused with the adjective mean, but it comes
from a third distinct root, probably connected with the
Sanscrit verb, to think.

As other instances of this casual ambiguity, I may
mention rent, a money payment, from the French rente
prendre, to return), or a tear, the result of the action of

32 OF THE AMBIGUITY [less.

rending^ this word being of Anglo-Saxon origin and one
of the numerous class beginning in ror ivr, which imitate
more or less perfectly the sound of the action which they
denote. Pounds from the Latin poiidiis, a weight, is con-
fused with poinid, in the sense of a village pinfold for ,
cattle, derived from the Saxon pyndati^ to pen up. Fell,
a mountain, is a perfectly distinct word from fell, a skin ,
or hide; Sind ptilse, a throb or beating, and pt^lse, peas,
beans, or potage, though both derived from the Greek or 4
Latin, are probably quite unconnected words. It is
curious that gm, in the meaning of trap or machine, is a
contracted form of engine, and when denoting the spirit-
uous liquor is a corruption of Geneva, the place where the ^
spirit was first made.

Certain important cases of confusion have been de-
tected in grammar, as between the numeral 07ie, derived
from an Aryan root, through the Latin tmns, and the in-
determinate pronoun, one (as in ^'' otie ought to do oji^s
duty"), which is really a corrupt form of the French
word homme or man. The Germans to the present day
use man in this sense, as in man sagt, i.e. one says.

2. By far the largest part of equivocal words have ,
become so by a transfer of the meaning from the thing
originally denoted by the word to some other thing ,
habitually connected with it so as to become closely as-
sociated in thought. Thus, in Parliamentary language, k,»,
the House means either the chamber in which the mem-
bers meet, or it means the body of members who happen t
to be assembled in it at any time. Similarly, the word
chiirch originally denoted the building {KvpiaKov, the ■'
Lord's House) in which any religious worshippers assem-
ble, but it has thence derived a variety of meanings ; it '
may mean a particular body of worshippers accustomed ,
to assemble in any one place, in which sense it is used in
Acts xiv. 23 ; or it means any body of persons holding

IV.] OF TERMS. 33

the same opinions and connected in one organization, as
in the Anglican, or Greek, or Roman Catholic Church ;
it is also sometimes used so as to include the laity as well
as the clergy ; but more generally perhaps the clergy and
religious authorities of any sect or country are so strongly
associated with the act of worship as to be often called
the church /^r ^;ir^//^;/r^. It is quite evident moreover
that the word entirely differs in meaning according as it
is used by a member of the Anglican, Greek, Roman
Catholic, Scotch Presbyterian, or any other existing
church.

The word foot has suffered several curious but very
evident transfers of meaning. Originally it denoted the
foot of a man or an animal, and is probably connected in
a remote manner with the Latin pes, pedis, and the Greek
TTouy, TToSos- ; but since the length of the foot is naturally
employed as a rude measure of length, it came to be
applied to a fixed measure of length ; and as the foot is
at the bottom of the body the name was extended by
analogy to the foot of a mountain, or the feet of a table ;
by a further extension, any position, plan, reason, or
argument on which we place ourselves and rely, is called
the foot or footing. The same word also denotes soldiers
who fight upon their feet, or infantry, and the measured
part of a verse having a definite length. That these very
different meanings are naturally connected with the ori-
ginal meaning is evident from the fact that the Latin
and Greek words for foot are subject to exactly similar
series of ambiguities.

It would be a long task to trace out completely the
various and often contradictory meanings of the word
fellow. Originally a fellow was wh^t follows another, that
is a companion ; thus it came to mean the other of a pair,
as one shoe is the fellow of the other, or simply an equal,
as when we say that Shakspeare "hath not a fellow,"

3

34 OF THE AMBIGUITY [less.

From the simple meaning of companion again it comes
to denote vaguely a person, as in the question "What
fellow is that?" but then there is a curious confusion of
depreciatory and endearing power in the word ; when a
man is called a mere fellow, or simply a fellow in a par-
ticular tone of voice, the name is one of severe contempt ;
alter the tone of voice or the connected words in the least
degree, and it becomes one of the most sweet and en-
dearing appellations, as when we speak of a dear or
good fellow. We may still add the technical meanings of
the name as applied in the case of a Fellow of a College,
or of a learned society.

Another good instance of the growth of a number of
different meanings from a single root is found in the
word post. Originally a post was something posited, or
placed firmly in the ground, such as an upright piece of
wood or stone ; such meaning still remains in the cases
of a lamp-post, a gate-post, signal-post, &c. As a post
would often be used to mark a fixed spot of ground, as in
a mile-post, it came to mean the fixed or appointed place
where the post was placed, as in a military post, the post
of danger or honour, &c. The fixed places where horses
were kept in readiness to facilitate rapid travelling during
the times of the Roman empire were thus called posts,
and thence the whole system of arrangement for the con-
veyance of persons or news came to be called the posts.
The name has retained an exactly similar meaning to the
present day in most parts of Europe, and we still use it
in post-chaise, post-boy, post-horse and postillion. A
system of post conveyance for letters having been organ-
ised for about two centuries in England and other coun-
tries, this is perhaps the meaning most closely associated
with the word post at present, and a number of expres-
sions have thus arisen, such as post-office, postage, postal-
guide, postman, postmaster, postal-telegraph, &c. Curi-

IV.] OF TERMS. 35

ously enough we now have iron letter-posts, in which the
word post is restored exactly to its original meaning.

Although the words described above were selected on
account of the curious variety of their meanings, I do not
hesitate to assert that the majority of common nouns
possess various meanings in greater or less number. Dr
Watts, in his Logic, suggests that the words book, bible,
fish, house, and elephant, are univocal terms, but the
reader would easily detect ambiguities in each of them.
Thus fish bears a very different meaning in natural his-
tory from what it does in the mouths of unscientific per-
sons, who include under it not only true fishes, but shell-
fish or mollusca, and the cetacea, such as whales and
seals, in short all swimming animals, whether they have
the character of true fish or not. Elephant, in a station-
er's or bookseller's shop, means a large kind of paper
instead of a large animal. Bible sometimes means any
particular copy of the Bible, sometimes the collection
of works constituting the Holy Scriptures. The word
man is singularly ambiguous ; sometimes it denotes man
as distinguished from woman ; at other times it is cer-
tainly used to include both sexes ; and in certain recent
election cases lawyers were unable to decide whether the
word man as used in the Reform Act of 1867 ought or
ought not to be interpreted so as to include women. On
other occasions man is used to denote an adult male as
distinguished from a boy, and it also often denotes one
who is emphatically a jna7i as possessing a masculine
character. Occasionally it is used in the same way as
groom, for a servant, as in the proverb, " Like master,
like man." At other times it stands specially for a hus-
band.

3. Among ambiguous words we must thirdly distinguish
those which derive their various meanings in a somewhat
different manner, namely by analogy or real resemblance.

3—2

36 THE AMBIGUITY OF TERMS. [less. iv.

When we speak of a sweet taste, a sweet flower, a sweet
tune, a sweet landscape, a sweet face, a sweet poem, it is
evident that we apply one and the same word to very
different things ; such a concrete thing as lump-sugar can
hardly be compared directly with such an intellectual
existence as Tennyson's May Queen, Nevertheless if the
word sweet is to be considered ambiguous, it is in a dif-
ferent way from those we have before considered, because
all the things are called sweet on account of a peculiar
pleasure which they yield, which cannot be described
otherwise than by comparison with sugar. In a similar
way, we describe a pain as sharp, a disappointment as
bitter, a person's temper as sour, the future as bright or
gloomy, an achievement as brilliant ; all these adjectives
implying comparison with bodily sensations of the sim-
plest kind. The adjective b?-illiant is derived from the
French brillery to glitter or sparkle ; and this meaning it
fully retains when we speak of a brilliant diamond, a
brilliant star, &c. By what a subtle analogy is it that we
speak of a brilliant position, a brilliant achievement,
brilliant talents, brilliant style ! We cannot speak of a
clear explanation, indefatigable perseverance, perspicuous
style, or sore calamity, without employing in each of these
expressions a double analogy to physical impressions,
actions, or events. It will be shewn in the sixth Lesson
that to this process we owe the creation of all names
connected with mental feelings or existences.

Read Watts' Logic, Chapter iv.

hoc\<i€s Essay on the Hiutiati Understandings Book III.
Chapters IX, and X.

LESSON V.

OF THE TWOFOLD MEANING OF TERMS—
IN EXTENSION AND INTENSION.

There is no part of the doctrines of Logic to which I
would more urgently request the attention of the reader
than to that which I will endeavour to explain clearly in
the present Lesson. I speak of the double meaning
which is possessed by most logical terms — the meaning
in extension, and the meaning in intension, I believe
that the reader who once acquires a thorough apprehen-
sion of the difference of these meanings, and learns to
bear it always in mind, will experience but little further
difficulty in the study of logic.

The meaning of a term in extension consists of the
objects to wMch the term may he applied ; its meaning in
intension consists of the qualities ■which are necessarily
possessed by objects bearing that name. A simple example
will make this distinction most apparent. What is the
meaning of the name "metal".? The iirst and most ob-
vious answer is that metal means either gold, or silver, or
iron, or copper, or aluminium, or some other of the 48
substances known to chemists, and considered to have a
metallic nature. These substances then form the plain
and common meaning of the name, which is the meaning
in extension. But if it be asked why the name is applied
to all these substances and these only, the answer must
be — Because they possess certain qualities which belong
to the nature of metal. We cannot, therefore, know to
what substances we may apply the name, or to what we

38 TWOFOLD MEANING OF TERMS- [less.

may not, unless we know the qualities which are indis-
pensable to the character of a metal. Now chemists lay
these down to be somewhat as follows: — (i) A metal
must be an element or simple substance incapable of
decomposition or separation into simpler substances by
any known means. (2) It must be a good conductor of
heat and electricity. (3) It must possess a great and
peculiar reflective power known as metallic lustre*.

These properties are common to all metals, or nearly
all metals, and are what mark out and distinguish a
metal from other substances. Hence they form in a
certain way the meaning of the name metal, the meaning
in intension, as it is called, to distinguish it from the
former kind of meaning.

In a similar manner almost any other common name
has a double meaning. "Steamship" denotes in exten-
sion the Great Eastern, the Persia, the Himalaya, or any
one of the thousands of steamships existing or which
have existed; in intension it means "a vessel propelled
by steam-power." Monarch is the name of Queen Vic-
toria, Victor Emmanuel, Louis Napoleon, or any one of a
considerable number of persons who rule singly over
countries ', the persons themselves form the meaning in
extension ; the quality of ridiiig alone forms the intensive
meaning of the name. Animal is the name in extension
of any one of billions of existing creatures and of indefi-
nitely greater numbers of other creatures that have ex-
isted or will exist; in intension it implies in all those
creatures the existence of a certain animal life and sense,
or at least the power of digesting food and exerting force,
which are the marks of animal nature.

• It is doubtfully true that all metals possess metallic lustre,
and chemists would find it very difficult to give any consistent
explanation of their use of the name ; but the statements in the
text are sufficiently true to furnish un example.

v.] IN EXTENSION AND INTENSION, 39

It is desirable to state here that this distinction of
extension and intension has been explained by logi-
cians under various fornis of expression. It is the pe-
culiar misfortune of the science of logic to have a super-
fluity of names or synonyms for the same idea. Thus the
intension of a term is synonymous with its comprelien-
Bion, or connotation, or depth; while the extension is
synonymous with the denotation or breadth. This may
be most clearly stated in the form of a scheme : —

The extension, extent, The intension, intent,

breadth, denotation, do- depth, connotation, or im-

main, sphere or application plication of a name con-

of a name consists of the sists of the qualities the

individual things to which possession of which by those

the name applies. things is implied.

Of these words, denotation and connotation are employed
chiefly by Mr J. S. Mill among modern logical writers,
and are very apt for the purpose. To denote is to mark
down, and the name marks the things to which it may be
applied or affixed; thus metal denotes gold, silver, cop-
per, &c. To connote is to mark alofig with (Latin con,
together; notare, to mark), and the connotation accord-
ingly consists of the quahties before described, the pos-
session of which is implied by the use of the name metal.
When we compare different but related terms we may
observe that they differ in the quantity of their extension
and intension. Thus the term ele7Hent has a greater
extension of meaning than ?7tetal, because it includes in
its meaning all metals and other substances as well.
But it has at the same time less intension of meaning;
for among the qualities of a metallic substance must be
found the qualities of an element, besides the other
qualities peculiar to a metal. If again we compare the
terms inetal and vialleable metal, it is apparent that the

40 TWOFOLD MEANING OF TERMS— [less.

latter term does not include the metals antimony, arsenic,
and bismuth, which are brittle substances. Hence mal-
leable metal is a term of narrower meaning in extension
than metal ; but it has also deeper meaning in intension,
because it connotes or implies the quality of malleability
in addition to the general qualities of a metal. White
malleable metal is again a narrower term in extension
because it does not include gold and copper ; and I can
go on narrowing the meaning by the use of qualifying ad-
jectives until only a single metal should be denoted by
the term.

The reader will now see clearly that a general law of
great importance connects the quantity of extension and
the quantity of intension, viz. — As the intension of a term
is increased tlie extension Is decreased. It must not be
supposed, indeed, that there is any exact proportion be-
tween the degree in which one meaning is increased and
the other decreased. Thus if we join the adjective redX.o
metal we narrow the meaning much more than if we join
the adjective white, for there are at least twelve times
as many w^hite metals as red. Again, the term white
man includes a considerable fraction of the meaning of
the term man as regards extension, but the term blind
man only a small fraction of the meaning. Thus it is
obvious that in increasing the intension of a terra we may
decrease the extension in any degree.

In understanding this law we must carefully discrimi-
nate the cases where there is only an apparent increase of
the intension of a term, from those where the increase is
real. If I add the term elementary to m.etal, I shall not
really alter the extension of meaning, for all the metals
are elements ; and the elementary metals are neither
more nor less numerous than the metals. But then the
intension of the term is really unaltered at the same time ;
for the quality of an element is really found among the

v.] IN EXTENSION AND INTENSION. 41

K qualities of metal, and it is superfluous to specify it over
again. A quality which belongs invariably to the whole
of a class of things is commonly called a property of the
class (see Lesson xil.), and we cannot qualify or restrict

' a term by its own property.

This is a convenient place to notice a distinction be-
tween terms into those w^hich are connotative and those
which are non-connotative, the latter consisting of the
terms which simply denote things without implying any
knowledge of their qualities. As Mr Mill considers this
distinction to ?je one of great importance, it will be v/ell

, to quote his ov/n words*: —

"A non-connotative term is one which signifies a sub-
ject only, or an attribute only. A connotative term is
one which denotes a subject, and implies an attribute.
By a subject is here meant anything which possesses
attributes. Thus John, or London, or England, are

-names which signify a subject only. Whiteness, length,
virtue, signify an attribute only. None of these names,
therefore, are connotative. But ivhite, loitg, virtuous,
are connotative. The word white denotes all white

^things, as snow, paper, the foam of the sea, &c., and
implies, or, as it was termed by the schoolmen, coftnotes
the attribute tuhiteftess. The word white is not predi-
<:ated of the attribute, but of the subjects, snow, &c. ; but
when we predicate it of them, we imply, or connote, that

the attribute whiteness belongs to them

"All concrete general names are connotative. The

^word man, for example, denotes Peter, James, John, and
an indefinite number of other individuals, of whom, taken
as a class, it is the name. But it is applied to them, be-
cause they possess, and to signify that they possess, cer-

* System of Logic, Vol. I. p. 31, 6th ed. Book I. Chap. il.
§5.

42 TWOFOLD MEANING OF TERMS— [less.

tain attributes What we call men, are the subjects, .

the individual Styles and Nokes ; not the qualities by
which their humanity is constituted. The name therefore
is said to signify the subjects directly, the attributes in-
directly; it denotes the subjects, and implies, or involves,
or indicates, or, as we shall say henceforth^ connotes, the
attributes. It is a connotative name ....

" Proper names are not connotative : they denote the
individuals who are called by them ; but they do not indi-
cate or imply any attributes as belonging to those indivi-
duals. When we name a child by the name Paul, or a dog
by the name Caesar, these names are simply marks used
to enable those individuals to be made subjects of dis-
course. It may be said, indeed, that we must have had
some reason for giving them those names rather than
any others ; and this is true ; but the name, once given, is
independent of the reason. A man may have been named
John, because that was the name of his father ; a town
may have been named Dartmouth, because it is situ-
ated at the mouth of the Dart. But it is no part of the
signification of the word John, that the father of the per-
son so called bore the same name ; nor even of the word
Dartmouth to be situated at the mouth of the Dart. If
sand should choke up the mouth of the river, or an earth-
quake change its course, and remove it to a distance from
the town, the name of the town would not necessarily be
changed."

I quote this in Mr Mill's own words, because though
it expresses most clearly the view accepted by Mr Mill
and many others, it is nevertheless probably erroneous.
The connotation of a name is confused with the etymo-
logical meaning, or the circumstances which caused it to
be affixed to a thing. Surely no one who uses the name
England, and knows what it denotes, can be ignorant of
the peculiar qualities and circumstances of the country,

v.] IN EXTENSION AND INTENSION. 43

^and these form the connotation of the term. To any one
who knows the town Dartmouth the name must imply the
possession of the circumstances by which that town is cha-
racterised at the present time. If the river Dart should be
destroyed or removed, the town would so far be altered,
and the signification of the name changed. The name
would no longer denote a town situated on the Dart, but
one which \\2iS formerly situated on the Dart, and it would
'be by a mere historical accident that the form of the name
did not appear suitable to the town. So again any proper
name such as John Smith, is almost without meaning until
we know the John Smith in question. It is true that the
name alone connotes the fact that he is a Teuton, and
is a male ; but, so soon as we know the exact individual
it denotes, the name surely implies, also, the peculiar fea-
tures, form, and character, of that individual. In fact, as
it is only by the peculiar qualities, features, or circum-
.stances of a thing, that we can ever recognise it, no name
could have any fixed meaning unless we attached to it,
mentally at least, such a definition of the kind of thing
denoted by it, that we should know whether any given
thing was denoted by it or not. If the name John Smith
does not suggest to my mind the qualities of John Smith,
how shall I know him when I meet him.? for he certainly
does not bear his name written upon his brow *.

This, however, is quite an undecided question; and
as Mr Mill is generally considered the best authority upon
the subject, it may be well for the reader provisionally to
accept his opinion, that singular or proper names are
non-connotative, and all concrete general names are con-
aotative. Abstract names, on the other hand, can hardly

. * Further objections to Mr Mill's views on tin's point will
be found in Mr Shedden's Elements of Logic. London, 1864,
pp. 14, &c.

44 TWOFOLD MEANING OF TERMS, [less.
possess connotation at all, for as they already denote the
attributes or qualities of something, there is nothing left
which can form the connotation of the name. Mr Mill,
indeed, thinks that abstract names may often be consi-
dered connotative, as when the Vi2xaQ fault connotes the
attribute of hurtfulness as belonging to fault. But if
fault is a true abstract word at all I should regard hurt-
fulness as a part of its denotation ; I am inclined to think
Xh'a.tfaultiness is the abstract name, and that fault is gene-
rally used concretely as the name of a particular action or
thing that is faulty, or possesses faultiness. But the sub-
ject cannot be properly discussed here, and the reader
should note Mr Mill's opinion that abstract names are
usually non-connotative, but may be connotative in some
cases.

The subject of Extension and Intension may be pur-
sued in Hamilton's Lectures on Logic^ Lect. VIII. ;
or in Thomson's Laws of Tho7ight, Sections 48 to
52. It is much noticed in Spalding's Logic (Ency-
clopsedia Britannica, 8th ed.).

LESSON VI.
THE GROWTH OF LANGUAGE.

tt
I

i'

■fa
As
for

Words, we have seen, become equivocal in at least three ™
different ways — by the accidental confusion of different ?'*'
words, by the change of meaning of a word by itsf^^
habitual association with other things than its original
meaning, and by analogical transfer to objects of a similar
nature. We must however consider somewhat more
closely certain changes in language which ajise out of the

VI.] THE GROWTH OF LANGUAGE. 45

last cause, and which are in constant progress. We can
almost trace in fact the way in which language is created
and extended, and the subject is to the logician one of a
highly instructive and important character. There are
two great and contrary processes which modify language
as follows : —

1. Generalization, by which a name comes to be
applied to a wider class of objects than before, so that

»the extension of its meaning is increased, and the inten-
sion diminished.

2. Specialization, by which a name comes to be re-
stricted to a narrower class, the extension being decreased
and the intension increased.

The first change arises in the most obvious manner,
from our detecting a resemblance between a new object,
which is without a name, and some well-known object.
To express the resemblance we are instinctively led to
apply the old name to the new object. Thus we are well
acquainted with glass, and, if we meet any substance
having the same glassy nature and appearance, we shall be
apt at once to call it a kind of glass ; should we often meet
with this new kind of glass it would probably come to share
the name equally with the old and original kind of glass.
The word coal has undergone a change of this kind ; ori-
ginally it was the name of charked or charred wood, which
was the principal kind of fuel used five hundred years ago.
As mineral coal came into use it took the name from the
fonner fuel, which it resembled more nearly than any-
thing else, but was at first distinguished as sea-coal or
pit-coal. Being now far the more common of the two, it
has taken the simple name, and we distinguish charred
wood as charcoal. Paper has undergone a like change ;
originally denoting the papyrus used in the Roman Em-
pire, it was transferred to the new writing material made
Df cotton or linen rags, which was introduced at a quite

46 THE GROWTH OF LANGUAGE, [less.

uncertain period. The word cha7'acter is interesting on
account of its logical employment; the Greek x^P^*^"^^?
denoted strictly a tool for engraving, but it became trans-
ferred by association to the marks or letters engraved
with it, and this meaning is still retained by the word when
we speak of Greek chai'actersy Arabic characters^ i. e. figures
or letters. But inasmuch as objects often have natural
marks, signs, or tokens, which may indicate them as well
as artificial characters, the name was generalized, and now
means any peculiar or distinctive mark or quality by which
an object is easily recognised.

Changes of this kind are usually effected by no parti-
cular person and with no distinct purpose, but by a sort
of unconscious instinct in a number of persons using the
name. In the language of science, however, changes are
often made purposely, and with a clear apprehension of
the generalization implied. Thus soap in ordinary life
is applied only to a compound of soda or potash with
fat ; but chemists have purposely extended the name
so as to include any compound of a metalHc salt with a
fatty substance. Accordingly there are such things as
lime-soap and lead-soap^ which latter is employed in
making common diachylon plaster. Alcohol at first de-
noted the product of ordinary fermentation commonly
called spirits of wine, but chemists having discovered that
many other substances had a theoretical composition,
closely resembling spirits of wine, the name was adopted
for the whole class, and a long enumeration of different
kinds of alcohols will be found in Dr Roscoe's lessons
on chemistry. The number of known alcohols is likewise
subject to indefinite increase by the progress of discover}'.
Every one of the chemical terms acid, alkali, metal, alloy,
earth, ether, oil, gas, salt, may be shown to have under-
gone great generalizations. *

In other sciences there is hardly a less supply of

VI.] THE GROWTH OF LANGUAGE. 47

instances. A lens originally meant a lenticular shaped

'^or double convex piece of glass, that being the kind of
glass most frequently used by opticians. But as glasses
of other shapes came to be used along with lenses^ the
name was extended to concave or even to perfectly flat

' pieces of glass. The words lever, plane, cone, cylinder,
arc, conic section, curve, prism, magnet, pendulum, ray,
light, and many others, have been similarly generalized.

^ In common language we may observe that even
proper or singular names are often generalized, as when

, in the time of Cicero a good actor was called a Roscius
after an actor of preeminent talent. The name Caesar

» was adopted by the successor of Julius Caesar as an official
name of the Emperor, with which it gradually became
synonymous, so that in the present day the Kaisers of
Austria and the Czars of Russia both take their title from
Caesar. Even the abstract name Cassarism has been
formed to express a kind of imperial system as established

iDy Caesar. The celebrated tower built by a king of
Eg}^pt on the island of Pharos, at the entrance of the
harbourof Alexandria, has caused lighthouses to be called
phares in French, and pharos in obsolete English. From

'the celebrated Roman General Quintus Fabius Maximus
any one who avoids bringing a contest to a crisis is said
to pursue a Fabian policy.

.^ In science also singular names are often extended, as
when the fixed stars are called distant S2ms^ or the com-
<panions of Jupiter are called his 7noo?ts. It is indeed one
theory, and a probable one, that all general names were
-created by the process of generalization going on in the
early ages of human progress. As the comprehension of
general notions requires higher intellect than the appre-
hension of singular and concrete things, it seems natural
that names should at first denote individual objects, and
should afterwards be extended to classes. We have a

48 THE GROWTH OF LANGUAGE, [less.

glimpse of this process in the case of the Austrahan natives
who had been accustomed to call a large dog Cadli, but
when horses were first introduced into the country they
adopted this name as the nearest description of a horse.
A very similar incident is related by Captain Cook of the
natives of Otaheite. It may be objected, however, that a
certain process of judgment must have been exerted before
the suitability of a name to a particular thing could have
been perceived, and it may be considered probable tliat^
specialization as well as generalization must have acted
in the earliest origin of language much as it does at
present.

Specialization is an exactly opposite process to gene-
ralization and is almost equally important. It consists in
narrowing the extension of meaning of a general name, so
that it comes to be the name only of an individual or a
minor part of the original class. It is thus we are fur-
nished with the requisite names for a multitude of new
implements, occupations and ideas with which we deal irt^
advancing civilization. The name physician is derived
from the Greek (pvcnKos, natural, and (fivcrts, nature, so that
it properly means one who has studied nature, especially
the nature of the human body. It has become restricted,
however, to those who use this knowledge for medical
purposes, and the investigators of natural science have
been obliged to adopt the new n2.vi\Q. physicist. The name
fiaturalist has been similarly restricted to those who study
living things. The name surgeon originally meant-
handicraftsman, being a corruption of chirurgeon, derived
from the Greek ;Y«povpyos-, hand-worker. It has long been
specialized however to those who perform the mechanical
parts of the sanatory art.

Language abounds with equally good examples. Min-
ister originally meant a servant, or one who acted as §
viinor of another. Now it often means specially the most

VI.] THE GROWTH OF LANGUAGE, 49

important man in the kingdom. A chancellor was a clerk
or even a door-keeper who sat in a place separated by
bars or cancelli in the offices of the Roman Emperor's
palace; now it is always the name of a high or even the
highest dignitary. Peer was an equal (Latin, Par\ and
we still speak of being tried by our peers ; but now, by the
strange accidents of language, it means the few who are
superior to the rest of the Queen's subjects in rank.
Deacon, Bishop, Clerk, Queen, Captain, General, are all
words which have undergone a like process of specializa-
tion. In such words as telegraph, rail, signal, station,
and many words relating to new inventions, we may
trace the progress of change in a lifetime.

One effect of this process of specialization is very soon
to create a difference between any two words which happen
from some reason to be synonymous. Two or more words
are said to be synonymous (from the Greek avv^ with, and
ovo\ia^ name) when they have the same meaning, as in the
case, perhaps, of teacher and instructor, similarity and
resemblance, beginning and commencement, sameness
and identity, hypothesis and supposition, intension and
comprehension. But the fact is that words commonly
called synonymous are seldom perfectly so, and there are
almost always shades of difference in meaning or use,
which are explained in such works as Crabb's Eiiglish
Syno7iy7ns. A process called by Coleridge desynonjoni-
zation, and by Herbert Spencer dififerentiatlon, is always
going on, which tends to specialize one of a pair of
synonymous words to one meaning and the other to
another. Thus wave and billow originally meant exactly
the same physical effect, but poets have now appropriated
the word 'billow,' whereas wave is used chiefly in practical
and scientific matters. Undulation is a third synonym,
which will probably become the sole scientific term for
a wave in course of time. Cab was originally a mere

4

50 THE GROWTH OF LANGUAGE, [less.

abbreviation of cabriolet, and therefore of similar meaning,
but it is now specialized to mean almost exclusively a
hackney cab. In America car is becoming restricted to
the meaning of a railway car.

It may be remarked that it is a logical defect in a
language to possess a great number of synonymous terms,
since we acquire the habit of using them indifferently
without being sure that they are not subject to ambiguities
and obscure differences of meaning. The English lan-
guage is especially subject to the inconvenience of having
a complete series of words derived from Greek or Latin
roots nearly synonymous with other words of Saxon or
French origin. The same statement may, in fact, be
put into Saxon or classical English; and we often, as
Whately has well remarked, seem to prove a state-
ment by merely reproducing it in altered language. The
rhetorical power of the language may be increased by the
copiousness and variety of diction, but pitfalls are thus
prepared for all kinds of fallacies. (See Lessons XX
and XXI.)

In addition to the effects of generalization and speci-
alization, vast additions and changes are made in lan-
guage by the process of analogous or metaphorical exten-
sion of the meaning of words. This change may be said,
no doubt, to consist in generalization, since there must
always be a resemblance between the new and old appli-,
cations of the term. But the resemblance is often one of
a most distant and obscure kind, such as we should call
analogy rather than identity. All words used metapho-
rically, or as similitudes, are cases of this process of ex-,
tension. The name metaphor is derived from the Greek
words \Lira, over, and (^epeii/, to carry ; and expresses ap-
parently the transference of a word from its ordinary to a
peculiar purpose. Thus the old similitude of a ruler to
the pilot of the vessel gives rise to many metaphors, as;

VI.] THE GROWTH OF LANGUAGE. 51

in speaking of the Prime Minister being at the Helm of
the State. The word governor, and all its derivatives, is,
in fact, one result of this metaphor, being merely a corrupt
form oi guberjtator, steersman. The words compass, pole-
star, ensign, anchor, and many others connected with na-
vigation, are constantly used in a metaphorical manner.
From the use of horses and hunting we derive another
set of metaphors ; as, in taking the reins of government,
overturning the government, taking the bit between the
teeth, the Government Whip, being heavily weighted, &c.
■No doubt it might be shewn that every other familiar
occupation of life has furnished its corresponding stock
of metaphors.

It is easy to shew, however, that this process, besides
going on consciously at the present day, must have acted
throughout the history of language, and that we owe to
it almost all, or probably all, the words expressive of re-
fined mental or spiritual ideas. The very word spirit, now
the most refined and immaterial of ideas, is but the Latin
spirittis, a gentle breeze or breathing; and inspiration,
esprit, or wit, and many other words, are due to this me-
taphor. It is truly curious, however, that almost all the
words in different languages denoting mind or soul imply
the same analogy to breath. Thus, soul is from the
Gothic root denoting a strong wind or storm ; the Latin
words animus and aniina are supposed to be connected
with the Greek avefios, wind; ^//■ux'7 is certainly derived
from ylrvxoi, to blow ; irvevfia, air or breath, is used in the
New Testament for Spiritual Being ; and our word ghost
has been asserted to have a similar origin.

Almost all the terms employed in mental philosophy
or metaphysics, to denote actions or phenomena of mindj
are ultimately derived from metaphors. Apprehension is
the putting forward of the hand to take anything ; com-
prehension is the taking of things together in a handful ;

4—2

52 THE GROWTH OF LANGUAGE, [less.

extension is the spreading out ; intention, the bending to ;
exphcation, the unfolding ; application, the folding to ;
conception, the taking up together ; relation, the carrying
back ; experience is the thoroughly going through a thing ;
difference is the carrying apart ; deliberation, the weighing
out ; interruption, the breaking between ; proposition, the
placing before; intuition, the seeing into; and the list
might be almost indefinitely extended. Our English
name for reason, the understanding, obviously contains
some physical metaphor which has not been fully ex-
plained ; with the Latin intellect there is also a metaphor.

Every sense gives rise to words of refined meaning ;
sapience, taste, insipidity, gout, are derived from the sense
of taste ; sagacity, from the dog's extraordinary power of
, smell ; but as the sense of sight is by far the most acute
and intellectual, it gives rise to the larger part of lan-
guage ; clearness, lucidity, obscurity, haziness, perspicuity,
and innumerable other expressions, are derived from this
sense.

It is truly astonishing to notice the power which lan-
guage possesses by the processes of generalization, speci?
alization, and metaphor, to create many words from one
single root. Prof. Max Miiller has given a remarkable
instance of this in the case of the root spec^ which means
sight, and appears in the Aryan languages, as in the San-
scrit spas, the Greek a-KeTTToaai, with transposition of con-
sonants, in the Latin specio, and even in the English spy.
The following is an incomplete list of the words deve-
loped from this one root ; species, special, especial, speci-
men, spice, spicy, specious, speciality, specific, specializa-
tion, specie (gold, or silver), spectre, specification, spec-
tacle, spectator, spectral, spectrum, speculum, specular,
speculation. The same root also enters into composi-
tion with various prefixes; and we thus obtain a series
of words, suspect, aspect^ circumspect, expect, inspect,

VI.] THE GROWTH OF LANGUAGE. 53

prospect, respect, retrospect, introspection, conspicuous,
perspicuity, perspective; with each of which, again, a
number of derivatives is connected. Thus, from suspect,
we derive suspicion, suspicable. suspicious, suspiciously,
suspiciousness. I have estimated that there are in all
at least 246 words, employed at some period or other in
the English language which undoubtedly come from the
one root spec.

J. S, Mill's Logic, Book iv. Chap. v. * On the Natural
History of the Variations in the Meanings of Terms.*
Archbishop Trench, Oil the Study of Words.
Max Miiller, Lectures on the Science of Language.

LESSON VII.

LEIBNITZ ON KNOWLEDGE.

In treating of terms it is necessary that we should clearly
understand what a perfect notion of the meaning of a
term requires. When a name such as monarch, or civili-
zation, or aiitonoiny is used, it refers the mind to some
thing or some idea, and we ought if possible to obtain
a perfect knowledge of the thing or idea before we use
the word. In what does this perfect knowledge consist?
What are its necessary characters.? This is a question
which the celebrated mathematician and philosopher
Leibnitz attempted to answer in a small treatise or tract
first published in the year 1684. This tract has been the
basis of what is given on the subject in several recent
works on Logic, and a complete translation of the tract

54 LEIBNITZ ON KNOWLEDGE. [less.-

has been appended by Mr Baynes to his translation of
the Port Royal Logic. As the remarks of Leibnitz him-
self are not always easy to understand, I will not confine
myself to his exact words, but will endeavour to give the
simplest possible statement of his views, according as
they have been interpreted by Dr Thomson or Sir W.
Hamilton.

Knowledge is either obscure or clear; either confused
or distinct; either adequate or inadequate; and lastly
either symbolical or intuitive. Perfect knowledge must
be clear, distinct, adequate and intuitive ; if it fails in any
one of these respects it is more or less imperfect. We
may, therefore, classify knowledge as in the following
scheme : —

Knowledge.

■ ' Clear.

Obscure.

Distinct.

Confused.

Adequate.

Inadequate.

ntuitive.
Perfect.

Symbolical.

A notion, that is to say our knowledge of a thing, is
obscure when it does not enable us to recognize the thing
again and discriminate it from all other things. We
have a clear notion of a rose and of most common flowers
because we can recognise them with certainty, and do not
confuse them with each other. Also we have a clear
notion of any of our intimate friends or persons whom we
habitually meet, because we recognise them whenever we
see them with the utmost certainty and without hesita-
tion. It is said that a shepherd acquires by practice a
clear notion of each sheep of his flock, so as to enable
him to single out any one separately, and a keeper of

VII.] LEIBNITZ ON KNOWLEDGE. 55

hounds learas the name and character of each hound,
while other persons have only an obscure idea of the
hounds generally, and could not discriminate one from
the other. But the geologist cannot give a clear idea of
what sandstone, conglomerate, or schist, or slate, or trap
rock consists, because different rocks vary infinitely in
degree and character, and it is often barely possible to
say whether a rock is sandstone or conglomerate, schist
or slate, and so on. In the lower forms of life the natu-
ralist hardly has a clear notion of animal life, as distin-
guished from vegetable hfe; it is often difficult to decide
whether a protophyte should be classed with animals or
plants.

Clear knowledge, again, is confused, when we cannot
distinguish the parts and qualities of the thing known,
and can only recognise it as a whole. Though any one
instantly knows a friend, and could discriminate him from
all other persons, yet he would generally find it impos-
sible to say how he knows him, or by what marks. He
could not describe his figure or features, but in the very
roughest manner. A person unpractised in drawing, who
attempts to delineate even such a familiar object as a
horse or cow, soon finds that he has but a confused notion
of its form, while an artist has a distinct idea of the form
of every limb. The chemist has a distinct as well as a
clear notion of gold and silver, for he can not only tell
with certainty whether any metal is really gold or silver,
but he can specify and describe exactly the qualities by
which he knows it ; and could, if necessary, mention a
great many other qualities as well. We have a very dis-
tinct notion of a chess-board, because we know it consists
of 64 square spaces ; and all our ideas of geometrical
figures, such as triangles, circles, parallelograms, squares,
pentagons, hexagons, (Sic. are or ought to be perfectly dis-,
tinct. But when we talk of a constihitional government^

56 LEIBNITZ ON KNOWLEDGE. [less.

or a civilized nation, we have only the vaguest idea of
what we mean. We cannot say exactly what is requisite
to make a Government constitutional, without including
also Governments which we do not intend to include ;
and so of civilized nations; these terms have neither dis-.
tinct nor clear meanings.

It is to be remarked that no simple idea, such as that
of red colour, can be distinct in the meaning here in-
tended, because nobody can analyse red colour, or de-
scribe to another person what it is. A person who has
been blind from birth cannot be made to conceive it ; and
it is only by bringing an actual red object before the eye
that we can define its character. The same is generally
true of all simple sensations, whether tastes, smells, co-
lours, or sounds; these then may be clearly known, but
not distijictly, in the meaning which Leibnitz gives to this
word.

To explain the difference which Leibnitz intended to
denote by the names adequate and inadequate, is not
easy. He says, "When everything which enters into a
distinct notion is distinctly known, or when the last ana-
lysis is reached, the knowledge is adequate, of which I
scarcely know whether a perfect example can be offered
—the knowledge of numbers, however, approaches near
to it."

To have adequate knowledge of things, then, we must
not only distinguish the parts which make up our notion
of a thing, but the parts which make up those parts. For
instance, we might be said to have an adequate notion of
a chess-board, because we know it to be made up of 64
squares, and we know each of those squares distinctly,
because each is made up of 4 equal right lines, joined
at right angles. Nevertheless, we cannot be said to have
a distinct notion of a straight line, because we cannot well
define it, or resolve it into anything simpler. To be com-

.- VIL] LEIBNITZ ON KNOWLEDGE. 57

^ pletely adequate, our knowledge ought to admit of analysis
after analysis ad injiftitufn, so that adequate knowledge
would be impossible. But, as Dr Thomson remarks, we
may consider any knowledge adequate which carries the
analysis sufficiently far for the purpose in view. A me-
chanist, for instance, has adequate knowledge of a ma-

'■ chine, if he not only know its several wheels and parts,
but the purposes, materials, forms, and actions of those

' parts; provided again that he know all the mechanical
properties of the materials, and the geometrical properties
of the forms which may influence the working of the
machine. But he is not expected to go on still further and
explain why iron or wood of a particular quality is strong
or brittle, why oil acts as a lubricator, or on what axioms
the principles of mechanical forces are founded.

Lastly, we must notice the very important distinction

^ of symbolical and intuitive knowledge. From the original

, meaning of the word, intuitive would denote that which
we gain by seehig (Latin, intueor, to look at), and any
knowledge which we have directly through the senses,
or by immediate communication to the mind, is called
intuitive. Thus we may learn intuitively what a square
or a hexagon is, but hardly what a chiliagon, or figure of

- 1000 sides, is.

We could not tell the difference by sight of a figure

' of 1000 sides and a figure of icxdi sides. Nor can we
imagine any such figure completely before the mind. It
is known to us only by name or symbolically. All large
numbers, such as those which state the velocity of light
(186,000 miles per second), the distance of the sun
(91,000,000 miles), and the like, are known to us only by
symbols, and they are beyond our powers of imagination.
Infinity is known in a similar way, so that we can in
an intellectual manner become acquainted with that of
which our senses could never inform us. We speak also

58 LEIBNITZ ON KNOWLEDGE, [less;

of nothings of zero, of that which is self-cofiiradictory,
of the 7ion-existent, or even of the unthinkable or incon-
ceivable, akhough the words denote what can never be
realized in the mind and still less be perceived through
the senses intuitively, but can only be treated in a merely
symbolical way.

In arithmetic and algebra we are chiefly occupied
with symbolical knowledge only, since it is not necessary
in working a long arithmetical question or an algebraical
problem that we should realise to ourselves at each step
the meaning of the numbers and symbols. We learn
from algebra that if we multiply together the sum and
difference of two quantities we get the difference of the
squares ; as, in symbols

{a^b)[a-b) = a^-b'^)
which is readily seen to be true, as follows :

a-\-b
a — b

d'- + ab
-ab-b^

d' + o -bK

In the above we act darkly or symbolically, using the
letters a and b according to certain fixed rules, without
knowing or caring what they mean ; and whatever mean-'
ing we afterwards give to a and b we may be sure the
process holds good, and that the conclusion is true with-
out going over the steps again.

But in geometry, we argue by intuitive perception of
the truth of each step, because we actually employ a re-
presentation in the mind of the figures in question, and
satisfy ourselves that the requisite properties are really
possessed by the figures. Thus the algebraical truth
shown above in symbols may be easily proved to hold true

^vii.] LEIBNITZ ON KNOWLEDGE, 59*

^ of lines and rectangles contained under those lines, as a
corollary of the 5th Prop, of Euclid's Second Book.

Much might be said concerning the comparative ad-
vantages of the intuitive and symbolical methods. The

i latter is usually much the less laborious, and gives the
most widely applicable answers ; but the symbolical sel-
dom or never gives the same command and comprehen-
sion of the subject as the intuitive method. Hence the

^ study of geometry is always indispensable in education,
although the same truths are often more readily proved
by algebra. It is the peculiar glory of Newton that he
was able to explain the motions of the heavenly bodies
by the geometric or intuitive method ; whereas the great-
est of his successors, such as Lagrange or Laplace, have
treated these motions by the aid of symbols.

What is true of mathematical subjects may be applied

• to all kinds of reasoning ; for words are symbols as much

. as ^, B, C, or x, _y, z, and it is possible to argue with
words without any consciousness of their meaning. Thus
if I say that " selenium is a dyad element, and a dyad
element is one capable of replacing two equivalents of
hydrogen," no one ignorant of chemistry will be able to
attach any meaning to these terms, and yet any one will

f be able to conclude that " selenium is capable of replacing
two equivalents of hydrogen." Such a person argues in a
purely symbolical manner. Similarly, whenever in com-
mon life we use words, without having in mind at the
moment the full and precise meaning of the words, we
possess symbolical knowledge only.

There is no worse habit for a student or reader to
acquire than that of accepting words instead of a know-
ledge of things. It is perhaps worse than useless to read
a work on natural history about Infusoria, Foraminifera,,
Rotifera and the like, if these names do not convey clear
images to the mind. Nor can a student who has not,

6o LEIBNITZ ON KNOWLEDGE. [less.

witnessed experiments, and examined the substances with
his own eyes, derive any considerable advantage from
works on chemistry and natural philosophy, where he will
meet with hundreds of new terms which would be to him
mere empty and confusing signs. On this account we
should lose no opportunity of acquainting ourselves, by
means of our senses, with the forms, properties and
changes of things, in order that the language we employ
may, as far as possible, be employed intuitively, and we
may be saved from the absurdities and fallacies into
which we might otherwise fall. We should observe, in
short, the advice of Bacon — ipsis consuescere rebus — ■
to accustom ourselves to things themselves.

Hamilton's Lectures on Logic. Lect. IX.
Baynes' Port Royal Logic. Part I. Chap. 9, and Ap-
pendix.

LESSON VIII.
KINDS OF PROPOSITIONS.

A TERM Standing alone is not capable of expressing truth;
it merely refers the mind to some object or class of objects,
about which something may be affirmed or denied, but
about which the term itself does not affirm or deny any-
thing. "Sun," "air," "table," suggest to every mind
objects of thought, but we cannot say that " sun is true,"
or " air is mistaken," or " table is false." We must join
words or terms into sentences or propositions before they
can express those reasoning actions of the mind to which

- VIII.] KINDS OF PROPOSITIONS. 6i

truth or falsity may be attributed. " The sun is bright,"
" the air is fresh," " the table is unsteady," are statements
which may be true or may be false, but we can certainly
entertain the question of their truth in any circumstances,

I Now as the logical term was defined to be any combina-
tion of words expressing an act of simple apprehension,
• so a logical proposition is any combination of words
expressing an act of judgment. The proposition is in

'' short the result of an act of judgment reduced to the form
of language.

What the logician calls a proposition the grammarian
calls a sentence. But though every proposition is a sen-
tence, it is not to be supposed that every sentence is a
proposition. There are in fact several kinds of sentences
more or less distinct from a proposition, such as a Sen-
tence Interrogative or Question, a Sentence Imperative
or a Command, a Sentence Optative, which expresses a

. wish, and an Exclamatory Sentence, which expresses an
emotion of wonder or surprise. These kinds of sentence
may possibly be reduced, by a more or less indirect mode
of expression, to the form of a Sentence Indicative, which
is the grammatical name for a proposition ; but until this
be done they have no proper place in Logic, or at least

- no place which logicians have hitherto sufficiently ex-
plained.

The name proposition is derived from the Latin words
pro, before, and pono, I place, and means the laying or
placing before any person the result of an act of judg-
ment. Now every act of judgment or comparison must
involve the two things brought into comparison, and
every proposition will naturally consist of three parts—
the two terms or names denoting the things compared,
and the copula or verb indicating the connection between
them, as it was ascertained in the act of judgment. Thus
the proposition, " Gold is a yellow substance," expresses

62 KINDS OF PROPOSITIONS. [less:

an agreement between gold and certain other substances
previously called yellow in regard to their colour. Gold
and yellow substance are evidently the two terms, and is
the copula.

It is always usual to call the first term of a proposi-
tion the subject, since it denotes the underlying' matter,
as it were (Latin, sub, under, and Jacttim, laid) about
which something is asserted. The second term is called
the predicate, whi-ch simply means that which is affirmed
or asserted. This name is derived from the Latin pra-
dlcare, to assert, whence comes the French name predi-
cateiir, corrupted into our preacher. This Latin verb is
not to be confused with the somewhat similar one pre-
dicercj which has the entirely different meaning to pre'_
diet or foretell. I much suspect that newspaper writers
and others, who pedantically use the verb "to predi-
cate," sometimes fall into this confusion, and really mean
to predict, but it is in any case desirable that a purely
technical term like predicate should not be needlessly
introduced into common language, when there are so
many other good words which might be used. This and
all other technical scientific terms should be kept to their
proper scientific use,^ and the neglect of this rule injures
at once the language of common life and the language of
science.

Propositions are distinguished into two kinds, accord-
ing as they make a statement conditionally or uncondi-
tionally. Thus the proposition, " If metals are heated
they are softened," is conditional, since it does not make
an assertion concerning metals generally, but only in the
"circumstances when they become heated. Any circum-
stance which must be granted or supposed before the
assertion becomes applicable is a condition. Conditional
propositions are of two kinds, Hypothetical and Disjuncr
thve, but their consideration will, be bes$ deferred to a

viii.] KINDS OF PROPOSITIONS. 63

subsequent Lesson (xix). Unconditional propositions
are those with which we shall for some time be solely
concerned, and these are usually called Categorical Pro-
positions, from the Greek verb /car/^yopeo) {kategoreo^ to
assert or affirm).

The following diagram will conveniently represent the
classification of sentences and propositions as far as we
have yet proceeded : —

Indicative ^ r Categorical ,„ , . ,
= Proposition .^ ^ T- • 1 J HypotneticaL
Sentence •! I"'^"-°g="ive ^ Conditional | Disjunctive.

Imperative

Optative

Exclamatory

It is now necessary to consider carefully the several
kinds of ' categorical propositions. They are classified
according to quality and according to quantity. As re-
gards quality they are either affirmative or negative ; as
regards quantity they are either universal or particular.

An aflrmative proposition is one which asserts a cer-
tain agreement between the subject and predicate, so that
the quahties or attributes of the predicate belong to the
subject. The proposition, "gold is a yellow substance,"
states such an agreement of gold with other yellow sub-
stances, that we know it to have the colour yellow, as
well as whatever qualities are implied in the name sub-
stance. A negative proposition, on the other hand, as-
serts a difference OT discrepancy, so that some at least of
the qualities of the predicate do not belong to the sub-
ject. "Gold is not easily fusible" denies that the qua-
lity of being easily fused belongs to gold.

Propositions are again divided according to quantity
into universal and particular propositions. If the propo-
sition affirms the predicate to belong to the whole of the
subject, it is an universal proposition, as in the example

64 KINDS OF PROPOSITIONS. [lESS.

" all metals are elements," which affirms that the quality
of being undecomposable or of being simple in nature is
true of all metals. But if we say " some metals are brit-
tle," the quality of brittleness is affirmed only of some
indefinite portion of the metals, and there is nothing in
the proposition to make us sure that any certain metal is
brittle. The name particular being derived from the
diminutive of the Latin pars would naturally signify a
small part, but in logic it must be carefully interpreted as
signifying any part, from the smallest fraction up to
nearly the whole. Particular propositions do not include
cases where a predicate is affirmed of the whole or of
none of the subject, but they include any between these
limits. We may accordingly count among particular
propositions all such as the following : —

A very few metals are less dense than water.

Most elements are metals.

Many of the planets are comparatively small bodies.

Not a few distinguished men have had distinguished
sons.

The reader must carefully notice the somewhat subtle
point explained further on, that the particular proposition
though asserting the predicate only of a part of the sub-
ject, does not deny it to be true of the whole.

Aristotle, indeed, considered that there were alto-
gether four kinds of proposition as regards quantity,
namely —

r Universal.
Particular.
Singular.
Indefinite.

The singular proposition is one which has a singular
term for its subject, as in —

Socrates was very wise.
London is a vast city.

Proposition

, viii.] KINDS OF PROPOSITIONS. 65

But we may fairly consider that a singular proposition
is an universal one ; for it clearly refers to the whole of
the subject, which in this case is a single individual thing.
Indefinite or indesignate propositions are those which
are devoid of any mark of quantity whatever, so that the
form of words gives us no mode of judging whether the

. predicate is applicable to the whole or only part of the
subject. Metals are useftil^ Comets are subject to the law

> of gravitatio7t, are indefinite propositions. In reality,
however, such propositions have no distinct place in
logic at all, and the logician cannot properly treat them
until the true and precise meaning is made apparent.
The predicate must be true either of the whole or of part
of the subject, so that the proposition, as it stands, is
clearly incomplete ; but if we attempt to remedy this and
supply the marks of quantity, we overstep the proper

"boundaries of logic and assume ourselves to be acquainted
with the subject matter or science of which the proposi-

" tion treats. We may safely take the preceding examples
to mean ^^ so?ne metals are useful" and ^^ all cornets are
subject to the law of gravitation," but not on logical
grounds. Hence we may strike out of logic altogether
the class of indefinite propositions, on the understanding

^that they must be rendered definite before we treat them.
I may observe, however, that in the following lessons I

•( shall frequently use propositions in the indefinite form as
examples, on the understanding that where no sign of

, quantity appears, the universal quantity is to be assumed.
It is probable that wherever a term is used alone, it
ought to be interpreted as meaning the whole of its class.
But however this may be, we need not recognize the inde-

^finite proposition as a distinct kind ; and singular propo-
sitions having been resolved into universals, there remain
only the two kinds, Universal and Particular.

Remembering now that there are two kinds of propo-

5

66 KINDS OF PROPOSITIONS. [less.

sition as regards quality, and two as regards quantity, we
shall be able to form altogether four varieties, thus : —

Proposition

Universal 1^,^^"^.^^^^^ ^

\_ Negative E

Particular/Affirmative I

L Negative 0

The vowel letters placed at the right hand are sym-
bols or abbreviated names, which are always used to
denote the four kinds of proposition; and there will be
no difficulty in remembering their meaning if we observe
that A and I occur in the Latin verb affinno, I affirm, and
E and 0 in nego, I deny.

There will not generally be any difficulty in referring
to its proper class any proposition that we meet with in
writings. The mark of universality usually consists of
some adjective of quantity, such as all, every, each, any,
nonej but whenever the predicate is clearly intended
to apply to the whole of the subject we may treat the pro-
position as universal. The signs of a particular proposi-
tion are the adjectives of quantity, some, certain, a few,
many, most, or such others as clearly indicate part at
least.

The negative proposition is known by the adverbial
particle not being joined to the copula; but in the propo-
sition E, that is the universal negative, we frequently use
the particle no or none prefixed to the subject Thus,
" no metals are compound," " 7ione of the ancients were
acquainted with the laws of motion," are familiar forms of
the universal negative.

The student must always be prepared too to meet with
misleading or ambiguous forms of expression. Thus the
proposition, " all the metals are not denser than water,"
might be taken as E or 0, according as we interpret it to

"" viiL] KINDS OF PROPOSITIONS. 67

mean "no metals are denser than water," or "not all
the metals," &c., the last of course being the true sense.
The little adjective few is very subject to a subtle am-
biguity of this kind ; for if I say '■'■few books are at once
learned and amusing," I may fairly be taken to assert
that a few books certainly are so, but what I really mean
to draw attention to is my belief that '■Hhe greater Clum-
ber of books are not at once learned and amusing." A
proposition of 'this kind is generally to be classed rather
as 0 than I. The word some is subject to an exactly
similar ambiguity between some but not all, and some at
least, it 7nay be all; the latter appears to be the coiTect
interpretation, as shewn in the following lesson (p 79).

As propositions are met with in ordinary language
they are subject to various inversions and changes of the
* simple logical form.

(i) It is not uncommon, especially in poetry, to find
the predicate placed first, for the sake of emphasis or
variety ; as in " Blessed are the merciful ;" " Comes some-
thing down with eventide ;" " Great is Diana of the Ephe-
sians." There is usually no difficulty in detecting such
an inversion of the terms, and the sentence must then
^ be reduced to the regular order before being treated in
logic.

(2) The subject may sometimes be mistaken for the
predicate when it is described by a relative clause, stand-
ing at the end of the sentence, as in " no one is free who
is enslaved by his appetites." Here free is evidently
the predicate, although it stands in the middle of the
sentence, and "one who is enslaved by his appetites"
^ is the real subject. This proposition is evidently of the
form E,

Propositions are also expressed in various modes dif-
fering from the simple logical order, and some of the
different kinds which arise must be noticed.

5-2

68 KINDS OF PROPOSITIONS. [less.

Exclusive propositions contain some words, such" as
only^ alo7te, 7i07ie but, which limit the predicate to the
subject. Thus, in " elements alone are metals," we are
informed that the predicate "metal" cannot be applied to
anything except "elements," but we are not to understand
that " all elements are metals." The same meaning is
expressed by "none but elements are metals;" or, again,
by " all that are not elements are not metals ;" and this we
shall see in the next lesson is really equivalent to "all
metals are elements." Arguments which appear fallacious
at first sight will often be found correct when they con-
tain exclusive propositions and these are properly inter-
preted.

Exceptive propositions affirm a predicate of all the
subject with the exception of certain defined cases, to
which, as is implied, the predicate does not belong. Thus,
" all the planets, except Venus and Mercury, are beyond
the earth's orbit," is a proposition evidently equivalent to
two, viz. that Venus and Mercury are not beyond the
earth's orbit, but that the rest are. If the exceptions
are not actually specified by name an exceptive proposi-
tion must often be treated as a particular one. For if
I say " all the planets in our system except one agree with
Bode's law," and do not give the name of that one excep-
tion, the reader cannot, on the ground of the proposition,
assert of any planet positively that it does agree with
Bode's law.

