Logic (1903)

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i

100 -CD

OXFORD HORACE HART, PRINTER TO THE UNIVERSITY

LOGIC

ST.

GEORGE STOCK,

M.A.

PEMBROKE COLLEGE, OXFORD

SECOND EDITION

3

B.

H.

BLACKWELL,

50 & 51

-^ n .,a

BROAD STREET

JSonfcon

SIMTKIX, MARSHALL, HAMILTON,

1903

KENT &

CO.

PREFACE THIS book of

is

a reissue with alterations

and additions

Deductive Logic published towards the close of

my

1888.

It

now

is

called

by a wider name because

the

treatment of Inductive Inference has been included.

My

main

obligations in preparing the

new

edition are

J. N. Keynes, who seems justly entitled to become one of our chief legislators on logical terminology.

Mr.

to

In a work which appeared at the same time as

my own

Father Clarke laid the English-speaking world under his debt by an exposition of the Scholastic Logic in which there

is

not a dull page from beginning to end.

Other books which

I

should like to mention are Shute

s

Manual of Logic, Minto

s

Discourse on Truth, Welton Logic, Inductive

s

and Deductive, and

the

new

edition of

the Palaestra Logica.

have to thank Mr. E. L. Hawkins of Merton College, and Mr. F. G. Brabant of Corpus Christi College, Oxford, I

for

some

helpful criticisms while the

work was

in progress.

The keen

eyes of Mr. George Holden, sub-librarian of

All

College, detected

Souls

edition which

16

MUSEUM ROAD, OXFORD, Jan.

some mistakes

had escaped other observation.

9,

1900.

in

the

first

PREFACE TO DEDUCTIVE LOGIC who was kind enough to look at this book manuscript, recommended me to abandon the design

ONE in

critic,

of publishing

on

it,

like all other logics

a considerable I

;

the

ground

amount of new

have followed

that

I trust,

me

The

matter.

;

novelties

which

I

was too

logic

the former has encouraged

that I shall not be considered guilty of

The few

my

another suggested to

io cut out

latter

me

advice

to

hope wanton innovation.

have ventured to retain

will,

be regarded as legitimate extensions of received

lines of teaching.

My

object has been to produce a

work which should

be as thoroughly representative of the present state of the of logic of the Oxford Schools as any of the text-books the past.

The

qualities

which

I

have aimed

at before all

others have been clearness and consistency.

task which I have taken qualification

now

teen years have in

logic

for

elapsed since

I

I

may

the

claim one

more than seven

took

my

first

pupil

Honour School of Moderations, and

the

during that time in

upon myself

that of experience; since

For

I

have been pretty continuously engaged

studying and teaching the subject.

In acknowledging my obligations to previous writers must begin with Archbishop Whately, whose writings The works of first gave me an interest in the subject.

I

PREFACE TO DEDUCTIVE

LOGIC.

and Hamilton have of course been

Mill

I

writers

exclusively, but

what seemed best

drawn

have endeavoured to assimilate

To

in both.

under a special debt. teaching from him in but his book

;

freely

have not followed either of those two great

upon.

jects

vii

I

had not the

into

my

privilege of personal

had

logic, as I

fell

am

Professor Fowler I

in

hands

some other sub an early period

at

my mental training, and was so thoroughly studied as to have become a permanent part of the furniture of my in

Much

mind.

the

same may be

said of

my

relation

to

the late Professor Jevons s Elementary Lessons in Logic.

Two

McCosh added the

Laws of

s

Watts

Deductive Logic

in

Bradley

s Principles

edition of

the

list

will

bound

mention with

of Aldrich If

Thought.

Logic, s

to

edition

Thomson

there s

be

Outlines

Deductive Logic, Jevons

and

Principles s

of

s

Science,

Elements of Logic,

be exhausted of modern works from which

conscious of having borrowed.

But, not to forget

the sun, while thanking the manufacturers of lamps candles, I should Aristotle

and

Murray, Ray s Text-book of Deduc s Rudiments of Logic, I think

Logic, and Weatherley

am

s

of Logic, Abbott

tive

I

s

Thought, Bain

Studies

Walker s

feel

Discursive

to the foregoing

Laws of

1

Mansel

emphasis, are

special

of

which

other books,

add

according

that I

to

the

and

have studied the works of

measure of

my

time

and

ability.

This work has had the great advantage of having been revised, while still in manuscript, by Mr. Alfred Robinson. Fellow of

New

College,

to

whom

I

cannot sufficiently

PREFACE TO DEDUCTIVE

viii

express

my

obligation.

I

LOGIC.

have availed myself to the full of was kind enough to send

the series of criticisms which he

As some

me.

cannot be less

additions have been

held in

kindly critics

any way responsible

may

W.

J.

Priest of

Merton

thanks are due also to

My

since then, he

for the faults

which

detect.

For the examples at the end others, and to a large extent to Rev.

made

I

am

my

mainly indebted

to

ingenious friend, the

College.

my

friend

and former

pupil,

Mr. Gilbert Grindle, Scholar of Corpus, who has been at the pains to compose an index, and to revise the proofs as they passed through the press.

And

last,

gratitude to

Majesty

s

but

not

must

on record

my

R. A. Stock, R.N., one of

Her

least,

Commander

I

set

Knights of Windsor, without whose brotherly

work might never have been written, and would certainly not have assumed exactly its present shape. aid this

OXFORD, October 22, 1888.

CONTENTS PREFACE

.....

PREFACE TO DEDUCTIVE LOGIC INTRODUCTION,

1-15

Of Terms,

PART!.

CHAT.

I.

Of Terms

as

16-52

....

distinguished

16-23

from

II.

Of

the Division of Things,

24, 5

III.

Of

the Divisions of Terms,

26-36

IV.

Of the Law sion

Of

II.

CHAP.

I.

other

.

21-23

.

24-49

and Intension, 38-136

37

.

.

.

5O~5 2

....

the Proposition as distinguished from 38-40 . other Sentences, .

II.

III.

Of the Copula,

Of the

41-3

44-55

60-76

56-60

.

V. Of the Quantification of the Predicate, 61-4

Of the Heads

VIII.

Of

IX.

Of

Definition,

Division,

65-91

of Predicates,

92-103

104-19. 120-36

53,54 55-59

Divisions of Propositions,

VII. Of the Categories,

53-136

....

IV. Of the Distribution of Terms,

VI.

16-20

.

of Inverse Variation of Exten

Propositions,

Of

vi-viii

1-15

16-37

Words,

PART

v

77-81

82-86

.

87-105

.

.

.

106-113

.

.

.

114-126

....

127-136

CONTENTS. PART

Of

III.

CHAP.

I.

Of

II.

Of

Of Imperfect

IV. Of Apparent

141-143

.

144-147

.

.

148-152

159-164

.

153-159

.

140-153

Induction,

154-8

Inductions,

....... .......

165-

VI. Of Observation and Experiment, 168

Of

174-80

the Conception of Cause,

181-90

IX. Of the Inductive Methods,

160-164

169-

Uniformities of Coexistence,

73 VIII.

137-14

.

.

.

V. Of the Axioms of Induction,

VII. Of

137-384

and the Inductive

143-148

Syllogism, III.

137-142

Inferences in general, Perfect Induction

PACES

....

137-434

Inferences,

165-168

.

169-175

.

176-194

X. Of the Nature of the Inductive Methods,

XI. Of some

other

points

.

.

203-5

XII. Of Deductive Inferences, XIIT. Of

with

connected

196-202

Induction,

.

.

.

..... ..... ..... ..... .....

Immediate Inference by Opposition, 200-15

200-206 207-209

210-216

XIV. Of Immediate Inference by Conversion, 216-24

XV. Of Immediate

Inference

225-8

XVI. Of

Compound 229-36

217-219

by Obversion,

Immediate

220, 221

Inferences,

222-229

XVII. Of other Forms of Immediate Inference, 237-40

XVIII. Of Immediate Complex

Inference

as

Proposition?,

applied

211-63

230-232

to .

233-249

CONTENTS.

xi PAGES

XIX. Of Mediate

or

Inferences

Syllogisms,

264-70

XX. Of Mood and XXI. Of the Canon XXII. Of

the

250-253

Figure,

271-7

of Reasoning,

General

Rules

278-84

of

.

254-256

.

257-260

.

Syllogism,

285-95

261-272

XXIII. Of the Determination of the Legitimate 296-300 . Moods, .

.

XXIV. Of

301, 302

XXV. Of

276-279

the Determination of the Valid in the

XXVI. Of

Four

Moods

303-11

Figures,

.

the

284-296

Syllogism

with Three

Figures,

323-332

XXVIII. Of Reduction,

XXIX. Of Complex

XXXIII. Of Trains

.

.

305-324 325-330

of the Partly Conjunctive

369-373

880-90

of Reasoning,

XXXIV. Of Fallacies,

.

357-368

408-34

.

.

331-334

374-9

.

335-338

.

.

339-348

.

349-360

.

Disjunctive Syllogism,

XXXII. Of the Dilemma,

INDEX

.

Syllogisms,

Syllogism,

XXXI. Of the

297-304 333-356

XXX. Of the Reduction

EXERCISES

280-283

the Specialities of the Four Figures,

312-22

XXVII. Of

273-275

the Special Rules of the Four Figures,

.

391-407

....

361-384 385-432

433-440

INTRODUCTION. Laws

the Science of the

1.

LOGIC

2.

Thought, as here used,

is

is

of Thought.

confined to the faculty

All thought involves comparison, that

of comparison.

is

to say, a recognition of likeness or unlikeness.

The laws of thought are the The word law however thinking.

conditions of correct

3.

it

will

it is

is

so ambiguous that

be well to determine more precisely in what sense

here used. 4.

We

laws of the land

talk of the

of nature, and

it

is

evident that

and of the

we mean very

laws

different

by these expressions. By a law in the political sense is meant a command imposed by a superior upon an inferior, and sanctioned by a penalty for disobedience. things

But by the formities

laws of nature

among

of gravitation

natural

means

are

meant merely

phenomena;

certain uni

for instance, the

law

that every particle of matter does

invariably attract every other particle of matter in the

universe with a force in direct proportion to the

and

mass

in inverse proportion to the square of the distance.

The word

law

one of these senses

command

is

transferred

to the other.

as that described above

by a metaphor from

The is

to

effect

of such a

produce a certain B

INTRODUCTION.

2

amount of uniformity in the conduct of men, and so, where we observe uniformity in nature, we assume that is

it

the result of such

thing really

Now is

command, whereas

a

to us

is

laws of thought

never can be so

l .

manner with

Can

The

?

itself.

laws of the land,

whereas the laws of nature

plain, are often violated,

in like

the only

the fact of uniformity

which of these two senses are we using the

in

expression it

known

the laws of thought be violated

the laws of the land

inviolable like the laws of nature

Or

?

are they

?

In appearance they can be, and manifestly often are violated. For how else could error be possible? But in reality they

when

tradiction

can not. it

No man

presents

itself to

ever accepts a con the

mind

as such

:

but owing to confusion of thought and the infinite per plexities of

language conclusions are often reached which

contain a latent contradiction.

It is the

business of logic

to bring these conclusions to the test of

In

this

The are

way

first

principles.

logic acts as the touchstone of truth.

laws of thought then in their ultimate expression

certain

uniformities

which invariably hold among

mental phenomena, and so far they resemble the laws of nature but in appearance they may be violated owing :

to error, as the laws of the land

may be

violated

by

crime.

1 There is a sense in which people frequently speak of the laws of nature being violated, as when one says that intemperance or celibacy is a violation of the laws of nature, but here by nature

is

meant an

ideal perfection in the conditions of existence.

INTRODUCTION. 5.

Logic

often

is

formal laws of thought. because

it

of the

defined

as

We have

avoided that expression

the

science

suggests that there are material laws of thought,

a phrase to which It is

3

would be

it

not equivalent to

With such

thought.

difficult to

assign a meaning.

laws relating to the matter of

not concerned, unless

laAvs logic is

they are so universal as to apply to every object thought about, of whatever nature

it

be, in

may

The

distinction

pervades

between form and matter

We

nature.

all

which case they

and not the matter.

are considered to belong to the form

of manufactured

articles.

are familiar with

A

cup,

for

one which

is

in the case

it

instance,

with

same form, may be composed of very precisely different matter gold, silver, pewter, horn, or what not. the

Similarly in every act of thought

we may

distinguish

two things (1) the object

thought about,

(2) the

which the mind thinks of

The

way

first

of Thought.

rogues/ or

is

in

called the Matter

Thus

I

;

it.

the second the

may judge

Porpoises are playful.

Form

Money-lenders are

The

these two cases quite different, but the

matter

form

is

is

in

the same,

namely, a judgement. Since the form different,

we may

the

in

way

may

be the same whilst the matter

say that logic

is

is

concerned only with

which the mind thinks, and has nothing to

do with the particular objects thought about. In other words, logic is concerned with the essential and necessary elements of thought as opposed to such as are accidental B 2

INTRODUCTION.

4

and contingent. By contingent is meant what holds true in some cases, but not in others. For instance, in the particular case of equilateral triangles

it is

true to say,

not only that

All equilateral triangles are equiangular/

but also that

All equiangular triangles are equilateral.

But the evidence

The one is it were, we

and

P

it is

which

We

6.

to call

it

distinct.

is

If

should be able to apply the same inference

to all matter is S,

two propositions

for these

not a formal consequence of the other.

we cannot

have defined logic as a

also

S

assert universally that if All

notorious that

Is

science.

The answer

an art!

is

P, All

do. it

correct

to this question

must

depend upon the meaning we assign to those terms. Broadly speaking, there is the same difference between Science and Art as there Science

Art

is

is

is

between knowing and doing.

systematized knowledge;

systematized action.

Science

Art

is

is

acquired by study;

acquired by practice.

Now logic is manifestly a branch of knowledge, and It is does not necessarily confer any practical skill. only the right use of

make men

rules

its

think better.

It is

in

thinking which can

therefore in the broad sense

of the terms wholly a science and not

But the word

art,

like

being often used not for for the

knowledge

most

skill

an is

art.

ambiguous,

displayed in practice, but

necessary thereto.

better conveyed by the term

at all

others,

This meaning

practical science.

is

INTRODUCTION. Science case that

we

is

Surgery In the

that

we may know;

a speculative science

human frame

study the

we may understand we may assist its

which

its

Whether

merely that we it

we study

may know what

a speculative science

;

we

if

in

the

in

structure;

needs.

If

treated.

is

it

;

a practical science.

we

case

first

is is

speculative or a practical science depends in

first

in the latter

do.

Anatomy

that

In the

either Speculative or Practical.

study merely that

we may

5

order

second

logic

be a

upon the way

the laws of thought

we

are making same laws with

they are,

study the

a view to deducing rules for the guidance of thought, are

making

Hence

logic

and the the

art

is

in

It

the art of thinking in

is

which grammar

not in

a knowledge of

In

be declared to be both the science

may

of thinking.

same sense

Grammar

it

is

to think

correctly,

or at

the art of speaking.

the right use of words, but

itself

men

enables

to use

same way a knowledge of

the

we

a practical science.

it

words

logic

correctly.

enables

men

events to avoid incorrect

all

thoughts. 7.

The Three Fundamental Laws of Thought.

The

laws of thought are

reducible to

all

following axioms, which are known as (i)

The Law

of Identity

Whatever Every

A

is is

is.

A.

the three

INTRODUCTION.

6 (2)

The Law

of Contradiction

Nothing can both be and not

No A (3)

is

The Law

be.

not A.

of Excluded Middle

Everything must either be or not be Everything

At

first

is

either

sight these three

A

or not A.

principles

For

able one from the other.

is

seem

be deriv

to

not the second,

may

it

be asked, the obverse and the third the converse by contraposition of the

first

And

J

?

are not obversion and

contraposition valid forms of inference?

validity

Yes,

we

shall

But recognise them as such. of these modes of inference depends upon

afterwards

have

the

to

We

laws of thought.

cannot therefore make

the

the laws of

thought depend upon them.

In

reality

each of these principles

is

independent and

self-evident.

If

it

violated,

were possible for the law of identity to be no violation of the law of contradiction would

necessarily ensue else,

without

:

for a thing

being

itself

at

might then be something the same time, whereas

what the law of contradiction forbids should be both

itself

and something

that a thing

is

else.

Neither would

the law of excluded middle be infringed. supposition, 1

a

thing would

be something

A is A. A is not-A (obverse of i). All but A is not-A (converse

For, on the else.

Now

(i) All (2)

(3)

No

by contraposition of

i).

INTRODUCTION. middle demands

that the law of excluded

all

should either be

A

or not.

itself

7

would

that

is

in

it

case

this

adopt the alternative of being not- A. Again, the violation of the law of contradiction does not involve

any violation of the

a thing might in that case be

owing not

law of contradiction not holding,

to the

itself at

law of identity; for itself, even though,

still

same

the

it

were

Neither would the law of

time.

excluded middle be infringed. For a thing would, on the supposition, be both itself and not itself, which is the very reverse of being neither. Lastly, the law of excluded middle

might be violated

without a violation of the law of contradiction

for

:

we

should then have a thing which was neither A nor not-A, but not a thing which was both at the same time. Neither would

we

law of identity be infringed.

the

For

should in this case have a thing which neither was

nor was identity

so

not,

could that

postulates

These

exist

whatever

which never was

to

conditions

the

that

not

be

to

is,

is

:

of the

here

law of

That

broken.

law

we have a thing

begin with.

principles are of so simple a character that the

discussion

of them

Especially

is

this

is

the

apt

to

be regarded as puerile.

case with regard

to

the law of

This principle in fact is one of those things identity. which are more honoured in the breach than in the observance.

not hold

Suppose

for a

moment

then what would become of

that

this

law did

our reasoning ? Where would be the use of establishing conclusions about all

8

INTRODUCTION.

things, if they

were able

to

evade us by a Protean change

of identity?

The remaining two laws supplement each other The law of contradiction enables following way.

in the

us to

two exhaustive and mutually exclusive alterna that it is impossible for both to be true; the law

affirm of tives

of excluded middle entitles us to add that impossible for both to be

it

is

equally

Or, to put the same

false.

thing in a different form, the law of contradiction lays

down

one of two such alternatives must be

that

the law of excluded middle adds that one

There are three

8.

which logic

is

must be

false;

true.

acts or processes of thought with

concerned

(1) Conceiving, (2) Judging,

(3) Inferring.

To

conceive

of anything.

I

Apprehension.

my

mind

to grasp in the

is

Hence Conception

mind is

also

conceive a triangle

the idea or notion

known when

the idea of a figure contained

by

I

as Simple

grasp in

three sides.

Conception, be it remembered, is an act of pure thought, and has nothing to do with sensuous imagination. We

can conceive things of which we can form no mental picture.

tion

;

Conception

but that

is

is

generally accompanied by imagina

a different matter.

To judge is to pronounce as to the agreement or disagreement of two ideas. E.g. we have in our minds the idea of a cup and the idea of a thing made of porcelain,

and we combine them

in

the

judgement

INTRODUCTION. This cup the

is

made

judgement

Judgement,

it

of porcelain

g

or separate

;

them

in

This cup is not made of porcelain. will be seen, is here confined to the

comparison of ideas already formed in the mind. Some times the term is extended to the comparison of nameless

But

sense-impressions.

this

amounts

to

identifying

judgement with thought in general.

To

infer is to

pass from one or more judgements to

Thus from

another.

the several judgements,

and the other thing made of porcelain to the universal judgement, Whatever lain

is brittle

we add

to

;

it

or,

we

rise

brittle/

is

made of porce

having already formed that judgement,

This cup

another,

and so descend

This, that,

is

to

the

is

made of

new judgement,

porcelain,

This cup

is

brittle.

9.

Corresponding to these three processes there are

three products of thought, namely (1)

(2) (3)

The Concept, The Judgement, The Inference.

Since our language has

a

tendency to confuse the between processes and products, it is the more We speak necessary to keep them distinct in thought.

distinction

quite

indiscriminately of Conception, Judgement, Infer

ence, Sensation, Imagination, Sight, Definition,

Thought, Division, and so on, whether we mean in any case

a process or a product. The distinction is much better observed both in Latin and Greek than in English. Thus in Latin visus or visio

is

used for the act of seeing, and

INTRODUCTION.

10 vis urn for the thing j/o

process,

^/m

seen

and

the act of sensation,

and so on

in

Greek VO T/O-IS stands thought

direct

object of logic

same time

of thought.

way

in

which

we it

But

are studying is

possible to

For the human mind cannot be both actor and

so.

spectator at once in

of sense,

the study of the

is

in studying the products

the processes in the only

do

ato-Byo-is for

;

ala-Orfrov for the object

products rather than of the processes at the

for the

in other cases.

The

10.

;

for the product of

;

we must

wait until a thought

our minds before we can examine

be already dead

in order to

Thought must be dissected ; there is no

Thus we can never know

vivisection of consciousness.

more of

formed

is

it.

the processes of thought than what

is

revealed

to us in their products.

11. Primarily

thought

;

and necessarily

the garment of thought.

and

may

in bed, as

it

If thought

were, in the

concerned with

remains

;

but

at

home

individual, if it

it

wishes to

must put on its clothes, and array or some other form of language. So speech

into society,

itself in

much

is

mind of an

perhaps dispense with language

go out

the

logic

secondarily and accidentally with language as

does the

Greeks as

it

tailor

a

make

nation

the

man

never

in this instance that

distinguished

between

thought and language. logic

is

Their word Aoyo?, from which stands derived, equally for both ; it corresponds

both to ratio and to oratio in Latin. of course were obliged

and

its

to

The

philosophers

distinguish between

thought

expression, which they did by calling one the

INTRODUCTION.

II

Aoyos j/8ta0eTos and the other the Aoyos 7rpo
This ambiguity in the name lends ground to a difference of opinion that has subsisted among logicians as to whether the subject-matter of their science pure and simple or thought

Granting that

it

is

When the

expressed

thought pure and simple,

impossible to discuss 12.

as

it

is

thought

in

language.

it is

obviously

except as clothed in language.

three products of thought are expressed

in language, they are called respectively

(1) (2) (3)

The Term, The Proposition, The Inference *.

13. It has

been declared that thought in general is the we have seen that there are

faculty of comparison, and

three products of thought.

It follows that

each of these

products of thought must be the result of a comparison of

some kind

or other.

The term is the result of comparing attributes. The proposition is the result of comparing terms. The inference is the result of comparing propositions. Not only

are

common

terms the results of comparison,

but singular terms, or the names of individuals, are so too. 1

Such

the term

is

the ambiguity of language that we have already used in three different senses (i) for the act

inference

or process of inferring, (2) for the result of that act as it exists in the mind, (3) for the same thing as expressed in language. Later on

we

shall

proposition, or

an inference.

have sometimes

what

is

otherwise

to

apply

known

it

to

an inferred

as the conclusion of

INTRODUCTION.

12

The

of thought

earliest result

and marked doubt the

off

first

intelligence of

requires

its

from the mass of

it.

exercise

of

No

surroundings.

nascent

thought to distinguish

The completeness

parts.

Hence even an

is

of the recognition

name, or singular term, Before the child can

individual

to the

meaning

It

this

announced by attaching a name

implies thought or comparison. attach a

its

impression produced upon an infant is that of a confused whole.

of an individual object to

to say, as distinguished

is

the

much

whole into

an

the recognition of

is

individual object as such, that

word

mother,

which

to

it

is

must have distinguished between the set of impressions produced in it by one object from those which are produced in it by others. Thus, when Vergil a singular term,

it

says Incipe, parve puer, risu cognosccre matrem,

he

is

exhorting the beatific infant to the exercise of the

faculty of comparison.

That a common term implies comparison does not need

to

be insisted on.

It

is

because things resemble

each other in certain of their attributes that we

by a

common name, and

ascertained except

some one. result of

Thus

this

by comparison a

call

them

resemblance could not be

common

at

term

some time and by

the compressed an indefinite number of comparisons, which lie

wrapped up

in

it,

like so

many

fossils,

is

witnessing to prior

ages of thought.

In the next product of thought, namely, the proposition,

we have

the result of a single act of comparison between

INTRODUCTION. For

two terms.

reason

this

13

others the proposition

among

has been called the unit of thought, as being the simplest

and most

direct result of comparison.

science the unit

nor the world is

Just as in social

not the individual on the one hand

is

at large

on

the other, but the state,

which

intermediate between the two, so in logic the unit

is

neither the term nor the inference, but the proposition,

which

is

intermediate between the two.

In the third product of thought, namely, the inference,

we have

a comparison of propositions. This need not be enlarged on at this point. For the present let us return to the 14.

to

much

product of thought.

first

The

nature of singular terms has not given

dispute, but the nature of

rise

common terms has What corre

been the great battle-ground of logicians. sponds to a singular term,

when

at least

easy to determine, for the thing of is

there to point to

like

man

to think

on

first

it

is

concrete, is

a

common

is

name term,

not so obvious as people are apt

hearing of the question.

term or class-name was known to mediaeval

logicians under the

the question

is

but the meaning of a

horse

or

A common

:

it

which

What

title is

of a Universal

a Universal

?

;

and

it

was on

that they split into

the three schools of Realists, Nominalists, and Conceptualists.

Here

are the answers of the three schools to this

question in their most exaggerated form Universals, said the Realists, are substances having an

independent existence in nature. Universals, said the Nominalists, are a

mere matter of

INTRODUCTION.

14

members of what we

words, the

common

thing in

call

a class having no

but the name.

Universals, said the Conceptualists, exist in the

mind

are the conceptions under which the

mind

alone.

They

regards external objects.

The

of pure Realism

origin

doctrine of

ideas

for

;

due

is

to Plato

and

Idealism, in this sense,

is

his

not

opposed to Realism, but identical with it. Plato seems to have imagined that, as there was a really existing thing corresponding to a singular term, such as Socrates, so there must be a really existing thing corresponding to the

common

term

existences.

But when once the existence of

man.

these general objects

is

For individual men

subject to growth, decay

of

man

is

swamp

admitted, they

and death

imperishable and

all

other

are fleeting and transitory

eternal.

whereas the idea It is

only by par

taking in the nature of these ideas that individual objects exist at

all.

Pure Nominalism was the swing of the pendulum of thought to the very opposite extreme ; while Conceptualism was an attempt to hit the happy

mean between

the

two.

Roughly

it

may

be said that the Realists sought for

the answer to the question

What

is

a Universal?

in

the matter of thought, the Conceptualists in the form,

and

A will

the Nominalists in the expression. full

answer to the question

What

is

a Universal

?

bring in something of the three views above given, Universal is

while avoiding the exaggeration of each.

A

INTRODUCTION. a

number of

things that are called

15

by the same name

;

but they would not be called by the same name, unless

under the same conception in the mind ; nor would they fall under the same conception in the mind, fell

they

unless

there

several

members of

similar

existed

actually

the

in

attributes

a class, causing us to regard

them

under the same conception and to give them the same name. Universals therefore do exist in nature, and not merely

mind of man:

the

in

dependent upon

but

existence

their

is

individual objects, instead of individual

objects depending for their existence

upon them.

Aristotle

very clearly, and marked the distinction between

saw

this

the

objects

common

corresponding to the

term

by

calling the

singular

and

to

the

former Primary and the

Secondary Existences. Rosinante and Excalibur are primary, but horse and sword secondary existences.

latter

15.

We

are each

being built

built

upon

itself into

The

have seen that the three products of thought

one stage

upon

in advance of the other, the inference

the

the term.

proposition, as the proposition

Logic

therefore

is

naturally divides

three parts. First Part of

Logic deals with the

Term

the Second Part deals with the Proposition

;

;

the Third Part deals with the Inference.

been proposed to add a fourth part called Method, which should deal with putting inferences to but not much has been gether into a systematic treatise It

has

:

done

in

that

Reasoning

direction.

really

falls

The

under

it.

treatment

of Trains

of

PART

I.

OF TERMS.

CHAPTER

I.

Of Terms as distinguished from 16.

A

TERM

so called because

is

In a proposition

of a proposition.

in a predicate

and end

:

there

is

we

other Words. is

the boundary

start

from a subject

it

nothing else in a pro

which is a mere sign of agreement position but the copula, or disagreement between the two. 17.

Hence

indicates that

it

it

appears that the term by

is arrived at

its

very

name

by an analysis of the pro

judgement or proposition that is the The proposition as true unit of thought and speech. terms which are the to in is a whole conception It is the

position.

prior

its

:

parts

but the parts must precede the whole in the

treatment. synthetic order of 18.

Only

All terms are words, but not

all

words are terms.

those words are terms which can be used by

them

selves as the subject or else as the predicate of a pro

position.

Such words are

called Categorematic,

which

TERMS AS DISTINGUISHED FROM OTHER WORDS. means

is

a predicate

it

test

simple

Can

to ask oneself

of what words

use this word as

I

All adjectives, participles,

?

and verbs are

a term and something more, involves the copula. Words which can only be

terms, though the verb since

A

predicable.

literally

are terms

17

is

used along with others to make up terms,

a proposition at

all, it

are conjunctions

and

is

e.g.

of/

very/

word does not enter

If a

are called Syncategorematic.

Of

Acategorematic.

this

into

nature

interjections, the vocative cases of

moods of

nouns, and the imperative and optative

verbs,

which are not used in making statements. From this point of view then a term may be defined as a word or collection of words which can be used by

enough

to say this, since

itself as

a predicate.

It is

any word which can be used as

a subject can also be used as a predicate. 19. In

grammar every noun

which

is

a separate

word

:

but

concerned with the thought rather than with the expression, it is indifferent whether a noun, or term (which is merely a noun as used in a proposition),

to logic,

is

one word or many. The latter are known In the following passage, many-worded names. taken at random from Butler s Analogy These several

consists of

as

observations, concerning the active principle of virtue

obedience to

God

s

commands,

obedience or resignation to His

and

are applicable to passive

we

will

find the subject

consisting of fourteen words and the predicate of nine. It is the

exception rather than the rule to find a predicate

which consists of a single word. in

English

often

consist

of

Many-worded names

clauses

introduced by the c

TERMS AS DISTINGUISHED

18

strict

That

that/ as

conjunction

conformity with

letters

nature

is

should be written in

true

often also of a

;

grammatical subject with a dependent clause attached to it,

He who

as 20.

with

We

fights

name is

interchangeably

noun/

or

A Name

and runs away. term

have used the word

a word or collection of words which serves

to recall or transmit the idea of a thing either in itself or

through some of

attributes.

its

A name or noun is either a substantive or an adjective. A Noun Substantive is the name of a thing in itself, i,

e.

without reference to

any particular

attribute,

e. g.

horse, bird.

A Noun because

it

Adjective

is

name which we add

a

possesses some

to a thing

particular attribute,

e. g.

lame,

grey, flying, singing.

Hence tributive.

noun

the It

adjective

includes the

is

called

in

an At

logic

participle which

is

a verbal

adjective.

The

verb as such

not recognised by logic, but

is

analysed into the copula and an attributive,

The 21.

When it

is

bird sings

an

= The

attributive

to

bird

e. g.

singing.

appears to be used as a

a grammatical ellipse.

owing Latin we say Boni sapientes sunt subject,

is

is

and

in

Thus

English

in

The

by the form in the one case, and by the usage of the language in the other, that men are signified. It is an

good are wise/ because inflexional

it

is

sufficiently declared

FROM OTHER WORDS. accident of language

how

can be used as

far adjectives

cease to be logical attributives the

They

subjects.

19

moment

they are so used.

There

22.

a

is

sense

which

in

become categorematic, namely, when as a word, to the neglect of

its

it

Very is

Greek by using the neuter

article

TO avOpuiros

Thus

in this case

known

was expressed

It

with a masculine or

the

word

man.

Univocal and Equivocal Words.

23.

A

e. g.

used simply

technically

as the supposilio materialis of a word. in

is

proper meaning.

we can say Very is an adverb. This sense means the word very.

feminine noun,

word may

every

Univocal

Word

has only one meaning,

e.

g.

jampot,

cyanide of potassium.

An

Word

Equivocal

has more than one meaning,

e. g.

Idealism.

gum, Most words are equivocal

Thus

minute

is

equivocal to the eye,

equivocal to the ear, and

and ear

to eye

mean

:

either to eye or ear or both.

with

the

ear

itself

is

I

or

eye

is

equivocal both

same pronunciation

it

may

organ of hearing or a spike of corn, or as

the

a verb, in old English to plough. It

is

usual to have terms divided

But an equivocal word

equivocal,

is

into

univocal and

two or more terms,

of which the definition in each case would be different.

Sometimes division.

analogous is added as a third head to the But employment by analogy is one of the ways C 2

20 TERMS AS DISTINGUISHED FROM in

which a word becomes equivocal.

for instance, is applied

in their

own

by analogy

OTHER WORDS.

The word

sweet/

to things so different

nature as a lump of sugar, a young lady,

Again, because the head is the highest part of man, the highest part of a stream

a tune, a poem, and so on.

is

called

by analogy

the head

functionary in a college.

;

as also

is

the highest

CHAPTER Of

the Division

BEFORE entering on

24.

necessary to advert for a

II.

of Things.

the divisions of terms

moment

to a division

it

is

of the

things whereof they are names.

By a thing is meant simply an object of thought whatever one can think about. The word is supposed by some

be etymologically connected with

to

as dinge in

German

think/

with denkcn, and res in Latin with

reri.

Things are

may

either Substances or Attributes.

Attributes

be subdivided into Qualities and Relations. Thing

Substance

Attribute

Relation.

Quality

A by

Substance

is

a thing which can be conceived to exist

itself.

Substances

body

is

are

either

material

a material substance;

substance.

or

the soul

immaterial. is

The

an immaterial

OF THE DIVISION OF THINGS.

22

Substances again are either Primary or Secondary.

This table

Table

An

Attribute

is

a primary substance.

is

a secondary substance.

a thing which depends for

is

upon

which cannot be conceived to hard,

A

its

existence

a substance, e.g. greenness, hardness, squareness, exist apart

from green,

and square substances. is an attribute which does not require more

Quality

than one

substance

for

its

The

existence.

which have just been mentioned are

attributes

qualities.

There

and squareness, if there might be greenness, hardness, were nothing in the universe but one green, hard, and square substance. A Relation is an attribute which requires two or more substances for 25. to exist

its

existence,

e. g.

likeness, nearness.

be conceived say that a substance can what is meant is that it can be conceived

When we by

itself,

to exist independently of other substances.

mean

to assert that substances

out of space and

We

do not

can be conceived to

exist

time, nor independently of attributes,

nor yet out of relation to a mind perceiving them. The which we are intuitively acquainted only substance with is

the Ego.

know

that,

are

only

we say

that

substances

by themselves, whereas

their existence

assertion

substances, so far as

collections

them,

therefore exist

Apart from

is

upon

this,

attributes that

can be conceived

attributes are

substances, the real

that

can be

it

is

only

to

dependent for

meaning of the

certain

conceived to

we

When

of attributes.

collections

of

exist independently,

OF THE DIVISION OF THINGS. whereas single attributes depend for others.

The

23

their existence

cannot be conceived apart from the extension, length,

upon

colour, smoothness, or hardness of a table

breadth, and

i.e.

the

thickness, whereas the whole cluster

of attributes which, as united by the mind, constitutes the table

can be conceived to

of other such clusters. if

exist altogether independently

We

can imagine a table to

exist,

the whole material universe were annihilated, and but

one mind

left

to perceive

we cannot imagine

it,

it.

since

Apart from mind however what we call the attributes

of a material substance are no more than the various

modes

in

which we find our minds

The above

division

affected.

of things belongs rather to the

domain of metaphysics than of

logic

:

but

it

is

indispensable basis of the division of terms, to which

now

proceed.

the

we

CHAPTER Of 26.

III.

of Terms.

the Divisions

Subject-term Division of terms accord-

Positive

Attributive

ing

Negative )

thought.

their

place

in

according to the kind of thing sig

Concrete Abstract

Term

to

Privative

nified.

/

Singular

according to Quantity in Extension.

Common

according to number of things involved

Relative

in the

Absolute Connotative

name.

according to number of Quantities.

,Non-connotative

Subject-term 27.

A

Subject-term

is

as a subject, c. g. Socrates,

An

Attributive

is

Attributive.

any term which can be used wisdom.

a term which signifies the presence

or absence of an attribute, Attributives

and

e.

g. wise,

unwise, not-wise.

can only be used as predicates.

They

OF THE DIVISIONS OF TERMS. we

contrivances of language whereby

are

a subject has a certain attribute.

This paper possesses

is

white,

we

25

indicate

that

Thus when we

say,

indicate that the subject paper

Logic however also signify the non-

the attribute whiteness.

recognises as attributives terms which

of attributes.

possession

Not-white

is

an

attributive

equally with white.

names of

Attributives are not

attributes,

but names

of the things which possess the attributes, in virtue of

Thus

our knowledge that they possess them. is

the

bute

name

of

whiteness,

all

white

the things which possess the

and

abstract quality, virtue,

virtuous itself,

is

attri

a name, not

of the

men and

actions

but of the

which possess it. It is clear that a term can only properly be said to be a name of those things whereof it

can be predicated. Now, we cannot intelligibly pre an attributive of the abstract quality, or qualities,

dicate

the possession of which

it

stance, predicate the term

of learning

:

but

we may

Varro and Vergil.

implies.

learned predicate

We

cannot, for in

of the abstract quality it

of the individuals,

Attributives then are to be regarded

as names, not of the attributes which they imply, but of the things in

which those

attributes are found.

however are names of things in a less direct way than that in which subject-terms may be the names of the same things. Attributives are names of Attributives

things

only in

names of horse

things

and

predication,

whereas subject-terms are The terms predication.

in or out of

Bucephalus

are

names of

certain things, in

OF THE DIVISIONS OF TERMS.

26

this case animals,

whether we make any statement about

but

the

become names of

the

them or not:

and

swift

When we

predicable of them.

Bucephalus was

terms

same things

fiery,

the

in

fiery

Horses are

say

terms

swift

only

of being

virtue

swift

and

or

fiery

as horse respectively of the same things of attributives as names function This Bucephalus.

become names and

the gram secondary sense is exactly expressed by not is attributive An noun adjective. matical term

in a

directly the

name

of anything.

in virtue of the possession attribute, or, in

some

It

is

a

name added on

by a given thing of a certain

cases, the non-possession.

be used as subjects, there used is nothing to prevent a subject-term from being as a predicate, and so assuming for the time being the

Although

attributives cannot

functions of an attributive.

a man,

we convey

attributes

to

the

When we mind

say

the idea

which are implied by the

Socrates was

of the same

attributive

human.

But those terms only are called attributives which can never be used except as predicates. This division into Subject-terms and Attributives may be regarded as a division of terms according to their in Attributives, as we have seen, are place

thought.

essentially predicates,

and can only be thought of

relation to the subject, whereas the subject for its

own

sake.

is

in

thought of

OF THE DIVISIONS OF TERMS. 28.

Positive, Privative,

27

and Negative.

This threefold division implies a preceding twofold division

Term

Positive

Non-positive

I

I

Privative It

Negative.

only of importance

is

as

to attributives,

applied

though may be extended to terms generally. A Positive term signifies the presence of an attribute, it

e. g.

wise/

A

full.

Negative term

attribute, e.g.

A

merely the absence of an

not-full.

not-wise,

Privative term signifies the absence of an attribute

a

in

signifies

capable

subject

of

possessing

it,

e.

g.

unwise,

in

meaning

empty V

Thus a

privative

term

stands

midway

between the other two, being partly positive and partly negative

negative in so far as

it

indicates the absence

of a certain attribute, positive in so far as the thing which

is

a nature as to be capable of possessing 1

The author

is

it

implies that

declared to lack that attribute it.

is

of such

A

purely

to find that the extension of

glad meaning which he gave in his Deductive Logic to the word privative/ has been adopted (not without acknowledgement) by Mr. Wclton, Vol.

I,

p. 83.

The name used

the absence of an attribute

might have been expected

to

to be confined to a term signifying

where

it

be present,

was once possessed or e. g.

blind.

OF THE DIVISIONS OF TERMS.

28

negative term conveys to the

mind no

dicated, but leaves us to seek for

things which

A

positive information

about the nature of the thing of which

at all

fail

among

it

it

is

pre

the universe of

to exhibit a given attribute.

privative term,

on

the other hand, restricts us within

The term empty

a definite sphere.

restricts

us within

the sphere of things which are capable of fulness, that is, if the term be taken in its literal sense, things which

possess extension in three dimensions.

A

and a negative term, which have the same

positive

matter, must exhaust the universe between them, e. g. white and not-white/ since, according to the law of

excluded middle, everything must be either one or the other.

To

say however that a thing

to say that the

merely Not-white

may be

term

white

is

is

not-white

inapplicable to

predicated of things which

possess extension as well as of those which do. pair of terms as

white

and

is it.

do not

Such a

not-white, in their relation

one another, are called Contradictories.

to

Contrary

terms

must

be

distinguished

from

con

1

Contrary terms are those which are most under the same head. Thus white and black opposed are contrary terms, being the most opposed under the tradictory

.

same head of

colour.

contraries, being the

Virtuous

and

vicious

again are

most opposed under the same head

of moral quality. 1

Called by Cicero

autem

hoc modo

:

disparata.

De

Inv.

I,

42

disparatum

quod ab aliqua re praepositione negationis separatur, sapcre et non sapcre.

est id,

OF THE DIVISIONS OF TERMS.

A

positive

and a

privative

either contraries, e. g.

wise

term

in the

and

unwise

same matter (

Words which

black

safe,

This

We

and of

danger

do so and

its

signifies not merely that there

thing, but that

questions

the case, for instance,

is

it

however are

thing involving

positively unsafe

being

Unhappy/ on

so.

is

talk of a

is

no

benefit to be derived

positively injurious.

for

to

the other hand, signifies

Similarly in Latin inulilis

the presence of actual misery.

from a

forms.

which connotes nothing more than

the absence of danger. positive

its

or

and

white

are positive in form are often privative in

meaning, and vice versa. with the word

one of

as

are

= foolish),

else the privative includes the contrary, e. g.

unwhite/ which includes

29

the

All such

grammarian or lexico For the latter it is

grapher, and not for the logician. sufficient to

know

that corresponding to every term which

signifies the presence of

some

attribute

there

may

be

imagined another which indicates the absence of the same attribute,

indicates

where its

it

might be possessed, and a third which whether it might be possessed

absence,

or not.

Negative terms proper are formed by the prefix or

non-, and are

mere figments of

logic.

We

not-

do not

in

practice require to speak of the whole universe of objects

minus those which possess a given of attributes.

attribute or collection

We

have often occasion to speak of things which might be wise and are not, but seldom, if ever, of all

things other than wise.

Every

privative attributive has, or

may

have, a corre-

OF THE DIVISIONS OF TERMS.

30

spending abstract term, and the same is the case with negatives: for the absence of an attribute is itself an attribute.

Corresponding to

corresponding term not-fulness.

The

to

it

Thus

not-white/ but

is

may

;

elements as well.

involves positive it

something more

is

Terms which, without being

besides.

is emptiness be imagined the

term always involves the

contrary of a given

contradictory, but

black

there

empty there

not-full

directly contrary,

involve a latent contradiction, are called Repugnant,

and

red

terms

All

blue.

attributes that exclude

e. g.

whatever which signify

one another may be called Incom

patible.

The preceding

division

is

based on what

known

is

as

the Quality of terms, a positive term being said to differ in

from a non-positive one.

quality

A

Concrete

and Abstract.

Concrete

29.

Term

the

is

name

of a substance,

e. g.

a man, this chair, the soul, God.

An

Abstract

whiteness

By

a

Term

is

the

name

of an attribute, e.g.

l ,

multiplication, act,

concrete thing

conceived of with

all its

is

purpose, explosion.

meant an

individual substance

attributes about

not confined to material substances.

A

it.

The term

spirit

is

conceived

1

Since things cannot be spoken of except by their names, there a constantly recurring source of confusion between the thing The Take for instance whiteness. itself and the name of it. is

attribute whiteness

is

a thing, the

word whiteness

is

a term.

OF THE DIVISIONS OF TERMS. of under

attributes

personal

as

concrete

as

is

31

plum-

pudding. Abstract terms are so called as being arrived at by

What

a process of Abstraction. will

templating a

number of

in

fix

it

common.

all

point, or points,

and

fix

or

which they have

number of

we may draw away our

their other qualities,

off,

their other characteristics,

in contemplating a

Thus,

cornered objects, all

some

only on

may draw

substances,

from

abstract, its attention

and

meant by Abstraction The mind, in con

is

be clear from a single instance.

it

three-

attention from

exclusively

upon

their

three-corneredness, thus constituting the abstract notion of

be performed equally well in the case of a single object but the mind would not originally have known on what points to fix its attention Abstraction

triangle.

may

:

except by a comparison of individuals. Abstraction too

may

well as substances.

be performed upon attributes as

Thus, having by abstraction already and so on, we

arrived at the notion of triangle, square,

may

fix

and so

our attention upon what these have in rise to

the

higher

abstraction of

thought becomes more complex, tion

on abstraction and

common, As figure.

we may have

attributes

abstrac

of attributes.

But,

however many steps may intervene, attributes may always be traced back to substances at last. For attributes of attributes

can mean

tence of attributes

at

in,

bottom nothing but the co-exis or in connexion with, the same

substances.

We

have said that abstract terms are so

called, as

being

OF THE DIVISIONS OF TERMS.

32

by abstraction

arrived at

:

but

must not be inferred from

it

by ab names would

terms which are arrived

this statement that all

were

If this

straction are abstract.

so, all

at

be abstract except proper names of individual substances. All

common

terms, including attributives, are arrived at

abstraction, but they are not therefore

Those terms only applied

to

human Socrates

is

are called abstract which cannot be

substances

are

by

abstract terms.

at

names of

a name.

man

The terms

all.

and

same substance of which

the

Humanity

a

is

name

only of certain

namely those which are shared names of concrete things then are concrete,

attributes of that substance,

by others.

All

whether they denote them individually or according to classes, and whether directly and in themselves, or in directly, as possessing

some given

attribute.

Since things are divided into substances and attributes, follows that any term which

it

is

not the

capable of being conceived to exist by

of a thing

must be an

Individual substances can alone be con

abstract term.

ceived to exist by themselves passions, and

name

itself

:

their qualities, actions,

all

inter-relations, all their states,

and

all

events

with regard to them, presuppose the existence of these All

individual substances.

names

therefore of such things

as those just enumerated are abstract terms. action,

for instance,

is

an abstract term.

there be action without an agent is

equally abstract for the

between abstract

action

and

act

?

The term The

same reason. is

The term

For how could act

also

difference

not the difference between

and concrete, but the difference between the name

OF THE DIVISIONS OF TERMS.

33

name of the corresponding product. Unless acts can be conceived to exist without agents they of a process and the

are as abstract as the action from which they result.

Since every term must be either abstract or concrete,

may be asked Are attributives abstract or The answer of course depends upon whether

concrete?

it

names of substances or names of tives,

it

must be remembered, are never

anything, in the

that

way

they are

But

attributes.

attribu

directly

names of

are

they are

subject-terms

;

only names of things in virtue of being predicated of them.

Whether an

attributive

abstract or concrete depends

is

the nature of the subject of which

When we

man

This

say

This act

say

being the

The

is

name

of a substance

the term

noble,

noble

based upon the kind of thing to

noble

but

:

is

is

when we

abstract, as

of an attribute.

division of terms into Abstract

reference

on

asserted or denied.

noble/ the term

is

name

concrete, as being the

it is

actual existence.

well as real substances.

and Concrete

signified.

It

involves

is

no

There are imaginary as

Logically a centaur

is

as

much

a substance as a horse.

30.

A the

Singular

Singular and Common.

Term

same sense

is

the capital of France,

A Common Term the

same sense

polis/

pen.

a

name which can be

one thing only,

to the

is

this

a

Paris,

John,

pen.

name which can be

to a class of things,

A common

e.g.

applied in

term

is

e. g.

applied in

metro

man,

also called General.

D

OF THE DIVISIONS OF TERMS.

34

In order that a term

number of

to a

be applied

is

it

things,

common

which are

attributes

may

in the

evident that

it

same sense

must

indicate

The term

them.

to all of

John is applicable to a number of things, but not in the same sense, as it does not indicate attributes, or, if it does,

When

they are different in each case.

name

is

applied

same proper thing, it becomes

more than one

to

the

ambiguous, but not common, being then more than one term.

Common

terms are formed, as we have seen already

( 29), by from the attributes

abstraction,

centrating

A

class

i. e. by withdrawing the attention which individuals differ and con

upon those which they have in common. need not necessarily consist of more than two

it

If the

things.

in

sun and

moon

were the only heavenly

bodies in the universe, the word still

be a

common

heavenly body

term, as indicating the attributes

would which

are possessed alike

by each. This being so, it follows that the division of terms into singular and common is as exhaustive as the preceding ones, since a singular term

a

common

whether the thing attribute ; nor does long as

it is

Since

common,

is

the

name

of one thing and

term of more than one. in it

question

matter

be

It

indifferent

is

a substance or

how complex

it

may

an

be, so

regarded by the mind as one.

every the

find their place

Subject-terms

term must thus be

members

either

singular

of the preceding divisions

under one or both heads of

may

fall

this

or

must one.

under either head of singular or

OF THE DIVISIONS OF TERMS. common

but attributives are essentially

:

Such names

as

green,

applicable, strictly in the

common

terms.

are

incongruous

gentle/

same

35

to

sense,

the

all

things

which possess the attributes which they imply. Are abstract terms then, it may be asked, singular or

To

common ? upon how in

one

this

we reply That depends The term virtue/ for instance,

question

they are used.

sense, namely, as signifying

general, without distinction of kind,

term, as being the

name

gentleness, and so on

being a

a

name which

it

is

a

in

a singular

strictly

but as applied

:

gene

justice,

common

term, as

same sense

applicable in the

is

class of attributes.

is

of one attribute

moral excellence

to different varieties of rosity,

moral excellence

Similarly the term

colour

to

in

a

one unvarying attribute possessed the by bodies, namely, power of affecting the eye, and in certain sense signifies

this

sense

various

it

a singular term

in

blue, green,

and every other to

becomes a common term a

higher

notion

may be

affected

is

it

term, being equally applicable to red,

abstraction

apply

but as applied to the

:

which the eye

common

evidently a

to

is

ways

is

colour.

attributes,

As soon the

as

we begin

higher

notion

in reference to the lower.

meant one which

a further process of abstraction.

is

The terms

By

formed by red/

blue/

from physical is at colour arrived abstraction from them, objects; by and contains nothing but what is common to all. It green/ &c., are arrived at by abstraction

therefore applies in the

common

term

in

same sense

to

each, and

relation to them.

D

2

is

a

OF THE DIVISIONS OF TERMS.

36

A

practical test as to whether an abstract term, in

given case, is

to try

being used as a singular or

is

whether the indefinite

plural can be attached to

name

but to talk of

:

numbers,

two, three, four/ &c., at

common

term.

the

Similarly

single attribute, admitting of

when

a

evidently using the

word

the

or

as a

it

denotes a

unity

no shades of

a writer begins to speak of

as the

admits of neither

number

once marks

term

any

term,

of the

article or the sign

The term number/

it.

of a single attribute of things,

of these adjuncts

common

distinction

but

:

he

the unities

for a class of things of

is

some

kind or other, namely, certain dramatical proprieties of composition.

The

division

of terms into singular and

based on their Quantity in Extension. be explained presently. 31.

common

This phrase

is

will

Proper Names and Designations.

Singular terms

be subdivided into Proper

may

Names

and Designations.

A to

a

Proper thing

Name in

is

a permanent singular term applicable

itself,

i.

e.

attributes; a Designation

irrespective

of

its

particular

a singular term devised for

is

the occasion, or applicable to a thing only in so far as

possesses some

Homer the Iliad

is

it

attribute.

a proper

name

this

;

man/

the author of

are designations.

The number

of things,

it

is

clear, is

infinite.

For,

granting that the physical universe consists of a definite

OF THE DIVISIONS OF TERMS.

37

number of atoms neither one more nor one less still we are far from having exhausted the possible number of All the manifold material objects, which are made things. the various combinations of these atoms, constitute

up by

separate objects of thought, or things, and the further

an

indefinite

mind has

power of conjoining and dividing

so as to furnish itself with materials of

these objects,

thought, and also of fixing

by abstraction

attention

its

attributes, so as to regard them as things, apart from

upon

the substances to which they belong.

This being

so,

only a very small

it is

number of

things,

which are constantly obtruding themselves upon the mind, that have singular terms permanently set apart to denote them.

Human

beings,

some domestic

divisions of time and place, to

them

in

have"

most languages, Easter,

January,

Ben-Nevis.

Belgium,

Besides

these,

John,

Mary,

Brussels,

the

abstract

all

and

proper names assigned (

e. g.

animals,

Grip,

Thames,

terms,

when

used without reference to lower notions, are of the nature of proper names, being permanently set apart to denote certain special

imagination,

attributes,

e. g.

indigestibility,

benevolence/

veracity,

retrenchment.

But the needs of language often require a singular term to denote some thing which has not had a proper name assigned to

and so

This

it.

limiting

it

is

effected

as to

make

by taking a it

given circumstances, to one thing only.

may

be effected

or the definite

in

common

applicable,

term,

under the

Such a

limitation

English by prefixing a demonstrative

article,

or by appending a description,

e.

g.

OF THE DIVISIONS OF TERMS.

38 1

this

a

name

proper

the last rose of summer.

the sofa,

pen/

unknown, or

is

for

may be had to a honourable member who spoke last

available, recourse

32. Collective terms

Collective

do not

common.

since every term

must

more than

only or of

A

Collective e. g.

things,

the

is

term which

regiment

is

to

The

a

is

is

not so

division

name

is

exhaustive,

of a group of similar

mankind.

Thus

Such a term may mankind is a

only to one group,

term which

is

applicable in the

different groups.

opposite of Collective

This

Terms.

applicable

common

many

the

one.

Term

flock, regiment,

same sense

c

be the name of one thing

be either singular or common. singular

e. g.

but one.

That

either

some reason un

designation,

under the same division

fall

with singular and

When

much

is

Distributive.

a division of terms as a distinction

between the uses of the same term.

Library

is

used

books which compose it, distributively of various collections of books, such as the Bodleian, collectively of the

Queen s Library, and so on. The distinction between use of a term

tributive

confusion

of the

When

said

it

is

two

The

is

is

the collective

and the

of importance, because

a

favourite

dis

the

source of fallacy.

read plays of Shakespeare cannot be

in a day/ the proposition meets with a different measure

of acceptance

according as

collectively or distributively.

its

subject

is

understood

OF THE DIVISIONS OF TERMS.

and

This key

A

name

latter the is.

collective singular

meant the name

of several considered

an individual term

a collective term

is

keys

distinguish between in

collective, by the former being

of one object, by the as one.

we may

singular terms

Among dividual

39

my

;

bunch of

but both are singular.

:

term

much

quite as

is

one thing as an individual term

is,

the

name

of

though the thing in ques

happens to be a group. A group is one thing, if we choose to think of it as one. For the mind, as we have tion

already seen, has an unlimited power of forming

Thus

things, or objects of thought.

mountain chain

in a

as

is

much one

though, physically speaking,

itself,

just as

the chain

itself

In the same

surface.

is

way

it is

its

own

a particular peak thing as the chain inseparable from

it,

inseparable from the earth

a necklace

thing as the individual beads which

is

compose

s

much one

as it.

We

have just seen that a collective term is the name of but every term which a group regarded as one thing :

is

the

name

term.

of such a group

London/

is

not necessarily a collective

for instance,

is

of objects considered as one thing. a collective term, whereas are.

Wherein then

lies

flock/

the

name

But

of a group

London

is

not

regiment/ and senate

the difference

?

It lies in this

and senate are groups composed of to a certain extent, similar, whereas

that flock, regiment,

objects which are,

London streets

and term

is

a group made up of the most dissimilar objects and squares and squalid slums, fine carriages

dirty faces, all

the

and so on.

members of

In the case of a true collective

the group will

come under some

OF THE DIVISIONS OF TERMS.

40

common name.

one

members of

the

common name,

A

An

the

a

name thing.

Absolute term

is

sheep/

under

the

Absolute.

given to a thing

name given

a

the group,

common name

and

some other

is

members of

group regiment and so on,

Relative

Relative term

the

the

soldier,

33.

reference to

all

come under

flock of sheep, all

Thus

wkh

direct

to a thing without

reference to anything else.

father,

veys

a

shepherd

is

are absolute terms.

to

to

to

Given one term of a

sheep/

ruler/

father

wife,

called the correlative,

relative of

Husband,

Husband con

are relative terms.

reference

direct

shepherd other

man

and

Hodge

e. g.

child/

relation, the

subject/

is

the cor

and conversely ruler of subject/

The

two terms are also spoken of as a pair of correlatives. The distinction between relative and absolute applies to attributives as well as subject-terms. like/ are instances of attributives

near/

Greater/

which everyone would

recognise as relative.

A

relation,

differing

it

will

be remembered,

from a quality

more substances than a

fact,

in

that

it

is

a kind of attribute,

necessarily involves

Every relation

one.

play a part.

A

relative

term connotes

from the point of view correlative

subject

other.

set of

bottom

substances,

Thus

facts,

at

this fact or facts

of one of the

from that of the imply the same

is

more substances

or series of facts, in which two or

ruler

its

and

looked at from

OF THE DIVISIONS OF TERMS. The

points of view.

opposite

garded from

rule

The names

and

subjection.

and

not themselves

are

of relations

Rule

terms.

series of facts itself, re

denoted by the corresponding

either side, is

abstract terms,

41

subjection

are not

two

relative

different

names with reference

things which receive their

to

one

another, but are the same fact looked at from opposite

points of view. are

names of two

Ruler

and subject/ on the other hand, each involving

distinct substances, but

This division then

a reference to the other.

on the number of things involved

to be based

A

and

Connotative

34.

Connotative term

is

may

be said

in the

name.

Non-connotative.

one which has Extension and

Intension distinct from one another.

A

Non-connotative term

only, or in

This

one which has Extension

is

which Extension and Intension coincide.

division of terms is

based on their possession of

one quantity or two. It will become intelligible when we have explained what is meant by the quantity of terms. 35.

A

term

is

The Quantity of Terms.

possessed of Quantity in two ways (1) in Extension;

(2) in Intension.

The Extension which

The which

it

of a term

the

number

of things to

the

number

of attributes

applies.

Intension of a term it

is

implies.

is

OF THE DIVISIONS OF TERMS.

42

To

man

take an example, the term

things, namely,

the

all

members of

have been,

are, or

extension.

But the term

and implies

ever will be:

man

applies to certain

human

the

this is

race that

quantity in.

its

has also a certain meaning,

certain attributes

rationality, animality,

and

a definite bodily shape, together with others which flow

from or are found conjoined with these attributes constitutes

The

its

:

the

sum

of these

quantity in intension.

between the two kinds of quantity term a is also coaveyed by a variety of possessed by which are here appended. expressions distinction

Extension

= breadth = compass = application = deno

tation.

Intension

= depth = com prehension = implication = con

notation.

Of

these various expressions,

plication their

a

more

synonym

which

Connotation

for intension.

a

It is

distinct

when it

it

is

intension

it

how

not quite exact as

the intension of a term

extension.

already note one thing before

We

and

Extension

usual.

possesses

another.

im

and

have the advantage of most clearly conveying

own meaning.

ever are

application

A

word must

can be said to connote

say then that a term connotes attributes

implies certain attributes at the

same time

that

applies to certain things distinct therefrom \ 1

By

the Schoolmen

the same sense in which

which

connotative

we

have used

was sometimes used in attributive, for a word

directly signifies the presence of an attribute

applies to a subject. said to be connoted

In this sense

and not the

it

was

attribute.

and indirectly

the subject which

was

OF THE DIVISIONS OF TERMS. The

man/ and

subject-term

butive,

its

They

attri

corresponding

human, have both extension and

from one another.

43

intension, distinct

But

are therefore connotative.

humanity, denotes the very collection

the abstract term,

of attributes which was before connoted by the concrete

man

terms,

human.

and

In

this

case,

therefore,

extension and intension coincide, and the term

non-

is

connotative.

The above remark must be understood terms become

common

denotes

red,

common

to those attributes.

Even when used

may be

said

to

green,

&c.,

possess connotation, to

some other

attribute

associated

Thus

Thus

colour is

an abstract term if

we

distinguish

which the name applies and

attribute

attribute

abstract

and connotes what

in a singular sense

between the

ence or necessity.

be limited

terms through the classification

of attributes, they become also connotative. blue,

to

When

to abstract terms in their singular sense.

therewith

whiteness

and connotes hurtfulness

by

experi

denotes a certain

to the eyes

and

also

extension.

Since or

all

terms are names of things, whether substances

attributes,

it

is

clear

that

all

terms must possess

extension, though the extension of singular terms

narrowest possible, as being confined to

is

the

one thing.

Are there then any terms which possess no intension ? ask this is to ask Are there any terms which have absolutely no meaning? It is often said that proper

To

names

are devoid of meaning,

and the remark

if,

in

OF THE DIVISIONS OF TERMS.