Some propositions are distinguished as explicative or
essential, because they merely affirm of their subject a
predicate which is known to belong to it by all who can
define the subject. Such propositions merely unfold ^
what is already contained in the subject. "A parallelo-
gram has four sides and four angles," is an explicative or
essential proposition. "London, which is the capital of
England, is the largest city of Europe," contains two pro-

. VIII.] KINDS OF PROPOSITIONS. 69

positions ; of which one merely directs our attention to
a fact which all may be supposed to know, viz. that
London is the capital of England.

AmpUative propositions, on the other hand, join a
new predicate to the subject. Thus to those who do not
know the comparative sizes of cities in Europe, the last

. example contains an ampliative proposition. The greater
number of propositions are of this kind.

Tautologous or Truistic propositions are those which
merely affirm the subject of itself, and give no informa-
tion whatever ; as in, " whatever is, is ;" " what I have
written, I have written."

It is no part of formal Logic to teach us how to inter-
pret the meanings of sentences as we meet them in writ-
ings ; this is rather the work of the grammarian and
philologist Logic treats of the relations of the different

" propositions, and the inferences which can be drawn from
them; but it is nevertheless desirable that the reader
should acquire some familiarity with the real logical
meaning of conventional or peculiar forms of expression,
and a number of examples will be found at the end of
the book, which the reader is requested to classify and
treat as directed.

In addition to the distinctions already noticed it has
long been usual to distinguish propositions as they are
pure or modaL The pure proposition simply asserts that
the predicate does or does not belong to the subject, while
the modal proposition states this cmn modo, or with an
intimation of the mode or manner in which the predicate
belongs to the subject. The presence of any adverb of
time, place, manner, degree, &c., or any expression equi-
valent to an adverb, confers modality on a proposition.
"Error is always in haste;" "justice is ever equal;" "a
perfect man ought always to be conquering himself," are
examples of modal propositions in this acceptation of

70 KINDS OF PROPOSITIONS. [less.

the name. Other logicians, however, have adopted a
different view, and treat modality as consisting in the
degree of certainty or probability with which a judgment
is made and asserted. Thus, we may say, " an equilateral
triangle is 7iecessarily equiangular ;" " men are generally
trustworthy;" "a falling barometer /r<?(5«<^/)/ indicates a
coming storm ;" "Aristotle's lost treatises may possibly be
recovered ;" and all these assertions are made with a dif-
ferent degree of certainty or modality. Dr Thomson is
no doubt right in holding that the modality does not
affect the copula of the proposition, and the subject could
only be properly treated in a work on Probable Reason-
ing.

Many logicians have also divided propositions ac-
cording as they are true or false, and it might well seem
to be a distinction of importance. Nevertheless, it is
wholly beyond the province of the logician to consider
whether a proposition is true or not in itself; all that he
has to determine is the comparative truth of propositions
— that is, whether one proposition is true when another
is. Strictly speaking, logic has nothing to do with a pro-
position by itself; it is only in converting or transmuting
certain propositions into certain others that the work of
reasoning consists, and the truth of the conclusion is only
so far in question as it follows from the truth of what we
shall call the premises. It is the duty of the special sci-
ences each in its own sphere to determine what are true
propositions and what are false, and logic would be but
another name for the whole of knowledge could it take
this duty on itself.

See Mr Mill's System of Logic, Book I. Chap. iv.
which generally agrees with what is given above. Chap-
ters V. and VI. contain Mr Mill's views on the Nature
and Import of Propositions, which subject may be further

IX.] THE OPPOSITION OF PROPOSITIONS. 71

studied in Mr Mill's Examination of Sir W. HamiltorCs
Philosophy^ Chap, xviil. ; Hamilton's Lectures on Logic^
No. XIII.; and Hansel's Prolegojnena Logica^ Chap. II.;
but the subject is too metaphysical in character to be
treated in this work.

LESSON IX.

THE OPPOSITION OF PROPOSITIONS.

We have ascertained that four distinct kinds of propo-
sitions are recognized by logicians, — the Universal affirm-
ative, the Particular affirmative, the Universal negative,
and the Particular negative, commonly indicated by the
symbols A, I, E, 0. It is now desirable to compare toge-
ther somewhat minutely the meaning and use of proposi-
tions of these various kinds, so that we may clearly learn
how the truth of one will affect the truth of others, or how
the same truth may be thrown into various forms of ex-
pression.

The proposition A expresses the fact that the thing or
class of things denoted by the subject is included in, and
forms part of the class of things denoted by the predicate.
Thus " all metals are elements " means that metals form
a part of the class of elements, but not the whole. As
there are altogether 63 known elements, of which 48 are
metals, we cannot say that all elements are metals. The
proposition itself does not tell us anything about elejnents
in general; it is not in fact concerned with elements,
metals being the subject about which it gives us informa-

72 THE OPPOSITION [LESS.

tion. This is best indicated by a kind of diagram, first
used by the celebrated mathematician Euler, in his letters
to a German princess. In Fig. i, the metals are supposed
to be enclosed in the small circle somewhat as sheep
might be in a pinfold, this circle containing all the metals
and nothing else. The greater circle is supposed to con-
tain in a similar manner all the elements and nothing
else. Now as the small circle is wholly within the larger
one, it follows that all the metals must be counted as

Fig. X.

elements, but of the part of the elements outside the
circle of metals we know nothing from the proposition.

The paxticulax afarmative proposition I exactly resem-
bles A in meaning, except that only part of the subject is
brought into question. When I say that " some metals
are brittle," I mean that of a collection of all the dif-
ferent metals a few at least might be picked out which
would be found to be brittle ; but the word some is ex-
ceedingly indefinite, shewing neither the exact number of
brittle metals, nor how we are to know them from the
others, unless indeed by trying whether they are brittle.
This proposition will be properly represented in Euler's
mode by two intersecting circles, one supposed to enclose
all metals, and the other all brittle substances. The
mere fact of the two circles intersecting proves that some

rx.]

OF PROPOSITIONS.
Fig. 1.

73

part of one class must coincide with some part of the
other class, which is what the proposition is intended to
express. Concerning the portions of the circles which do
not overlap the proposition tells us nothing.

The universal negative proposition E denies the ex-
istence of any agreement or coincidence between the sub-
ject and predicate. Thus from " no metals are compound
substances," we learn that no metal is to be found among
compound substances, and it follows necessarily that no
compound substance can be found among the metals.
For were there a compound substance among the metals,
there would evidently be one metal at least among the
compound substances. This entire separation in thought
of the two classes is well shewn in Euler's method by
two disconnected circles.

Fig. 3.

The reader will easily see that the proposition E is

74 '^HE OPPOSITION [less.

distinguished from A and I, by the fact that it gives us
some information concerning the whole of the predicate,
because we learn that none of the objects included in the
predicate can be found among those included in the sub-
ject. The affirmative propositions, on the other hand,
warranted us in holding that the objects denoted by the
subject, or some particular part of them, were included in
the predicate, but they give us no warrant for saying
that any specified part of the predicate is in the subject.
Because we merely know that a substance is an element,
we do not learn from the proposition " all metals are ele-
ments" whether it is a metal or not. And from the pro-
position " some metals are brittle," we certainly cannot
ascertain whether any particular brittle substance is a
metal. We must seek the information from other sources.
But from "no metals are compounds" we learn of any
compound substance that it is not a metal, as well as of
a metal that it is not a compound substance.

The important difference above explained is expressed
in technical language by saying that the proposition E
distributes its predicate, whereas the affirmative proposi-
tions A and I do not disti'ibiite their pj-edicates. By dis-
tribution of a term is simply meant taking it universally,
or referring to all parts of it; and as the validity of any
argument or syllogism will usually depend upon the suffi-
cient distribution of the terms occurring in it, too much
attention cannot be paid to this point.

Judging from the examples we have had, it will be
seen that the universal affirmative distributes its subject,
but not its predicate ; for it gives us some information
concerning all metals, but not all elements. The parti-
cular affirmative distributes neither subject nor predicate;
for we do not learn anything from our example concern-
ing all metals nor concerning all brittle substances. But
the universal negative distributes both subject and predi-

IX.]

OF PROPOSITIONS.

7S

cate, for we learn something of all metals and also of all
compound substances.

The particular negative proposition 0 will be found to
distribute its predicate, but not its subject. When I say
some metals are 7iot brittle, I intentionally refer only to
a part of the metals, and exclude them from the class
of brittle substances; but I cannot help at the same time
referring to the whole of the brittle substances. If the
metals in question coincided with any part of the brittle
substances they could not be said to be excluded from
the class. To exclude a thing from any space, as from
a particular chamber of a house, it must not merely be
removed from some part, but from any part, or from the
whole of that space or chamber. Euler's diagram for
this proposition may be constructed in the same manner
as for the proposition I as follows : —
Fig. 4.

It is apparent that though part of the metals fall into
the circle of brittle substances, yet the remaining portion
are excluded from any part of the predicate.

We may state the result at which we have now arrived
in the following form : —

Universal it^'^.^'^'^^t-
( Negative E.

T, _^. 1 \ Affirmative I.
Particular Kt ■

( Negauve 0.

Subject.

Distributed.

Distributed.

Undistributed.

Undistributed.

Predicate.
Undistributed-
Distributed.
Undistributed.
Distributed.

76 THE OPPOSITION [less.

We shall now discover with great ease the relations of
the four propositions, each to each, that is to say, the way
in which they are opposed to each other. It is obvious
that the truth of a proposition may interfere more or less
completely with the truth of another proposition having
the same subject and predicate. If " all metals are ele-
ments," it is impossible that "some metals are not ele-
ments," and still more palpably impossible, so to say, that
" no metals should be elements." The proposition A, then,
is inconsistent with both E and 0 ; and, vice versd, E and
0 are inconsistent with A. Similarly, E is inconsistent
with A and I. But this important difference must be noted,
that if A be false, 0 is necessarily true, but E may or may
not be true. If it is not true that " all men are sincere,"
it follows that " some men are not sincere," but it does
not in the least follow that " no men are sincere." This
difference is expressed by saying that A and 0 are con-
tradictory propositions, whereas A and E are called con-
trary propositions. It is plain that A and E, as in " all
men are sincere" and "no men are sincere," represent
the utmost possible contrariety of circumstances. Id
order to prove the falsity of A, it is sufficient to establish
the truth of 0, and it is superfluous, even if possible, to
prove E ; similarly E is disproved by proving I, and it
is superfluous to prove A. Any person who asserts a uni-
versal proposition, either A or E, lays himself under the
necessity of explaining away or disproving every single
exception brought against it. An opponent may always
restrict himself to the much easier task of finding in-
stances which apparently or truly contradict the univer-
sality of the statement, but if he takes upon himself to
affirm the direct contrary, he is himself open to easy at-
tack. Were it to be asserted, for instance, that "All
Christians are more moral than Pagans," it would be
easy to adduce examples showing that " Some Christians

IX.] OF PROPOSITIONS. 77

are not more moral than Pagans," but it would be absurd
to suppose that it would be necessary to go to the con-
trary extreme, and shew that " No Christians are more
moral than Pagans." In short A is sufficiently and best
disproved by 0, and E by I. It will be easily apparent
that, vice versa, 0 is disproved by A, and I by E ; nor is
there, indeed, any other mode at all of disproving these
particular propositions.

When we compare together the propositions I and 0
we find that they are in a certain sense contrary in na-
ture, one being affirmative and the other negative, but
that they are still consistent with each other. It is true
both that " Some metals are brittle," for instance Anti-
mony, Bismuth and Arsenic ; but it is also true that
" Some metals are not brittle." And the reader will ob-
serve that when I affirm " Some metals are elements,"
there is nothing in this to prevent the truth of " Some
metals are not elements," although on other grounds we
know that this is not true. The propositions I and 0 are
called subcontraries each of the other, the name con-
noting a less degree of contrariety than exists between A
and E.

As regards the relation of A to I and E to 0, it is plain
that the truth of the universal includes and necessitates
the truth' of the particular What may be affirmed or
denied of all parts of a class may certainly be affirmed or
denied similarly of some part of the class. From the
truth of the particular we have no right to infer either
the truth or falsity of the universal of the same quality.
These pairs of propositions are called subalterns, i. e.
one under the other (Latin siib under, and alter the other
of two), or we may say more exactly that I and 0 are
respectively the subalternates of A and E, each of which
is a subalternans.

78

THE OPPOSITION

[LESS.

The relations of the propositions just described are
all clearly shown in the following scheme : —

A Contraries

.^

V ^^^

c°^

^^

'^/.

^fr-

m

I Subcontraries 0

It is so highly important to apprehend completely and
readily the consistency or opposition of propositions, that
I will put the matter in another form. Taking any two
propositions having the same subject and predicate, they
must come under one of the following statements : —

1. Of contradictory propositions, one must be true
and one false.

2. Of contrary propositions, both cannot be true, and
both may be false.

3. Of subcontrary propositions, one only can be false,
and both may be true.

4. Of subalterns, the particular is true if the universal
be true ; but the universal may or may not be true when
the particular is true.

I put the same matter in yet another form in the fol-
lowing table, which shows how the truth of each of A, E,
I, and 0, affects the truth of each of the others.

IX.] OF PROPOSITIONS. 79

A

E

I

0

is

is

is

is

[f A be true

true

false

true

false.

J> •" J5 J>

false

true

false

true.

» I „ „

doubtful

false

true

doubtful.

» 0 „ „

false

doubtful

doubtful

true.

It will be evident that from the affirmation of univer-
sals more information is derived than from the affirmation
of particulars. It follows that more information can be
derived from the denial ^f particul^^than from the
denial of universals, that i»b say, the^^^less cases left
doubt/til, as in the above^)le. ^||h

The reader may weJ^K cautioned, however, against
an ambiguity which tjSMpiisled some even of the most
eminent logicians. In ^ittticular propositions the adjec-
tive some is to be carefully interpreted as sofne, and there
may or may not be inore or all. Were we to interpret it
as some, not more nor all^sj^ii it would really give to the
proposition the force of f an^b combined. If I say " some
men are sincere," I must not be taken as implying that
" some men are not sincere ;" I must be understood to
predicate sincerity of some men, leaving the character of
the remainder wholly unaffected. It follows from this
that, when I deny the truth of a particular, I must not be
understood as implying the truth of the universal of the
same quality. To deny the truth of " some men are mor-
tal" might seem very natural, on the ground that not sotne
but all men are mortal ; but then the proposition denied
would really be some men are not mortal, i. e. 0 not I.
Hence when I deny that "some men are immortal" I
mean that "no men are immortal ;" and when I deny that
"some men are not mortal," I mean that "all men are
mortal."

It has long been usual to compare propositions as

8o OPPOSITION OF PROPOSITIONS, [less. ix.

regards the quality of the subject matter to which they
refer, and what is technically called the matter was dis-
tinguished into three kinds, necessary, contingent, and im-
possible. Necessary matter consists of any subject in
which the proposition A may be affirmed ; impossible in
which E may be affirmed. Any subject or branch of know-
ledge in which universal statements cannot usually be
made is called contingent matter, and it implies the truth
of I and 0. Thus "comets are subject to gravitation,"
though an indefinite or indesignate proposition (p. 65),
may be interpreted as A, because it refers to a part of
natural science where such general laws obtain. But
"men are sincere" would be properly interpreted as par
ticular or I, because the matter is clearly contingent. The
truth of the following statements is evident.

In necessary matter A and I are true ; E and 0 false.

In contingent matter I and 0 are true ; A and E false.

Inimpossible matter E and 0 are true ; A and I false.

In reality, however, this part of logical doctrine is
thoroughly illogical, because in treating a proposition we
have no right, as already explained (p. 70), to assume
ourselves acquainted with the science to which it refers.
Our duty is to elicit the exact consequences of any state-
ments given to us. We must learn in logic to transform
information in every possible way, but not to add extra-
neous facts.

LESSON X.

CONVERSION OF PROPOSITIONS, AND
IMMEDIATE INFERENCE.

We are said to Infer whenever we draw one truth
from another truth, or pass from one proposition to
another. As Sir W. Hamilton says, Inference is " the
carrying out into the last proposition what was virtually
contained in the antecedent judgments.'' The true
sphere of the science of logic indeed is to teach the
principles on which this act of inference must be per-
formed, and all the previous consideration of terms
and propositions is only useful or pertinent so far as
it assists us to understand the processes of inference.
We have to consider in succession all the modes in
which the same information may be moulded into differ-
ent forms of expression often implying results of an
apparently different character. Logicians are not agreed
exactly as to what we may include under the name
Inference, and what we should not All would allow
that there is an act of inference when we see drops of
water on the ground and believe that it has rained.
This is a somewhat complicated act of inference, which
we shall consider in later lessons under the subject of
Induction. Few or none would say that there is an act
of inference in passing from "The Duke of Cambridge
is the Commander-in-chief," to "The Commander-in-
chief is the Duke of Cambridge." But without paying
much regard to the name of the process I shall in this

6

Vij vp

82 CONVERSION OF PROPOSITIONS, [less.

lesson point out all the ways in which we can from a
single proposition of the forms A, E, I or 0, pass to another
proposition.

We are said to convert a proposition when we
transpose its subject and predicate; but in order that
the converse or converted proposition shall be inferred
from the convertend, or that which was to be converted,
we must observe two rules (i) the quality of the pro-
position (affirmative or negative) must be preserved, and
(2) no ter7n must be distributed in the Converse unless it
was distributed in the Convertend.

If in " all metals are elements " we were simply to
transpose the terms, thus — " all elements are metals," we
imply a certain knowledge about all elements, whereas
it has been clearly shewn that the predicate of A is un-
distributed, and that the convertend does not really give
us any information concerning all elements. All that
we can infer is that "some elements are metals;" this
converse proposition agrees with the rule, and the pro-
cess by which we thus pass from A to I is called Con-
version by Limitation, or Per accidens.

When the converse is a proposition of exactly the
same form as the convertend the process is called simple
conversion. Thus from "some metals are brittle sub-
stances" I can infer "some brittle substances are
metals," as all the terms are here undistributed. Thus
I is simply converted into I.

Again, from " no metals are compounds," I can pass
directly to "no compounds are metals," because these
propositions are both in E, and all the terms are there-
fore distributed. Euler's diagram (p. 73, Fig. 3) clearly
shows, that if all the metals are separated from all the
compounds, all the compounds are necessarily separated
from all the metals. The proposition E is then simply
converted into E.

X.] AND I M MEDIA TE INFERENCE. 83

But in attempting to convert the proposition 0 we
encounter a peculiar difficulty, because its subject is un-
distributed; and yet the subject should become by con-
version the predicate of a negative proposition, which
distributes its predicate. Take for example the propo-
sition, "some existing things are not material substances."
By direct conversion this would become "all material
substances are not existing things ;" which is evidently
absurd. The fallacy arises from existing things being
distributed in the converse, whereas it is particular in
the convertend ; and the rules of the Aristotelian logic
prevent us from inserting the sign of particular quantity
before the predicate. The converse would be equally
untrue and fallacious were we to make the subject par-
ticular, as in " some material substances are not exist-
ing things." We must conclude, then, that the propo-
sition 0 cannot be treated either by simple conversion or
conversion by limitation. It is requisite to apply a new
process, which may be called Conversion by Negation,
and which consists in first changing the convertend into
an affirmative proposition, and then converting it simply.
If we attach the negation to the predicate instead of
to the copula, the proposition becomes "some exist-
ing things are iinmaterial substances," and, converting
simply, we have — "some immaterial substances are ex-
isting things," which may truly be inferred from the con-
vertend. The proposition 0, then, is only to be converted
by this exceptional method of negation.

Another process of conversion can be applied to the
proposition A, and is known as conversion by contra-
position. From "all metals are elements," it neces-
sarily follows that "all not-elements are not metals."
If this be not at the first moment apparent, a little re-
flection will render it so, and from fig. 5 we see that if
all the metals be among the elements, whatever is not ele-

6—2

84 CONVERSION OF PROPOSITIONS, [less.

ment, or outside the circle of elements, must also be
outside the circle of metals. We may also prove the truth

of the contrapositive proposition in this way, if we may
anticipate the contents of Lesson XXIII.: — If what is not-
element should be metal, then it must be an element by
the original proposition, or it must be at once an ele-
ment and not an element ; which is impossible accord-
ing to the Primary Laws of Thought (Lesson xiv.), since
nothing can both have and not have the same property.
It follows that what is not-element must be not-metal.

Mistakes may readily be committed in contrapositive
conversion, from a cause which will be more apparent in
Lesson xxil. We are very liable to infer from a pro-
position of the form "all metals are elements," that all
not-metals are not-elenients, which is not only a false
statement in itself, but is not in the least warranted by
the original proposition. In fig. 5, it is apparent that
because a thing lies outside the circle of metals, it does
not necessarily lie outside the circle of elements, which is
wider than that of metals. Nevertheless the mistake is
often made in common life, and the reader will do well
to remember that the process of conversion by contra-
position consists only in taking the negative of the pre-
dicate of the proposition A, as a new subject, and affirm-
ing of it universally the negative of the old subject.

X.] AND IMMEDIATE INFERENCE. 85

Contrapositive conversion cannot be applied to the
particular propositions I and 0 at all, nor to the propo-
sition E, in that form ; but we may change E into A by-
attaching the negation to the predicate, and then the
process can be applied. Thus "no men are perfect,"
may be changed into "all men are not-perfect," i.e.
"are imperfect," and then we infer by contraposition
" all not-imperfect beings are not-men." But not-im-
perfect is really the same as perfect, so that our new
proposition is really equivalent to " all perfect beings are
not men," or " no perfect beings are men," (E) the sim-
ple converse of the original proposition.

There remain to be described certain deductions
which may be drawn from a proposition without convert-
ing its terms. They may be called immediate inferences,
and have been very clearly described by Archbishop
Thomson in his " Outline of the Necessary Laws of
Thought" (pp. 156, &c.).

Immediate Inference by Privative Conception consists
in passing from any affirmative proposition to a negative
proposition implied in it, or equivalent to it, or vice versa^
in passing from a negative proposition to its correspond-
ing affirmative. It is also called Obversion.

The following table contains a proposition of each
kind changed by privative conception into an equivalent
proposition :

jA all metals are elements.
)E no metals are compounds.
JE no men are perfect.
(A all men are imperfect.
fl some men are trustworthy.
(0 some men are not untrustworthy.
JO some men are not trustworthy.
(I some men are untrustworthy.
The truth of any of the above can be clearly illustrated

86 CONVERSION OF PROPOSITIONS, [less.

by diagrams ; thus it will be apparent that if the whole
circle of metals lies inside the circle of elements, no part
can lie outside of that circle or among the compounds.
Any of the above propositions may be converted, but the
results will generally be such as we have already ob-
tained. Thus the simple converse of " no metals are
compounds" is "no compounds are metals," or "no not-
elements are metals," the contrapositive of "all metals
are elements." From the last example we get also by
simple conversion " some untrustworthy beings are men,''
which is obviously the converse by negation, as before
explained. Applying this kind of conversion to " some
men are not untrustworthy," we have " some not-untrust-
worthy beings are men." Lastly, from "all men are
imperfect" we may obtain through conversion by limita-
tion, " some imperfect beings are men."

Immediate Inference by added determinants consists
in joining some adjective or similar qualification both to
the subject and predicate of a proposition, so as to ren-
der the meaning of each term narrower or better deter-
mined. Provided that no other alteration is rnade the
truth of the new proposition necessarily follows from the
truth of the original in almost all cases.

From "all metals are elements," we may thus inf^
that " all very heavy metals are very heavy elements."
From "a comet is a material body" we infer "a visible
comet is a visible material body." But if we apply this
kind of inference too boldly we may meet with fallacious
and absurd results. Thus, from "all kings are men,"
we might infer " all incompetent kings are incompetent
men ;" but it does not at all follow that those who are
incompetent as kings would be incompetent in other
positions. In this case and many others the qualifying
adjective is liable to bear different meanings in the sub-
ject and predicate ; but the inference will only be true of

X.] AND IMMEDIATE INFERENCE. Z7

necessity when the meaning is exactly the same in each
case. With comparative terms this kind of inference
will seldom be applicable ; thus from " a cottage is a
building," we cannot infer "a huge cottage is a huge
building," since a cottage may be large when compared
with other cottages, but not with buildings generally.

Immediate Inference by Complex Conception is closely
similar to the last, and consists in employing the subject
and predicate of a proposition as parts of a more com-
plex conception. From " all metals are elements," I can
pass to " a mixture of metals is a mixture of elements."
From "a horse is a quadruped" I infer "the skeleton of
a horse is the skeleton of a quadruped." But here again
the reader must beware of applying the process where
the new complex conception has a different meaning in
the subject and predicate. Thus, from " all Protestants
are Christians," it does not follow that "a majority of
Protestants are a majority of Christians," nor that "the
most excellent of the Protestants is the most excellent of
the Christians."

The student is recommended to render himself fami-
liar with all the transformations of propositions, or im-
mediate inferences described in this lesson ; and copious
examples are furnished for the purpose. It is a good
exercise to throw the same proposition through a series
of changes, so that it comes out in its original form at
last, and thus proves the truth of all the intermediate
changes ; but should conversion by limitation have been
used, the original universal proposition cannot be re-
gained, but only the particular proposition corresponding
to it.

On Im7nediate Inference, Archbishop Thomson,
Outline of the Laws of Thought, \\ 85 — 92.

LESSON XL

LOGICAL ANALYSIS OF SENTENCES.

Propositions as they are usually to be found in writ-
ten or spoken compositions seldom exhibit the simple
form, the conjunction of a subject, copula, and predicate,
which we have seen to be the proper logical construction.
Not only is the copula often confused with the predicate,
but several propositions may be combined into one gram-
matical sentence. For a full account of the analysis
of sentences I shall refer to several excellent little works
devoted to the subject ; but I will here attempt to give a
sketch of the various ways in which a sentence may be
constructed.

So often is the copula united to the predicate in
ordinary language, that the grammarian treats the propo-
sition as composed of only two parts, the subject and
predicate, or verb. Thus the proposition, "The sun
rises," apparently contains nothing but a subject "the
sun," and a predicate "rises;" but the proposition is
really equivalent to "the sun is rising," in which the
copula is distinctly shown. We shall, therefore, con-
sider the verb or grammatical predicate as containing both
copula and logical predicate. In Latin one single word
may combine all the three parts of the proposition, as in
su7n,, "I am ;" and the celebrated exclamation of Cassar,
Veni, vicfi, vici, " I came, I saw, I conquered," contains
three distinct and complete propositions in three words.
These peculiar cases only arise, however, from the parts
of the proposition having been blended together and dis-

LESS. XL] ANALYSIS OF SENTENCES. 89

guised in one word ; and in the Latin stan, the letter m
is a reHc of the pronoun me, which is the real subject of
^ the proposition. If we had a perfect acquaintance with
the Grammar of any language it would probably not con-
tradict the logical view of a sentence, but would perhaps
explain how the several parts of the complete proposition
had become blended and apparently lost, just as the
words will and not are blended in the colloquial " I wont."
A grammatical sentence may contain any number of
distinct propositions, which admit of being separated but
' which are combined together for the sake of brevity. In
the sentence,

"Art is long and Time is fleeting,"
there are two distinct subjects, Art and Time, and two
predicates, "long" and "fleeting," so that we have simply
. two propositions connected by the conjunction and. We
may have however several distinct subjects with one and
the same predicate ; as in

"Thirty days hath September,
April, June, and November. "
In this well-known couplet the predicate " having
thirty days " is placed first for the sake of emphasis, and
there are four subjects, September, April, &c., of each of
which it is affirmed. Hence these lines really contain four
distinct propositions.

Again, there may be one subject with a plurality of
predicates, so that several different propositions are as-
serted without the repetition of the subject and copula.
Thus the sentence

"Nitrogen is a colourless, tasteless, inodorous gas,
slightly lighter than air," contains one subject only, Ni-
trogen, but four or five predicates ; it is plainly equiva-
lent to "Nitrogen is colourless," "Nitrogen is tasteless,"
" Nitrogen is a gas," and so on.

Lastly, we may have several subjects and several

90 LOGICAL ANALYSIS [less.

predicates all combined in the same sentence, and with
only one copula, so that each predicate is asserted of
each subject ; and a great number of distinct propositions ,
are condensed into one brief sentence. Thus in the sen-
tence, "Iron, Copper, Lead and Zinc are abundant, cheap
and useful metals|" we have evidently four subjects, and
we may be said to have four predicates, "abundant,"
"cheap," "useful,'' and "metal." As there is nothing to
prevent our applying each predicate to each subject the
sentence really contains i6 distinct propositions in only
II words; thus "Iron is abundant," "Iron is cheap,"
"Copper is abundant," "Copper is cheap," and soon.
In the curious sentence, —

" Hearts, tongues, figures, scribes, bards, poets, can-
not think, speak, cast, write, sing, number, his love to
Antony*," Shakspeare has united six subjects and six
predicates, or verbs, so that there are, strictly speaking,
six times six or thirty-six propositions.

In all the cases above noticed the sentence is said to
be compound, and the distmct propositions combined
together are said to be coordinate with each other, that is
of the same order or rank, because they do not depend
upon each other, or in any way affect each other's truth.
The abundance, cheapness, or utility of iron need not
be stated in the same sentence with the qualities of cop-
per, lead or zinc ; but as the predicates happen to be the
same, considerable trouble in speaking or writing is
saved by putting as many subjects as possible to the
same set of predicates. It is truly said that brevity
is the soul of wit, and one of the great arts of compo-
sition consists in condensing as many statements as
possible into the fewest words, so long as the meaning is
not confused thereby.

* Antony and Cleopatra, Act III. Sc. a.

XI.] OF SENTENCES. 91

Propositions are however combined in a totally dif-
ferent manner when one proposition forms a part of the
subject or predicate of the other. Thus in the sen-
tence, "The man who is upright need not fear accusa-
tion," there are two verbs, and two propositions, but one
of these only describes the subject of the other; "who
is upright " evidently restricts the application of the pre-
dicate " need not fear accusation " to a part of the class
" man. " The meaning of the whole sentence might be
expressed in the form

" The upright man need not fear accusation. "
And it is clearly seen that the clause or apparent propo-
sition is substituted for an adjective. Such a clause or
proposition is called subordinate, because it merely as-
sists in the formation of the principal sentence, and has
no meaning apart from it ; and any sentence containing
a subordinate clause is said to be complex. Almost any
part of a sentence may thus be replaced by a subordinate
clause. Thus in "Oxygen and Nitrogen are the gases
which form the largest part of the atmosphere," there is a
subordinate clause making part of the predicate, and the
meaning might be expressed nearly as well in this way,
" Oxygen and Nitrogen are the gases forming the largest
part of the atmosphere."

In the case of a modal proposition (see p. 69), or one
which states the manner in which the predicate belongs
to the subject, the mode may be expressed either by an

* adverb, or by a subordinate clause. "As a man lives so
he dies" is such a proposition; for it means, "a man
dies as he lives," and " as he lives " is equivalent to an
adverb ; if he lives well, he dies well ; if he lives badly,
he dies badly. Adverbs or adverbial clauses may also
specify the time, place, or any other circumstance con-
cerned in the truth of the main proposition.

^ Assuming the reader to be acquainted with the gram-

92 LOGICAL ANALYSTS [less.

matical terms used, we may thus state the parts of which
the most complex sentence must consist.
The subject may consist of —

1. A noun ; as in " The Qiieeti reigns."

2. A pronoun ; as in " She reigns."

3. An adjective converted into a noun ; as in " Whites
are civiHzed."

4. A gerund ; as " Seeing is believing."

5. An infinitive ; as " To see is to believe."

6. A subordinate clause ; as " Who falls from virtue
is lost."

The subject may be qualified or restricted by combin-
ing with it an attribute which may be expressed in any of
the following ways :

1. An adjective ; as, '''■Fresh air is wholesome."

2. A participle ; as " Fallijig stars are often seen."

3. A noun used as an adjective ; as " Iron ships are
now much employed."

4. A noun and preposition ; as "ships of iron are now-
much employed."

5. A possessive case ; as " ChathanHs son was the
great minister Pitt."

6. A noun in apposition ; as " The Metropolis London
is the most populous of cities."

7. A gerund or dative infinitive ; as, " The desire to go
abroad is common in Englishmen."

The predicate consists almost always of a verb, which
often has some object or qualifying words ; thus it may
be—

1. A simple tense of a complete verb ; as "The sun
rises^^

2. A compound tense ; as " The sun has risenP

3. An incomplete verb and complement ; as " The
sea seems rouo;hP

XI.] OF SENTENCES. 93

4. The verb " to be" and an adjective : as " Time is
fleetingP

5. A verb with an object ; as " Warmth tnelts iceP

6. A verb with an adverbial; as "The snow falls
thickly"

The object of a verb is usually a noun or pronoun,
but any other of the six kinds of expressions which may
serve as a subject may also serve as an object.

The adverbial qualifying a verb and expressing the
manner, time, place, or other circumstance affecting the
proposition may be —

1. An adverb ; as " The days pass slowly ^^

2. A noun and preposition ; as " The resolution was
passed by a large tHajority^

3. An absolute phrase; as "The snow melts, the sun
havifig risen."

4. A dative infinitive ; as " She stoops to conquer"

5. Any phrase equivalent to an adverb ; as " The divi-
dends are paid twice a yearP

Various modes of exhibiting the construction of sen-
tences by symbols and names for the several parts have
been invented ; but I believe that by far the simplest and
most efficient mode is to exhibit the construction in the
form of a diagram. Any two or more parts of a sen-
tence which are co-ordinate with each other, or bear the
same relation to any other part, are written beside each
other, and coupled together by a bracket ; thus the dia-
gram,—

Iron I r abundant.

Copper I I cheap.

Lead j ^^^ j useful

Zinc J I metals,

clearly shows that there are four co-ordinate subjects.

94 LOGICAL ANALYSIS [less.

and four co-ordinate predicates in the example previously
taken.

Whenever one part of a sentence is subordinate to
another part it may be connected with it by a line drawn
in any convenient direction. Thus the analysis of the
following sentence is readily shown by the diagram below
it :—

"No one who is a lover of money, a lover of pleasure,
and a lover of glory, is likewise a lover of mankind ; but
only he who is a lover of virtue."

{a lover of money,
a lover of pleasure,
a lover of glory,
one is not

, . , a lover of mankind,
he only is

I
who is a lover of virtue.

We see that the sentence is both compound and com-
plex, that is to say it contains two principal coordinate
propositions with a common predicate, " a lover of man-
kind." The first proposition is negative and its subject is
described by three subordinate clauses, while the second
proposition is affirmative and has one subordinate clause.

I conclude this somewhat lengthy lesson with the
analysis of a few sentences, of which the first consists
of some remarkably complex lines from a poem of Bur-
bidge :

"He who metes, as we should mete,
Could we His insight use, shall most approve.
Not that which fills most space in earthly eyes,
But what — though Time scarce note it as he flies —
Fills, like this little daisy at my feet.
Its function best of diligence in love."

XI.] OF SENTENCES. 95

which fills most space in earthly eyes

I ,

-_ , „ ( not that

He shall most approve j ^^^ ^^^^ ^^^^ ^^^^

who metes its function of like this little

as we should mete diligence in daisy at my

I love feet,

could we His insight use. *T T~^- ' ^ -^

^ though Time scarce note it

as he flies.
" Most sweet it is with unuplifted eyes

To pace the ground, if path there be or none.
While a fair region round the traveller lies

Which he forbears again to look upon ;
Pleased rather with some soft ideal scene,
The work of fancy, or some happy tone
Of meditation slipping in between.
The beauty coming, and the beauty gone."

Wordsworth.
It is most sweet
I
To pace the ground

with unuplifted if path while a fair region

eyes ^^^^ j be round the |

i or none traveller lies |

, ^ 1

which (region) he (the traveller) forbears to look upon
' f some soft ideal scene

pleased ) , r— — — '

rather with ) the work of fancy

( or some happy tone of meditation

sHpping in between the beauty coming
and the beauty gone.
In the above sentence there is evidently one subject

o6

LOGICAL ANALYSIS

[LESS.

" to pace the ground," which by means of the pronoun //,
is connected with the predicate most sweet. The main
part of the sentence however consists of three adverbials,
expressing the manner and surrounding circumstances,
and the third adverbial is developed in a very complicated
manner. The sentence is not compound, but is complex
on account of four subordinate propositions.

In the following sentence there is strictly but one
principal proposition, " We find," but this is only a mode
of introducing the true purport of the sentence, " the two
classes of intellectual operations have much that is differ-
ent, much that is common."

" When the notions with which men are conversant in
the common course of life, which give meaning to their
familiar language and which give employment to their
hourly thoughts, are compared with the ideas on which
exact science is founded, we find, that the two classes of
intellectual operations have much that is different, much
that is common."
we find — that the two classes (* f)

I of intellectual j much that is different

I operations have ( much that is common

When the notions ^ are compared ,

with the ideas f

I
on which

exact science is

founded.

with which which give which give
men are meaning employ-
conversant to their ment to
in the familiar their hourly
common language thoughts
course
of life

Here the two classes form a collective term, and have
two coordinate predicates rendering the sentence so far a
compound one. The greater part of the sentence, how-
ever consists of a comphcated subordinate sentence of

XL]

OF SENTENCES.

97

the nature of an adverbial, expressing the time or occa-
sion when this is found to be the case.

As a last example we take the sentence given below: —
" The law of gravitation, the most universal truth at
which human reason has yet arrived, expresses not merely
the general fact of the mutual attraction of all matter ; not
merely the vague statement that its influence decreases as
the distance mcreases, but the exact numerical rate at
which that decrease takes place ; so that when its amount
is known at any one distance it may be exactly calculated
for any other."

at which human reason has yet arrived

I
the most universal truth

The law of gravitation expresses

not merely the
general fact

of the mutual

attraction of all

matter

not merely the
vague statement

that its influence

decreases

I
as the distance

increases

but the exact
numerical rate

I

at which that

decrease takes

place

so that its amount may be calculated for any other dis-

I [tance

when it is known at any one distance.

W. S. Dalgleish's Grammatical Analysis^ or
J. D. Morell's Analysis of Se7ite7ices.
Alex. Bain's English Compositioji and Rhe-
toric^ pp.91 — Ii7j treats of construction of
sentences.

LESSON XII.

THE PREDICABLES, DIVISION, AND
DEFINITION.

It is desirable that the reader, before proceeding further,
should acquire an exact comprehension of the meaning of
certain logical terms which are known as the Predicables,
meaning the kinds of terms or attributes which can always
be predicated of any subject. These terms are five in
number; genus, species, difference, property, and acci-
dent ; and when properly employed are of exceeding use
and importance in logical science. It would neither be
possible nor desirable in this work to attempt to give any
idea of the various and subtle meanings which have been
attributed to the predicables by ancient writers, and the
most simple and useful view of the subject is what alone ^
can be given here.

Any class of things may be called a genus (Greek
yeVoff, race or kind), if it be regarded as made up of two
or more species. "Element" is a genus when we con-
sider it as divided into the two species "metallic and
non-metallic." Triangle is a genus as regards the species
acute-angled, right-angled, and obtuse-angled.

On the other hand, a species is any class which is re-
garded as forming part of the next larger class, so that
the terms genus and species are relative to each other,
the genus being the larger class which is divided, and the
species the two or more smaller classes into which the
genus is divided.

It is indispensable, however, to regard these expres-
sions in the double meaning of extension and intension.

LESS. XII.] THE PREDICABLES, ETC. 99

From the explanation of these different meanings in
Lesson V. it will be apparent that the extent of a genus
or species is simply the number of individuals included
in it, and there will always be fewer individuals in the
species than in the genus. In extent the genus book in-
cludes all books of whatever size, language, or contents ;
if divided in respect to size the species of book are folio,
quarto, octavo, duodecimo, &c. ; and, of course, each of
these species contains much fewer individual books than
the whole genus.

In intension the genus means, not the individual
things contained in it, but the sum of the qualities com-
mon to all those things, and sufficient to mark them out
clearly from other classes. The species similarly means
the sum of the qualities common to all the individuals
forming part of the species, and sufficient to mark them out
from the rest of the genus, as well as from all other things.
It is evident, therefore, that there must be more qualities
implied in the meaning of the species than of the genus,
for the species must contain all the qualities of the genus,
as well as a certain additional quality or qualities by
which the several species are distinguished from each
other. Now these additional qualities form the difference,
which may be defined as the quality or sum of qualities
which mark out one part of a genus from the other part or
parts. The difference (Latin differetitia^ Greek hia-
<^opa) cannot have any meaning except in intension,

* and when we use all the terms wholly in intension we may
say that the difference added to the ge?ius makes the species.
Thus if "building" be the genus, and we add the differ-
ence "used for a dwelling," we get the species "house."
If we take "triangle" as the genus, it means the sum of
the qualities of " three-sided rectilineal figure ;" if we add
the quahty of "havmg two sides equal," we obtain the

, species " isosceles triangle."

7—2

loo THE PREDICABLES, DIVISION, [LESS.

It will easily be seen that the same class of things
may be both a genus and a species at the same time, ac-
cording as we regard it as divided into smaller classes or
forming part of a larger class. Thus triangle, which is
a genus as regards isosceles triangle, is a species as re-
gards right-lined geometrical figures. House is a species
of building, but a genus with respect to mansion, cottage,
villa, or other kinds of houses. We may, in fact, have an
almost interminable chain of genera and species, each
class being a species of the class next above it, and a
genus as regards that next below. Thus the genus Bri-
tish subject has the species Born in the United Kingdom,
Colonial-born, and Naturalised. Each of these becomes
a genus as regards the species male and female; each
species again may be divided into adult and minor, edu-
cated, uneducated, employed in some occupation or un-
employed, self-maintaining, maintained by friends, or
pauper; and so on. The subdivision may thus proceed
until we reach a class of so restricted extent, that it
cannot be divided except into individuals; in this case
the species is called the lowest species or inflma species.
All the intermediate genera and species of the chain are
called subaltern (Latin sub, under, and alter^ the other of
two), because they stand one under the other. If there be
a genus which is not regarded as a species, that is as
part of any higher genus, it is called the summum genus,
the highest genus, or genus generalissimum^ the most
general genus. It is questionable whether we can thus '
set any limit to the chain of classes. The class British
subject is certainly not an absolute su7ninum genus,
since it is but a species of man, which is a species of
animal, living being, portion of the earth, substance,
and so on. If there were any real summum genus it
would probably be " Being," or " Thing," or " Object con-
ceivable ;" but we may usefully employ the term to signify

XII.] AND DEFINITION. loi

the highest class of things comprehended in any science
or classification. Thus "material substance" is the sum-
mum genus examined in the science of chemistry; "in-
habitant of the United Kingdom" is the summum genus
enumerated and classified in the British census. Logi-
cal terms are only a species of words or phrases, but they
are the summum genus as regards logic, which has no-
thing to do with the various parts of speech and the
relations of words, syllables, and letters, examined by
grammarians.

Several very useful expressions have been derived
from the words genus and species. When a thing is
so peculiar and unlike other things that it cannot easily
be brought into one class with them, it is said to be sui
generis, or of its own genus ; thus the rings of Saturn are
so different from anything else among the heavenly bodies
that they may fairly be called sici generis. In zoology,
the Ornithorhynchus, or Australian Duck-bill, the Amphi-
oxus, and some other animals, are so peculiar that they
may be called stci generis. When a substance is the
same in all its parts, or when a number of things are all
alike, we say that they are Jiomogeneotis (Greek oiiU., like,
yevoff, kind), that is of the same nature ; otherwise they
may be called heterogeneous (Greek erepo^, other).

It is necessary to distinguish carefully the purely lo-
gical use of the terms genus and species from their pecu-
liar use in natural history. A species is there a class
of plants and animals supposed to have descended from
common parents, and to be the narrowest class possessing
a fixed form ; the genus is the next higher class. But if
we accept Darwin's theory of the origin of species, this
definition of species becomes entirely illusory, since dif-
ferent genera and species must have according to this
theory descended from common parents. The species
then denotes a merely arbitrary amount of resemblance

I02 THE PREDICABLES, DIVISION, [less.

which naturalists choose to fix upon, and which it is not
possible to define more exactly. This use of the term,
then, has no connection whatever with the logical use,
according to which any class of things whatever is a
species, provided it is regarded as part of a wider class or
genus.

The fourth of the Predicables is Property (Latin pro-
prium, Greek Xbiov, own), which it is hardly possible to
define in a manner free from objection and difficulty, but
which may perhaps be best described as any quality
which is common to the whole of a class, but is not neces-
sary to mark out that class from other classes. Thus it is
a property of the genus "triangle" to have the three in-
ternal angles equal to two right angles; this is a very
remarkable circumstance, which is always true of tri-
angles, but it is not made a part of the genus, or is not
employed in defining a triangle, because the possession of
three straight sides is a sufficient mark. The properties of
geometrical ^gures are very numerous; the Second Book
of Euclid is occupied in proving a few properties of rect-
angles ; the Third Book similarly of circles. As we com-
monly use the tertn property it may or may not belong to ■
other objects as well as those in question; some of the
properties of the circle may belong also to the ellipse ;
some of the properties of man, as for instance the power
of memory, or of anger, may belong to other animals.

Logicians have invented various subtle divisions of pro-
perties, but it will be sufficient to say that a peculiar pro-
perty is one which belongs to the whole of a class, and to
that class only, as laughter is supposed to belong only to
mankind ; the property of containing the greatest space in
a line of given length is peculiar to circles. When a pro-
perty is not peculiar, it may belong to other classes of
objects as well as that of which it is called the property.
We may further distinguish the Generic Property, or that

XII.] AND DEFINITION 103

which belongs to the whole of the genus, from the
Specific Property, which belongs to the whole of a lowest
species.

Lastly, an accident (Latin accidens, Greek o-vh^c^t}-
Kos) is any quality which may indifferently belong or
not belong to a class, as the case may be, without
affecting the other qualities of the class. The word
means that which /a/Is or happens by chance, and has no
necessary connection with the nature of a thing. Thus
the absolute size of a triangle is a pure accident as
regards its geometrical properties; for whether the side
of a triangle be ^ of an inch or a million miles, what-
ever Euclid proves to be true of one is true of the other.
The birthplace of a man is an accident concerning him, as
are also the clothes in which he is dressed, the position in
which he rests, and so on. Some writers distinguish se-
parable and inseparable accidents. Thus the clothes in
which a man is dressed is a separable accident, because
they can be changed, as can also his position, and many
other circumstances ; but his birthplace, his height, his
Christian name, &c., are inseparable accidents, because
they can never be changed, although they have no neces-
sary or important relation to his general character.

As an illustration of some part of the scheme of clas-
sification described under the name of Predicables, I may
here give, as is usual in manuals of Logic, the Tree of
Porphyry, a sort of example of classification invented by
one of the earliest Greek logicians, named Porphyrius.
I have simplified the common form in which it is given
by translating the Latin names and omitting superfluous
words.

In this Tree we observe a succession of genera and
species — Substance, Body, Living Being, Animal and
Man. Of these Substance is the sum7nic7n genus, because
it is not regarded as a species of any higher class ; Man

I04 THE PREDICABLES, DIVISION, [less, i^

is the iiifima species, because it is a class not divided in-
to any lower class, but only into individuals, of whom it is

Substance, r

Socrates, Plato, and others.

usual to specify Socrates and Plato. Body, Living Being,
and Animal are called subaltern genera and species, be-
cause each is a species as regards the next higher genus,
and a genus as regards the next lower species. The
qualities imphed in the adjectives Corporeal, Animate,
Sensible {i.e. capable of feeling) and Rational are the
successive differences which occasion a division of each
genus into species. It will be evident that the negative
parts of the genera, namely Incorporeal Substance, In-

XII.] AND DEFINITION. 105

animate Body, &c., are capable of subdivision, which has
not been carried out in order to avoid confusing the
figure.

Logical division is the name of the process by which
we distinguish the species of which a genus is composed.
Thus we are said to divide the genus " book " when we
consider it as made up of the groups foHo, quarto, octavo,
duodecimo books, &c., and the size of the books is in this
case the ground, basis, or principle of division, commonly
called the Fimdamentum Divisionis. In order that a quality
or circumstance may be taken as the basis of division, it
must be present with some and absent with others, or
must vary with the different species comprehended in the
genus. A generic property of course, being present in the
whole of the genus, cannot serve for the purpose of divi-
sion. Three rules may be laid down to which a sound
and useful division must conform :

1. The constituent species must exclude each other.

2. The constituent species must be equal when add-
ed together to the genus.

3. The division must be founded upon one principle
or basis.

It would be obviously absurd to divide books into
folio, quarto, French, German and dictionaries, because
these species overlap each other, and there may be French
or German dictionaries which happen to be quarto or
folio and belong to three different species at once. A
division of this kind is said to be a Cross Division, because
there is morfe than one principle of division, and the seve-
ral species in consequence cross each other and produce
confusion. If I were to divide rectilineal figures into tri-
angles, parallelograms, rectangles and polygons of more
than four sides, I should commit all the possible faults in
one division. The species parallelogram and rectangle
do not exclude each other, since all rectangles must be

[o6 THE PREDICABLES, DIVISION^ [less.

parallelograms ; the constituent species are not altogether
equal to the genus rectilineal figure, since irregular four-
sided figures which are not parallelograms have been
omitted ; and there are three principles of division, namely
the number of sides, the directions of those sides, and the
angles contained. But when subdivision is employed,
and each of the species is considered as a genus which
may be subjected to a further separation, a new principle
of division may and in fact must be employed each time.
Thus I can divide rectilineal figures according to the three
principles mentioned above :

Rectilineal Figure

3 sides 4 sides more than 4 sides

Triangle Quadrilateral Polygon

I ' \ 1

with parallel sides without parallel

Parallelogram sides

Trapezium.

Here the principles of division are the number of their
sides, and in the case of four-sided figures their paral-
lelism. Triangles do not admit of division in this second
respect We may make a new division of parallelograms,
adopting the equality of sides and the size of the angles
as the principles ; thus :

Parallelogram

. ' ; ' ; — T"!

adjoining sides adjoining sides

equal not equal

right- not right- right- not right-

angled angled angled angled

Square Rhombus Oblong Rhomboid.

The most perfect divisions in a logical point of view
are produced by continually dividing each genus into two

XII.] AND DEFINITION. 107

species by a difference, of which an example has been
given in the Tree of Porphyry. This process is called
Dichotomy (Greek hlxa, in two ; reTu/o), to cut) ; it is also
called Exhaustive Division because it always of necessity
obeys the second rule, and provides a place for every
possible existing thing. By a Law of Thought to be con-
sidered in the next Lesson, every thing must either have
a quahty or not have it, so that it must fall into one or
other division of the genus. This process of exhaustive
division will be shewn to have considerable importance in
Lesson XXII I., but in practice it is not by any means
always necessary or convenient. It would, for instance,
produce a needlessly long classification if we divided rec-
tilineal figures thus :

Rectilineal figure

3-sided not 3-sided
Triangle , : ,

4-sided not 4-sided

Quadrilateral

5-sided not 5-sided

Pentagon &c.

As we know beyond all doubt that every figure must
have 3, 4, 5, 6, or more sides, and no figure can belong to
more than one group, it is much better at once to enume-
rate the parts as Triangle, Quadrilateral, Pentagon, Hexa-
gon, &c. Again, it would be very awkward if we divided
the counties of England into Middlesex and not-Middle-
sex; the latter into Surrey and not-Surrey; the latter,
again, into Kent and not-Kent. Dichotomy is useless,
and even seems absurd in these cases, because we can
observe the rules of division certainly in a much briefer
division. But in less certain branches of knowledge our
divisions can never be free from possible oversight unless
they proceed by dichotomy. Thus, if we divide the popula-
tion of the world into three branches, Aryan, Semitic, and

io8 THE PREDICABLES, DIVISION, [less.

Turanian, some race might ultimately be discovered which
is distinct from any of these, and for which no place has
been provided ; but had we proceeded thus —

Man

Aryan not-Aryan

Semitic not-Semitic

Turanian not-Turanian,

it is evident that the new race would fall into the last
group, which is neither Aryan, Semitic, nor Turanian. All
the divisions of naturalists are liable to this inconvenience,
If we divide Vertebrate Animals into Mammalia, Birds,
Reptiles, and Fish, it may any time happen that a new
form is discovered which belongs to none of these, and
therefore upsets the division.

A further precaution required in Division is not to
proceed from a high or wide genus at once to a low
or narrow species, or, as the phrase is, divisio non faciat
saltum (the division should not make a leap). The
species should always be those of the proximate or next
higher genus ; thus it would obviously be inconvenient to
begin by dividing geometrical figures into those which
have parallel sides and those which have not; but this
principle of division is very proper when apphed to the
proximate genus.

Logical division must not be confused with physical
division or Partition, by which an individual object, as a
tree, is regarded as composed of its separate parts, root,
trunk, branches, leaves, &c. There is even a third and
distinct process, called Metaphysical Division, which con-
sists in regarding a thing as an aggregate of qualities,
and separating these in thought ; as when we discriminate
the form, colour, taste, and smell of an orange.

Closely connected with the subject of this Lesson is

XII.] AND DEFINITION. 109

the process of Logical Definition, by which we determine
the common quahties or marks of the objects belonging
to any given class of objects. We must give in a defini-
tion the briefest possible statement of such qualities as
are sufficient to distinguish the class from other classes,
and determine its position in the general classification of
conceptions. Now this will be fulfilled by regarding the
class as a species, and giving the proximate genus and
the difference. The word genus is here used in its inten-
sive meaning, and denotes the qualities belonging to all
of the genus, and sufficient to mark them out ; and as the
difference marks out the part of the genus in question,
we get a perfect definition of the species desired. But we
should be careful to give in a definition no superfluous
marks ; if these are accidents and do not belong to the
whole, the definition will be improperly narrowed, as if
we were to define Quadrilateral Figures as figures with
four equal sides ; if the superfluous marks belong to all
the things defined they are Prope?'ties, and have no effect
upon the definition whatever. Thus if I define parallelo-
grams as " four-sided rectilineal figures, with the opposite
sides equal and parallel, and the opposite angles equal,"
I have added two properties, the equality of the opposite
sides and angles which necessarily follow from the paral-
lelism of the sides, and only add to the complexity of the
definition without rendering it more precise.

There are certain rules usually given in logical works
which express the precautions necessary in definition.

1. A definition should state the essejitial attributes of
the species defified. So far as any exact meaning can be
given to the expression "essential attributes," it means,
as explained above, the proximate genus and difference.

2. A definition must not co7itain the na7ne defined.
For the purpose of the definition is to make the species
known, and as long as it is not known it cannot sei-ve to

no THE PREDICABLES, DIVISION, [less.

make itself known. When this rule is not observed, there
is said to be ' circulus in deji^tiendo^ or ' a circle in defin-
ing,' because the definition brings us round again to the
very word from which we started. This fault will usually
be committed by using a word in the definition which is
really a synonym of the name defined, as if I were to
define "Plant" as "an organized being possessing vege-
table life," or elements as simple substances, vegetable
being really equivalent to plant, and simple to elementary.
If I were to define metals as " substances possessing me-
tallic lustre," I should either commit this fault, or use the
term metallic lustre in a sense which would admit other
substances, and thus break the following rule.

3. The definition must be exactly equivalent to the
species defined^ that is to say, it must be an expression the
denotation of which is neither narrower nor wider than
the species, so as to include exactly the same objects.
The definition, in short, must denote the species, the
whole species, and nothing but the species, and this may
really be considered a description of what a definition is.

4. A definition must not be expressed in obscure^figura-
tive or a7nbiguous laiiguage. In other words, the tenns
employed in the definition must be all exactly known,
otherwise the purpose of the definition, to make us ac-
quainted with the sufficient marks of the species, is
obviously defeated. There is no worse logical fault than
to define ignotum per ignotius, the unknown by the still
more unknown. Aristotle's definition of the soul as ' The
Entelechy, or first form of an organized body which has
potential life,' certainly seems subject to this objection.

5. And lastly,^ definition must not be iiegative where
it can be affirmative. This rule however is often not
applicable, and is by no means always binding.

Read Mr Mill on the nature of Classification and the

XII.] AND DEFINITION. in

five Predicables, System of Logic, Book I. Chap.
VII. For ancient Scholastic Views concerning De-
finition, see Mansel's Artis Logics Rudimenta
(Aldrich), App. Note C.