44

When we

a certain sense, true.

call

a being by the

name man/ we do so because that being possesses human attributes, but when we call the same being by the name, John, we do not mean to indicate the presence of any Johannine

We

attributes.

simply wish to distinguish

and language, from other beings of

that being, in thought

Roughly speaking therefore proper names are devoid of meaning or intension. But no name can be the

same kind.

entirely devoid of

which

fact,

is

indicate the sex

a

name

of the owner, the

proper names

mere

act of giving

to a thing implies at least that the thing exists,

whether in

fact or

thinghood small

For, even setting aside the

meaning.

not universally true, that

thought

implies what

it

;

we may

so that every term must carry with

:

amount of

call

some

intension.

another point of view however proper names

From

For when

possess more intension than any other terms.

we know

a person, his

name

calls

individual attributes with which

must be

far

are conveyed

we

up

by any the

who knows him

common

to our

attorney,

This however

the

term which can be applied

name John means more

than

all

and these

the attributes which

is

to a

conservative,

vestry-man, or any other term which

apply to him.

minds

are familiar,

more numerous than

Thus

to him.

or

it

person

scamp,

may happen

to

the acquired intension of

a term, and must be distinguished from the original inten sion.

than

Edwin and he

meaning.

or

she

:

Angelina later

at first signify

no more

on they may acquire a world of

While then the acquired intension of a proper

OF THE DIVISIONS OF TERMS. name may be

larger than that of

original intension

names, but

may

evident that family

is

it

amount of connotation from John with give

this

any other term,

its

be next to nothing.

we have been speaking

Hitherto

45

the

only of christening-

names have a

certain

For when we dub

first.

the additional appellation of Smith,

we do

not

second name as a mere individual mark, but

intend thereby to indicate a relationship to other persons.

The amount

of connotation

that

proper names

is

Let us take

an example the

Roman

for

be said

full

name

of a distinguished

Publius Cornelius Scipio Aemilianus Africanus

Here

minor.

can be conveyed by

very noticeable in the Latin language.

to

only the praenomen, Publius, that can

is

it

be a mere individual mark, and even

distinctly indicates the sex

of the

owner.

proper, Cornelius, declares the wearer of the

illustrious

further

gens

to

belong to

The cognomen, Scipio, member of a distinguished

Cornelia.

him

specifies

it

this

The nomen

as

a

The agnomen adoptivum indicates by adoption from one gens to another.

family in that gens. his transference

The second agnomen

recalls the fact

of his victory over

the Carthaginians, while the addition of the distinguishes title.

The name,

imply attributes.

same

itself

1 .

Homeric

epithets,

is

such as

A Roman 66) does not agree here. very strongly suggests, but does not But was not the name Gaius Julius Caesar

Mr. Welton (Vol.

name, according

the

instead of being devoid of meaning,

a chapter of history in 1

word minor

him from the former wearer of

I,

p.

to him,

given to a particular infant to indicate his possession of certain

OF THE DIVISIONS OF TERMS.

46

The

1

The

Cloud-compeller,

Earth-shaker

of intensive proper names.

are instances

of our

Many

own

family

names

are obviously connotative in their origin, implying

either

some personal

shank, Courteney

;

peculiarity,

Armstrong, Cruik-

e. g.

or the employment, trade, or calling of

the original bearer of the name, Smith, Carpenter, Baker,

Leach, Archer, and so on

Clark,

domain, or nationality, as French, Langley

or

;

De

Caen,

simply the

Davids,

Price,

a term its

Fitzgerald,

is

origin,

&c.

parent, as Jackson,

The

Macdonald, Apjohn, question however whether

connotative or not has to be decided, not by

but by

its

use.

We

have seen that there are

in a

rough sense, may be said

other kind of singular terms, namely designations,

We

31) are obviously connotative.

(

of descent from

O Connor,

some proper n,ames which, to possess no intension.

The

De Montmorency,

fact

some presumably more noteworthy

Thomson,

or else his abode,

;

cannot employ

even the simplest of them without conveying more or less information about the qualities of the thing which they are

used to denote. this

table/

When, for indicate we book/

instance,

the

speaker of the object in question.

we say

proximity

to

family

?

the

Other designations

have a higher degree of intension, as when we say attributes

this

the

Gaius to indicate his sex, Julius his clan, Caesar his proper name is never to be allowed to have a mean

If a

Welton ought rather to contend that a Roman proper name was not in the strict sense a proper name at all, since

ing, Mr.

it

to

might apply in the same sense generation any one of a particular sex, clan, and family.

after generation

OF THE DIVISIONS OF TERMS. minister

prime

present

of

honourable

the

England/

member who brought forward

47

motion

this

to-night.

Such terms have a good deal of significance in them selves, apart from any knowledge we may happen to possess of the individuals they denote.

We

have seen

no terms which

speaking quite

we may apply

purposes,

on

that,

are non-connotative

singular abstract terms

whether we

we cannot

on

coincide.

call the call

there are

the expression to proper names,

the ground that they possess

and intension

strictly,

but, for practical

:

the

no

latter

and

to

that their extension

ground

In the

intension,

case

it

is

indifferent

quantity extension or intension.

Only

connotation, because that implies two

it

quantities distinct

from one another.

denote a subject before

can

it

A

term must already

be said

to

connote

its

attributes.

Names

36.

The

of Homogeneous Substances.

terms which the student

difficult to classify are

such as gold,

air,

names

chalk,

of

probably find most

will

homogeneous substances,

milk,

sugar,

nitrogen,

snow,

Such terms have been variously called Substantial, not very happily however, Material, and Homogeneous

coal.

for these

names

are applicable to the things denoted

by

the terms, not to the terms themselves.

Names

of this sort present

of abstract terms. (i)

it is

some of

the characteristics

For

the intensive force that

minds when we use them

;

is

uppermost

in

our

OF THE DIVISIONS OF TERMS,

48

do not as a

(2) they

rule

admit of the plural or of

the indefinite article.

But although they are

like abstract terms,

not abstract, so that there

on

that

point.

According

no room

they are plainly for controversy

Are they then singular or common ? Bain 1 they are singular and

Professor

to

according to Mr. Keynes they are common. such a question cannot be argued in the abstract.

collective

Now

We

is

;

must take a

When we

words.

particular use

say

Oil

is

some one of

of

world

is

mean

much

that the specific gravity of

like to take is less

Now

oil in

less of

it

;

rather

any portion of

oil

If

when used when

so

case

1

we

it

you

general stands to this or that specimen of

oil

is

common

thus found to be a

as a subject, is

we

than that of an equal portion of water.

in the relation of a class to the individuals contained it.

the

oil in

lighter than the entire collection of water, which

obvious from there being so

is

we do

lighter than water/

not wish to assert that the entire collection of

these

much more

used as a predicate.

will

For

it

oil

under

term even

be found to be

in this particular

can use the indefinite article and the sign of the

Bain, Logic, Deduction, pp. 48, 49

Names

of Material

earth, stone, salt, mercury, water, flame

each

are singular. They denote the entire collection of one species of material.

The term

oil is classified by Jevons (Studies in Deductive Logic, Mr. Welton (Manual of Logic, Vol. I, 21) as collective. substantial terms as p. 6l) follows Dr. Venn in regarding a peculiar kind of collective terms. Minto (Logic, Inductive and

ch.

i,

Deductive, p. 59) argues in the same direction. view see Keynes (Formal Logic, third edit. pp.

For the opposite 9, 10, ifl).

OF THE DIVISIONS OF TERMS.

We

plural.

This substance

can say

But

these substances are oils/

which This

it

is

is

a milk

cow

is

or

milk and

not follow that milk

This

or a

is

is,

oil/ or

All

We

cannot say

a sugar/ in the same way as This is a plant. But it does

a

common

are not

sugar

of course,

an

is

us take instances in

not natural to speak thus.

we say This

The

let

49

singular

term, but

terms. it

is

individual rather than collective, since the continuity of

the parts of milk prevents us from regarding

separate

things

but

:

milk/

like

cow,

is

them as

applicable

any primary substance which possesses attributes, and is therefore as much a common

dislributively to

certain

term as in a

cow

1 .

The absence of

the sign of the plural

word, and the impropriety of using the indefinite

article

with

it,

are sure indications that the attention

concentrated upon

its

intension.

is

Whenever the extension

becomes of importance, the distinction between singular and plural reappears. A waiter will understand you, if you order three milks or an ice. The remark just made as to extension applies not only to these

concrete terms, but also to the abstract terms

which they resemble

(cp.

29).

Aristotle (Top. I. 7, 3) says that water from the same well differs from the ordinary case of individuals of the same species only in the higher degree of resemblance. 1

CHAPTER Of

IV.

Law of Inverse Variation of Extension and Intension.

the

37. IN a series of terms

which

fall

under one another

as the extension decreases, the intension increases, vice versa,

Take

and

for instance the following series

Thing Substance Matter I

Organism

Animal I

Vertebrate

Mammal I

Ruminant I

Sheep This sheep.

Here

the term at the top possesses the widest possible

extension, since

time

it

it

applies to everything.

possesses the least possible

But

at the

amount of

same

intension,

implying nothing more than mere existence, whether in fact or thought. On the other hand, the term at the

bottom possesses the greatest amount of intension, since it implies all the attributes of an individual superadded

LAW OF INVERSE

OF THE

to those of the class to is

which

it

VARIATION, ETC.

belongs

:

but

51

extension

its

the narrowest possible, being limited to one thing.

At each step which

is

in the descent

Summum

called the

we decrease

the extension

Thus by adding on

at the top,

the

individual,

to

genus,

by increasing the

intension.

to the bare notion of a thing the idea

we descend

of independent existence,

This process

stance.

from the term

known

is

as

to the

term

sub

Determination,

or

Specialisation.

Again, by withdrawing our attention from the individual characteristics of a particular sheep,

those which are

same

kind,

common

we

arrive

and

is

fixing

it

upon

with other animals of the

common

the extension

This process

Generalisation

it

the

at

Here we have increased intension.

to

known

term,

sheep.

by decreasing the

as Generalisation.

implies abstraction,

but

we may have

abstraction without generalisation.

The following example is useful, as illustrating to the eye how a decrease of extension is accompanied by an At each step of the descent here

increase of intension.

we

visibly tack

on a

fresh attribute

l .

Ship Steam-ship

Screw steam-ship Iron screw steam-ship British iron

1

This example

is

screw steam-ship.

borrowed from Professor Jevons.

E 2

OF THE LA W OF INVERSE VAR1A T1ON,

52

Could we see the

classes denoted

pyramid would be exactly

ETC.

by the names, the

inverted.

law of inverse variation of extension and intension must of course be confined to the inter-relations of a series terms of which each can be predicated of the other

The

of

until

we

arrive at the

bottom of the

to apply to the extension

The of

scale.

It is

not meant

and intension of the same term.

increase of population does not diminish the

baby.

meaning

PART OF

II.

PROPOSITIONS.

CHAPTER

I.

the Proposition as distinguished from

Of

other Sentences. 38.

ALL

are

propositions

not

but

sentences,

all

sentences are propositions.

Sentences

may

(3)

To To To

(4)

To make

(1) (2)

be used for a variety of purposes

ask a question

express a feeling

(2) (3)

;

a statement.

These various uses give (1)

;

give an order;

rise respectively to

The Interrogative; The Imperative The Exclamatory ;

>-

Sentence.

Indicative (4) It is

The cative

The

Enunciative

with the

last

] l

T

Potential

of these only that logic

is

proposition, therefore, corresponds

and Potential sentences of grammar.

concerned. to

the Indi

For

it

must

OF THE PROPOSITION.

54 be borne

in

mind

that

between a statement of

to-morrow

rain

is

as

logic

recognises

no difference

and a supposition.

fact

much

a proposition as

It is

may

It

raining

now. 39. sition,

Leaving the grammatical aspect of the propo it from the purely logical

we must now consider

point of view.

A

proposition

a judgement

is

is

a judgement expressed in words

a direct comparison

l ;

and

between two con

cepts.

The same

thing

be expressed more briefly by

may

saying that a proposition

is

a direct comparison between

two terms.

We

say direct comparison/ because the syllogism also be described as a comparison between two terms may but in the syllogism the two terms are compared indi :

rectly, or

40.

A

by means of a

third term.

proposition consists of three parts Subject,

Predicate,

Copula.

The Subject is that of which something is said. The Predicate is that which is said of the subject. The Copula is the sign of agreement or disagreement between the two. It

is

apparent from the definitions that the subject

thought of for

its

own

sake,

and

is

the predicate for the sake

of the subject. Plat. Phil,

38 E Kal \6yos

brj

-ytyovtv CVTUS o rurt Soaz/ (KaXov^tv.

CHAPTER Of THERE

41.

and one

are

the Copida.

two kinds of copula, one

to

expressed by some part of the

is

with or without the negative, or else

be,

wrapped up

The

for affirmative

for negative statements.

Materially the copula

verb

II.

in

some

inflexional

material form of the copula

an accident of lan

is

The

guage, and a matter of indifference to logic. boils is

here

For

may

is

it

a mere sign of agreement between the two

and conveys no notion of actual

terms,

kettle

form of expression as The kettle must be remembered that the word

as logical a

is

boiling.

is

is

form of a verb.

existence.

It

be used indeed with equal propriety to express nonwhen St. Paul says An idol is nothing.

existence, as

When known it

is,

the verb

in

grammar

to

be

as

expresses existence in

the substantive

when we

predicate as well as copula, as

is

which

may

be analysed,

if

we

fact,

In

verb."

this

it

is

use

God God is

say

please, into

existent.

42.

kinds

We

have laid

of copula,

logicians

down above

affirmative

have maintained

affirmative.

that there are

and negative

that

the

:

copula

but is

two

some always

OF THE COPULA.

56

What

it

then,

be asked, on

may

To

meaning of negative propositions?

this

view,

the

is

which the answer

an agreement be tween the subject and a negative term. When, for instance, we say The whale is not a fish, this would be interpreted is,

that a negative proposition asserts

to

mean The whale

in

Undoubtedly any negative proposition may be exhibited an affirmative form, since, by the law of excluded

is

a not-fish.

middle, given a pair of contradictory terms, wherever the

one can be asserted, the other can be denied, and vice

We

versa.

to

shall find later

on

that this principle gives rise

The only

one of the forms of immediate inference.

Which

question then can be, legitimate form of

suppose not-fish

do

is

that

we

the

is

the agreement of

and

natural

seems

It

expression?

assert

more

simpler

whale

to

with

by implication only, and that what we directly between whale and

to predicate a disagreement

the positive attributes connoted by

fish.

For

since

not-

must apply to every conceivable object of thought except those which fall under the positive term fish, to fish

say that a whale

a

is

not-fish

is

to say that

we have

whale throughout the whole universe of a limited minus portion; which is only a more being, that it is not to be found in that clumsy way of saying still

to search for

portion.

Again, the term its

in

intension or in its

intension,

not-fish its

what

it

must be understood

extension.

connotes

is

If

it

either in

be understood

simply the absence of

the positive qualities which constitute a fish, a

meaning

OF THE COPULA, which

is

tion.

We

equally conveyed by the negative form of proposi

gain nothing in simplicity by thus confounding

assertion with denial.

taken

57

in

If,

this

extension,

on the other hand, it is to be involves the awkwardness of

supposing that the predicative power of a term resides its

in

extensive capacity.

We kinds

therefore

recognise predication

and negation

affirmation

as

being of two

corresponding to which

there are two forms of copula. 43.

On

that there

the other hand, other logicians have maintained are

kinds of copula, since the copula

many

must vary according to the various degrees of probability with which we can assert or deny a predicate of a subject. This view

is

known

technically

as the doctrine of

The Modality of It

may

the Copula.

be maintained that the division of

plausibly

propositions into affirmative and negative tive

is

not an exhaus

one, since the result of an act of judgement

mind

always to lead the denial, but to leave

it

more or

in

less

is

P, or S

not

doubt as to whether

the predicate applies to the subject or not.

saying simply S

is

to a clear assertion or a clear

is

not P,

we may be

Instead of led to

one

of the following forms of proposition

The

S

is

possibly P.

S

is

probably P.

S

is

certainly P.

adverbial expression which thus appears to qualify

the copula

is

known

as

the

mode.

OF THE COPULA.

58

When we

The accused may be

guilty

a proposition of very different force from

The

say

and yet the terms appear

guilty,

to

We

obvious answer.

many

seem

is

Wherein

be the same. In the copula

then does the difference lie?

there are as

we have accused

the

is

therefore driven to admit that

different kinds of copula as there are

different degrees of assurance with

which a statement may

be made.

But there

may

is

another way in which modal propositions Instead of the mode being attached to

be regarded.

the copula,

it

may be

considered as

itself

constituting the

predicate, so that the above propositions would be analysed

thus

The

That S

is

That S

is

That S

is

subject here

is

P P P

itself

is

possible.

is

probable.

is

certain.

a proposition, of which

predicate various degrees of probability.

In

this

way

we the

and negative is For wherever before we had a

division of propositions into affirmative

rendered

exhaustive.

doubtful assertion,

we have now an

assertion of doubt

fulness.

If degrees of probability

the copula,

much more

can thus be eliminated from

so can expressions of time, which

may always be regarded as forming part of the The sun will rise to-morrow may be analysed sun

is

going to

rise

to-morrow.

belongs equally to the predicate.

predicate. into

The

In either case the tense It is often

an awkward

task so to analyse propositions relative to past or future

OF THE COPULA.

59

time as to bring out the copula under the form not

:

but fortunately there

is

no

since, as has

been said before

of copula

a matter of indifference to

is

in affirmative propositions the

subject and predicate agreement, e. g. Most It

is

because

all

is

or

verbs, as

gone

mere juxtaposition of

the

all.

may

we

Moreover the awkwardness of is

a mere accident of language.

say with equal propriety

in the analytic

;

Sol orietur

while past time

form

in the case of

Caesar est in Galliam profectus

may

also

deponent Caesar

is

into Gaul.

The is,

form

Indeed

often sufficient to indicate their

Sol est oriturus eras

be expressed

logic.

haste, worst speed, ^aXcTra ra /caXa.

expression just alluded to

eras

41), the material

(

is

propositions are not affirmative that

require a copula at

In Latin we

or

is

necessity for so doing,

copula then

as indicating

may always be

regarded as pure, that

mere agreement or disagreement between

the two terms of the proposition.

CHAPTER the Divisions

Of 44.

III.

of Propositions.

True

/

Division according to Quality of Matter.

False

Simple

1 i

,

Complex

Conjunctive

(

>

.

\

according to Form.

[

Disjunctive

I

Verbal Proposition

according to Matter.

<

Real

Universal

Definite

j

Particular

>

according to Quantity.

Indefinite

Affirmative

according to Quality of Form.

Negative

True and 45.

A

proposition

False.

when

true

is

its

things

of which

separated in is

proposition All truth

propositions. it is

they are

nature. false

A

1

tlvai

are

this

is

put

together

not the

the

or

case the

1 .

concept

false.

an imaginary one.

is

When

and falsehood

not true or

names

terms are put

same way as

together or separated in speech in the

confined to judgements and

is

may be

Horse But

is

real or imaginary,

a real concept,

centaur

by

413 A TI ou TO TO. OVTO. 8o6.(iv Ar. Met. 0, 10, i a\r)dtvft p.lv 6

Plat. Rep.

StaipuffOat nal TO ffvyted/jifvov

itself is a\t]Gev(ii

but

centaur neither Soxti

ffoi

OF THE DIVISIONS OF PROPOSITIONS. true nor false.

or enunciate

emerges,

e. g.

It is not until I form some judgement some proposition that truth or falsehood I met a Centaur yesterday, as I came

Again, an inference

round Carfax. but

invalid,

it

not true

is

perfectly valid inference

and lands us

To

6l

or

which

false.

starts

may be valid We may have

from

false

or

a

premisses

in a false conclusion.

be true or

a proposition

;

false is the

Quality of the Matter of

to be affirmative or negative

is

the Quality

of the Form.

Simple and Complex. 46.

A Simple

proposition

makes

a statement directly

Sis P. S It is also called

A some

Complex

is

not P.

Categorical.

proposition

makes a statement

subject to

condition.

Hence

the

complex proposition

is

known

also

as

Con

ditional,

Every complex proposition consists of two parts (1) Antecedent, (2)

Consequent.

The Antecedent ment

is

is

the condition under which the state

made.

The Consequent is The antecedent is consequent

in

the statement

made

so called because

subject to

the order of thought, but

precede or follow

it

in the

it.

precedes the

it

it

order of language.

may

either

OF THE DIVISIONS OF PROPOSITIONS.

62

If the wind drops Thus we may say indifferently have We shall we shall have rain/ or rain, if the wind

drops.

There are two kinds of complex proposition or Hypothetical. (1) Conjunctive If

A

is

If the

B,

C

is

D.

wind drops, we

shall

have rain.

(2) Disjunctive.

Either

A

is

B

C

or

Either rain must

is

come

D. or the crops will be spoilt.

The conjunctive proposition may also assume the forms

A B is. A is B, A is C. If A is C, B is C,

If

is,

If

The disjunctive proposition may also assume the forms Either

A

A

B or C. A or B is C.

is

or

B

is.

either

Either

As

is

the double nomenclature

a scheme

is

may

cause some confusion,

appended.

Proposition

Complex

Simple

(Conditional)

(Categorical)

Conjunctive (Hypothetical)

Disjunctive.

In the older writers the places of Hypothetical and

OF THE DIVISIONS OF PROPOSITIONS. Conditional

are

being the

Hypothetical

interchanged,

63

The one word

genus and Conditional the species.

is

merely a translation of the other. In the conjunctive proposition the truth of the ante

cedent involves the truth of the consequent.

In the disjunctive proposition the

of the ante

falsity

cedent involves the truth of the consequent.

The

a conjunctive with a

is

proposition

disjunctive

negative antecedent.

A

Either

is

B

These points

When,

for

C

what

is

D=

we say

is

it

that the sky will

If

made

be

will

instance,

catch larks,

Not

or

that

fall,

A

is

not B,

clearer

If the

we

by

sky

really

and not

we

is

D.

illustration.

we

falls,

mean

that

C

shall

to assert? shall

catch

larks, but a certain connexion between the two, namely,

that the truth of the antecedent involves the truth of the

consequent.

Hence

this

form of proposition

called

conjunctive/ because in

sequent

is

what

is

we

really

say

meant

Jones is either a knave or a If you do to be asserted is

not find Jones to be a knave, you a fool.

aptly

conjoined to the truth of the antecedent.

Again, when fool/

is

the truth of the con

it

Here

it

is

may be

sure that he

is

the falsity of the antecedent which

and the proposition is known as disjunctive/ because the truth of the con sequent is disjoined from the truth of the antecedent. involves the truth of the consequent

The complex

proposition then

;

is

a proposition about

which they stand It may be to one another as regards truth and falsity. propositions,

showing

the relation in

OF THE DIVISIONS OF PROPOSITIONS.

64

condensed

into a simple proposition of

which the terms

are themselves propositions. If the

sky

we

falls,

Sky-falling

And

shall catch larks

=

lark- catching.

is

generally

A

If

is

B,

C

is

D=

A being B are cases of C being D. convenience we shall express as follows

Cases of

Which

for

AB

is

CD.

Ultimately then every proposition

simple form

Hence

S

is,

or

is

is

reducible

to the

not, P.

upon the form of expression, be founded on the simplicity or com

this division turns

and may be

said to

plexity of the terms employed in a proposition.

Sentences.

Compound 47.

from a

The

A

Complex proposition

Compound

Sentence

is

to

be distinguished

1 .

merely a contrivance of language for abbreviating expression, in which several distinct state1

latter

is

This was called by the Stoics di cu//a

avuirrrrXfyiJitvov.

They

divided diw/xaTa into airXa and ov\ dn\a, and among the latter distinguished the avvrmntvov (conjunctive) as If it is day, it is As it is day, it is light, the the TrapaavvriniJ.tvov, as light, It is both day and light, the Stt^tvypevov as ffvnTTcn\tyn(t>ov, (disjunctive), as (causative), as

Either

it

is

day or night,

and the amwSes

The Antecedent day, it is light. was called by them TO &p\t>nevov or TO ^yov/j.fvov and the Con See Diog. Laert. VII, 68-73. sequent TO Because

\fjyoi>.

it

is

OF THE DIVISIONS OF PROPOSITIONS. combined

are

merits

a

into

sentence.

single

65 In a

complex proposition there appears to be more than one subject or predicate or both, while in reality there is

only a single statement

as

we have

and

;

this

statement refers,

connexion between two pro

seen, to a certain

Thus when we say Either the Carthaginians were of Semitic origin or argument from language is of positions.

no value in

in

we have two

ethnology,

propositions only

appearance.

In a compound sentence on the other hand there logically,

is

and not merely grammatically, more than one

Thus when we

subject or predicate or both.

say

The

Jews and Carthaginians were Semitic peoples and spoke a

Semitic

we have

language/

four

propositions

com

pressed into a single sentence for the sake of brevity.

Verbal and Real. 48.

A

Verbal proposition gives the definition or part

of the definition of the subject.

A

Real proposition states some fact about the subject which is not contained in its definition.

To

say that a triangle or that

sides

propositions.

proposition the is

former

;

it

To

is

a

a figure or that

is

three-sided

say that

it

has three angles

has three all

verbal

is

a real

for this fact, although equally obvious with

and

directly

indicated

no part of the concept

sides.

it

figure are

figure

by the etymology, contained by three

Of THE DIVISIONS OF PROPOSITIONS.

66

be

will

It

and

real

seen

the

that

between verbal

distinction

assumes

propositions

a

precise meaning of terms, that

to say, a

is

of

knowledge

the

knowledge

of definitions.

To

who does

not

terms a verbal proposition

will

a

person

mation as a at

To

real one.

know

the

meaning of

convey as much infor is in mid-heaven

The sun

say

noon, though a merely verbal proposition,

information to a person

who

will

convey

being taught to attach

is

We

a meaning to the word

noon.

without

meaning, that a merely verbal

their

knowing

proposition appears a revelation to there are people is

who

a cat, though in

class

The

cat.

use so

many terms

minds.

many

Thus

are surprised to hear that the lion

its

definition

reason of this

lion is

referred to the

is

that

we know

material

objects far better in their extension than in their intension, that

is

to say,

we know what

things a

name

applies to

without knowing the attributes which those things possess in

common. There

is

to inform us is

nothing in the mere look of a proposition whether it is verbal or real the difference ;

wholly relative

of the subject.

to,

When we

tion of a triangle that sides,

statement

the

and constituted by, the

it

becomes a

proposition

Man

For though rationality,

have accepted as the defini a figure contained by three

of the

three angles

is

is

real

further

there

progressive

is

fact

proposition. is

his progressiveness is a

still

definition

it

has

Again,

the

that

a real proposition.

consequence of his

no actual reference

to progressive-

OF THE DIVISIONS OF PROPOSITIONS.

67

Man

ness contained in the usually accepted definition,

is

a rational animal.

we were

If

all

tion,"

in

under the term

to admit,

verbal proposi

statements which, though not actually contained

the definition of the subject, are implied

by

it,

the

whole body of necessary truth would have to be pro nounced merely verbal, and the most penetrating con clusions of mathematicians set down as only another way of stating the simplest axioms from which they started.

For the propositions of which necessary

truth

is

composed

are so linked together that, given one, the rest can always

But necessary

follow.

that

is,

the

by

mind

contingent truth,

which

truth,

which

arrived at a priori,

is

own working,

s

is

quite as real as

arrived at a posteriori, or

is

by

the teachings of experience, in other words, through our

own

senses or those of others.

The

process by which real truth, which

deductive, E.g.

arrived at a priori

is

The mind

is

other than

is

known

as Intuition.

sees that a figure with three sides cannot

but have three angles.

Only such verbal

as

facts

must

then

propositions

state

expressly

be

considered

mentioned

in

the

and

real

definition.

The same propositions

and

is

distinction

as

between

verbal

conveyed by the expressions Analytical or and Explicative Ampliative/

Synthetical,

judgements.

A up

verbal proposition

the subject into

its

is

called analytical, as breaking

component

notions. F

2

OF THE DIVISIONS OF PROPOSITIONS.

68

A

real

Among

called synthetical, as attaching

is

proposition

some new notion

to the subject.

verbal

the

scholastic

logicians

were known as

Essential,

because what was stated in the

definition

was considered

be of the essence of the subject,

to

known

while real propositions were

Definite

A

49.

is

quantity

An

Definite

propositions

and

as

Accidental.

Indefinite. is

proposition

one

which

of

the

determined as either Universal or Particular.

Indefinite proposition

one of which the quantity

is

undetermined.

is left

The

quantity of a proposition

is

determined by the

quantity in extension of its subject.

A

Universal proposition

used in

explicitly

A

is

An

in

which the subject

is

in

which the subject

is

whole extent.

its

Particular proposition

explicitly used

one

in part of

is

one

extent.

its

Indefinite proposition

one

is

apparent whether the subject

which

in

used in

is

its

it

is

not

whole extent

or not. All

men

are

Some men

liars.

Men are liars. When the value

r>

particular. is

Hence

-

t

i

r

Definite.

Particular.)

liars.

Indefinite.

of

some quantity

of prudent calculation highest.

Universal.)

,.

are

the

that

it

should not be put

indefinite

proposition

Sometimes however the nature of

such as to determine

it

is

it

varies,

as universal, e.g.

a rule at

ranks

its

as

the matter

when we

say

OF THE DIVISIONS OF PROPOSITIONS.

have their three angles equal to two right known that all triangles are meant. But

Triangles

is

it

angles,

on the other hand when we say

we

not

are

69

Apprentices are

mean

to

supposed

there

that

idle,

no such

is

thing as an industrious apprentice, but only that idleness is

the prevailing characteristic of the class.

The word mean some

some

we were

If

only.

Some cows chew

conversation

in

is

often taken

to

to inform a person that

he might reasonably infer but th s our belief that there are some that do not the cud,

:

When

implication never attaches to the word in logic.

Some men

we say to

be denying that

may

are sinners/ all

have reason to

some men,

true of

we must not be taken

are included under sin, but

know

e. g.

ourselves,

and not wish to go

beyond our evidence in the statement. particular proposition then does not, indefinite,

we

the proposition holds

that

The

definitely

any more than

the

exclude the possibility of the universal being

true.

The

definitely particular proposition,

means one

in

part of the

Whether

which a statement

subject

this

part

is

it

is

be

it

remembered,

explicitly

made

of

means

itself

that and nothing more. determined or undetermined

does not enter into the question. Here again we are of word the the some/ which ambiguity perplexed by is

to

sometimes equivalent to the Latin quidam, sometimes ah qufs but this difference, though important in

other

:

respects, does

proposition.

not

affect

the

dcfiniteness

of the

OF THE DIVISIONS OF PROPOSITIONS.

70

The ticular

division of propositions is

based upon

into universal

and par

their Quantity.

Singular and General. 50. Universal

propositions

may be

subdivided into

Singular and General.

A

is

Singular proposition

one of which the subject

is

one of which the subject whole extent.

is

a singular term.

A

General proposition a common term taken in (

John

Singular \ Virtue

General

A

5 1

a

is

its

man. beautiful.

is

All men A

is

are mortal.

.