LESSON XIII.

PASCAL AND DESCARTES ON METHOD.

It may be doubted whether any man ever possessed a
more acute and perfect intellect than that of Blaise
Pascal He was born in 1623, at Clermont in Auvergne,
and from his earliest years displayed signs of a remark-
able character. His father attempted at first to prevent
his studying geometry, but such was Pascal's genius and
love of this science, that, by the age of twelve, he had
found out many of the propositions of Euclid's first book
without the aid of any person or treatise. It is difficult
to say whether he is most to be admired for his mathe-
matical discoveries, his invention of the first calculating
machine, his wonderful Provincial Letters written against
the Jesuits, or for his profound Pensees or Thoughts, a
collection of his reflections on scientific and religious
topics.

Among these Thoughts is to be found a remarkable
fragment upon Logical method, the substance of which is
also given in the Port Royal Logic. It forms the second
article of the Pensees, and is entitled Reflexions sur la
Geovietrie en general. As I know no composition in
which perfection of truth and clearness of expression are
more nearly attained, I propose to give in this lesson a
free translation of the more important parts of this

112 PASCAL AND DESCARTES [less

fragment, appending to it rules of method from the
Port Royal Logic, and from Descartes' celebrated Essay
on Method. The words of Pascal are nearly as follows.

**The true method, which would furnish demonstra-
tions of the highest excellence, if it were possible to
employ the method fully, consists in observing two prin-
cipal rules. The first rule is not to employ any term of
which we have not clearly explained the meaning; the
second rule is never to put forward any proposition which
we cannot demonstrate by truths already known ; that is
to say, in a word, to define all the terms ^ and to prove all
the propositions. But, in order that I may observe the
rules of the method which I am explaining, it is neces-
sary that I declare what is to be understood by Definition.

"We recognise in Geometry only those definitions
which logicians call Nominal Definitions, that is to say,
only those definitions which impose a name upon things
clearly designated in terms perfectly known ; and I speak
only of those definitions."

Their value and use is to clear and abbreviate dis-
course by "expressing in the single name which we
impose what could not be otherwise expressed but in
several words ; provided nevertheless that the name im-
posed remain divested of any other meaning which it
might possess, so as to bear that alone for which we
intend it to stand.

" For example, if we need to distinguish among
numbers those which are divisible into two equal parts,
from those which are not so divisible, in order to avoid
the frequent repetition of this distinction, we give a name
to it in this manner : — we call every number divisible into
two equal parts an Even Number.

" This is a geometrical definition, because after having
clearly designated a thing, namely any number divisible
into two equal parts, we give it a name divested of every

XIII.] ON METHOD. 113

other meaning, which it might have, in order to bestow
upon it the meaning designated.

" Hence it appears that definitions are very free, and
that they can never be subject to contradiction, for there
is nothing more allowable, than to give any name we wish
to a thing which we have clearly pointed out. It is only
necessary to take care that we do not abuse this liberty of
imposing names, by giving the same name to two differ-
ent things. Even that would be allowable, provided that
we did not confuse the results, and extend them from
one to the other. But if we fall into this vice, we have a
very sure and infallible remedy ; — it is, to substitute men-
tally the definition in place of the thing defined,' and to
hold the definition always so present in the mind, that
every time we speak, for instance, of an even number, we
may understand precisely that it is a number divisible
into two equal parts, and so that these two things should
be so combined and inseparable in thought, that as often
as one is expressed in discourse, the mind may direct it-
self immediately to the other.

" For geometers and all who proceed methodically
only impose names upon things in order to abbreviate
discourse, and not to lessen or change the ideas of the
things concerning which they discourse. They pretend
that the mind always supplies the entire definition of the
brief terms which they employ simply to avoid the con-
fusion produced by a multitude of words.

" N othing prevents more promptly and effectively the
insidious fallacies of the sophists than this method, which
we should always employ, and which alone suffices to
banish all sorts of difficulties and equivocations.

" These things being well understood, I return to my
explanation of the true method, which consists, as I said,
in defining everything and proving everything.

" Certainly this method would be an excellent one,

8

TT4 PASCAL AND DESCARTES [less.

were it not absolutely impossible. It is evident that the
first terms we wished to define would require previous
terms to serve for their explanation, and similarly the
first propositions we wished to prove, would presuppose
other propositions preceding them in our knowledge ; and
thus it is clear that we should never arrive at the first
terms or first propositions.

"Accordingly in pushing our researches further and
further, we arrive necessarily at primitive words which we
cannot define, and at principles so clear, that we cannot
find any principles more clear to prove them by. Thus
it appears that men are naturally and inevitably incapa-
ble of treating any science whatever in a perfect method ;
but it does not thence follow that we ought to abandon
every kind of method The most perfect method avail-
able to men consists not in defining everything and de-
monstrating everything, nor in defining nothing and de-
monstrating nothing, but in pursuing the middle course
of not defining things which are clear and understood by
all persons, but of defining all others ; and of not proving
truths known to all persons, but of proving all others.
From this method they equally err who undertake to de-
fine and prove everything, and they who neglect to do it
in things which are not self-evident."

It is made plain in this admirable passage that we
can never by using words avoid an ultimate appeal to
things, because each definition of a word must require
one or more other words, which also will require defini-
tion, and so on ad infinitum. Nor must we ever return
back upon the words already defined ; for if we define A
by B^ and B by C, and C by Z>, and then Z) by ^, we
commit what may be called a circulus in definiendo; a
most serious fallacy, which might lead us to suppose that
we know the nature of ^, B^ C, and Z>, when we really
know nothing about them.

XIII.] ON METHOD. 115

Pascal's views of the geometrical method were clearly
summed up in the following rules, inserted by him in the
Port Royal Logic*.

1. To admit no terms in the least obscure or equivo-
cal without defining them.

2. To employ in the definitions only terms perfectly
known or already explained.

3. To demand as axioms only truths perfectly evi-
dent.

4. To prove all propositions which are at all obscure,
by employing in their proof only the definitions which
have preceded, or the axioms which have been accorded,
or the propositions which have been already demonstrated,
or the construction of the thing itself which is in dispute,
when there may be any operation to perform.

5. Never to abuse the equivocation of terms by failing
to substitute for them, mentally, the definitions which
restrict and explain them.

The reader will easily see that these rules are much
more easy to lay down than to observe, since even geo-
meters are not agreed as to the simplest axioms to assume,
or the best definitions to make. There are many differ-
ent opinions as to the true definition of parallel lines, and
the simplest assumptions concerning their nature ; and
how much greater must be the difficulty of observing
Pascal's rules with confidence in less certain branches of
science. Next after Geometry, Mechanics is perhaps the
most perfect science, yet the best authorities have been
far from agreeing as to the exact definitions of such
notions zs force, mass, fnoment, power, inertia, and the
most different opinions are still held as to the simplest
axioms by which the law of the composition of forces may
be proved Nevertheless if we steadily bear in mind, in

* Mr Spencer Bajoies' Translation^ p. 317.

8—2

ii6 PASCAL AND DECARTES [less.

studying each science, the necessity of defining every term
as far as possible, and proving each proposition which
can be proved by a simpler one, we shall do much to clear
away error and confusion.

I also wish to give here the rules proposed by the
celebrated Descartes for guiding the reason in the attain-
ment of truth. They are as follows : —

1. Never to accept anything as true, which we do
not clearly know to be so ; that is to say, carefully to
avoid haste or prejudice, and to comprise nothing more
in our judgments than what presents itself so clearly and
distinctly to the mind that we cannot have any room to
doubt it.

2. To divide each difficulty we examine into as many
parts as possible, or as may be required for resolv-
ing it.

3. To conduct our thoughts in an orderly manner,
commencing with the most simple and easily known
objects, in order to ascend by degrees to the knowledge
of the most complex.

4. To make in every case enumerations so complete,
and reviews so wide, that we may be sure of omitting
nothing.

These rules were first stated by Descartes in his ad-
mirable Discowse on Method^ in which he gives his reflec-
tions on the right mode of conducting the reason, and
searching for truth in any of the sciences. This little
treatise is easily to be obtained in the original French, and
has also been translated into English by Mr Veitch*.
The reader can be strongly advised to study it. Always to
observe the rules of Descartes and Pascal, or to know
whether we in every case observe them properly, is im-

* Published at Edinburgh in 1 850.

XIII.] ON METHOD. 117

possible, but it must nevertheless be valuable to know at
what we ought to aim.

Read Locke's brief Essay on the Conduct of the Un-
derstandings which contains admirable remarks on
the acquirement of exact and logical habits of
thought.

LESSON XIV.

THE LAWS OF THOUGHT.

Before the reader proceeds to the lessons which treat
of the most common forms of reasoning, known as the
syllogism, it is desirable that he should give a careful
attention to the very simple laws of thought on which all
reasoning must ultimately depend. These laws describe
the very simplest truths, in which all people must agree,
and which at the same time apply to all notions which
we can conceive. It is impossible to think correctly and
avoid evident self-contradiction unless we observe what
are called the Tliree Primary Laws of Tliouglit, which may
be stated as follows :

1. The Law of Identity. Whatever is, is.

2. The Law of Contradiction. NotMng can both be and

not be.

3. The Law of Excluded Middle. Everything must

either be or not be.
Though these laws when thus stated may seem ab-
surdly obvious, and were ridiculed by Locke and others
on that account, I have found that students are seldom
able to see at first their full meaning and imponance.
It will be pointed out in Lesson XXI 1 1, that logicians b^ve

ii8 THE LAWS OF THOUGHT, [less.

overlooked until recent years the very simple way in which
all arguments may be explained when these self-evident
laws are granted ; and it is not too much to say that the
whole of logic will be plain to those who will constantly
use these laws as the key.

The first of the laws may be regarded as the best
definition we can give of identity or sameness. Could
any one be ignorant of the meaning of the word Identity,
it would be sufficient to inform him that everything is
identical witli itself.

The second law however is one which requires more
consideration. Its meaning is that nothing can have
at the same time and at the same place contradic-
tory and inconsistent qualities. A piece of paper may
be blackened in one part, while it is white in other parts;
or it may be white at one time, and afterwards become
black; but we cannot conceive that it should be both
white and black at the same place and time. A door
after being open may be shut, but it cannot at once be
shut and open. Water may feel warm to one hand and
cold to another hand, but it cannot be both warm and
cold to the same hand. No quality can both be present
and absent at the same time ; and this seems to be the
most simple and general truth which we can assert of all
things. It is the very nature of existence that a thing
cannot be otherwise than it is ; and it may be safely said
that all fallacy and error arise from unwittingly reason-
ing in a way inconsistent with this law. All statements
or inferences which imply a combination of contradictory
qualities must be taken as impossible and false, and the
breaking of this law is the mark of their being false. It
can easily be shewn that if Iron be a metal, and every
metal an element, Iron must be an element or it can be
nothing at all, since it would combine qualities which are
inconsistent (see Lesson xxiii).

XIV.] THE LAWS OF THOUGHT. 119

The Law of Excluded Middle is much less self-evident
than either of the two preceding ones, and the reader will
not perhaps see at the first moment that it is equally
important and necessary with them. Its meaning may
be best explained by saying that it is impossible to men-
tion any thing and any quality or circumstance, without
allowing that the quality or circumstance either belongs
to the thing or does not belong. The name of the law
expresses the fact that there is no third or middle course ;
the answer must be Yes or No. Let the thing be rock
and the quality hard; then rock must be either hard or
not-hard. Gold must be either white or not white j a
line must be either straight or not straight ; an action
must be either virtuous or not virtuous. Indeed when
we know nothing of the terms used we may never-
theless make assertions concerning them in accordance
with this law. The reader may not know and in fact
chemists m.ay not really know with certainty, whether
vanadium is a metal or not a metal, but any one knows
that it must be one or the other. Some readers may not
know what a cycloid is or what an isochronous curve is ;
but they must know that a cycloid is either an isochro-
nous curve or it is not an isochronous curve.

This law of excluded middle is not so evident but that
plausible objections may be suggested to it. Rock, it
may be urged, is not always either hard or soft, for it may
be half way between, a little hard and a little soft at the
same time. This objection points to a distinction which
is of great logical importance, and when neglected often
leads to fallacy. The law of excluded middle affirmed
nothing about hard and soft^ but only referred to hard
and not-hard J if the reader chooses to substitute soft for
not-hard he falls into a serious confusion between opposite
terms and contradictory terms. It is quite possible that
a thmg may be neither hard nor soft, being half way

I20 THE LAWS OF THOUGHT. [less.

between ; but in that case it cannot be fairly called hard,
so that the law holds true. Similarly water must be
either warm or not-warm, but it does not follow that it
must be warm or cold. The alternative not-warm evi-
dently includes all cases in which it is cold besides cases
where it is of a medium temperature, so that we should
call it neither warm nor cold. We must thus carefully
distinguish questions of degree or quantity from those of
simple logical fact. In cases where a thing or quality
may exist to a greater or less extent there are many alter-
natives. Warm water, for, instance may have any tempe-
rature from 70° perhaps up to 120°. Exactly the same
question occurs in cases of geometrical reasoning; for
Euclid in his Elements frequently argues from the self-
evident truth that any line must be either greater than,
equal to, or less than any other line. While there are
only two alternatives to choose from in logic there are
three in Mathematics ; thus one line, compared with
another, may be —

{greater greater i ^

not-greater...j ••••••^^^"^=^1 (Mathematics.

Another and even more plausible objection may be
raised to the third law of thought in this way. Virtue
being the thing proposed, and tria7igular the quality, the
Law of Excluded Middle enables us at once to assert that
virtue is either triangular or not -triangular. At first sight
it might seem false and absurd to say that an immaterial
notion such as virtue should be either triangular or not,
because it has nothing in common with those material
substances occupying space to which the notion of figure
belongs. But the absurdity would arise, not from any
falseness in the law, but from misinterpretation of the
expression net-triangular. If in saying that a thing is

XIV.] THE LAWS OF THOUGHT. 121

"not triangular" we are taken to imply that it has some
figure though not a triangular figure, then of course the
expression cannot be applied to virtue or anything im-
material. In strict logic however no such implied mean-
ing is to be allowed, and not-triangular will include both
things ^vhich have figure other than triangular, as well as
things which have not the properties of figure at all; and
it is in the latter meaning that it is applicable to an im-
material thing.

These three laws then being universally and neces-
sarily true to whatever things they are applied, become
the foundation of reasoning. All acts of reasoning pro-
ceed from certain judgments, and the act of judgment
consists in comparing two things or ideas together and
discovering whether they agree or differ, that is to say
whether they are identical in any qualities. The laws of
thought inform us of the very nature of this identity with
which all thought is concerned. But in the operation
of discourse or reasoning we need certain additional
laws, or axioms, or self-evident truths, which may be thus
stated :

1. Two terms agreemg- with o?ie and the same third
term agree with each other.

2. Two terms of which one agrees and the other does
not agree with one and the same third term^ do not agree
with each other.

These self-evident truths are commonly called the
Canons or Fundamental Principles of Syllogism, and they
are true whatever may be the kind of agreement in ques-
tion. The example we formerly used (p. 3) of the a-
greement of the terms "Most useful metal" and "cheapest
metal" with the third common term " Iron," was but
an instance of the first Canon, and the agreement con-
sisted in complete identity. In the case of the " Earth,"
the " Planets," and " Bodies revolving in elliptic orbits,"

122 THE LAWS OF THOUGHT, [less.

the agreement was less complete, because the Earth is
orxly one of many Planets, and the Planets only a small
portion of all the heavenly bodies, such as Satellites,
Comets, Meteors, and Double-Stars which revolve in
such orbits.

The second of the Canons applies to cases where there
is disagreement or difference, as in the following example :
Venus is a planet.
Planets are not self-luminous.
Therefore Venus is not self-luminous.
The first of these propositions states a certain agree-
ment to exist between Venus and planet, just as in the
previous case of the Earth, but the second proposition
states a disagreement between Planet and self-luminous
bodies; hence we infer a disagreement between Venus
and self-luminous body. But the reader will carefully
observe that frotn two disagreemetits we can never infer
anythifig. If the following were put forth as an argu-
ment it would be evidently absurd : —
Sirius is not a planet.
Planets are not self-luminous.
Therefore Sirius is not self-luminous.

Both the premises or propositions given are true,
and yet the conclusion is false, for all the fixed stars are
self-luminous, or shine by their own light. We may, in
fact, state as a third Canon that —

3. Two terms both disagreeing with 07te and the
same third term 7nay or may not agree with each other.

Self-evident rules, of an exactly similar nature to these
three Canons, are the basis of all mathematical reasoning,
and are usually called axioms. Euclid's first axiom is
that "Things which are equal to the same thing are equal
to one another ;" and whether we apply it to the length of
lines, the magnitude of angles, areas, solids, numbers,

XIV.] THE LAWS OF THOUGHT. 123

degrees, or anything else which admits of being equal or
unequal, it holds true. Thus if the lines A and B are each
equal to C it is evident that each is equal to the other.

Euclid does not give axioms corresponding to the second
and third Canons, but they are really used in Geometry.
Thus if ^ is equal to B, but D is not equal to B, it follows
that A is not equal to Z>, or things of which one is equal,
but the other unequal to the same third thing, are unequal
to each other. Lastly, A and E are two lines both un-
equal to D and unequal to each other, whereas A and B
are two lines both unequal to D but equal to each other ;
thus we plainly see that " two things both unequal to the
same thing may or may not be equal to each other."

From what precedes it will be apparent that all rea-
soning requires that there should be one agreement at
least; if there be two agreements we may reason to a
third agreement; if there be one agreement and one
difference we may reason to a second difference ; but if
there be two differences only we cannot reason to any
conclusion whatever. These self-evident principles will
in the next Lesson serve to explain some of the rules of
the Syllogism.

Logicians however have not confined themselves to
the use of these Canons, but have often put the same
truth into a different form in an axiom called the Dictum
de ofnjti et nullo of Aristotle. This celebrated Latin
phrase means " Statement concerning all and none," and
the axiom, or rather pair of axioms, is usually given in
the following words :

124 THE LAWS OF THOUGHT. [less.

Whatever is predicated of a term distributed whether
affirmatively or negatively^ may be predicated in like
manner of everything contained under it.
Or more briefly :

What pertains to the higher class pertains also to the
lower.

This merely means, in untechnical language, that
what may be said of all the things of any sort or kind
may be said of any one or any part of those things ; and,
secondly, what may be denied of all the things in a class
may be denied of any one or any part of them. What-
ever may be said of "All planets" may be said of Venus,
the Earth, Jupiter, or any other planet ; and, as they may
all be said to revolve in elliptic orbits, it follows that
this may be asserted of Venus, the Earth, Jupiter, or any
other planet. Similarly, according to the negative part
of the Dicta, we may deny that the planets are self-
luminous, and knowing that Jupiter is a planet may deny
that Jupiter is self-luminous. A little reflection would
show that the affirmative Dictum is really the first of the
Canons in a less complete and general form, and that the
negative Dictum is similarly the second Canon. These
Dicta in fact only apply to such cases of agreement be-
tween terms as consist in one being the name of a smaller
class, and another of the larger class containing it Lo-
gicians have for the most part strangely overlooked the
important cases in which one term agrees with another to
the extent of being identical with it ; but this is a subject
which we cannot fitly discuss here at any length. It is
treated in my little work called The Substitution of
Similars'*.

Some logicians have held that in addition to the three
laws which are called the Primary Laws of Thought,

* Macmillan and Co. 1869.

XIV.] THE LAWS OF THOUGHT. 125

there is a fourth called " The Principle or Law of Suffi-
cient Reason." It was stated by Leibnitz in the following
words :

Nothing happens without a reason why it should be
so rather than otherwise. For instance, if there be a pair
of scales in every respect exactly alike on each side and
with exactly equal weights in each scale, it must remain
motionless and in equilibrium, because there is no reason
why one side should go down more than the other. It is
certainly a fundamental assumption in mechanical science
that if a body is acted upon by two perfectly equal forces
in different directions it will move equally between them,
because there is no reason why it should move more to
one side than the other. Mr Mansel, Sir W. Hamilton
and others consider however that this law has no place
in logic, even if it can be held self-evident at all ; and the
question which appears open to doubt need not be dis-
cussed here.

I have so freely used the word axiom in this lesson
that it is desirable to clear up its meaning as far as pos-
sible. Philosophers do not perfectly agree about its deri-
vation or exact meaning, but it certainly comes from the
verb a^i6u>, which is rendered, to think worthy. It gene-
rally denotes a self-evident truth of so simple a character
that it must be assumed to be true, and, as it cannot be
proved by any simpler proposition, must itself be taken as
the basis of reasoning. In mathematics it is clearly used
in this sense.

See Hamilton's Lectures on Logic, Lectures 5 and 6.

LESSON XV.
THE RULES OF THE SYLLOGISM.

Syllogism is the common name for Mediate Inference,
or inference by a medium or middle term, and is to be
distinguished from the process of Immediate Inference, or
inference which is performed without the use of any third
or middle term.

We are in the habit of employing a middle term or
medium whenever we are prevented from comparing two
things together directly, but can compare each of them
with a certain third thing. We cannot compare the sizes
of two halls by placing one in the other, but we can
measure each by a foot rule or other suitable measure,
which forms a common measure, and enables us to ascer-
tain with any necessary degree of accuracy their relative
dimensions. If we have two quantities of cotton goods
and want to compare them, it is not necessary to bring
the whole of one portion to the other, but a sample is cut
off, which represents exactly the quality of one portion,
and, according as this sample does or does not agree with
the other portion, so must the two portions of goods agree
or differ.

The use of a middle term in syllogism is closely pa-
rallel to what it is in the above instances, but not exactly
the same. Suppose, as an example, that we wish to
ascertain whether or not "Whales are viviparous," and
that we had not an opportunity of observing the fact
directly ; we could yet show it to be so if we knew that
"whales are mammalian animals," and that "all mam-

XV.] THE RULES OF THE SYLLOGISM. 127

malian animals are viviparous." It would follow that
"whales are viviparous;" and so far as the inference is
concerned it does not matter what is the meaning we
attribute to the words viviparous and mammalian. In
this case " mammalian animal " is the middle term.

The name Syllogism means the joining together in
thought of two propositions, and is derived from the
Greek words o-yi/, together, and Xoyos, thought. It
is thus exactly the equivalent of the word Co7nputatio7i,
which means thinking together (Latin con, together,
puto, to think), or reckoning. In a syllogism we so unite
in thought two premises, or propositions put forward, that
we are enabled to draw from them or infer, by means of
the middle term they contain, a third proposition called
the conclusion. Syllogism may thus be defined as the
act of thought by which from two given propositions we
proceed to a third proposition, the truth of which neces-
sarily follows from the truth of these given propositions.
When the argument is fully expressed in language it is
usual to call it concretely a syllogism.

The special rules of the syllogism are founded upon
the Laws of Thought and the Canons considered in the
previous Lesson. They serve to inform us exactly under
what circumstances one proposition can be inferred from
two other propositions, and are eight in number, as
follov/s : —

1. Every syllogism has three and only three terms.
These terms are called the major term, the minor

term, and the middle term.

2. Every syllogism contains three, and only three
propositions.

These propositions are called the major premise, the
minor premise, and the conclusion.

3. The middle term must be distributed once at leasts
and must not be ambiguous.

128 THE RULES OF THE SYLLOGISM, [less.

4. No ter7n inust be distribiited in the conclusion
which was not distributed in one of the premises.

5. From negative premises nothing can be inferred.

6. If one pretnise be negative^ the conclusion must
be negative; and vice versa, to prove a negative con-
elusion one of the premises must be negative.

From the above rules may be deduced two subor-
dinate rules, which it will nevertheless be convenient to
state at once.

7. From two particular pretnises no conclusion can
be drawn.

8. If 07ie premise be particular^ the conclusion must
be particular.

All these rules are of such extreme importance that it
will be desirable for the student not only to acquire a
perfect comprehension of their meaning and truth, but to
commit them to memory. During the remaindejr of this
lesson we shall consider their meaning and force.

As the syllogism consists in comparing two terms by
means of a middle term, there cannot of course be less
than three terms, nor can there be more ; for if there
were four terms, say A^ B, C, D, and we compared A
with B and C with D, we should either have no common
medium at all between A and D, or we should require a
second syllogism, so as first to compare A and C with B,
and then A and D with C.

The middle term may always be known by the fact
that it does not occur in the conclusion. The major term
is always the predicate of the conclusion, and the minor
term the subject. , These terms are thus called because in
the universal affirmative proposition (A) the predicate is
necessarily a wider or greater or major term than the
subject ; thus in " all men are mortals," the predicate in-
cludes all other animals as well as men, and is obviously
a major term or wider terra than men.

XV.] THE RULES OF THE SYLLOGISM, 129

Again, the syllogism necessarily consists of a premise
called the major premise, in which the major and middle
terms are compared together ; of a rhinor premise which
similarly compares the minor and middle terms ; and of
a conclusion, which contains the major and minor terms
only. In a strictly correct syllogism the major premise
always stands before the minor premise, but in ordinary
writing and speaking this rule is seldom observed ; and
that premise which contains the major term still con-
tinues to be the major premise, whatever may be its
position.

The third rule is a very important one, because many
fallacies arise from its neglect. By the middle term being
distributed once at least, we mean (see p. 74) that the
whole of it must be referred to universally in one premise,
if not both. The two propositions —

All Frenchmen are Europeans,

All Russians are Europeans,
do not distribute the middle term at all, because they
are both affirmative propositions, which have (p. 75)
undistributed predicates. It is apparent that French-
men are one part of Europeans, and Russians another
part, as shown in Euler's method in Fig. 6, so that

Y\z. 6.

130 THE RULES OF THE SYLLOGISM, [less.

there is no real middle term. Those propositions would
equally allow of Russians being or not being Frenchmen ;
for whether the two interior circles overlap or not they
are equally within the larger circle of Europeans. Again,
the two propositions

All Frenchmen are Europeans,

All Parisians are Europeans,
do not enable us to infer that all Parisians are French-
men. For though we know of course that all Parisians

Fig. 7.

are included among Frenchmen, the premises would
allow of their being placed anywhere within the circle of
Europeans. We see in this instance that the premises
and conclusion of an apparent argument may all be true
and yet the argument may be fallacious.

The part of the third rule which refers to an amM-
guous middle term hardly requires explanation. It has
been stated (Lesson IV.) that an ambiguous term is one
which has two different meanings, implymg different con-
notations, and it is really equivalent to two different terms
which happen to have the same form of spelling, so that
they are readily mistaken for each other. Thus if we
were to argue that because " all metals are elements and

XV.] THE RULES OF THE SYLLOGISM, 131

brass is metal, therefore it is an element," we should be
committing a fallacy by using the middle term metal in
two different senses, in one of which it means the pure
simple substances known to chemists as metals, and in
the other a mixture of metals commonly called metal in
the arts, but known to chemists by the name alloy. In
many examples which may be found in logical books the
ambiguity of the middle term is exceedingly obvious, but
the reader should always be prepared to meet with cases
where exceedingly subtle and difficult cases of ambiguity
occur. Thus it might be argued that "what is right
should be enforced by law, and that charity is right and
should therefore be enforced by the law." Here it is
evident that right is applied in one case to what the
conscience approves, and in another case to what public
opinion holds to be necessary for the good of society.

The fourth rule forbids us to distribute a term in the
conclusion unless it was distributed in the premises. As
the sole object of the syllogism is to prove the conclusion
by the premises, it is obvious that we must not make a
statement concerning anything unless that thing was
mentioned in the premises, in a way warranting the state-
ment Thus if we were to argue that " because many
nations are capable of self-government and that nations
capable of self-government should not receive laws from a
despotic government, therefore no nation should receive
laws from a despotic government," we should be clearly
exceeding the contents of our premises. The minor term,
ma7iy stations, was particular in the minor premise, and
must not be made universal in the conclusion. The pre-
mises do not warrant a statement concerning anything but
the viany nations capable of self-government. The above
argument would therefore be fallacious and would be
technically called an illicit process of the minor term,
meaning that we have improperly treated the minor term.

9—2

132 THE RULES OF THE SYLLOGISM, [less.

Such a breach of the fourth rule as is described above
is exceedingly easy to detect, and is therefore very seldom
committed.

But an illicit process or improper treatment of the
major term is more common because it is not so trans-
parently false. If we argued indeed that "because all
Anglo-Saxons love liberty, and Frenchmen are not Anglo-
Saxons, therefore they do not love liberty," the fallacy
would be pretty apparent ; but without a knowledge of
logic it would not be easy to give a clear explanation of
the fallacy. It is apparent that the major term loving
liberty^ is undistributed in the major premise, so that
Anglo-Saxons must be assumed to be only a part of those
who love liberty. Hence the exclusion of Frenchmen
from the class Anglo-Saxons does not necessarily exclude
them from the class who love liberty (see Fig. 8). The

Fig. 8.

conclusion of the false argument being negative distri-
butes its predicate, the major term, and as this is un-
distributed in the major premise we have an illicit major
as we may briefly call this fallacy. The following is an
obscurer example of the same fallacy;—" Few students

t/W?^y ('S^^^^^ ^^4^^^^

XV.] THE RULES OF THE SYLLOGISM. 133

are capable of excelling in many branches of knowledge,
and such as can so excel are deserving of high commen-
dation ;" hence " few students are deserving of high com-
mendation." The little word "few" has here the double
meaning before explained (p. (i'j), and means that "a
few are, &c., and the rest are not." The conclusion is
thus really a negative proposition, and distributes the
major term "deserving of high commendation." But
this major term is clearly undistributed in the major
premise, which merely asserts that those who can excel
in many branches of knowledge are deserving, but says
or implies nothing about other students.

The fifth rule is evidently founded on the principle
noticed in the last lesson, that inference can only proceed
where there is agreement, and that two differences or
disagreements allow of no reasoning. Two terms, as the
third Canon states, may both differ from a common term
and yet may or may not differ from each other. Thus if

Fig. 9.

\

Colonists

we were to argue that Americans are not Europeans, and
Virginians are not Europeans, we see that both terms
disagree with the middle term Europeans, and yet they

134 THE RULES OF THE SYLLOGISM, [less.

agree between themselves. In other cases the two nega-
tive premises may be plainly true while it will be quite
uncertain whether the major and minor terms agree or
not. Thus it is true, for instance, that "Colonists are
not Europeans, and Americans are not Europeans," but
this gives us no right to infer that Colonists are or
are not Americans. The two negative premises are re-
presented in fig. 9, by excluding the circles of Colonists
and Americans from that of Europeans ; but this exclusion
may still be effected whether Colonists and Americans
coincide partially, or wholly, or not at all. A breach of
this rule of the syllogism may be conveniently called the
fallacy of negative premises. It must not however be
supposed that the mere occurrence of a negative particle
{7iot or no) in a proposition renders it negative in the
manner contemplated by this rule. Thus the argument

" What is not compound is an element.
Gold is not compound ;
Therefore Gold is an element."

contains negatives in both premises, but is nevertheless
valid, because the negative in both cases affects the middle
term, which is really the negative term not-compoimd.

The truth of the sixth rule depends upon that of the
axiom, that if two terms agree with a common third term
they agree with each other, whence, remembering that a
negative proposition asserts disagreement, it is evident
that a negative conclusion could not be drawn from really
affirmative premises. The corresponding negative axiom
prevents our drawing an affirmative conclusion if either
premise should be really negative. Only practice how-
ever will enable the student to apply this and the
preceding rules of the syllogism with certainty, since
fallacy may be hidden and disguised by various forms of
expression. Numerous examples are given at the end of

XV.] THE RULES OF THE SYLLOGISM. 135

the book by which the student may acquire faciHty in
the analysis of arguments.

The remaining rules of the syllogism, the 7th and 8th,
are by no means of a self-evident character and are in
fact corollaries of the first six rules, that is consequences
which follow from them. We shall therefore have to
shew that they are true consequences in a future Lesson.
We may call a breach of the 7th rule 2. fallacy of parti-
cular premises^ and that of the 8th rule the fallacy of a
universal conclusion from a particular pre7nise^ but these
fallacies may really be resolved into those of Illicit
Process, or Undistributed Middle.

For many details concerning the Aristotelian and
Scholastic Views of the Syllogism, and of Formal
Logic generally, see the copious critical notes to
Mansel's edition of Aldrich's Artis Logiccz Rudi-
menta. 2nd Ed. Oxford, 1852.

LESSON XVI.

THE MOODS AND FIGURES OF THE
SYLLOGISM.

We are now in full possession of those principles of rea-
soning, and the rules founded upon them, by which a
true syllogism may be known from one which only seems
to be a true one, and our task in the present Lesson is to
ascertain the various shapes or fashions in which a
process of mediate inference or syllogism may be met
with. We know that every syllogistic argument must
contain three propositions and three distinct terms each
occurring twice in those propositions. Each proposition

136 THE MOODS AND FIGURES [less.

of the syllogism may, so far as we yet know, be either
affirmative or negative, universal or particular, so that it
is not difficult to calculate the utmost possible varieties of
modes in which a syllogism might conceivably be con-
structed. Any one of the four propositions A, E, I, or 0 may
in short be taken as a major premise, and joined with any
one of the same four as a minor premise, and any one of
the four again may be added as conclusion. We should
thus obtain a series of the combinations or modes of
joining the letters A, E, I, 0, a few of which are here writ-
ten out :

AAA

AEA

AIA

AOA

EAA

EEA

AAE

AEE

AIE

AOE

EAE

EEE

AAI

AEI

All

AOI

EAI

EEI

AAO

AEO

AIO

AOO

EAO

&c.

It is obvious that there will be altogether 4x4x4 or 64
such combinations, of which 23 only are given above.
The student can easily write out the remainder by carry-
ing on the same systematic changes of the letters. Thus
beginning with AAA we change the right-hand letter suc-
cessively into E, I, and 0, and then do the same beginning
with AEA instead ; after the middle letter has been carried
through all its changes we begin to change the left-hand
letter. With each change of this we have to repeat all
the sixteen changes of the other letters, so that there will
obviously be altogether 64 different conceivable modes
of arranging propositions into syllogisms.

We call each of these triplets of propositions a mood or
form of the syllogism (Latin modus , shape), and we have
to consider how many of such forms can really be used in
valid arguments, as distinguished from those which break
one or more of the rules of the syllogism. Thus the mood
AEA would break the 6th rule, that if one premise be
negative the conclusion must be so too : AIE breaks the

XVI.] OF THE SYLLOGISM. 137

converse part of the same rule, that a negative conclusion
can only be proved by a negative premise ; while EEA,
EEE &c., break the 5th rule, which prohibits our reasoning
at all from two negative premises. Examples of any of
these moods can easily be invented, and their falsity would
be very apparent ; thus for AEA we might take

All Austrians are Europeans,
No Australians are Europeans ;
Therefore, all Australians are Austrians.

Many of the 64 conceivable moods are excluded by the
7th and 8th rules of the syllogism. Thus AIA and EIE
break the rule, that if one premise be particular the con-
clusion must be so also, while IIA, 100, 010 and many
others, break the rule against two particular premises.
Some combinations of propositions may break more than
one rule ; thus 000 has both negative premises and parti-
cular premises, and OOA also violates as well the 6th
rule. It is an admirable exercise in the use of the syl-
logistic rules to write out all the 64 combinations and
then strike out such as break any rule ; the task if pur-
sued systematically will not be so long or tedious as
might seem likely. It will be found that there are only
twelve moods which escape exclusion, and may so far be
considered good forms of reasoning, and these are

AAA EAE lAI OAO

AAI EAO (lEO)

AEE EIO

AEO

All

AOO

Of these however EEO will have shortly to be rejected,
because it will be found really to break the 4th rule, and
involves Illicit process of the major term. There are,

138 THE MOODS AND FIGURES {less.

then, only eleven moods of the syllogism which are really
valid; and we may thus account for the whole of the''
sixty-four moods.

Number
Excluded by of moods.

Negative premises, Rule 5 16

Particular premises „ 7 12

One negative premise „ 6 12

One premise particular „ 8 8

Negative conclusion „ 6 4

Illicit major „ 4 i

Total excluded 53

Valid moods 11

Total 64

We have by no means exhausted as yet all the
possible varieties of the syllogism, for we have only de-
termined the character, affirmative or negative, general
or particular of the propositions, but have not decided
the ways in which the terms may be disposed in them.
The major term must be the predicate of the conclusion,
but it may either be subject or predicate of the major
premise, and similarly the minor term or subject of the
conclusion, may be either the subject or predicate of the
minor premise. There thus arise four different ways, or
as they are called Figures, in which the terms can be
disposed. These four figures of the syllogism are shewn
in the following scheme, taking

X to denote the major term

Y middle „

Z minor „

I St Fig. 2nd Fig. 3rd Fig. 4th Fig.

Major Premise YX XY YX XY

Minor „ ZY ZY YZ YZ

Conclusion ZX ZX ZX ZX

XVI.] OF THE SYLLOGISM. 139

These figures must be carefully committed to memory,
"which will best be done by noting the position of the
middle term. This term stands Jirst as subject of the
major premise in the ist Figure, second 2iS predicate in
both premises of the 2nd Figure, yfn-/ again as subject of
both premises in the 3rd Figure, and in an intermediate
position in the 4th Figure. In the conclusion, of course,
the major and minor terms have one fixed position, and
■when the middle term is once correctly placed in any
figure we easily complete the syllogism.

The reader will hardly be pleased to hear that each of
the eleven valid moods will have to be examined in each
of the four figures separately, so that there are 44 cases
still possible, from which the valid syllogisms have to be
selected. Thus the mood AEE in the first figure would be
as follows :

All K's are JTs,
No Z's are K's ;

Therefore No Z^s are X^s.

This would break the 4th rule and be an Illicit Major,
because X is distributed in the conclusion, which is a
negative proposition, and not in the major premise. In
the second figure it would be valid:

All ^'s are F's,
NoZ'sareK's;
Therefore No Z's are X^s.

In the third figure it becomes

All K's are JTs,
No K's are Z's,
No Z's are ^s,

and again breaks the 4th rule, as regards the major term.
Lastly in the 4th figure it is valid, as the reader may
easily satisfy himself.

I40 THE MOODS AND FIGURES [less.

When all the valid moods are selected out of the 44
possible ones, there are found to be altogether 24, which
are as follows:

Valid Moods of the Syllogism.

First Second Third Fourth

Figure. Figure. Figure. Figure.

AAA EAE AAI AAI

£A£ A££ lAI AEE

All EIO All lAI

EIO AOO EAO EAO
OAO EIO

[AAI] [EAO] EIO

[EAO] [AEO] [AEOJ

Five of the above moods are set apart and enclosed in
brackets, because though valid they are of little or no use.
They are said to have a weakened conclusion, because the
conclusion is particular when a general one might have ,
been drawn. Thus AAI, in the first figure is represented
by the example :

All material substances gravitate,
All metals are material substances ;
Therefore some metals gravitate.

It is apparent that the conclusion only states a part of
the truth, and that in reality all metals gravitate. It is
not actually an erroneous conclusion, because it must
be carefully remembered (p. ']']) that the affirming of a
subaltern or particular proposition does not deny the
corresponding general proposition. It is quite true that •
some metals gravitate, and it must be true because all of
them do so. But when we can as readily prove that all
do gravitate it is desirable to adopt this conclusion.

If we agree with most logicians to overlook the ex- "
istence of the five syllogisms with weakened conclusions,

XVI.] OF THE SYLLOGISM, 141

^there will remain nineteen which are at once valid and
useful. In the next lesson certain ancient mnemonic
lines will be furnished by which alone it would be possible
for most persons to carry in the memory these 19 combi-
nations ; but the reader will in the mean time be able to
gather from the statement of the moods in p. 140 the
truth of the following remarks concerning the peculiai
character of each figure of the syllogism.

The first figure is the only one which proves the pro-
position A, or has A for its conclusion. It is the only
figure, too, which can prove any one of the four proposi-
tions A, E, I, 0. As regards the premises, it is especially
important to note that the major premise is always
universal (A or E), and the minor premise affirmative (A or
I) : this peculiarity will be further considered in the next
lesson.

The second figure only proves negative conclusions
,(E or 0), and the reason is easily apparent. As the middle
term in this figure is the predicate of both premises it
would necessarily be undistributed in both premises if
these were affirmatives, and we should commit the fallacy
exemplified in p. 137. It follows that one premise must
be negative and of course one only, so that of the major
and minor terms one must be included or excluded wholly
from the middle, and the other at the same time excluded
"or included at least partially. To illustrate this we may
take X^ Kand Z" to represent, as before, the major, mid-
dle and minor terms of a syllogism, and the four moods of
this figure are then

EAE AEE

no X\ are I^s, all X's are Vs,

all Z's are F's ; no Z's are K's ;

•', no Z's are Jf 's. .-. no Z's are ^'s.

142

THE MOODS AND FIGURES [LESS.

EIO

no ^'s are K's,
some Z's are F's ;
*. some Z's are not ^'s.

AOO

all X's are F^s,
some Z's are not Vs ;
.'. some Z's are not AT's.

The nature of the moods of the second figure is clearly
shewn in the following figures :

Fig. lo.
(Cesare.)

Fig. II.
(Camestres.)

Fig. \^.
(Festino.)

It will also be observed that in the second figure the
minor premise may be any of the four A, E, I, 0.

The third figure only proves particulars (I or 0), and
it always has an affirmative minor premise (A or I). It
also contains the greatest number of moods, since in no
case is the conclusion a weakened one.

XVI.] OF THE SYLLOGISM. 143

The fourth figure is usually considered unnatural and
comparatively useless, because the same arguments can
be more clearly arranged in the form of the first figure,
which in some respects it resembles. Thus it proves all
the propositions except A, namely, E, I, 0, and its first
mood AAI, is in reality a weakened form of AAA in the
first figure. Many logicians, including in recent times
Sir W. Hamilton, have rejected the use of this figure
' altogether.

It is evident that the several figures of the syllogism
possess different characters, and logicians have thought
that each figure was best suited for certain special pur-
poses. A German logician, Lambert, stated these pur-
poses concisely as follows :— "The first figure is suited to
the discovery or proof of the properties of a thing ; the
second to the discovery or proof of the distinctions be-
tween things; the third to the discovery or proof of in-
stances and exceptions ; the fourth to the discovery, or
exclusion, of the different species of genus."

It may be added that the moods Cesare and Cames-
tres are often used in disproving a statement, because
they give a universal negative conclusion, founded upon
the exclusion of one class from another. Thus if any
one were still to assert that light consists of material
particles it might be met by the following syllogism :

" Material particles communicate impetus to
whatever they strike.
Light does not communicate impetus to
whatever it strikes ;
Therefore light is not material particles."

The moods Baroko and Festino are less used, but
allow of a particular conclusion being established.

When we wish however to establish objections or

144 THE IMPERFECT FIGURES [less.

exceptions to a general statement, whicli is indeed the
natural way of meeting it, we employ the third figure. ^
The statement that "all metals are solids" would at
once be disproved by the exception viercury^ as follows :

Mercury is not solid,
Mercury is a metal ;
Therefore some metal is not solid.

Were any one to assert that what is incomprehensible ,
cannot exist, we meet it at once with the argument that
Infinity is incomprehensible, but that infinity certainly ♦
exists, because we cannot otherwise explain the nature of
a curve line, or of a quantity varying continuously ; there- i-
fore something that is incomprehensible exists. In this
case" even one exception is sufficient entirely to negative
the proposition, which really means that because a thing
is incomprehensible it cannot exist. But if one incom-
prehensible thing does exist, others may also; and all
authority is taken from the statement.

According to the Aristotelian system the third figure
must also be employed whenever the middle term is a '
singular term, because in Aristotle's view of the subject a ^
singular term could not stand as the predicate of a pro-
position.

LESSON XVII.

REDUCTION OF THE IMPERFECT FIGURES
OF THE SYLLOGISM.

In order to facilitate the recollection of the nineteen valid
and useful moods of the syllogism, logicians invented, at
least six centuries ago, a most curious system of artificial
words, combined into mnemonic verses, which may be

XVII.] OF THE SYLLOGISM, 145

readily committed to memory. This device, however in-
genious, is of a barbarous and wholly unscientific cha-
racter ; but a knowledge of its construction and use is still
expected from the student of logic, and the verses are
therefore given and explained below.

Barbara, Celarent, Darii, Fertoo^ue, prions;
CesarCj Cajnesires, Fesiino, Baroko, secundas;
Tertia, Darapti, Disamis, Daiisi, Felapton,
Bokardo, Ferisojt, habet ; Quarta insuper addit
Brajnantip, Caiiieiies, Dwia?'is, FesapOj Fresison.

The words printed in ordinary type are real Latin
words, signifying that four moods whose artificial names
are Barbara, Celarent, Darii and Ferio, belong to the
first figure ; that four others belong to the second \ six
more to the third ; while the fourth figure moreover
contains five moods. Each artificial name contains
three vowels, which indicate the propositions forming
a valid mood ; thus, CY.lkrY.nt signifies the mood of the
first figure, which has E for a major premise, A for the
minor, and E for the conclusion. The artificial words
altogether contain exactly the series of combinations of
vowels shown in p. 140, excepting those in brackets.

These mnemonic lines also contain indications of the
mode in which each mood of the second, third and fourth
figures can be proved by reduction to a corresponding
mood of the first figure. Aristotle looked upon the first
figure as a peculiarly evident and cogent form of argu-
ment, the Dictum de oniiii et niUlo being directly ap-
plicable to it, and he therefore called it the Perfect Figure.
The fourth figure was never recognised by him, and it is
often called the Galenian figure, because the celebrated
Galen is supposed to have discovered it. The second
and third figures were known to Aristotle as the Imperfect
Figures, which it was necessary to reduce to the first

146 THE IMPERFECT FIGURES [less. ,

figure by certain conversions and transpositions of the
premises, for which directions are to be found in the ^
artificial words. These directions are as follows : —

s indicates that the proposition denoted by the pre-
ceding vowel is to be converted simply.

p indicates that the proposition is to be converted per
accidens, or by limitation.

m indicates that the premises of the syllogism are to
be transposed, the major being made the minor of a new
syllogism, and the old minor the new major. The m is
derived from the Latin imitare^ to change. ,

B, C, Z>, F, the initial consonants of the names, in-
dicate the moods of the first figure, which are produced -t-
by reduction; thus Cesare, Camestres and Camenes are
reducible to Celarent, Darapti, &c., to Darii, Fresison to
Ferio and so on.

k denotes that the mood must be reduced or proved
by a distinct process called Indirect reduction, or reductio
ad iinpossibile, which will shortly be considered.

Let us now take some syllogism, say in Camestres, and
follow the directions for reduction. Let the example be

All stars are self-luminous (i) ^^

All planets are not self-luminous (2)

Therefore no planets are stars (3)

The first s in Camestres shows that we are to convert
simply the minor premise. The ;;z instructs us to change
the order of the premises, and the final s to convert the
conclusion simply. When all these changes are made t
we obtain

No self-luminous bodies are planets Converse of (2)

All stars are self-luminous (i)

Therefore no stars are planets Converse of (3)

This, it will be found, is a syllogism in Celarent, as
might be knoWn from the initial C in Camestres.

xviL] OF THE SYLLOGISM. 147

As another example let us take Fesapo, for instance ;
No fixed stars are planets,
All planets are round bodies ;
Therefore some round bodies are not fixed stars.
According to the directions in the name, we are to
convert simply the major premise, and by limitation the
minor premise. We have then the following syllogism in
Ferio :

No planets are fixed stars,
Some round bodies are planets ;
Therefore some round bodies are not fixed stars.

The reader will easily apply the same process of con-
version or transposition to the other moods, according to
the directions contained in their names, and the only
moods it will be necessary to examine especially are
Bramantip, Baroko and Bokardo. As an example of
Bramantip we may take :

All metals are material substances, ^ ^

All material substances are gravitating bodies ;
Therefore some gravitating bodies are metals.
The name contains the letter ?n, which instructs us to
transpose the premises, and the letter p, which denotes
conversion by limitation ; effecting these changes we
have :

All material substances are gravitating bodies,

All metals are material substances ;

Therefore some metals are gravitating bodies.

This is not a syllogism in Barbara, as we might have

expected, but is the weakened mood AAI of the first

figure. It is evident that the premises yield the conclusion

"all metals are gravitating bodies," and we must take the

letter p to indicate in this mood that the conclusion is

weaker than it might be. In truth the fourth figure is so

10 — 2 /

148 THE IMPERFECT FIGURES [less.

imperfect and unnatural in form, containing nothing but
ill-arranged syllogisms, which would have been better
stated in the first figure, that Aristotle, the founder of
logical science, never allowed the existence of the figure
at all. It is to be regretted that so needless an addition
was made to the somewhat complicated forms of the
syllogism.

The two peculiar moods called Baroko and Bokardo
give a good deal of trouble, because they cannot be re-
duced directly to the first figure. To show the mode of
treating these moods we will take X^ V, Z to represent the
major, middle and minor terms of the syllogism, and
Baroko may then be stated as follows :

All ^'s are K's,
Some Z^s are not F's ;
Therefore Some Z's are not ^'s.

Now if we convert the major premise by Contrapo-
sition (p. 83) we have " all not- F's are not J^'s," and,
making this the major premise of the syllogism, we have

All not- F's are not X's,
Some Z's are not- F's ;
Therefore Some Z's are not ^'s.

Although both the above premises appear to be nega-
tive, this is really a valid syllogism in Ferio, because
two of the negative particles merely affect the middle
term (see p. 134), and we have therefore effected the re-
duction of the syllogism.

Bokardo, when similarly stated, is as follows :

Some F's are not ^'s,
All F's are Z's;
Therefore Some Z's are not X'^,

XVII.] OF THE SYLLOGISM. 149

To reduce this, convert the major premise by nega-
tion, and then transpose the premises. We have:
All K's are Z's,
Some not-X's are F's;
Therefore Some not-^'s are Z's.

This conclusion is the converse by negation of the
former conclusion, the truth of which is thus proved by
reduction to a syllogism in Darii.

Both these moods, Baroko and Bokardo, may however
be proved by a peculiar process of Indirect reduction,
closely analogous to the indirect proofs often employed by
Euclid in Geometry. This process consists in supposing
the conclusion of the syllogism to be false, and its con-
tradictory therefore true, when a new syllogism can easily
be" constructed which leads to a conclusion contradictory
of one of the original premises. Now it is absurd in logic
to call in question the truth of our own premises, for the
very purpose of argument or syllogism is to deduce a con-
clusion which will be true when the p7'emises are trtte.
The syllogism enables us to restate in a new form the in-
formation which is contained in the premises, just as a
m.achine may deliver to us in a new form the material
which is put into it. The machine, or rather the maker
of the machine, is not responsible for the quality of the
materials furnished to it, and similarly the logician is not
responsible in the least for the truth of his premises, but
only for their correct treatment. He must treat them, if
he treat them at all, as true ; and therefore a conclusion
which requires the falsity of one of our premises is alto-
gether absurd.

To apply this method we may take Baroko, as be-
fore:

All ^s are F's (i)

Some Z's are not K's (2)

Therefore Some Z's are not ^s (3)

ISO THE IMPERFECT FIGURES [less.

If this conclusion be not true then its contradictory,
*a.\lZ's are ^'s' must of necessity be regarded as true
(pp. 76 — 79). Making this the minor premise of a new
syllogism with the original major premise we have :

All ^s are F's (i)

All Z's are X's contradictory of (3)

Hence All Z's are F's.

Now this conclusion in A, is the contradictory of our old
minor premise in 0, and we must either admit one of our
own premises to be false or allow that our original con-
clusion is true. The latter is of course the alternative
we choose.

We treat Bokardo in a very similar manner ;

Some F's are not ^s (i)

All K's are Z's (2)

Therefore Some Z's are not ^'s (3)

If this conclusion be not true then 'all Z's are Jf's' must

be true. Now we can make the syllogism :

All Z's are ^'s Contradictory of (3)

AllK'sareZs (2)

Hence All K's are ^'s.

This conclusion is the contradictory of (i), the original
major premise, and as this cannot be allowed, we must
either suppose (2) the original minor premise to be false,
which is equally impossible, or allow that our original
conclusion is true.

It will be observed that in both these cases of Indirect
Reduction or Proof we use a syllogism in Barbara, which
fact is indicated by the initial letters of Baroko and Bo-
kardo. The same process of Indirect proof may be
applied to any of the other moods, but it is not usual to
do so, as the simpler process of direct or as it is often
called ostensive reduction is sufficient.

XVII.] OF THE SYLLOGISM. 151

It will be remembered that when in Lesson XV. (p. 135)
we considered the rules of the syllogism, there were two
supplementary rules, the 7th and 8th, concerning particu-
lar premises, which were by no means of a self-evident
character, and which require to be proved by the six more
fundamental rules. We have now sufficiently advanced
to consider this proof with advantage. The 7th rule
forbids us to draw any conclusion from two particular pre-
mises ; now such premises must be either n, 10, 01, or 00.
Of these II contain no distributed teim at all, so that the
3rd rule, which requires the middle term to be distributed,
must be broken. The premises 00 evidently break the
5th rule, against negative premises. The conclusion of
the pair 10 must be negative by the 6th rule, because one
premise is negative ; the major term therefore will be
distributed, but as the major premise is a particular
affirmative it cannot be distributed without committing
the fallacy of illicit process of the major, against rule 4,
Lastly the premises 01 contain only one distributed term,
the predicate of the major premise. But as the conclusion
must be negative by rule 6th, the major term must be
distributed; we ought to have then in the premises two
distributed terms, one for the middle term, the other for
the major term ; but as the premises contain only a single
distributed term, we must commit the fallacy either of
undistributed middle or of illicit process of the major
term, if we attempt to draw any conclusion at all. We
thus see that in no possible case can a pair of particular
premises give a valid conclusion.

The 8th rule of the syllogism instructs us that if one
premise of a syllogism be particular the conclusion must
also be particular. It can only be shown to be true by
going over all the possible cases and observing that the
six principal rules of the syllogism always require the
conclusion to be particular. Suppose for instance the

152 IRREGULAR AND COMPOUND [less.

premises are A and I ; then they contain only one dis-
tributed term, the subject of A, and this is required for
the middle term by rule 3. Hence the minor term cannot
be distributed without breaking rule 4, so that the con-
clusion must be the proposition I. The premises AO would
contain two distributed terms, the subject of A and the
predicate of 0; but if we were to draw from them the
conclusion E, the major and minor terms would require
to be distributed, so that the middle term would remain
undistributed against rule 3. The reader can easily prove
the other cases such as EI by calculating the number of
distributed terms in a similar manner: it will always be
found that there are insufficient terms distributed in the
premises to allow of a universal conclusion.

LESSON XVIII.

IRREGULAR AND COMPOUND SYLLOGISMS.

It may seem surprising that arguments which are met
with in books or conversation are seldom or never thrown
into the form of regular syllogisms. Even if a complete
syllogism be sometimes met with, it is generally employed
in mere affectation of logical precision. In former cen-
turies it was, indeed, the practice for all students at the
Universities to take part in public disputations, during
which elaborate syllogistic arguments were put forward
by one side and confuted by precise syllogisms on the
other side. This practice has not been very long dis-
continued at the University of Oxford, and is said to be
still maintained in some continental Universities ; but
except in such school disputations it must be allowed that
perfectly formal syllogisms are seldom employed.

XVIII.] SYLLOGISMS. 153

In truth, however, it is not syllogistic arguments which
are wanting; wherever any one of the conjunctions,
therefore, because, for, since, hence, inasmuch as, conse-
quently occurs, it is certain that an inference is being
drawn, and this will very probably be done by a tine
syllogism. It is merely the complete statement of the
premises and conclusion, which is usually neglected be-
cause the reader is generally aware of one or other of the
premises, or he can readily divine what is assumed; and
it is tedious and even offensive to state at full length what
the reader is already aware of. Thus, if I say "atmo-
spheric air must have weight because it is a material
substance," I certainly employ a syllogism ; but I think
it quite needless to state the premise, of which I clearly
assume the truth, that " whatever is a material substance
has weight." The conclusion of the syllogism is the first
proposition, viz. "atmospheric air has weight." The
middle term is "material substance," which does not occur
in the conclusion; the minor is "atmospheric air," and the
major, "having weight." The complete syllogism is evi-
dently :

All material substances have weight.
Atmospheric air is a material substance ;
Therefore atmospheric air has weight.

This is in the very common and useful mood Barbara.

A syllogism when incompletely stated is usually called
an enthsrmeme, and this name is often supposed to be
derived from two Greek words {Iv, in, and 6v\io^, mind),
so as to signify that some knowledge is held by the mind
and is supplied in the form of a tacit, that is a silent or
understood premise. Most commonly this will be the
major premise, and then the enthymeme may be said to
be of the First Order. Less commonly the minor premise
is unexpressed, and the enthymeme is of the Second

154 IRREGULAR AND COMPOUND [less.

Order. Of this nature is the following argument:
" Comets must be subject to the law of gravitation ; for
this is true of all bodies which move in elliptic orbits."
It is so clearly implied that comets move in elliptic orbits,
that it would be tedious to state this as the minor premise
in a complete syllogism of the mood Barbara, thus :

All bodies moving in elliptic orbits are subject to

the law of gravitation ;
Comets move in elliptic orbits ;
Therefore comets are subject to the law of gravitation.

It may happen occasionally that the conclusion of a
syllogism is left unexpressed, and the enthymeme may then
be said to "belong to the Third Order. This occurs in the
case of epigrams or other witty sayings, of which the very
wit often consists in making an unexpressed truth ap-
parent. Sir W. Hamilton gives as an instance of this
kind of enthymeme the celebrated epigram written by
Porson the English scholar upon a contemporary German
scholar :

" The Germans in Greek

Are sadly to seek ;

Not five in five score,

But ninety-five more ;

All, save only Hermann,

And Hermann's a German."

It is evident that while pretending to make an exception
of Hermann, the writer ingeniously insinuates that since
he is a German he has not a correct knowledge of Greek.
The wonderful speech of Antony over the body of Caesar,
in Shakspeare's greatest historical play, contains a series
of syllogistic arguments of which the conclusions are
suggested only.

Even a single proposition may have a syllogistic force
if it clearly suggest to the mind a second premise which

. XVIII.] SYLLOGISMS. 155

thus enables a conclusion to be drawn. The expression
of Home Tooke, "Men who have no rights cannot justly
complain of any wrongs," seems to be a case in point ; for
there are few people who have not felt wronged at some
time or other, and they would therefore be likely to argue,
whether upon true or false premises, as follows :

Men who have no rights cannot justly complain of

any wrongs;
We can justly complain;
Therefore we are not men who have no rights.

In other words, we have rights.

Syllogisms may be variously joined and combined
together, and it is convenient to have special names for
the several parts of a complex argument. Thus a syllo-
gism which proves or furnishes a reason for one of the
premises of another syllogism is called a Prosyllogism ;
and a syllogism which contains as a premise the conclu-
sion of another syllogism is called an Episyllogism.

Take the example :

All ^'s are A%
And all Cs area's;
Therefore all Cs are A's.
But all Z^'s are Cs;
Therefore All Us are A's.

This evidently contains two syllogisms in the mood Bar-
bara, the first of which is a Prosyllogism with respect to
the second, while the second is an Episyllogism with
respect to the first.

The peculiar name Epicheirema is given to a syllogism
when either premise is proved or supported by a reason
implying the existence of an imperfectly expressed pro-
syllogism ; thus the form,

156 IRREGULAR AND COMPOUND [less.

All ^'s are A's, for they are P's,
And all Cs are ^'s, for they are Qs ;
Therefore all C's are A^s,
is a double Epicheirema, containing reasons for both
premises. The reader will readily decompose it into
three complete syllogisms of the mood Barbara.

A more interesting form of reasoning is found in the
chain of syllogisms commonly called the Sorites, from the
Greek word acopos, meaning /lea^p. It is usually stated in
this way :

All ^'s are B's,
All ^'s are C's,
All C's are Ds,
All Ds are E's ;
Therefore all A^s are £'s.

The chain can be carried on to any length provided it is
perfectly consecutive, so that each term except the first
and last occurs twice, once as subject and once as predi-
cate. It hardly needs to be pointed out that the sorites
really contains a series of syllogisms imperfectly ex-
pressed; thus

First Syllogism. Second Syllogism. Last Syllo.gism.

^'s are C's, C's are Z>'s, Z^'s are -£"'s,

A's are ^'s ; A''s are C's ; A's are Z>'s ;

.-. ^'s areC's. .'. ^'s are Z>'s. .: A's are E's.

Each syllogism furnishes a premise to the succeeding one,
of which it is therefore the prosyllogism, and any syllo-
gism may equally be considered the episyllogism of that
which precedes.

In the above sorites all the premises were universal
and affirmative, but a sorites may contain one particular
premise provided it be the first, and one negative premise
provided it be the last. The reader may easily assure
himself by trial, that if any premise except the first were

> XVIII.] SYLLOGISMS. 157

particular the fallacy of undistributed middle would be
committed, because one of the middle terms would be the
predicate of one affirmative premise and the subject of
another particular premise. If any premise but the last
were negative there would be a fallacy of illicit process of
the major term.

It is not to be supposed that the forms of the syllogism
hitherto described are all the kinds of reasoning actually
employed in science or common life. In addition to the
hypothetical and disjunctive syllogisms and some other
forms to be described in succeeding lessons, there are
really many modes of reasoning of which logicians have
not taken much notice as yet. This was clearly pointed
out more than two hundred years ago by the writers of
the Port Royal Logic, a work first printed in the year 1662,
but which has been since reprinted very often and trans-
lated into a great many languages. The book is named
from a place near Paris where a small religious com-
munity lived, of which the authors of the book, namely
Arnauld and Nicole, and a contributor to it the great
philosopher and mathematician Pascal, were the most
celebrated members. The Port Royal Logic was to a
considerable extent the basis of the well-known Watts'
Logic, but the reader can now be referred to an admirable
translation of the original work made by Professor Spencer
Baynes, of St Andrew's.

Many improvements of Logic may be found in this
work, such as the doctrine of Extension and Intension
explained in Lesson v. In the 9th Chapter of the 3rd
Part moreover it is wisely pointed out that "little pains
are taken in applying the rules of the syllogism to reason-
ings of which the propositions are complex, though this
is often very difficult, and there are many arguments of
this nature which appear bad, but which are nevertheless
very good; and besides, the use of such reasonings is

158 IRREGULAR AND COMPOUND [less.

much more frequent than that of syllogisms which are .
quite simple." Some examples are given of the complex
syllogisms here referred to; thus:

The sun is a thing insensible,

The Persians worship the sun ;

Therefore the Persians worship a thing insensible.

This is an argument which cannot be proved by the rules
of the syllogism, and yet it is not only evidently true, but
is an exceedingly common kind of argument. Another
example is as follows :

The Divine Law commands us to honour kings ;
Louis XIV. is a king ;

Therefore the Divine Law commands us to honour
Louis XIV.

The reader will also find that arguments which are
really quite valid and syllogistic are expressed in language
so that they appear to have four distinct terms and thus to .
break one of the rules of the syllogism. Thus if I say
" Diamonds are combustible, for they are composed of
carbon and carbon is combustible," there are four terms
employed, namely, diamonds, combustible, composed of
carbon, and carbon. But it is easy to alter the construc-
tion of the propositions so as to get a simple syllogism
without really altering the sense, and we then have :

What is composed of carbon is combustible ;
Diamonds are composed of carbon ;
Therefore diamonds are combustible.

Examples are given at the end of the book of concise
arguments, taken from Bacon's Essays and other writings,
which the student can reduce to the syllogistic form by
easy alterations ; but it should be clearly understood that
these changes are of an extra-logical character, and belong
more properly to the science of language.

XVIII.] SYLLOGISMS. 159

I may here explain that the syllogism and the sorites
can be expressed either in the order of extension or that
of intension. In regard to the number of individual
things the noble metals are part of the metals, and the
metals are part of the elements; but in regard to in-
tension, that is to say the qualities impHed in the names,
element is part of metal, and metal is part of noble metal.
So again in extension the genus of plants Anemone is
part of the order Ranunculaceas, and this is part of
the great class Exogens; but in intension the cha-
racter of Exogen is part of the character of Ranuncu-
laceas, and this is part of the character of Anemone.
Syllogistic reasoning is equally valid and evident in either
case, and we might represent the two modes in ordinary
language as follows :

Exte7isive Syllogism.
All Ranunculaces are Exogens ;
The Anemone is one of the Ranunculaceas ;
Therefore the Anemone is an Exogen.

Intensive Syllogism.
All the qualities of Ranunculacese are qualities of

Anemone ;
All the qualities of Exogen are quaUties of Ranun-
culaceas ;
Therefore all the qualities of Exogen are qualities of
Anemone.
Any sorites can be similarly represented either in ex-
tension or intension.

Concerning the Aristotelian doctrine of the Enthy-
meme, see Mansel's Aldrich, App. Note F, and Hamil-
ton's Lectures on Logic, Lecture XX. Port Royal Logic,
translated by T. Spencer Baynes, 7th ed. Edinburgh.

i6o OF CONDITIONAL [less.

LESSON XIX.
OF CONDITIONAL ARGUMENTS.

It will be remembered that when treating of propositions
we divided them into two distinct kinds, Categorical Pro-
positions, and Conditional Propositions. The former kind
alone has hitherto been considered, and we must now
proceed to describe Conditional propositions and the ar-
guments which may be composed of them.

Logicians have commonly described Conditional pro-
positions as composed of two or 7nore Categofical pro-
positiofis united by a conjunction. This union may
happen in two ways, giving rise to two very different
species of conditionals, which we shall call Hypothetical
Propositions and Disjunctive Propositions. The way in
which the several kinds of propositions are related will
be seen in the following diagram :

{v^ategoncai.
^_.^.,^ Hypothetical
Disjunctive.

A conditional proposition may be further described
as one which makes a statement under a certain con-
dition or qualification restricting its application. In the
hypothetical form this condition is introduced by the
conjunction if, or some other word equivalent to it.
Thus—

" If iron is impure, it is brittle "

is a hypothetical proposition consisting of two distinct
categorical propositions, the first of which, " Iron is im-
pure," is called the Antecedent; the second, "It is brittle,"

^ XIX.] ARGUMENTS. i6i

the Consequent. In this case " impurity " is the condition
or qualification which limits the application of the pre-
dicate brittle to iron. It was asserted by Home Tooke in
his celebrated work The Diversio7is of Picrley^ that all
conjunctions are the remains or corrupted forms of verbs.
This is certainly true in the case of the hypothetical con-
junction ; for the word if in old English is written gif or
gyf and is undoubtedly derived from the verb to give.
We may actually substitute at present any verb of similar
meaning, as for instance — g7'a?it, allow^ suppose. Thus
we may say —

" Grant that iron is impure, and it is brittle."
" Supposing that iron is impure, it is brittle."
The hypothetical proposition might be employed in
arguments of various form, but only two of these are of
sufficient importance to receive special names. The hy-
pothetical syllogism consists of two premises, called the
major and minor, as in the case of the ordinary syllo-
gism. The major premise is h}^othetical in form ; the
minor premise is categorical, and according as it is af-
firmative or negative the argument is said to be a Construc-
tive or a Destructive hypothetical syllogism. Thus the form.

If ^ is ^, C is D\
^ But ^ is ^;

Therefore C is Z>,
is a constructive hypothetical syllogism.

It must be carefully observed that the minor premise
afifirms the antecedent of the major premise, whence the
argument is said to be of the modus poneiis^ or mood
which posits or affirms. It is probably one of the most
familiar and common kinds of argument. The form,

\i A \s B, C \% D;

But C is not D ;

Therefore A is not B-

II

i62 OF CONDITIONAL [less.

represents the corresponding Destructive hypothetical
syllogism, also called the modus tollens, or the mood
which removes the consequent. It must be carefully ob-
served again that it is the consequent, not the antecedent,
which is denied.

The only rule which is requisite for testing the validity
of such syllogisms embodies what we have observed
above; viz. Xhdl either the antecedent imist be affirmedy
or the conseqiient denied. If either part of this rule be
broken, a serious fallacy will be committed. Thus the
apparent argument,

If A is B, C is n ;
But C is D;
Therefore A is B,

is really a fallacy which we may call sXv^ fallacy of affirm-
ing the consegue7it, and its fallacious nature is readily un-
derstood by reflecting that " A being B " is not stated to
be the only condition on which C is D. It may happen
that when E is F^ or G is //", or under a hundred other
circumstances, C is D, so that the mere fact of C being D
is no sufficient proof that A is B. Thus, if a man's cha-
racter be avaricious he will refuse to give money for useful
purposes ; but it does not follow that every person who •
refuses to give money for such purposes is avaricious.
There may be many proper reasons or motives leading
him to refuse ; he may have no money, or he may con-
sider the purpose not a useful one, or he may have more
useful purposes in view.

A corresponding fallacy arises from denying the ante-
cede fit y as in the form —

If ^ is ^, C is Z> ;
But A is not B ;
Therefore C is not D,

XIX.] ARGUMENTS. 163

The error may be explained in the same way ; for as
"-4 being j5" is not stated to be the only condition of
C being i9, we may deny this one condition to be true,
but it is possible that the consequent may happen to be
true for other reasons, of which we know nothing. Thus
if a man is not avaricious we cannot conclude that he will
be sure to give money whenever asked. Or take the fol-
lowing example :

"If the study of Logic furnished the mind with a multi-
tude of useful facts like the. study of other sciences, it
would deserve cultivation; but it does not furnish the
mind with a multitude of useful facts ; therefore it does
not deser\^e cultivation."

This is evidently a fallacious argument, because the
acquiring of a multitude of useful facts is not the only
ground on which the study of a science can be recom-
mended. To correct and exercise the powers of judgment
and reasoning is the object for which Logic deserves to
be cultivated, and the existence of such other purpose is
ignored in the above fallacious argument, which evidently
involves the doiial of the antecedent.

Although it is usual in logical works to describe the
hypothetical proposition and syllogism as if they were
different in nature from the categorical proposition and
syllogism, yet it has long been known that the hypo-
theticals can be reduced to the categorical form, and
brought under the ordinary rules of the syllogism. As a
general rule the hypothetical proposition can be readily
converted into a universal affirmative proposition (A) of
exactly the same meaning. Thus our instance, "If iron
is impure, it is brittle," becomes simply "Impure iron is
brittle." In making this alteration in a hypothetical syl-
logism it will be found necessary to supply a new minor
term ; thus in the case,

II— 2

i64 OF CONDITIONAL [less. ^

If iron is impure it is brittle ;
But it is impure ; ^

Therefore it is brittle,
we have to substitute for the indefinite pronoun //, the
iron in question, and we obtain a correct categorical syl-
logism in the mood Barbara :
Impure iron is brittle ;
The iron in question is impure iron ;
Therefore the iron in question is brittle. ^

Sometimes the reduction requires a more extensive
change of language. For instance,

If the barometer is falling, bad weather is coming ;
But the barometer is falling ;
Therefore bad weather is coming,
may be represented in the following form :
The circumstances of the barometer faUing are the cir-
cumstances of bad weather coming ;
But these are the circumstances of the barometer fall-
ing;
Therefore these are the circumstances of bad weather
coming.
As an instance of the Destructive Hypothetical syl-
logism we may take :
If Aristotle is right, slavery is a proper form of society;
But slavery is not a proper form of society;
Therefore Aristotle is not right.
This becomes as a categorical :
The case of Aristotle being right is the case of slavery

being a proper form of society;
But this is not the case ;
Therefore this is not the case of Aristotle being right.

If not reducible by any other form of expression, hypo-
theticals can always be reduced by the use of the words
case of.

XIX.] ARGUMENTS. 165

It will now be easily made apparent that the fallacy of
affirming the consequent is really a breach of the 3rd
rule of the syllogism, leading to an undistributed middle
term. Our example may be as before :

If a man is avaricious he wiU refuse money ;

But he does refuse money ;

Therefore he is avaricious.

This becomes as a categorical syllogism,
All avaricious men refuse money ;
But this man refuses money ;
Therefore this man is avaricious.

This is the mood AAA in the second figure ; and the
middle term, refusing money, is undistributed in both
premises, so that the argument is entirely fallacious.

Again, the fallacy of denying the antecedent is equiva-
lent to the illicit process of the major. Our former
example (p. 163) may thus be represented:

"A science which furnishes the mind with a multitude
of useful facts deserves cultivation ; but Logic is not such
a science ; therefore Logic does not deserve cultivation."

This apparent syllogism is of the mood AEE in the
first figure, which breaks the fourth rule of the syllogism,
because the major term, deserving cultivation, is dis-
tributed in the negative conclusion, but not in the affirma-
tive major premise.

We now pass to the consideration of the disjunctive
proposition, which instead of a single predicate has
several alternatives united by the disjunctive conjunction
or, any one of which may be affirmed of the subject. "A
member of the House of Commons is either a representa-
tive of a county, or of a borough, or of a University," is an
instance of such a proposition, containing three alterna-
tives ; but there may be any number of alternatives from
two upwards.

166 OF CONDITIONAL [less.

The disjunctive syllogism consists of a disjunctive
major premise with a categori-cal proposition, either af-
firmative or negative, forming the minor premise. Thus
arise two moods, of which the affirmative mood is called
by the Latin words modus po7iendo tollens (the mood
which by affirming denies), and may be thus stated :

A is either B or C,

Butyi is^;

Therefore A is not C.
This form of argument proceeds on the supposition
that if one alternative of a disjunctive proposition be held
true, the others cannot also be true. Thus " the time of
year must be either spring, summer, autumn or winter,"
and if it be spring it cannot be summer, autumn or winter ;
and so on. But it has been objected by Whately, Han-
sel, Mill, as well as many earlier logicians, that this does
not always hold true. Thus if we say that " a good book
is valued either for the usefulness of its contents or the
excellence of its style," it does not by any means follow
because the contents of a book are useful that its style is
not excellent. We generally choose alternatives which
are inconsistent with each other; but this is not logically
necessary.

The other form of disjunctive syllogism, called the
modus tollendopone7ts (the mood which by denying affirms),
is always of necessity cogent, and is as follows :

A is either B or C^

But ^ is not ^;

Therefore A is C.
Thus if we suppose a book to be valued only for the
usefulness of its contents or the excellence of its style, it
follows that if a book be valued but not for the former
reason it must be for the latter; and vice versa. If the
time of year be not spring, it must be summer, autumn or

XIX.] ARGUMENTS. 167

winter; if it be not autumn nor winter, it must be either
spring or summer; and so on. In short if any alternatives
be denied, the rest remain to be affirmed as before. It
will be noticed that the disjunctive syllogism is governed
by totally different rules from the ordinary categorical
syllogism, since a negative premise gives an affirmative
conclusion in the former, and a negative conclusion in
the latter.

There yet remains a form of argument called the
Dilemma, because it consists in assuming two alternatives,
usually called the horns of the dilemma, and yet proves
something in either case (Greek 5t- two ; Xrjfifia, assump-
tion). Mr Mansel defines this argument as " a syllogism,
having a conditional major premise with more than one
antecedent, and a disjunctive minor." There are at least
three forms in which it may be stated. The first form is
called the Simple Constructive Dilemma :

If A is B,C\s D\ and \i E \s F, C \s D \
But either A is B, or E is F;
Therefore C is D.

Thus "if a science furnishes useful facts, it is worthy of
being cultivated; and if the study of it exercises the
reasoning powers, it is worthy of being cultivated ; but
either a science furnishes useful facts, or its study
exercises the reasoning powers ; therefore it is worthy of
being cultivated."

The second form of dilemma is the Complex Con-
structive Dilemma, which is as follows :

If^ is^, C'ls D] and if^isi^, 6^ is H ;
But either ^ is ^, or ^ is i^;
Therefore either C is D, or G is H.

It is called complex because the conclusion is in the
disjunctive form. As an instance we may take the argu-

i68 OF CONDITIONAL [less.

ment, "If a statesman who sees his former opinions to
be wrong does not alter his course he is guilty of deceit ;
and if he does alter his course he is open to a charge
of inconsistency ; but either he does not alter his course
or he does ; therefore he is either guilty of deceit, or he is
open to a charge of inconsistency." In this case as in
the greater number of dilemmas the terms A^ B, C, D, &c.
are not all different.

The Destructive Dilemma is always complex, because
it could otherwise be resolved into two unconnected de-
structive hypothetical syllogisms. It is in the following
form:

If ^ is ^, C is Z>; and if ^ is F, G is H;
But either C is not D, or G is not H;
Therefore either A is not B, or E is not F.

For instance, " If this man were wise, he would not
speak irreverently of Scripture in jest; and if he were
good, he would not do so in earnest ; but he does it either
in jest or earnest; therefore he is either not wise, or not
good*."

Dilemmatic arguments are however more often fal-
lacious than not, because it is seldom possible to find
instances where two alternatives exhaust all the possible
cases, unless indeed one of them be the simple negative
of the other m accordance with the law of excluded mid-
dle (p. 119). Thus if we were to argue that "if a pupil is
fond of learning he needs no stimulus, and that if he dis-
likes learning no stimulus will be of any avail, but as he
is either fond of learning or dislikes it, a stimulus is either
needless or of no avail," we evidently assume improperly
the disjunctive minor premise. Fondness and dislike are
not the only two possible alternatives, for there may be

♦ Whately. h ^""*

•iv

XIX.] ARGUMENTS. 169

some who are neither fond of learning nor dishke it, and
to these a stimulus in the shape of rewards may be de-
sirable. Almost anything can be proved if we are allowed
thus to pick out two of the possible alternatives which are
in our favour^ and argue from these alone.

A dilemma can often be retorted by producing as
cogent a dilemma to the contrary effect. Thus an Athe-
nian mother, according to Aristotle, addressed her son in
the following words : " Do not enter into public business ;
for if you say what is just, men will hate you ; and if you
say what is unjust, the Gods will hate you." To which
Aristotle suggests the following retort : " I ought to enter
into public affairs ; for if I say what is just, the Gods will
love me ; and if I say what is unjust, men will love me."

Mansel's Aldrich, App. Note I, on the Hypothetical
Syllogism.

LESSON XX.

LOGICAL FALLACIES.

In order to acquire a satisfactory knowledge of the rules
of correct thinking, it is essential that we should become
acquainted with the most common kinds of fallacy ; that
is to say, the modes in which, by neglecting the rules of
logic, we often fall into erroneous reasoning. In previous
lessons we have considered, as it were, how to find the
right road ; it is our task here to ascertain the turnings at
which we are most liable to take the wrong road.

In describing the fallacies I shall follow the order and
adopt the mode of classification which has been usual
for the last 2000 years and more, since in fact the great

I70 LOGICAL FALLACIES. [less.

teacher Aristotle first explained the fallacies. According
to this mode of arrangement fallacies are divided into two
principal groups, containing the logical and the material
fallacies.

1. The logical fallacies are those which occur in the
mere form of the statement ; or as it is said in the old
Latin expressions, in diciwne, or 2?i voce. It is supposed
accordingly that fallacies of this kind can be discovered
without a knowledge of the subject-matter with which the
argument is concerned.

2. The material fallacies, on the contrary, arise out-
side of the mere verbal statement, or as it is said,, extra
dicttonejft; they are concerned consequently with the sub-
ject of the argument, or in re (in the matter), and cannot
be detected and set right but by those acquainted with
the subject.

The first group of logical fallacies may be further di-
vided into t\ve pU7'ely logical and the semi-logical, and we
may include in the former class the distinct breaches of
the syllogistic rules which have already been described.
Thus we may enumerate as Purely Logical Fallacies :

1. Fallacy of four terms {Qiiaternio Ter7ninortiiri) —
Breach of Rule i ;

2. Fallacy of undistributed middle — Breach of Rule 3 ;

3. Fallacy of ilHcit process, of the major or minor
term — Breach of Rule 4 ;

4. Fallacy of negative premises — Breach of Rule 5 ;
as well as breaches of the 6th rule, to which no distinct
name has been given. Breaches of the 7th and cSth rules
may be resolved into the preceding (p. 151), but they
may also be described as in p. 135.

The other part of the class of logical fallacies contains
Semi-logical fallacies, which are six in number, as follows ;

-XX.] LOGICAL FALLACIES. 171

1. Fallacy of Equivocation.

2. Fallacy of Amphibology.

3. Fallacy of Composition.

4. Fallacy of Division.

5. Fallacy of Accent.

6. Fallacy of Figure of Speech.

* *These I shall describe and illustrate in succession.

Equivocation consists in the same term being used
in two distinct senses ; any of the three terms of the syl-
logism may be subject to this fallacy, but it is usually the
middle term which is used in one sense in one premise

' and in another sense in the other. In this case it is often
called the fallacy of ambiguoics middle, and when we dis-
tinguish the two meanings by using other suitable modes
of expression it becomes apparent that the supposed syl-
logism contains four terms. The fallacy of equivocation

-.may accordingly be considered a disguised fallacy of four
terms. Thus if a person were to argue that " all criminal
actions ought to be punished by law; prosecutions for
theft are criminal actions ; therefore prosecutions for

► theft ought to be punished by law," it is quite apparent
that the term "criminal action" means totally different

' things in the two premises, and that there is no true
middle term at all. Often, however, the ambiguity is of

*"a subtle and difficult character, so that different opinions
may be held concerning it. Thus we might argue :

" He who harms another should be punished. He
who communicates an infectious disease to another per-
son harms him. Therefore he who communicates an
infectious disease to another person should be punished."
This may or may not be held to be a correct argument

^, according to the kinds of actions we should consider to
come under the term harm, according as we regard negli-
gence or malice requisite to constitute harm. Many

172 LOGICAL FALLACIES. [LESS,-

difficult legal questions are of this nature, as for in- .
stance :

Nuisances are punishable by law ;

To keep a noisy dog is a nuisance ;

To keep a noisy dog is punishable by law.

The question here would turn upon the degree of
nuisance which the law would interfere to prevent. Or
again ;
Interference with another man's business is illegal;
Underselling interferes with another man's business;
Therefore underselling 4s illegal.

Here the question turns upon the kind of interference,
and it is obvious that underselling is not the kind of in-
terference referred to in the major premise.

The Fallacy of Amphibology consists in an ambiguous ^
grammatical structure of a sentence, which produces mis-
conception. A celebrated instance occurs in the prophecy y
of the spirit in Shakspeare's Henry VI. : " The Duke yet
lives that Henry shall depose," which leaves it wholly
doubtful whether the Duke shall depose Henr>'-, or Henry
the Duke. This prophecy is doubtless an imitation of
those which the ancient oracle of Delphi is reported to
have uttered; and it seems that this fallacy was a great"
resource to the oracles who were not confident in their
own powers of foresight. The Latin language gives great
scope to misconstructions, because it does not require
any fixed order for the words of a sentence, and when
there are two accusative cases with an infinitive verb, it
may be difficult to tell except from the context which
comes in regard to sense before the verb. The double ^^
meaning which may be given to *' twice two and three"
arises from amphibology; it may be 7 or 10, according 4
as we add the 3 after or before multiplying. In the
careless construction of sentences it is often impossible to

^xx.] LOGICAL FALLACIES. 173

tell to what part any adverb or qualifying clause refers.
Thus if a person says " I accomplished my business and
returned the day after," it may be that the business was
accomplished on the day after as well as the return ; but
it may equally have been finished on the previous day.
Any ambiguity of this kind may generally be avoided by
^a simple change in the order of the words; as for instance,
" I accomplished my business, and, on the day after,
returned." Amphibology may sometimes arise from con-
fusing the subjects and predicates in a compound sentence,
as if in "platinum and iron are very rare and useful
metals " I were to apply the predicate useful to platinum

' and rare to iron, which is not intended. The word " re-
spectively" is often used to shew that the reader is not at
liberty to apply each predicate to each subject.

The Fallacy of Composition is a special case of equivo-
cation, arising from the confusion of an universal and a
collective term. In the premises of a syllogism we may
' affirm something of a class of things distribii lively, that is,
of each and any separately, and then we may in the con-
clusion infer the same of the whole piit together. Thus we
may say that " all the angles of a triangle are less than two
right angles," meaning that any of the angles is less than

' ^wo right angles ; but we must not infer that all the angles.
put together are less than two right angles. We must not

^argue that because every member of a jury is veiy likely
to judge erroneously, the jury as a whole are also very
likely to judge erroneously ; nor that because each of the
witnesses in a law case is liable to give false or mis-

' taken evidence, no confidence can be reposed in the con-
current testimony of a number of witnesses. It is by a
fallacy of Composition that protective duties are still
sometimes upheld. Because any one or any few trades

^' which enjoy protective duties are benefited thereby, it is
supposed that all trades at once might be benefited simi-

174 LOGICAL FALLACIES. [less.^

larly; but this is impossible, because the protection of one
trade by raising prices injures all others.

The Fallacy of Division is the converse of the pre-
ceding, and consists in using the middle term col-
lectively in the major premise but distributively in the
minor, so that the whole is divided into its parts. Thus
it might be argued, "All the angles of a triangle are^,
(together) equal to two right angles; ABC is an angle of
a triangle; therefore ABC is equal to two right angles.",
Or again, " The inhabitants of the town consist of men,
women and children of all ages ; those who met in the
Guildhall were inhabitants of the town; therefore they
consisted of men, women and children of all ages;" or,
" The judges of the court of appeal cannot misinterpret
the law; Lord A. B. is a judge of the court of appeal;
therefore he cannot misinterpret the law."

The Fallacy of Accent consists in any ambiguity^-
arising from a misplaced accent or emphasis thrown upon
some v/ord of a sentence. A ludicrous instance is liable'^
to occur in reading chapter xiii. of the First Book of
Kings, verse 27, where it is said of the prophet "And he
spake to his sons, saying, Saddle me the ass. And they
saddled JiimP The italics indicate that the word him
v/as suppHed by the translators of the authorized version^^
but it may suggest a very difterent meaning. The Com-
mandment " Thou shalt not bear false witness against -.
thy neighbour " may be made by a slight emphasis of the
voice on the last word to imply that we are at liberty to .
bear false witness against other persons. Mr De Morgan
who remarks this also points out that the erroneous -
quoting of an author, by unfairly separating a word from
its context or italicising words which were not intended
to be italicised, gives rise to cases of this fallacy.

It is curious to observe how many and various may be *■
the meanings attributable to the same sentence according

xx.] LOGICAL FALLACIES. 175

as emphasis is thrown upon one word or another. Thus
the sentence "The study of Logic is not supposed to
communicate a knowledge of many useful facts," may be
made to imply that the study of Logic does communicate
such a knowledge although it is not supposed to ; or that
it communicates a knowledge of a few useful facts ; or
that it communicates a knowledge of many useless facts.
This ambiguity may be explained by considering that if
you deny a thing to have the group of qualities A, B, C, D,
the truth of your statement will be satisfied by any one
quality being absent, and an accented pronunciation will
often be used to indicate that w^hich the speaker believes
to be absent. If you deny that a particular fruit is ripe
and sweet and well-flavoured, it may be unripe and sweet
and well-flavoured ; or ripe and sour and well-flavour-
ed; or ripe and sweet and ill-flavoured; or any two or
even all three qualities may be absent. But if you deny
it to be ripe and sweet and well-fiavoicred^ the denial
would be understood to refer to the last quality. Jeremy
Bentham was so much afraid of being misled by this
fallacy of accent that he employed a person to read to
him, as I have heard, who had a peculiarly monotonous
manner of reading.

The Fallacy of the Figure of Speech is the sixth and
last of the semi-logical fallacies, and is of a very trifling
character. It appears to consist in any grammatical
mistake or confusion between one part of speech and an-
other. Aristotle gravely gives the following instance :
" Whatever a man walks he tramples on ; a man walks
the whole day; therefore he tramples on the day." Here
an adverbial phrase is converted into a noun object.

LESSON XXI.

MATERIAL FALLACIES.

The Material fallacies are next to be considered; and their
importance is very great, although it is not easy to
illustrate them by brief examples. There are altogether
seven kinds of such fallacies enumerated by Aristotle and
adopted by subsequent logicians, as follows :

1. The Fallacy of Accident.

2. The Converse Fallacy of Accident.

3. The Irrelevant Conclusion.

4. The Petitio Principii.

5. The Fallacy of the Consequent or Non sequitur.

6. The False Cause.

7. The Fallacy of Many Questions.

Of these the two first are conveniently described to-
gether. The fallacy of accident consists in arguing erro-
neously from a general rule to a special case, where a
certain accidental circumstance renders the rule inappli- '
cable. The converse fallacy consists in arguing from a
special case to a general rule. This latter fallacy is usu-
ally described by the Latin phrase a dicto seamdurn quid
ad dictum simpliciter, meaning " from a statement under
a condition to a statement simply or without that con-
dition." Mr De Morgan has remarked in his very inte-
resting Chapter on Fallacies* that we ought to add a
third fallacy, which would consist in arguing froDi one
special case to another special case.

• Formal Logic^ Chapter XIII.

LESS. XXL] MATERIAL FALLACIES. 177

I will try by a few examples to illustrate these kinds of
fallacy, but much difficulty is often encountered in saying
to which of the three any particular example is best re-
ferred. A most ancient example repeated in almost every
logical hand-book is as follows : " What you bought yes-
terday you eat to-day ; you bought raw meat yesterday ;
therefore you eat raw meat to-day." The assertion in the
conclusion is made of meat with the accidental quality of
rawness added, where the first premise evidently speaks of
the sabstance of the meat without regard to its accidental
condition. This then is a case of the direct fallacy.
If it is argued again that because wine acts as a poison
when used in excess it is always a poison, we fall into the
converse fallacy.

It would be a case of the direct fallacy of accident
to infer that a magistrate is justified in using his power
to forward his own religious views, because every man
has a right to inculcate his own opinions. Evidently
a magistrate as a man has the rights of other men, but
in his capacity of a magistrate he is distinguished from
other men, and he must not infer of his special powers
in this respect what is only true of his rights as a
man. For another instance take the following : "He who
thrusts a knife into another person should be punished ;
a surgeon in operating does so ; therefore he should be
punished." Though the fallacy of this is absurdly
manifest, it is not so manifest how we are to classify the
error. We may for instance say that as a general rule
whoever stabs or cuts another is to be punished unless it
can be shewn to have been done under exceptional cir-
cumstances, as by a duly qualified surgeon acting for the
good of the person. In this case the example belongs to
the direct fallacy of accident. In another view we might
interpret the first premise to mean the special case of
thrusting a knife maliciously; to argue from that to the

12

178 MATERIAL FALLACIES. [less.

case of a surgeon would be to infer from one special case
to another special case.

It is undoubtedly true that to give to beggars promotes
mendicancy and causes evil ; but if we interpret this to
mean that assistance is never to be given to those who
solicit it, we fall into the converse fallacy of accident,
inferring of all who solicit alms what is only true of those
who sohcit alms as a profession. Similarly it is a very
good rule to avoid lawsuits and quarrels, but only as a
general rule, since there frequently arise circumstances
in which resort to the law is a plain duty. Almost all
the difficulties which we meet in matters of law and
moral duty arise from the impossibility of always ascer-
taining exactly to what cases a legal or moral rule does
or does not extend ; hence the interminable differences
of opinion, even among the judges of the land.

The Third Material Fallacy is that of the Irrelevant
Conclusion, technically called the Igiioratio Elenchi^ or
literally Ignorance of the Refutation. It consists in
arguing to the wrong point, or proving one thing in such
a manner that it is supposed to be something else that is
provec^. Here again it would be difficult to adduce con-
cise examples, because the fallacy usually occurs in the
course of long harangues, where the multitude of words
and figures leaves room for confusion of thought and
forgetfulness. This fallacy is in fact the great resource of
those who have to support a weak case. It is not un-
known in the legal profession, and an attorney for the
defendant in a lawsuit is said to have handed to
the barrister his brief marked, " No case ; abuse the
plaintiff's attorney." Whoever thus uses what is known as
argu7nentum ad hominem^ that is an argument which
rests, not upon the merit of the case, but the character or
position of those engaged in it, commits this fallacy. If
a man is accused of a crime it is no answer to say that.

XXI.] MATERIAL FALLACIES. ijg

the prosecutor is as bad. If a great change in the law is
proposed in Parliament, it is an Irrelevant Conclusion to
argue that the proposer is not the right man to bring it
forward. Everyone who gives advice lays himself open
to the retort that he who preaches ought to practise, or
that those who live in glass houses ought not to throw
stones. Nevertheless there is no necessary connection
between the character of the person giving advice and
the goodness of the advice.

The argujnentum ad poptihim is another form of
Irrelevant Conclusion, and consists in addressing argu-
ments to a body of people calculated to excite their feel-
ings and prevent them from forming a dispassionate
judgment upon the matter in hand. It is the great
weapon of rhetoricians and demagogues.

Petitio Principii is a familiar name, and the nature of
the fallacy it denotes is precisely expressed in the phrase
begging the guestiojt. Another apt name for the fallacy is
circuhis in probanda, or "a circle in the proof." It con-
sists in taking the conclusion itself as one of the premises
of an argument. Of course the conclusion of a syllogism
must always be contained or implied in the premises, but
only when those premises are combined, and are dis-
tinctly different assertions from the conclusion. Thus in
the syllogism,

^is C,

A isB,

therefore A is C,

the conclusion is proved by being deduced from two
propositions, neither of which is identical with it; but if
the tnith of one of these premises itself depends upon
the following syllogism,

CisB,

A is C,

tlierefore A is i?,

12—2

i8o MATERIAL FALLACIES. [less.

it is plain that we attempt to prove a proposition by itself,
which is as reasonable as attempting to support a body
upon itself. It is not easy to illustrate this kind of fal-
lacy by examples, because it usually occurs in long argu-
ments, and especially in wordy metaphysical writings.
We are very likely to fall into it however when we employ
a mixture of Saxon and Latin or Greek words, so as to
appear to prove one proposition by another which is
really the same expressed in different terms, as in the
following: "Consciousness must be immediate cognition
of an object ; for I cannot be said really to know a thing
unless my mind has been affected by the thing itself."

In the use of the disjunctive syllogism this fallacy is
likely to happen ; for by enumerating only those alterna-
tives which favour one view and forgetting the others it is
easy to prove anything. An instance of this occurs in the
celebrated sophism by which some of the ancient Greek
philosophers proved that motion was impossible. For,
said they, a moving body must move either in the place
where it is or the place where it is not ; now it is absurd
that a body can be where it is not, and if it moves it can-
not be in the place where it is; therefore it cannot move
at all. The error arises in the assumption of a premise
which begs the question; the fact of course is that the
body moves between the place ivhej^e it is at one moment
and the place whei'e it is at the next moment.

Jeremy Bentham however pointed out that the use
even of a single name may imply a Petitio Principii.
Thus in a Church assembly or synod, where a discussion
is taking place as to whether a certain doctrine should be
condemned, it would be a Petitio Principii to argue that
the doctrine is hei'esy, and therefore it ought to be con-
demned. To assert that it is heresy is to beg the question,
because every one understands by heresy a doctrine
which is to be condemned. Similarly in Parliament a

XXI.] MATERIAL FALLACIES, i8i

bill is often opposed on the ground that it is unconstitu-
tional and therefore ought to be rejected ; but as no
precise definition can be given of what is or is not con-
stitutional, it means little more than that the measure is
distasteful to the opponent. Names which are used in
this fallacious manner were aptly called by Bentham
Q,uestio7i-begging Epithets. In like manner we beg the
question when we oppose any change by saying that it is
U7i-E7iglish.

The Fallacy of the Consequent is better understood
by the familiar phrase 7io?i seqjutiir. We may apply
this name to any argument which is of so loose and
inconsequent a character that no one can discover any
cogency in it. It thus amounts to little more than the
assertion of a conclusion which has no connection with
the premises. Prof. De Morgan gives as an example
the following: "Episcopacy is of Scripture origin; the
Church of England is the only episcopal Church in Eng-
land; ergo, the Church established is the Church that
should be supported."

By the Fallacy of the False Cause I denote that which
has generally been referred to by the Latin phrase 7io7t
causa pro caiisd. In this fallacy we assume that one
thing is the cause of another without any sufficient
grounds. A change in the weather is even yet attributed
to the new moon or full moon which had occurred shortly
before, although it has been demonstrated over and over
again that the moon can have no such effect. In former
centuries any plague or other public calamity which fol-
lowed the appearance of a comet or an eclipse was
considered to be the result of it. The Latin phrase /^j/
hoc ergo propter hoc (after this and therefore in conse-
quence of this) exactly describes the character of these
fallacious conclusions. Though we no longer dread signs
and omens, yet we often enough commit the fallacy; as

l82 MATERIAL FALLACIES, [less. xxi.

when we assume that all the prosperity of England is the
result of the national character, forgetting that the plenti-
ful coal in the country and its maritime position have
contributed to our material wealth. It is no doubt equally
fallacious to attribute no importance to national character,
and to argue that because England has in past centuries
misgoverned Ireland all the present evils of Ireland are
due to that misgovernment.

Lastly there is the somewhat trivial Fallacy of Many
Questions, which is committed by those who so combine
two or three questions into one that no true answer can
be given to them. I cannot think of a better example
than the vulgar pleasantry of asking, " Have you left off
beating your mother.'"' Questions equally as unfair are
constantly asked by barristers examining witnesses in a
court of justice, and no one can properly be required to
answer Yes or No to every question which may be ad-
dressed to him. As Aristotle says, " Several questions
put as one should be at once decomposed into their
several parts. Only a single question admits of a single
answer: so that neither several predicates of one subject,
nor one predicate of several subjects, but only one predi-
cate of one subject, ought to be affirmed or denied in a
single answer."

Read Prof, de Morgan's excellent and amusing Chapter

on Fallacies, Formal Logic, Ch. Xlll.
Whatel/s remarks on Fallacies, Elements of Logic ^

Book III., are often very original and acute.

LESSON XXII.

THE QUANTIFICATION OF THE PREDICATE.

The syllogism has been explained in the preceding three
lessons almost exactly in the form in which it has been
taught for more than two thousand years. Just as Geo-
metry has been taught in the way and order first adopted
by the ancient Greek ^vriter Euclid, so Logic has been
taught nearly as Aristotle taught it about the year 335 B.C.

But within the last few years teachers hav'e at last
come to the conclusion in England that Euclid's ideas of
Geometry are not as perfect as could be desired. During
the last 30 or 40 years also it has been gradually made
apparent that Aristotle's syllogism is not an absolutely
perfect system of logical deduction. In fact, certain
eminent writers, especially Sir William Hamilton, Pro-
fessor De Morgan, Archbishop Thomson and Dr Boole,
have shewn that we need to make imiprovements from the
very basis of the science.

This reform in Logic is called by the somewhat mys-
terious name of the quantification of tlie predicate, but
the reader who has found no insuperable difficulty in
the preceding lessons need not fear one here. To quan-
tify the predicate is simply to state whether the whole or
the part only of the predicate agrees with or diff'ersfrojn
the stcbject. In this proposition,

" All metals are elements,"

1 84 THE QUANTIFICATION [less.

the subject is quantified, but the predicate is not; we
know that all metals are elements, but the proposition
does not distinctly assert whether metals make the whole
of the elements or not. In the quantified proposition

" All metals are soine elements,"
the httle word some expresses clearly that in reality the
metals form only a part of the elements. Aristotle avoid-
ed the use of any mark of quantity by assuming, as we
have seen, that all affirmative propositions have a par-
ticular predicate, like the example just given ; and that
only negative propositions have a distributed or universal
predicate. The fact however is that he was entirely in
error, and thus excluded from his system an infinite
number of affirmative propositions which are universal
in both terms. It is true that —
"All equilateral triangles are all equiangular triangles,"
but this proposition could not have appeared in his system
except in the mutilated form —

"All equilateral triangles are equiangular."
Such a proposition as

"London is the capital of England,"
or " Iron is the cheapest metal,"

had no proper place whatever in his syllogism, since both
terms are singular and identical with each other, and
both are accordingly universal.

As soon as we allow the quantity of the predicate to
be stated the forms of reasoning become much simplified.
We may first consider the process of conversion. In our
lesson on the subject it was necessary to distinguish be-
tween conversion by limitation and simple conversion.
But now one single process of simple conversion is suffi-
cient for all kinds of propositions. Thus the quantified
proposition of the form A,

"All metals are some elements,"

XXII.] GF THE PREDICATE. 185

is simply converted into

"Some elements are all metals."
The particular affirmative proposition

" Some metals are some brittle substances "
becomes by mere transposition of terms

" Some brittle substances are some metals."
The particular negative proposition

" Some men are not (any) trustworthy persons "
is also converted simply into

" Not any trustworthy persons are some men/'
though the result may appear less satisfactory in this form
than in the affirmative form, as follows,

" Some men are some not-trustworthy persons,"
converted simply into

" Some not-trustworthy persons are some men."
The universal negative proposition E is converted
simply as before, and finally we have a new affirmative
proposition universal both in subject and predicate ; as in

"All equilateral triangles are all equiangular triangles,"
which may obviously be converted simply into
"All equiangular triangles are all equilateral triangles."
This doubly universal affirmative proposition is of
most frequent occurrence; as in the case of all definitions
and singular propositions ; I may give as instances
"Honesty is the best policy," "The greatest truths are
the simplest truths," "Virtue alone is happiness below,"
" Self-exaltation is the fool's paradise."

When affirmative propositions are expressed in the
quantified form all immediate inferences can be readily
drawn from them by this one rule, that whatever we do
with one term we should do with the other term. Thus
from the doubly universal proposition, "Honesty is the
best policy," we infer that "what is not the best nohcy is

1 86 THE QUANTIFICATION [less.

not honesty," and also " what is not honesty is not the best
poHcy." From this proposition in fact we can draw two
contrapositives ; but the reader will carefully remember
that from the ordinary unquantified proposition A we
can only draw one contrapositive (see p. 84). Thus if
"metals are elements" we must not say that "what are
not metals are not elements." But if we quantify the
predicate thus, "All metals are sotne elements," we may
infer that " what are not metals are not soine elements."
Immediate inference by added determinant and complex
conception can also be applied in either direction to
quantified propositions without fear of the errors noticed
in pp. 86-7.

It is clear that in admitting the mark of quantity before
the predicate we shall double the number of propositions
which must be admitted into the syllogism, because the
predicate of each of the four propositions A, E, I, 0 may
be either universal or particular. Thus we arrive at a list
of eight conceivable kinds of propositions, which are
stated in the following table.

U All ^ is all Y, 1

I Some X is some Y. I Affirmative

A All X is some Y. j propositions,

Y Some X is all K J

E NoJiTis (any) K j

« Some X is not some Y. (, Negative

Tj No ^ is some Y. j propositio}is,

O Some X is no K

The letters X and Y are used to stand for any subject
and predicate respectively, and the reader by substituting
various terms can easily make propositions of each kind.
The symbolic letters on the left-hand side were proposed
by Archbishop Thomson as a convenient mode of refer-

XXII.] OF THE PREDICATE. 1S7

ring to each of the eight propositions, and are very
suitably chosen. The doubly universal affirmative pro-
position is called U \ the simple converse of A is called
Y; the Greek letter y\ {Eta, e) is applied to the proposi-
tion obtained by changing the universal predicate of E
into a particular predicate ; and the Greek « {Omega, 0)
is applied to the proposition similarly determined from 0.
All these eight propositions are employed by Sir W. Ha-
milton, but Archbishop Thomson considers that two of
them, 11 and «, are never really used. It is remarkable
that a complete table of the above eight propositions was
given by Mr George Bentham in a work called Outliiie
of a New Systein of Logic, published in 1827, several
years previous to the earliest of the logical publications of
Sir W. Hamilton. But Mr Bentham considered that some
of the propositions are hardly to be distinguished from
others; as Y from A, of which it is the simple converse; or
T] from 0.

The employment even of the additional two proposi-
tions U and Y introduced by Thomson much extends
the list of possible syllogisms, making them altogether 62
in number, without counting the fourth figure, which is
not employed 'oy Hamilton and Thomson. When the
whole eight propositions are admitted into use we are
obhged to extend the list of possible syllogisms so as to
contain 12 affirmative and 24 negative moods in each of
the three first figures. The whole of these moods are
conveniently stated in the table on the next page, given by
Archbishop Thomson at p. 188 of his Laws of Thotight,

Sir W. Hamilton also devised a curious system of
notation for exhibiting all the moods of the syllogism in a
clear manner. He always employed the letter 3/ to denote
the middle term of the syllogism, and the two letters C
and r (the Greek capital letter Gamma) for the two
terms appearing in the conclusion. The copula of the

THE QUANTIFICATION

[less.

Table of Moods of the Syllogis7n.

First Figure.

Second Fig.

Third Figure.

Affirm.

Neg.

Affirm.

Neg.

Affirm.

Neg.

1

UUU

EUE

UEE

UUU

EUE
UEE

UUU

EUE

UEE

ii

AYI

77Y CO

AOco

YYI

OYco
YOco

AAI

7; Aco
At; CO

iii

AAA

YAA

OAt;

AYA

t;Y,;
AOt;

iv

YYY

OYO
YOO

AYY

77YO
AOO

YAY

OAO
Yt;0

V

All

A CO CO

YII

OIo,
Ycoco

All

t; I CO

A CO CO

vi

lYI

CO Yco
lOco

lYI

toYco
lOco

lAI

coAco
I t; 00

vii

UYY

EYO
UOO^

UYY

EYO
UOO

UAY

EAO
Ut;0

viii

AUA

^U^
AE;;

YUA

OUj;
YE,;

AUA

t;Ut;
AEt;

ix

UAA

EAE

UAA

EAE
U^t;

UYA

EYE

UOt;

X

YUY

ouo

YEE '

AUY

7;UO

AEE I

YUY

OUO
YEE

xi

UII

EIO
Ucoo) 1

UII

EIO ;

U CO 0)

UII

EIO
U CO a»

xii

lUI

CO U 0)

IE,

lUI

coUco i
IE,; 1

lUI

CO U CO

IE,;

proposition was indicated by a line thickened towards
the subject ; thus C i^i AT means that " Cisi^."

To indicate the quantity of the terms Hamilton inserted a

.. XXII.] OF THE PREDICATE, 1S9

colon (:) between the term and the copula when the
quantity is universal, and a comma (,) when the quantity
_^ is particular. Thus we readily express the following
affii'mative propositions.

C : m Mil , ill All Cs are some J/'s (A)

C : mm : M All C's are aU ATs (U)

C , smm^^^- — , M Some C's are some J/'s (I)

and so on. Any affirmative proposition can be converted
into the corresponding negative proposition by drawing a
* stroke through the line denoting the copula, as in the
following —

C : JIM,,, p '.M No C is any Af (E)

C , i^BBBB^M— — : il/ Some C is not any J/ (0)
C , H^iBB^v— ^ , M Some C is not some M («)

Any syllogism can be represented by placing Af the

middle term in the centre and connecting it on each side

with the other terms. The copula representing the con-

. elusion can then be placed below ; Barbara is expressed

as follows —

C, ■■■■ :M,

The negative mood Celarent is similarly-

+

Cesare in the second figure is thus represented—
C: is3Es»- ,M: j,,,, :r

Sir W. Hamilton also proposed a new law or supreme
xanon of the syllogism by which the vaHdity of all forms

I90 THE QUANTIFICATION [LESS.

of the syllogism might be tested. This was stated in the
following words : "What worse relation of subject and
predicate subsists between either of two terms and a
common third term, with which both are related, and one
at least positively so — that relation subsists between these
two terms themselves."

By a woi'se I'elation, Sir William means that a negative
relation is worse than an affirmative and a particular than
a universal. This canon thus expresses the rules that if
there be a negative premise the conclusion must be nega-
tive, and if there be a particular premise the conclusion
must be particular. Special canons were also developed
for each of the three figures, but in thus rendering the
system complex the advantages of the quantified form of
proposition seem to be lost.

Prof. De Morgan also discovered the advantages of
the quantified predicate, and invented a system differing
greatly from that of Sir W. Hamilton. It is fully ex-
plained in his Formal Logic, The Syllabtcs of a new
Systejn of Logic, and various important memoirs on the
Syllogism in the Transactions of the Cambridge Philo-
sophical Society. In these works is also given a com-
plete explanation of the " Numerically Definite Syllogism."
Mr De Morgan pointed out that two particular premises
may often give a valid conclusion provided that the
actual quantities of the two terms are stated, and when
added together exceed the quantity of the middle term.
Thus if the majority of a public meeting vote for the first
resolution, and a majority also vote for the second, it
follows necessarily that some who voted for the first voted
also for the second. The two majorities added together
exceed the whole number of the meeting, so that they
could not consist of entirely different people. They may
indeed consist of exactly the same people ; but all that
we can deduce from the premises is that the excess of the

XXII.] OF THE PREDICATE. 191

two majorities added together over the number of the
meeting must have voted in favour of each resolution.
This kmd of inference has by Sir W. Hamilton been
said to depend on ultra-total distribution ; and the name
of Plurative Propositions has been proposed for all those
which give a distinct idea of the fraction or number of the
subject involved in the assertion.

T. Spencer Baynes, Essay on the new Analytic of

Logical Forms; Edinburgh, 1850.
Prof. Bowen's Treatise on Logic or the Laws of Pure

Thotight, Cambridge, U. S. 1866 (Trubner and

Co.) gives a full and excellent account of Hamilton's

Logic.

LESSON XXIII.

BOOLE'S SYSTEM OF LOGIC

It would not in the least be possible to give in an ele-
mentary work a notion of the system of indirect inference
first discovered by the late Dr Boole, the Professor of
Mathematics at the Queen's College, Cork. This system
was founded as mentioned in the last lesson upon the
Quantification of the Predicate, but Dr Boole regarded
Logic as a branch of Mathematics, and believed that he
could arrive at every possible inference by the principles
of algebra. The process as actually employed by him
is very obscure and difficult ; and hardly any attempt to
introduce it into elementary text-books of Logic has yet
been made.

I have been able to arrive at exactly the same results

192 BOOLE'S SYSTEM OF LOGIC. [less.

as Dr Boole without the use of any mathematics; and
though the very simple process which I am going to
describe can hardly be said to be strictly Dr Boole's
logic, it is yet very similar to it and can prove everything
that Dr Boole proved. This Method of Indirect Inference
is founded upon the three primary Laws of Thought
stated in Lesson XIV., and the reader who may have
thought them mere useless truisms will perhaps be sur-
prised to find how extensive and elegant a system of
deduction may be derived from them.

The law of excluded middle enables us to assert that
anything must either have a given quality or must have it
not. Thus if h^on be the thing, and cojnbustibility the
quality, anyone must see that

"Iron is either combustible or incombustible."

This division of alternatives may be repeated as often
as we like. Thus let Book be the class of things to be di-
vided, and English and Scientific two qualities. Then any
book must be either English or not English; again an
English book must be either Scientific or not Scientific,
and the same may be said of books which are not English.
Thus we can at once divide books into four classes —

Books, English and Scientific.

Books, English and not-Scientific.

Books, not-English and Scientific.

Books, not-English and not-Scientific.
This is what we may call an exhaustive division of the
class Books; for there is no possible book which does
not fall into one division or other of these four, on
account of the simple reason, that if it does not fall into
any of the three first it must fall into the last. The pro-
cess can be repeated without end, as long as any new
circumstance can be suggested as the ground of division.
Thus we might divide each class again according as the

xxiiL] BOOLE'S SYSTEM OF LOGIC. 193

books are octavo or not octavo, bound or unbound, pub-
lished in London or elsewhere, and so on. We shall call
this process of twofold division, which is really the pro-
cess of Dichotomy mentioned in p. 107, the development
of a term, because it enables us always to develope the
utmost number of alternatives which need be considered.
As a general rule it is not likely that all the alterna-
tives thus unfolded or developed can exist, and the next
point is to ascertain how many do or may exist. The Law
of Contradiction asserts that nothing can combine con-
tradictory attributes or qualities, and if we meet with any
term which is thus self-contradictory we are authorized at
once to strike it out of the list Now consider our old
example of a syllogism :

Iron is a metal ;

All metals are elements ;

Therefore iron is an element.

We can readily prove this conclusion by the indirect
method. For if we develope the term iron, we have four
alternatives , thus —

Iron, metal, element.