All virtues are praiseworthy.

singular proposition

is

necessarily universal

1

in the

sense in which that term has been defined, because the subject, if

used

The most

at

all,

must be used

in its

whole extent.

usual signs of generality are the words

all/

p. 274) maintains that the singular the extreme form of the particular. Materially But it is a case where extremes meet, this cannot be denied. 1

Father Clarke (Logic,

proposition

is

and the singular proposition coincides formally with the universal. In the proposition Caesar is famous in history the predicate is asserted of each and all the individuals comprised under the It subject (Ibid. p. 272). as This stone is valuable.

is

the subject is the class-name part of it any more than the

otherwise in such a proposition it may be maintained that

There

stone,

some

and that

this

forms no

forms part of the subject did, it would no longer be

of a particular proposition for, if it true to say that the predicate does not apply to the whole of the ;

subject.

OF THE DIVISIONS OF PROPOSITIONS. each/

every,

in affirmative,

and the words

no/

71

none/

not one, &c., in negative propositions.

There

is

another use of the word

general/ in which

means one

a general truth or a general proposition

that

holds true in the main, though not absolutely without It

exception. sense, that

men

is

a general

will

buy

Affirmative 51.

This division

Form, which

is

truth, for

instance, in this

in the cheapest market.

and Negative.

based on the Quality of the commonly called simply the Quality of is

a proposition. It is

should be noticed that the quality of a proposition

not affected by the quality of

mined by

the copula.

All not-S

terms, but

its

is

not-P

is

is

deter

an affirmative

proposition.

The Fourfold Division of Propositions. 52.

By combining

the division according to quantity

with that according to quality

we

obtain four kinds of

propositions, namely,

Universal Affirmative. Universal Negative. Particular Affirmative.

Particular Negative. Indefinite

All S

No

S

is

P.

P.

is

Some S Some S is

propositions have

they can be brought under this

(A) (E)

is

P.

not P.

(I)

(O)

be quantified before This is classification.

to

a matter of convenience, and does not imply any slur

OF THE DIVISIONS OF PROPOSITIONS.

72

on the character of the

indefinite proposition,

which

as legitimate a form of expression as any other. function

is

to

make

strongly in

Men

its

a statement without raising the ques

This

tion of quantity.

is

done when the subject

what we wish

used

is

Thus when we say

intensive capacity.

are fallible/

is

Its

to lay stress

the attributes of humanity involve that of

on

that

is

fallibility.

If

any one asks the awkward question whether they always and necessarily involve it, he forces us to quantify our subject.

When is

taken with this proviso, the above classification

exhaustive.

form

may

heads.

be,

Every proposition, no matter what its must fall under one or other of these four

For every proposition must be

or particular, in the sense that the

be known to be used

in

its

either universal

must

subject

either

and

whole extent or not;

any proposition, whether universal or

particular,

must

be either affirmative or negative, for by denying modality of the copula we have excluded everything intermediate

between downright assertion and denial. This classifica tion therefore may be regarded as a Procrustes bed, into which every proposition

is

bound

to

fit

at

its

proper

peril.

These four kinds of propositions are represented spectively by the symbols A, E,

The vowels A and

I,

I,

re

O.

which denote the two

affirmatives,

E and O, occur in the Latin words affirm o and aw which denote the two negatives, occur in the Latin word ;

nego.

OF THE DIVISIONS OF PROPOSITIONS.

73

Extensive and Intensive Propositions. 53. The same proposition may be read in extension or in intension or partly in one and partly in the other.

Thus when we say Cows are ruminants/ the may be understood to mean that the smaller is

contained in the larger class

attributes

cow

or that the

ruminant,

which make up the concept

proposition class

cow

contain, or

are accompanied by, the attribute of chewing the cud. the former case the proposition sion, in the latter case

natural

mode

As

in intension.

wholly

of interpretation

a

is

In

read wholly in exten

is

a rule the

mixed one, the subject

being used in extension and the predicate in intension. We have just seen that in the indefinite proposition the attention

on the

concentrated

is

But

a term.

never be wholly

lost

When we

sight of.

we mean things which possess bovine, with which

we

might be puzzled as ruminants

predicate their

strictly

there will

The

bovine

be found

are

to

all

how of

cows

of us familiar, though

we mean

cows,

or

attribute

fact that the subject

talk of

certain attributes called

extensive force of the subject

by the

capacity of

we

When we

to express them.

attributes,

the

intensive

a subject the extension can

in the case of

that

among

superadded thereto, of chewing

the cud.

marked

language

is

must always be a

in

substantive.

The

predicate on the other hand is generally an adjective, but may be a substantive. This substantive is usually

employed

in

its

necessarily the

His name

is

intensive

case.

John

capacity,

For example, the

predicate

though in is

this

is

not

the proposition

not

intended to

OF THE DIVISIONS OF PROPOSITIONS.

74

convey the idea of any attributes at all. What is meant to be asserted is that the name of the person in question is that particular name, John, and not Zacharias or Abi-

nadab or any other name that might be given him. Let it be noticed that when a proposition is read extension

when

it

the

predicate

read in

is

the

intension

Viewed

predicate.

externally,

ruminant

breadth of the notion,

the

contains

subject,

contains

subject

or

in

reference

cow

contains

internally, or in reference to their depth,

cow

in

whereas

to ;

the the

viewed

contains

ruminant.

Exclusive and Exceptive Propositions. 54.

of

all

An

Exclusive proposition denies

but the subject,

None It is its

generally an

the predicate

e. g.

but the good are happy.

E

proposition with a negative term for

subject

No No An

not-good not-S

is

men

are happy.

P.

of the Exceptive proposition affirms the predicate

whole subject with the exception of a certain All is lost save honour. All but It is

an

A

two of

All not-S

is

exclusive proposition

e. g.

are taken.

for proposition with a negative term

All not-honour

An

my pawns

part,

its

subject.

is lost.

P.

may

always be turned into an

of exceptive by changing the quality

its

predicate.

OF THE DIVISIONS OF PROPOSITIONS. No

one but the sage is mad.

No One is

not-S

is

sane

P

is

= Every one =A11 not-S

of these propositions

we

75

but the sage

is

not-P.

shall find later to

be what

called the obverse of the other.

The the

exclusive proposition

word

The good

e. g.

alone,

The word

may

except

sometimes introduced by

is

alone are happy. occur either in an exceptive

or in an exclusive proposition.

except Second Peter are

All the Catholic Epistles

Exceptive.

genuine.

No

one

except

would

yourself

have

done

this.

Exclusive. It

a nice question what

is

the exact

is

veyed by the exclusive proposition. but the good are happy, are are

happy

we

We certainly seem

?

meaning con

When we

None good men do this, especially if we say

asserting that to

throw the proposition into the form The good alone are happy. It then appears to convey two statements at once (1)

The good

(2)

No

The than

first

it is

one

else

is.

statement however must not be taken for more

worth.

good men

are happy.

are

If quantified,

happy.

it

only amounts to

Some

This proposition follows as a

All happy men are good, consequence from which may be deduced from the original proposition

formal

it.

is

;

good men are happy does not follow from But what if the Pessimist be right, and no one at all

whereas

All

or can

be happy?

In that case the

first

statement

OF THE DIVISIONS OF PROPOSITIONS.

76 is

we have none

not true, but

the less asserted

If

it.

we

use terms which have nothing real to correspond to them,

our statements

The

will naturally turn

out to be unreal.

manner seems

exceptive proposition in like

convey two

statements.

distinct

except two, condemned the prisoner

Two

(1)

of the judges did not

to

All the judges,

E.g.

equivalent to

is

condemn

the prisoner.

(2) All the rest did.

The

exclusive proposition, though generally E,

confined

animals I I

is

form.

that

to

men

All

alone

are

is

not

rational

an exclusive proposition so is the form of O Some S only is P. This last is the ;

which implies

proposition of

we say

stance,

common Some of

closed at nightfall/ are

left

we

conversation. the

for in

When,

gates into the park are

are understood

to

mean

Some

open.

Tantologoits or Identical Propositions. 55.

A

Tautologous or Identical proposition affirms

the subject of itself

Every I

am

A

is

A.

I.

Here we have the proposition at the minimum of meaning. Sometimes a proposition of this form has more mean ing than appears at

which

first

signifies that a

sight, e. g.

man

is

accidents of birth or fortune

;

A man

s

a

man/

not to be judged by the

What

have written/ in which the implication will not be altered.

I is

have written,

I

that the writing

CHAPTER Of

of Terms.

the Distribution

THE

50.

IV.

of this subject

treatment

falls

under the

logic, because distribution is not an attri bute of terms in themselves, but as used in a proposition.

second part of

A

term

used in

whole extent,

its

things of which

When known

About

it is

known

with reference to

i.e.

to be

all

the

is

not

a name.

used only in part of

is

it

it is

to be used in the whole,

57.

no

when

said to be distributed

is

it is

its

extent, or

called undistributed.

the subject of a proposition there can be

difficulty.

If the proposition

If

the

universal, the subject

is

is

proposition

particular,

the

is

distributed.

subject

is

un

distributed. If the proposition

taken

as

is

indefinite,

unless

undistributed,

the subject has to be

the

matter

determines

otherwise. 58.

The

predicate

however cannot be disposed of

quite so easily. If the proposition to

is

affirmative, the predicate has always

be taken as undistributed, on the same principle as

the subject of an indefinite proposition is

nothing ruminants

to is

determine true,

if

its

(

quantity.

sheep chew

49).

All

the cud.

For there sheep are Its

truth

is

OF THE DISTRIBUTION OF TERMS. not affected by the or

question whether sheep are

of the animals that possess then we may say that All S all

this attribute.

P

is

some

Generally

may mean, when

taken in extension

some

(1) All

S

is

(2) All

S

is all

P.

P.

As we do not know which take

it

On

at its

lower value.

is

hand the predicate of a negative pro No S is P, when taken always distributed.

extension, can only

whole of P.

the

from

means, we are bound to

the other

position in

it

mean

S

that

is

excluded from

For suppose it were only excluded would be some P left which is S,

part, then there

and consequently some S which

No

the original assertion.

is

P, which contradicts

horses chew the cud

would

were admitted that a single animal which chews the cud is a horse. Hence the proposition must be upset,

if

it

be interpreted 59. in

The

to

mean No

difference

an affirmative and

horses are any cud-chewers. between the use of a predicate

in a negative proposition

illustrated to the- eye as follows.

may mean

either that

A

are exactly co-extensive.

is

To

included in

say

B

All

or that

may

be

A is B A and B

OF THE DISTRIBUTION OF TERMS.

A

As

\ve

to

B

cannot be sure which of these two relations of is

when we know say

B

meant, the predicate

undistributed, since a term

To

79

that

No A

it is

is

is

held to be distributed only

used in

B

has to be reckoned

its

however

whole extent. is

to say that

A

falls

wholly outside of B, which involves the consequence that

B

falls

wholly outside of A.

Let us

now apply

same mode of

the

illustration to the

particular forms of proposition. There are, from the point of view of extension, two things which may be meant when we say Some A is B

(i)

That

A

and

one another,

common,

B

that

e. g.

is

are two classes which overlap to say,

Some

have some members

cats are black.

in

OF THE DISTRIBUTION OF TERMS.

8o

That B

(2)

inverted

is

way

wholly contained of saying that

all

A, which

in

B

is

A,

e. g.

is

an

Some

animals are men.

we cannot be

Since

sure which of these two

again reckoned undistributed. above are all that I ever means, but

the predicate

The

is

meant,

is

it

is

not

incompatible with the two relations of terms exhibited in the diagrams already given for A. All that

but

it

is

O

ever means

is

one of these two things

not incompatible with the relation of

total

ex

clusion represented in the diagram for E.

From

60.

the

above considerations we

elicit

the

following

Pony Rules for

the Distribution of Terms.

1.

All universal propositions distribute their subject.

2.

No

particular propositions distribute their subject.

OF THE DISTRIBUTION OF TERMS.

81

3.

All negative propositions distribute their predicate.

4.

No

affirmative

propositions distribute their pre

dicate.

The will

distribution or non-distribution

of the subject,

it

be observed, depends upon the quantity, that of the

upon

predicate

The above of the edifice

the quality, of the proposition.

four rules are the basis is

When

attention.

They

built.

upon which

the rest

therefore merit particular

applied to the four forms of proposition,

they lead to the following results

A E

distributes

its

subject only,

distributes both subject

and predicate,

I distributes neither subject

O These

distributes results

help to the

its

nor predicate,

predicate only.

have been embodied

in

the

following

memory

As Eb In Op: but

it

is

on

the four rules themselves, rather than

application of them, that

it

is

important

on the

to fix the attention.

CHAPTER Of 61.

the Quantification

of the Predicate.

ATTEMPTS have been made

build logic

on another foundation.

maintained

were

recent times to

in

Sir William

although the predicate

that,

in language, this

V.

must always be quantified

it

we should

so,

require eight,

Hamilton

not quantified

is

in thought.

If

instead of four,

For hitherto we have taken account

forms of proposition.

only of the quantity of the subject in determining the quantity of a proposition, but on this view we should have to take account equally of the quantity of the predicate.

The

eight propositions which result, together with the symbols

which have been devised for them, are as follows

A

[.All Sis

all P.

All S

some

2.

4.

is

some

P.

5.

Some S

is all

P.

S

is

any

S

7.

Some S Some S

1 8.

Some S

6.

I

is

(u).

P.

No No

3.

It

is

evident that

it

(A).

P.

(E). (77).

(Y).

is

some

is

not any P.

is

not some P.

P.

(I).

(O). (<>).

is

the second of the

positions which represents the original A,

with the rule that their predicate

The

(

No

in

above pro accordance

affirmative propositions distribute

60).

third represents the original E, in accordance with

OF THE QUANTIFICATION OF THE PREDICATE. the

All

rule that

distribute

negative propositions

83 their

predicate.

The

sixth represents the original

No

the rule that

I,

in

accordance with

affirmative propositions distribute their

predicate.

The

seventh represents the original O, in accordance

with the rule that their

All negative propositions

distribute

predicate.

Four new symbols are required, predicate as well as that of the

if

the quantity of the

subject be taken

into

account in the classification of propositions. These have been supplied, somewhat fancifully, as follows

The first, All S is all P/ which distributes both subject and predicate, has been called u, to mark its extreme universality.

The

No

fourth,

S

some

is

P,

is

contained in E, and

has therefore been denoted by the symbol connexion with E.

The

Some S

fifth,

All S

the second,

is

is

all

P,

is

17,

to

show

its

the exact converse of

some P/ and has

therefore been

denoted by the symbol Y, which resembles an inverted A.

The

is

eighth

contained in O, as part in whole, and has

therefore had assigned to 62.

some

The

attempt

curious results.

proposition.

to

it

the symbol w.

quantify the predicate leads to

Let us take, for instance, the u

Either the sign of quantity

all

must be

understood as forming part of the predicate or not. If it is then the u All P S is all seems to not, proposition contain within

itself,

not one proposition, but two, namely, G

2

OF THE QUANTIFICATION OF THE PREDICATE

84

All S all

u

All

P

But

S.

is

on the other hand

if

understood to form part of the predicate, then

is

When

not really a general but a singular proposition.

is

we

P and

is

men

All

say,

we have

are rational animals,

a true

general proposition, because the predicate applies to the subject

mean

and not

distributively,

are

the predicate

rational animals,

all

affirmed of every

But when we say All men no longer applies

man.

individual in the class,

What we

collectively.

may be

rational animal

that

is

For

to the subject distribuiively, but only collectively. is

obvious that

all

means

that

is

cannot be affirmed

rational animals

What

of every individual in the class, man. the class,

man,

the proposition

co-extensive with

is

The same meaning may be

class, rational animal.

it

the

ex

pressed intensively by saying that the one class has the attribute of co-extension with the other.

Under both

the

head of u come

and

subject

Homer

propositions in which

all

are

predicate

was the author of the

singular

Iliad,

Virtue

e. g.

terms, the

is

way

to happiness.

The

proposition y conveys very

No

the mind.

A

S

is

proposition in the

animals All

that

may men

be

the

77.

to

same

No

known

Even though

is

little

information to

compatible with the

No men

true, while at the

same time

men,

some

are it

is

true

for instance, are

as kangaroos.

proposition conveys

For w

is

matter.

are animals.

the particular animals

The

some P

still

less information

than

compatible, not only with A, but with u.

All

men

are

all

rational animals/

it

is still

OF THE QUANTIFICATION OF THE PREDICATE. 85 Some men are not some rational animals for no human being is the same rational animal as any other. Nay, even when the u is an identical proposition, w will

true that

:

given

still

hold in the same matter. rational animals

all

All rational animals are

animals are not some others. position therefore 63.

That

is

last

one another

in point of extension

be gathered from the following scheme

or not

four ordinary propositions, A, E,

whole ground between

1

i

(2), I

On

si ed.

and

O

this point

95.

,

:

must either

entirely coincide

and

many

the fact that they outrun the possi

Two Terms

The

rational

form of pro

almost wholly devoid of meaning.

ble relations of terms to

may

This

the eight forms of proposition are too

may be argued also from as

Some

but, for all that,

:

them,

to both (3) I

am

A

and

I,

O, cover the

corresponding to (i)

(4),

and

E

to (5).

indebted to Mr. Keynes, Formal Logic,

OF THE QUANTIFICATION OF THE PREDICATE.

86 It

is

and

(2), (4),

(5),

The

64.

on occasions

useful

certainly

Y

from A, possibly also be regarded as of no

from

I

:

w

v?

77

u

fairly

satisfied

is

covers the ground of

is

that

it

by

all.

reduces every affirmative

an exact equation between

As a consequence every

admit of simple conversion, that

and

distinguish

chief advantage claimed for the quantifica

proposition to predicate.

to

and w may

practical value.

while

tion of the predicate

subject

but

predicate

transposed

change term which

will

be

explained

proposition would

to say, of having the

without

The forms

in the proposition.

(a

is

subject and

its

any further

also of Reduction

later

on)

would be

and generally the introduction of the quantified simplified predicate into logic might be attended with certain ;

The

of

the

mechanical

advantages.

however

not to invent an ingenious system, but to

arrive

at

is

a

true

admitted that in subject the

is

used

ground

analysis

object

of thought.

the ordinary form

in extension

for the doctrine

Now,

logician

if

it

of proposition

be the

and the predicate in intension, is at once cut away. For, if

the predicate be not used in

its

extensive capacity at

all,

we plainly cannot be called upon to determine whether it is used in its whole extent or not.

CHAPTER Of 65.

A

A

Heads of

the

PREDICATE

predicable

The Heads

is

is

VI. Predicables.

that which

is

said of a subject.

anything which can be said of a subject.

of Predicables are the different kinds of

things which can be said of a subject.

The Heads

of Predicables then are

meant

as a classifi

cation of the different relations in which the predicate

can stand to the subject in a proposition. Hence the treatment of them falls under the second part of logic.

These

relations are

reckoned as

five

Genus, Species,

Difference,

Property,

Accident. G6.

We

will

begin by defining these terms as they

are used at the present day, and will afterwards inquire into their original

Genus

is

meaning.

a larger class viewed in

smaller class contained under All Species

is

larger class

men

relation

to

some

it.

(genus) are animals.

a smaller class viewed in relation to some

under which

it

is

contained. (species)

Some animals

are

men.

OF THE HEADS OF PREDICABLES.

88

Under

the

first

two heads,

it

be observed, we have

will

a predication of classes, expressed by a noun substantive

under the remaining three we

a predication

;

of

expressed by a noun adjective.

attributes,

is

Difference (differentia]

mark

have

the attribute or attributes which

from a genus.

off a species

(difference)

Men from

all

man

supposed to be distinguished other animals, which are called brutes.

this attribute

By

are rational. is

N.B. Genus + Difference

Definition.

(difference) (genus)

Men is

Property

are rational animals.

an attribute which

definition of a term, but

A

generic

is

property

is

not contained in the

which follows from

it.

one which follows from the

genus. (generic property)

Men It is as

A

men

animals that

specific

have appetites.

property

is

have appetites.

one which follows from the

difference.

Men It is in virtue

of

studying

(specific property) are capable of studying logic.

of their rationality that

logic.

A

cow has no

men

are capable

aptitude

in

this

direction.

Accident

is

an attribute which

is

the definition of a term nor follows

neither contained in

from

it.

OF THE HEADS OF PREDICABLES. An

inseparable accident

members of

is

one which belongs

89

to all the

a class. (inseparable accident)

Animals which chew the cud divide the hoof.

A

accident

separable

some members

one which belongs only to

is

of a class. ^separable accident)

Some Blackness

is

animals have four legs.

a separable accident of

man, an inseparable

accident of coals.

The

distinction

accidents

An

between

also applied to

is

inseparable accident of an individual

belongs to

it

at all times, e.g.

of a particular person that he

A

and

inseparable

separable accident

belongs to

separable

an individual.

it is

is

is

one which

an inseparable accident

a native of India.

of an individual

is

one which

only at a certain time or times, e.g.

it

is

a separable accident of a particular person that he

is

it

visiting India.

Again is

made

it

of

employed

an inseparable accident of

is

steel

it is

;

this

a separable accident that

pen it is

that

it

being

in writing.

The

which belong to anything may be under the two heads of essential distinguished broadly and non-essential, or accidental. The essential attributes G7.

attributes

are those which are contained the definition. can,

in

the

Now

nature

inseparable accident.

belong invariably

it

may be

in,

questioned whether there

of things, be

For

to all the

if

an

or which flow from,

such a thing as an were found to

attribute

members of

a class,

we should

OF THE HEADS OF PRED1CABLES.

90

suspect that there was

and the

it

attributes

we should

is,

and

essential

some causal connexion between

which constitute the

suspect

the

our ignorance,

may

whenever

is

it

found that an attribute all

has been observed

It

so.

be

term

the

the

members of

class, without there being any apparent reason

should do

to

question

be retained as a cloak for

does, as a matter of fact, belong to

a

definition, that

Nevertheless

not accidental.

inseparable accident

in

attribute

which have horns chew the cud.

that

why

it

quadrupeds

As no one can adduce

any reason why animals that have horns should chew more than animals which have not, we may

the cud any

chewing the cud an inseparable accident If there really is no reason why, of horned animals. call

the fact of

then

an inseparable accident, and belongs

is

it

domain of uniformities which are not

to the

results of causa

tion.

68.

It

must be noticed

that

we have not

really

defined the term

accident/ not having stated what

but only what

is

it

not.

it

is,

has in fact been reserved

It

as a residual head to cover any attribute which

is

neither

a difference nor a property. 69.

In dealing with

the

above

classification

it

is

important to bear in mind that it assumes an acquaintance essences of things, that is, in modern language,

with the

assumes a knowledge of definitions. Take this away and the whole thing becomes unintelligible. When, for

it

instance,

Man

is

we say Man progressive,

is

an animal,

there

is

Man

is

rational,

nothing in the nature of

OF THE HEADS OF PREDICABLES. statements

these

stantival

themselves,

form of the

first,

indeed

except

It is

a tacit reference to the accepted definition of

becomes evident

to us.

Similarly

from merely hearing the word of a triangle the fact of is

three

having

its

its

is

only by

man

that

we cannot know that the

fact

difference,

and

triangle

sides

is

There having three angles a property. than another it in one rather way

a reason for defining

but,

if

we

:

are unacquainted with

show us

that

difference

and the three-sidedness

there

it,

three-corneredness

the

nothing to

is

may

not be

the property.

two attributes are so connected together is

sub

the

to tell us that the predicate

genus, difference, or property respectively.

this

gi

that,

the

For these whichever

postulated, the other will necessarily follow. 70. If the

above

five

terms were presented as an

exhaustive classification of the possible relations in which the predicate can stand to the subject in a proposition,

there are certain obvious criticisms that might be made. (1)

No In

notice

is

predicate

is

such

a

taken

of

case

the

in

which

the

a singular term.

proposition

as

This

man

is

John,

we have

neither a predication of class nor

attribute,

but merely the identification

term with another as

applying

to

of

of one

the

same

object.

(2)

It

is

defective

tion.

For

(a] there

is

even as regards general predica

no room

for

the

case

in

which the

OF THE HEADS OF PRED1CABLES.

92

a mere synonym for the subject,

is

predicate e-g-

A (b)

a camelopard

;

no account of those

takes

it

is

giraffe

dication

which

in

class

forms

and

of

pre are

attribute

combined.

Under which of

the five heads

the following propositions

Man Man

fall

would the predicates

in

?

is

a rational animal.

is

a featherless biped.

(3) It altogether omits particular propositions.

we were

71. But, if

propositions and

to

to confine predication to universal

common

terms, and were to grant

must always take the form of class or and never of both, the classification would then

that a predicate attribute

admit of defence by logic. For when the predicate is a class, the term predicated is called a Genus, if the subject

individual

an

be a

itself 1

class,

When, on

.

attribute,

it

may

or

a

Species,

some

which case

it is

1

Here

it

will

an

be

the other hand, the predicate

members

of the

called the Difference, or

connected with the

attribute

or not connected with

it

is

be either the very attribute which

distinguishes the subject from other class, in

if

it,

i.e.

it

same

may be

definition, i.e. Property,

Accident.

be observed that

we

are using

species

in a

In which it was defined above. the language of the Schoolmen it is now species pmcdicabilin, whereas before it was species snbjidbilis. different sense

from that

in

OF THE HEADS OF PREDICABLES. These

may be

results

exhibited

in

the

93

following

scheme Predicate

Class

Such

criticism

Attribute

however and such defence would be

equally beside the mark, the fact being that the five terms

have been applied

to a

purpose for which they were not

originally intended.

72.

The Five Words of Porpliyry. The Heads of Predicables, as usually

given, are

not taken from Aristotle, but from the Introduction of

who wrote some

Porphyry, a Neo-Platonic philosopher, six centuries later. this

short

But Porphyry

work was not

to

s

own

give

a

object in writing

of

list

Heads of

Predicables, but merely to supply an easy introduction to

Aristotle s

property, accident.

difference,

predicates,

thing.

the

which

predicates,

Had

he

begins

like

his object

and

Categories

explaining the five

generally by

singular

on

treatise

words

to

logic

genus, species,

These are

five

general

by distinguishing

from

man,

this

Socrates,

this

then been to classify the relations

OF THE HEADS OF PREDICABLES.

94

which a predicate can stand to a subject in a proposi tion, he would certainly have given us six and not five heads. But in point of fact he had no such object. in

73.

On

the metaphysical

questions connected

with

what was afterwards known as Realism and Conceptualism

Porphyry

professes is

assumption throughout with real differences

not

that

to

classes

enter exist

mark them, which

to

but

:

in

his

nature

in

no way

depend upon our minds. 74.

The

later writers

of substance

of Porphyry

tree

1 ,

is

a device added by

but in the text of the treatise the category

is

arranged as follows Substance

Body Living body

Animal Rational animal

Man

Socrates

Here Substance

Plato is

the

&c.

summurn genus or genus generais always genus and

lissimum (yevLKtararov yeVos), which

never species, as having no class above 1

.

Man

is

an

For the most graphic picture of the tree see Father Clarke

Logic, p. 2

2 it

1

s

8 1.

We might suppose

that thing or being could be predicated substance, but Porphyry, following Aristotle, regards each of the ten categories as a distinct smnmum genus. He will not

of

allow that

being

is

predicable of them

all in

the

same

sense.

OF THE HEADS OF PREDICABLES. infima species

(ct

SiKo miTov c*8o?),

which

and never genus, as having no

The

is

95

always species

classes below

real

intermediate terms are Subaltern Species and

it.

Genera

KOL ye vT/), being species in relation to the above them, genera in relation to those below

(vTrdX\7)\a classes

f"8f)

them.

Hence

used in two senses

is

species

For any class in reference which it falls.

(1)

For the lowest

(2)

Genus

(yeVos)

relative, that

is

(eTSos)

are

so

essentially

Porphyry does not attempt to define one

His

definition of

genus

is

that

predicated in the category of substance of several

things different in kind that

is

species

under

class in reference to individuals.

and Species

apart from the other.

which

to a higher class

which

is

(

= species),

and

his definition

of

arranged under the genus, and of

which the genus is predicated in the category of sub stance. But infima species is defined as that which is predicated in the category of substance of several things

numerically different.

This kinds in

last definition is

as

metals

presents so feel

A

such natural

homogeneous

substances,

many

no bar

heterogeneous

substance,

differ

only

like

man,

points of individual difference, that here

tinguishes between is

class

to further subdivision.

75. Neither of

It

to

which the members of the same

numerically.

we

most conformable

and other

course did Porphyry. specific

and ordinary

But he

dis

differences.

only the former which mark off real kinds.

Add

OF THE HEADS OF PREDICABLES.

96

and you get man, a being different species from a horse but add blackness or a snub nose man, and you get a difference indeed, but not such as

rationality to animality,

in to to

:

mark a new Since

species.

may form

attribute

any

things in the loose sense is

used by Porphyry for attribute generally.

differences are

and

divided

and

between

a difference

of the term, Difference (Sta^opa)

into Separable,

In this sense

such as motion

and Inseparable, such as snub-nosed, rational and irrational. Inseparable differences are subdivided into Accidental and Essential, hook-nosed and snub-nosed being instances of health

rest,

hook-nosed

disease,

and

the former, rational

and

irrational of the latter.

Essential differences in the definition

rational

those

are

which are contained

of a thing, or which follow from

Thus

it.

and mortal and the being receptive of knowledge The first two are con

are essential differences of man.

tained in the definition, the third

Porphyry It

s definition

man

of

is

follows from

it.

For

a rational, mortal animal.

follows from his reason that he

is

receptive of

know

ledge.

Further we are told that essential differences do not

admit of degree, whereas accidental do.

more

or less black, or

more or it

less rational.

be accepted, what

more This

is

to

A

being

may be

or less snub-nosed, but not is

a hard saying, but, unless

become of the

species fixed

The

great law of continuity is fatal to this ancient realism, which has indeed all along been a protest

by nature

?

against the flux of matter.

If nature s species

run into

OF THE HEADS OF PREDICABLES. one another,

it

would seem realism must be interpreted

as a theory of types, by approximation from which the place of a sensible thing of nature has to be determined.

On

Divisive.

recedence

to or

in the hierarchy

are subdivided into Constitutive

Essential differences

and

97

the whole then

we

get this scheme

Difference I

Inseparable

Separable

Accidental

Essential I

Constitutive

Divisive.

To illustrate the distinction between constitutive and divisive An animal differences, let us take the case of animal. is

a

tive

sensitive

living,

substance;

mortal or immortal.

irrational,

is

it

Here

are differences which constitute

and

rational

irrational,

differences

which divide

of a genus

become

added

to the

it.

mortal

also

and

immortal

are

divisive differences

constitutive of a species.

Thus, when

genus animal, rational rational irrational

irrational

+ + + +

= man = god = brute mortal immortal = mortal

immortal

?

from adding a fourth species such individuals as Cerberus and Pegasus. It Porphyry

or

sensi

whereas

animal,

and

But the

rational

living

refrains

to contain is

H

curious

OF THE HEADS OF PREDICABLES.

98

towards the end of the treatise he substitutes

to note that l

for

angel

as falling along with

god,

man

rational/

difference

Essential differences, whether constitutive are alike specific. butes,

and as

whereby

that

we

A

under the

it is

or divisive,

This means that there are

classes are

marked

off

real attri

from one another,

our business to find these, instead of dividing

please.