Iron, metal, not-element.

Iron, not-metal, element.

Iron, not-metal, not-element.

But if we compare each of these alternatives with the
premises of the syllogism, it will be apparent that several
of them are incapable of existing. Iron, we are informed,
is a metal. Hence no class of things "iron, not-metal"
can exist. Thus we are enabled by the first premise to
strike out both of the last two alternatives which combine
iron and not-metal. The second alternative, again, com-
bines metal and not-element ; but as the second premise
informs us that "all metals are elements," it jnust be
struck out. There remains, then, only one alternative

13

194 BOOLE'S SYSTEM OF LOGIC. [less.

which is capable of existing if the premises be true, and as
there cannot conceivably be more alternatives than those
considered, it follows demonstratively that iron occurs
only in combination with the qualities of metal and ele-
ment, or, in brief, that it is an element.

We can, however, prove not only the ordinary syllo-
gistic conclusion, but any other conclusion which can be
drawn from the same premises ; the syllogistic conclusion
is in fact only one out of many which can usually be ob-
tained from given premises. Suppose, for instance, that
we wish to know what is the nature of the term or class
not-element, so far as we can learn it from the premises
just considered. We can develope the alternatives of this
term, just as we did those of iron, and get the following —

Not-element, iron, metal.

Not-element, iron, not-metal.

Not-element, not-iron, metal.

Not-element, not-iron, not-metal.

Compare these combinations as before with the premises.
The first it is easily seen cannot exist, because all metals
are elements ; for the same reason the third cannot exist ;
the second is likewise excluded, because iron is a m.etal
and cannot exist in combination with the qualities of not-
metal. Hence there remains only one combination to
represent the class desired — namely,

Not-element, not-iron, not-metal.
Thus we learn from the premises that every not-ele-
ment is not a metal and is not iron-
As another example of this kind of deductive process
I will take a case of the Disjunctive Syllogism, in the ne-
gative mood, as follows : —

A fungus is either plant or animal,
. A fungus is not an animal ;
Therefore it is a plar.t.

XXIII.] BOOLE'S SYSTEM OF LOGIC. 195

Now if we develope all the possible ways in which
fungus, plant and animal can be combined together, we
obtain for the term fungus —

(i) Fungus, plant, animal.

(2) Fungus, plant, not-animal.

(3) Fungus, not-plant, animal.

(4) Fungus, not-plant, not-animal.

Of these however the 4th cannot exist because by
the prem.ise a fungus must be a plant, or if not a plant an
animal. The ist and 3rd again cannot exist because the
minor premise informs us that a fungus is not an animal.
There remains then only the second combination,
Fungus, plant, not-animal,

from which we learn the syllogistic conclusion that
" a fungus is a plant."

The chief excellence of this mode of deduction consists
in the fact that it is not restricted to any definite series
of forms like the syllogism, but is applicable, without any
additional rules, to all kinds of propositions or problems
which can be conceived and stated. There may be any
number of premises, and they may contain any number of
terms ; all we have to do to obtain any possible inference
is to develope the term required into all its alternatives
and then to examine how many of these agree with the pre-
mises. What remain after this examination necessarily
form the description of the term. The only inconvenience
of the method is that, as the number of terms increases,
the number of alternatives to be examined increases very
rapidly, and it soon becomes tedious to write them all out.
This work may be abbreviated if we substitute single
letters to stand for the terms, somewhat as in algebra;
thus we may take^, B, C, D, &c., to stand for the affirm-
ative terms, and a^ b, c, d, &c., for the corresponding nega-
tive ones. Let us take as a first example the premises —

13—2

196 BOOLE'S SYSTEM OF LOGIC. [LESS

Organic substance is either vegetable or animal.
Vegetable substance consists mainly of carbon, hydrogen,

and nitrogen. ^

Animal substance consists mainly of carbon, hydrogen,

and nitrogen.

It would take a long time to write out all the combi-
nations of the four terms occurring in the above ; but if
we substitute letters as follows —

A = organic substance,

^ = vegetable substance,

C= animal substance,

Z> = consisting mainly of carbon, hydrogen, and
nitrogen,
we can readily represent all the combinations which can
belong to the term A.

(i) ABCD

(2) ABCd

(3) ABcD

(4) ABcd

Now the premises amount to the statements, that
A must be either B or C,
B must be D^
C must be D.

The combinations (7) and (8) are inconsistent with the
ftrst premise ; the combinations (2) and (4) with the second
premise; and (6) is inconsistent with the third premise.
There remain only,

ABCD
ABcD
AbCD.

Whence we learn at once that "organic substance {A)
always consists mainly of carbon, hydrogen and nitrogeii,"

AbCD

(5)

AbCd

(6)

AbcD

(7)

Abed

(8)

XXIII.] BOOLE'S SYSTEM OF LOGIC. 197

because it always occurs in connexion ^vith D. The reader
may perhaps notice that the term A BCD impHes that or-
. ganic substance may be both vegetable {B) and animal (C),
If the first premise be interpreted as meaning that this is
not possible, of course this combination should also be
struck out. It is an unsettled point whether the alter-
natives of a disjunctive proposition can coexist or not
(see p. 166), but I much prefer the opinion that they
can; and as a matter of fact it is quite likely that there
exist very simple kinds of living beings, which cannot be
"distinctly asserted to be vegetable only or animal only,
but partake of the nature of each.

As a more complicated problem to shew the powers of
this system, let us consider the premises which were
treated by Dr Boole in his Laws of Thought^ p. 125, as
follows :

" Similar figures consist of all whose corresponding
angles are equal, and whose corresponding sides are
proportional.

Triangles whose corresponding angles are equal have
their corresponding sides proportional ; and vice versa.

Triangles whose corresponding sides are proportional
have their corresponding angles equal "

Now if we take our symbol letters as follows :

A = similar figure,

^ = triangle,

C= having corresponding angles equal,

Z> = having corresponding sides proportional,

the premises will be seen to amount to the statements that

A is identical with CD,
and that

BC is identical with BD;
,in other words, all A's ought to be CUs, CD's ought to

198 BOOLE'S SYSTEM OF LOGIC. [less.

be A\ all BCs ought to be BU^ and all Biys ought to
be BCs.

The possible combinations in which the letters may be
united are 16 in number and are shewn in the following
table :

ABCD

aBCD

ABCd

aBCd

ABcD

aBcD

ABcd

aBcd

AbCD

abCD

AbCd

abCd

AbcD

abcD

A bed

abed

Comparing each of these combinations with the premises
we see that ABCd, ABeD, A Bed, and others, are to be
struck out because every A is also to be CD. The com-
binations aBCD and abCD are struck out because every
CD should also be A. Again, aBCd is inconsistent with
the condition that ever)' BC is also to be BD\ and ii
the reader carefully follows out the same process of ex-
amination, there will remain only six combinations, which
agree with all the premises, thus —

ABCD aBed

AbCD abCd

abcD

abed

From these combinations we can draw any description
we like of the classes of things agreeing with the premises.
The class A or similar figures is represented by only two
combinations or alternatives ; the negative class a or
dissimilar figures, by four combinations, whence we may
draw the following conclusion: "Dissimilar figures con
sist of all triangles which have not their corresponding
angles equal, and sides proportional (aBed), and of al}

XXIII.] BOOLE'S SYSTEM OF LOGIC. 199

figures, not being triangles, which have either their angles
equal and sides not proportional iabCd), or their cor-
responding sides proportional and angles not equal
{abcD), or neither their corresponding angles equal nor
corresponding sides proportional {abed)."

In performing this method of inference it is soon seen
to proceed in a very simple mechanical manner, and the
only inconvenience is the large number of alternatives or
combinations to be examined. I have, therefore, devised
several modes by which the labour can be decreased;
the simplest of these consists in engraving the series
of 16 combinations on the opposite page, which occur
over and over again in problems, with larger and smaller
sets, upon a common writing slate, so that the excluded
ones may be readily struck out with a common slate
pencil, and yet the series may be employed again for any
future logical question. A second device, which I have
called the "Logical abacus," is constructed by printing the
letters upon slips of wood furnished with pins, contrived
so that any part or class of the combinations can be
picked out mechanically with very little trouble ; and a
logical problem is thus solved by the hand, rather than
by the head. More recently however I have reduced the
system to a completely mechanical form, and have thus
embodied the whole of the indirect process of inference
in what may be called a Logical Machine. In the front
of the machine are seen certain moveable wooden rods
carrying the set of 16 combinations of letters which are
seen on the preceding page. At the foot are 21 keys like
those of a piano; eight keys towards the left hand are
marked with the letters A, a, B, b, C, c, D, d, and are
intended to represent these terms when occurring in the
subject of a proposition. Eight other keys towards the
right hand represent the same letters or terms when oc-
curring in the predicate. The copula of a proposition is

200 BOOLE S SYSTEM OF LOGIC. [LESS.

represented by a key in the middle of the series ; the full
stop by one to the extreme right, while there are two other
keys which serve for the disjunctive conjunction <?r, ac-
cording as it occurs in subject or predicate. Now if the
letters be taken to stand for the terms of a syllogism or
any other logical argument, and the keys of the instru-
ment be pressed exactly in the order corresponding to the
words of the premises, the i6 combinations will be so
selected and arranged thereby that at the end only the
possible combinations will remain in view. Any question
can then be asked of the machine, and an infallible answer
will be obtained from the combinations remaining. The
internal construction of the machine is such, therefore, as
actually to perform the work of inference which, in Dr
Boole's system, was performed by a very complicated
mathematical calculation. It should be added, that there
is one remaining key to the extreme left which has the
effect of obliterating all previous operations and restoring
all the combinations to their original place, so that the
machine is then ready for the performance of any new
problem.

An account of this logical machine may be found in
the Proceedings of the Royal Society for Jan. 20th, 1870,
the machine having on that day been exhibited in action to
the Fellows of the Society. The principles of the method
of inference here described are more completely stated in
The Substitution of Similars* ^ and the Prijiciples of Sci-
ence^, which I published in the years 1869 and 1874. I
may add, that each of these works contains certain views as
to the real nature of the process of inference which I do

* The Substituth)i of Similars, the true PHnciple of Reason-
ing, derived from a modification of Aristotle^ s Dictum. Mac-
millan and Co. 1869.

f The Principles of Science : a Treatise on Logic and Scientific
Melhod. 1 vols. Macmillan and Co.

XXIII.] BOOLE'S SYSTEM OF LOGIC. 201

not think it desirable to introduce into an elementary work
like the present, on account of their speculative character.
The process of inference, on the other hand, which I have
derived from Boole's system is of so self-evident a charac-
ter, and is so clearly proved to be true by its reduction to
a mechanical form, that I do not hesitate to bring it to the
reader's notice.

George Boole, Mathe??tatical Afialysis of Logic, 1847.
An Investigation of the Laws of Thought. London,
Walton and Maberly, 1854.

LESSON XXIV.

ON METHOD, ANALYSIS AND SYNTHESIS.

It has been held by many writers on Logic that, in addi-
tion to the three parts of logical doctrine which treat
successively of Terms, Propositions and Syllogisms, there
was a fourth part, which treats of method. Just as the
doctrine of Judgment considers the arranging of terms
and their combination into Propositions, and the doc-
trine of Syllogism considers the arranging of propositions
that they may form arguments, so there should in like
-» manner be a fourth part, called Method, which should
govern the arrangement of syllogisms and their combina-
tion into a complete discourse. Method is accordingly
defined as consisting in such a disposition of the parts of
a discourse that the whole 7nay be most easily intelligible.
The celebrated Peter Ramus, who perished in the
massacre of St Bartholomew, first proposed to make
method in this manner a part of the science of Logic : but

202 ON METHOD, ANALYSIS [less.

it may well be doubted whether any definite set of rules
or principles can be given to guide us in the arrangement
of "arguments. Every different discourse must consist of
arguments arranged in accordance with the peculiar nature
of the subject ; and no general rules can be given for treat-
ing things which are infinitely various in the mode of treat-
ment required. Accordingly the supposed general rules
of method are no better than truisms, that is, they tell us
nothing more than we must be supposed to know before-
hand. Thus, we are instructed in composing any dis-
course to be careful that —

1. Nothing should be wanting or redundant.

2. The separate parts should agree with each other.

3. Nothing should be treated unless it is suitable to
the subject or purpose.

4. The separate parts should be connected by suit-
able transitions.

But it is evident that the whole difficulty consists in
deciding what is wanting or redundant, suitable or con-
sistent. Rules of this kind simply tell us to do what we
ought to do, without defining what that is.

There exist nevertheless certain general modes of
treating any subject which can be clearly distinguished,
and should be well understood by the logical student.
Logic cannot teach him exactly how and when to use
each kind of method, but it can teach him the natures
and powers of the methods, so that he will be more likely
to use them rightly. We must distinguish,

1. The method of discov^ery,

2, The method of instruction.

The method of discovery is employed in the acquisi-
tion of knowledge, and really consists in those processes
of inference and induction, by which general truths are
ascertained from the collection and examination of par-

XXIV.] AND SYNTHESIS. 203

ticular facts. This method will be the subject of most of
our remaining Lessons. The second method only applies
when knowledge has already been acquired and express-
ed in the form of general laws, rules, principles or truths,
so that we have only to make ourselves acquainted with
these and observe the due mode of applying them to
particular cases, in order to possess a complete acquaint-
ance with the subject.

A student, for example, in learning Latin, Greek,
French, German, or any well-known language, receives a
complete Grammar and Syntax setting forth the whole of
the principles, rules and nature of the language. He
receives these instructions, and takes them to be true on
the authority of the teacher, or the writer of the book;
and after rendering them familiar to his mind he has
nothing to do but to combine and apply the rules in read-
ing or composing the language. He follows, in short,
the method of Instruction. But this is an entirely differ-
ent and opposite process to that which the scholar must
pursue who has received some writings in an unknown
language, and is endeavouring to make out the alpha-
bet, words, grammar, and syntax of the language. He
possesses not the laws of grammar, but words and sen-
tence§ obeying those laws, and he has to detect the
laws if possible by observing their effects on the written
language. He pursues, in short, the method of discovery
consisting in a tedious comparison of letters, words, and
phrases, such as shall disclose the more frequent combi-
nations and forms in which they occur. The process
would be a strictly inductive one, such as I shall partially
exemplify in the Lessons on Induction ; but it is far more
difficult than the method of Instruction, and depends to a
great extent on the happy use of conjecture and hypothesis,
which demands a certain skill and inventive ability.

Exactly the same may be said of the investigation of

204 ON METHOD, ANALYSIS [LESS

natural things and events. The principles of mechanics,
of the lever, inclined plane, and other Mechanical Powers,
or the Laws of Motion, seem comparatively simple and
obvious as explained to us in books of instruction. But
the early philosophers did not possess such books ; they
had only the Book of Nature, in which is set forth not
the laws but the results of the laws, and it was only
after the most patient and skilful investigation, and after
hundreds of mistakes, that those laws were ascertained.
It is very easy now to understand the Copernican system
of Astronomy, which represents the planets as revolving
round the sun in orbits of various magnitude. Once know-
ing the theory we can readily see why the planets have
such various movements and positions, and why they
sometimes stand still ; it is easy to see, too, why in ad-
dition to their own proper motions they all go round the
earth apparently every day in consequence of the earth's
diurnal rotation. But all these changes were exceedingly
puzzling to the ancients, who regarded the earth as stand-
ing still.

The method of discovery thus begins with facts ap-
parent to the senses, and has the difficult task of detecting
those universal laws or general principles which can only
be comprehended by intellect. It has been aptly said
that the method of discovery thus proceeds from things
better kno'W7i to us, or our senses {nobis notiora), to those
which are more simple or better known in nature {notiora
naturcE). The method of Instruction proceeds in the
opposite direction, beginning with the things notiora
natures, and proceeding to show or explain the things
nobis notiora. The difference is almost like that between
hiding and seeking. He who has hidden a thing knows
where to find it; but this is not the position of a discoverer,
who has no clue except such as he may meet in his own
diligent and sagacious search.

XXIV.] AND SYNTHESIS. 205

Closely corresponding to the distinction between the
methods of Discovery and Instruction is that between
the methods of Analysis and Synthesis. It is very im-
portant indeed that the reader should clearly apprehend
the meanings of these terms in their several applications.
Analysis is the process of separating a whole into its
parts, and synthesis the combination of parts into a
whole. The analytical chemist, who receives a piece of
mineral for examination, may be able to separate com-
pletely the several chemical elements of which it is
composed and ascertain their nature and comparative
quantities; this is chemical analysis. In other cases the
chemist mixes together carefully weighed quantities of
certain simple substances and combines them into a new
compound substance ; this is chemical synthesis. Logical
analysis and synthesis must not be confused with the
physical actions, but they are nevertheless actions of
mind of an analogous character.

In logical synthesis we begin with the simplest possible
notions or ideas, and combine them together. We have
the best possible example in the elements of Geometry.
In Euchd we begin with certain simple notions of points,
straight lines, angles, right angles, circles, &c. Putting
together three straight lines we make a triangle ; joining
to this the notion of a right-angle, we form the notion of
a right-angled triangle. Joining four other equal lines at
right angles to each other we gain the idea of a square,
and if we then conceive such a square to be formed upon
each of the sides of a right-angled triangle, and reason
from the necessary qualities of these figures, we discover
that the two squares upon the sides containing the right
angle must together be exactly equal to the square upon
the third side, as shewn in the 47th Proposition of
Euclid's first book. This is a perfect instance of com-
bining simple ideas into more complex ones.

2o6 ON METHOD, ANALYSIS [less.

We have often, however, in Geometry to pursue the
opposite course of Analysis. A complicated geometrical
figure may be given to us, and we may have, in order to
prove the properties which it possesses, to resolve it into
its separate parts, and to consider the properties of those
parts each distinct from the others.

A similar distinction between the analytical and syn-
thetic methods can be traced throughout the natural
sciences. By keeping exact registers of the appearance
and changes of the weather v/e may readily acquire an
immense collection of facts, each such recorded fact
implying a multitude of different circumstances occurring
together. Thus in any storm or shower of rain we have
to consider the direction and force of the wind ; the tem-
perature and moistness of the air ; the height and forms of
the clouds; the quantity of rain which falls, or the light-
ning and thunder which occur with it. If we proceed by
analysis only to explain the changes of the weather we
should have to try resolving each storm or change of
weather into its separate circumstances, and comparing
each with every other to discover what circumstances
usually go together. We might thus ascertain no doubt
with considerable certainty what kinds of clouds, and
what changes of the wind, temperature, moisture, &c.,
usually precede any kind of storm, and we might even in
time give some imperfect explanation of what takes place
in the atmosphere.

But we might also apply with advantage the syn-
thetical method. By previous chemical investigations we
know that the atmosphere consists mainly of the two
fixed gases, oxygen and nitrogen, with the vapour of
water, the latter being very variable in quantity. We
can try experimentally what takes place when portions
of such air of various degrees of moistness are com-
pressed or allowed to expand, or are mixed together, as

XXIV.] AND SYNTHESIS. 207

often happens in the atmosphere. It is thus discovered
that whenever moist air is allowed to expand cloud
is produced, and it may be drops of rain. Dr Hut-
ton, too, found that whenever cold moist air is mixed
with warm moist air cloud is again produced. We can
safely argue from such small experiments to what takes
place in the atmosphere. Putting together synthetically,
from the sciences of chemistry, mechanics, and electricity,
all that we know of air, wind, cloud and lightning, we are
able to explain what takes place in a thunder-storm far
more completely than v/e could do by merely observing
directly what happens in the storm. We are here how-
ever anticipating the methods of inductive investigation,
which we must consider in the following lessons. It will
appear that Induction is equivalent to analysis, and that
the deductive kinds of reasoning which we have treated
in prior lessons are of a synthetic character.

It has been said that the synthetic method usually
corresponds to the method of instruction and the analytic
method to that of discovery. But it may be possible to
discover new truths by synthesis and to teach old ones
by analysis. Sir John Herschel in his well-known Out-
lines of Astronomy partially adopts the analytic method ;
he supposes a spectator in the first place to survey the
appearances of the heavenly bodies and the surface of
the earth, and to seek an explanation ; he then leads
him through a course of arguments to show that these
, appearances really indicate the rotundity of the earth, its
revolution about its own axis and round the sun, and its
subordinate position as one of the smaller planets of the
solar system, Mr Norman 'Locky ex's Ele7nenta7y Lessojis
i?i Astronomy is a clear example of the synthetic method
of instruction ; for he commences by describing the sun,
the centre of the system, and successively adds the planets
and other members of the system, until at last we have

2o8 ON METHOD, ANALYSIS [less.

the complete picture ; and the reader who has temporarily
received everything on the writer's authority, sees that
the description corresponds with the truth. Each method,
it must be allowed, has its own advantages.

It must be carefully observed that the meaning of
analysis, and therefore that of synthesis, varies according
as we look to the intension or extension of terms. To
divide or analyse a class of things in extension I must add
a quality or difference. Thus I divide the class organism
when I add the quality vegetable, and separate vegetable
organism from what is not vegetable. Analysis in exten-
sion is therefore the same process as synthesis in inten-
sion ; and 'vice versa, whenever I separate or analyse a
group of qualities each part belongs to a larger class of
things in extension. When I analyse the notion vegetable
organism, and regard the notion organism apart from
vegetable, it is apparent that I really add the whole class
of animal organisms to the class I am considering — so
that analysis in intension is synthesis in extension. The
reader who has well considered the contents of Lessons
V. and XII. will probably see that this connection of the
two processes is only a re-statement of the law, (p. 40),
that "as the intension of a term is increased the extension
is decreased."

To express the difference between knowledge derived
deductively and that obtained inductively the Latin
phrases a priori and a posteriori are often used. By
A priori reasoning we mean argument based on truths
previously known ; A posteriori reasoning, on the contrary,
proceeds to infer from the consequences of a general
truth what that general truth is. Many philosophers con-
sider that the mind is naturally in possession of certain
laws or truths which it must jjecognise in every act of
thought; all such, if they exist, would be a priori truths.
It cannot be doubted, for instance, that we must always

XXIV.] AND SYNTHESIS. 10^

recognise in thought the three Primary Laws of Thought
considered in Lesson xiv. We have there an a priori
knowledge that "matter cannot both have weight and be
without weight," or that "every thing must be either self-
luminous or not self-luminous." But there is no law of
thought which can oblige us to think that matter has
weight, and luminous ether has not weight ; that Jupiter
and Venus are not self-luminous, but that comets are to
some extent self-luminous. These are facts which are no
doubt necessary consequences of the laws of nature and
the general constitution of the world ; but as we are not
naturally acquainted with all the secrets of creation, we
have to learn them by observation, or by the a posteriori
method.

It is not however usual at the present time to restrict
the name a priori to truths obtained altogether without
recourse to observation. Knowledge may originally be
of an a posteriori origin, and yet having been long
in possession, and having acquired the greatest certainty,
it may be the ground of deductions, and may then be said
to give a priori knowledge. Thus it is now believed by
all scientific men that force cannot be created or destroy-
ed by any of the processes of nature. If this be true the
force which disappears when a bullet strikes a target must
be converted into something else, and on <2/r/^r/ grounds
we may assert that heat will be the result. It is true that
we might easily learn the same truth a posteriori^ by
picking up portions of a bullet which has just struck a
target and observing that they are warm. But there is a
great advantage in a priori knowledge ; we can often
apply it in cases where experiment or observation would
be difficult. If I lift a stone and then drop it, the most
deHcate instruments could hardly show that the stone
was heated by striking the earth ; yet on a priori %xo\xxidL.^
I know that it must have been so and can easily calcu-

14

2IO PERFECT INDUCTION AND [LESS.

late the amount of heat produced. Similarly we know,
without the trouble of observation, that the Falls of Ni-
agara and all other waterfalls produce heat. This is
fairly an instance of a priori knowledge because no one
that I have heard of has tried the fact or proved it a pos-
teriori; nevertheless the knowledge is originally founded
on the experiments of Mr Joule, who observed in certain
well-chosen cases how much force is equivalent to a
certain amount of heat. The reader, however, should
take care not to confuse the meaning of a priori thus
explained with that given to the words by the philoso-
phers who hold the mind to be in the possession of know-
ledge independently of all observation.

It is not difficult to see that the a prio7'i method is
equivalent to the synthetic method (see p. 205) considered
in intension, the a posteriori method of course being equi-
valent to the analytic method. But the same difference is
really expressed in the words deductive and inductive;
and we shall frequently need to consider it in the following
lessons.

For general remarks upon Method see the Port Royal
Logic^ Part iv.

LESSON XXV.

PERFECT INDUCTION AND THE INDUCTIVE
SYLLOGISM.

We have in previous lessons considered deductive rea-
soning, which consists in combining two or more propo-
sitions synthetically, and thus arriving at a conclusion
which is a proposition or truth of less generahty than

XXV.] THE INDUCTIVE SYLLOGISM. 211

the premises, that is to say, it applies to fewer indi-
vidual instances than the separate premises from which
it was inferred. When I combine the general truth that
"metals are good conductors of heat." with the truth that
•'aluminium is a metal," I am enabled by a syllogism in
the mood Barbara to infer that "aluminium is a good con-
ductor of heat." As this is a proposition concerning one
metal only, it is evidently less general than the premise,
which referred to all metals whatsoever. In induction, on
the contrary, we proceed from less general, or even from
individual facts, to more general propositions, truths, or,
as we shall often call them, Laws of Nature. When it is
known that Mercury moves in an elliptic orbit round the
Sun, as also Venus, the Earth, Mars, Jupiter, &c., we are
able to arrive at the simple and general truth that "all the
planets move in elliptic orbits round the sun." This is an
example of an inductive process of reasoning.

It is true that we may reason without rendering our
conclusion either more or less general than the premises,
as in the following : —

Snowdon is the highest mountain in England or Wales.
Snowdon is not so high as Ben Nevis.
Therefore the highest mountain in England or Wales is
not so high as Ben Nevis,

Again :

Lithium is the lightest metal known.

Lithium is the metal indicated by one bright red line in

the spectrum *.
Therefore the lightest metal known is the metal indicated

by a spectrum of one bright red line.

In these examples all the propositions are singular
propositions, and merely assert the identity of singular

* Roscoe's Lessons in Elei^ientary Chemistry.

14—2

212 PERFECT INDUCTION AND [LESS.

terms, so that there is no alteration of generality. Each
conclusion applies to just such an object as each of the
premises applies to. To this kind of reasoning the apt
name of Traduction has been given.

Induction is a much more difficult and more important
kind of reasoning process than Traduction or even Deduc-
tion ; for it is engaged in detecting the general laws or
uniformities, the relations of cause and effect, or in short
all the general truths that may be asserted concerning the
numberless and very diverse events that take place in the
natural world around us. The greater part, if not, as
some philosophers think, the whole of our knowledge, is
ultimately due to inductive reasoning. The mind, it is
plausibly said, is not furnished with knowledge in the
form of general propositions ready made and stamped
upon it, but is endowed with powers of observation, com-
parison, and reasoning, which are adequate, when well
educated and exercised, to procure knowledge of the world
without us and the world within the human mind. Even
when we argue synthetically and deductively from simple
ideas and truths which seem to be ready in the mind, as
in the case of the science of geometry, it may be that we
have gathered those simple ideas and truths from previous
observation or induction of an almost unconscious kind.
This is a debated point upon which I will not here speak
positively ; but if the truth be as stated. Induction will be
the mode by which all the materials of knowledge are
brought to the mind and analysed. Deduction will then
be the almost equally important process by which the
knowledge thus acquired is utilised, and by which new
Inductions of a more complicated character, as we shall
see, are rendered possible.

An Induction, that is an act of Inductive reasoning, is
called Perfect when all the possible cases or instances to
which the conclusion can refer, have been examined and

XXV.] THE INDUCTIVE SYLLOGISM. 213

enumerated in the premises. If, as usually happens, it is
impossible to examine all cases, since they may occur at
future times or in distant parts of the earth or other
regions of the universe, the Induction is called Imperfect.
The assertion that all the months of the year are of less
length than thirty-two days is derived from Perfect In-
duction, and is a certain conclusion because the calendar
is a human institution, so that we know beyond doubt how
many months there are, and can readily ascertain that
each of them is less than thirty-two days in length. But
the assertion that all the planets move in one direction
round the sun, from West to East, is derived from Imper-
fect Induction ; for it is possible that there exist planets
more distant than the most distant-known planet Nep-
tune, and to such a planet of course the assertion would
apply.

Hence it is obvious that there is a great difference
between Perfect and Imperfect Induction. The latter
includes some process by which we are enabled to make
assertions concerning things that we have never seen or
examined or even known to exist. But k must be care-
fully remembered also that no Imperfect Induction can
give a certain conclusion. It may be highly probable or
nearly certain that the cases unexamined will resemble
those which have been examined, but it can never be
certain. It is quite possible, for instance, that a new
planet might go round the sun in an opposite direction to
the other planets. In the case of the satellites belonging
to the planets more than one exception of this kind has
been discovered, and mistakes have constantly occurred
in science from expecting that all new cases would
exactly resemble old ones. Imperfect Induction thus
gives only a certain degree of probability or likelihood
that all instances will agree with those examined. Per-
fect Induction, on the other hand, gives a necessar)- and

214 PERFECT INDUCTION AND [less.

certain conclusion, but it asserts nothing beyond what
was asserted in the premises.

Mr Mill, indeed, differs from almost all other logicians
in holding that Perfect Induction is improperly called
Induction, because it does not lead to any new knowledge.
He defines Induction as inference from the known to the
unknown, and considers the unexamined cases which are
apparently brought into our knowledge as the only gain
from the process of reasoning. Hence Perfect Induction
seems to him to be of no scientific value whatever, be-
cause the conclusion is a mere reassertion in a briefer
form, a mere summing up of the premises. I may point
out, however, that if Perfect Induction were no more than
a process of abbreviation it is yet of great importance, and
requires to be continually used in science and common
life. Without it we could never make a comprehensive
statement, but should be obliged to enumerate every par-
ticular. After examining the books in a library and
finding them to be all English books we should be unable
to sum up our results in the one proposition, '*all the books
in this library are English books ;" but should be required
to go over the list of books every time we desired to make
any one acquainted with the contents of the library. The
fact is, that the power of expressing a great number of
particular facts in a very brief space is essential to the pro-
gress of science. Just as the whole art of arithmetic
consists in nothing but a series of processes for abbreviat-
ing addition and subtraction, and enabling us to deal with
a great number of units in a very short time, so Perfect
Induction is absolutely necessary to enable us to deal with
a great number of particular facts in a very brief space.

It is usual to represent Perfect Induction in the form
of an Inductive Syllogism, as in the following instance :—
Mercury, Venus, the Earth, &c., all move round the sun
from West to East.

XXV.] THE INDUCTIVE SYLLOGISM. 215

Mercury, Venus, the Earth, &c., are all the known Planets.
Therefore all the known planets move round the sun from
West to East.

This argument is a true Perfect Induction because the
conclusion only makes an assertion of all known planets,
which excludes all reference to possible future discoveries;
and we may suppose that all the known planets have been
enumerated in the premises. The form of the argument
appears to be that of a syllogism in the third figure,
namely Darapti, the middle term consisting in the group
of the known planets. In reality, however, it is not an
ordinary syllogism. The minor premise states not that
Mercury, Venus, the Earth, Neptune, «S:c., are contamed
among the known planets, but that they are those planets,
or are identical with them. This premise is then a
doubly universal proposition of a kind (p. 184 — 7) not re-
cognised in the Aristotelian Syllogism. Accordingly we
may observe that the conclusion is a universal proposi-
tion, which is not allowable in the third figure of the syl-
logism.

As another example of a Perfect Induction we m.ay
take —
January, February, December, each contam less

than 32 days.

January December are all the months of the year.

Therefore all the months of the year contain less than 32

days.

Although Sir W. Hamilton has entirely rejected the
notion, it seems worthy of mquiry whether the Inductive
Syllogism be not really of the Disjunctive form of Syllo-
gism. Thus I should be inclined to represent the last
example in the form:

A month of the year is either January, or February,
or March or December; but January has less

2i6 PERFECT INDUCTION AND [LESS.

than 32 days ; and February has less than 32 days ; and
so on until we come to December, which has less than
32 days.

It follows clearly that a month must in any case have
less than 32 days; for there are only 12 possible cases,
and in each case this is affirmed. The fact is that the
major premise of the syllogism on the last page is a
compound sentence with twelve subjects, and is therefore
equivalent to twelve distinct logical propositions. The
minor premise is either a disjunctive proposition, as I have
represented it, or something quite different from anything
we have elsewhere had.

From Perfect Induction we shall have to pass to Im-
perfect Induction ; but the opinions of Logicians are not
in agreement as to the grounds upon which we are war-
ranted in taking a part of the instances only, and con-
cluding that what is true of those is true of all. Thus if
we adopt the example found in many books and say—?

This, that, and the other magnet attract iron ;
This, that, and the other magnet are all magnets ;
Therefore all magnets attract iron,

we evidently employ a false minor premise, because this,
that, and the other magnet which we have examined,
cannot possibly be all existing magnets. In whatever
form we put it there must be an assumption that the mag-
nets which we have examined are a fair specimen of all
magnets, so that what we find in some we may expect in
all. Archbishop Whately considers that this assumption
should be expressed in one of the premises, and he repre-
sents Induction as a Syllogism in Barbara as follows: —
That which belongs to this, that, and the other magnet,

belongs to all ;
Attracting iron belongs to this, that, and the other ;
Therefore it belongs to all.

XXV.] THE INDUCTIVE SYLLOGISM 217

But though this is doubtless a correct expression of the
assumption made in an Imperfect Induction, it does not
in the least explain the grounds on which we are allowed
to make the assumption, and under what circumstances
such an assumption would be likely to prove true. Some
writers have asserted that there is a Principle called the
Unifomiity of Nature, which enables us to affirm that
what has often been found to be true of anything will
continue to be found true of the same sort of thing. It
must be observ^ed, however, that if there be such a principle
it is liable to exceptions; for many facts which have held
true up to a certain point have after^vards been found not
to be always true. Thus there was a wide and unbroken
induction tending to show that all the Satellites in the
planetary system went in one uniform direction round
tl.eir planets. Nevertheless the Satellites of Uranus when
discovered were found to move in a retrogi-ade direction,
or in an opposite direction to all Satellites previously
known, and the same peculiarity attaches to the Satellite
of Neptune more lately discovered.

We may defer to the next lesson the question of the
varying degree of certainty which belongs to induction in
the several branches of knowledge.

The advanced student may consult the following with
advantage : — Hansel's Aldrich, Appendix, Notes G and H.
Hamilton's Lectures on Logic ^ Lecture xvii., and Appen-
dix VII., On Induction and Example^ Vol. II., p.. 358. J. S.
Mill's System of Logic ^ Book ill. Chap. 2, Of Inductio7is
improperly so-called.

2i8 INDUCTION, ANALOGY [less.

LESSON XXVI.

GEOMETRICAL AND MATHEMATICAL INDUC-
TION, ANALOGY AND EXAMPLE.

It is now indispensable that we should consider with
great care upon what grounds Imperfect Induction is
founded. No difficulty is encountered in Perfect Induc-
tion because all possible cases which can come under the
general conclusion are enumerated in the premises, so
that in fact there is no information in the conclusion which
was not given in the premises. In this respect the In-
ductive Syllogism perfectly agrees with the general prin-
ciples of deductive reasoning, which require that the in-
formation contained in the conclusion should be shown
only from the data, and that we should merely unfold,
or transform into an explicit statement what is contained
in the premises implicitly.

In Imperfect Induction the process seems to be of a
wholly diff"erent character, since the instances concerning
which we acquire knowledge may be infinitely more
numerous than those from which we acquire the icnow-
ledge. Let us consider in the first place the process of
Geometrical Reasoning which has a close resemblance to
inductive reasoning. When in the fifth proposition of the
first book of Euclid we prove that the angles at the base
of an isosceles triangle are equal to each other, it is done
by taking one particular triangle as an example. A
figure is given which the reader is requested to regard as
having two equal sides, and it is conclusively proved that
if the sides be really equal then the angles opposite to
those sides must be equal also. But Euchd says nothing
about other isosceles triangles ; he treats one single
triangle as a sufficient specimen of all isosceles triangles,

XXVI.] AND EXAMPLE. 219

and we are asked to believe that what is true of that is
true of any other, whether its sides be so small as to be
only visible in a microscope, or so large as to reach to the
furthest fixed star. There may evidently be an infinite
number of isosceles triangles as regards the length of the
equal sides, and each of these may be infinitely varied by
increasing or diminishing the contained angle, so that the
number of possible isosceles triangles is infinitely infinite ;
and yet we are asked to believe of this incomprehensible
number of objects what we have proved only of one single
specimen. This might seem to be the most extremely
Imperfect Induction possible, and yet every one allows
that it gives us really certain knowledge. We do know
with as much certainty as knowledge can possess, that
if lines be conceived as drawn from the earth to two stars
equally distant, they will make equal angles with the line
joining those stars; and yet we can never have tried the
experiment.

The generality of this geometrical reasoning evidently
depends upon the certainty with which we know that all
isosceles triangles exactly resemble each other. The pro-
position proved does not in fact apply to a triangle unless
it agrees with our specimen in all the qualities essential
to the proof The absolute length of any of the sides or
the absolute magnitude of the angle contained between
any of them were not points upon which the proof de-
pended— they were purely accidental circumstances ;
hence we are at perfect liberty to apply to all new cases
of an isosceles triangle what we learn of one case. Upon
a similar ground rests all the vast body of certain know-
ledge contained in the mathematical sciences — not only
all the geometrical truths, but all general algebraical
truths. It was shown, for instance, in p. 58, that if
a and b be two quantities, and we multiply together
their sum and difference, we get the difference of the

aao INDUCTION, ANALOGY [less.

squares of a and b. However often we try this it will be
found true ; thus '\{ a — \o and b — 'j, the product of the
sum and difference is 17 x 3 = 51; the squares of the
quantities are 10 x 10 or 100 and 7 x 7 or 49, the differ-
ence of which is also 51. But however often we tried the
rule no certainty would be added to it ; because when
proved algebraically there was no condition which re-
stricted the result to any particular numbers, and a
and b might consequently be any numbers whatever.
This generality of algebraical reasoning by which a pro-
perty is proved of infinite varieties of numbers at once, is
one of the chief advantages of algebra over arithmetic.
There is also in algebra a process called Mathematical
Induction or Demonstrative Induction, which shows the
powers of reasoning in a very conspicuous way. A good
example is found in the following problem : — If we take
the first two consecutive odd numbers, i and 3, and add
them together the sum is 4, or exactly twice two; if we
take tht-ee such numbers r +3 + 5, the sum is 9 or exactly
three times three; if we takey^wr, namely 1+3 + 54-7 the
sum is 16, or exactly y(??^r times four; or generally, if we
take any given number of the series, 1+3 + 5 + 7 + .. . the
sum is equal to the number of the terms multiplied by
itself. Anyone who knows a very little algebra can prove
that this remarkable law is universally true, as follows —
Let n be the number of terms, and assume for a moment
that this law is true up to n terms, thus —

T+3 + 5 + 7 + + {271 — I ) = n'K

Now add in + i to each side of the equation. It fol-
lows that —

1+3 + 5 + 7 + +(2«-l) + (2«+l) = «2+2«+I.

But the last quantity n^4-2n+iis just equal to (« + i)';
so that if the law is true for // terms it is true also for «+ i
terms. We are enabled to argue from each single case of

XXVI.] AND EXAMPLE. 221

the law to the next case ; but we have already shown that
it is true of the first few cases, therefore it must be true of
all. By no conceivable labour could a person ascertain by
trial what is the sum of the first billion odd numbers, and
•yet symbolically or by general reasoning we know with
certainty that they would amount to a billion billion, and
neither more nor less even by a unit. This process of
Mathematical Induction is not exactly the same as Geo-
metrical Induction, because each case depends upon the
last, but the proof rests upon an equally narrow basis of
experience, and creates knowledge of equal certainty and
generality.

Such mathematical truths depend upon observation
of a few cases, but they acquire certainty from the per-
ception we have of the exact similarity of one case to
another, so that we undoubtingly believe what is true of
one case to be true of another. It is very instructive to
contrast with these cases certain other ones where there
is a like ground of observation, but not the same tie of
similarity. It was at one time believed that if any integral
number were multiplied by itself, added to itself and then
'added to 41, the result would be a prime number, that is
a number which could not be divided by any other in-
tegral number except unity ; in symbols,
x^ + x + 4.1 = prime number.

This was believed solely on the ground of trial and
experience, and it certainly holds for a great many values
of jr. Thus when x is successively made equal to the
•numbers in the first line below, the expression ;r2 + ;r + 4i
gives the values in the second line, and they are all prime
numbers :

0123456789 10
41 43 47 53 61 71 83 97 113 131 151

No reason however could be given why it should

222 INDUCTION, ANALOGY [LESS.

always be true, and accordingly it is found that the rule
does not always hold true, but fails when jr=40. Then
we have 40x404-40 + 41 = 1681, but this is clearly equal
to 41 X 40 + 41 or 41 X41, and is not a prime number.

In that branch of mathematics which treats of the
peculiar properties and kinds of numbers, other proposi-
tions depending solely upon observation have been as-
serted to be always true. Thus Fermat believed that

X

2^ + I always represents a prime number, but could not
give any reason for the assertion. It holds true in fact
until the product reaches the large number 4294967297,
which was found to be divisible by 641, so that the gene-
rality of the statement was disproved.

We find then that in some cases a single instance
proves a general and certain rule, while in others a very
great number of instances are insufficient to give any
certainty at all ; all depends upon the perception we have
of similarity or identity between one case and another.
We can perceive no similarity between all prime numbers
which assures us that because one is represented by a •
certain formula, also another is; but we do find such
similarity between the sums of odd numbers, or between
isosceles triangles.

Exactly similar considerations apply to inductions in
physical science. When a chemist analyses a few grains
of water and finds that they contain exactly 8 parts of
oxygen and i of hydrogen for 9 parts of water, he feels
warranted in asserting that the same is true of all pure '
water whatever be its origin, and whatever be the part of
the world from which it comes. But if he analyse a piece
of granite, or a sample of sea-water from one part of the
world, he does not feel any confidence that it will resem-
ble exactly a piece of granite, or a sample of sea-water
from another part of the earth ; hence he does not venture
to assert of all granite or sea- water, what he finds true of

XXVI.] AND EXAMPLE. 223

a single sample. Extended experience shows that gra-
nite is very variable in composition, but that sea-water is
rendered pretty uniform by constant mixture of currents.
Nothing but experience in these cases could inform us
how far we may assert safely of one sample what v.'e have
ascertained of another. But we have reason to beheve
that chemical compounds are naturally fixed and invari-
able in composition, according to Dalton's laws of com-
bining proportions. No a priori reasoning from the
principles of thought could have told us this, and we only
learn it by extended experiment. But having once shown
it to be true with certain substances we do not need to
repeat the trial with all other substances, because we have
every reason to believe that it is a natural law in which
all chemical substances resemble each other. It is only
necessary then for a single accurate analysis of a given
fixed compound to be made in order to inform us of the
composition of all other portions of the same substance.

It must be carefully observed however that all induc-
tions in physical science are only probable, or that if cer-
tain, it is only hypothetical certainty they possess. Can
I be absolutely certain that all water contains one part
of hydrogen in nine ? I am certain only on two con-
ditions : —

1. That this was certainly the composition of the
sample tried.

2. That any other substance I call water exactly
resembles that sample.

But even if the first condition be undoubtedly true, I
cannot be certain of the second. For how do I know
what is water except by the fact of its being a transparent
liquid, freezing into a solid and evaporating into steam,
possessing a high specific heat, and a number of other
distinct properties ? But can I be absolutely certain that
every liquid possessing all these properties is water?

224 INDUCTION, ANALOGY [less.

Practically I can be certain, but theoretically I cannot.
Two substances may have been created so like each other
that we should never yet have discovered the difference ;
we might then be constantly misled by assuming of the
one what is only true of the other. That this should ever,
happen with substances possessing the very distinct quali-
ties of water is excessively improbable, but so far is it
from being impossible or improbable in other cases, that
it has often happened. Most of the new elements dis-
covered in late years have, without doubt, been mistaken
previously for other elements. Cassium and Rubidium
had been long miistaken for each other, and for Potassium,
before they were distinguished by Bunsen and Kirchhoff'
by means of the spectroscope. As they are now known
to be widely distributed, although in small quantities, it is
certain that what was supposed to be Potassium in many
thousands of analyses was partly composed of different
substances. Selenium had probably been confused with
Sulphur, and there are certain metals — for instance, Rho-
dium, Ruthenium, Iridium, Osmium, and Beryllium —
Yttrium, Erbium, Cerium, Lanthanum, and Didymium—
Cadmium and Indium — which have only recently been
distinguished. The progress of science will doubtless
show that we are mistaken in many of our identifications,
and various difficulties thus arising will ultimately be ex-
plained.

Take again a very different case of induction. Are
we certain that the sun will rise again to-morrow morning
as it has risen for many thousand years, and probably for
some hundred million years.? We are certain only on this
condition or hypothesis, that the planetary system proceeds
to-morrow as it has proceeded for so long. Many causes
may exist which might at any moment defeat all our
calculations ; our sun is believed to be a variable star, and
for what we know it might at any moment suddenly

XXVI.] AND EXAMPLE. 225

explode or flare up, as certain other stars have been ob-
served to do, and we should then be all turned into thin
luminous vapour in a moment of time. It is not at all
impossible that a collision did once occur m the planet-
ary system, and that the minute planets or asteroids are
the result. Even if there is no large meteor, comet or
other body capable of breaking up the earth by collision,
yet it is probable that the sun moves through space at the
rate of nearly 300 miles per minute, and if some other
star should meet us at a similar rate the consequences
would be inconceivably terrible. It is highly improbable
however that such an event should come to pass even in
■ the course of a million years.

The reader will now see that no mere Imperfect In-
duction can give certain knowledge ; all inference proceeds
upon the assumption that new instances will exactly re-
semble old ones in all material circumstances ; but in
natural phenomena this is purely hypothetical, and we
may constantly find ourselves in error. In Mathematical
Induction certainty arose from the cases being hypotheti-
cal in their own nature, or being made so as exactly to
, correspond with the conditions. We cannot assert that
any triangle existing in nature has two equal sides or two
equal angles, and it is even impossible in practice that
any two lines or angles can be absolutely equal. But it
is nevertheless true that if the sides are equal the angles
are equal. All certainty of inference is thus relative and
hypothetical. Even in the syllogism the certainty of the
conclusion only rests on the hypothesis of certainty in the
premises. It is probable, in fact, that all reasoning reduces
itself to a single type — that what is true of one thing will
be true of another thing, on condition of there being an
exact resemblance between them in all material circum-
stances.

The reader wiU now understand with ease the nature

15

226 INDUCTION, ANALOGY [less.

of reasoning by analogy. In strictness an analogy is not
an identity of one thing with another, but an identity of
relations. In the case of numbers 7 is not identical with
10 nor 14 with 20, but the ratio of 7 to 10 is identical with
the ratio of 14 to 20, so that there is an analogy between
these numbers. To multiply two by two is not the same
thing as to construct a square upon a line two units
long; but there is this analogy— that there will be just as
many units of area in the square as there are units in the
product of two by two. This analogy is so evident that
we fearlessly assert a square mile to consist of 1760 x 1760
square yards without any trial of the truth. In ordinary
language, however, analogy has come to mean any re-
semblance between things which enables us to believe of
one what we know of the other.

Thus the planet Mars possesses an atmosphere, with
clouds and mist closely resembling our own ; it has seas
distinguished from the land by a greenish colour, and
polar regions covered with snow. The red colour of the
planet seems to be due to the atmosphere, like the red
colour of our sunrises and sunsets. So much is similar
in the surface of Mars and the surface of the Earth
that we readily argue there must be inhabitants there
as here. All that we can certainly say however is,
that if the circumstances be really similar, and similar
germs of life have been created there as here, there must
be inhabitants. The fact that many circumstances are
similar increases the probability. But between the Earth
and the Sun the analogy is of a much fainter character ;
we speak indeed of the sun's atmosphere being subject to -
storms and filled with clouds, but these clouds are heated
probably beyond the temperature of our hottest furnaces ;
if they produce rain it must resemble a shower of melted
iron ; and the sun-spots are perturbations of so tremend-
ous a size and character, that the earth together with

XXVI.] AND EXAMPLE. 227

half-a-dozen of the other planets could readily be swal-
lowed up in one of them*. It is plain then that there is
little 01 no analogy between the Sun and the Earth, and
ve can therefore with difficulty form a conception of any-
thing going on in a sun or star.

Argument from analogy may be defined as direct
inductive inference from one instance to any similar
instance. It may, as Mr Mill says, be reduced to the
following formula : —

"Two things resemble each other in one or more
respects ; a certain proposition is true of the one ; there-
fore it is true of the other." This is no doubt the type of
all reasoning, and the certainty of the process depends
entirely upon the degree of resemblance or identity be-
tween the cases. In geometry the cases are absolutely
identical in all material points by hypothesis, and no
doubt attaches to the inference ; in physical science the
identity is a question of probability, and the conclusion is
in a like degree probable. It should be added that Mr
IVIill considers Geometrical and Mathematical Induction
not to be properly called Induction, for reasons of which
the force altogether escapes my apprehension ; but the
reader will find his opinions in the 2nd chapter of the
3rd book of his System of Logic.

On-e form of analogical or inductive argument consists
in the constant use of examples and instances. The best
way to describe the nature of a class of things is to pre-
sent one of the things itself, and point out the properties
which belong to the class as distinguished from those
peculiar to the thing. Throughout these Lessons, as
throughout every work on Logic, instances of propositions,
of compound or complex sentences, of syllogisms, &c., are
continually used, and the reader is asked to apply to all

* Ivockyer's Elementary Lessons in Astronomy^ § 108.

15—3

228 OBSERVATION [less.

similar cases what he observes in the examples given.
It is assumed that the writer selects such examples as
truly exhibit the properties in question.

While all inductive and analogical inferences rest
upon the same principles there are wide differences be-
tween the sources of probability. In analogy we have two
cases which resemble each other in a great many proper-
ties, and we infer that some additional property in one is
probably to be found in the other. The very narrow
basis of experience is compensated by the high degree of
similarity. In the processes more commonly treated
under the name Induction, the things usually resemble
each other only in two or three properties, and we require
to have more instances to assure us that what is true of
of these is probably true of all similar instances. The
less, in short, the intension of the resemblance the greater
must be the extension of our inquiries.

We proceed to the ordinary processes of Induction in
the following Lessons.

Mr Mill's System of Logic, Book III. Chap. XX. Of
Analogy. Mansel's Aldrich, App. Note H. On
Example a7id Analogy.

LESSON XXVII.

OBSERVATION AND EXPERIMENT.

All knowledge, it may be safely said, must be ultimately
founded upon experience, which is but a general name foi
the various feelings impressed upon the mind at any period
of its existence. The mind never creates entirely new
knowledge independent of experience, and all that the
reasoning powers can do is to arrive at the full meaning

XXVII.] AND EXPERIMENT. 229

of the facts which are in our possession. In previous
centuries men of the highest abib'ty have held that the
mind of its own power alone could, by sufficient cogita-
tion, discover what things outside us should be, and
would be found to be on examination. They thought
that we were able to anticipate Nature by evolving
from the human mind an idea of what things would be
made by the Creator. The celebrated philosopher Des-
cartes thus held that whatever the mind can clearly
conceive may be considered true; but we can conceive
the existence of mountains of gold or oceans of fresh
water, which do not as a fact exist. Anything that we
can clearly conceive must be conformable to the laws of
thought, and its existence is then not impossible, so far as
our intellect is concerned; but the forms and sizes and
manners in which it has pleased the Creator to make
things in this or any other part of the universe, cannot
possibly be anticipated by the exceedingly limited wisdom
of the human mind, and can only be learnt by actual ex-
amination of existing things.

In the latter part of the 13th century the great Roger
Bacon clearly taught in England the supreme importance
of experience as the basis of knowledge ; but the same
doctrine was also, by a curious coincidence, again upheld
in the 17th century by the great Chancellor Francis
Bacon, after whom it has been called the Baconian Phi-
losophy, I believe that Roger Bacon was even a greater
man than Francis, whose fame is best known ; but the
words in which Francis Bacon proclaimed the importance
of experience and experiment must be ever memorable.
In the beginning of his great work, the Novum Organum, or
New Instrumejit^ he thus points out our proper position
as learners in the world of nature.

"Man, the Servant and Interpreter of Nature, can do
and understand as much as he has observed concerning

230 OBSER VA TION [less.

the order of nature in outward things or in the mind;
more, he can neither know nor do."

The above is the first of the aphorisms or paragraphs
with which the Novum Orga7ium commences. In the
second aphorism he asserts that the unaided mind can
effect little and is liable to err ; assistance in the form of
a definite logical method is requisite, and this it was the
purpose of his New Instrument to furnish. The 3rd and
4th aphorisms must be given entire ; they are : —

"Human science and human power coincide, because
ignorance of a cause deprives us of the effect. For nature
is not conquered except by obedience ; and what we dis-
cover as a cause by contemplation becomes a rule in
operation."

"Man can himself do nothing else than move natural
bodies to or from each other ; nature working within
does the rest."

It would be impossible more clearly and completely
to express the way in which we discover science by inter-
preting the changes we observe in nature, and then turn
our knowledge to a useful purpose in the promotion of
the arts and manufactures. We cannot create and we .
cannot destroy a particle of matter ; it is now known that
we cannot even create or destroy force ; nor can we really
alter the inner nature of any substance that we have to
deal with. All that we can do is to observe carefully how
one substance by its natural powers acts upon another
substance, and then by moving them together at the right
time we can effect our object; as Bacon says, "Nature
working within does the rest." Had it not been the
nature of heat when applied to water to develope steam
possessing elastic power, it is needless to say that the
steam-engine could never have been made, so that the
invention of the steam-engine arose from observing the
utility of the force of steam, and employing it accordingly.

XXYILJ AND EXPERIMENT. 231

It is in this sense that Virgil has proclaimed him happy
who knows the causes of things —

Felix qui potuit rerum cognoscere causas,

and that Bacon has said, Knowledge is Power. So far
as we have observed how things happen in nature, and on
what occasion particular effects are brought to pass, we
are enabled to avoid or utilise those effects as we may
desire, not by altering the natures of things, but by
allowing them in suitable times and circumstances to
manffest their own proper powers. It is thus, as Tenny-
son has excellently said, that we

" Rule by obeying Nature's Powers."

Inductive logic treats of the methods of reasoning by
which we may successfully interpret nature and learn the
natural laws which various substances obey in different
circumstances. In this lesson we consider the first requi-
site of induction, namely, the experience or examination
of nature which is requisite to furnish us with facts. Such
experience is obtained either by observation or experiment.
To observe is merely to notice events and changes which
"are produced in the ordinary course of nature, without
being able, or at least attempting, to control or vary those
changes. Thus the early astronomers obsen^ed the mo-
tions of the sun, moon and planets among the fixed stars,
and gradually detected many of the laws or periodical
returns of those bodies. Thus it is that the meteorologist
observes the ever-changing weather, and notes the height
of the barometer, the temperature and moistness of the
air, the direction and force of the wind, the height and
character of the clouds, without being in the least able to
govern any of these facts. The geologist again is gene-
nerally a simple observer when he investigates the nature
and position of rocks. The zoologist, the botanist, and

232 OBSERVATION [LESS.

the mineralogist usually employ mere observation when
they examine animals, plants, and minerals, as they are
met with in their natural condition.

In experiment, on the contrary, we vary at our will
the combinations of things and circumstances, and then
observe the result. It is thus that the chemist discovers
the composition of water by using an electric current to
separate its two constituents, oxygen and hydrogen. The
mineralogist may employ experiment when he melts two
or three substances together to ascertain how a particular
mmeral may have been produced. Even the botanist and
zoologist are not confined to passive observation ; for by
removing animals or plants to different climates and dif-
ferent soils, and by what is called domestication, they
may try how far the natural forms and species are capable
of alteration.