Difference Specific or Essential

is

two

defined in

ways, as (1) that

whereby the species exceeds the genus,

man (2) that

exceeds animal by rational

which

is

+

mortal

e.g.

;

predicated in the category of quality

of several things different in kind, e.g. rational is

76.

so predicated both of

Both genus

man and

god.

and difference form part of the

essence (ovo-ia) of a thing, but in different ways, the genus to the being analogous to the matter and the difference form.

As

a sculptor carves a statue out of a block of

marble by imposing form upon it, so from the rough matter of animal nature carves out the species man (

by adding thereto is

rational

called the Material

and mortal.

Hence genus

and difference the Formal part of

the essence. 1 Porphyry (A. D. 263), the great opponent of Christianity, is himself suspected of Christian antecedents. Simplicius (A.D. 500), another Pagan writer, speaks in the same way of angelic or It does not divine virtues (Comment, in Epict. Ench, cap. viii).

therefore

seem necessary

tampered with.

to

suppose that the text has been

OF THE HEADS OF PREDICABLES. The genus

77.

If

differences.

could

the

it

potentially contains all the divisive

did not potentially contain them,

species

99

get them

If

?

whence

actually contained

it

them, the law of contradiction would be violated.

Of Property

78.

are four (tStov) there

kinds recognised

by Porphyry (1) that which belongs only to

not to e.g.

all

medicine or geometry

sense of (2) that

man

one

though

species,

members of it,

the

is

a property in this

;

which belongs

to a

whole species, though

not to that only, e.g.

being a biped

is

a property in this sense of

man; (3) that

which belongs

that only,

e.g. the

to a

though not

in old

growing grey

in this sense of

man

and

species,

and

to

age

is

a property

;

(4) that which belongs to a that only,

whole

at all times,

whole species, and

to

at all times,

e.g. a capacity for laughter is a property in this

sense of man.

This us

last is the strict

call

it

sense of the word

for distinction

proprium, or

79. Accident (o-u/^/Je/^Kos)

may be

is

Let

property.

peculiar property.

defined as

that

which

there or not without destruction to the subject.

Accidents are divided into Separable and Inseparable.

To

be asleep

ness

is

is

a separable accident of an animal.

Black

an inseparable accident of a crow or of an

H

2

OF THE HEADS OF PREDICABLES.

100

Ethiopian

a mere accident, for

still it is

:

we can conceive

a crow to be white or an Ethiopian to change his skin.

Accident

defined negatively

also

is

as

which

that

is

genus nor difference nor species nor property,

neither

but which always exists in the subject.

This account of Porphyry s teaching on the five words may fitly be concluded by the neat summary of it which was made by the Scholastic 80.

subject of the

1

that

Philosophy

every

common

individuals, signifies either their their essence, or If If

term,

in

relation

to

whole essence, or part of

something joined to their essence. whole essence, it is Species.

signifies their

it

signifies the material part of their essence,

it

is

the formal part of their essence,

it

is

it

Genus. If

it

signifies

Difference. If

it

essence, If

it

essence,

signifies it

is

Property.

signifies it

something contingently joined

to call that the essence of a thing

accepted definition, we 81.

to their

Accident.

is

Nothing could be more satisfactory than only knew what the essence of a thing was.

its

their

something necessarily joined to

In spite of

its

may

still

name

the

which

is

this,

if

we

we agree

If

contained in

use the classification. subject of

Heads of

Predicables was treated by the Schoolmen under the

first

part of Logic, as dealing with the relations of terms to

one

another, in themselves rather than in the proposition. 1

See Father Clarke

s Logic, p. 175.

OF THE HEADS OF PREDICABLES.

Aristotle s

Predicables.

himself really did aim at the object

Aristotle

82.

Heads of

IOI

which we have considered

to

be proper to the Heads

of Predicables, namely, to classify the relations in which a predicate can stand to a subject.

room

before referred to

His

70).

(

Accordingly there

is

mixed forms of predication

in his division for the

list

*

contains four heads,

namely,

Genus

(yevos),

Definition (opos),

Proprium

(tStov),

Accident

At

83.

he gives only three, saying that every

first

proposition in a syllogism, whether premiss or conclusion, signifies either

genus, property, or accident.

Property

here a vague term covering any predicate which vertible

with

definition

the

By

subject.

splitting

and proprium 2 he reaches the ,

this

fourfold

is

up

is

con into

list

Genus f Definition

Property \ |

Proprium

Accident. 84. 1

But what,

Top. 1.4,

2

i,

2;

it

may

5,

differ-

i.

Proprium is used here the same word tStov is used sense.

be asked, has become of

for

convenience.

in the

wider and

With

Aristotle

in the

narrower

OF THE HEADS OF PREDICABLES.

102

ence, which

surely a legitimate predicable

is

?

The answer

absorbed into genus. say Man is an animal or Man is rational we are equally referring him to something wider than himself. is

that

Whether we

it is

f

Species too

be there

to

absent from the

is

When

?

list.

known

infimae species

an accident,

it is

e.g.

;

Some

when

extensive with things.

And

subject or not,

its

if

it

is

predicated of a class,

may i.e.

be seen to be

easily

every predicate must

For

a right

animals are horses.

85. Aristotle s classification

exhaustive.

it

on the assumption

indistinguishable from genus, except

of

But has

predicated of an individual,

either

be co

predicable of the same

the two terms coincide in extension, the

predicate must either coincide also in intension with the subject or not.

A

predicate which coincides

intension with

One which

its

subject

is

both

in

extension

and

of the nature of a Definition.

coincides in extension without coinciding in

which applies to the same things without expressing the whole meaning of the subject, is what is intension, that

is,

known If,

as a Proprium or Peculiar Property. on the other hand, the two terms are not co

extensive,

the

predicate

must

either

in intension with the subject or not

l .

partially

This

is

coincide

equivalent

case could not arise of a predicate which was entirely coincident in intension with a subject with which it was not 1

The

co-extensive. For, if the extension of the predicate were greater than that of the subject, its intension would be less, and if less, greater, in accordance with the law of inverse variation of the

two

quantities

(

37).

OF THE HEADS OF PREDICABLES. to saying that

it

must

genus and cate

either state part of the definition of

Now

the subject or not.

103

is made up of form the predi may

the definition

difference, either of

which

but as the two are indistinguishable in relation to

:

a single subject, they are

for the present

lumped together

purpose under the one head, Genus. When the predicate, not being co-extensive, is not even partially co-intensive with its subject, it is called an Accident. In the work in which this classification occurs

86.

Aristotle expressly disclaims scientific precision of treat

The want

ment. in

the division

of exactness however

but in his not

itself,

members of

definitions to the

the four terms in what

and

to

aggregate

He

it.

was already

doubtful

is

cases

prefers to define

their accepted sense,

round whichever of

them they were most like. 87. Genus is defined in the same way as

that

which

not discernible

having suited his

as

by Porphyry,

predicated in the category of substance

is

of several things different in kind.

Under

head difference

this

is

thrown, although

not comply with the definition, since

also

be

referred

property of

man

the

to

that

it

is

same head.

It

does

predicated in

Generic properties

the category of quality.

it

(

is

131) a

may

generic

he possesses irrational impulses,

since this follows from his nature as an animal (genus). 88. Definition

Under

this

defined as

is

the nature of a thing

a phrase which signifies

V

head must be included any predicate which

1

Top.

I.

5,

i

\o-yos 6 TO ri

fjv

tlvai arj/^a vcav.

OF THE HEADS OF PRED1CABLES.

104 is

a mere synonym of the subject,

A

a cloak/

Hebrew

Alexander

captain/

is

in

predicate coincides

be considered to

may

Paris/

indeed

make

is

the

In such propositions the the

extension with coincide in

defined as

is

the

plain

is

subject,

and

intension, where the is

at

zero, as

names.

in the case of proper

Proprium

mantle

skipper

intension of both subject and predicate

89.

A

e. g.

The

a Jew/

is

that

of a

nature

which does not thing,

but which

belongs to that thing only, and can be predicated instead of

it/

e.g.

able to learn

and can be put Designations

under

grammar can be

man

and descriptions ( 119) will fall Mr. Balfour is the present Prime

31)

(

said only of

man.

in place of

this head, e.g.

Man is a mammal with hands Minister of England/ and without a hairy skin. Here, while the terms are coincident in extension, they are far from being so in intension.

90. Accident

is

defined

(1) negatively, as

that

which

is

neither definition

nor proprium nor genus, but which belongs to the thing

;

(2) positively, as

belong

to

that which may belong or not one and the same individual.

The second

of these definitions

better, since

it

postulates a

is

complete in

is

itself,

declared to be the

whereas the

first

knowledge of the other heads of predicables.

OF THE HEADS OF PREDICABLES. 91.

These

results

may

105

be exhibited in the following

scheme Predicate j

i

i

Coextensive with the subject

Cointensive with the subject

not coextensive

not cointensive

not at

partially cointensive

Wiop

yeVos

Accident

opos

Definition

Synonym Designa-

Descrip-

Peculiar

tion

Property

tion

Thus up,

if

all

truiu/3f/3>7icd

Aristotle s four

we

Genus

heads of predicables

please, into nine 1.

Definition

2.

Synonym

3.

Designation

4.

Description

>

6 pos.

5. Peculiar Property 6.

Genus

\

>

L^LOV.

/ \

7.

Difference

8.

Generic Property /

9.

Accident

/>

yeVos-

o-vfj.j3fj3r)K6s.

Differ-

Generic

ence

Property.

may be

split

CHAPTER Of 92. us, will

VII.

the Categories.

THE Four Heads

of Predicables, Aristotle

tells

Ten Categories. These summa genera which contain all possible Hence they were known among the School Ten Predicaments,

always be found in the

last are certain 1

predicates

men

.

as the

While

93.

the

predicate in relation at

in

it

94.

heads

of

to its

subject, the categories

a

consider

predicables

look

itself.

The

or less complete form

more

categories in a

occur everywhere in the Aristotelian writings, but they

have also been thought worthy of a special

which we extract a passage, as the

treatise,

from of

way

simplest

bringing the subject before the reader

Every word used by

itself

signifies

either substance

or quantity or quality or relation or place or time or

As an example

posture or having or doing or suffering. of substance "

two cubits

we may

take

"man,"

of quantity

"

"

three

long,"

cubits

long

of relation

"grammatical;"

"white,"

"horse;"

of quality

;

"double,"

"half," "

"

of place

"

greater

of time

;

in the Lyceum,"

"

"

in the

Agora

"

"

"

yesterday,"

of state

"sitting;"

last

year

of posture

;

"armed;"

"shod,"

of doing

"

lying,"

"cutting,"

"

"

burning 1

;

;

TO. ytvt]

of suffering TUf Karrjyopiwi

,

"

"

being An.

Post.

cut,"

I.

22,

being 7

;

burned."

Top.

I.

9,

i.

OF THE CATEGORIES. The Greek names

95.

for

the ten

107 categories with

their Latin equivalents are as follows ova-ia

substantia

substance

TTOO-OV

quantitas

quantity

qualitas

quality

relatio

relation

irov

ubi

place

77-oVe

quando

time

situs

posture

habitus

having

actio

doing

passio

suffering.

TL

96. Mill (Logic criticisms to bear

I.

3,

upon

i)

has brought some damaging

these categories

they are in the Metaphysics IV. tion of Existences

mark

when given

4) as an

7,

(as

enumera

but he seems to have overshot the

:

saying that the distinction between Ubi and of lie merely verbal. For Situs means the a thing, that is to say, its posture, or, as we should Situs

call

it

in

is

in

the case of a person,

a difference difference,

of

conception, and

between

this

changing every

die occupies the

instant.

same

uppermost, but the difference to the

Or

its

It

is

will

is

verbal

A

place.

place, but

again, a

question

There

mere

a

its

spin Situs

backgammon

place, whichever of

latter

game.

attitude.

not

and the idea of

ning-top asleep does not change is

its

its

sides

be

all

the

make

true that the posture of

anything depends upon the place which

its

parts

occupy

OF THE CATEGORIES.

Io8 relatively to

one another, but in reference to the object and the Kilo-Oat, its place and its posture,

itself the TTOII

are distinct conceptions. 97. Aristotle gives us

no clue to the way

in

which

he came by the categories. There they are, and there they seem to have been from the beginning, in his

But

philosophy.

it

is

plain

that

his

direct

object in

forming them was not to work out a classification of things in general. to speak

of the

of predication

a

Kar^yopta means

predication/ and

classes of predication/ or

(Met. IV.

more extended, but not a

7,

4),

the forms

only gives the term

different

meaning. It might be thought therefore that the problem which Aristotle set himself to solve was this What different notions can be affirmed or denied of the subject by means of the copula?

But to put the matter in this way would be between ancient dialectic

to overlook the great difference

and modern

logic.

A

syllogism with us

bination of three propositions.

But

in

means a com Greek

dialectic

was no proposition at all in the syllogism. For was propounded as a question, in a form

there

the conclusion

which a

left

the matter open to discussion,

good or not

?

and then assent

to

one

e. g.

Is pleasure

side or the other

was obtained by putting questions which demanded the answer Yes or No/ e.g. Is every good praiseworthy?

The

conclusion, as thus put forward interrogatively,

known

was

problem/ and each of the technically which determined the answer to it was called questions a protasis.

as

a

OF THE CATEGORIES. Now

98.

the

which

task

Aristotle

accomplish was not to make out a

109 himself to

set

list

of

all

possible

Given any object of main questions which can be

objects of thought, but rather this

what are the

thought,

asked about

that can be

and the answers

it

returned

them?

to

To

we may ask what a

begin with,

told that

fourteen hands

receive the answer

That

information

about

spirited or

learned.

Or we may want thing the

else,

its

of

somebody.

Or,

may

inquire

or

A

is

That

year ago.

its

is

parts

is

be interested in

its

That

something the

is

Where

is

it

category of Doing.

and

is

receive

an event, we yesterday

stand with regard that

may That

its finger.

Or

it

is

it

is

one

to

upside-

Or we may

learn that is

of

the category

is

the category of Time.

Or we may ask what

get the reply that

else or

category

it ?

That

belongings and

is

bears to some

the category of Posture.

shoes on or a ring on of Having.

it

like

and receive the information

That

it

category of Quality.

took place, and be told

it

request

that

told

the thing in question be

if

when

we may ask how down.

it

and

it ?

Or we may

the relation

told that

In the market-place.

the answer

of Place.

the

is

Or we may ask

Relation.

another,

know

to

and be

servant

That

is

six feet high.

and be

nature,

and be

is,

the category

big

or

the category of Quantity.

is

is

How

Or we may ask

of Substance.

thing

That

a horse or a man.

is

it

it

has

the category

engaged in and That is the

eating or teaching.

Or,

lastly,

we may want

to

know

OF THE CATEGORIES.

110

how

it

that

it

being acted on by something

is

or being

being eaten

is

else,

and be

That

taught.

is

told

the

category of Suffering. 99.

That

arrived at

was

this

his

really the

may

categories

in

way be

which Aristotle

gathered from

the

by which they are designated. Thus the category of Substance is commonly spoken of as the interrogative forms

What

category of

How Time

big

is

the next as the category of

it ?

and so on through the

?

list

1

Moreover,

.

could not have

appeared as a category except For at the possible answers to questions. by looking We cannot the adverb of time is not categorematic. predicate

it

we may

of anything, but 2

pendent answer

to a question

it

give

couched

as an inde

in a particular

form. 100. It did not escape Aristotle ri

eon

For

that the question

answer under any of the the thing of which we are speaking

might really receive

categories.

3

if

its

be not a substance, but a quantity or quality or relation, then the answer to the question What is it ? comes

under one of these other categories.

we ask

What

is

maternity?

Suppose for instance the answer will be, It is

the relation of a mother to her child. of maternity that

is

it

a quality, and so on.

it is

It

is

the ova-ia

a relation, the OWTLO. of virtue that

But such things have no ovo-t a This is why

in the strict sense of substantial existence. 1

This fact

2

Kara

3

is

commonly obscured by the

f*tj5f/j.tav ffVfj.n\oKT]v,

Met. VI.

4,

12

;

Top,

I.

Cat. 4, 9,

2.

I.

accentuation.

OF THE CATEGORIES.

Ill

and Porphyry deny that the ten categories can be brought under one head, except equivocally. The Aristotle

vague term

enables us to express what

thing

to all with less risk of ambiguity.

that this

with

word should be so instead

substance/

summum

absolute

It is

is

common

a pity therefore

often used interchangeably

of

being

reserved

for

the

for everything, even the most

genus:

abstract quiddity or entity,

must

still

be a thing of some

kind.

101.

The

nine categories other than that of Substance

be regarded as a division of Attribute.

may

Quantity

and Quality are attributes inherent in a single substance, the one belonging to its matter, the other to its form, and so both

fall

under

we have used of one

quality

the term

Relation seems

102.

As

to

wide sense in which

The

rest are all relations

the

special category of

24).

(

kind or another

which have a

in the

:

but

be reserved by Aristotle for things

distinct correlative.

Aristotle s

with language,

it

is

problem was

essentially

concerned

not surprising that he should have

by aid of grammatical distinctions, and that in so doing he should have struck out the parts of speech, so far as they are capable of supplying an sought to solve

it

answer to a question.

The noun

to the category of Substance, the

substantive

noun

led

him

adjective in its

various forms to those of Quantity, Quality, and Relation

adverbs like

Time

;

here

and

now

to

;

those of Place and

the active and passive voices of the verb obviously

supplied the categories of

Doing and Suffering;

while

OF THE CATEGORIES.

112 Posture

and Having seem from

instances to have

his

been suggested by the neuter verb and the middle voice. 103. We pass on now to the two subjects of Definition in

which the

utility

and Division,

of the second part of logic culmi

nates.

These two processes correspond

to the

two kinds of

quantity possessed by terms. Definition

Division

the analysis of a term in intension.

is

is

the analysis of a term in extension.

Definition imparts clearness to our thoughts by setting

we

before us the meaning of the terms

are using.

Division imparts distinctness to our thoughts by

show

ing us the different kinds of things that are called by a

common name. Neither process

a purely formal one:

is

to take account of the matter of thought.

suggests a division; of each of

man

members.

its

of animal divided

into

animal

rational into

many

;

division

and

man

Definition, involving in the

is

definition

Thus when we have we have suggested a and and

irrational,

we have

brute.

generalisation,

seeing the

defined division

when we have

irrational;

rational

supplied definitions of

Every

supplies a definition

every division

as a rational animal,

both have

is

many

seeing the one in the one.

am

myself enamoured/ says Socrates in the Phaedrus (266 B), of these divisions and generalisations, in order that I may be able to speak and think and if I deem I

;

that another

is

able to see a

One and

a

Many

in nature,

OF THE CATEGORIES. him

I

follow after, in his

footsteps, as

113 though he were

a god.

The

treatment of the two processes

second part of with the

logic,

Heads of

because

Predicables.

it

falls

under the

involves an acquaintance

CHAPTER Of 104. DEFINITION

we speak both

To

Definition.

Hence

of things through names.

is

of defining things and of defining terms.

a thing

define

VIII.

is

to

fix

most

its

upon

essential

attributes.

To of

its

define a term

is

to state the

most

essential

part

intension

we

intension.

105. Let

it

be understood that by

mean

all the attributes in any way implied or suggested by a term, whether they are essential to the thing of which it is a name or not. A capacity for laughter is

of the

part

of the term

intension

not

man/ though

essential to a rational animal.

106.

the essential attributes of a thing

By

those without which

it

would not be what

it

we mean

Man

is.

would not be man, if he were either not an animal or not rational. He would still be man, if it never occurred to him to laugh; much more so, if his skin were not white.

other

But a disembodied

name

than

man

;

spirit

were wholly absent, though more be entitled to be called .

107.

Among

are primary

must be

human man than

in

by some

whom

reason

form, would

to follow

from another

Any is

no

a statue.

the essential attributes of a thing

and others secondary.

can be shown

called

and a being from

attribute

some which

plainly secondary

OF DEFINITION. to that other.

Thus

to rationality

among

gressive because he is

115

a capacity for progress

is

is

secondary

He

man.

the attributes of

is

pro

not rational because he

rational,

progressive.

The

essential

and primary

of a thing are

attributes

what constitute the meaning

of

its

name

fixed

as

by

definition.

Rules for Definition.

108.

MATERIAL.

I.

The

attributes selected

must be

(1) truly predicable of the thing,

(2) important, (3) fundamental.

Violations,

(i)

The sun

is

the

brightest

of the

heavenly bodies that go round the earth.

This

all

definition

ought to be

:

but

we have changed

and no one would now accept the

that,

because

it

is

definition,

not true.

Man

(2)

The

given by Plato (Theaet. 208 D) as a model of

is

what a

is

a featherless biped.

story runs that,

when

man

Plato had defined

as

a featherless biped/ Diogenes plucked a cock and in

troduced Plato

it

into his school as

added the

(Diog. Laert. VI,

further

Plato

difference

s

man. with

Thereupon broad nails

40). i

2

OF DEFINITION.

Il6

A

(3)

In

than the

B

attribute

A

definition

is

not a good

Because the angles depend upon the sides

Why?

rather

by

a figure with three angles.

and important, and yet the

dicable

one.

is

triangle

case the attributes selected are both truly pre-

this

is

upon the

sides

angles.

Generally,

if

found to follow from A, we should define

and not by B. FORMAL.

II.

A

(1)

defined,

i.

e.

it

the

must apply to precisely the same

more nor

neither

must be convertible with

definition

term

things,

less.

Caviare

Violations.

is

a kind of food.

A triangle is a figure with three equal sides. defined. (2) A definition must be clearer than the term Violation. A net is a reticulated fabric, decussated at regular intervals.

The

violation of this rule

is

called ignotum per ignotius

or per aeque ignotum.

A

(3)

definition

must contain the fewest

attributes

that suffice to distinguish the thing defined.

Violation.

A

triangle

is

a figure with three sides and

three angles. (4)

A

definition

Violation. (5)

A

must not be metaphorical.

Bread

definition

either directly or

the staff of

life.

by implication.

Violation. Virtue

The

is

must not contain the name defined

is

acting virtuously.

violation of this rule

or defining in a circle.

is

called circulus in definiendo,

OF DEFINITION.

A

(6)

definition

117

must not be negative,

if

can be

it

affirmative.

A

Violation.

neither

Turanian language Aryan nor Semitic.

one which

is

is

Briefly, a definition

should be convertible with the subject, clear,

should not be metaphorical,

The

first

of these formal rules

meaning, or we have

tautologous,

name

apply or excludes things to which

negative.

it

meaning,

name does

if

not

does.

object of definition being to explain what a thing

is

it

is,

and

has no definite

failed to discover that

our definition includes things to which the

The

terse,

the best test that can be

is

Either a

applied to a definition.

or

clear that

we

defeat our

own

object,

if

we

use

language which is as unintelligible as the name of the thing we wish to define (ignotum per aeque ignotum], or if

we attempt

to explain the name by itself or by any other term which implies an acquaintance with it (circulus in definiendo), or if we use a metaphor about the subject,

which

is

merely to say what

ourselves to saying what

The

second

definition, so.

may

For a

rule,

it is

it

is

like,

or

which provides

for

seemingly be violated when

definition

may

context, would appear absurd. it is

correct

we

confine

clearness in a it is

not really

be correct enough from a

special point of view, which, apart

of conic sections,

if

not.

from that particular

From

enough

as that section of a cone which

is

the point of view

to define a triangle

formed by a plane

passing through the vertex perpendicularly to the base,

OF DEFINITION.

Il8

but this could not be expected to a person

who was

inquiring

meaning of the word

The

third rule,

triangle.

is it

good Again the fourth

all

is

a precept of perfection,

practical purposes without

But as brevity

it.

also of a

be violated

serve

may

the observance of

things clearer to

which guards against there being any

thing superfluous in a definition, since a definition

make

for the first time into the

the soul of wit, so

is

definition. rule, against defining in a circle,

may

appearance without being violated in reality. Thus Euclid, or rather his translator 1 defines an acutein

,

angled triangle as

that

which has three acute angles.

This seems a glaring violation of the correct in

what

and

is

all

its

context

for

;

is

now

but

is

perfectly

has already been explained

it

meant by the terms that

rule,

and

triangle is

required

acute angle,

to distinguish the acute-

angled triangle from other kinds of triangle.

The

fifth rule,

not only define

it

we

if

against defining in a circle,

define

a thing by

by

its

contrary, as

or

by

its

darkness,

Light

is

A

correlative, as

is

violated,

but also

itself,

if

we

the absence of

ruler is

one who

has subjects under him.

The are

sixth rule

privative in

For

cannot always be observed.

many terms force.

there

though positive in form, are Such terms serve as residual heads

which,

under which to throw everything within a given sphere 1

Euclid s

fwrltu,

acute.

1

own words

are ogvyuviov 5

an acute-angled triangle

is

that

TO

rcta

which has

oetas t\ov three angles

rptfs its

OF DEFINITION. which does not exhibit certain this

that

the definition which

is

amounted merely which was neither a

of Accident, which

was any

it

attribute

Of

attributes.

positive

unavoidably negative nature

we gave

119

to saying

difference

nor a property. 109. a thing

There are two ways

may e.

definition of

primary and essential attributes, when we have enumerated the attributes of

by

(1)

which a

in

be given

detailing

g.

its

a yellow,

shining colour, of solidity, heaviness,

hardness,

of

solubility in

defined (2)

aqua

we

regia,

Here

is

figure is

figure

difference, or differences

limit/ of

referred to the genus

and the

point,

110.

is

A

differentiated

definition

by being the

serves

which

which are the

From

of the surface and of the line respectively.

these figure

*,

the limit of a solid.

the other species are the line limits

and

are considered to have

gold;

by giving a genus and a

e. g.

fixedness,

fusibility,

ductility,

of a solid.

limit

the practical

purpose of

enabling us mentally to distinguish the thing defined from all

This

other things.

but, if

may

it

at

fails first

to

do

sight

is

not

this, it

is

all

that a definition does,

not a definition.

seem an endless task

to

Now

it

distinguish

a given thing from everything else in the world, but there a short cut to the desired end.

is

thing defined from the things which 1

may

On

definition

by genus and

see Aulus Gellius, IV.

i.

If it

we is

distinguish the

most

like,

much

differences the classical reader

OF DEFINITION.

120

more is

we have

shall

This

less like.

just

what

genus and the difference. If we were asked to define a

from things which

it

distinguished is

it

effected by giving the

is

triangle,

we would not begin

by distinguishing it from a hawser, but from a square and other figures with which it is more possible to con found

The

it.

class into

which a thing falls is called its attributes which distinguish it

Genus, and the attribute or from other members of that

class are called

its

Difference.

111. Care should be taken that the genus chosen

Thus

the proximate genus.

not to refer

it

to the class

in defining

is

we ought

square

figure/ but to the nearer class

quadrilateral or four-sided figure.

112.

word

The

highest class of

all,

which we express by the is no genus

thing/ cannot be defined, because there

above

it

which

to

it

can be referred.

It also baffles defini

tion for another reason, namely, that the attribute connoted

by

it,

that of pure existence,

113.

Definition

is

is

absolutely simple.

an analysis of the subject

in inten

breaking up a concept into the simpler concepts which compose it. In order then for a thing to admit of sion.

It is

some way complex. Names of simple attributes defy definition, but at the same We know what is meant by such time do not require it. definition, the idea of

it

must be

in

attributes as redness, sweetness, pleasure, pain, likeness,

existence, but

who

we

are unable to define them.

To

a

man

has never enjoyed sight, no language can convey

an idea of the greenness of the grass or the blueness of the sky and if a person were unaware of the mean;

OF DEFINITION, ing of the term,

121

sweetness/ no form of words could convey

We

might put a lump of sugar into his mouth, but that would not be a logical definition. Definition cannot, any more than reasoning, be pushed

him an idea of

to

indefinitely

The

art

it.

backwards. of giving a good definition

to seize

is

salient characteristics of the thing defined

upon the

and those where-

from the largest number of other attributes can be deduced as consequences. To do this well requires a special know ledge of the thing in question, and the

mere

We

not the province of

is

logician.

have seen already, in treating of the Heads of Pre-

dicables

(

difference

difference between genus and one hand and property on the other is some assumed definition. Now defini

69), that the

on

the

wholly relative to

tions are to a certain extent arbitrary,

the point of view from which to be defined.

Thus

we

man

is

of him to say that he

it is

point of view

incorporeal

man would

vary with

held a sufficient

a rational animal.

is

But a theologian might be more anxious with supposed

will

usually contrasted with

brute/ and from this point of view definition

and

consider the thing required

intelligences,

to contrast

man

and from

this

be defined as an

embodied

spirit.

In the two definitions just given it will be noticed that we have really employed exactly the same attributes, only their place as is

man

s

him from

genus and difference has been reversed.

rational, or spiritual, nature

the brutes

:

but this

is

just

It

which distinguishes what he is supposed

OF DEFINITION.

122 to have in

common

whom

differentiated

he

This is

is

with incorporeal intelligences, from

by

his

animal nature.

illustration is sufficient to

no absolute

fixed genus

show us

while there

that,

definition of anything, in the sense of a

and

difference, there

may

at the

same time be

which permanently distinguish the bers of a given class from those of all other classes. certain attributes

114. Definition

concrete

An

common

is

confined to abstract terms and to

terms which can be used as subjects.

does not admit of definition, because

attributive

has no meaning out of predication

;

but

it

may

through the corresponding abstract term,

through

A

mem

it

be defined

e. g.

merry

mirth.

concrete singular term,

i.

e.

the

name

of a primary

substance, does not admit of definition, because no one attribute

can be considered more essential to an individual In the case of a class the essential attributes

than another. are,

the

or are found among, those which are

members

:

such criterion.

common

but in the case of an individual

To

John

as

John

it is

to all

we have no

no more

essential

If the that he possesses reason than that his hair is red. concrete singular term however be of the kind known as

OF DEFINITION.

123

a designation, it may be defined through the common term which is used in making it up. When we say The

Pope

present

cognised head of the

Roman

is

to the definition of

raneous existence.

The

Pope

it is

present

Pope

by super-

the attribute of

is

only one

not applicable to

contempo

such a term

fact is that

really singular, though, as there

given moment,

moment the re Church/ we have

at this

Catholic

meaning of the term

fixed the

adding

who

the priest

is

now

is

not

at

any

more than one

thing

at a time.

115.

There

is

admit of definition.

a sense in which even proper names

For

in so far as a

ing that meaning can be set forth. is

the

name

may be

the

the answer

we wish the

of a male person.

name

to define

same word.

kind of which a

it

say

John

be objected that John

monkey, ship, or institution, most words are equivocal, and that if

any term, we must choose one sense of Such a definition however is not of the

we have

hitherto been speaking.

nominal

but a

real

Thus we can

of a dog, cat,

that

is

If

word has a mean

the nature of the being

ing of the word

definition.

known

John

It

It

as John, but only the

before

it

is

not

does not expound

mean

has been applied to

a given individual. 116. This brings us to the recognised distinction be

tween Real and Nominal Definitions.