It is obvious that experiment is the most potent and
direct mode of obtaining facts where it can be applied.
We might have to wait years or centuries to meet acci-
dentally with facts which we can readily produce at any
moment in a laboratory ; and it is probable that most of
the chemical substances now known, and many exces-
sively useful products, would never have been discovered
at all by waiting till nature presented them spontaneously
to our observ^ation. Many forces and changes too may
go on in nature constantly, but in so slight a degree as to
escape our senses, and render some experimental means
necessary for their detection. Electricity doubtless ope-
rates in every particle of matter, perhaps at every mo-
ment of time ; and even the ancients could not but notice
its action in the loadstone, in lightning, in the Aurora
Borealis, or in a piece of rubbed amber \elect7-u7n). But
in lightning electricity was too intense and dangerous;
in the other cases it was too feeble to be properly under-
stood. The science of electricity and magnetism could

xxviL] AND EXPERIMENT. 233

only advance by getting regular supplies of electricity
from the common electric machine or the galvanic bat-
tery, and by making powerful electro-magnets. Most if
not all the effects which electricity produces must go on in
nature, but altogether too obscurely for observation.

Experiment, again, is rendered indispensable by the
fact that on the surface of the earth we usually meet sub-
stances under certain uniform conditions, so that we
could never learn by observation what would be the
nature of such substances under other conditions. Thus
carbonic acid is only met in the form of a gas, proceeding
from the combustion of carbon ; but when exposed to
extreme pressure and cold, it is condensed into a hquid,
and may even be converted into a snow-like solid sub-
stance. Many other gases have in like manner been
liquefied or solidified ; and there is reason to believe that
every substance is capable of taking all the three forms of
solid, liquid and gas, if only the conditions of temperature
and pressure can be sufficiently varied. Mere observation
of nature would have led us, on the contrary, to suppose
that nearly all substances were fixed in one condition
only, and could not be converted from solid into liquid
and from liquid into gas.

. It must not be supposed however that we can draw
any precise line between observation and experiment, and
say where the one ends and the other begins. The dif-
ference is rather one of degree than of kind ; and all we
can say is that the more we vary the conditions artificially
the more we employ experiment. I have said that me-
teorolog>' is a science of nearly pure observation, but if we
purposely ascend mountains to observe the rarefaction
and cooling of the atmosphere by elevation, or if we make
balloon ascents for the same purpose, like Gay Lussac
and Glaisher, we so vary the mode of observation as
almost to render it experimental. Astronomers again

334 OBSERVATION [LESS.

may almost be said to experiment instead of merely ob-
serving when they simultaneously employ instruments as
far to the north, and as far to the south, upon the earth's
surface as possible, in order to observe the apparent dif-
ference of place of Venus when crossing the sun in a
transit, so as thus to compare the distances of Venus and
the sun with the dimensions of the earth.

Sir John Herschel has excellently described the dif-
ference in question in his Discourse on the Study of Na-
tural Philosophy*. " Essentially they are much alike,
and differ rather in degree than in kind ; so that perhaps
the terms passive and active observation might better
express their distinction ; but it is, nevertheless, highly
important to mark the different states of mind in inqui-
ries carried on by their respective aids, as well as their
different effects in promoting the progress of science.
In the former, we sit still and listen to a tale, told us, per-
haps obscurely, piecemeal, and at long intervals of time,
with our attention more or less awake. It is only by after
rumination that we gather its full import ; and often, when
the opportunity is gone by, we have to regret that our
attention was not more particularly directed to some point
which, at the time, appeared of little moment, but of
which we at length appreciate the importance. In the
latter, on the other hand, we cross-examine our witness,
and by comparing one part of his evidence with the other,
while he is yet before us, and reasoning upon it in his
presence, are enabled to put pointed and searching ques-
tions, the answer to which may at once enable us to make
up our minds. Accordingly it has been found invariably,
that in those departments of physics where the pheno-
mena are beyond our control, or into which experimental
enquiry, from other causes, has not been carried, the pro-

* p. 77-

XXVII.] AND EXPERIMENT. 235

gress of knowledge has been slow, uncertain and irregu-
lar ; while in such as admit of experiment, and in which
mankind have ag^reed to its adoption, it has been rapid,
sure, and steady."

Not uncommonly, however, nature has, so to speak,
made experiments upon a scale and for a duration with
which we cannot possibly compete. Thus we do not need
to try the soil and situation which suits any given plant
best ; we have but to look about and notice the habitat or
situation in which it is naturally found in the most flou-
rishing condition, and that, we may be sure, indicates the
result of ages of natural experiment. The distances of
the fixed stars would probably have been for ever un-
known to us did not the earth by describing an orbit with
a diameter of 182,000,000 miles make a sort of experimen-
tal base for observation, so that we can see the stars in
very slightly altered positions, and thus judge their dis-
tances compared with the earth's orbit*. Eclipses, tran-
sits, occupations and remarkable conjunctures of the pla-
nets, are also kinds of natural experiments which have
often been recorded in early times, and thus afford data
■ of the utmost value.

Logic can give little or no aid in making an acute or
accurate observer. There are no definite rules which can
be laid down upon the subject. To observe well is an art
which can only be acquired by practice and training ; and
it is one of the greatest advantages of the pursuit of the
' Natural Sciences that the faculty of clear and steady ob-
servation is thereby cultivated. Logic can however give
us this caution, which has been well pointed out by Mr
Mill — to discrhninate accurately betiveeji what we really
do observe and what we only infer from the facts observed.
So long as we only record and describe what our senses

* See Lockyer's Elemeiitary Lessons in Astronomy, N05.

XLVI, XLVII.

236 OBSERVATION [less.

have actually witnessed, we cannot commit an error ; but
the moment we presume or infer anything we are liable to
mistake. For instance, we examine the sun's surface
with a telescope and observe that it is intensely bright
except where there are small breaks or circular openings
in the surface with a dark interior. We are irresistibly
led to the conclusion that the inside of the sun is colder
and darker than the outside, and record as a fact that we
saw the dark interior of the sun through certain openings
in its luminous atmosphere. Such a record, however,
would involve mistaken inference, for we saw nothing but
dark spots, and we should not have done more in observ-
ation than record the shape, size, appearance and change
of such spots. Whether they are dark clouds above the
luminous surface, glimpses of the dark interior, or, as is
now almost certainly inferred, something entirely different
from either, can only be proved by a comparison of many
unprejudiced observations.

The reader cannot too often bear in mind the cau-
tion against confusing facts observed with inferences from
those facts. It is not too much to say that nine-tenths of
what we seem to see and hear is inferred, not really felt.
Every sense possesses what are called acquired percep-
tions, that is, the power of judging unconsciously, by long
experience, of many things which cannot be the objects of
direct perception. The eye cannot see distance, yet we
constantly imagine and say that we see things at such
and such distances, unconscious that it is the result of
judgment. As Mr Mill remarks, it is too much to say
" I saw my brother." All I positively know is that I
saw some one who closely resembled my brother as far
as could be observed. It is by judgment only I can
assert he was my brother, and that judgment may possi-
bly be wrong.

Nothing is more important in observation and experi-

xxvil] and EXPERTMENT. 237

ment than to be uniniluenced by any prejudice or theoiy
in correctly recording the facts observed and allowing to
them their proper weight. He who does not do so will
almost always be able to obtain facts in support of an
opinion however erroneous. Thus the belief still exists
with great force in the majority of uneducated persons,
that the moon has great influence over the weather. The
changes of the moon, full, new and half moon, occur four
times in every month, and it is supposed that any change
may influence the weather at least on the day preceding
or following that of its occurrence. There will thus be
twelve days out of every 28 on which any change of wea-
ther would be attributed to the moon, so that during the
year many changes will probably be thus recorded as
favourable to the opinion. The uneducated observer is
struck with these instances and remembers them care-
fully, but he fails to observe, or at least to remember, that
changes of weather often occur also when there is no
change of the moon at all. The question could only
be decided by a long course of careful and unbiassed
observation in which all facts favourable or unfavour-
able should be equally recorded. All observations which
have been published negative the idea that there can be
any such influence as the vulgar mind attributes to the
moon.

But it would at the same time be an error to suppose
that the best observer or experimentalist is he who holds
no previous opinions or theories on the subject he inves-
tigates. On the contrary, the great experimentalist is he
who ever has a theory or even a crowd of theories or ideas
upon his mind, but is always putting them to the test of
experience and dismissing those which are false. The
number of things which can be observed and experimented
on are infinite, and if we merely set to work to record
facts without any distinct purpose, our records will have

238 OBSERVATION, &^c. [LESS.

no value. We must have some opinion or some the-
ory to direct our choice of experiments, and it is more
probable that we hit upon the truth in this way than
merely by haphazard. But the great requisite of the
true philosopher is that he be perfectly unbiassed and
abandon every opinion as soon as facts inconsistent with
it are observed.

It has been well said by the celebrated Turgot, that
" the first thing is to invent a system ; the second thing
is to be disgusted with it ;" that is to say, we ought to
have some idea of the truth we seek, but should im-
mediately put it to a severe trial as if we were inclined to
distrust and dislike it rather than be biassed in its favour.
Few men probably have entertained more false theories
than Kepler and Faraday ; few men have discovered or
established truths of greater certainty and importance.
Faraday has himself said that —

" The world little knows how many of the thoughts
and theories which have passed through the mind of a-
scientific investigator, have been crushed in silence and
secrecy by his own severe criticism and adverse examina-
tion ; that in the most successful instances not a tenth of
the suggestions, the hopes, the wishes, the preliminary
conclusions have been reahzed"*^."

The student is strongly recommended to read Sir
J. Herschel's Preliminary Discourse on the Study
of Natural Philosophy (Lardner's Cabinet Cyclo-
pcEdia), especially Part ii. Chaps. 4 to 7, concerning
Observation, Experiment, and the Inductive Pro-
cesses generally.

* Modern Ctdhtre, edited by Yoiimans, p. ■2I2. [Macmillan
and Co.]

XXVIII.] METHODS OF INDUCTTON. 239

LESSON XXVIII.

METHODS OF INDUCTION.

We have now to consider such methods as can be laid
down for the purpose of guiding us in the search for gene-
ral truths or laws of nature among the facts obtained by
observation and experiment. Induction consists in infer-
ring from particulars to generals, or detecting a^general
truth_among its particular occurrences^ But in physical
science the truths to be discovered generally relate to
the connection of cause and effect, and we usually call
them laws of causation or natural laws. By the Cause of
an event we mean the circumstances which must have
preceded in order that the event should happen. Nor is
it generally possible to say that an event has one single
cause and no more. There are usually many different \
things, conditions or circumstances necessary to the pro- I
duction of an effect, and all of them must be considered/
causes or necessary parts of the cause. Thus the cause
of the loud explosion in a gun is not simply the pulling of
the trigger, which is only the last apparent cause or
occasion of the explosion; the qualities of the powder;
the proper form of the barrel ; the existence of some re-
sisting charge ; the proper arrangement of the percussion
cap and powder; the existence of a surrounding atmo-
sphere, are among the circumstances necessary to the
loud report of a gun : any of them being absent it would
not have occurred.

The cause of the boiling of water again is not merely
the application of heat up to a certain degree of tempera^-

240 METHODS OF INDUCTION. [less.

ture, but the possibility also of the escape of the vapour
when it acquires a certain pressure. The freezing of
water similarly does not depend merely upon the with-
drawal of heat below the temperature of o° Centigrade.
It is the work of Induction then to detect those circum-
stances which uniformly will produce any given effect ;
and as soon as these circumstances b€€om£ Joiown^ we__
have a law or uniforraity^ofnature of greater^^less gene-
rality.

In this and the following Lessons I shall often have to
use, in addition to cause and effect, the words antecedent
and consequent, and the reader ought to notice their
meanings. By an antecedent we mean any thing, condi-
tion, or circumstance which exists before or, it may be, at
the same time with an event or phenomenon. By a con-
sequent we mean any thing, or circumstance, event, or
phenomenon, which is different from any of the antecedents
and follows after their conjunction or putting together.
It does not follow that an antecedent is a cause, because
the effect might have happened without it. Thus the
sun's light may be an antecedent to the burning of a
house, but not the cause, because the house would burn
equally well in the night. A necessary or indispensable
antecedejit is however idefttical with a cause, being that
without which the effect would not take place.

The word phenomenon will also be often used. It
means simply anything which appears^ and is therefore
observed by the senses ; the derivation of the word from
the Greek word cf)aLv6fX€vov, that which appears, exactly
corresponds to its logical use.

The first method of Induction is that which Mr Mill
has aptly called the Method of agreement. It depends
upon the rule that " If two or more instances of the phe-
nomenon under investigation have only one circumstance
in common, the circumstance in which alone all the in-

XXVIII.] METHODS OF INDUCTION. 241

stances agree, is the cause (or effect) of the given pheno-
menon." The meaning of this First Canon of inductive
inquiry might, I think, be more briefly expressed by saying
that the sole invariable antecedent of a pheno7)ienon is
probably its cause.

To apply this method we must collect as many in-
stances of the phenomenon as possible, and compare
together their antecedents. Among these the causes will
lie, but if we notice that certain antecedents are present or
absent without appearing to affect the result, we conclude
that they cannot be necessary antecedents. Hence it
is the one antecedent or group of antecedents always
present, when the effect follows, that we consider the cause.
For example, bright prismatic colours are seen on bub-
bles, on films of tar floating upon water, on thin plates
of mica, as also on cracks in glass, or between two pieces
of glass pressed together. On examining all such cases
they seem to agree in nothing but the presence of a very
thin layer or plate, and it appears to make no appreciable
difference of what kind of matter, solid, liquid, or gaseous,
the plate is made. Hence we conclude that such colours
are caused merely by the thinness of the plates, and this
conclusion is proved true by the theory of the interference
of light. Sir David Brewster beautifully proved in a
similar way that the colours seen upon Mother-of-pearl
are not caused by the nature of the substance, but by the
form of the surface. He took impressions of the Mother-
of-pearl in wax, and found that although the substance
was entirely different the colours were exactly the same.
And it was afterwards found that if a plate of metal had
a surface marked by very fine close grooves, it would have
iridescent colours like those of Mother-of-pearl. Hence
it is evident that the form of the surface, which is the
only invariable antecedent or condition requisite for the
production of the colours, must be their cause.

16

242 METHODS OF INDUCTION. [less.

The method of agreement is subject to a serious
difficulty, called by Mr Mill the Plurality of Causes, con-
sisting in the fact that the same effect may in different
instances be owing to different causes. Thus if we in-
quire accurately into the cause of heat we find that it is
produced by friction, by burning or combustion, by elec-
tricity, by pressure, &c. ; so that it does not follow that if
there happened to be one and the same thing present in
all the cases we examined this would be the cause. The
second method of induction which we will now consider
is free from this difficulty, and is known as the Method of
Difference. It is stated in Mr Mill's Second Canon as
follows : —

" If an instance in which the phenomenon under inves-
tigation occurs, and an instance in which it does not
occur, have every circumstance in common save one, that
one occurring only in the former ; the circumstance m
which alone the two instances differ, is the effect, or the
cause, or an indispensable part of the cause, of the phe-
nomenon."

In other words, we may say that/ the antecedent which
is invariably present when the phenomenon follows, and
invariably absent when it is absent, other circumstances
remaining the same, is the cause of the phenomenon in
those circumstances. (

Thus we can clearly prove that friction is ofie cause of
heat, because when two sticks are rubbed together they
become heated; when not rubbed they do not become
heated. Sir Humphry Davy showed that even two pieces
of ice when rubbed together in a vacuum produce heat,
as shown by their melting, and thus completely demon-
strated that the friction is the source and cause of the
heat. We prove that air is the cause of sound being
communicated to our ears by striking a bell in the re-
ceiver of an air-pump, as Hawksbee first did in 1705, and

XXVIII.] METHODS OF INDUCTION. 343

then observing that when the receiver is full of air we
hear the bell ; when it contains little or no air we do
not hear the bell. We learn that sodium or any of its
compounds produces a spectrum having a bright yellow
double line by noticing that there is no such line in the
spectrum of light when sodium is not present, but that if
the smallest quantity of sodium be thrown into the flame
or other source of light, the bright yellow line instantly
appears. Oxygen is the cause of respiration and life,
because if an animal be put into a jar full of atmospheric
air, from which the oxygen has been withdrawn, it soon
becomes suffocated.

This is essentially the great method of experiment,
and its utihty mainly depends upon the precaution of only
varying one ciraunstance at a time, all other circum-
stances being niai7itained just as they were. This is
expressed in one of the rules for conducting experiments
given by Thomson and Tait in their great treatise on
Natural Philosophy., Vol. i. p. 307, as follows: —

" In all cases when a particular agent or cause is to
be studied, experiments should be arranged in such a way
as to lead if possible to results depending on it alone ; or,
if this cannot be done, they should be arranged so as to
increase the effects due to the cause to be studied till
these so far exceed the unavoidable concomitants, that
the latter maybe considered as only disturbing, not essen-
tially modifying the effects of the principal agent."

It would be an imperfect and unsatisfactory experi-
ment to take air of which the oxygen has been converted
into carbonic acid by the burning of carbon, and argue
that, because an animal dies in such air, oxygen is the
cause of respiration. Instead of merely withdrawing the
oxygen we have a new substance, carbonic acid, present,
which is quite capable of killing the animal by its own
poisonous properties. The animal in fact would be suffo-

244 METHODS OF INDUCTION, [LESS.

cated even when a considerable proportion of oxygen
remained, so that the presence of the carbonic acid is a
disturbing circumstance which confuses and vitiates the
experiment.

It is possible to prove the existence, and even to mea-
sure the amount of the force of gravity, by delicately sus-
pending a small ball about the size of a marble and then
suddenly bringing a very heavy leaden ball weighing a
ton or more close to it. The small ball will be attracted
and set in motion; but the experiment would not be of the
least value unless performed with the utmost precaution.
It is obvious that the sudden motion of the large leaden
ball would disturb the air, shake the room, cause currents
in the air by its coldness or warmth, and even occasion
electric attractions or repulsions; and these would pro-
bably disturb the small ball far more than the force of
gravitation.

Beautiful instances of experiment according to this
method are to be found, as Sir John Herschel has pointed
out, in the researches by which Dr Wells discovered the
cause of dew. If on a clear calm night a sheet or other
covering be stretched a foot or two above the earth, so
as to screen the ground below from the open sky, dew will
be found on the grass around the screen but not beneath
it. As the temperature and moistness of the air, and other
circumstances, are exactly the same, the open sky must
be an indispensable antecedent to dew. The same expe-
riment is indeed tried for us by nature, for if we make
observations of dew during two nights which differ in no-
thing but the absence of clouds in one and their presence
in the other, we shall find that the clear open sky is requi-
site to the formation of dew.

It may often happen that we cannot apply the method
of difference perfectly by varying only one circumstance
at a time. Thus we cannot, generally speaking, try the

XXVIII.] METHODS OF INDUCTION. 245

qualities of the same substance in the sohd and liquid
condition without any other change of circumstances, be-
cause it is necessary to alter the temperature of the sub-
stance in order to liquefy or solidify it. The temperature
might thus be the cause of what we attribute to the liquid
or solid condition. Under such circumstances we have
to resort to what Mr Mill calls the joint method of agree-
ment and difference, which consists in a double applica-
tion of the method of agreement, first to a number of
instances where an effect is produced, and secondly, to a
number of quite different instances where the effect is not
produced. It is clearly to be understood, however, that
the negative instances differ in several circumstances
from the positive ones ; for if they differed only in one
circumstance wemight apply the simple method of differ-
ence. Iceland spar, for instance, has a curious power of
rendering things seen through it apparently double. This
phenomenon, calfed- double refraction, also belongs to
many other crystals ; and we might at once prove it to be
due to crystaUine structure could we obtain any transpa-
rent substance crystallized and uncrystallized, but subject
to no other alteration. We have, however, a pretty satis-
factory proof by observing that uniform transparent un-
crystallized substances agree in not possessing double
refraction, and that cr)^stalline substances, on the other
hand, with certain exceptions which are easily explained,
agree in possessing the power in question. The principle
of the joint method may be stated in the following rule,
which is ]\Ir Mill's TMrd Canon : —

"If two or more instances in which the phenomenon
occurs have only one circumstance in common, while two
or more instances in which it does not occur have nothing
in common save the absence of that circumstance; the
circumstance in which alone the two sets of instances
(always or invariably) differ, is the effect, or the cause.

246 METHODS OF INDUCTION. [less.

or an indispensable part of the cause, of the pheno-
menon.^

I have inserted the words in parentheses, as without
them the canon seems to me to express exactly the oppo-
site of what Mr Mill intends.

It may facilitate the exact comprehension of these in-
ductive methods if I give the following symbolic repre-
sentation of them in the manner adopted by Mr Mill.
Let A, B, C, D, E^ &c., be antecedents which may be
variously combined, and let «, b, c, d, e, &c., be effects
following from them. If then we can collect the following
sets of antecedents and effects —

Antecedents. Consequents.

ABC abc

ADE ade

AFG afg

AHK ahk

we may apply the method of agreement, and little doubt
will remain that A^ the sole invariable cintecedent, is the
cause of a.

The method of difference is sufficiently represented by-
Antecedents. Consequents.
ABC abc
BC be
Here while B and C remain perfectly unaltered we find
that the presence or absence of A occasions the presence
or absence of a, of which it is therefore the cause, in the
presence of B and C. But the reader may be cautioned
against thinking that this proves A to be the cause of a
under all circumstances whatever.

The joint method of agreement and difference is similarly
represented by —

XXVIII.] METHODS OF INDUCTION. 247

Antecedents.
ABC

Consequents.
ode

ADE

adc

AFG
AHK

"PQ
RS

pq

rs

TV

tv

XV

xy

Here the presence of A is followed as in the simple method
of agreement by a ; and the absence of ^, in circumstances
differing from the previous ones, is followed by the ab-
sence of a. Hence there is a very high probability that
A is the cause of a. But it will easily be seen that A is
not the only circumstance in which the two sets of in-
stances differ, otherwise to any pair we might apply the
simple method of difference. But the presence oi A is a
circumstance in which one set invariably, or uniformly,
or always, differs, from the other set. This joint method is
thus a substitute for the simpler method of difference in
cases where that cannot be properly brought into action.

Herschel's Discourse^ part II. chap. 6, p. 144.
Mill's System of Logic ^ book III. chaps. 8 and 9.

LESSON XXIX.

METHODS OF QUANTITATIVE INDUCTION.

The methods of Induction described in the last Lesson
related merely to the happening or not happening of the
event, the cause of which was sought. Thus we learnt
that friction was one cause of heat by observing that two

248 METHODS OF [less.

solid bodies, even two pieces of ice, rubbed together, pro-
duced heat, but that when they were not rubbed there
was no such production of heat. This, however, is a very
elementary sort of experiment ; and in the progress of an
investigation we always require to measure the exact
quantity of an effect, if it be capable of being more or
less, and connecting it with the quantity of the cause.
There is in fact a natural course of progress through
which we proceed in every such inquiry, as may be stated
in the following series of questions.

1. Does the antecedent invariably produce an effect?

2. In what direction is that effect.? ^

3. How much is that effect in proportion to the cause?

4. Is it uniformly in that proportion?

5. If not, according to what law does it vary? »
Take for instance the effect of heat in altering the

dimensions of bodies. The first question is, whether the
heating of a solid body, say a bar of iron, alters its length ;
the simple method of difference enables us to answer that
it does. The next inquiry shows that almost all sub-
stances are lengthened or increased in dimensions by
heat, but that a very few, such as india rubber, and water
below 4'o8° Cent., are decreased. We next ascertain the
proportion of the change to each degree of temperature,
which is called the coefficient of expansion. Thus iron
expands 0*0000122 of its own length for every i" Centi-
grade between o^ and 100".

Still more minute inquiry shows, however, that the
expansion is not uniformly proportional to temperature;
most metals expand more and more rapidly the hotter
they are, but the details of the subject need not be con-
sidered here.

The fixed stars, again, have often been mentioned in
these Lessons, but the reader is probably aware that they
are not really fixed. Taking any particular star, the

XXIX.] QUANTITATIVE INDUCTION. 249

astronomer has really to answer the several five questions
stated below.

Firstly. Does the star move ?

2ndly. In what direction does it move.^

3rdly. How much does it move in a^^ear or a century.^

4thly. Does it move uniformly.?

5thly. If not, according to what law does the motion
vary in direction and rapidity .?

Every science and every question in science is first a
matter of fact only, then a matter of quantity, and by
degrees becomes more and more precisely quantitative.
Thirty years ago most of the phenomena of electricity and
electro-magnetism were known merely as facts ; now they
can be for the most part exactly measured and calculated.

As soon as phenomena can thus be measured we
can apply a further Method of Induction of a very im-
portant character. It is the Method of Difference indeed
applied under far more favourable circumstances, where
every degree and quantity of a phenomenon gives us
a new experiment and proof of connection between cause
and effect. It may be called the Method of Concomitant
Variations, and is thus stated by Mr Mill, in what he
entitles the Fifth Canon of Induction :

"Whatever phenomenon varies in any manner when-
ever another phenomenon varies in some particular man-
ner, is either a cause or an effect of that phenomenon, or
is connected with it through some fact of causation."

Sir John Herschel's statement of the same method is
as follows : — " Increase or diminution of the effect, with the
increased or diminished intensity of the cause, in cases
which admit of increase and diminution," to which he
adds, " Reversal of the effect with that of the cause."

The illustrations of this method are infinitely nu-
merous. Thus Mr Joule, of Manchester, conclusively
proved that friction is a cause of heat by expending exact

250 METHODS OF [less.

quantities of force in rubbing one substance against
another, and showed that the heat produced was exactly
greater or less in proportion as the force was greater or
less. We can apply the method to many cases which
had previously been treated by the simple method of dif-
ference ; thus instead of striking a bell in a complete
vacuum we can strike it with a very little air in the
receiver of the air-pump, and we then hear a very faint
sound, which increases or decreases ever)' time we in-
crease or decrease the density of the air. This experi-
ment conclusively satisfies any person that air is the cause
of the transmission of sound.

It is this method which often enables us to detect the
material connection which exists between two bodies.
For a long time it had been doubtful whether the red
flames seen in total eclipses of the sun belonged to the
sun or the moon ; but during the last eclipse of the sun
it was noticed that the flames moved with the sun, and
were gradually covered and uncovered by the moon at
successive instants of the eclipse. No one could doubt
thenceforth that they belonged to the sun.

Whenever, again, phenomena go through Periodic
Changes, alternately increasing and decreasing, we should
seek for other phenomena which go through changes in
exactly the same periods, and there will probably be a
connection of cause and effect. It is thus that the tides
are proved to be due to the attraction of the moon and
sun, because the periods of high and low, spring and
neap tides, succeed each other in intervals corresponding
to the apparent revolutions of those bodies round the
earth. The fact that the moon revolves upon its own
axis in exactly the same period that it revolves round the
earth, so that for unknown ages past the same side of the
moon has always been turned towards the earth, is a most
perfect case of concomitant variations, conclusively prov-

XXIX.] QUANTITATIVE INDUCTION. 251

ing that the earth's attraction governs the motions of the
moon on its own axis.

The most extraordinary case of variations howevei
consists in the connection which has of late years been
^ shown to exist between the Aurora Boreahs, magnetic
storms, and the spots on the sun. It has only in the
last 30 or 40 years become known that the magnetic
compass needle is subject at intervals to very slight but
curious movements ; and that at the same time there are
usually natural currents of electricity produced in tele-

* graph-wires so as to interfere with the transmission of mes-
sages. These disturbances are known as magnetic storms,

* and are often observed to occur when a fine display of
the Northern or Southern Lights is taking place in some
part of the earth. Observations during many years have
shown that these storms come to their worst at the end of
every eleven years, the maxnnum taking place about the
present year 1870, and then diminish in intensity until
the next period of eleven years has passed. Close obser-
vations of the sun durmg 30 or 40 years have shown that
the size and number of the dark spots, which are gigantic

J. storms going on upon the sun's surface, increase and
decrease exactly at the same periods of time as the mag-
netic storms upon the earth's surface. No one can doubt,
then, that these strange phenomena are connected to-
gether, though the mode of the connection is quite un-
known. It is now believed that the planets Jupiter,
Saturn, Venus and Mars, are the real causes of the dis-
turbances ; for Balfour Stewart and Warren de la Rue

~'have shown that an exact correspondence exists between
the motions of these planets and the periods of the sun-
spots. This is a most remarkable and extensive case of
concomitant variations.

We have now to consider a method of Induction
which must be employed when several causes act at once

252 METHODS OF [LiiSS.

and their effects are all blended together, producing a
joint effect of the same kind as the separate effects. If
in one experiment friction, combustion, compression and
electric action are all going on at once, each of these
causes will produce quantities of heat which will be added
together, and it will be difficult or impossible to say how
much is due to each cause separately. We may call this
a case of the homogeneous intermixture of effects, the name
indicating that the joint effect is of the same kind as
the separate effects. It is distinguished by Mr Mill from
cases of the heterogeneous, or, as he says, the hetero-
pathic intermixture of effects, where the joint effect is
totally different in kind from the separate effects. Thus
if we bend a bow too much it breaks instead of bending
further ; if we warm ice it soon ceases to rise in tempera-
ture and melts ; if we warm water it rises in temperature
homogeneously for a time but then suddenly ceases, and
an effect of a totally different kind, the production of
vapour, or possibly an explosion, follows.

Now when the joint effect is of a heterogeneous kind
the method of difference is sufficient to ascertam the cause
of its occurrence. Whether a bow or a spring will break
with a given weight may easily be tried, and whether
water will boil at a given temperature in any given state
of the barometer may also be easily ascertained. But in
the homogeneous intermixture of effects we have a more
complicated task. There are several causes each pro-
ducing a part of the effect, and we want to know how
much is due to each. In this case we must employ a
further Inductive Method, called by Mr Mill the Method
of Residues, and thus stated in his Fourth Canon : —

"Subduct from any phenomenon such part as is known
by previous inductions to be the effect of certain antece-
dents, and the residue of the phenomenon is the effect of
the remaining antecedents."

XXIX.] QUANTITATIVE INDUCTION. 253

If we know that the joint effect a, b, c is due to the
causes A, B, and C, and can prove that a is due to A and
b to Bf it follows that c must be due to C. There cannot
be a simpler case of this than ascertaining the exact

^ weight of any commodity in a cart by weighing the cart
and load, and then subtracting the tare or weight of the
cart alone, which had been previously ascertained. We
can thus too ascertain how much of the spring tides is
lue to the attraction of the sun, provided we have pre-
viously determined the height of the tide due to the moon,
which will be about the average height of the tides during
the whole lunar month. Then subtracting the moon's

' tide the remainder is the sun's tide.

Newton employed this method in a beautiful experi-
ment to determine the elasticity of substances by allow-
ing balls made of the substances to swing against each
other, and then observing how far they rebounded com-
jDared with their original fall. But the loss of motion is
due partly to imperfect elasticity and partly to the resist-
ance of the air. He determined the amount of the latter
effect in the simplest manner by allowing the balls to

■* swing without striking each other, and observing how
much each vibration was less than the last. In this way
he was enabled easily to calculate the quantity that must
be subtracted for the resistance of the air.

It is this method that we employ in making allowance
for the errors or necessary corrections in observations.
Few thermometers are quite correct ; but if we put a ther-
mometer into melting snow, which has exactly the tem-
perature of o" Centigrade, or 32" Fahr., we can observe
exactly how much below or above the true point the
mercury stands, and this will indicate how much we
^ught to add or subtract from readings of the thermometer
to make them correct. The height of the barometer is
affected by several causes besides the variation of ihe

254 METHODS OF [less.

pressure of the air. It is decreased by the capillary
repulsion between the glass tube and the mercury ; it is
increased by the expansion of the mercury by heat, if the
temperature be above 32^* Fahr. ; and it may be increased
or decreased by any error in the length of the measure
employed to determine the height. In an accurate obser-
vation all these effects are calculated and allowed for in
the final result.

In chemical analysis this method is constantly em-
ployed to determine the proportional weight of substances
which combine together. Thus the composition of water
is ascertained by taking a known weight of oxide of
copper, passing hydrogen over it in a heated, tube, and
condensing the water produced in a tube containing sul-
phuric acid. If we subtract the original weight of the
condensing tube from its final weight we learn how much
water is produced ; the quantity of oxygen in it is found
by subtracting the final weight of the oxide of copper
from its original weight. If we then subtract the weight
of the oxygen from that of the water we learn the weight
of the hydrogen, which we have combined with the oxygen.
When the experiment is very carefully performed, as de-
scribed in Ur Roscoe's Lessons in Elementary Chemistry^
(p. 38), we find that SS'Sg parts by weight of oxygen unite
with in I parts of hydrogen to form 100 parts of water.

In all sciences which allow of measurement of quan-
tities this method is employed, but more especially in
astronomy, the most exact of all the sciences. Almost all
the causes and effects in astronomy have been found out
as residual phenomena, that is, by calculating the effects of
all known attractions upon a planet or satellite, and then
observing how far it is from the place thus predicted.
When this was very carefully done in the case of Uranus,
it was still found that the planet was sometimes before
and sometimes behind its true place. This residual effect

XXIX.] QUANTITATIVE INDUCTION. 255

pointed to the existence of some cause of attraction not
then known, but which was in consequence soon dis-
covered in the shape of the planet Neptune. The motions
of several comets have in this way been calculated, but it
is observed that they fail to return at the expected time.
There is a discrepancy which points to the existence of
some obstructive power in the space passed through, the
nature of which is not yet understood.

Mill's System of Logic, Book III. Chap. 10, Of the
Plurality of Causes ; and of the Intermixtjire of
Effects.

LESSON XXX.

EMPIRICAL AND DEDUCTIVE METHODS.

We have hitherto treated of Deduction and Induction as
if they were entirely separate and independent methods.
In reality they are frequently blended or employed alter-
nately in the pursuit of truth ; and it may be said that all
the more important and extensive investigations of science
rely upon one as much as upon the other. It is probably
the greatest merit in Mr Mill's logical writings that he
points out the entire insufficiency of what is called the
Baconian Method to detect the more obscure and difficult
laws of nature. Bacon advised that we should always
begin by collecting facts, classifying them according to
their agreement and difference, and gradually gathering
from them laws of greater and greater generality. He
protested altogether against "anticipating nature," that is,
forming our own hypotheses and theories as to what the
laws of nature probably are, and he seemed to think that
systematic arrangement of facts would take the place of

/

256 EMPIRICAL AND DEDUCTIVE [less.

all other methods. The reader will soon see that the
progress of Science has not confirmed his opinions. \

When a law of nature is ascertained purely by indue- \
tion from certain observations or experiments, and has no
other guarantee for its truth, it is said to be an empirical 1
law. As Mr Mill says, "Scientific inquirers give the name
of Empirical Laws to uniformities which observation or
experiment has shown to exist, but on which they hesitate
to rely in cases varying much from those which have been-
actually observed, for want of seeing any reason why
such a law should exist." The name is derived from the
Greek word efinetpla, meaning experience or trial. In-
stances of such laws are abundant. We learn empiri-
cally that a certain strong yellow colour at sunset, or an
unusual clearness in the air, portends rain ; that a quick
pulse indicates fever; that horned animals are always
ruminants ; that quinine affects beneficially the nervous
system and the health of the body generally ; that strych-_.
nine has a terrible effect of the opposite nature : all these
are known to be true by repeated observation, but we can
give no other reason for their being true, that is, we
cannot bring them into harmony with any other scientific -
facts ; nor could we at all have deduced them or antici-
pated them on the ground of previous knowledge. The
connection between the sun's spots, magnetic storms,
auroras, and the motions of the planets mentioned in the '
last Lesson, is perhaps the most remarkable known
instance of an empirical induction ; for no hint has yet
been given of the way in which these magnetic influences
are exerted throughout the vast dimensions of the planet-
ary system. The qualities of the several alloys of metals
are also good instances of empirical knowledge. No
one can tell before mixing two or three metals for the
first time in any given proportions what the quahties of
the mixture will be — that brass should be both harder

XXX.] METHODS. 257

and more ductile than either of its constituents, copper
and zinc ; that copper alloyed with the very soft metal tin
should make hard and sonorous bell-metal ; that a certain
mixture of lead, bismuth, tin and cadmium, should melt
with a temperature (65° cent.) far below that of boiling
water*.

However usetul may be empirical knowledge, it is yet
of slight im.portance compared with the well-connected
and perfectly explained body of knowledge which con-
stitutes an advanced and deductive science. It is in
fact in proportion as a science becomes deductive, and
enables us to grasp more and more apparently uncon-
nected facts under the same law, that it becomes perfect.
He who knows exactly why a thing happens, will also
know exactly in what cases it \\ ill happen, and what dif-
ference in the circumstances -will prevent the event from
happening. Take for instance the simple effect of hot
water in cracking glass. This is usually learnt empiri-
cally. Most people have a confused idea that hot water
has a natural and inevitable tendency to break glass, and
that thin glass, being more fragile tlian other glass, will be
more easily broken by hot water. Physical science, how-
ever, gives a very clear reason for the effect, by showing
that it is only one case of the general tendency of heat to
expand substances. The crack is caused by the success-
ful effort of the heated glass to expand in spite of the
colder glass with which it is connected. But then we
shall see at once that the same will not be true of thin
glass vessels ; the heat will pass so quickly through that
the glass will be nearly equally heated ; and accordingly
chemists habitually use thin uniform glass vessels to hold
or boil hot liquids without fear of the fractures which would
be sure to take place in thick glass vessels or bottles.
The history of science would show conclusively that

* Roscoe's Lessons in KUmentary C/ie?nistr)'.

17

258 EMPIRICAL AND DEDUCTIVE [LESb.

deduction was the clue to all the greatest discoveries.
Newton, after Galileo the chief founder of experimen-
tal philosophy, possessed beyond all question the great-
est power of deductive thought which has ever been
enjoyed by man. It is striking indeed to compare his
results in optics with those in chemistry or alchemy. It
is not generally known that Newton was really an alche-
mist, and spent days and nights in constant experiments
in his laborator)'^, trying to discover the secret by which
metals could be transmuted into gold. But in these re-
searches all was purely empirical, and he had no clue to
guide him to successful experiments. A few happy
guesses given in his celebrated Queries are all the result
of this labour. But in the science of Optics it was quite
otherwise ; here he grasped general laws, and every ex-
periment only led him to devise and anticipate the results
of several others, each more beautiful than the last. Thus
he was enabled to establish beyond all doubt the founda-
tions of the science of the Spectrum, now bearing such
wonderful results. Some persons may suppose that
Newton, living shortly after Bacon, adopted the Baconian
method, but I believe that there is no reference to Bacon
in Newton's works ; and it is certain that he did not
employ the method of Bacon. The Priucipia, though
containing constant appeals to experiment and observa-
tion, is nevertheless the result of a constant and sustained
effort of deductive mathematical reasoning.

What Mr Mill has called the Deductive Method, but
which I think might be more appropriately called the
Combined or Complete Method, consists in the alternate
use of induction and deduction. It may be said to have
three steps, as follows: —

1. Direct Induction.

2. Deduction, or, as Mr Mill calls it, Ratiocination.

3. Veriiication.

XXX.] METHODS. 259

The tirst process consists in such a rough and simple
appeal to experience as may give us a glimpse of the laws
which operate, without being sufficient to establish their
truth. Assuming them as provisionally true, we then
proceed to argue to their effects in other cases, and a
further appeal to experience either verifies or negatives
the truth of the laws assumed. There are, in short, two
appeals to experience connected by the intermediate use
of reasoning. Newton, for instance, having passed a ray
of sun-light through a glass prism found that it was spread
out into a series of colours resembhng those of the rainbow.
He adopted the theory that white hght was actually com-
posed of a mixture of different coloured lights, which
became separated in passing through the prism. He saw
that if this were true, and he were to pass an isolated ray
of the spectrum, for instance, the yellow ray, through a
second prism, it ought not to be again broken up into
different colours, but should remain yellow whatever was
afterwards done with it. On trial he found this to be the
case, and afterwards devised a succession of similar con-
firmatory experiments which verified his theory beyond all
possible doubt.

It was no mere accident that led Pascal to have a
barometer carried up to the top of the mountain Puy de
, Dome in France. Galileo, indeed, became acquainted by
accident with the fact that water will not rise in an ordi-
nary pump more than 33 feet, and was thus led to assert
that the limited weight of the atmosphere caused it to
rise. Torricelli, reasoning from this theory, saw that
mercury, which is fourteen times as heavy as water,
should not rise more than one -fourteenth part of the dis-
tance, or about 29 or 30 inches. The experiment being
'tried verified the theory. It was the genius of Pascal,
however, which saw that the experiment required to be
varied in another way by carrying the mercurial barome-

17—2

26o EMPIRICAL AND DEDUCTIVE [less.

ter to the top of a mountain. If the weight of the atmo- .
sphere were really the cause of the suspension of the mer- \
cury, it ought to stand lower on the mountain than below,
because only the higher parts of the atmosphere pressed
upon the mountain. The success of the experiment com-
pletely verihed the original hypothesis. The progress of
the experimental sciences mainly depends upon the mode
in which one experiment thus leads to others, and dis- ;
closes new facts, which would in all probability have never *
come under our notice had we confined ourselves to the
purely Baconian method of collecting the facts first and
performing induction afterwards.

The greatest result of the deductive method is no less
than the theory of gravitation, which makes a perfect
instance of its procedure. In this case the preliminary
induction consisted, we may suppose, in the celebrated
fall of the apple, which occurred while Newton was sitting
in an orchard during his retirement from London, on
account of the Great Plague. The fall of the apple, we
are told, led Newton to reflect that there must be a power
tending to draw bodies towards the earth, and he asked
himself the question why the moon did not on that account
fall upon the earth. The Lancashire astronomer Horrocks
suggested to his mind another fact, namely, that when a
stone is whirled round attached to a string, it exerts a
force upon the string, often called centrifugal force. Hor-
rocks remarked that the planets in revolving round the
sun must tend in a similar way to fly off from the centre.
Newton was acquainted with Horrocks' views, and was
thus possibly led to suppose that the earth's attractive
force might exactly neutralise the moon's centrifugal
tendency, so as to maintain that satellite in constant
rotation.

But it happened that the world was in possession of
certain empirical laws concerning the motions of the pla-

XXX.] AfETHOnS. 261

nets, without which Newton could scarcely have proceeded
further. Kepler had passed a lifetime in observing the
heavenly bodies, and forming hypotheses to explain their
motions. In general his ideas were wild and unfounded,
but the labours of a lifetime were rewarded in the esta-
blishment of the three laws which bear his name, and
describe the nature of the orbits traversed by the planets,
and the relation between the size of such orbit and the
lime required by the planet to traverse it. Newton was
able to show by geometrical reasoning that if one body
revolved round another attracted towards it by a force
decreasing as the square of the distance increases, it would
necessarily describe an orbit of which Kepler's laws would
be true, and. which would therefore exactly resemble the
orbits of the planets. Here was a partial verification of
his theory by appeal to the results of experience. But
several other philosophers had gone so far in the investi-
gation of the subject. It is Newton's chief claim to ha
nour, that he carried on his deductions and verifications
until he attained complete demonstration. To do this it
was necessary first of all to show that the moon actually
does fall towards the earth just as rapidly as a stone would
if it were in the same circumstances. Using the best
information then attainable as to the distance of the
moon, Newton calculated that the moon falls through the
space of 13 feet in one minute, but that a stone, if elevated
so high, would fall through 15 feet. Most men would
have considered this approach to coincidence as a proof
of his theory, but Newton's love of certain truth rendered
him different even from most philosophers, and the dis-
crepancy caused him to lay " aside at that time any fur-
ther thoughts of this matter."

It was not till many years afterwards (probably 15
or 16) that Newton, hearing of some more exact data
from which he could calculate the distance of the moon.

262 EMPIRICAL AND DEDUCTIVE [less.

was able to explain the discrepancy. His theon' of gra-
vitation was then verified so far as the moon was con-
cerned ; but this was to him only the beginning of a long
course of deductive calculations, each ending in a verifica-
tion. If the earth and moon attract each other, and also
the sun and the earth, similarly there is no reason why
the sun and moon should not attract each other. Newton
followed out the consequences of this inference, and showed
that the moon would not move as if attracted by the
earth only, but sometimes faster and sometimes slower.
Comparisons with Flamsteed's observations of the moon
showed that such was the case. Newton argued again,
that as the w^aters of the ocean are not rigidly attached to
the earth, they might attract the moon, and be attracted
in return, independently of the rest of the earth. Certain
daily motions would then be caused thereby exactly
resembling the tides, and there were the tides to verify
the fact. It was the almost superhuman power with
\vhich he traced out geometrically the consequences of his
theory, and submitted them to repeated comparison with
experience, which constitutes his preeminence over all
philosophers.

What he began has been going on ever since. The
places of the moon and planets are calculated for each
day on the assumption of the absolute truth of Newton's
law of gravitation. Every night their places are observed
as far as possible at Greenwich or some other observatory;
comparison of the observed with the predicted place is
always in some degree erroneous, and if coincident w^ould
be so only by accident. The theory is never proved com-
pletely true, and never can be ; but the more accurately the
results of the theory are calculated, and the more perfect
the instruments of the astronomer are rendered, the more
close is the correspondence. Thus the rude observations
of Kepler and the few slight facts which worked on New-

XXX.] METHODS. 263

ton's mind, were the foundation of a theory which yielded
• indefinite means of anticipating new facts, and by con-
stant verification, as far as human accuracy can go, has
been placed beyond all reasonable doubt.

Were space available it might be shown that all other
great theories have followed nearly the same course.
The undulator}^ theory of sound was in fact almost verified
by Newton himself, though when he calculated from it
the velocity of sound there was again a discrepancy, which
only subsequent investigation could explain. This theory
no doubt suggested the corresponding theory of light,
which when followed out by Young, Fresnel, and others,
always gave results which were ultimately in harmony
with observation. It even enabled mathematicians to
anticipate results which the most ardent imagination
could hardly have guessed, and which mere haphazard
experiment might never have revealed. Dalton's laws of
equivalent proportions in chemistry, if not his atomic
' theory, were founded on experiments made with the
simplest and rudest apparatus, but results deduced from
them are daily verified in the nicest processes of modern
chemical analysis. The still more modem theory of the
Conservation of Energy, which had been vaguely antici-
pated by Bacon, Rumford, Montgolfier, Seguin, Mayer
and possibly others, was by Mr Joule brought to the test
of experimental verification in some of the most beautiful
and decisive experiments which are on record. It will be
long before scientific men shall have traced out all the
consequences of this grand principle, but its correspond-
ence with fact already places it far beyond doubt.

It will now be apparent, I think, that though observ^a-

tion and induction must ever be the ground of all certain

knowledge of nature, their unaided employment could

- never have led to the results of modern science. He who

merely collects and digests facts will seldom acquire a

264 EXPLANATION, TENDENCY, [less.

comprehension of their laws. He who frames a theory
and is content with his own deductions from it, like Des-
cartes, will only surprise the world with his misused
genius ; but the best student of science is he who with a
copious store of theories and fancies has the highest
power of foreseeing their consequences, the greatest dili-
gence in comparing them with undoubted facts, and the
greatest candour in confessing the ninety-nine mistakes
he has made in reachins;^ the one true law of nature.

LESSON XXXI.

EXPLANATION, TENDENCY, HYPOTHESIS,
THEORY, AND FACT.

In the preceding Lessons I have used several expressions
of which the meaning has not been defined. It will now
be convenient to exemplify the use of these terms, and to
arrive as far as possible at a clear understanding of their
proper meanings.

Explanation is literally the making plain or clear, so
that there shall be nothing uneven or obscure to inter-
rupt our view. Scientific explanation consists in harmo-
nizing fact with fact, or fact with law, or law with law,
so that we may see them both to be cases of one uniform
law of causation. If we hear of a great earthquake in
some part of the world and subsequently hear that a
neighbouring volcano has broken out, we say that the
earthquake is thus partially explained. The eruption
shows that there were great forces operating beneath the
earth's syurface, and the earthquake is obviously an effect
of such causes. The scratches which maybe plainly seen
upon the surface of rocks in certain parts of Wales and
Cumberland, are explained by the former existence of gla-
ciers in those mountains; the scratches exactly harmonize

xxxi.l HYPOTHESIS, THEORY, AND FACT. 265

with the effects of <]:laciers now existing in Switzerland,
Greenland, and elsewhere. These may be considered ex-
planatlons of fact by fact.

A fact may also be explained by a general law of

, nature, that is the cause and mode of its production may
be pointed out and shown to be the same as operates in
many apparently differeni cases. Thus the cracking of
glass by heat was explained (p. 257) as one result of the
* universal law that heat increases the dimensions of solid
bodies. The trade-winds are explained as one case of

. the general tendency of warm air to rise and be displaced
by cold and dense air. The very same simple laws of heat

' and mechanics which cause a draught to flow up a chimney
when there is a fire below, cause winds to blow from each
hemisphere towards the equator. At the same time the
easterly direction from which the winds come is explained
by the simplest laws of motion ; for as the earth rotates
^ from west to east, and moves much more rapidly at the
equator than nearer the poles, the air tends to preserve
its slower rate of motion, and the earth near the equator
moving under it occasions an apparent motion of the wind

. from east to west.

There are, according to Mr Mill, three distinct ways
in which one law may be explained by other laws, or
brought into harmony with them.

The first is the case where there are really two
or more separate causes in action, the results of which
are combined or added together, homogeneously. As
was before explained, homogeneous intermixture of effects
(p. 252) means that the joint effect is simply the sum of the
separate effects, and is of the same kind with them. Our
last example of the trade-winds really comes under this
case, for we find that there is one law or tendency which
causes \vinds to blow from the arctic regions towards the
equator, and a second tendency which causes then to blow

266 EXPLANATTON, TENDENCY, [less.

from east to west. These tendencies are combined to-
gether, and cause the trade-winds to blow from the North-
East in the northern hemisphere, and from the South-East
in the southern hemisphere. The law according to which
the temperature of the air is governed in any part of the
earth is a very complicated one, depending partly on the
law by which the sun's heating power is governed, partly
on the power of the earth to radiate the heat away into
space, but even more perhaps on the effect of currents of
air or water in bringing warmth or carrying it away.
The path of a cannon-ball or other projectile is deter-
mined by the joint action of several laws ; firstly, the
simple law of motion, by which any moving body tends
to move onward at an uniform rate in a straight line;
secondly, the law of gravity, which continually deflects
the body towards the earth's surface ; thirdly, the resist-
ance of the air, which tends to diminish its velocity.

The reader will perhaps have noticed the frequent use
of the word tendency, and I have repeatedly spoken of a
cause as tending to produce its effect. If the joint and
homogeneous action of causes has been clearly explained,
it will now be clear that a tendency means a cause which
will produce an effect unless there be opposite causes,
which, in combination with it, counteract and disguise
that effect. Thus when we throw a stone into the air the
attractive power of the earth tends to make it fall, but the
upward motion we have impressed upon it disguises the
result for a certain time. The interminable revolving
motion of the moon round the earth is the result of two
balanced tendencies, that towards the earth, and that to
proceed onward in a straight line. The laws of motion
and gravity are such that this balance must always be
preserved ; if the moon by any cause were brought nearer
to the earth its tendency to fly off would be increased,
and would exceed the effect of gravity until it had regained

XXXI.] HYPOTHESIS, THEORY, AND FACT. 267

its proper distance. A tendency then is a cause which
.may or may not be coiotteracted.

In the second case of explanation an efifect is shown
to be due, not to the supposed cause directly, but to an
Intermediate effect of that cause. Instead o{ A being the

< cause of C, it is found that A is the cause of ^, and Bt\\Q
cause of C, so that B constitutes an intermediate link.
This explanation may seem to increase the complexity of
the matter, but it really simplifies it ; for the connection of
'A with B may be a case of a familiar and simple law, and
so may that of B with C ; whereas the law that A pro-
duces C may be purely empirical and apparently out of
harmony with everything else. Thus in lightning it
seems as if electricity had the power of creating a loud
explosion ; but in reality electricity only produces heat,
and it is the heat which occasions sound by suddenly
expanding the air. Thus thunder comes into harmony
with the sound of artillery, which is also occasioned by
♦the sudden expansion of the heated gases emitted by the
powder. When chlorine was discovered it was soon found
to have a strong power of bleaching, and at the present
day almost all bleaching is done by chlorine instead of

^ the sun, as formerly. Inquiry showed however that it was
not really the chlorine which destroyed colour, but that
oxygen is the intermediate and active agent Chlorine
decomposes water, and taking the hydrogen leaves the
oxygen in a state of great activity and ready to destroy
the organic colouring matter. Thus a number of facts
are harmonized ; we learn why dry chlorine does not

, bleach, and why there are several other substances which
resemble chlorine in its bleaching power, for instance,
ozone, peroxide of hydrogen, sulphurous acid, and a pecu-
har oxide of vanadium, lately discovered by Dr Roscoe.
4lt would be impossible to understand the effect at all un-
less we knew that it is probably due to active oxygen or

268 P:XPLANATI0N, TENDENCY, [less.

ozone in all the cases, even in the old method of bleach-
ing by exposure to the sun *.

The third and much more important case of ex-
planation is where one law is shown to be a case of a
more general law. As was explained in Lesson XX i v. we
naturally discover the less general first, and gradually
penetrate to the more simple but profound secrets of
nature. It has often been found that scientific men were
in possession of several well-known laws without perceiv-
ing the bond which connected them together. Men, for
instance, had long known that all heavy bodies tended to
fall towards the earth, and before the time of Newton it
was known to Hooke, Huyghens, and others, that some
force probably connected the earth with the sun and moon.
It was Newton, however, who clearly brought these and
many other facts under one general law, so that each fact
or less general law throws light upon every other.

The science of Electricity now harmonizes a vast
series of partial laws and facts between which it was"
a truly difficult task to discover any resemblance. The
chief properties of the magnet had been fairly known
since the time of Gilbert, the physician of Queen Eliza-
beth ; common frictional electricity was carefuUy stu-
died by Otto von Guericke, Epinus, Coulomb, and others ;
Galvanism was elaborately investigated almost as soon
as Galvani and Volta discovered the fact that the che--
mical action of one substance on another may produce
electricity. In the early part of this century there were
three distinct sciences, Magnetism, Electricity and Gal-
vanism ; now there is but one science. Oersted of
Copenhagen gave in 1819 the first link between them, by
pointing out that an electric current may cause move-
ments in a compass- needle. Ampere and Faraday worked

* Watts' Dictionary oj Chemistry^ Vol. I. p. 601.

Kxxi.] HYPOTHESIS, THEORY, AXD FACT. 269

out the complicated relations of the three sciences, com-
prehending them finally in a wider science, which may be
called Electro-magnetism, or we may perhaps conveniently
generalize the name Electricity so as to comprehend all
the phenomena connected with it.

A number of minor laws and detached facts are com-
prehended and explained in the theory now generally
accepted, that heat, electricity, light, and in fact all the
phenomena of nature, are but manifestations in different
forms of one same kind of energy. The total amount of
energy existing in the universe is held to be fixed and un-
alterable, like the quantity of matter ; sometimes it is
disguised by affecting only the insensible molecules; at
other times it is seen to produce palpable mechanical
effects, as in the fall of a stone, or the expansion of
steam. Now it had been previously known, ever since the
time of the Greeks, that a simple lever, although greatly
altering the character of force by making its action slower
or faster, does not alter its amount, because the more
intense the force the slower and more limited is its action.
In modern times a similar truth was proved of every kind
of machine ; and it was recognised that, apart from friction,
no kind of mechanism either creates or destroys energy.
It had been independently recognised that electricity
produced in the galvanic battery was exactly proportional
to the amount of chemical action, and that almost any
one of the forces named could be converted into any one
of the others. All such facts are now comprehended
under one general theory, the details of v^hich are being
gradually rendered more certain and accurate, but the
main principle of which is that a certain amount of me-
chanical energy is equal to a certain amount of heat, a
certain amount of electricity, of chemical action, or even
of muscular exertion.

The word hypothesis is much used in connection with

270 EXPLANATIOA', TENDENCY, [less

the subject we are discussing, and its meaning must be -
considered. It is derived from the Greek words Jtto,
iuider, and dearis, plcicing, and is therefore exactly synony-
mous with the Latin word supposition a placing under,
whence our common word supposition. It appears to '
mean in science the imagining of some thing, force or
cause, which underlies the phenomena we are examining,
and is the agent in their production without admitting of
direct observation. In making an hypothesis we assert
the existence of a cause on the ground of the effects
observed, and the probability of its existence depends
upon the number of diverse facts or partial laws that we ^
are thus enabled to explain or reduce to harmony. To be
of any value at all a hypothesis must harmonize at least
two different facts. If we account for the effects of opium
by saying with Moliere that it possesses a dorniitive
power, or say that the magnet attracts because it has a
magnetic power, every one can see that we gain nothing. "
We know neither more nor less about the dormitive or
magnetic power than we do about opium or the magnet.
But if we suppose the magnet to attract because it is
occupied by circulating currents of electricity the hypo-
thesis may seem a very improbable one, but is valid,
because we thus draw a certain analogy between a magnet
and a coil of wire conveying electricity. Such a coil of ,
wire attracts other coils exactly in the way that one mag-
net attracts another ; so that this hypothesis enables us
to harmonize several different facts. The existence of
intense heat in the interior of the earth is hypothetical in
so far as regards the impossibility of actually seeing and
measuring the heat directly, but it harmonizes so many
facts derived from different sources that we can hardly
doubt its existence. Thus the occurrence of hot springs ^
and volcanoes are some facts in its favour, though they
might be explained on other grounds ; the empirical law

XXXI.] HYPOTHESIS, THEORY, AND FACT. 271

that the heat increases as we sink mines in any part of
the earth's surface is stronger evidence. The intensely
heated condition of the sun and other stars is strongly
confirmatory as showing that other bodies do exist in the

' supposed condition of the earth's interior. The cool
state of the earth's surface is perfectly consistent with its
comparatively small size and the known facts and laws
concerning the conduction and radiation of heat. And

" the more we learn concerning the way in which the sun's
heat is supplied by the fall of meteoric matter, the more
it is probable that the earth may have been intensely
heated like the sun at some former time, although for an
immense period it has been growing slowly colder. A
supposition coinciding with so many facts, laws, and other
probable hypotheses, almost ceases to be hypothetical,
and its high probability causes it to be regarded as a
known fact.

Provided it is consistent with the laws of thought there
is nothing that we may not have to accept as a probable
hypothesis, however difficult it may be to conceive and
understand. The force of gravity is hypothetical in so
far that we know it only by its effects upon the motions
of bodies. Its decrease at a distance harmonizes exactly
indeed with the way in which light, sound, electric or
magnetic attractions, and in fact all influences which

" emanate from a point and spread through space, decrease ;
hence it is probable that the law of the inverse square is
absolutely true. But in other respects gravity is strongly
opposed to all our ideas. If sound could travel to the
sun as rapidly as in the earth's atmosphere it would re-
quire nearly fourteen years to reach its destination ; were
the sun and earth united by a solid continuous bar of iron,

. a strong pull at one end would not be felt at the other
until nearly three years had passed. Light indeed comes
from the sun in rather more than eicrht minutes ; but what

272 EXPLANATION, TENDENCY, [less.

are we to think of the force of gravity, which appears to
reach the sun in an instant — so short that no calculations
have yet been able to detect any interval at all ? In fact
there seems some reason to suppose that gravity is felt
instantaneously throughout the immeasurable regions of
space.

The undulatory hypothesis of light presents features
equally extraordinary and inconceivable. That light does
consist of minute but excessively rapid vibrations of.
something occupying space, is almost certain, because of
tlie great harmony which this hypothesis introduces into
the exceedingly various and complicated phenomena of
light, and the explanation which it affords of the analog)'
of light to sound. It is difficult indeed to imagine that
anything can oscillate so rapidly as to strike the retina
of the eye 831,479,000,000,000 in one second, as must be
the case with violet light according to this hypothesis.
But this is nothing to the difficulty of imagining space to
be filled with solid ether of extreme rigidity and elasticity, '
but which nevertheless offers no appreciable resistance to
the passage through it of ordinary matter, and does not
itself possess any gravity*. It has been asserted indeed
that the retardation in the return of comets is due to
friction against this ether, and Mr Balfour Stewart be-
lieves he has produced heat by friction of a metallic disc
against the ether in a vacuum. Should these assertions .
prove to be true we have new facts in harmony with the
theory of light, which would thereby become less hypo-
thetical than before.

There is no difficulty now in perceiving the part which
hypothesis plays in the deductive method of scientific
investigation considered in the last lesson. The pre-
liminary induction is replaced more or less completely by

• See Sir John Herschel's Familiar Lectures, p. 315, &c

XXXI.] HYPOTHESIS, THEORY, AND FACT. 273

imagining the existence of agents which we think adequate

" to produce the known effects in question. If it is our
object to explain the causes of ebbing and flowing wells,
which occur in many parts of the world, we cannot

J possibly proceed by first exploring the interior of the
earth, until we can discover the source of a spring, and
observe its circumstances. We are obliged to imagine
cavities and channels of various forms, until we conceive

^ such an apparatus as will, in accordance with known laws
of hydrostatics, occasion the irregular flowing of water in
the way observed. If we can show that cavities of a
particular form will produce that effect, and can think of

' no other mode in which it could be produced, the hypo-
thesis becomes established as almost a certain fact.

It is the same with any great hypothesis like that of the
theory of light. We have no means of directly observing
and measuring the qualities of the ether which is the
medium of light. All we know about this ether at present
is derived from the observed phenomena of light. Hence
we are driven to invent something and endow it with
qualities from which we may calculate, according to some

, of the principles of mechanics, the effect to be expected ;
and finding that these effects may be made to harmonize
with those actually observed, we depend upon this coinci-
dence to prove the existence of the ether. The truth of
a hypothesis thus altogether depends upon subsequent
verification and accordance with observed facts. To
invent hypotheses which cannot thus be verified, or to
invent them and then neglect the verification, leads to no
result at all, or to fallacy. But when the verification is
careful and complete no reproach can be brought against
the employment of hypothesis. It becomes, perhaps, as
certain as any other mode of investigation, and is at any
rate indispensable. There was, in fact, little truth or
reason in Newton's celebrated protest against the use of

18

274 EXPLANATION, TENDENCY, [less.

hypothesis — "Hypotheses non fingo." The fact is that as
his theon' of gravitation rested upon the greatest and
most successful of hypotheses, so his views of the material
nature of light and the causes of its peculiar phenomena
involved a false hypothesis, which has long since been
completely disproved.

The word theory has constantly been used in the
last few lessons, and deserves some examination. It
comes from the Greek de-copia, meaning contemplation,
reflection or speculation; but this gives us little clue to its
modern use. In reality the word is highly ambiguous,
being sometimes used as equivalent to hypothesis, at
other times as equivalent to general law or truth. When
people form theories concerning comets, the sun, the
cause of earthquakes, &c., they imagine a great many
things which may or may not exist ; such theories are
really complicated hypotheses, and should be so called.
In this sense there are two theories of electricity, one of
which supposes the existence of a single fluid w^hich
accumulates in some places and has then a tendency to
discharge itself towards places where there is a deficiency,
just as water always tends to find its level ; the other
supposes the existence of two fluids which are commonly
united, but when separated tend to rush back into union
again. These so-called theories are really hypotheses, be-
cause we have no independent evidence of the existence
of any fluid, and it is now almost certain that there is no
such thing. The atomic theory, again, is really a hypo-
thesis suggested by Dalton to explain the remarkable
laws which he detected in the proportions of chemical
elements which combine together. It is a valid hypothesis
in so far as it does really explain the fixedness of the
quantities which combine; but it is purely h>'pothetical
as regards the shapes, properties or absolute magnitudes
of the atoms, because we have no facts which it can har-

XXXI.] HYPOTHESIS, THEORY, AND FACT. 275

monise in these respects, and no apparent means of
gaming them.

In another and more proper sense theory is opposed
to practice, just as the general is opposed to the particular.
The theory of gravitation means all the more general laws
of motion and attraction on which Newton founded his
system of the Universe. We may know what those laws
are without being able to determine the place of a planet
or make any practical use of them ; the particular results
must be calculated out by skilful astronomers before
navigators, travellers or others can make practical use of
them in the determination of the latitude or longitude.
When we speak of the mathematical theory of sound, the
lunar theory, the theory of the tides, the word is employed
without any special reference to hypothesis, and is merely
equivalent to general knowledge or science, implying the
possession of a complete series of general and accurate
, laws, but in no way distinguishing them from accurate
knowledge in general. When a word is really used in an
equivocal manner like theory, it is not desirable to attempt
to give it an accurate definition which would be imagi-
nary and artificial.

The word fact is used very often in this as in most
books, and demands a few remarks. It is derived from
factum, the past participle of facere, to do, and would
thus mean something which is done, an act, or deed ; but
the meaning is evidently greatly extended by analogy.
We usually oppose to each other fact and tlieory, but just
as theory seems to have two ambiguous meanings, so
I believe that fact is ambiguous. Sometimes it means
wliat is certain and known by the evidence of the senses,
as opposed to what is known only probably by hypothesis
and inference; at other times it is contrasted to a general
law, and is equivalent to a particular instance or case. A
law of great generality may often be as certain and true,

18—2

276 CLASSIFICATION, [less.

especially in mathematics, as the particular facts coming
under it, so that the contrast must in this case be that
between the general and particular. We often use the
word too in common life, as merely equivalent to truth;
thus we might say, " It is a fact that the primary laws of -
thought are the foundation of reasoning." In short, as
theory means ambiguously what is hypothetical, general,
abstract or uncertain, so fact is equally ambiguous, and
means confusedly what is intuitively known, particular,
concrete or certain.

Mill's Systein of Logic, Book in. Chapters 12, 13 and
14, Of Explanation, and Hypothesis.

LESSON XXXII.
CLASSIFICATION, AND ABSTRACTION.

In an earlier Lesson, upon the subject of the Predicables,
we considered the doctrine of classification as it was
treated by logicians many centuries ago. The progress
of science, however, during the last two centuries has
caused great attention to be given to the true principles
on which we can arrange a great multitude of diverse
objects in order, and we have to consider what are the
characteristics of a natural and perfect system of classifi-
cation.

It maybe said, indeed, that the subject we are treating
is coextensive with the science of logic. All thought, all
reasoning, so far as it deals with general names or general
notions, may be said to consist in classification. Every
common or general name is the name of a class, and every
name of a class is a common name. "Metal" is the name

xxxiL] AND ABSTRACTTON. 277

of one class of substances so often used in our syllogistic
examples ; '' Element" of another class, of which the former
class is part. Reasoning has been plausibly represented
to consist in affirming of the parts of a class whatever
may be affirmed of the whole. Every law of nature which
we arrive at enables us to classify together a number of
facts, and it would hardly be too much to define logic as
the theory of classification.

Here we deal, however, with that more conscious and
distinct arrangement of objects or notions, which is espe-
cially employed in the natural sciences, such as Botany,
Zoology, Mineralogy and Palaeontology.

The derivation of the word class is somewhat curious.
In ancient Rome it was the practice to summon the
whole people together at certain periods, and this cere-
mony was known as a cldsis, from the Greek xXaa-ty, or
kXtjo-is, derived from /caXe'o), to call together. Serv-ius
Tullius is said to have divided the people into six orders,
according to the amount of tribute they could pay, and
these orders were not unnaturally called the classes of the
people. Hence the name came by degrees to be applied
to any organized body of people, such as an army ; thence
it was transferred to a fleet of vessels as marshalled in a
fixed order, and was finally extended by analogy to any
collection of objects carefully arranged. When, however,
we now speak of the lower or higher classes of the people
It is curious that we ire restoring the word very nearly to
its original meaning.

Classification may perhaps be best defined as ^Ae ar-
rangement of things, or our notions of them, according to
their resemblances or identities. Every class should so
be constituted as to contain objects exactly resembling
each other in certain definite qualities, which are stated
in the definition of the class. The more numerous and
extensive the resemblances which are thus indicated by

278 CLASSIFICATION, [less.

any system of classes, the more perfect and useful must
that system be considered.

Mr Mill thus describes his view of the meaning —
"Classification is a contrivance for the best possible
ordering of the ideas of objects in our minds ; for causing
the ideas to accompany or succeed one another in such a
way as shall give us the greatest command over our know-
ledge already acquired, and lead most directly to the
acquisition of more. The general problem of classifica-
tion, in reference to these purposes, may be stated as
follows : To provide that things shall be thought of in
such groups, and those groups in such an order, as will
best conduce to the remembrance, and to the ascertain-
ment of their laws."

A collection of objects may generally be classified in an
indefinite number of ways. Any quality which is possess-
ed by some and not by others may be taken as the first
difference, and the groups thus distinguished may be sub-
divided in succession by any other qualities taken at will.
Thus a library of books might be arranged, (i) according
to their size, (2) according to the language in which they
are wi itten, (3) according to the alphabetic order of their
authors' names, (4) according to their subjects ; and in
various other ways. In large libraries and in catalogues
such modes of arrangement ate adopted and variously
combined. Each different arrangement presents some
peculiar convenience, and that mode must be selected
which best meets the especial purpose of the library
or catalogue. The population of a kingdom, again, may
be classified in an almost endless number of ways with
regard to different purposes or sciences. The popu-
lation of the United Kingdom may be divided according
to their place of birth, as English, Welsh, Scotch, Irish,
colonial-born, and aliens. The ethnographer would
divide them into Anglo-Saxons, Cymri, Gaels, Picts,

XXxil] and abstraction. 2^9

Scandinavians, &c. The statist arranges them accord-
ing to age ; to condition, as married, unmarried, wdowed,
&c. ; to state of body, as able, incapacitated, blind, im-
becile. The political economist regards the innumerable
trades which are carried on, and classifies them in a
complex manner. The lawyer again treats every one as a
minor, an adult, a feme sole, a feme couverte, a guardian,
ward, trustee, felon, and so on.

In the natural world, again, we may make various
classifications. Plants may be arranged according to the
country from which they are derived; the kind of place
or habitat in which they flourish ; the time they live, as
annual, biennial, perennial; their size, as herbs, shrubs,
trees; their properties, as esculents, drugs, or poisons:
all these are distinct from the classifications which the
botanist devises to represent the natural affinities or
relationships of plants. It is thus evident that in making
a classification we have no one fixed method wliich can
be ascertained by rule, but that an indefinite number of
choices or alternatives are usually open to us. Logic
cannot in such cases do much ; and it is really the work
of the special sciences to investigate the character of the
classification required. All that logic can do is to point
out certain general requirements and principles.

The first requisite of a good classification is, that it
shall be appropriate to the purpose in liand ; that is to
say, the points of resemblance selected to form the leading
classes shall be those of importance to the practical use
of the classification. All those things must be arranged
together which require to be treated alike, and those
things must be separated which require to be treated
separately. Thus a lawyer has no need to classify per-
sons according to the counties of England they were born
in, because the law is the same independently of counties ;
but so far as a Scotchman, a Manx man, or an alien, is

28o CLASSIFICATION, [less.

under different laws from the English born man, we shall
require to classify them apart. A gardener is quite right
in classifying plants as annuals, biennials, perennials; as
herbs, shrubs, trees ; as evergreen and deciduous ; or
according to the soil, temperature and other circumstances
which affect them, because these are points which must
guide him in treating some differently from others.

Another and, in a scientific point of view, the most
important requisite of a good classification, is that it shall
enable the greatest possible number of general assertions
to be made. This is the criterion, as stated by Dr
Whewell, which distinguishes ajiatural from an artificial
system of classification, and we must carefully dwell upon
its meaning. It will be apparent that a good classification
is more than a mere orderly arrangement ; it involves a
process of induction which will bring to light all the more
general relations which exist between the things classified.
An arrangement of books will generally be artificial ; the
octavo volumes will not have any common character ex-
cept being of an octavo size. An alphabetical arrange-
ment of names again is exceedingly appropriate and con-
venient to many purposes, but is artificial because it
allows of few or no general assertions. We cannot make
any general assertion whatever about persons because
their names happen to begin with an A or a B, a P or a
W. Even those who agree in bearing the name Sm.ith or
Taylor or Robinson might be submitted to the inductive
method of agreement without the discovery of any
common circumstance which could be stated in a general
proposition or law. It is true that if we investigated the
antecedents of the Evanses and Joneses we should find
them nearly all to be Welsh, and the Campbells to be
Scotch, and those who bear a very peculiar name would
often be found to descend from common ancestors. So
far even an alphabetic arrangement embodies something

xxxii.] AND ABSTRACTION. 281

that is natural in it, and enables general assertions to be
made. Hardly any arrangement can be made, in fact,
which will not indicate some vestiges of important rela-
tions and resemblances ; but what we want is a system
which will reveal all the most important general truths.

For this purpose we must select as the ground of
union those characters which carry with them most other
characters. In Lesson xil. we considered the proprium
as a quality which belongs to the whole of a class without
forming part of the definition of the class. Now we
ought to frame the definition of a class that it may con-
tain as few characters as possible, but that as many other
characters, properties, or propria, as possible, shall be
attributable to the things contained in the class. Every
one can see, for instance, that animals form one great
group of beings, which have many characters in common,
and that plants form another group. Animals have sen-
sation, voluntary motion, consume carbonaceous food, and
evolve carbonic acid, possess a stomach, and produce
fat. Plants are devoid of sensation and voluntary motion,
produce carbonaceous tissue, absorb carbonic acid, and
evolve oxygen, possess no stomach, and produce starch.
At one time it might have been thought that almost any
of the characters named was a sufficient mark of the
group to which a being belonged. Whatever had a
stomach, was an animal ; whatever had not, was a plant ;
whatever produced starch or evolved oxygen was called a
plant ; whatever absorbed oxygen or produced fat was an
animal. To the present day these statements remain
generally true, so that we may make assertions in the form
of the proposition U, that "all animals are all beings
that evolve carbonic acid, and all plants are all beings
that absorb carbonic acid." But in reality the exceptions
are many, and increasing research makes it continually
more apparent that there is no definite line to be drawn

282 CLA SSIFICA TION, [LEsa

between animal and vegetable life. This, of course, is
not a failure of logical science, but a fact of great sig-
nificance concerning the things themselves.

In a classification of plants we meet again with most
deep and natural distinctions between the great classes
called Exogens, Endogens, and Acrogens. The latter
have no true sexual flowers and seeds, are formed almost
wholly of cellular tissue, and have an epidermis without
cuticular pores. The former two classes have much in
common ; they have true flowers, woody tissue and
cuticular pores, and hence may be united into one wider
class, Vasculares. But exogens and endogens are also
most strongly distinguished. Exogens have a stem or
trunk consisting of distinct bark, pith, and wood in con-
centric layers, leaves with reticular veins, seeds with two
seed-leaves and a naked radicle ; generally speaking, too,
the parts of the flower are some multiple of two or five in
number. Endogens, on the contrary, have no distinct
bark, pith, and wood, no concentric layers, leaves with
parallel veins, seeds with one seed-leaf, and a radicle not
naked ; they have, too, the parts of the flower generally a
multiple of three in number.

These are the very widest classes in what is called
the natural system of botanical arrangement ; but similar
principles are observed in all its minor classes. The
continual efforts of botanists are directed to bringing the
great multitudes of plants together in species, genera,
orders, classes, and in various intermediate groups, so
that the members of each group shall have the greatest
number of points of mutual resemblance and the fewest
points of resemblance to members of other groups. Thus
is best fulfilled the great purpose of classification, which
reduces multiplicity to unity, and enables us to infer of aU
the other members of a class what we know of any one
member, provided we distinguish properly between those

XXXII.J AND ABSTRACTION. 283

qualities which are likely or are known to belong to the
class, and those which are peculiar to the individual. It
is a necessary condition of correct classification, as re-
marked by Prof. Huxley, that the definition of a group
shall hold exactly true of all members of the group, and
not of the members of any other group. To carry out this
condition in the natural sciences is, however, very difficult,
because kinds of plants or animals are continually dis-
covered which stand in an intermediate position between
classes which would otherwise be well distinguished.
Thus ferns much embarrass the fundamental division of
plants, because though they have no true flowers, and in
this and other respects agree with other acrogens, yet
they have abundance of woody fibre, which would entitle
them to rank with vasculares, the larger group of which
exogens and endogens are the subdivisions.

It may be remarked that the progress of chemistry is
rapidly rendering it a science of classification ; and in fact
the whole theory of chemical combination now depends
on a correct grouping of elements and compounds. Dr
Roscoe in his Lessons in Elementary Chemistry enu-
merates no less than eleven classes of metals, each class
having a number of properties in common. Thus the
metals of the alkalies, namely. Potassium, Sodium, Caesium,
Rubidium, Lithium, form a remarkably natural class.
They are all soft, easily fusible, volatile at high tempera-
tures ; they combine with great force with oxygen, decom-
pose water at all temperatures, forming oxides which are
very soluble in water, and become powerfully caustic and
alkaline bodies from which water cannot be expelled by
heat. Their carbonates are soluble in water, and each
metal forms only one compound with chlorine.

The metals of the alkaline earths, Calcium, Strontium,
and Barium, also form a very natural class, distinguished
by the fact that their carbonates are insoluble in pure

284 CLASSIFICATION, [lkss.

water, but soluble in water containing carbonic acid in
solution. The gold class contains the rare or valuable
metals Gold, Platinum, Palladium, Rhodium, Ruthenium,
Iridium, and Osmium, which are not acted on by nitric
acid, and can only be dissolved by chlorine or the mixture
of acids called aqua rcgia. The oxides can be reduced
or deoxidised by simply heating them.

Natural classifications give us the deepest resemblances
and relations, and may lead us ultimately to a knowledge
of the way in which the varieties of things are produced.
They are, therefore, essential to a true science, and may
almost be said to constitute the framework of the science.
Yet it does not follow that they are appropriate for all
purposes. When our purpose is merely to recognise the
name of a chemical element, a plant or an animal, its
character as defined in a natural system would give us
little or no assistance. The chemist does not detect
potassium by getting it into the state of metal, and trying
whether it would decompose water. He merely observes
which, among all the com^pounds of potassium, have the
best marked and most peculiar characters ; thus a com-
pound of potassium, platinum, and chlorine is most
distinctive or characteristic of the metal, and is generally
used as a means of recognising it ; but a fine violet
colour which potash gives to the flame of a lamp was
also used as an indication of its presence long before
the spectroscope was introduced to analyse such colours.
An artificial classification of the elements is thus ne-
cessary to the detection of substances, and accordingly
in any book on chemical analysis will be found arrange-
ments of the elements according to characters of very
minor importance, but which are selected on account of
the ease and certainty with which they can be observed.

In Botany, again, the natural system of classification is
far from being well suited for determining the name of a

xxxii.J AND ABSTRACTION, 285

plant, because the classes are often defined by the form of
minute parts of the seed, the arrangement of the seed-
vessel, and other parts which it is usually difficult or
sometimes impossible to examine. Accordingly botanists
usually arrange their genera and species in the order of
the natural system, but contrive a sort of key or artificial
arrangement, in which the most simple and apparent
characters, often called characteristics, are employed for
the discrimination of the plants. The best arrangement
of this kind as regards British plants is to be found in
Bentham's British Flora. In reality the celebrated
Linna^an arrangement of plants was intended by its
author to serve in this way. Linnaeus was too profound
a philosopher to suppose that the numbers of stamens
and pistils usually expressed the real relationships of
plants. Many of his classes were really natural classes,
but the stamens and pistils were selected as the general
guide to the classes and orders, as being very plain and
evident marks.

Closely connected with the process of classification
is that of abstraction. To abstract is to separate the
qualities common to all individuals of a group from the
peculiarities of each individual. The notion " triangle "
is the result of abstraction in so far as we can reason
concerning triangles, without any regard to the particular
size or shape of any one triangle. All classification im-
plies abstraction, for in framing and defining the class
I must separate the common qualities from the peculiari-
ties. When I abstract, too, I form a general conception,
or one which, generally speaking, embraces many objects.
If, indeed, the quality abstracted is a peculiar property of
the class, or one which belongs to the whole and not to
any other objects, I may not increase the extent of the
notion, so that Mr Herbert Spencer is, perhaps, right in
holding that we can abstract without generalizing. We

286 CLASSIFICATION, &c. [less.

often use this word generalization, and the process may be
defined as inferring of a whole class what we know only of
a part. Whenever we regard the qualities of a thing as
not confined to that thing only but as extended to other
objects ; when, in fact, we consider a thing only as a
member of a class, we are said to generalize. If, after
studying the properties of the circle, we proceed to those
of the ellipse, parabola and hyperbola, it is soon found
that the circle is only one case of a whole class of curves
called the conic sections, corresponding to equations of
the second degree ; and I generalize when I regard cer-
tain of the properties of the circle as shared by many
other curves.

Dr Whewell added to the superabundance of terms to
express the same processes when he introduced the ex-
pression Colligation of facts. Whenever two things are
found to have similar properties so as to be placed in the
same class they may be said to be connected together.
We connect together the places of a planet as it moves
round the sun, when we conceive them as points upon a
common ellipse. Whenever we thus join together pre-
viously disconnected facts, by a suitable general notion or
hypothesis, we are said to colligate them. Dr Whewell
adds that the general conceptions employed must be
(i) clear, and (2) appropriate ; but it may well be ques-
tioned whether there is anything really different in these
processes from the general process of natural classification
which we have considered.

\KxnL]OFA PHILOSOPHICAL LANGUAGE. 287

LESSON XXXIII.

REQUISITES OF A PHILOSOPHICAL
LANGUAGE.

Among the subsidiary processes requisite to the successful
prosecution of inductive reasoning must be placed the
construction of a suitable language. It is in fact impos-
sible to over-estimate the importance of an accurate and
copious language in any science ; and the study of things
would be almost useless without names to denote those
things and record our observations concerning them.
I It is easily apparent, indeed, that language serves
Y^hree distinct and almost independent purposes : —

1. As a means of communication.

2. As a mechanical aid to thought.

3. As an instrument of record and reference.

I In its first origin language was used chiefly if not exclu-
sively for the first purpose. Savage tribes exist in great
numbers at the present day who seem to accumulate no
knowledge. We may even say that the lower animals
often possess some means of communication by sounds
or natural signs which constitute language in the first
sense, though they are incapable of reasoning by general

j notions.

Some philosophers have held that it is impossible 10
carry on reasoning without the use of language. The
true nominalist went so far as to say that there are no
such things as general notions, and that general names
therefore constitute all that is general in science and

288 REQUISITES OF A [less.

reasoning. Though this is no doubt false (see p. 13), it
must nevertheless be allowed that unless general ideas
were fixed and represented by words, we could never
attain to sustained thought such as we at present enjoy.
The use of language in the second pui-pose is doubtless
indispensable in a practical point of view, and reasoning
may almost be considered identical with the correct use
of words. When language is used solely to assist reason-
ing there is no need that the meaning of each word
should be fixed ; we might use names, as the letters x, y, z,
a, b, c^ &c., are used in algebra to denote any quantity
that happens to occur in a problem. All that is requisite
is never to confuse the meaning attributed to a word in
one argument with the different meaning attributed in
another argument. Algebra may, in fact, be said to con-
sist of a language of a very perfect kind adapted to the
second purpose only, and capable of leading a person to
the solution of a problem in a symboHcal or mechanical
manner.

Language, as it is furnished to us ready made by the
habitual growth of centuries, is capable of fulfilling all
three purposes, though by no means in a perfect manner.
As words possess a more or less fixed customary meaning
we can not only reason by their aid, but communicate our
thoughts or record them ; and it is in this last respect we
have now to treat the subject

The multitude of facts required for the establishment
of a science could not be retained in the memory with
sufficient accuracy. Hence an indispensable subsidiary
of induction is the means of describing and recording our
observations. Thus only can knowledge be accumulated,
so that each observer shall start with the advantage of
knowing what has been previously recorded and proved.
It will be necessary then to consider the mode in which
language serves for the registration of facts, and to investi-

XXXIII.] PHILOSOPHICAL LANGUAGE, 289

gate the requisite qualities of a philosophical language
suitable to the needs of science.

As an instnunent of record language must evidently
possess two principal requisites :

1. Precision or definiteness of meaning.

2. Completeness.

A name is worse than useless unless, when used to
record a fact, it enables us to ascertain what was the
nature of the fact recorded. Accuracy and precision is
then a more important quality of language than abun-
dance. The want of an appropriate word will seldom
give rise to actual error and fallacy ; it will merely oblige
us to employ a circumlocutory phrase or else leave the
fact unrecorded. But it is a self-evident convenience that
whenever a thing, notion, or quality has often to be refer-
red to there should be a name appropriated to the
purpose, and there ought only to be one name. Let lis
consider in succession what must be the character of a
precise and complete language.

It may not previously have struck the reader, but it is
certainly true, that description is impossible without the
assertion of resemblance between the fact described and
some other fact. We can only describe a thing by giving
it a name ; but how can we learn the meaning of that
name? If we describe -the name by other names we only
have more names of which the meanings are required.
We must ultimately learn the meanings, not from names
but from things which bear those names. If anyone
were ignorant of the meaning of blue he could not be in-
formed buw by reference to something that excited in him
the sensation of blueness^ and had he been blind from
birth he could not acquire any noiion of what blueness
was. There are indeed a mmiber of words so familiar
to us from childhood that we cannot tell when or how we
learnt their meanings, though it must have been by refer-

19

290 REQUISITES OF A (less.

ence to things. But when we come to the more precise
use of names we soon have to make fresh reference to
physical objects. Then we should describe the several
kinds of blue colour as sky-blue, azure-blue, indigo-blue,
cobalt-blue ; green colour we likewise distinguish as sea-
green, olive-green, emerald-green, grass-green, &c. The
shapes of leaves are described in Botany by such names
as ovate, lanceolate, linear, pinnate, peltate, referring the
mind respectively to an ^gg^ a lance, a line, a feather,
and a shield. In recording dimensions it is equally im-
possible to avoid comparison with the dimensions of
other things. A yard or a foot has no meaning unless
there be a definite standard yard or foot which fixes its
meaning ; and the reader is probably aware that when the
physical standard of a length is once completely lost it
can never be recovered. The word is nothing unless we
somewhere have the thing to which it corresponds.

The first requisite of a philosopWcal language evident-
ly is that "every general name must have a certain and
knowable meaning." It need hardly be mentioned that
singular or proper names, the names of distinct objects,
must likewise be known; but as such names are merely
marks imposed upon the things they do not need the
same consideration. General names are a more difficult
subject, because, as we have seen in Lesson v., they have a
double meaning in denotation or extension, and connota-
tion or intension. Of these two meanings the connotation
is the one which must be fixed ; the other cannot as
a general rule be limited and defined. Had the name
planet been restricted to Jupiter, Saturn, Mars, Venus,
and Mercury, the planets known before the invention of
the telescope, we should have had to find a new name for
those subsequently discovered, and should even then
commit the fault of calling by different names those things
which are closely similar. But if by planet we mean any

xxxiii.] PHILOSOPHICAL LANGUAGE. 291

round body revolving round the sun in an orbit of slight

ellipticity, it will include all such bodies as may be dis-
covered from time to time, of which more than 100 are
already known. Similarly locomotive engine is not merely
the name of a number of engines now actually existing ;
for if so a new name must be needed every week
as some new engine is made or an old one destroyed.
What is fixed in a general name is its connotation, or the
qualities implied in the things bearing the name. We
ought therefore as far as possible to define the meaning
of every general name we use, not by naming the objects
which it denotes, but the qualities, which it connotes.
Having however considered the subject of definition in
previous Lessons (XII. and Xlll.), we need only inquire
here how far it is desirable to employ words which are
in current use in preference to newly invented terms.

The advantage of an old term is that it possesses force
of meaning for all persons, and so far saves the necessity
of learning the meaning of a strange technical expression.
Every one knows what heat is, and the expression science
of heat bears meaning to every person however unlearned.
But there is this objection against old terms to be noted,
that they are almost always subject to ambiguity; accord-
ingly it will be found that the scientific man really uses
the word heat differently from other persons. All things
are more or less hot in science, whereas in common life
we could never say that ice was hot or contained heat.
In fact heat means ordinarily the excess of temperature
above the ordinary mean, and the notion is purely relative
to that of cold. We also apply the word analogously to
sensations of taste, as when we say pepper is hot, or
even to purely mental phenomena, as in a hot dispute, a
hot temper, &c. If to avoid these ambiguities we invent
a new term, Caloric^ we may give it any precision of
meaning we like, but we raise one more obstacle to the

19—2

292 REQUISITES OF A [less

study of science, because there is one more technical
term to be learnt

This difficulty is especially great in the science of
political economy. We there deal with such familiar
ideas as wealth, money, value, currency, capital, labour,
exchange, but it is the very familiarity of the ideas which
occasions the greatest difficulty, because different people
attach different meanings to the words, and infinite logo-
machy (Greek Xoyor, word ; /iax*?' battle), or disputes
arising on merely verbal questions, is the result. Even if
a writer carefully defines the meaning in which he uses
ihose terms he cannot oblige other persons to bear the
definitions in mind. The other alternative of inventing
wholly new terms is out of the question, as it would un-
doubtedly render a work intolerable to most readers.
The only advice that can be given is to introduce a new
term where it is likely to be readily accepted and to dis-
place an old ambiguous term ; but otherwise to endeavour
to remove the ambiguity of the old term by constantly
keeping in view a precise definition of the intended
meaning.

A complete philosophical language will be composed
of two distinct kinds of terms, which form respectively
the descriptive terminology and the nomenclature of the
science.

A descriptive terminology, as pointed out by Dr
WTiewell, must include all the terms required to describe
exactly what has been observed concerning any object or
phenomenon, in order that we may possess a permanent
record of the obser\'^ation. For every quality, shape,
circumstance, degree or quantity there must be an appro-
priate name or mode of expression. Thus in recording
the discovery of a new inineral we ought to be able to fix
in words its exact crystalhne form, its colour, its degree
of iiardness, its specific gravity, smell and taste if any, ^

xxxiii.] PHILOSOPHICAL LANGUAGE. 293

and many other qualities which may possess importance.
Modern botany arose from the efforts of Linnasus to
create a system of terms by which every part and
character of a plant can be accurately described. The
language of botany, as since improved, presents the most
complete instance of a scientific terminology. Geology
suffers much, as I apprehend, from the difficulty of find-
ing accurate terms ; such names as trap, basalt, gneiss,
granite, tuff, greenstone, trachyte, porphyry, lava, &c.,
are very vague, and there are no precise descriptive terms
by which to define and distinguish them. Where a quality
does not admit of degree or quantity it only requires a
single name ; otherwise we must find some mode of exact
measurement and expression. The invention of any in-
strument for measuring a quality which has been before
unmeasured is always an important step in science, and
the construction of the thermometer by Fahrenheit and the
pendulum clock by Huyghens were great eras in science.

On the other hand, each science requires a nomen-
clature or collection of names for the distinct objects or
classes of objects treated in it. In mineralogy the names
of separate minerals, such as hasmatite, topaz, amphibole,
epidote, blende, polybasite, form the nomenclature ; in
chemistry we have all the names of the elements, together
with a vast apparatus of names for organic and other
compounds, such as ethyl, acetyl, cyanogen, napthalin,
benzol, &c. In astronomy the names of the planets,
satellites, nebulas, constellations or individual stars, form
a nomenclature of by no means a perfect or convenient
kind ; and geology has similarly a nomenclature neces-
sarily of an incomplete character, in the names of the
successive formations, silurian, devonian, carboniferous,
permian, triassic, eocene, miocene, pHocene, post-plio-
cene, &c.

It is evident that a nomenclature must possess names

294 REQUISITES OF A [less.

of various degrees of generality, including individual
objects if they need separate record, infimcc species if
such there be, with wider classes, up to the summa
g^enera, or widest notions embraced in the science. In
astronomy we deal chiefly with the names of individual
objects, and there is as yet but little scope for classi-
fication. In such natural sciences as botany or zoology
there is seldom or never any need of names for indi-
viduals, as an indefinite multitude of individuals generally
resemble each other very closely in a great number of
properties, so as to constitute what has been called a
natural kind. Mr Mill uses this term to denote " one of
those classes which are distinguished from all others, not
by one or a few definite properties, but by an unknown
multitude of them ; the combination of properties on
which the class is grounded being a mere index to an
indefinite number of other distinctive attributes."

According to Mr Mill's language he seems to include
in a nomenclature only the names of supposed species ;
for he says : — "A nomenclature maybe defined, the collec-
tion of names of all kinds with which any branch of
knowledge is conversant ; or more properly, of all the
lowest kinds, or uifimcE species, those which may be sub-
divided indeed, but not into kinds, and which generally
accord with what in natural history are termed simply
species." But the fact is that naturalists have now aban-
doned the notion that the species is any definite form ;
many species are divided already into subspecies and
varieties, or even varieties of varieties; and according to
the principles of Darwin's theory the subdivision might
go on indefinitely. It is surely most reasonable to regard
the natural kingdoms of vegetables and animals as ar-
ranged in an indefinite series of classes and subclasses,
and all the names attaching to any such classes belong
to the nomenclature.

NXXiTi.] PHILOSOPHICAL LANGUAGE. 295

Again, Mr Mill does not include in the nomenclature
such general names as denote conceptions artificially
formed in the course of induction and investigation. Ac-
cordingly, besides a terminology suited for describing
with precision the individual facts observed, there is a
branch of language containing " a name for every com-
mon property of any importance or interest, which we
detect by comparing those facts : including (as the con-
cretes corresponding to those abstract terms) names for
the classes which we artificially construct in virtue of
those properties, or as many of them, at least, as we have
frequent occasion to predicate any thing of." As exam-
ples of this class of names he mentions Circle, Limit,
Momentum, Civilization, Delegation, Representation.
While the nomenclature contains the names of natural
classes, this third branch of language would apparently
contain the names of artificial ideas or classes.

But I feel great difficulty in giving a clear account of
Mr Mill's views on this subject, and, as my object in these
Lessons does not allow of the discussion of unsettled
questions, I must conclude by referring the reader who
desires to continue the subject, to the 4th and 6th chap-
ters of the 4th Book of Mr Mill's System of Logic ^ which
treat of the Requisites of a Philosophical Language,

See Dr Whewell's " Aphorisms concerning the Lan-
guage of Science," at the end of his Philosophy of
the Inductive Sciences.

Thomson's Outline of the Laws of Thought, con-
tains most interesting remarks on the general nature
and use of Language, §§ 17 — 31.

QUESTIONS AND EXERCISES.

Lesson I. — Introduction.

1. What are the meanings of a Law of Nature, and a

Law of Thought ?

2. Explain the distinction between the Fonn of

Thought, and the Matter of Thought.

3. In what sense may Logic be called the Science of

Sciences ?

4. What is the derivation of the name Logic ?

5. How does a Science differ from an Art, and why is

Logic more in the form of a Science than an
Art ?

6. Can we say that Logic is a necessary aid in correct

reasoning, when persons who have never studied
logic reason correctly ?

Lesson \\.— Three Parts of Logic.

1. Name the parts of which a syllogism is composed.

2. How far is it correct to say that Logic is concerned

with language t

3. What are the three acts of mind considered in

Logic? Which of them is more especially the
subject of the Science ?

4. Can you state exactly what is meant by a general

notion, idea, or conception ?

5. How do the Nominalists, Realists, and Concep-

tualists differ in their opinions as to the nature
of a general notion ?
5. What is the supposed fourth part of Logic ?

QUESTIONS AND EXERCISES. 297

Lesson III. — Terms.

1. Define a name or term.

2. What is a categorematic term ?

3. Explain the distinction between a collective and a

general term.

4. Distinguish the collective and distributive use of
the word all in the following : —

(i) Non omnis moriar {i.e. I shall not all die).

(2) " All men find their own in all men's good,

And all men join in noble brotherhood."

Te7inyson.

(3) Non omnia possumus omnes {i.e. we cannot all

do all things).

5. Which of the following are abstract terms ?

Act, ingratitude, home, hourly, homeliness, intro-
duction, individuality, truth, true, trueness,
yellow, yellowness, childhood, book, blue, in-
tention, reason, rationality, reasonableness.

6. Define a negative term, and mention the mark by

which you may recognise it.

7. Distinguish a privative from a negative term, and

find some instances of privative terms.

8. Describe the logical characters of the following

terms, with the precautions given at p. 26.

Metropolis

Consciousness

Sect

Book

Lord Chancellor

Nation

Library

Vegetable Kingdom

Institution

Great Britain

Brilliance

Light

Csesar

Weight

Observation

Void

Sensation

Tongue

Gold

Cffisar

Air

Prime Minister

Csesarism

Mentor

Indigestibility

Application

Anarchy

Manchester

Individual

Retribution

Recollection

Volume

Solemnitv

2Q8

QUESTIONS AND EXERCISES.

/

Insignificant Language Understanding

Brilliant Adornment Geology

Independence Agreement Demeanour

Heaviness Obliquity Resemblance

Illustration Motionless Departure

Section Henry VIII. Nestor

Whiteness Formal Logic Alexander

Lesson IV. — Ambiguity of Terms.
T. Define univocal terms, and suggest some terms
which are perfectly univocal.

2. What are the other names by which equivocal'

terms are often called ?

3. Distinguish the three kinds of ambiguous terms,

and find instances of each.

4. Distinguish the three causes by which the third and

most important class of ambiguous terms have
been produced.

5. Explain the ambiguity of any of the following

terms, referring each to its proper cause, and *
tracing out as far as possible the derivation of ^
each separate meaning from the original m^eaning.

Bill

Minister

Subject

Letter

Table

Clerk

Object

Star

Term

Order

Earth

Pole

School

Wood

Law

Reason

Air

BuU

Sensation

Bed

Glass

Volume

Art

Bowl

Peer

Scale

Interest

End

Sense

Feeling

Paper

Division

Ball

Kind

Bolt

Class

Lesson V. — Twofold meaning of Terms.
I, Distinguish very carefully the meanings in ex-
tension and intension of the terms —
Quadruped, railway, human being, engine, moun-
tain, Member of Parliament.

QUESTIONS AND EXERCISES.

299

2. Enumerate the synonyms or other nam.es used

instead of extension and intension.

3. According to what law is the quantity of extension

connected with the quantity of intension ? Show
that the law holds true of the following series of
terms —
(i) Iron, metal, element, matter, substance.

(2) Matter, organized matter, animal, man.

(3) Ship, steamship, screw-steamship, iron screw-

steamship, British iron screw steamship.

(4) Book, printed book, dictionary, Latin dic-

tionary.

4. Distinguish between the connotation and deno-

tation of a term.

5. Select from the list of terms under Lesson in.,

Question 8 (p. 297), such terms as are non-con-
notative according to Mr Mill's views.

6. Arrange the following terms in series as in ques-

tion 3, placing each term of greater extension
before a term of less extension. Point out
which are the terms of greatest and least inten-
sion in each series.

Emperor

Animal

Planet

Teacher

Dissenter

Mammalian

Baptist

Individual

Matter

Timber

Jupiter

Solicitor

Person

Ruler

Quadruped

Horse

Organized substance

Being

Heavenly body

Lawyer

Napoleon III

Christian

Alexander

Episcopalian

Lesson VI. — Growth of Language,

I. Trace out the generalization or specialization which
has taken place in any of the following words: —

3<5o QUESTIONS AND EXERCISES.

Kind, genus, class, species, order, rank, Augustus,
president, speaker, Utopia, rock. Commons,
doctor.

2. Point out metaphors derived from the notions of

weight, straightness, rock, wind.

3. Distinguish as accurately as possible the meanings

of the following synonyms : —
Sickness, malady ; mud, mire ; confutation, refu-
tation ; boundary, limit ; mind, intellect ; recol-
lection, reminiscence ; procrastination, dilato-
riness ; converse, reverse, obverse, inverse.
4- Form lists of all the words derived from any of the
following roots :—
(i) Tendere, to stretch, as in intention, attention,

(2) Ponere, to place, as in position, supposition.

(3) Genus, tribe or kind, as in genus, generation.

(4) Munus, gift, as in remuneration, common (Latin,

Commufiis).
1^5) Modus, shape or fashion, as in mood, moderate.

(6) Scribere, to write, as in scribe, inscription, de-

scribe.

(7) Capere to take, as in deception, incipient.

Lesson VII. — Leibnitz on Knoivledge.

1. What are the characters of perfect knowledge ?

2. Describe the character of the knowledge which we

have of the following notions or objects : —
A syllogism.
Electricity.
Motion.
A triangle.
Eternity.

The weight of the eanh (5852 trillions of tonsl
The colour of the sky.

QUESTIONS AND EXERCISES. 301

3, Explain exactly what you mean by intuitive know-
ledge.

Lesson VIII. — Propositions.

1. Define a proposition, and name the parts of which

it is composed.

2. How are propositions classified.-*

3. Name the four kinds of categorical propositions,

and their symbols.

4. Under v/hich classes are singular and indefinite

propositions placed ?

5. Enumerate the most usual signs of the quantity of

a proposition.

6. What are modal propositions according to early

logicians, and according to Thomson .''

7. How far do logicians consider propositions with

regard to their truth or falsity ?

Lesson IX. — Opposition of Propositiojts.

1. State the quantity of the subject and predicate in

each of the propositions A, E, I, 0.

2, Select out of the following propositions, pairs of

contrary, contradictory, subaltern, and subcon-
trary propositions : —

(1) Some elements are known.

(2) No elements are known.

(3) All elements are known.

(4) Not all elements are known.

(5) Some elements are not known.
(6't All elements are not known.

3. What propositions are true, false, or doubtful,
(i) when A is false, (3) when I is false,
(2) when E is false, (4) when 0 is false?

4, Prove by means of the contradictory propositions

302 QUESTIONS AND EXERCISES.

that subcontrary propositions cannot both be
false.

5. Show by means of the subcontrary propositions

that contrary propositions may both be false.

6. What quantity would you assign to each of the

following propositions "i
(i) Knowledge is power.

(2) Nebulae are material bodies.

(3) Light is the vibration of an ether.

(4) Men are more to be trusted than we think.

(5) The Chinese are industrious.

7. Why is it desirable in controversy to refute a state-

ment by its contradictory and not by its contrary?

Lesson X. — Conversion and Iininediate Infer etice.

1. Define inference and conversion.

2. What are converse and convertend propositions }

3. State the rules of valid conversion.

4. Name all the kinds of conversion.

5. By what process do we pass from each of the fol-

lowing propositions to the next .?
(i) No knowledge is useless.

(2) No useless thing is knowledge.

(3) All knowledge is not useless.

(4) All knowledge is useful.

(5) What is not useful is not knowledge.

(6) What is useless is not knowledge.

(7) No knowledge is useless.

6. Give the logical opposites of the following propo-

sition, and the converse of its contradictor}' : —
" He cannot become rich who will not labour."

7. Apply negative conception to the proposition " All

men are fallible ;" then convert and show that
the result is the contrapositive of the original

QUESTIONS AND EXERCISES. 303

8. Classify the propositions subjoined into the four
following groups: —
a. Those which can be inferred from (i).
d. Those from which (i) can be inferred.
c. Those which do not contradict (i), but cannot

be inferred from it.
a. Those which contradict (i).
(i) All just acts are expedient acts.

(2) No expedient acts are unjust.

(3) No just acts are inexpedient.

(4) All inexpedient acts are unjust.

(5) Some unjust acts are inexpedient.

(6) No expedient acts are just.

(7) Some inexpedient acts are unjust.

(8) All expedient acts are just.

(9) No inexpedient acts are just.

(10) All unjust acts are inexpedient.

(11) Some inexpedient acts are just acts.

(12) Some expedient acts are just.

(13) Some just acts are expedient.

(14) Some unjust acts are expedient.

Lessons VIII. IX. and X. — Examples of Propositiotis.

The reader is desired to ascertain the logical character
of each of the following propositions; he is to state of
each whether it is affirmative or negative, universal, par-
ticular, singular or indefinite, pure or modal, exclusive or
exceptive, &c. ; when irregularly stated he is to reduce the
proposition to the simple logical order; he is then to
convert the proposition, and to draw immediate inferences
from it by any proces's which may be applicable.

(i) All birds are feathered.

(2) No reptiles are feathered.

(3) Fixed stars are self-luminous.

304 QUESTIONS AND EXERCISES.

(4) Perfect happiness is impossible.

(5) Life every man holds dear.

(6) Every mistake is not a proof of ignorance.

(7) Some of the most valuable books are seldom read

(8) He jests at scars who never felt a wound.

(9) Heated metals are softened.

(10) Not one of the Greeks at Thermopylae escaped.

(11) Few are acquainted with themselves.

(12) Whoso loveth instruction loveth knowledge.

(13) Nothing is harmless that is mistaken for a virtue.

(14) Some of our muscles act without volition. ♦

(15) Metals are all good conductors of heat.

(16) Fame is no plant that grows on mortal soil.

(17) Only the brave deserve the fair.

(18) No one is free who doth not command himself.

(19) Nothing is beautiful except truth.

(20) The wicked shall fall by his own wickedness.

(21) Unsafe are all things unbecoming.

(22) There is no excellent beauty that hath not some

strangeness in the proportion.

(23) It is a poor centre of a man's actions, himself.

(24) Mercy but murders, pardoning those that kill.

(25) I shall not all die. {No7i otmiis moriar.)

(26) A regiment consists of two battalions.

(27) 'Tis cruelty to load a falling man.

(28) Every mistake is not culpable.

(29) Quadrupeds are vertebrate animals

(30) Not many of the metals are brittle.

(31) Many are the deserving men who are unfortunate.

(32) Amalgams are alloys of mercur>\

(33) One kind of metal at least is Hquid.

(34) Talents are often misused.

(35) Some parallelograms have "their adjoinmg sides

equal.

(36) Britain is an island.

(37) Romulus and Remus were twins.

QUESTIONS AND EXERCISES. 305

(38) A man's a man.

(39) Heaven is all mercy.

(40) Every one is a good judge of his own interests.

(41) All parallelograms have their opposite angles equal.

(42) Familiarity breeds contempt.

(43) No one is always happy.

(44) Many a little makes a mickle.

Lesson XI. — Logical Analysis of Sentmces.

. How does the grammatical predicate differ from the

logical predicate .?
, Distinguish between a compound and a complex

sentence ; and between coordinate and subordinate

propositions.
, Enumerate the grammatical expressions which may

form
(i) A subject. (4) An object.

(2) An attribute. (5) An adverbial.

(3) A predicate.

, Examine the following sentences, ascertain which
are compound or complex, and point out the co-
ordinate or subordinate propositions,
(i) Happy is the man that findeth wisdom, and the
man that getteth understanding.

(2) Heat, being motion, can be converted into me-

chanical force.

(3) Ceres, Pallas, Juno, and Vesta are minor planets,

or asteroids.

(4) Knowledge comes, but wisdom lingers.

(5) Fortune often sells to the hasty what she gives to

those who wait.

(6) Thousands at His bidding speed.
And post o'er land and ocean without rest ;
They also serve who only stand and wait.

20

3o6 QUESTIONS AND EXERCISES.

(7) Pride that dines on vanity, sups on contempt.

(8) Nobody can be healthful without exercise, neither

natural body, nor politic.

(9) Nature is often hidden, sometimes overcome,

seldom extinguished.
(10} It is impossible to love and be wise.

(11) Though gods they were, as men they died.

(12) He that is not industrious envieth him that is.

(13) Ye are my friends, if ye do whatsoever I command

you. — John xv. 14.

(14) The wisdom that is from above is first pure, then ""

peaceable, gentle, and easy to be intreated,
fiill of mercy, and good fruits, without par-
tiality, and without hypocrisy. — James iii. 17.
5. Analyse in the form of a scheme or diagram any of
the following sentences :—

(1) The first aphorism of Bacon's AW?^;// Organum^

on p. 229.

(2) Some judgments are merely explanatory of their

subject, having for their predicate, a conception-
which it fairly implies, to all who know and can
define its nature.

(3) There be none of the affections which have been

noted to fascinate or bewitch, but love and

envy : they both have vehement wishes ; they

frame themselves readily into imaginations and

suggestions ; and they come easily into the eye,

especially upon the presence of the objects,

which ai'e the points that conduce to fascination.

if any such there be.

Further examples for analysis must be sought in

Dalgleish's Gra^nfnatical Analysis^ with Progressive Ex-

".rciscs. (Oliver and Boyd.) Edinburgh, r 866. Price 9^/

QUESTIONS AND EXERCISES.

307

Lesson XII.— 7>/^r Prcdicadles, etc.

1. Define each of the live predicables.

2. In what sense may we say that the genus is part of

the species, and in what sense that the species is
pan of the genus ?

3. Select from the terms in the 6th Question of Les-

son v., p. 299, such as are genera, species,
highest genera, or lowest species of other terms.

4. Explain the expressions sui generis, homogeneous,

heterogeneous, summum genus, infima species,
tree of Porphyry.

5. Name a property and accident of each of the follow-

ing classes : — Circle, Planet, Bird, Member of
Parliament, Ruminant Animal.

6. What are the rules of correct logical division.

7. The first name in each of the following series of

terms is that of a class which you are to divide
and subdivide so as to include all the subjoined
minor classes in accordance with the laws of
division.

(3) Reasoning.
Induction (Imperfece)
Deduction
Mediate luference
Induction

Hypothetical Syllogism
Disjuncdve Syllogism

(i) People. (2) Triangle.

Laity Equiangular

Aliens Isosceles

Naturalized Right-angled

Subjects Scalene

Peers Obtuse-angled

Natural-born

Subjects
Clergy
Baronets
Commons

8. Divide any of the following classes : — Governments,

Sciences, Logical terms. Propositions.

9. Of what does a logical definition consist 1

20 — 2

3o8 QUESTIONS AND EXERCISES.

10. What are the rules of correct definition ?

1 1. What rules do the following definitions break ?
(i) Life is the sum of the vital functions.

(2) Genus is the material part of the species.

(3) Illative conversion is that in which the truth of

the converse can be inferred from that of the
convertend. «

(4) Mineral substances are those which have not

been produced by the powers of vegetable or
animal life.

(5) An equilateral triangle is a triangle whose sides "

and angles are respectively equal.

(6) An acute-angled triangle is one which has an

acute angle.

Lesson XIII. — Pascal and Descartes on Method.

(i) What is the use of nominal definitions?

(2) How must we employ definitions in order to avoid

confusion ?

(3) How far can we be said to be free to use any name -

for any object.?

(4) What according to Pascal is the true method of

avoiding error ?

(5) How do we learn the meanings of words which

cannot be defined .?

(6) Give instances of words which can be clearly de-

fined and of others which cannot
^^7) State the five rules of method given in the Port

Royal Logic.
(8) Explain Descartes' rules for the attainment of

truth.

Lesson XIV. — Laws of Tlwught.

I, State the three Fundamental Laws of Thought, and
apply them to the following notions : —

QUESTIONS AND EXERCISES. 309

(i) Matter, organic, inorganic.

(2) Undulations, polarized, non-polarized.

(3) Figure, rectilinear, curvilinear.

2. Is it wrong to assert that animal cannot both be

vertebrate and invertebrate, seeing that some
animals are vertebrate and some are not .'*

3. Select from the following such terms as are nega-

tives of the others, and such as are opposites : —
Light, plenum, gain, heat, decrease, loss, darkness,
cold, increase, vacuum.

4. How is Aristotle's dictum applicable to the follow-

ing arguments?
(i) Silver is a good conductor of electricity ; for such

are all the metals.
(2) Comets cannot be without weight ; for they are

composed of matter, which is not without weight

Lesson XV. — Syllogism: the Rules.

1. Distinguish mediate and immediate inference.

2. Define syllogism, and state with what it is synony-

mous.

3. What are the six principal and two subordinate

rules of the syllogism t

4. In the following syllogisms point out in succession

the conclusion, the middle term, the major term,
the minor term, the major premise and the minor
premise, observing this precise order,
(i) All men are fallible ;
All kings are men ;
Therefore all kings are fallible.
(2) Platinum is a metal ;

All metals combine with oxygen ;
Therefore Platinum combines with oxygen.