A Nominal a

A

name

definition only explains the

meaning of

;

Real definition does

this

of the thing denoted by

by determining the nature it.

OF DEFINITION.

124

Hence

there

may be

a nominal definition of a thing which

has no real existence.

The The

definition of a stag or of a goat is a real definition. definition of a

As

117.

terms

it

is

more easy

The

crete terms.

terms

lies

to apply

a nominal definition.

is

goat-stag

do with the intension of

definition has to

reason of this

than to con

to abstract

it

is

that the force of abstract

The

wholly in their intension.

kind of abstract

terms that are most easy to define are mathematical con ceptions, such as

triangle,

square/

which belong

circle,

to the region of necessary truth.

Such things have no have accidents such as

we confuse

If a triangle

accidents. size

and

position,

it is

the abstract concept triangle with

representation of

appears to

only because

some

sensible

it.

In concrete terms on the other hand the extension

This

uppermost, not the intension.

hard to define them.

We

have no

ing the things that are denoted chair/

plant/

the attributes

notes.

what makes

difficulty in

to another like

attributes

common

But the definition of a

at

all,

is

so

recognis

by such names as

animal/

it

until at last there are

to the things

class

which

and have

by a new definition, in and restamped.

to

it

de

must be found some

where among the attributes which are common to members. Hence such names have ceased to be

names

it

book/ but we have a very dim idea of For the name gets extended connoted.

from one thing perhaps no

is

be recalled from

their

just as defaced coin has to

all its

class

vagueness

be called

OF DEFINITION. 118. are the

The

names

classes of

are either

125

which concrete

made by nature

common

terms

Those

or by man.

which are made by nature are called real kinds/ e.g. man, The members of such classes agree in dog, cat, pig. various attributes which have no discoverable connexion with one

another,

and some of which must therefore

be regarded as inseparable accidents in relation to those which are selected as constituting the definition. Such

made about them,

classes admit of real propositions being e. g.

The same

All cats have whiskers.

the genera under which these species division,

e.g.

we can

On

cloven hoofs.

make a

say

the other

can be made when a

class

is

in a natural

we can

hand no such propositions

We

purely arbitrary.

can

members

predicate nothing but their green

ness or whiteness, unless e. g.

have

animals

class of green or white things, but of the

of such a class

butes,

fall

All ruminant

true of

is

thing

it

be some attribute of these

attri

of green things that they are restful to the eye

and of white things that they are hurtful. Apart from the difficulty of determining the more or essential nature of attributes

ing connected, nature

s classes

factorily defined owing to

They shade degrees that

Who

off into it

single attribute,

do not admit of being

satis

the great law of continuity.

one another by such imperceptible

impossible to

shall tell us exactly

animal begins?

mon

is

less

which are united without be

fix

the boundary-line.

where the plant ends and the

Under such circumstances there

much

less

any group of attributes,

to every individual thing to

which the name

is

is

no

com

applied.

OF DEFINITION.

126

The

best

we can do

is

to lay

down a

type of the class in

most perfect form and include or exclude individuals less conform to it.

its

according as they more or

From

119.

definition

must be distinguished Descrip

tion.

Definition

the analysis of a concept.

is

the setting forth of the mental picture

is

Description

which accompanies some concepts. Definition is an appeal to thought. Description

Hence

an appeal

is

description

is

to imagination.

applicable primarily to individuals,

John Smith is the tall man with sandy whiskers who lives next door on the right-hand side and passes by every secondarily to the classes which morning at nine o clock e.g.

;

lie

nearest to individuals and of which

definite

we can form some

mental picture, e.g. the Skye terrier is from four and from twelve to fourteen long, it is

to six inches high

usually either grey or blue-black with dropping ears,

long silky

hair,

covers the eyes

and

which in perfect specimens altogether

1 .

Description serves equally well with definition to distin all other things, but it accomplishes of accidents with or with an enumeration by out the mention of some class-name.

guish the subject from that object

1

It is

From

A

Discourse on Tntt/i, by Richard Shute, M.A., p. 70.

given by the author as an instance of a

definition.

CHAPTER Of

IX.

Division.

120. LOGICAL division consists in breaking into

its

component

121.

From

this

up a genus

species. it is

common

manifest that only

terms

can be divided, and also that the members of a division

must themselves be common terms. 122.

An

individual

(aro/xov)

admitting of logical division.

cow

into classes,

name

the

cow

so

is

We may

called

as

not

divide the term

as Jersey, Devonshire, &c., to which

will

be applicable, but the parts of

still

an individual cow are no longer called by the name of the whole, but are 123.

makes no

known

as beefsteaks, briskets, &c.

Whether common terms be

abstract or concrete

difference as regards the possibility of dividing

them, since we 124.

may classify attributes as well as substances. The term divided is called the Divided Whole as given to be divided, it may be called The classes into which it is split up are Dividing Members (Membra Dividentia). A class of which the members were absolutely

(Toium Divisuni) the

;

dividend.

called the

125.

homogeneous could not be

divided.

practical purposes with coins of the

as issued from the

by

same

mint.

This

is

the case for

same type and

Division

is

date,

only possible

difference.

The

first

thing then that

is

requisite in

making a

division

OF DIVISION.

128 is

some

to find

differ

attribute in

from others.

the Division

This

which some members of a

class

attribute is called the Basis of

(Fundamentum Divisionis\

After coins have

been put in circulation, we important distinction

an external and coins:

it

may find such a basis in the between meum and tuum. This is

superficial principle

on which

to divide

not as coins that they are so divided, but

is

But it is important to notice that the basis of a division must always be sought in some separable accident of the class divided. If we were to base a division as property.

on the

difference of the divided whole, or

properties, or

on one of

its

even on an inseparable accident, all the by the name would be found in a single

individuals denoted

compartment of the division, and the other compartments would be left empty. Thus if we were to divide Kan garoos into Australian kangaroos and others, we should find all the kangaroos on one side of the division. 126. Division, like definition, varies with the purpose

The same e.g. we may

in hand. bases,

class

may

divide

be divided on different

animals according to the

element which they principally inhabit, according to the legs, according to the mode in which they

number of their produce

young, according to the nature of their food, indefinitely. Again, men may be divided on

their

and so on

the basis of colour, or

on

that of locality, or

race or language or sex or temperament:

on

A

the point of view

good

which

on

that of

all

depends

interests us at a given

moment.

it

division follows the natural lines of cleavage

a process of carving, not of hacking.

:

it is

OF

MAIN RULES.

I.

(1)

division

129

Rules for Division.

127.

The

DIVISION.

must be conducted on a

single basis.

Churches into Gothic, episcopal, high, and

Violation.

low.

The

(2)

basis

must be a separable accident of the

genus.

Men

Violation.

The

(3)

species,

and

into rational

when added

irrational.

must be co

together,

extensive with the genus. Violations.

Triangles into right-angled and acute-

angled.

Coins into gold,

The is

bronze, and bank-notes.

silver,

effect of violating the first rule is to

called a

The

produce what

cross-division.

effect of violating the

second rule

is

to

have the

form of division without the matter.

The

effect of violating the third rule is

(a) that the division (6) that

it is

The above

is

twofold

not exhaustive

1 ,

redundant.

rules

are

all

that are

necessary,

but the

be found useful in testing a division and it from other distinguishing processes which are something following will

like

it.

128. (4)

The term

II.

ADDITIONAL RULES.

divided must be predicable of each of

the dividing members. 1

Cum

Cic. Off.

praeterire aliquid I,

maxumum

vitium in dividendo

10.

K

sit.

OF DIVISION.

130

Horse

Violation.

into cart-horse, pony, mule,

and

donkey.

Each member of

(5)

the division

must be a common

term.

Great Britain into England, Wales, and

Violation.

Scotland.

The

(6) sive,

e.

i.

members must be mutually exclu no individual must find a place under more than dividing

one of them.

Man

Violation.

and

These additional rules

into philosopher, red-haired, Greek,

slave.

rules

are

corollaries

and from the conception of

(4) If the species,

it

is

from the main

logical division.

genus be not predicable of each of the plain

that

the

species,

when added

gether, cannot exactly make up the genus. (5) If each member of the division be not a

term,

we run

to

common

counter to the definition from which we

started.

(6) If the division

be conducted on a single basis, the

constituent species must exclude one another.

verse however does not always hold true.

a division consisting of mutually exclusive yet involves a mixture of different bases,

The con

We may

have

members which e. g. if

we were

and equiangular. attributes may be found

to divide triangle into scalene, isosceles,

This happens because two

distinct

in invariable conjunction.

The

sixth rule

may be

partial inclusion of one

violated either

of the

by the total or members in the other.

OF DIVISION. The first will be own species,

its

the case, if,

for

if

131

a genus be co-ordinated with

we were

instance,

to divide the

parts of speech into noun, article, pronoun, substantive,

and

adjective, verb,

noun, verb, and

When

noun.

The

particle.

particle,

true division

the inclusion of one

member

in the other

only partial, the species are said to overlap,

is

the example previously given.

may

tetus

very well

compartments of

into

is

the rest being sub-divisions of

An

have found

philosopher,

as in

individual like Epic-

a

place

red-haired/

in

four

all

Greek, and

slave.

In testing a division the sixth rule on.

or

If there

more

is

the best to begin

be any individuals that would fall under two we may be sure that two or more different

heads,

bases have been mixed in

the

were to be divided

division.

If

man,

into

for

Asiatic.

European, Aryan, and Semitic, the species would overlap ; for both Europe and Asia contain inhabitants of Aryan and Se instance,

We

mitic origin.

have here a division based on

locality,

mixed up with another based on race as indicated by language. 129.

As

the differences between species are separable

accidents of the genus to which they belong,

is

it

plain

an appeal to experience. Prior to have we experience only the form of division without the that division involves

matter.

We

know

not-white, but

white

men

men are either white or we do not know whether there are any Thus the only any but white men.

for instance

or

that

K

2

OF

132

purely formal division

DIVISION. a hypothetical division by dicho

is

tomy.

Here

is

a series of such divisions.

Man I

White

(if

not-white

any)

Black

(if

Brown

any)

not-black

any)

(if

(if

Division by Dichotomy

any)

not-brown

any)

Red

(if

(if

not-red

any)

means

(if

any)

(if

any).

the division of a genus

into two species, one of which possesses a given attribute 1 while the other does not It is division by means of .

Hence

a pair of contradictory terms. side in such a division

Experience assures us that yellow/ and

substitute

of

man on

plain that

not-red

for

one

men we may

so arrive at the fivefold division

the basis of colour

ii

Man I

r White 130.

it is

must always be negative.

i

i

brown

black

Any

red

yellow.

correct logical division in which there are

more than two

species

series of divisions

is

the

compressed

by dichotomy.

result

of a

Thus, to take another

example, the term quadrilateral, or four- sided rectilinear 1

Called by the Stoics uvriStaipfffts (Diog. Laert. VII,

61).

OF

DIVISION.

133

figure, is correctly divided into square, oblong,

rhomboid, and

The

trapezium.

of

steps

rhombus,

which

this

division consists are as follows Quadrilateral

|

|

Trapezium

Parallelogram I

I

I

Non-rectangle

Rectangle

Square

Rhombus

Oblong

Rhomboid.

131. In such a scheme of division and sub-division

Summum Genus

the

the

is

highest

class

the

taken;

Infimae Species (lowest kinds) are the classes

at

1

which

the division stops.

and Species

Subaltern Genera

are the classes

inter

mediate between the highest and lowest, which are genera in

relation

to the

classes

below them and species

in

above them.

relation to the classes

Cognate Species (kindred kinds) are those which fall immediately under the same genus ; Cognate Genera are the classes under which a lower class successively falls, e.g. rectangle, parallelogram,

and quadrilateral are cog

nate genera of square.

The

relation of cognate species to

that of children of

genera resemble a 1

Diog. ad.

Siaipe

Laert.

same

the

one another

is

like

parents, whereas cognate

tine of ancestry.

VII,

61

Tnooiatpeans

5e

tan

Siaipcais

trrl

OF DIVISION.

134

The

Specific Difference of anything

which distinguish

attributes e. g.

of a square that

difference

it

is

opposed triangles.

The

rule

that

its

division

to

subdivide, basis,

to the

attribute differ

on

its

must

of a square

e. g.

own

diagonal.

be conducted on

we not only may, but ex hypothesi the old

since

colour of their skins,

subdivide any of the classes,

men

as

Thus, having divided men if we wish to

one has been exhausted.

plexion

an attribute which

is

generic difference,

the

adopt a new

fresh

proximate

applies only to a single act of division.

When we go on

according

its

an oblong, that it is divisible into two isosceles A Generic Property of anything is an attribute

a single basis

must,

specific

Generic

angles are right angles.

half the size of the square

it is

A The

a square specific difference, e. g. of

its

which follows from that

its

Property of anything

follows from to

cognate species,

equal.

the difference of

genus, e.g. of a square that Specific

its

said to constitute the species.

is

Difference of anything

A

from

sides are

its

the attribute or

is

wherein

from

we must look out

for

some

some men of the same com

others,

e.g.

we might

divide

black

into woolly-haired blacks, such as the Negroes,

and

straight-haired blacks, like the natives of Australia.

What

is

called

divided whole with reference to

the

a single act of division becomes the there

spond

subdivision.

is

to

the

summum genus where

Similarly the infimae species corre

dividing

members

of

a

single

act

of

division.

In reckoning up the infimae species care must be taken

OF DIVISION. not

to include

divided

l ,

which has already been sub

class

any

in the division of

e. g.

135

rectangle

quadrilateral

must not be mentioned along with square and oblong. No harm is done however by mixing an undivided class, trapezium, with

like

species

the

of

subdivisions

;

under a

will represent the

132. Enumeration things to

is

which a name

As

further.

the statement of the individual

Like

applies.

members, December.

month

e. g.

133. Partition

when we

name

division, the

in

the

g.

is

say

branches, twigs,

is

predicable of

is

an

carried

.

all .

.

tree

consists

of roots,

stem,

leaves, or that a proposition consists

physical division

to

is

it

a statement of parts, not of kinds,

that a

and

it

division,

of January, February

of subject, predicate, and copula. fined

cognate

deceased parent.

analysis of a term in extension, only that

e.

its

the latter represent the higher class, as children

Partition

indeed

;

its

is

not con

chief use

is

in

rhetoric.

In a partition the

name

of the whole

is

not predicable

of each of the parts. 134. Distinction

of the

a distinction the

is

the separation

from one another

meanings of an equivocal word.

different

name

members, but the

only

definition

is

In

predicable of each of the

is

in

135. Metaphysical division

each case is

different.

the analysis of a sub-

Cicero, Dclnv. I, 33 ad init. hocigiturvitandumest, ne, cuius genus posueris, eius, sicuti aliquam diversam rem ac dissimilem, partem ponas in eadem partitione. 1

rei

OF

136 stance into solidity,

its

DIVISION.

attributes, e. g. of a

hardness,

man

of

&c.,

marble into roundness, into

animality

and

rationality.

A

must be distinguished from

whole

metaphysical

a logical whole.

A A

Logical

Whole

is

a whole in extension.

Metaphysical Whole

is

a whole in intension.

Considered extensively, species

Man

Considered intensively, genus

is

Animal + 136. illustrate

The

part of genus. animal.

part of species. = man.

rational

following classification of inferences

and subdivision and

division

serve as a

is

+ brute

map

of the country which

at the

will

same time

we have next

to

explore. Inference

Deductive

Inductive

Perfect

by Simple Enumeration

Imperfect

Scientific

Immediate

Simple

Compound

Mediate

Simple

Complex.

PART OF

III.

INFERENCES.

CHAPTER

I.

Inferences in General.

Of

we

137. IN the widest sense of the term to

when we

infer/

some

arrive at

experience, but as a consequence of

already known. rice, you do not

If

you

infer

said

not by direct

some

truth or truths

a door-step strewn with

that there

is

rice

on the door

but you will probably infer that

you see that;

step

see

are

truth,

there has been a wedding from the house, and be right in

your inference.

experience of a

when they

leave

Why?

Because of your previous

happy couple being pelted with If a house on their honeymoon.

rice this

experience has already formed in your mind the general proposition

Wherever the door-step

strewn with

is

there has been a wedding/ your inference if

this

general proposition

inference

is

inductive.

is

now being

But however you

conclusion, you would equally be said in to

is

rice,

deductive;

formed, your arrive at

common

your

language

infer.

Inference then, in the sense of inferring, of the

An

mind from one or more propositions inference

is

the result of inferring.

is

the passage

to another.

OF INFERENCES IN GENERAL.

138

138. Every inference consists of two parts the

(1)

or truths

truth

already known, which

are

called the Antecedent; (2) the

which we

truth

arrive

at

therefrom, which

called the Consequent.

is

N.B. to

Antecedent and Consequent are here applied the two parts of an inference ; previously

they were applied to the two parts of a complex proposition.

The word

inference

sometimes applied to sometimes ;

is

antecedent and consequent together it is

used of the consequent alone.

139. Inferences are either Inductive or Deductive.

The

antecedent in an inductive inference

number of

of one, two, or any inference

propositions

;

may

consist

in a deductive

consists of one or of two propositions, accord

it

ing as the inference

is

Immediate or Mediate.

In the mediate inference, or Syllogism, the two pro

which

positions called

the

form

the

premisses,

extended to the

antecedent

and

antecedent

this

in

an

to

commonly

is

sometimes

inductive inference.

The consequent is in all cases a single is otherwise known as the conclusion. Inductive Inference leads

are

term

proposition,

general truths (eVi ras

deductive inference starts from them

That must the

two processes,

difference that there

and

in the

modern

suffice for the present

until is

induction

(o.7ro

TWV

to distinguish

we have recognised

between

sense.

and

the strong

in the ancient

OF INFERENCES IN GENERAL.

139

140. Since inferences, whether inductive or deductive, are combinations of propositions, while propositions are

combinations of terms,

it

evident that the

is

first

two

parts of logic are equally necessary as an introduction to the study either of induction or of deduction.

141. But under the third part of logic to it

is

natural

is

induction which supplies us for the most part with

major premisses from which deduction

the

it

of inductive before deductive inferences, since

treat

ordinary course

In the

starts.

climbing of a mountain

of things the

must precede the descending of it on the other side, but we may have been born on the top, or have been deposited there by a balloon,

Even so

or, like

Noah, by a

flood.

the universal propositions, which are required

for deduction, are usually arrived at

by the toilsome road

of experience, but they may be supplied to us by intuition or hypothesis or authority. 142.

The meaning which

word

to the

inference

is

Hamilton or of John Stuart principal

legislators

for

has been assigned above

not that either of Sir William Mill,

who have been

terminology in

logical

the

Great

Britain.

Inference with Sir William Hamilton consists in carrying out into the

last

proposition what was

contained in the antecedent judgments

XV,

54)-

called

This excludes a

inference

at

all.

in

virtually

(Lectures on Logic,

real induction

For

the

from being

a real induction the

last

proposition, or conclusion, must be

sum

of the particulars from which

it is

more than

derived.

the

OF INFERENCES IN GENERAL.

140

On

the other hand, Mill declares that all

consequently rests

upon

knowledge of truths

induction.

He

will

inference,

not

and

self-evident,

not allow that there

is

from the known

to

any inference except when we pass the

all

unknown/

Thus

Sir

William Hamilton

excludes induction, while Mill

s

s

definition

of inference

excludes deduction from

In adopting a definition which wide enough to include both views, we seem to have

coming under the term. is

the further advantage of being

common

language than

either.

more

in

accordance with

CHAPTER Of

Perfect Induction

II.

and

the Inductive

Syllogism. 143. Inductive inference to universal truths.

It is

is

*

the process from particular

of two kinds

perfect

and im

perfect.

In a Perfect Induction

all

the particulars are examined

;

an Imperfect Induction only so many as are held to be sufficient, perhaps no more than one. Imperfect induction in

in

its

highest form

The two evidence. plete

is

called scientific induction.

kinds of process appeal to

Perfect induction rests

enumeration of the instances;

on the uniformity of nature. introduce the idea of cause

on

its

;

different

quite

validity

on a com

scientific

induction

Perfect induction does not scientific

induction

is

founded

that idea.

Perfect Induction. 144. Perfect induction consists in asserting or denying

of a whole class what has already been found true of every member. 1

Particular as here used means simply not-general. includes both particular and singular propositions.

It

PERFECT INDUCTION

142

When we

have

ourselves

satisfied

that

the

names

Stephen, Philip, Prochorus, Nicanor, Timon, Parmenas,

and Nicolaus are Greek, we may sum up the result by saying All the seven deacons had Greek names/ 145. Perfect induction

is

not limited to the enumera

We

tion of individual instances.

make

a perfect induction

whenever we predicate any attribute of a genus on the The truths strength of its being found in every species. from which we

start are in this case particular as

compared

with the conclusion.

The

146.

the fact that

statement. all

the

scientific

It

value of perfect induction

substitutes

it

much

is

week than

lies in

a compendious for a prolix

easier to say that

to say that

it

has rained

it

has rained on Sunday,

Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday.

The Inductive Syllogism. 147. Perfect induction

may

be thrown into the form

of a syllogism, thus

X, Y, Z are A, X, Y, Z are B, .-.

All

Bis A;

where X, Y, Z

represent

of a species or

the species of a genus.

all

argument

and yet

perfectly valid.

is

the

individual

We

members shall see

violates the rules of the syllogism,

later that this it

all

The

reason of

this is that

the rules of syllogism are not designed to meet the case

of a quantified predicate such as

we have

in the

second

AND THE INDUCTIVE When we

proposition.

make up

they

This

them.

X, Y,

We may

B.

will

say

SYLLOGISM.

Z

are

143

B/ we mean

that

B

for

therefore substitute

appear more clearly from a concrete

instance.

Matihew, Mark, Luke, and John were Jews. Matthew, Mark, Luke, and John were the four Evangelists. /.

The

four Evangelists were Jews.

148. Perfect induction from this point of view

may

be regarded as the syllogism reversed. Read the pro positions backwards and we get a set of syllogisms proving the particulars from which

we

started

in

the

induction.

The

four Evangelists were Jews.

Matthew

(or

Mark

or

Luke

or John) was one of

the four Evangelists. .

.

Matthew

(or

In the syllogism

Mark or Luke or John) was a Jew. we argue that what is true of all

is

true of each.

In perfect induction

each

is

true of

all.

we argue

that

what

is

true of

CHAPTER Of

III.

Imperfect Induction.

149. IN a perfect induction the universal conclusion at

which we

arrive

is

no wider than

the

sum

of the

particulars.

In an imperfect induction the conclusion

beyond the cases examined, so as

to

extended

is

include

all

like

cases.

The to the

process from the part to the whole, from the less more general, can never be a certain one, but

there are different degrees of hazard attending

it.

Induction by Simple Enumeration. 150. Induction by Simple Enumeration consists in

affirming

something as a universal truth on the mere

ground of uncontradicted experience, without any attempt to arrive at a cause.

and the

first

six

seventh to be so.

If

one draws marbles from a bag,

prove to be green, one expects the On this ground all swans were in

ancient times asserted to be white, and even

may be

forests in Africa

be black.

This 1

is

the

where

all

induction

Novum Organwn,

Lib.

I,

men

now

which Bacon Aph.

there

are believed to

cv.

1

con-

OF IMPERFECT INDUCTION. demned

a childish thing, precarious in

as

and exposed

to risk

notwithstanding over

adult

custom

to

its

childishness,

Hume

intelligences.

mould

its

conclusions,

from a contradictory instance.

of Cause

conception

145

itself

it

indeed found

nothing

But,

has great influence

but

this

in

the

power of

the mind.

Scientific Induction.

an attempt to arrive at by detecting the real connexion of

151. Scientific Induction

laws

of causation

is

things which underlies superficial connexions.

The connexion between

and white

the swan-nature

is

a superficial connexion, as was shown by the discovery in Australia of black swans,

which the Ancients took as

typical of the prodigious

Rara

But

avis in terris, nigroque simillima cygno.

could be duly established by observation and

if it

experiment that there was something in the climate of Europe, and not in that of Australia, which blanched the feathers

of a

swan,

we should then have

induction, valid as far as

it

a scientific

went, though doubtless not

penetrating to the ultimate fact of causation. 152.

The

specific difference

between an imperfect

and a perfect induction has come of late to overshadow in importance the difference between induction generally and deduction so that it is now often said that perfect ;

induction

is

a form of deductive inference.

When

people

OF IMPERFECT INDUCTION.

146

the

differentiated

from deductive

point

general

;

The same

thing

may be

is

is this

we proceed from Deduction we do not.

the

In Induction in

inference

whereby inductive

speak thus,

less

to the

more

expressed more technically

thus

In an inductive inference the consequent the antecedent

This

;

an exhaustive

is

arrived at

in a deductive inference

division

is

it is

wider than

not.

of inferences, being

by dichotomy.

153. If therefore

induction

alternative for deduction,

it

will

be given as the sole not do to say that in

in

we proceed from the less to the more general This deduction from the more to the less general.

is

like forgetting that there

induction

on a For

flat

;

is

such a thing as walking

surface as well as ascending or descending a

the consequent

may

be neither more nor

less

than, but just as general as, the antecedent.

admissible

is it

to say that in induction

particular to the universal, in deduction

to the particular.

For, in addition to

hill.

general less

Still

we argue from

the

from the universal

what has

just

been

is based may said, the propositions on which an induction in a statement themselves be universals, which are merged

of

still

higher universality.

Traduction.

The name Traductive antecedent.

Inference

is

sometimes applied

which the consequent is just as wide as the Under this head come the inductive syllogism,

to the case in

OF IMPERFECT INDUCTION.

147

most forms of immediate deductive inference, and gisms made up of singular propositions, Brutus was the founder of

syllo

e. g.

Roman

liberty.

Brutus was a patrician. .

.

A

patrician

was the founder of

Traductive inference,

it

will

Roman

be observed,

is

liberty.

a species of

deductive inference.

L

2

CHAPTER Of Apparent LET

154.

it

is

known

as

not in this

or

scientific

have seen already that perfect induction In this chapter sense an induction at all. in

Mill

follow

shall

distinguishing

apparent from real induction. 155. When a mathematician line

straight

we

induction

real

We

induction.

we

Inductions.

be understood that by

mean henceforward what

is

IV.

cannot meet a

circle

has in

of

cases

other

proved that a more than two

established the same thing succes points, and has then the parabola, and the hyperbola, sively of the ellipse,

does he

make an

universal

property

answer the

is

No

!

unknown.

induction in of the

there

Mill

s

is

is

sections

the

strably

the

of perfect induction

is

that

a true generalisation, although

ways

a

The

known

with being nothing to the facts, the cases dealt all

as

cone?

of the

no process from

down

to

reason for distinguishing this from

an ordinary instance conclusion here

laying this

in

which

to be intersected by a plane.

it

is

possible

for

it

the

adds

demona cone

This however does not

form of the argument, which, like any other the head of traduction. perfect induction, falls under

affect the

OF APPARENT INDUCTIONS. when we have proved of

156. Again,

ABC

triangle

of

all

triangles?

name would be

priate

But he

we

If

angles

infer a universal

in asserting the

an appro

do, says Mill,

For though we not. have when we conclusion only examined

we do

a particular instance, the conclusion nevertheless

on the evidence of the

believed believe

because

it

which

stration

applied to question

;

two

induction by parity of reasoning.

of opinion that

is

the particular

are equal to

do we make an induction

right angles,

same

that

three

its

149

is

not

is

We

particular instance.

\ve perceive that the process of

demon

one case might equally well be how Mill himself answers the

applied to

This

all.

is

but those who, in spite of Berkeley,

retain

still

a belief in abstract ideas would say that the demonstration

never referred to a particular triangle at

all,

but to the

idea of a triangle, or to the concept three-sided figure.

There

When,

is

therefore in this case

as in the

no room

for generalisation.

seventh proposition of the

book

first

of Euclid, there are different cases to be considered,

do make a generalisation, when we result that

it is

assert as

the

we

final

impossible in any case that there should be

two similar triangles on the same side of the same base. But here again the generalisation adds nothing to the facts,

and the argument

falls

under perfect induction.

157. Again a mathematician, after having calculated

a sufficient the

number of terms

law of the

series,

subsequent terms theless

this

to arrive at

what

called

is

does not hesitate to assume that the

will

resemble the preceding.

Never

cannot properly be called induction.

For

OF APPARENT INDUCTIONS.

150

be

his conviction of uniformity, in order to rest

on a priori considerations

been arrived

and,

;

when

the assumption of uniformity has

at,

must

valid,

these have not

some

As an instance of how we may times proved fallacious. be deceived by trusting to uniformity in arithmetic, take the following series of

numbers i, 1,

Each of

these

is

3

1

2

ist

1=

i

81=

7

2

power

3rd

128

7th

each

term

in

What more tempting

ninth

3

i.

1

= 127. is

a

then than

to

lay

any odd power of Yes a prime number ?

The

1

series

the

that

series.

diminished by

321=

5th

And

I2 7-

,

an odd power of

number.

prime

down

law

the

2

diminished by

:

but try the next term of the

power of

2

i

will give

diminished by

i

is

us

511,

We

have here then only the precarious induction by simple enumeration upset by

which

is

divisible

by

7.

a contradictory instance. 1

58.

The

true induction

last is

process which Mill distinguishes from

what was called by Dr. Whewell

Colligation of Facts.

The

both by Whewell and

Mill, will serve to

of this process.

the

well-worn instance, employed

show

the nature

Kepler wished to discover what kind

of orbit the planet Mars

moved

in.

observe

was impossible to but a number of

It

its progress continuously; detached observations had been made as to the apparent

places occupied by the planet.

The

question for Kepler

OF APPARENT INDUCTIONS. was what kind of

orbit the spaces

would make, supposing them After a

good

to

between these points

be

all

a

in

description

was no

there

Mill,

says

joined together.

deal of unsuccessful guessing Kepler dis

covered that an ellipse exactly suited here,

151

general

the

terms

induction,

of

a

For there was nothing

set

case.

Now

but

merely of observed

the conclusion phenomena. which was not already contained in the observations on which it was based. We might as well say that a navi gator, after sailing round some newly-discovered land,

makes an induction when he

The term

it

is

to

be an island.

associated in the

Logic with a somewhat tedious Mill accuses his opponent of confounding

minds of readers of Mill controversy.

with induction

it

declares

Colligation of Facts

in

;

and

s

that this charge

is

not unjust

may

be gathered from the following passage in the Philosophy

of

the Inductive Sciences (Vol.

p.

I,

43)

The

discovery

of a truth by induction consists in finding a conception or

combination of conceptions which agrees with, connects, and arranges the facts/ But at the same time a Colli gation of Facts, according to Dr. Whewell,

is

more than

mere sum of them, since in it there is introduced a mental conception which is not in the facts themselves. the

The

facts are

nected,

till

the

known, but they are insulated and uncon discoverer supplies from his own store

a principle of connexion. will

not hang together

To

this

conception

till

The

pearls are there, but they

some one

provides the string.

Mill answers, fairly enough, that is

not in

the

facts

it

is

true the

themselves, but that the

OF APPARENT INDUCTIONS.

152

properties conceived of are;

be a correct one,

and

that, if the

conception

must be a copy of something

Sometimes however, owing

facts.

vation, facts

it

the conception

is

to difficulties

in the

of obser

not derived directly from the

contemplated, but the mind has to supply various

conceptions

till

one

is

found

to

fit

them.

The

latter,

Mill

acknowledges, was the case with Kepler. Nevertheless the fitting conception can only be that which describes the actual state of the facts.

may

The

selection of conceptions

be called guesswork, but such guessing

the gift of

is

genius.

The

upshot of the matter seems to be that induction is something more than finding a conception to fit certain facts. it

is

Every induction indeed a form of finding the

colligation of facts

is

is

One

a colligation of facts in the

not an induction.

are certain facts in the Latin language.

and feminine nouns with nominative feminine

;

all

the rest are masculine.

as they stand are arbitrary.

when we

find that those

We

but every

Many

Here, for instance,

Among in -or

masculine

only arbor

These

facts

is

taken

reduce them to

which have a long vowel

law in

the stem are masculine, while the only one which has

This may be said to be the But fitting conception whereby we colligate the facts. has for been no there is no induction there here, discovery a short vowel

of a cause.

is

feminine.

CHAPTER Of it is

V.

Axioms of Induction.

the

159.

HAVING seen

now

time to attend to what

sufficiently

what induction

is

not,

it is.

is the process by which we arrive at general by the way of experience. induction is to begin from the beginning, it must

Induction truths If start

from particular

These

facts.

facts

particular

Experience

perience.

to us

by Ex

either external or internal.

is

External experience

become known

is

on

the use of the senses either

the part of ourselves or of others. If

human being were to own experience,

each

the limits of his

knowledge would be of the truths that to us

possible.

we suppose

very

source of

all

is

that great

called History.

called

little

up within

progress in

far the greater

ourselves to

from the senses of other people.

senses at second-hand

is

By

shut himself

number

know come

This use of the This

Testimony.

is

the

department of knowledge which

Science has to depend largely upon

but seeks to bring everything to the test

it,

of immediate

perception.

Internal experience

within our

This

is

is

what passes think, and will.

the consciousness of

own minds when we

feel,

the ultimate source of that other great department

OF THE AXIOMS OF INDUCTION.

154 of

human knowledge,

or rather speculation, which

is

called

Philosophy. 160. But here a difficulty presents

Experience,

the aid of

by but

it

memory

what

testifies to

to say as to the

:

Again experience only

immediately before

is

;

can be extended to the past

it

silent as to the future.

is

it?elf at the outset.

speaking, only refers to the present

strictly

it

has nothing

it

:

innumerable things and events even in

the present which are

beyond its ken. If experience is here and now, how can we by its elsewhere or what is yet to be ? How,

thus limited to what

what

aid divine

is

is

can we ever reach general truths by the ? Experience can assure me that this

in other words,

aid of experience fire

burns and

crush

me

?

water wets.

this

I to

know

I

fire

because we judge of

after repeated experience,

it

we have by some means truths,

am

But how

meet may not cool or the next water The question sounds nonsensical, but that is

that the next

namely, that

when

or other arrived at two general

burns and water wets.

fire

By what means then were these general truths arrived Not by any elaborate process of reasoning. The method was a very simple one. We took them for at?

granted on the since

first

experience, and

been verifying our hypothesis.

only, but the burnt puppy

ductive instinct

without

it

no

is

also,

Nature has ever

Not

the burnt child

dreads the

fire.

The

in

rooted deep in our animal nature, and

intelligence

have preserved that body would all have shattered

that possessed a

in

body could

a universe like ours.

their

organisms

They

long ago

in

OF THE AXIOMS OF INDUCTION. a blind collision with natural forces. inductive instinct that,

established in our

when once

this

which Nature

fails

to verify.

An

always.

eclipse

in all cases

This inductive

oftens sets

It

to the

things, such as fire

connexion holds

is fact

not infallible.

owing

a connexion has been

minds between two

and burning, we assume that and that what is fact once instinct is

It is

155

up hypotheses

may be

followed

one instance by a national calamity, or a comet by a good vintage, but it does not follow that all eclipses and

in

all

comets

The

will

have the same attendant circumstances.

hypotheses that are not verified have to be dropped

by the race as well as by the individual. Observe then that in the very possibility of arriving at general knowledge by experience there are two assump tions

involved

first,

that there is a

events, secondly, that this

connexion

two assumptions convert our world Let us for a

moment

refuse

to

connexion between

will continue.

These

into a rational system.

make them.

Let

us

suppose ourselves transported from the causal world in

which we

live into

In such a

a purely casual world.

world events would take place anyhow, and always on their

own

account, without the least connexion with what

went before or what followed

after

them.

Chance and

If contact spontaneity would be the order of the day. with fire happened on a given occasion to be followed

by the pain we arose of

itself

circumstance.

call

burning,

we should

say that the pain

without any connexion with the antecedent

Under such a system

possible would be a

the only

knowledge These

register of particular facts.

OF THE AXIOMS OF INDUCTION.

156

would furnish no clue

particular facts

we

should never

because

we

rise to a

in

live

and

to other cases, It is

only

a world in which antecedents

an:!

general proposition.

consequents have a fixed relation that general knowledge is

possible to us.

But now without

let

make

us

the

first

of these assumptions

Let us

second.

the

suppose that there is a connexion between events, but deny that this connexion is bound to continue. Should we be any nearer the of general

possibility

knowledge than before

If the

?

water which wet us once were to bite us another time instead, or the

entertain

involved in causes,

if

which burnt us yesterday were

fire

us with a concert to-day, all

resemble capricious

to call

It

161.

if fire

When

so, in

wills,

belief

to

be

The

such a world would

whose action could not

we might hold

as to causation

would be an hypothesis which Nature would be as reasonable to hold that

burning took place of instance,

them

human

Any

in a particular case failed to verify.

still

the perplexity of a casual universe.

we chose

be relied upon.

we should

itself

as that

fire

burnt us in a single

acted differently again. the

two assumptions above spoken of are

clothed in philosophical language, they assume the form of the two axioms of induction, which are (1)

(2)

The Law

The Law The Law

of Causation. of Uniformity.

of Causation lays

down

that

Every event has a cause.

known

as

OF THE AXIOMS OF INDUCTION. It

denies that things take place of their

spontaneously

157

own accord

or

;

but whenever an event happens, directs

us to something that went before, as having brought

it

to pass.

The Law of Uniformity asserts further that The same cause always produces the same in other words, that

under

effect/ or,

circumstances like results

like

ensue. 162.

When

these axioms have once been laid down,

inductive inference

all

was an animal

is

turned into

instinct that could give

deductive.

no account of

What itself

now assumes

the dignity of reasoning.

inference, as

Archbishop Whately declared, may be

garded

and

as a syllogism with the

this

major,

when

true of the cases

similar cases.

and the other

may be

re

major premiss suppressed ; down that what holds

supplied, lays

under consideration

will

hold true of

all

Thus when, having found that this, that, magnet attract iron, we advance to the All

general proposition,

ing

Every inductive

attract iron/

magnets

our reason

expressed as follows

Whatever holds

true

of

magnet holds true of

this,

that,

and the other

all.

Attracting iron holds true of this, that,

and the other

magnet. .-.

Attracting iron holds true of

Now the assumed then do

major here

we come by

it ?

It

all.

is

is

not self-evident. plain that

it

How

rests for its

evidence on the larger assumption of uniformity in the course of nature.

While the immediate major premiss

OF THE AXIOMS OF INDUCTION.

158

then in every instance of induction

some

premiss

is

Law

the

of induction

is

of Uniformity

to ascertain

In order to solve

fact

into the

The

real

problem

are warranted in

problem we have

this

we

to eliminate at the

arrive

of sequence which underlies the appearances.

163. Mill admits that

every induction

form of a syllogism/ and

may be thrown

when

that,

this is

done,

of the uniformity of the course of nature

the principle will

itself.

when we

the unessential circumstances until

pure

the affirmation of

what holds true of one case holds true of

asserting that all.

all

is

particular kind of uniformity, the ultimate major

appear as the ultimate major premiss of (III. 3, i): but, in accordance with his

tions

induc

all

restriction

of inference, and along with it of proof, to induction, he maintains that the major premiss does not at all con tribute to prove the conclusion, though it is a necessary its being proved; since no conclusion is proved for which there cannot be found a true major

condition of

premiss

in

we

other words

are

drawing a particular except on the

would

suffice

for a

But

universal.

warranted in

never

same evidence as if

we

subtract the

major premiss from the proof, what is there left but the inductive instinct which leads us from one particular case to another like

it ?

This

admit that brutes reason

may but

:

be called reasoning,

who

will

call

it

if

we

proof?

might be better however to say that human reason rests upon this animal intelligence than that this animal in It

telligence

is

itself

realises itself in

reason.

man,

it

When

this

brute

becomes converted

instinct

into

faith

OF THE AXIOMS OF INDUCTION. in the

scientific as faith in

we can

find

no physical order,

it

God no

to the religious

mind.

Without

spiritual order, without the other

in the universe.

164. Reverting let

a faith as essential to the

uniformity of nature

the one

159

now

to the first of our

two axioms,

us be careful not to put more meaning into

The Law

properly conveys.

Every event has a cause. thing has a cause.

where, put

it

It

it

than

of Causation asserts that

does not assert that every

There must be an uncaused some

where we

will,

whether in matter or in mind,

or in something behind and above

them both.

CHAPTER Of

Observation

and Experiment.

may be

165. EXPERIENCE

VI.

divided into two branches

(1) Observation.

Experiment.

(2)

Observation

is

passive experience.

Experiment

is

active experience.

In observation

we

study things under nature

s

conditions.

In experiment we impose conditions of our own. The object of both is to furnish us with true

on which

our reasoning.

to base

importance

of the

Hence

two processes, since they form the

foundation of the temple of knowledge.

looking

facts

A

imagined. difficulties

a

in

the face

teacher

which

book which

arise lies

it

is

is

is

much

often called

the

upon

faculty for

might be to

combat

merely from the student misreading

The mistake

some prepossession

with the book of nature.

phantoms obsess

The

rarer than

open before him.

generally traceable to

So

facts

the extreme

in his

mind.

All sorts of baleful

mind of man and prevent

seeing things as they are.

is

it

from

OF OBSERVATION AND EXPERIMENT. 166. Experiment

is

a

advantages which (1) (2)

(3)

We We We

can

more potent engine of

The

covery than observation.

161 dis

the chief

following are

possesses over the sister process

it

isolate the

phenomenon.

can vary the circumstances. can reproduce the phenomenon

at will.

Again experiment is more precise, more subtle, and more expeditious than observation. It is more precise, because

we can surround

the

phenomenon under

exact

set

of circumstances

vestigation

we

require.

with the It is

more

subtle,

because

it

It is

more

expeditious, because

enables us to

mere observa

detect small changes, which might escape tion.

in

which

can give us in

it

a short time what nature might present to us only after a long period, or might never present to us at

On

the other

hand we may say

all.

that observation has

two advantages over experiment 1. It can be applied to many branches of knowledge where experiment is out of the question. For instance, we can observe the courses of the

stars,

as if they

we cannot ex

but

were so

periment upon them, many billiard what from the we can observe issue results Again

balls.

intermarriage of a lunatic and an

but

idiot,

it

would be

highly improper to experiment in this direction. 2.

It

can be used in the search for causes as well

as in the search for effects, whereas experiment, from the

nature of the case,

is

limited to the latter.

a cause and experiment as to

its

effect

:

We

can take

we cannot

M

take

1

OF OBSERVATION AND EXPERIMENT.

62

an

and experiment as to its cause for ignorance cause, as Bacon says, deprives us of the effect.

effect

of the

;

we can do then is to watch till we see the produced, unless indeed we produce it by accident. All that

167.

There

however no

is

observation and experiment it

;

one runs

into the other

Even

a question of degree, not of kind.

is

between

essential difference

the

effect

;

most

the

attention. passive observation involves the mental act of at the foot observations said to take is meteorologist of a mountain ; but if he carries his barometer up to the

A

amounts

top, that

to

an experiment,

The

the circumstances.

for he

is

is

productive of light as 1G8.

What we

if

we had done

Berkeley

sat

down

to

and

write

If this is

as

for ourselves.

a process con

is

partly of inference. his

Theory of Vision, he took

Essay towards a

When New

for granted as

agreed by and immediately, cannot be By distance he meant distance in the line of sight.

that distance

seen.

of

we suppose

relates to a third

it

itself,

was agreed then even

of what

The

it

observation

call

sisting partly of sensation

It

that are usually

the great object of experiment.

any case done for us by nature, the result

in

all,

then varying

separating things that usually

go together and the combining things found separate

is

in

his time

that

ourselves to see

dimension of space

novelty of his theory consisted

all is

a large part in fact

that

really inferred.

only in

the

new

ground on which he declared the inference to be based. These inferences which enter into perception by the senses are

instinctive

but

not

infallible.

I

remember

OF OBSERVATION AND EXPERIMENT. as a

boy lying on the grass on a summer

into the

up

very high up

saw, as

I

sky.

in the air.

was mistaken and

that I

I

day looking

thought, a very big bird

In another that

s

163

moment

found

I

what had

really happened was that a very small fly had passed quite close to my eye. I had somehow drawn a wrong inference from the sensa

tion actually experienced.

The

large range for inference that there

what makes

is

due

within

it

limits

own and

our

Even a passing thought

make

to

instance, fast I

open,

as I

my

in observation

other people

mind may

senses.

s

serve at times

For

not in them.

is

was coming down

to

break

study and, the door being partly

saw, as I imagined,

who was his

in the

us read into the facts what

some years ago

heard a noise in I

is

not unphilosophical for us to distrust

the

inside

room a Parsee

house with me, with the cap on head which he usually wore. When he came down staying in the

to the dining-room, I referred to his having

been

in the

study, and he assured me that he had only that moment come down from his bedroom. I have no doubt that

what

I

really

the room,

me

and

caught sight of was the housemaid dusting that

some untraceable current

of thought

impose on her the appearance of the Parsee. Again here is an experience which is not uncommon with me and which I do not suppose is peculiar to myself.

led

I see

a

to

some one whom

crowded

street.

I

On

know advancing towards me getting nearer I find that I

mistaken, but very soon afterwards

who had been

in

my

mind.

I

in

am

see the real person

Perhaps

this fact

M

may 2

be

OF OBSERVATION AND EXPERIMENT.

164

that really I have seen the person in the distance without attending to the impression, and that

accounted

this

At

for thus

impression then fixes

all

never

itself

on

the

wrong

individual.

events I hold that as a working hypothesis.

known

the experience occur

was round a corner.

when

I

have

the real person

CHAPTER

VII.

Uniformities of Coexistence.

Of

169. INDUCTIVE inference relation of cause

and

effect,

mainly concerned with the

is

because

the establishment of general truths,

it

is

concerned with

and things

as a rule

do not hold true generally unless there be a cause why I say as a rule/ because there are they should do so.

some general

truths

that

do not

rest

upon

causation.

Truths of causation are uniformities of succession

;

but

besides these there are uniformities of coexistence. 170. Let us begin with a

own

science.

are valid in

It is all

humble instance from our

a general truth that exactly six

the figures, yet

aware, can be assigned for the

has

its

special rules

and we can show

that there are six

moods which do not break any of them.

As

this is the

case with each, a perfect induction assures us that

with

all.

But that

all

moods

no reason, so far as I am fact. Each figure indeed

it is

so

should coincide in the same number

mere piece of undesigned symmetry. All that we can But suppose some one say is, it so happens that they do. were to supply us with a reason for believing that there is

a

must be the same number of moods this

would not make the

truth

valid in

to be

each

figure,

one of causation.

1

OF UNIFORMITIES OF COEXISTENCE.

66

For a reason with

A

it.

is

not a cause, though

reason

of deduction, not of induction.

when

it is

often confounded

something that belongs to the region

is

It is in fact

stated fully, the premisses

a premiss or,

which prove some con

clusion.

The

171.

general truths with which the purely mathe

matical sciences deal are uniformities of coexistence, not

of succession.

and the

the triangle

is

inference

different properties, for instance, of circle

can be shown by reasoning, or

intuition, to inhere in the

appear by there

The

not arrived at by the 172.

Coming

way of

experience.

then to physical truths, to which the

notion of cause alone applies, place

same concept; but

no question of causation involved. Inductive has nothing to do with them, because they are

that

we may

notice in the

which are directly traceable to causation, as being effects of a

first

there are certain uniformities of coexistence

common

and darkness

joint

cause, e.g. the coexistence of light

in the opposite

hemispheres of our globe

ubi primus equis Oriens afflavit anhelis, sera rubens accendit lumina Vesper.

Nosque Illic

There are also many cases of coexistence

may

suspect causation but

attributes possessed in

cannot prove

common by

in

which we

it,

as in the

natural kinds.

Nobody

can show a cause why animals that chew the cud should divide the hoof: but there stands the fact for all that. It rests

only upon an induction by simple enumeration. of mind with body, and of mind in its higher

The union

manifestations with a complex structure of brain,

is

a law

OF UNIFORMITIES OF COEXISTENCE. of coexistence

which no exception has as yet been disembodied intelligence is not

to

admitted

generally

:

recognised by science, nor do metal entertaining us with

amount of mind-stuff

The

widest of

167

there

we

wit

its

ever find a

may be

latent in

laws of coexistence

all

lump of

and wisdom, whatever

is

it.

the connexion

between the two attributes of body known as inertia and a connexion which, within the limits of our gravity is

experience,

found

to

pervade

a rather misleading term. of bodies

refusal

It

all

nature.

Inertia

move, unless force be applied

to

them, but also their refusal to stop moving, unless counteracting

Now

is

has to cover, not only the to

some

be brought to bear upon them. an attribute distinct from inertia may

cause

that gravity

is

be seen from the matter for matter,

fact that gravity, or the attraction of is itself

one of the counter agents to the This force at last brings

continued motion of a projectile. it

to

earth,

where

resistance of that

though thus exact

its

motion

And

body.

yet these two attributes,

distinct, are invariably

proportion

to

soon stopped by the

is

found together, and in

one another.

It

is

not,

properly

body which prevents your surface, but the inertia which is

speaking, the weight of a heavy

pushing

it

along a level

proportional to the weight. 1

73.

The

truths with which the

grammarian and the

student of language deal are uniformities of coexistence,

not of succession.

Grammar.

Let us take an instance from Greek

By employment of the Method of Agreement it may be shown that the only common element a wide

1

OF UNIFORMITIES OF COEXISTENCE.

68

in all

mood

forms of the optative

But when our inductive survey that iota

is

the single letter iota.

is

complete,

we do not say

the cause of the optative, but only that

sign of the optative.

A

sign

The same

from a cause. effect,

is

but the same sign

is

something

is

the

always the same

cause has

may

it

quite different

have different

significates.

Thus, though iota is the sign of the optative, that does not prevent it from being the sign of the dative too ]

.

We

Method of Difference

cannot apply the

since they involve, at least directly,

no causation.

to signs,

Nor

in

chosen can we employ the Method of Concomitant Variations, since neither iota nor the force of

the particular case

the optative

is

a variable quantity

:

but

we can employ the known force

Method of Residues and argue from the

of the other formative suffixes that the special force of the optative

must be

signified

by the

are anticipating, as the inductive

explained.

remark

that,

We

will therefore

Here however we

iota.

methods have yet

to

be

quit this subject with the

though a great deal has been done for the little attention has been bestowed

logic of succession, very

upon the logic of coexistence, which seems still Bacon or its Mill. This is perhaps due to

to await

that it rests solely upon Agreement, and has been deemed of minor importance.

therefore

its

the fact

Hume (Essays, Vol. II, p. 64 n, ed. Green and Grose) dis Cause is different tinguishes between Cause and Sign thus from a Sign ; as it implies Precedency and Contiguity in Time and Place, as well as constant Conjunction. Sign is nothing but 1

A

A

a correlative Effect from the

same Cause.

CHAPTER Of

VIII.

the Conception

174. SINCE

it is

of Cause.

the relation of cause

and

effect that

supplies us with most of the general truths which

we reach

by the way of experience, and since induction consequently is chiefly concerned with this relation, it becomes of im portance to attain,

if

we

can, a right conception of cause. In

order to do so, we must begin by defining some other words. 175. First

As used

in

let

us take the word

common

phenomenon. means some

phenomenon

life

An

eclipse,

much more

readily

thing out of the ordinary course of nature.

a comet, or

an aurora borealis

phenomenon than a an announcement of the

called a

see

is

When w e

sunrise or sunset.

not expect an ordinary baby.

infant

r

phenomenon/ we do

This connexion wilh the

marvellous however must be entirely rejected from the

meaning of Again

the term as used in logic.

in ordinary parlance

phenomenon tends

confined to an appearance to the eye.

But

use of the term the peal of the thunder

phenomenon

to be

in the scientific is

no

less

a

than the flash of the lightning, the smell of

a rose no less than the colour, the feel of furniture in the

dark no

less

than the

sparks

which result from knocking

one s eye against it. In short a phenomenon which presents itself to the senses.

is

anything

OF THE CONCEPTION OF CAUSE.

170

Here we might

there were

if

stop,

none but physical

be taken into the account. But people speak phenomena also of mental phenomena. We must therefore enlarge our to

and say

definition is

that a

is

anything which

presented in experience either external or internal 176.

universe

may are

it

big toe

.

the whole history of the

be divided into the events which follow that

phenomenon and follow

s

l

say, a twinge of

Now, given any phenomenon

gout in somebody

the

called

landmark of

events

which do

Consequents;

Thus

called Antecedents.

a

phenomenon

history, dividing

that

that

do not are serves as

phenomenon

every it

all

All

not.

by a sharp dichotomy.

Let the reader notice that we have not attempted to divide

the course of events into those which

and those which come would be with

it.

of gout

to leave

slates of

after a all

given phenomenon.

At the moment when somebody felt that twinge his big toe there were innumerable events in every quarter of the globe

system and

in

the

and throughout

abysses of space and in

being beyond our ken.

All these are, properly

speaking, Concomitants of the given phenomenon 1

This

the events contemporaneous

in

happening the solar

out

go before

The word

phenomenon

seems

to

:

but, for

have been pitched upon

with a view to expressing the facts from which we start in our inductive inquiries without raising any metaphysical questions as It is consequently a very wide and to a reality underlying them.

vague term, confusing as it does under one head material sub stances and the sensations into which we resolve them, together with all states of consciousness, and all events, which are relations

between substances.

OF THE CONCEPTION OF CAUSE.

171

convenience of expression, the accompanying are merged with the preceding circumstances under the one head of

Antecedents.

An Antecedent then may be defined as anything which precedes or accompanies a given phenomenon ; and a Consequent as anything which follows a given phenomenon

.

Now among

177.

phenomenon upon

]

there are

the innumerable antecedents of

some

that

production and others that have none.

its

any

have a certain bearing

ceding the supposed twinge of gout there

was

Pre

that has

all

happened in our universe from the time of the solar nebula and whatever may have gone before that down to the nineteenth century. But we do not regard all these events as contributing to the

line

antecedents.

a body,

it

question.

would be very difficult to between contributary and non-contributary

In a certain sense indeed

draw the

in

phenomenon

For,

if

it

we remember

becomes evident

that

all

that

gout implies

the changes

on the

earth s surface which rendered possible the existence of

animal organisms are at once brought of looking at the thing would

an endless postulate

in.

But

make any such

this

way

speculation

So we cut short the inquiry by a task. Given a human body, what are the antecedents

which have some bearing upon the production of a twinge of gout?

The proximate

cause

is

the

presence of uric

The words antecedent and consequent are very hard worked. This is the third time that we have had to define them in different senses. See 138. 1

OF THE CONCEPTION OF CAUSE.

172

But what are the antecedents of

acid in the blood.

Let us say that they may be heads of inherited tendencies indulgence in

free

good

summed

in the constitution

?

and a too

Neither of these by

living.

this

up under the two itself

would produce the phenomenon but, if either were taken away, the phenomenon would not occur. The inherited :

tendencies might be there, and yet gout never be de if

veloped,

a careful rule of living were observed

on the other hand the too on the it

particular

living

would not produce the

effects,

phenomenon which we have

want a term

it.

while

;

good

part of a person not of gouty constitution, though

would have other bad

the

free indulgence in

in view.

to separate off the antecedents

Now we

connected with

phenomenon from those which are unconnected with The term which does this is condition. A Condition

then

we

menon,

define as an indispensable antecedent of a or, that

The word

178.

pheno

without which something would not be.

cause

popularly used for the

is

in particular condition which happens to be uppermost

the

mind

nexion.

at

a given

Thus

moment

or in

might be said

to be the properties

the setting

to

fire

some

the cause of an explosion by

it

special

con

gunpowder

of the gunpowder, or

by knocking the ashes out of a pipe,

or the culpable carelessness of the

man who smoked

it.

Philosophically speaking, however, the cause

but

all

is

near

not one

of these.

Again let us suppose that a labourer has been killed by The British jury returns a verdict a fall from a ladder. of

accidental death.

But

let

us look into the case

more

OF THE CONCEPTION OF CAUSE. The

in detail.

173

accident took place in the morning; there

had been rain the night before, and the rungs of the ladder were wet ; the man was carrying a hod of bricks

on

his shoulder

his foot slipped

;

that the weight got shifted

The

he came.

on one of the rungs, so

he lost his balance and

;

overseer might in his

own mind

set

down down

the wetness of the rungs to be the cause of the death

and

be more careful in future to have the ladders kept under a mechanician might attribute the disaster to the the consequent loss of shifting of the weight and cover

;

equilibrium it

;

while the physical philosopher might see in

an instance of the attraction of matter

now

The man

jury.

that

for matter.

us supply a detail which failed to

let

morning.

s wife

On

The

difference.

come

But

before the

had accompanied him to his work way they had had a speculative

the

wife with a parting shot

had emphasized

her view of the case, which caused her husband to look

round before he was

safe

on

the scaffolding,

whereupon

The poor widow might for the rest her own unseasonable argumentative-

the accident ensued.

of her

life

regard

ness as the sole cause of the phenomenon, to the exclusion

of the part played by lubricity and gravitation.

speaking occasion

however was not of

her

husband

s

the death.

meant the change which brings cause into operation. of gunpowder.

cause,

Her

but rather the

By an Occasion

is

the other parts of the

spark which lights a train burning of the Pope s Bull was

It is the

Luther

s

not the cause, but might be said to have been the occasion of the Reformation.

OF THE CONCEPTION OF CAUSE.

174

While the term

some

salient

occasion

and

thus be

may

positive incident

employed

for

which completes the

collocation of circumstances required for the production effect, nothing but the whole collocation of cir cumstances can in the full sense be considered the cause.

of a given

We

therefore

sum of which, Effect

now

reach a definition of Cause as the

the conditions of a

or

phenomenon,

takes

when

takes place,

179. In avoid, the

a given set of conditions

another

word

sense,

cause

is

of heat or that a

use the term

man

given

which

is

it

is,

struck a blow.

when speaking of

an or

is fulfilled.

impossible

used for any substance

garded as an agent, as when we say that

we

or, that,

Conversely

place. something may be defined as something which always is,

fire

to re

the cause

is

It is in this

sense

the

Combination of Causes. two or more causes acting together produce more of the same kind of effect which each would have

When

produced singly, we have what is known as Mechanical Combination of Causes or Mechanical Intermixture of

When

two or

Effects, e.g.

two horses pulling a

more causes

acting together produce a different kind of

effect

load.

from what any of them would have produced singly, is known as Chemical Combination of

we have what

Causes or Chemical Intermixture of Effects,

e.

g.

oxygen

and hydrogen producing water. Mechanical combination of causes Mill

the Composition of Causes.

mechanical causes

is

the

same

as the

is

The

also joint

sum of

called effect

by of

the separate

OF THE CONCEPTION OF CAUSE. even when

effects,

il

seems

least

be

to

175

Thus when

so.

two equal forces acting in opposite directions keep a body is the same as though one had pushed it so far and in one direction and then the other had pushed it back at rest, this

;

again when two

forces acting

a body at right angles

upon

same

though the body had reached the same point by describing two sides of a square under the action of the forces separately. propel

On is

it

in a diagonal line, this

the other

hand the

is

the

as

joint effect of chemical causes

not calculable from that of the separate effects, but

requires

chemistry

a is

fresh

to

appeal

experience.

This

is

why

not a deductive science.

Mechanical intermixture of

effects

is

also called

Homo

geneous.

Chemical intermixture of geneous or Heteropathic. Mechanical intermixture ception.

All objects in

effects

is

some

also called

Hetero

the rule, chemical the ex respects

However

composition of causes.

is

obey the law of

startling the

transforma

which substances undergo through chemical com bination, the weight of the compound is always found to

tions

be the precise equivalent of the weight of the elements. 180.

The maxim

that effects are proportional to their

causes applies only to the case of homogeneous inter

mixture of

effects,

this

maxim

for

where

effects

are heterogeneous

no proportion between them.

Neither

is

applicable to the apparent cause

known

as

there can be

the occasion.

One

as effective as two.

spark igniting gunpowder

is

quite

CHAPTER Of

IX.

the Inductive MetJiods.

THE Inductive or Experimental Methods are the which the mind naturally adopts of establishing by ways 181.

aid of experience the effect of a given cause or the cause

of a given

They

effect.

and methods of

are both methods of discovery

proof, but

it

under the

is

latter

aspect

only that logic has to deal with them. 182.

These methods are

(2)

The Method The Method

(3)

The

(1)

The Method The Method

(4)

(5)

183.

causes

Canons

Indirect

in

five

number.

of Agreement.

of Difference.

Method of

Difference.

of Concomitant Variations.

of Residues.

These methods may be applied

or

to

will

proving

effects,

but

for

either to proving

simplicity

their

here be stated only from the former point

of view.

Canon of

the

If several instances

Method of Agreement.

of the occurrence of a

agree only in one thing, that thing

is

phenomenon

probably the cause

or part of the cause. 1 Mill speaks of four methods and gives five. It seems to be the Indirect Method of Difference which he does not consider

independently. Chapter 8 of Book III. is the Four Methods of Experimental Inquiry. Some times Mill speaks of the Inductive Methods (III. 9, 6).

entitled

to

entitled

Of

rank

OF THE INDUCTIVE METHODS.

177

Canon of the Method of Difference. If

an instance of the occurrence and an instance of

the non-occurrence of the in

one thing, which

is

in the latter, that thing

Canon of

same phenomenon

differ

only

present in the former and absent is

the cause or part of the cause.

the Indirect

Method of

Difference.

which a phenomenon occurs in one and several instances different thing agree only from the former, in which it might be expected to occur instances in

If several

but does not, agree in the absence of the same thing, that is

thing

probably the cause or part of the cause.