3IO QUESTIONS AND EXERCISES.

(3) Hottentots are capable of education ; for Hotten-
tots are men, and all men are capable of edu-
cation.
5. Explain carefully what is meant by non-distribution
of the middle term.

Lesson XVI. — The Moods and Figures of the
Syllogism.

r. Name the rules of the syllogism which are broken
by any of the following moods, no regard being
paid to figure : —
AIA, EEI, TEA, lOI, IIA, AEI.

2. Write out all the 64 moods of the syllogism and

strike out the 53 invalid ones.

3. Show in what figures the following premises give a

vahd conclusion : — AA, AI, E A, OA.

4. In what figures are I E O and E 1 O valid ?

5. To what moods do the following valid syllogisms

belong ? Arrange them in correct logical order.
(i) Some Y's are Z's. (2) All Z's are Y's.

No X's are Y's. No Y's are X's.

Some Z's are not X's. No Z's are X's.

(3) No fish suckles its young ;

The whale suckles its young ;
Therefore the whale is no fish.

6. Deduce conclusions from the following premises :

and state to what mood the syllogism belongs.
(l) Some amphibious animals are mammalian.

All mammalian animals are vertebrate.
{2) All planets are heavenly bodies.

No planets are self-luminous.

(3) Mammalian animals are quadrupeds.
No birds are quadrupeds.

(4) Ruminant animals are not predacious
The lion is predacious.

QUESTIONS AND EXERCISES. 311

7. Invent examples to show that false premises may

give true conclusions.

8. Supply premises to the following conclusions : —
(i) Some logicians are not good reasoners.

(2) The rings of Saturn are material bodies.

(3) Party government exists in every democracy.

(4) All fixed stars obey the law of gravitation.

Lesson XVI I.— r^^ Syllogism; Reduction.

r. State and explain the mnemonic lines Barbara,
Celarent, &c.

2. Construct syllogisms in each of the following moods,

taking X, Y, Z, for the major, middle, and minor
terms respectively, and show how to reduce them
to the first ngure : —
Cesare, Festino, Darapti, Datisi, Ferison, Camenes,
Fesapo.

3. What is the use of Reduction ?

4. Prove that the following premises cannot give a

universal conclusion — EI, I A, OA, IE.

5. Prove that the third figure must have an affirmative

minor premise, and a particular conclusion.

6. Reduce the moods Cesare and Camenes by the

Indirect method, or Reductio ad Impossibile.

Lesson XVIII. — Irregular and Compound Syllogisms.

1. Describe the meaning of each of the terms — En-

thymeme, Prosyllogism, Episyllogism, Epichei-
rema. Sorites.

2. Make an example of a syllogism in which there are

two prosyllogisms.

3. Construct a sorites of four premises and resolve it

into distinct syllogisms.

4. What are the rules to which a sorites must conform?

312 QUESTIONS AND EXERCISES.

5. The reader is requested to analyse the following
arguments, to detect those which are false, and to
ascertain the rules of the syllogism which they
break ; if the argument appears valid he is to
ascertain the figure and mood to which it belongs,
to state it in correct logical form, and then if it be
in an imperfect figure to prove it by reduction to
the first figure. The first six of the examples
should be arranged both in the extensive and
intensive orders.

1. None but mortals are men.

Monarchs are men.

Therefore monarchs are mortals. .

2. Personal deformity is an affliction of nature.

Disgrace is not an affliction of nature.
Therefore personal deformity is not disgrace.

3. Some statesmen are also authors ; for such are

Mr Gladstone, Lord Derby, Lord Russell, and
Sir G. C. Lewis.

4. This explosion must have been occasioned by gun-

powder; for nothing else would have possessed
sufficient force.

5. Every man should be moderate ; for excess will

cause disease.

6. Blessed are the merciful; for they shall obtain

mercy.

7. As almost all the organs of the body have a

known use, the spleen must have some use.

8. Cogito, ergo sum. (I think, therefore I exist.)

9. Some speculative men are unworthy of trust ; for

they are unwise, and no unwise man can be
trusted.
10. No idle person can be a successful writer of his-
tory; therefore Hume, Macaulay, Hallam and
Grote must have been industrious.

QUESTIONS AND EXERCISES. 313

11. Who spareth the rod, hateth his child; the parent

who loveth his child therefore spareth not the
rod.

12. Comets must consist of heavy matter; for other-

wise they would not obey the law of gravitation.

13. Lithium is an element ; for it is an alkali-pro-

ducing substance, which is a metal, which is
an element.

14. Rational beings are accountable for their actions ;

brutes not being rational, are therefore exempt
from responsibility.

15. A singular proposition is a universal one ; for

it applies to the whole of its subject.

16. Whatever tends to withdraw the mind from pur-

suits of a low nature deserves to be promoted ;
classical learning does this, since it gives us
a taste for intellectual enjoyments; therefore it
deserves to be promoted.

17. Bacon was a great lawyer and statesman; and as

he was also a philosopher, we may infer that any
philosopher may be a great lawyer and statesman.

18. Immoral companions should be avoided ; but some

immoral companions are intelligent persons, so
that some intelligent persons should be avoided.

19. Mathematical study undoubtedly improves the

reasoning powers; but, as the study of logic is
not mathematical study, we may infer that it does
not improve the reasoning powers.

20. Every candid man acknowledges merit in a rival ;

every learned man does not do so; therefore
every learned man is not candid.

Lesson XIX. — Conditioftal Arguments.

I. What are the kinds of conditional propositions,
and by what signs can you recognise them?

314 QUESTIONS AND EXERCISES.

2. What are the rules of the hypothetical syllogism ?

3. To what categorical fallacies do breaches of these

rules correspond?

4. Select from the following such as are valid argu-

ments, and reduce them to the categorical form ;
explain the fallacious reasoning in the others,
(i) Rain has fallen if the ground is wet ; but the
ground is not wet ; therefore rain has not fallen.

(2) If rain has fallen, the ground is wet ; but rain has

not fallen ; therefore the ground is not wet.

(3) The ground is wet, if rain has fallen ; the ground

is wet ; therefore rain has fallen.

(4) If the ground is wet, rain has fallen ; but rain has

fallen ; therefore the ground is wet.
N. B. In these as in other logical examples the
student must argue only from the premises, and not from
any other knowledge of the subject-matter.

5. Show that the canons of syllogism (p. 121) may

be stated indifferently in the hypothetical 01
categorical form.

6. State the following in the form of a Disjunctive 01

Dilemmatic argument, and name the kind to
which it belongs.
If pain is severe it will be brief; and if it last long it
will be slight; therefore it is to be patiently borne-

Lessons XX. and XXI — Fallacies.

1. Classify fallacies.

2. Explain the following expressions :

A dicto secundum quid ad dictum simpHciter ; igno-
ratio elenchi ; argumentum ad hominem ; argu-
mentum ad populum ; petitio principii ; circulus
in probando ; non sequitur ; post hoc ergo
propter hoc.

QUESTIONS AND EXERCISES. 315

3. What is arguing in a circle; and what is a ques-

tion-begging epithet?

4. What differences of meaning may be produced m

the following sentence bv varying the accent?
" Newton's discovery of gravitation is not generally
believed to have been at all anticipated by
several philosophers in England and Holland."

5. Point out the misinterpretations to which the fol-

lowing sentences might be liable.
(i) He went to London and then to Brighton by
the express train.

(2) Did you make a long speech at the meeting?

(3) How much is five times seven and nine?

MISCELLANEOUS EXAMPLES.
Lessons IX. to XXI.

( Continued from /, 313.)

The following examples consist partly of true and
partly of false arguments. The reader is requested to
treat them as follows :

1. If the example is not in a simple and complete

logical form, to complete it in the form which
appears most appropriate.

2. To ascertain whether it is a valid or fallacious

argument.

3. To assign the exact name of the argument or fal-

lacy as the case may be.

4. If a categorical syllogism, to reduce it to the first

figure.

5. If a hypothetical syllogism, to state it in the cate-

gorical form.
21. Elementary substances alone are metals. Iron is
a metal : therefore it is an elementarv substance

3i6 QUESTIONS AND EXERCISES.

22. No Athenians could have been Helots ; for all the
Helots were slaves, and all Athenians were free
men.

23. Aristotle must have been a man of extraordinary

industry; for only such a man could have pro-
duced his works.

24. Nothing is better than wisdom ; dry bread is

better than nothing ; therefore dry bread is better
than wisdom.

25. Pitt was not a great and useful minister; for

though he would have been so had he carried
out Adam Smith's doctrines of Free Trade, he
did not carry out those doctrines.

26. Only the virtuous are truly noble; some who are

called noble are not virtuous ; therefore some
who are called noble are not truly noble.

27. Ireland is idle and therefore starves ; she starves,

and therefore rebels.

28. No designing person ought to be trusted; en-

gravers are by profession designers; therefore
they ought not to be trusted.

29. Logic as it was cultivated by the schoolmen

proved a fruitless study ; therefore Logic as it is
cultivated at the present day must be a fruitless
study likewise.

30. Is a stone a body? Yes. Then is not an animal

a body.? Yes. Are you an animal ? I think so.
Ergo, you are a stone, being a body. — Lucian.

31. If ye were Abraham's children, ye would do the

works of Abraham. — John viii. 39.

32. He that is of God heareth God's words : ye there-

fore hear them not, because ye are not of God.
— John viii. 47.
S3. Mahomet was a wise lawgiver ; for he studied the
character of his people.

QUESTIONS AND EXERCISES. 317

34. Every one desires virtue, because every one

desires happiness.

35. His imbecility of character might have been in-

ferred from his proneness to favourites ; for all
weak princes have this failing. — De Morgan.

36. He is brave who conquers his passions ; he who

resists temptation conquers his passions; so .that
he who resists temptation is brave.

37. Suicide is not always to be condemned ; for it is

but voluntary death, and this has been gladly
embraced by many of the greatest heroes of
antiquity.

38. Since all metals are elements, the most rare of all

the metals must be the most rare of all the
elements,

39. The express train alone does not stop at this sta-

tion ; and as the last train did not stop it must
have been the express train.

40. Peel's remission of taxes was beneficial ; the taxes

remitted by Peel were indirect; therefore the
remission of indirect taxes is beneficial.

41. Books are a source both of instruction and amuse-

ment; a table of logarithms is a book; there-
fore it is a source both of instruction and amuse-
ment.

42. All desires are not blameable ; all desires are liable

to excess ; therefore some things liable to excess
are not blameable.

43. Whosoever intentionally kills another should suffer

death ; a soldier, therefore, who kills his enemy
should suffer death.

44. Projectors are unfit to be trusted; this man has

formed a project ; therefore he is unfit to be
trusted.
46. Few towns in the United Kingdom have more than

3i« QUESTIONS AND EXERCISES.

3CXD,ooo inhabitants ; and as all such towns ought
to be represented by three members in Parlia-
ment, it is evident that few towns ought to have
three representatives.

46. All the works of Shakspeare cannot be read in

a day ; therefore the play of Hamlet, being one
of the works of Shakspeare, cannot be read in
a day.

47. In moral matters we cannot stand still ; therefore

he who does not go forward is sure to fall behind.

48. The people of the country are suffering from famine ;

and as you are one of the people of the country
you must be suffering from famine.

49. Those substances which are lighter than water

can float upon it ; those metals which can float
upon it are potassium, sodium, lithium, &c. ;
therefore potassium, sodium, lithium, &c., are
lighter than water.

60. The laws of nature must be ascertained by De-

duction, Traduction or Induction ; but the former
two are insufficient for the purpose ; therefore
the laws of nature must be ascertained by In-
duction.

61. A successful author must be either very industrious

or very talented ; Gibbon was very industrious,
therefore he was not very talented.

62. You are not what I am ; I am a man ; therefore

you are not a man .

53. The holder of some shares m a lottery is sure to

gain a prize ; and as I am the holder of some
shares in a lotter)' I am sure to gain a prize.

54. Gold and silver are wealth ; and therefore the

diminution of the gold and silver in the country
by exportation is the diminution of the wealth
of the country.

QUESTIONS AND EXERCISES. 319

65. Over credulous persons ought never to be believed ;
and as the Ancient Historians were in many
instances over credulous they ought never to be
believed.

56. Some mineral compounds are not decomposed by

heat ; all organic substances are decomposed by
heat; therefore no organic substances are mi-
neral compounds.

57. Whatever schools exclude religion are irreligious ;

Non-sectarian schools do not allow the teaching
of religious creeds ; therefore they are irreligious.

58. Night must be the cause of day; for it invariably

precedes it.

59. The ancient Greeks produced the greatest master-

pieces of eloquence and philosophy ; the Lace-
daemonians were ancient Greeks ; therefore they
produced the greatest masterpieces of eloquence
and philosophy.

60. All presuming men are contemptible; this man,

therefore, is contemptible ; for he presumes to
believe his opinions are correct.

61. If a substance is solid it possesses elasticity, and

so also it does if it be liquid or gaseous ; but all
substances are either solid, liquid or gaseous ;
therefore all substances possess elasticity.

62. If Parr's life pills are of any value those who take

them will improve in health ; now my friend who
has been taking them has improved in health ;
therefore they are of value.

63. He who calls you a man speaks truly ; he who calls

you a fool calls you a man ; therefore he who
calls you a fool speaks truly.

64. Who is most hungry eats most; who eats least is

most hungry ; therefore who eats least eats most.

65. What produces intoxication should be prohibited ;

320 QUESTIONS AND EXERCISES.

the use of spirituous liquors causes intoxication ;
therefore the use of spirituous Hquors should be
prohibited.

66. What we eat grew in the fields ; loaves of bread

are what we eat ; therefore loaves of bread grew
in the fields.

67. If light consisted of material particles it would

possess momentum ; it cannot therefore consist
of material particles, for it does not possess
momentum.

68. Everything is allowed by law which is morally

right ; indulgence in pleasures is allowed by law ;
therefore indulgence in pleasures is morally right.

69. All the trees in the park make a thick shade ; this

is one of them, therefore this tree makes a thick
shade,

70. All visible bodies shine by their own or by re-

flected light. The moon does not shine by its
own, therefore it shines by reflected light ; but
the sun shines by its own light, therefore it cannot
shine by reflected light.

71. Honesty deserves reward; and a negro is a fellow-

creature ; therefore, an honest negro is a fellow-
creature deserving of reward.

72. Nearly all the satellites revolve round their planets

from west to east; the moon is a satellite; there-
fore it revolves round its planet from west to east.

73. Italy is a Catholic country and abounds in beg-

gars ; France is also a Catholic country, and
therefore abounds in beggars.

74. Every law is either useless or it occasions hurt to

some person ; now a law that is useless ought to
be abolished ; and so ought every law that occa-
sions hurt; therefore every law ought to be
abolished.

QUESTIONS AND EXERCISES. 321

75. The end of a thing is its perfection ; death is the

end of life ; therefore death is the perfection of
hfe.

76. When we hear that all the righteous people are

happy, it is hard to avoid exclaiming, What ! are
all the unhappy persons we see to be thought
unrighteous ?

77. I am offered a sum of money to assist this person

in gaining the office he desires ; to assist a
person is to do him good, and no rule of morality
forbids the doing of good; therefore no rule of
morality forbids me to receive the sum of money
for assisting the person,

78. Ruminant animals are those which have cloven

feet, and they usually have horns; the extinct
animal which left this foot-print had a cloven
foot; therefore it was a ruminant animal and
had horns. Again, as no beasts of prey are rumi-
nant animals it cannot have been a beast of prey.

79. We must either gratify our vicious propensities,

or resist them ; the former course will involve
us in sin and misery; the latter requires self-
denial; therefore we must either fall into sin
and misery or practise self-denial.

80. The stonemasons are benefitted by the masons'

union; the bricklayers by the bricklayers' union;
the hatmakers by the hatmakers' union; in
short, every trade by its own union ; therefore
it is evident that if all workmen had unions all
workmen would be benefitted thereby.

81. Every moral aim requires the rational means of

attaining it ; these means are the establishment
of laws ; and as happiness is the moral aim of
man it follows that the attainment of happiness
requires the establishment of laws.

21

322 QUESTIONS AND EXERCISES,

82. He that can swim needs not despair to fly ; for to

swim is to fly in a grosser fluid, and to fly is to
swim in a subtler.

83. The Helvetii, if they went through the country of

the Sequani, were sure to meet with various
difficulties ; and if they went through the Roman
province, they were exposed to the danger of
opposition from Cassar; but they were obliged
to go one way or the other ; therefore they were
either sure of meeting with various difficulties,
or exposed to the danger of opposition from
Caesar. — De Bello Gallico, lib. I. 6.

84. Riches are for spending, and spending for honour

and good actions; therefore extraordinary ex-
pense must be limited by the worth of the occa-
sion.— Bacon.

85. If light is not refracted near the surface of the

moon, there cannot be any twilight; but if the
moon has no atmosphere light is not refracted
near its surface ; therefore if the moon has no ■
atmosphere there cannot be any twilight.

86. The preservation of society requires exchange;

whatever requires exchange requires equitable
valuation of property ; this requires the adoption
of a common measure ; hence the preservation
of society requires the adoption of a common
measure.

87. The several species of brutes being created to

prey upon one another proves that the human
species were intended to prey upon them.

88. The more correct the logic, the more certainly

the conclusion will be wrong if the premises are
false. Therefore where the premises are wholly
uncertain, the best logician is the least safe
guide.

QUESTIONS AND EXERCISES. 323

89. If our rulers could be trusted always to look to

the best interests of their subjects, monarchy
would be the best form of government; but
they cannot be trusted; therefore monarchy is
not the best form of government

90. If men were prudent, they would act morally for

their own good ; if benevolent, for the good of
others. But many men will not act morally,
either for their own good, or that of others ; such
men, therefore, are not prudent or benevolent.

91. He who bears arms at the command of the magis-

trate does what is lawful for a Christian; the
Swiss in the French service, and the British in
the American service, bore arms at the command
of the magistrate ; therefore they did what was
lawful for a Christian. — Whately.

92. A man that hath no virtue in himself ever envieth

virtue in others ; for men's minds will either feed
upon their own good or upon others' evil ; and
who wanteth the one will prey upon the other. —
Bacon.

93. The object of war is durable peace; therefore

soldiers are the best peace-makers.

94. Confidence in promises is essential to the inter-

course of human life ; for without it the greatest
part of our conduct would proceed upon chance.
But there could be no confidence in promises, if
men were not obhged to perform them ; the obli-
gation, therefore, to perform promises is essential
to the same ends and in tne same degree.
96. If the majority of those who use public-houses
are prepared to close them, legislation is unne-
cessary ; but if they are not prepared for such a
measure, then to force it on them by outside
pressure is both dangerous and unjust.

21 — 2

324 QUESTIONS AND EXERCISES.

96. He who believes himself to be always in the right

in his opinion, lays claim to infallibility ; you
always believe yourself to be in the right in youi 4
opinion ; therefore you lay claim to infallibility.
— Whately. -^

97. If we never find skins except as the teguments of

animals, we may safely conclude that animals, ^
cannot exist without skins. If colour cannot
exist by itself, it follows that neither can any-
thing that is coloured exist without colour. So,
if language without thought is unreal, thought
without language must also be so.

98. No soldiers should be brought into the field who

are not well qualified to perform their part ; none
but veterans are well qualified to perform their '
part ; therefore none but veterans should be
brought into the field. — Whately.

99. The minimum visibile is the least magnitude which

can be seen ; no part of it alone is visible, and
yet all parts of it must affect the mind in order
that it may be visible ; therefore, every part of
it must affect the mind without being visible.

100, The scarlet poppy belongs to the genus Papaver,

of the natural order Papaveraceae ; which again
is part of the subclass Thalamiflorse, belonging
to the great class of Dicotyledons. Hence the
scarlet poppy is one of the Dicotyledons.

101. Improbable events happen almost every day ; but

what happens almost every day is a very pro-
bable event ; therefore improbable events are
very probable events. — Whately.

Lesson Yy^ii.— Quantification of the Predicate.
I- What does the quantification of the predicate mean?

QUESTIONS AND EXERCISES. 325

2. Assign to each of the following propositions its

proper symbol, and the symbol of its converse :
(i) Knowledge is power.

(2) Some rectangles are all squares.

(3) Only the honest ultimately prosper.

(4) Princes have but their titles for their glories.

(5) In man there is nothing great but mind.

(6) The end of philosophy is the detection of unity.

3. Draw all the contrapositive propositions and imme-

diate inferences you can from the following pro-
positions:—
(i) London is a great city.

(2) London is the capital of England.

(3) All ruminant animals are all cloven-footed ani-

mals.

(4) Some members of parliament are all the minis-

ters.

4. Write out in Hamilton's notation the moods Baroko,

Darapti, Felapton, Bokardo.

Lesson XXI IL — Boole's System of Logic.

1. Apply this system of inference to prove the syl-

logisms on p. 141, in Cesare, and Camestres.

2. Show that if all A's are not ^'s, then no ^'s are

A's ; and that if all yi's are all £'s, then all not
A's are all not ^'s.

3. Develope the term substance^ as regards the terms

vegetable^ a?iiinal, organic; then select the com-
binations which agree with these premises :
" What is vegetable is not animal but is or-
ganic ; what is animal is organic."

4. Test the validity of this argument : " Good always

triumphs, and vice always fails ; therefore the
victor cannot be wrong, nor the vanquished
right."

326 QUESTIONS AND EXERCISES.

5. It is known of a certain class of things that —
(i) Where the quality A is, B is not.

(2) Where B is, and only where B is, C and D are.
What can we infer from these premises of
the class of things in which A is not pre-
sent but C is present ?

6. If all A's are ^'s ; all ^'s are C's ; all C's are Us ;

shew that all y^'s are Z>'s, and that all notZ>'s are
not yi's.

Lesson yiXW .—Method.

1. What is the supposed position of method accord-

ing to former logical writers, and what are the
rules of method .?

2. Explain the expressions nobis noiiora, and notiora

naturcE.

3. Of what kind is the usual method of instruction .?

4. Prove that analysis in extension is synthesis in in-

tension, using some of the series of terms in
Question 6, Lesson v. as illustrations.

5. Explain the exact meanings of the expressions a

priori and a posterioi'i knowledge.

6. To which kind belongs our knowledge of the fol-

lowing facts ?
(i) The light of the stars takes a long time \o
reach us.

(2) Vaccination is a preservative against small-pox.

(3) A meteor becomes heated in passing through the

air.

(4) There must be either some inhabitants or no

inhabitants upon Jupiter.

Lesson XXV. — Pet^fect hiduction.

1. Define and distinguish Deduction, Induction, and
Traduction.

QUESTIONS AND EXERCISES. 327

2. Find an instance of reasoning in Traduction.

3. Distinguish Perfect and Imperfect Induction.

4. How does Mr Mill define Induction, and what is

his opinion of Perfect Induction?

5. What is the use of Perfect Induction?

6. Construct some instances of the inductive syllo-

gism, and show that they may be thrown into a
disjunctive form.

Lesson XXVI. — Iftduction, Analogy and Example.

1. From what circumstance arises the certainty and

generality of reasoning in geometry ?

2. Find other instances of certain and general reason-

ing concerning the properties of numbers.

3. Why are inductive conclusions concerning prime

numbers uncertain and not general?

4. Why is a single instance sometimes sufficient to

warrant a universal conclusion, while in other cases
the greatest possible number of concurring in-
stances, without any exception, is not sufficient to
warrant such a conclusion?

5. What are the strict and ordinary meanings of the

word analogy?

6. Explain the use of Examples.

7. Explain exactly the difference between analogical

argument and ordinary induction.

Lesson XXVII. — Observation and Experwte7tt.

1. What is the false method of Science against

which Bacon protested?

2. Explain the exact meaning of Bacon's assertions,

that man is the Servant and Interpreter of Nature,
and that Knowledge is Power.

3. How does experiment differ from obser/atiou?

328 QUESTIONS AND EXERCISES.

4. Classify the sciences according as they employ

passive observation, experiment, or both.

5. Name the chief points in which experiment is

superior to mere observation.

6. What is the principal precaution needful in obser-

vation "i

7. Explain how it is possible to anticipate nature and

yet establish all conclusions upon the results of
experience.

Lessons XXVIII. and XXIX.— Methods of Induction.

1. Define exactly what is meant by a cause of an

event, and distinguish cause, occasion, antece-
dent.

2. Point out all the causes concerned in the following

phenomena :
(i) The burning of a fire.

(2) The ordinary growth of vegetables.

(3) The cracking of a glass by hot water.

3. State and explain in your own words Mr Mill's

first three Canons of Inductive Method.

4. Point out exactly how the Joint Method differs

from the simple Method of Difference.

5. Give some instances of simple experiments fulfil-

ling completely the conditions of the Method of
Difference.

6. What can you infer from the following instances?

Antecedents. Consequents.

ABDE stqp

BCD qsr

BFG vqu

ADE tsp

BHK zqw

ABFG .pquv

ABE i>qt.

QUESTIONS AND EXERCISES. 329

7. (i) Friction alters the temperature of the bodies

rubbed together.
(2) The sun is supposed to move through space.
(31 A ray of hght passing into or out of a denser
medium is deflected.
Point out the successive questions which would
have to be decided in the investigation of the
above phenomena.

8. Find some simple instances of the homogeneous

and heterogeneous intermixture of effects, and
of the methods of concomitant variations and
residues.

9. Since 1842 there has been a great reform of the

British tariff, and a great increase of British
trade. Does this coincidence prove that the
first circumstance is the cause of the second?
10. Supposing us to be unacquainted with the causes of
the following phenomena, by what methods
should we investigate each ?

(i) The connection between the barometer and the
weather.

(2) A person poisoned at a meal.

(3) The connection between the hands of a clock.

(4) The effect of the Gulf-stream upon the climate of

Great Britain.

Lesson YJ^^.— Empirical mid Deductive Methods.

1. Define Empirical Law, and find a few additional

instances of such laws.

2. What are the three steps of the Deductive Method ?

3. Trace some of the successive steps in the progress

of the theory of gravitation, showing that it was
established by this method.

330 QUESTIONS AND EXERCISES.

Lesson ^XXl.— Explanation, &c.

1. What do you mean by the explanation of a fact ?

2. State the three ways in which a law of nature may

be explained, and suggest some additional in-
stances of each case.

3. Define tendency. Do all causes consist only of

tendencies, or can you find examples to the con-
trary ?

4. Give a definition of hypothesis. How may a valid

be distinguished from an invalid hypothesis ?

5. What place does hypothesis hold in the Deductive

Method ?

6. Explain the ambiguities of the words theory and

fact.

Lesson XXXIL — Classification.

1. Define classification, and give the derivation of the

word.

2. What do you mean by important characters in

classification .'*

3. State Dr Whewell's criterion of a good natural

arrangement.

4. Distinguish between a natural and artificial system

of classification.

5. What do you mean by a characteristic quality ? Is

it always an important quality ?

6. Define abstraction, generalization, and colligation

of facts.

7. What are the characters of a notion properly abs-

tracted ?

Lesson XXXIII. — Requisites of a Philosophical

Language.
I. What are the three purposes for which we use
language 1

QUESTIONS AND EXERCISES. 331

2. What are the two chief requisites of a philosophical

language ?

3. By what considerations should we be guided in

choosing between a new and old scientific term ?

4. Distinguish a Descriptive Terminology and a No-

menclature ; separate the following terms ac-
cording as they belong to one or the other: —
Rose, Rosacese, Rose-like, Potassium, Alkaloid,
Ruminant Animal, Ruminating, Ruby, Ruby-red.

5. What does Mr Mill mean by the expression Na-

tural Kind ?

INDEX.

AND CONCISE VOCABULARY OF LOGICAL AND PHILOSOPHICAL
TERMS,

Abacus^ die logical, 199

Abscissio Infiniti (the cutting

off of the infinite or negative part;,
the process by which we determine
the position of an object in a sj'stem
of classes, by successive comparison
and rejection ofthose classes to which
it does not belong.

Absolute terms, i.e. non-relative
terms, 25 ; sometimes used as name
of non-connotative terms, 41

Abstract terms, 20, 43

Abstraction^ 285

Accent^ fallacy of, 174

Accident, fallacy of, 176 ; the pre-
dicable, 103

Accidental definition is a defi-
nition which assigns the properties
of a species, or the accidents of an
iiuiividual ; it is more commonly
called a Description.

Acquired perceptions, 236
Added determinants, inference

by, 86
Adequate knowledge, 56
A dicto secundum quid, &c.,

fallacy of, 176
Adjectives, 21
Adverbials, 93

Affirmative propositions, 63
Algebraic reasoning, 58, 219
Ambigruity of all, 20 ; oisome, 79

of many old terms, 291 ; of terms in

Political Economy, 292
Ambiguous middle terra, 130, 171
AmpbibolOgy, fallacy of, 172
Ampliative propositions, 69
Analogue, a thing analogous to

some other thing.
Analysis, method of, 205

Analogy, the cause of ambiguity,
35) 50; reasoning by, 226 — 8

Analytics, [ja ' kvoXvuKo.,) the title '
given in the second century to por-
tions of the Organon, or Logical
Treatises of Aristotle ; they were
distinguished as the Prior and Pes
terior Analytics.

Analytic syllogism, a syllogism

in which the conclusion is placed
first, the premises following as the
reasons. See SyntJietic Syllogism;
the distinction is unimportant.

Antecedent, of a hypothetical pro-
position, 160; of an event, »40

Anticipation of nature, 229

Antinomy [6.vri, against; v6[lo<;,
law) , the opposition of one law or rule
to another. Kant.

A posteriori knowledge, 208

A priori knowledge, 208

Arbor Forpbyriana. see Tree of

Porphyry.
Argument, (Latin, urgiis, from
dp-yos, clear, manifest, ) the process of
reasoning, the shewing or proving
that which is doubtful by that which
is known. See In/ere?ice. The mid-
dle term of a syllogism is sometimes
called specially tJie argument.

Argumentum a fortiori, an

argument in which we prove that
the case in question is more strong
or probable than one already con-
ceded to be sufficiently so.

Argumentum ad hominem,

178
Argumentum ad judicium,

an appeal to the common sense ofi
mankind.

INDEX.

333

Argumentum ad ig^oranti-
ani; an argument founded on the

ignorance of adversaries.
Argtunentum ad populuxn^

179
Argumentuin ad verecun-

diani; an appeal to our respect for

some great authority.

Arguxnentum ex concesso,

a proof derived from a proposition
already conceded.

Aristotle's Dicta^ 123

Art and Science, distinction of, 7
Artificial Classification, 284
Assertion^ {ad, to; sero, to join,)
a statement or proposition, affirma-
tive or negative.
Association of ideas, [associo, to
, accompany; sochis, a companion,)
the natural connection existing in
the mind between impressions which
have previously coexisted, or which
are similar. Any idea tends to bring
into the mind its associated ideas, in
accordance with the two great laws
of association, the Law of Conti-
guity, and the Law of Similarity.
Assumption, [assumo, to take for
granted,) any proposition taken as
the basis of argument; in a special
sense, the minor premise of a cate-
gorical syllogism.
Attribute^ [attribzw, to give or
ascribe to,) a quality or circumstance
which may be affirmed (or denied)
of a thing; opposed to Substance^
which see.
Attribute in grammar, 92
Attributive term, i. e. Connotative

term, 41
Axioxn^ defininition of, 125

Baconian method, 255; Philoso-
phy, 229
Barbara, Celarent, &c., 145
Begging the Question, 179

Belief, assent to a proposition, ad-
mitting of any degree of strength,
from the slightest probability to the
fullest certainty ; see Probability.

Bentliam, George, new .system of
Logic, 187

Boole^ George, his system of Logic,
191 ; his Laws of Thought, 197 ;
his logical works, 201

Canons of syllogism, 121 — 2; HamQ-

ton's supreme Canon, 189
Ccinons of Mill's Inductive Methods,

First, 240 ; Second, 242 ; Third, 245 ;

Fourth, 252; Fifth, 249

Categorematic words, 18
Categorical propositions, 63

Categories, the sttuuna genera, or
most extensive classes into which
things can be distributed ; they are
ten in number, as follows :

OvcrCa, Substance ; Uoaov, Quan-
tity ; notov, Quality ; IIpo? n, Re-
lation ; TJoLeiv, Action ; Udaxfi-v,
Passion, or suffering ; Uov, Place ;
IIoTe, Time ; KeiTOai, Position :
'Exetv, Habit or condition.

Ever>'thing which can be affirmed
must come under one or other of these
highest predicates, which were de-
scribed in the first treatise of Aris-
totle's Organou, called the Catego-
ries.

Cause, meaning of, 239

Aristotle distinguished four kinds
of causes for the existence of a thing
— I. The Material Cause, the sub-
stance or matter composing it ; 2.
The Formal Cause, the pattern, type
or design, according to which it is
shaped ; 3. The Efficient Cause, the
force employed in shaping it ; 4.
The Final Cause, the end, motive
or purpose of the work.

Cliance, ignorance of the causes
which are in action ; see Probability.

Character^ derivation of the word,
46

Cbaracteristics, 285

CirculUS in definiendo, no, 114
CirculUS in probando, 179

Clearness of knowledge, 54
Cognition, {cog^wsco, to know,)

knowledge, or the action of mmd in

acquiring knowledge.
Colligation of Facts, Dr Whewell's

expression for the mental union of

facts by some suitable conception,

see 2S6
Collective terms, 19
Combined or complete method of

investigation, 258
Comparison, com, together ; par,

equal or like,) the action of mind by

which we judge whether two objects

334

INDEX.

of thought are the same or different
in certain points. See yudgment.

Compatible terms are those which,
though distinct, are not contradic-
tory, and can therefore be affirmed
of the same subject ; as " large " and
" heavy ; " " bright-coloured " and
"nauseous."

Complex conception, inference
by, 87

Complex sentence, 91 ; syllogism,
158

Composition of Causes, the
principle which is exemplified in all
cases in which the joint effect of
several causes is identical with the
sum of their separate effects, y. S.
Mill. See pp. 252, 265

Composition, fallacy of, 173

Compound sentence, go

Comprehension of terms, see In-
tension.

Computation, 127

Concept, that which is conceived,
the result of the act of conception ;
nearly synonymous with general no-
tion, idea, thought.

Conception {con, together ; capio,
to take). An ambiguous term, mean-
ing properly the action of mind in
which it takes several things toge-
ther, so as to form a general notion ;
or again, in which it forms " a men-
tal image of the several attributes
given in any word or combination of
words." Mansel.

Conceptualists, 13

Conclusion of syllogism, 15, 127 ;
weakened, 140

Concrete terms, 20

Conditional propositions, 62, 160

Confusion of words, ambiguity
from, 31

Conjugate words, those which come
from the same root or stock, as
kfwwn, knowing, knowingly, know-
ledge.

Connotation of terms, 39, 41;
ought to be exactly fixed, 290

Consciousness, the immediate
knowledge which the mind has of
its sensations and thoughts, and, in
general, of all its present operations.
Reid.

Consectary = Corollary.

Consequence, the connection be-
tween antecedent and consequent ;
but often used ambiguously for the
latter.

Consequent of a hypothetical pro-*
position, 161

Consequent or effect of a cause,
240

Consequent, fallacy of the, 181

Conservation of energy, 263, 269

Consilience of Inductions, thb
agreement of inductions derived
from different and independent series
of facts, as when we learn the mo-
tion of the earth by entirely different
modes of observation and reasoning.
Wliewell.

Consistency of propositions, 78

Consistent terms, see compatible
terms.

Contingent, [contingo, to touch,)
that which may or may not happen ;
opposed to the necessary and itn'
possible.

Contingent matter, 80

Continuity, Law of, the principle
that nothing can pass from one ex-
treme to another without passing
through all the intermediate degrees;
motion, for instance, cannot be instan-
taneously produced or destroyed.

Contradiction, Law of, 117, 193

Contradictory terms, 24, 119;

propositions, 76
Contraposition, conversion by,

83, 186
Converse fallacy of accident, 176
Conversion of propositions, 82—85;

with quantified predicate, 184

Convertend, 82
Coordinate propositions, 90
Copula, 16

Corollary, a proposition which fol-
lows immediately from another which
has been proved.

Correction of observations, 253

Correlative terms, 25

Criterion [kpi.tt,p>.ov, from KpCvm, to
judge), any fact, rule, knowledge,
or means requisite to the formation
of a judgment which shall decide a
doubtful question.

Cross division, 105

Data, (plural of datum, that which

INDEX.

ll"^

is given,) the facts or assertions from
1 which an inference is to be drawn.

Deduction and Induction, 212
.Reductive or combined method,

258, 272
De factO; what actually or really
^ happens : opposed to de jure, what
ought to happen by law or right.
DeSnition^ the logical process, 109,
1 12 ; of logic, I
^Seg^ee^ terms expressing, 24; ques-
tions of, 120
Demonstration, [demottstro, to

point out,) strictly the pointing out
the connection between premises and

w- conclusion. The term is more ge-
nerally used for any argument or
reasoning regarded as proving an

^ asserted conclusion. A demonstra-
tion is either Direct or Indirect. In
the latter case we prove the conclu-
sion by disproving its contradictory,
or shewing that the conclusion cannot
be supposed untrue.
Demonstrative Induction, 220

-De Morgan's logical discoveries

and writings, 190
Denotation of terms, 39

'Depth of a notion, see hitension.
Derivatives from the root sj>ec,

^ sight, 52

Descartes on Method, 116, 229

Description, see Accidental Deji-

r nit ion.

1>escriptive terminology, 292
Destructive dilemma, 168; hypo-
thetical syllogism, 162 — 4

Des3monymization of terms, 49

Determination, the distinguishing

of parts of a genus by reunion of the

genus and difference. Se.& Division.

Development of a teim, 193

Diagrams, of sentences, 93 — 7 ; of

^ syllogisms, 129 — 133, 142; of pro-
positions, 72 — 75

jDialectiC (StoAexTi»cij reKvri, the art
of discourse, from SioAeyeaOai, to
discourse). The original name of
Logic, perhaps invented by Plato ;
also used to denote the Logic of
Probable Matter (Aristode), the
right use of Reason and Language,
the Science of Being ; it is thus a
highly ambiguous term.

Dichotomy, division by, 107, 193

Dicta de omni et nullo, 123
Difference, the predicable, 99
Differentiation of terms, 49
Dilemma, 167

Disbelief, the state of mind in which
we are fully persuaded that some
opinion is not true. y. S. Mill. It
is equivalent to belief in the contra-
dictory opinion or assertion, and is
not to be confused vi\\.\^.Do2ibt, which
see.

Discourse, or reasoning, 15

Discovery, method of, 202

Disjunctive, propositions, 62, 160;
syllogism, 166, 194

Distinct knowledge, 55

Distribution of terms, 19, 74—5,
82, 129

Division, logical, 105 ; metaphysical,
108; fallacy of, 174

Doubt, [diibito, to go two ways,) the
state of mind in which we hesitate
between two or more inconsistent
opinions. See Disbelief.

Drift of a proposition, the varying
meaning which may be attributed to
the same sentence according to ac-
centuation. See Fallacy of accent,
174—5

Empiricism (e/xjreipia, experience),
the doctrine of those who consider
that all knowledge is derived merely
from experience.

Empirical Law, 256

Entli3rmeme, 153

Epicbeirema, 155

Episyllog^sm, 155

Equivocal terms, 29

Equivocation, 30 ; causes of, 31 ;
fallacy of, 171

Essence, [essentia, from esse, to be,)
" the very being of anything, where-
by it is what it is." Locke. It is an
ancient scholastic word, which can-
not be really defined, and should be
banished from use.

Essential propositions, 68

Euler'S diagrams, 72 — 5, 1-29 — 133,

Evidence, [e, and videre, to see,)
literally the seeing of anything.
The word now means any facts ap-
prehended by the mind and made
the grounds of knowledge and belief.

33^

INDEX.

Examples, use of, 227
Exceptive propositions, 68
Excluded middle, law of, 117,

119, 19?
Exclusive propositions,'68

Exhaustive division, 107, 192
Experience, 228

Experimentum CruciS, an ex-
periment which decides betweentwo
rival theories, and shews which is to
be adopted, as a finger-post shews
which of two roads is to be taken.

Explanation, of facts, 264; of laws,

265
Explicative propositions, 68
Exposita, a proposition given to be

treated by some logical process.
Extension and intension, 37, 208

Extensive Syllogfism, 159

Extremes of a proposition, are its
ends or terms, the subject and predi-

Fact, 275

Fallacy, purely logical, 170; semi-
logical, 170 — 175 ; materia], 176^
182 ; in hypothetical syllogism, 162 ;
in dilemma, r68
False cause, fallacy of, 181
False propositions, 70
Figure of speech, fallacy of, 175
Figures of the syllogism, 138; their

uses, 143
Form and matter of thought, 4
Fundamentum divisionis,io5
Fundamentum relationis,the

ground of relation, i.e. the series oC
events or circumstances which es-
tablish a relation between two cor-
relative terms.
Fundamental principles of syllo-
gism, 121

Galenian, or 4th figure of the syl-
logism, 145
General notions, 13 ; terms, 18

Generalization, 286 ; of names,

^^^ -

Generic property, 102

Genus, gS : generalissimum, 100

Geometrical reasoning, 58, 218;
Pascal on, 115 ^

Grammatical predica£&, 88 ; sen-
tence, 89

Gravitation, theory of, 260

Hamilton, Sir W., Method of No-
tation, 187
Herschel, Sir J., on active and

passive observation, 234
Heterogeneous, loi ; intermi}**-

ture of eff"ects, 252
Homogeneous, loi ; intermixture

of effects, 252, 265

HomolOgue, whatever is kotnolo-
gous.

Homology, a special term for the,-
analogy existing between parts or
different plants and animals, as be-
tween the wing of a bird and the
fore leg of a quadruped, or between
the scales of a fish and the feathers
of a bird. n

Homonymous terms, 30
H3rpotliesis, 269, 270
H3rpotlietical propositions, 62, 160 /■
syllogism, 161 — 2

Idea (i6ea, elSos, image), a term used
ambiguously, but generally equiva-
lent to thought, notion, concept.
Defined by Locke as "Phantasm,^
notion, species, or v/hatever it is
which the mind can be employed
about in thinking." To have an idea/
of a thing is to think of that thing.

Identity, law of, 117— 8

Idol (etSwAoi', e!6os, image), Bacon'^
figurative name for the sources of
error ; he enumerated four kinds ;
Idols of the Tribe, which affect al,'
people ; Idols of the Cave, which are
peculiar to an individual ; of the
Forum, which arise in the inter-,
course of men ; of the Theatre, which"
proceed from the systems of philoso-
phers.

Ignoratio Elenchi, 178 1

Illation [illatum, past participle of
in/ero, to bring in). See Inference

Illative, that which can be inferrea.

Illicit process, of the minor term,
131 ; of the major term, 132, 139

Immediate inference, 85—7

Imperfect figures of the syllo-
gism, 145

Imperfect Induction, 213 «

Impossible matter, 80

Inconsistent terms imply qualities
which cannot coexist in the same
thing. See co}7ipatible terms.

INDEX.

337

Inconsistent propositions, 76
Indefinite propositions, 65

Indefinite or infinite term, is a ne-
gative term which only marks an
object by exclusion from a class.

Indesignate propositions. See In-
definite propositions.

Indirect demonstration. See De-
nt&nsiration.

Indirect inference, method of,
192

Indirect reduction of the syllo-
gism, 146, 148 — 9.

Individual; what cannot be divided
without losing its name and distinc-
tive qualities, although generally
capable of physical division or par-
tition, which see.

Induction, 212

Inductive syllogism, 211, 214

Inference, defined, Si ; immediate,
85 — 87 ; mediate, 126

In fiina species, 100
Innate ideas, see a priori truths,iQZ
Inseparable accident, 103
Instances, use of, 227
Intension and extension of terms,
37, 99, 208 ; law of relation, 40

Intensive syllogism, 159

Intention, first and second, a dis-
tinction between terms thus defined
by Hobbes : — " Of the first inten-
tion are the names of things, a man,
stone, &c. ; of the second are the
names of names, and speeches, as
universal, particular , geJiits, species,
sylU^gisrn, and the like." A term of
the second intention expresses the
mode in which the mind regards or
classifies those of the first intention.

Intermediate link, explanation

by, 267
Intuitive knowledge, 57
Inversion of subject and predicate,

67
Irrelevant conclusion, fallacy of,

178

Judgment, 12

1 Language, the subject of logic, 10

I Language, requisites of philoso-
phical, 290 ; three purposes of, 287
Laws of thought, I, 117 ; of nature.

•23Q

Leibnitz on Knowledge, 53
Lemma (Aa/u./3a'i'u>, to uke or as-
sume), a proposition, a premise
granted ; in geometry, a preliminary
proposition.
Limitation, conversion by, 82, 87
Logic, derivation of name, 6
Logical abacus, slate and machine,

199
Logomachy, 293
Lowest species, 100

IXEaclline; the logical, igg
nSajor, term, 128 ; premise, 129
Many questions, fallacy of, 182
IVIaterial fallacies, 170, 176

SSatliematical induction, 220

nSatter of thought, 4 ; of proposi-
tions, 80

IVCatter is defined by J. S. Mill as
" the external cause to which we
ascribe our sensations," or as Per-
manent Possibility of Sensation.

Mediate inference, 126

nSembra dividentia, the parts
into which a class is divided ; the
constituent species of a genus.

Metaphor, 50
^Metaphysical division, 108

IffetaphysiCS [ra. ixerd ra ^vaiKo),
the works of Aristotle which fol-
lowed or were studied after his
Physics. First Philosophy, or the
so-called science of things in theii
own nature ; ontology or the science
of Being.

Method {fiedoBo^, fxera and bS6<i,
way), mode, way or instrument of
accomplishing an end.

Method, the fourth part of logic,
15, 201; Pascal on, 114; Descartes'
Discourse on, 116; of indirect infer-
ence, 192

Methods of Induction, Agreement,
240; Difference, 242; of Experi-
ment, 243 ; Jomt Method, 245 ;
Residues, 252 ; Concomitant Varia-
tions, 249

Metonymy (/lera, and ovofj.a,name),
grammatical name for the transfer
of meaning of a word to a closely
connected thing, as when we speak
of the church, me.-ining the people in
it. See Transfer of meaiiing.

Middle Term, 126, 128

338 INDEX.

ISIill; J. S., on Connotative terms,
41 ; on Induction, 214 ; on Analogy
and Induction, 227 ; on Observation,
235 ; on Terminology and Nomen-
clature, 294
ASinor term, 128; premise, 129
BUnemoniC verses, Barbara, &c.,

144
IlSodal proposition, 69, 91
SSodUS; ponens, 161 ; tollens, 162
Modus ) pojiendo tollens, 166; tel-
le ttdo pone f IS, 166
Koods of the syllogism, 136 ; ac-
cording to Hamilton, t88

ITaxne^ or term, ry

Natural Classification, 280
Natural Kinds, 294
Necessary matter, 80

Necessity 'ne, not; and cesso, to
cease), that which always is and can-
not but be.

Negation, conversion by, 83

Negative, terms, 22; propositions,
63, 83 ; premises, fallacy of, 133 — 4

Newton's experiments, 253, 259

Nomenclature, 293

Nominal definitions, 112
Nominalists, 13
Non causa pro causa, 181
Non sequitur, 181

Notion [nosco, to know), the action
of apprehending or taking note of
the various qualities of an object ; or
more commonly the result of that
action. See Idea, Co^tcept.

Notiora naturae, 204

Novum Organum, first aphor-
isms of, 229

Numerically definite syllogism,
190

Object of verb, 93

Objective, that which belongs to

the object of thought, the non-ego;

opposed to Subjective, which see.
Obscure knowledge, 54

Observation, 231, 235
Obversion is a name used by Pro-
fessor Alexander Bain to denote the
process previously called Immediate
Inference by Privative Conception, 85
Opposite terms, 24, 119
Opposition of propositions, 78
Organon (op-yai/oi/, Latin Organum,

Instrument), a name for Aristotle's
logical treatises, first generally used ;
in the 15th century, implying that
they may be regarded as an instru- ^
ment to assist the mind. The name ^'
was adopted by Bacon for his Novutn '
OrguJium,

Paradox (7ra/ja, ho^a^ contrary to
opiiaion), an assertion contrary to
common opinion, and which may or •*•'
may not prove true ; often wrongly
used to mean what is self-contradic-
tory and absurd.

Paralogism tTrapoAoyi'^Ojaat, to rea-
son wrongly), a purely logical fallacy,
or breach of the rules of deductive
logic.

Parity of reasoning, an expression ^.
used to denote that when one case
has been demonstrated, other simi-
lar cases can be demonstrated by a
like course of reasoning.

Paronymous words, see Conju-
gate words.

Particular propositions, 63 — 6,72,79
Particular premises, fallacy of, 135,

151 . .
Partition or physical division, 108 '
Per accidens, conversion, 82
Perfect Figure of the Syllogism,.^

145
Perfect knowledge, characters

of, 53

Periodic changes, 250 '

Peripatetic Philosophy (TreptTrarew,
to walk about), the name usually
given to the doctrines of Aristotle f.'
and his followers, who are said to
have carried on their studies and
discussions while walking about the \
halls and promenades of the Lyceum.

Petitio Principii, 179

Phenomenon, 240

Pliilosopbical language, re-
quisites of, 290

Physical definition assigns the
parts into which a thing may be
separated by partition or physical
division.

Plurative propositions, 191

Polylemma, an argument of the
same form as a dilemma, but in which ^,
there are more than two alternatives.

Porphyry, tree of, 103

INDEX,

33f^

Port Ztoyal ZiO^c, m, 157

Positive terms, 22

Post hoc, ergfo propter hoc,

181

Postulate \postulatum, a thing de-
manded), a proposition wliich is ne-
cessarily demanded as a basis of ar-
gument ; in geometry, the postulates
define the practical conditions re-
quired

Predi<;^ble8, 98

PredicAiinents {prcedicamenta,
what can be predicated), see Cate-
gories.

Predicate, 62, 88, 92; quantified,
183

Premise, or Premiss, 15, 127

Primary Laws of Thought, 117

Principle [principimn, beginning),
the first source of anything : some-
times specially used to mean the
major prenaise of a syllogism.

Privative conception, inference

by, 85

Privative terms, 24

Probability, quantity or degree of
belief, or more truly, quantity of in-
formation concerning an uncertain
event, measured by the ratio of the
number of cases favourable to the
event to the total number of cases
which are possible.

Probability, of propositions, 70 ; of
inductions, 223

Problem {npoPKrifLo., that which is
thrown down), an assertion put for-
ward for proof or disproof.

Proof, the assigning a reason or ar-
gument for the support of a given
propositi or..

Proper names, 18

Property ox proprium, 41, 102, 109

Propositions, 10, 16 ; several kinds
of, 60; affirmative and negative, 63;
categorical, 63 ; conditional, 62, 160;
disjunctive, 62, 160; essential or ex-
plicative, 68 ; exclusive, exceptive,
63 • hypothetical, 62, i6j ; indefinite
or indesignate, 65 ; modal, 69, 91 ;
opposition of, 78; particular, 63—6,
72, 79; pure, 69; plurative, 191 ; ir-
regular, 67 ; quality and quantity of,

63
FrosyllGsism, 155
Proslxnate genus, 108

Quantification of preJizate, iS^
Quantity of propositions, 63 ; quftb

tions of quantity, 120
Quatemio terminorum, 17c

Bamean tree, see Tree of Por^

Phyry.
Ratiocination, a name equivalent

to Syllogism or Deduction, adopted .»

by J. S. Mill.
Realism, 13

Reason {ratio, from reor^ to thiuk),
a terra of wide and ambiguous mean-
ing ; it has sometimes been specially
used to denote the minor premise of
a syllogism.

Reasoning, or discourse-; 15

Record, language as instrument of,
289

Reductio ad absurdum or ad

hnpossibile, an indirect demonstra-
tion founded upon the impossibility
of a contradictory supposition, 146

Reduction of the syllogistic figures,
145 ; ef hypothetical to categorical
syllogisms, 163 — 5

Relation {relatum, past participle
of re/ero, to bear back), any con-
nection in thought or fact between
two things, ei

Relative terms, 25

Residual phenomena, 254

Residues, method of, 252

Rules of the syllogism, 127

Scholastic Philosophy, a ge

neral name for the systems of philo-
sophy taught during the middle ages
from the 9th to the i6th century,
flourishing chiefly in the 13th and
14th centuries. The subject was
chiefly the logic of Aristotle, varied
with theology, metaphysics, gram-
mar, or rhetoric.

Second Intention, see Intention.

Secundi adjacentis, of the se-
cond adjacent, an expression in in«
correct Latin, applied to a gram-"
matical sentence or proposition con-
taining only two parts, the subjeci
and verb, without a distinct cofdila.

Self-contradictory terms, 193

SemilOgiC£Ll fallacies, 171
Sentence, grammatical, 61, 8g
Separable accident, 103

S40

INDEX.

fignificat^S of a term are things
deaoted or signified by it.

SimilaxS; substitution of, 124, "^^^

Simple^ apprehension, ii ; conver-
sion, 82, 184

SingXllary terms, 18 ; propositions, 64

Sopllism (cr6(^(o-/u.a, from aro(f>Ca., wis-
dom), a false argument ; the name
often implies that a false argument
is consciously used for deception.

Borites;, 156

Specialization of names, 45, 48

Species, in logic, 98 ; in natural
history, loi

Subaltern^ propositions, 77; genera
and species, 100

Subaltemans, subaltern-
ates, 77

Subcontrary Propositions, 77

Subject of a proposition, 62, 92

Subjective, that which belongs to
. the thinking subject, the ego, or
mind engaged in thought ; opposed
to objective, which see.

Subordinate propositions, 91

Substance {sub, under ; statu from
stare, to Stand,', that which underlies
and bears phenomena or attributes ;
strictly speaking it is either mind or
matter, but it is more commonly
used in the material sense.

Substitution of similars, 124, 200

Subsuniption (sitb, under ; sumo,
to take or put), a name used by Sir
W. Hamilton for the minor premise
of a syllogism, because it brings or
subsumes a special case under the
rule expressed in the major premise
or sumption.

Subsumption of a law is Mr
Mill's expression for the third mode
of explaining a law by shewing it to
be a particilar case of a more ge-
neral law, a68

Sufficient Reason, Principle or
Law of, 125

Sui generis, loi

Summum genus, 100

Sumption {sumo, to take), Sir W.
Hamilton's name for the major pre-
mise of a syllogism.

Supposition, 270

Syllogism, 10, 127; inductive, 211,

214
Symbolical knowledge, 57

Simcategorematic words, 18

S3mtlieBis, 205

Syntbetic syllogism, a syllo.

gism in which the conclusion standj

last ; see A nalytic syllogism.
System, (o-u'cmjfxo, from oi'vianj^i

to put together), a connected body at

knowledge.

Tacit premise, 153

TautOlogOUB propositions, 69

Tendency, 266

Terminology, 292

Terms, 10, 16, 17

Tertii adjacentis, of the third
adjacent, an expression in incorrect
Latin, applied to a grammatical sen-
tence or proposition in which the
subject, copula and predicate, are
all distinctly stated.

Theory (^empia, contemplation),
knowledge of principles, as opposed
to practice ; ambiguously used, see

. P- 274

Thesis (0€cri5, from ti^tj/xi, to place],
an assertion or proposition which is
put forth to be proved or supported
by arguments.

Thoughts on things, the object of
logic, 10

Totum divisum, a class or notion
which is divided into parts by 2
difference.

Traduction, 212

Transfer of meaning of terras, 33

Tree of Porphyry, 103

Trilemma, an argument resem-
bling a dilemma, but in which there
arc three alternatives.

Truisms, 69

Truth, conformity of our knowledge
with the things known.

Ultra-total distribution, iqi
Uniformity of nature, 217
Universal propositions, ej,

66; affirmative, 71 ; negative, 7?
Univocal terms, 29

Variations, method of, 249: pc»

riodic, 250
Verb, 88

Weakened conclusion, 140
Worse relation (Hamilton), i^