Canon of

When by some

the

Method of Concomitant

Variations.

two phenomena vary together, they are connected tie

of causation.

Canon of the Method of Residues. If

from a whole

as are

of the

effect there

known causes, the unknown cause or causes. due

to

of the Method of Agreement.

Illustration

Antecedents.

Consequents.

ABC ADE

abc

AFG Let

be subtracted such parts residue will be the effect

a

be an

effect, of

ade afg.

which we wish to establish the

cause.

The argument assumes

the following form.

N

OF THE INDUCTIVE METHODS.

778

G

Neither B, C, D, E, F, nor

is

the cause of

a,

for

it is

present where they are not. But a must have a cause.

A

.-.

is

the cause.

This argument

known

is

as Plurality of Causes

down

has been laid

It

not conclusive,

produces the same

same

this that the

what

is

that it

same cause always

the

cannot be inferred from

always produced by the same death, for instance, may be due

effect is

The same

cause.

to

.

but

effect,

owing

l

effect,

to such different causes as starvation, thirst, suffocation, disease, accident, violence, or decay.

Now

it

is

F or common to

possible that the effect

B

instance to

or C, in the second to

due

in the first

a

is

D

or E, in the third

G, and that A, though the only antecedent If to all the cases, had nothing to do with it.

a doctor were to cure the same disease on three separate

occasions by three different drugs administered each time in orange wine, it would not follow that orange wine

was a grand

specific

for

that

the non-medical observer might that

it

In 1

jump

to the conclusion

was. the

The

possibility

of a

fact of plurality of

who

of causes

lies

causes has often been denied.

Nature, Part

heartily here as to say that ledge of nature is built is

have the same cause sect. 24).

plurality

the

Hume

Sect. xv. 4) lays down the same effect never arises but from the same cause. differs from him in so much else, agrees with him so

Human

(Treatise of axiom that the

Reid,

form of malady, though

III,

the axiom upon which all our know that effects of the same kind must

(Inquiry into the

Human

Mind, chap,

vi,

OF THE INDUCTIVE METHODS. inherent weakness of the

179

Method of Agreement.

It

always conceivable, though not probable, that the effect

may be produced by we

cases

the

are

them

this

and

some purely

that

same time be present The more instances we collect, the less likely

all.

may

Number

becomes.

in order to

method,

a different cause in each of

considering,

irrelevant circumstance in

is

same

The Method

at the

of instances then

is

of value in this

exclude the chance of coincidence.

of Agreement

is

a method

chiefly

of

can point to laws of sequence, but, apart from experiment, we cannot be sure that they are laws observation.

of

It

causation.

185.

Let

chief

Its

applications of the

use

Method of

Illustration of the

indeed

in

is

suggesting

Difference.

Method of

Difference.

Antecedents.

Consequents.

ABCD BCD

abed

be an

a

bed.

effect,

of which

we wish

to establish the

cause.

The argument assumes the following The same cause always produces

Now

D

B, C, and

They

/.

A

But

The difficulty

same

effect.

a.

are not the cause.

must have a cause.

a

is

the

occur in the second instance

without being followed by .-.

form.

the cause.

reasoning is

to

here

make

is

conclusive.

sure that

The

practical

we have got two such N

2

OF THE INDUCTIVE METHODS.

l8o

instances as are required.

with them

:

Method of

Nature seldom presents us

The

we have to contrive them for ourselves. Difference

therefore

is

the great method of

experiment.

A

room

quite dark

is

flooded with

;

Why

light.

you press a button and it is do you believe that the pressing

of the button had something to do with the production

Because you find no other difference between the circumstances of the room at the one moment, when

of light?

it

is

in darkness,

and

at

the

next,

when

it

is

in

light.

to call the It elliptical way of speaking is the cause of the button light, but it pressing of the In the occasion. a good instance of what we have called

would be a very

a

room unsupplied

with

electric

apparatus

you might

of time without any production press a button to the end

But suppose that there were no accessory cir cumstances and nothing intermediate between the single

of

light.

antecedent of pressing a button and the consequent

we should then be

justified in

light,

saying that the light was

caused by the pressing of the button. When Gyges found that he became invisible, he ascribed the cause to the collet of his ring being turned inwards, because that difference discoverable between the moment was the

only

when he was (Plat.

visible

and the moment when he was not

Rep. 359, 360).

is to make sure great difficulty in an experiment the effect Sometimes that there is no hidden antecedent.

The

is

due,

negative,

not

to

which

the

change

itself,

we introduce

whether positive or

into

a

set

of

known

OF THE INDUCTIVE METHODS. but to the

conditions,

doubt on

If there is

means taken

this

point,

it

to

bring

l8l it

about.

has to be settled by

other experiments.

Method

Ideally the

of Difference

to the complexity of nature,

sure that

perfect, but,

Illustration of

tJie

*.

Consequents.

ABC

abc

ADE AFG BH DK

ade afg

bh dk

FL

fl.

the probable conclusion reached in the positive

instances by the

cause of

a,

Method of Agreement,

where

A

is

come

positive ones

;

within

the

is

An

is

the

the

negative

fact

as

the

otherwise the absence of the given ante

the illustration 1

that

same range of

cedent would be of no significance. in

A

not.

must of course be understood

instances

that

confirmed by the negative evidence of the

is

a/

absence of It

absolutely

Method of

Indirect

Difference Antecedents.

Here

owing

conditions are complied with.

its

186.

is

we can never be

by

This

the retention of one

is

indicated

of the old

name for this method proposed by Mill himself Method of Agreement and Difference. He also a double employment of the Method of Agreement Hence Professor Bain suggests the name Method

alternative

the Joint

speaks of it as 4).

(III. 8,

of Double

Agreement

entitled

the Double

it

and Professor Fowler has Method of Agreement.

(Induction, p. 61)

OF THE INDUCTIVE METHODS.

182

antecedents

each of the

in

negative

instances.

This

reason \vhy in the statement of the canon

also the

is

183) we inserted the words in which the phenomenon might be expected to occur but does not.

(

Further

be noticed

should

it

that

the

negative

in

from the positive in more points than the mere absence of A. If, for instance, instead of stances

B

H

.

.

must

b h we had

.

ABC

with

differ

.

.

.

BC

.

.

.

b

c,

the comparison of this

a b c would give us the direct

Method of

Difference, and all the other instances would be super fluous. This is why in the statement of the canon we inserted the words different from the former. If

the

negative

instances

our presumption that

A

is

are

to

really

the cause

a

of

the is

point,

greatly

argument does not reach the demonstrative certainty which is attained, at least formally, It would only do so, if by the Method of Difference. Still

strengthened.

the

the negative instances were so contrived as to eliminate the antecedents other than

all

Antecedents.

A

*.

Consequents.

ABC ADE AFG BE

abc

ade afg be

CF

cf

DG 1

On

this point

I

am

dg. indebted to Mr. Charles Cannan of Trinity claims no monopoly, in the idea, and my

He College, Oxford. only wish is to indicate the source from which

it

came

to

me.

OF THE INDUCTIVE METHODS.

183

Here we may argue as in the Method of Difference itself. The same cause always produces the same effect.

Now

G

B, C, D, E, F,

occur in the second set of

instances without being followed by .

.

They But

.

.

A

are not the cause.

must have a cause.

a

the cause.

is

The above is

a.

therefore

the ideal type of the Joint Method.

is

called the Indirect

fitly

Method of

It

Difference.

Instead of proving our point directly by a comparison of two instances

we

by a comparison of

attain the

same end more

In practice however the Indirect

has to be very roughly used. this

by

method

that

small-pox in the

Method of Difference

Doctors

vaccination

They compare a number of unvaccinated

prevents

his

my

expectation

the

distemper,

or

there

came young

:

tar-water

had

it

all

the

either

very favourably.

veiy well

child

tried

it

small-pox raged

trial/

he says,

my

those within

having

He

effect.

fully

knowledge

escaped that In one family

was a remarkable instance of seven all

number

of the same method Berkeley satisfied

own neighbourhood, when And the violence.

who took

small-pox.

and point to the absence of former and its presence in the latter.

great

answered

themselves

of vaccinated with a

himself that tar-water had the same

with

satisfy

districts,

By an employment in

circuitously

several.

children,

who

through the small-pox except one

which could not be brought to drink

water as the rest had done

(Sin s,

2).

tar-

OF THE INDUCTIVE METHODS.

184

The

Method

Indirect

of Difference

is

sometimes regard

ed as a double application of the Method of Agreement (1) to instances in which the phenomenon occurs, (2) to instances in

which

it

does not occur.

But the Method of Agreement

is really inapplicable in the latter case, since the negative instances must agree in

the absence of innumerable antecedents.

187.

Illustration of the

Method of Concomitant

Variations.

Antecedents.

Consequents.

EC EC 8A EC

i2A xoA Let

A

an

be

the cause.

lish

effect

We

6a be

5a be 4 a be. of which

we wish

obtain instances of

it

to

estab

which vary

amount or degree. Then, if among the antecedents we find one, and only one, which varies correspondingly,

in

we come

to the conclusion that there

is

a causal connexion

between the two. If

we could be

certain that there were

no antecedents

with any bearing on the effect except those before us, we could say that is the cause of a, since the cause must

A

be looked for

among the antecedents. The argument would then assume the following form. No constant factor can be the cause of changes in an effect.

.

.

E and C B and C

are constant factors. are not causes of changes in

a.

OF THE INDUCTIVE METHODS. But the changes ..

The changes

The major premiss

must have a cause.

a

in

A

in

are the cause of them.

down

laid

above, that

factor can be the cause of changes in

a disguised form of the axiom that

without a cause. the cause

For,

if

185

an

No

effect

an

No

effect

constant is

only

event takes place

were

to vary while

remained constant, we should then have a

certain event, namely, a

change

in the effect,

which took

place without a cause.

But the assumption that we have all the conditions is too hazardous to be made. Accordingly we

before us leave

it

effects

supposed that both A and a are joint For instance, the hour of some common cause.

open

to be

hand and minute hand of a watch present us with a case of concomitant variations, but we do not suppose the

movements of one

to cause those of the other

both caused by the works within. also serve to

show

any analysis into influence of the

between the

This

:

they are

illustration

may

method may be used without The antecedents and consequents.

that this

moon on

barometer

the tides

and

the

instances of concomitant variations.

and the connexion

weather are obvious

We

are able in both

these cases to distinguish correctly between antecedents

and consequents.

But suppose a savage to see a baro meter in the house of a European and to become aware of the fact

that the

mercury went up and down with would probably

the changes in the weather, his inference

be that he was in the presence of some potent rain maker.

1

OF THE INDUCTIVE METHODS.

86

Statistics are often

an application of

this

Let

method.

us take an imaginary example.

A

1890 has 5 public-houses and there are 100 cases of drunkenness in the year. village in

In 1892

has 4 public-houses and there are 80 cases

it

of drunkenness in the year.

In 1894

has 3 public-houses and there are 60 cases

it

of drunkenness in the year.

These

might seem

figures

to

show

that public-houses

are the cause of drunkenness, but the decrease of both

may

be due to some moral reform in the locality or merely

to a decline in population. It

should also be noticed that the two phenomena

vary inversely as one

absence

of

one

of

the

presence

summer

In this case

another.

that

it

may

is

the

causally connected with the

is

The

other.

length

of

the

days

in

not the cause of the shortness of the nights,

is

nor conversely; but both phenomena depend upon the

same

cause, namely, the position of the earth with regard

sun

to the

at that season.

From one tions

is

In the

aspect the

Method of Concomitant Varia

an approximation

Method

antecedent;

in this

diminution.

It is

the heat of bodies.

precision to

we

Method

entirely

method we observe

of Difference.

remove a

of,

It

of the

e.g.

the attraction

may

also be applied with

Method of

its results.

certain

the effect of

useful in the case of causes that

be wholly got rid

tage after the

to the

of Difference

its

cannot earth,

advan

Difference, to give quantitative

OF THE INDUCTIVE METHODS.

Illustration of the

188.

To The

Method of

187

Residues.

Antecedents.

Consequents.

ABCD BCD

abed

the eye this

is

bed.

the

same

Method

as the

between the two methods

distinction

of Difference.

lies

only in the

way in which the negative instance is arrived at. In the Method of Difference it is got by immediate experience in the Method of Residues it is the result of previous ;

This however makes no difference

knowledge.

to the

1

reasoning

.

This potent instrument of discovery and proof

more than a sum

in subtraction.

comes

It

science after a certain advance has been

observation of it

our daily

life.

made

method of reasoning Thus, suppose a

by a society consisting at the

But

familiar to us all in

man

moment

no

the

in

phenomena and the study of causes.

of course a

is

is

into use in

to

be black-balled

of twelve

members

:

he knows that ten were prepared to vote for him, he ascribes his exclusion to one or other of the remaining

if

Or suppose

two.

that

some Sunday morning

country parish there appears the sovereign

in

the

offertory;

repeated experience that

chance 1

It

is

give

the

all.

his flock ever

silver

not really necessary in this

instance to be stated at

poor

phenomenon of a halfclergyman knows by

none of

more than a

in a

threepenny,

method

by any he

but

for the negative

OF THE INDUCTIVE METHODS.

1 88

has perceived a stranger present in the congregation does he hesitate to regard him as the cause of the

phenomenon

?

189. In further illustration of the methods

answer a question put by Jevons

What can you

infer

from the following instances

Antecedents.

ABDE BCD BFG ADE

let

us

now

1

?

Consequents.

stqp qsr

vqu

.... .....

BHK ABFG ABE

tsp

zqw pquv pqt.

and searching for the what can be done by the use of

Starting this time from the cause effect,

the

we

will first try

Method of Agreement

alone.

In the four cases in which are stqp, tsp,

pquv, pqt.

of these makes to

them

all is

it

A

occurs the consequents

more orderly arrangement

easier to see that the

one thing

pq

st

p

st

uv

pq

t.

therefore infer that the effect of

1

common

p

pq

We

A

Elementary Lessons

A

is

in Logic, p. 328.

p.

In the

OF THE INDUCTIVE METHODS. same manner

the

student

Method of Agreement

may

189

assure himself that the

yields altogether these results

A

p

B

q

D

s

E

t.

FG

About C, HK, and

can only

it

tell

us what

we

already see before us.

But the Method of Agreement

Can we

its results.

Yes

way ?

then confirm our conclusions in any

by a comparison of these two cases

:

.... ....

BFG

ABFG we become

at best uncertain in

is

sure that

Altogether by the

A

quv pquv

the cause of p.

is

Method of

Difference

we can

establish

these results

A B

P q

D But we are

left

s.

uncertain as to E, and wholly in the

dark about C.

The

Indirect

Method

previous presumption

E

t

is

on

it

is,

rely

;

E

E

is

and where

much

of Difference

that

is

strengthens

the cause of

not,

t

is

not.

in the case of C, since there

instance of the presence of that antecedent. as

it

goes,

it

points to

C

C

is

not.

for

:

We is

our

where cannot

only one

Still,

as far

being the cause of r:

for r

occurs in the one case in which

where

t

C

is,

and nowhere occurs

OF THE INDUCTIVE METHODS.

190

But

at

this point

avail ourselves of a

BCD

.

.

.

we

of the investigation

more

drastic

method.

are able to

In the instance

qrs we know already by the Method of Differ is the cause of Therefore it q and D of s.

B

ence that

remains that

C

is

cause of

the

The same Method

r.

of Residues enables us also to assert that responsible for

uv and

HK

for

FG

are jointly

wz.

A fallacious appearance of simplicity is imparted methods by the use of letters, which represent events as already analysed into antecedents and con 190.

to these

sequents, whereas the whole difficulty of inquiry consists

We

in this process.

cause

is

are tempted also to think that a

a single antecedent, whereas

junction of several.

Moreover

seldom appear side by in a single sum.

side,

may

it

be the con

in actual experience effects

but

are

indistinguishably

merged

Suppose the phenomenon under investigation

to

be

Let us imagine a party of undergraduates table-turning. assembled in the rooms of a man whom we will call Jones.

He

is

the

modate

owner of a small round

three

persons, while

table

which

the whole

will

accom

party numbers

seven

Jones himself, Smith, Brown, Robinson, Taylor, Various sets of three are tried Williams, and Thomas.

in

turn.

The experiment

is

uniformly successful,

table exhibiting surprising physical agility,

mental power in the way of answering questions by at a certain letter it

has in this

when

way

in the absence of

the alphabet

is

recited to

spelt out a sentence.

Jones the

the

and even some tilting

it,

until

Next morning

rest of the party are discussing

OF THE INDUCTIVE METHODS.

191

Smith declares evening before. he had nothing to do with the occurrence of the

their experience of the

that

in confirmation of his assertion

phenomenon, appealing

was equally

to the fact that the table

In

it.

Then

the remaining five

in

good

this

except one.

Jones was a is

now

same

the

occurs

eliminated.

is

declaration,

now

all

eliminated

our investigators that

to

of every set that was formed.

Jones

thereupon convicted in his absence of being the cause

of the

phenomenon, on the ground

common is

It

member

make

antecedents are

the

All

faith.

when he was

lively

way one of the antecedents

not at

that he

This conclusion,

antecedent.

is

the only

w ill be r

it

seen,

reached by the Method of Agreement.

Taylor however, who this

of the

phenomenon

of the

seven

been asked table

is

The solemn

In

this

view he

nevertheless the question

is

is

question, which has

moving

this

be answered in

the

theoretically unassailable

answered

more materially-minded of

his

Thomas, who has imbibed from the great principle of

Occam

canda praeter necessitatem. Williams, who never agrees help it, expresses an opinion whatever to do with the result. tician

and has noticed

that

all

to

in the persons

Is there a spirit

at the seance

demurs

possible causes

all

summed up

are not

sitters.

cannot, he declares, ever

?

negative.

the

mystically inclined,

conclusion on the ground that

in the negative

associates,

his

led

:

by by

philosophy-tutor

Entia non sunt multipli-

w-ith

that

He

is

any one, if he can Jones had nothing a bit of a

mathema

the combinations of sitters

OF THE INDUCTIVE METHODS.

192

other than Jones were not exhausted during the course

of the evening.

Instead of the fifteen sets of three which

were possible with Jones present every time, only twelve were actually tried. Having kept an eye on the point, he

is

able to assert

that

the

following three

sets

were

omitted

On

Jones

Jones

Jones

Taylor

Taylor

Williams

Williams

Thomas

Thomas.

the strength of his calculations he starts a theory

of his own.

but

is

it

Jones,

is

it

was present every time Brown, or Robinson

true,

:

also true that either Smith,

took part in every set that was formed, and any of these, he maintains, was more likely to have been the cause than

He,

Jones. calls the

it

will

be observed, has

hit

Agreement, which lurks

upon what Mill Method of

of the

characteristic imperfection

in the possibility of

Plurality of

Causes.

As a meet

result of ihe discussion

again in

The

first set

Williams, and

Jones to

s

rooms

that evening.

experiment on

Thomas.

The

our inquirers agree to

occasion are Taylor,

this

result

is

a

Those who already suspected Jones of being of the matter are

on the evening set,

the

from the is

now confirmed

before,

manifestations table,

in

occurred

;

failure.

bottom

For

their opinion.

when Jones formed

they do not occur.

dead at the

part of every

now, in his absence

This, so far as

it

goes,

an application of the Indirect Method of Difference.

OF THE INDUCTIVE METHODS.

193

After this the following sets are tried

Jones

Jones

Robinson

Brown

Jones Smith

Thomas

Williams

Taylor

and with

striking success in

third of these sets

is

each case.

of the table, a happy idea occurs to

Thomas.

He

calls

Jones complies, and Here we have the Method of

Jones, take your hands off!

out the

But, while the

in full career following the gyrations

table

stops

dead.

if the experiment is rigorous, proves be the cause or part of it. Accordingly the Jones to

Difference, which,

Jones theory are now triumphant. Taylor however, who contends for the presence of

partisans of the

unknown Jones

is

antecedents,

not satisfied.

is

the cause, but admits

the cause, regarding

him

to

He

denies that

be connected with

him merely

as the medium/ through But now the party discover that they have reckoned without their host. For Jones bethinks himself that two can play at the game of Hands

whom

off

!

the

and the

ment

is

operates.

spirit

first

the sceptic

withdrawn,

the

whom he selects for his experi Thomas. When Thomas s hands are

person

table

equally

comes

a

to

standstill.

Flushed with success, Jones continues his researches, until he has brought home the production of the phenomenon to

each of the party in turn, on the same evidence on

which

it

was attributed

to himself.

Thomas

declare that at

Here

is

Plurality of

But Taylor, Williams, and least they cannot be the cause,

Causes with a vengeance

!

o

OF THE INDUCTIVE METHODS.

194

would not

for the table is

found to stand the

now borne

It is

that the cause to imagine.

test

in

for

them

and

;

this

fact

all

statement

of repeated experience.

upon

the

minds of our investigators

not so simple as they were at

They

mere

yet the

is

stir

first

inclined

have something to do with

it,

and

of any three people having their hands

on the table is not enough to produce the phenomenon. Apart then from unknown antecedents, it must be some particular combination of persons that is essential to the Eventually they satisfy themselves that, though

result.

the only person

Jones

is

to the

phenomenon,

less

he

some

is

member

facts they are far,

is

is

invariably fatal

not effectual un

supported by Smith, Brown, or Robinson and

third

physical or

got so

whose absence

yet his operation

of the party indifferently.

psychical conditions

unable to divine

even

if

:

but

underlie it is

these

something

they can get no further.

What surface to

have

CHAPTER Of

the Natiire

191. IT

Methods the

if

of the Inductive Methods,

evident that what are called the Inductive

is

are really applications of deductive inference to

facts

which

X.

They are types, to we may be certain

supplied by experience.

we can

get facts to conform,

of our inferences with regard to them. this

compliance on the

since

part of facts

is

But

to procure

the real difficulty,

the subtlety of nature far exceeds the subtlety of

human sense or understanding. Nothing can be maxim of Bacon s. But when the Father

truer than

of Induc

this

tion goes stringit,

on

non

to assert that the syllogism assensum con-

he equally worthy of credence

res, is

unless by the syllogism he truths

which serve

of the syllogism

meant

it.

accordance with

major premisses. The cogency based on this principle that things

is

If the fact,

premisses we

There start

is

therefore

from are in

then the conclusions we arrive

be in accordance with fact also. strains things

Not

for its

must be consistent with themselves.

no escaping

?

the supposed general

at will

Whether the mind con

or things constrain the

mind or whether

both are constrained by something behind them question which concerns the logician as such.

is

He o 2

not a

simply

NATURE OF THE INDUCTIVE METHODS.

196

assumes the

fact that the laws of thought are laws of things. were not, reasoning would be unavailing. The great desideratum then is that our supposed general truths should be really in accordance with fact, and the use of

If they

methods

the

by which

that they supply us with so

is

Even

to try this accordance.

never be

complied with,

strictly

this

if

many

standards

methods can

the

does not diminish

their value as standards.

Method of Agreement

192. For the

we must

cessfully

This however can

cidence. sufficient

number

easily

An

of instances.

no connexion with the

under investigation

effect

of causes must be allowed if

phenomenon the case of

A

M

and

a/

mere coin

is

may be

hardly likely to be

After this the possibility of a plurality

present in many.

But

be applied suc

be done by taking a antecedent which has

present in one or two instances, but

ated.

to

eliminate the chance of

first

N

this

for, since

it

cannot be elimin

are alternative causes with

A of the

can be proved in the same way as in

itself.

Suppose however that

any amount, not merely of

after

observation, but of experiments carefully conducted, still

is

f

then warranted in declaring

we

A

found to be the sole invariable antecedent of a/ are we it

to

are prepared to assert that

be the cause all

stances are within our knowledge.

enough

to

make

this assertion

But who

period

several

we breathe

will

be bold

Until within the last couple

?

of years chemists imagined that they knew tuents of the air

Not unless

?

the material circum

;

all

the consti

nevertheless within that

new ones have been

discovered.

The

NATURE OF THE INDUCTIVE METHODS.

197

however of the Method of Agreement to Let us go on to the Method is admitted.

insufficiency

prove causation of Difference. 193. If

who

will,

we can

shall

deny

A and by its means produce

take

one

that the

is

Certainly no one can deny that there

But how are we

nexion.

know

to

a

at

the cause of the other

that

a

is is

?

a causal con

really

caused by

A, and not by some latent antecedent involved in the taking

A

Let us suppose however that that contingency is guarded against. Even now we cannot be sure that we of

?

have reached the pure

fact of

sequence.

Nature

is

infi

nitely complex, and what we regard as the single phe nomenon A may really be compounded of a, fi, y of these ;

/3

and y may be wholly

a in

A

that

is

the cause of

The

194.

irrelevant,

Indirect

and

may

it

only be the

a.

Method of

Difference, the

Method

of Concomitant Variations, and the Method of Residues are

Method of

modifications of the

all

Difference.

Hence

methods are reduced by Mill himself to these two Agreement and Difference. We must either compare to all

the

gether instances in which the

compare

instances in which

which

does not occur

it

instances in

together

would be misses.

:

it

it

which

of no it

more use comparing

does not occur than

it

frame a syllogism with two negative pre But may we not go one step further and say that only one method

is

after all

thing

is

the cause of another

be.

or else

does occur with instances in

to

there

can

is

phenomenon occurs

They

are

all

alike

?

We

prove that one

that nothing else

by showing methods of elimination,

that

is,

NATURE OF THE INDUCTILE METHODS.

ig8

discarding antecedents which are not conditions, or

of

consequents which are not

The Method

effects.

of Agreement stands on the ground that

whatever can be eliminated

nomenon by a law. The Method of

is

not connected with the phe

Difference has for

whatever cannot be

eliminated

is

its

foundation, that

connected with the

phenomenon by a law (Mill, III. 8, 3). In the former we reach by elimination a agreement

;

single point of

in the latter a single point of difference.

In the Method of Agreement the cases

differ in all

respects save one.

In the Method of Difference the cases agree in

all

respects save one.

As it is

one point of agreement or of difference is vital, which gives the name to the method. 195. When Whewell objected against Mill s methods the

this

whereby discoveries had actually been made, Mill replied firstly that Dr. Whewell s argument, if good at all, was good against all inferences

that they were not the processes

from experience, for if any discoveries were made by observation and experiment, it was by processes reducible to

one or other of those methods

;

they were not methods of discovery, true

secondly, that it

would be no

if

less

were the sole methods of proof. Mill himself as supplying rules and models for

that they

regarded

inductive inference such as the syllogism for ratiocination (III. 9, ising

even

6).

Was

and

its

rules are

he not rather rational

the inductive instinct by bringing

its

conclusions

NATURE OF THE INDUCTIVE METHODS. under the Axioms of Induction?

we

199

His methods, unless

take them as confined to Agreement and Difference,

lack the demonstrative exhaustiveness of the four figures

of the syllogism. tions,

Nevertheless, despite

won

they have

their

way

have become part of the

This

we

is

are

Whewell

s

objec

to general acceptance

common

and

stock of thought.

because they represent living processes which all

conscious of employing in the daily exercise

of the rational

dependent

of

But these processes are not in This is admitted by Mill

life.

deduction.

himself (III.

8,

Residues, but

it

7) is

in

the

case

equally true of

all.

of the

The

Method of fact

is,

Mill s

an important contribution to the fourth part of logic which deals with Method. treatment of induction

is

CHAPTER XL Of some

other points connected with Induction.

The Deductive Method.

196.

The

perfect

of

type

scientific

consists

reasoning

neither wholly of induction nor wholly of deduction, but

of a due admixture of both.

Method and

It is

called the Deductive

consists of three steps

(1) Induction,

arrived

whereby some wide general

truth

is

at.

whereby certain

(2) Deduction,

consequences are

inferred from this truth.

whereby an

(3) Verification,

nature

see

to

whether

appeal these

is

made

to

consequences

actually ensue.

197.

Sometimes

the

first

Hypothesis.

step

in

the deductive

method

is

supplied by Hypothesis.

By an Hypothesis general law

or,

is

meant the assumption of some to the same thing, the

what comes

assumption of a cause to account for phenomena. Hypothesis reverses the order of induction. In indue-

OTHER POINTS CONNECTED WITH INDUCTION. tion

we

first

collect facts

we

in hypothesis for facts to

start

support

and from them

we had

if

:

by assuming a law and then look

with unfailing regularity, certainty as

some law

it.

an hypothesis enables us

If

infer

2OI

to

we hold

predict

phenomena

with nearly the same

it

discovered a cause by observation

or experiment.

Conditions of a (1)

The

Valid Hypothesis.

cause assumed must be a vera causa,

known

something of a kind (2)

The

any of the (3) It

(4)

It

(5) It

The

we ascribe known laws of

operation

to

it

must not

violate

nature.

must be adequate to account for the phenomena. must reconcile at least two different facts.

must admit of

investigation, at least indirectly.

hypothesis of the Ancients that the

Aetna were due beneath

i.e.

to exist in nature.

to the

fires

of

Mount

Typhoeus being chained

giant

it

Alta iacet vasti super ora

Typhoe os Aetne, humus

cuius anhelatis ignibus ardet

Ovid, Fast. IV. 491, fulfils

none of these conditions

(1)

Typhoeus

(2) that

fire

that

age

he

after

did,

age

would account only

It defies

from

fire

;

his lungs

con

what we know of the laws of nature

breathing

(5)

a fiction of the poets

even granting

(4) This

2.

for

he should breathe

tradicts

(3)

is

:

investigation.

could

he go

?

for

one volcano.

;

on

OF SOME OTHER POINTS

202 Contrast

with this

the

which not only accounts

and the heat of mines and

springs

we know of the account for

that does it

fire,

but also for hot

consistent with what

is

nature of the heavenly bodies.

For an hypothesis to

of a central

hypothesis for volcanoes,

to

be accepted,

ought not only

it

the facts, but to be the only hypothesis

all

account for them.

E. g. In a criminal

trial

not sufficient to show that the prisoner had a motive

is

and an opportunity

for

committing the crime, be shown that others had also. 198.

if

it

can

Crucial Instance.

A Crucial Instance is some observation or experiment which decides a point under dispute. It is so called from crux in the sense of a sign-post, as pointing the

A

to truth,

way

where there are conflicting hypotheses.

bacteriologist affords a

person,

when he

dines off

crucial

199.

Analogy means an equality said to argue

of ratios

we

infer

a and b c

as used

and

(ICTOT^S

that

a

b

:

:

:

c

:

hold

true

also

laid

Aristotle,

We

down

are

that

d

what holds true of the

will

by

Aoywv).

from analogy, when, having

As

own

Analogy.

in the strict sense,

I.

instance in his

bacilli.

relation

between

of the relation between

d.

E. g.

As a

child

is

to

its

the mother-country.

parent, so

is

a colony to

CONNECTED WITH INDUCTION. Here we might argue

that, since

parent, a colony ought to

its

203

a child ought to obey

obey the mother-country,

or conversely, that since a parent ought to support the

mother-country ought to support the colony.

child, the

In either case

we

should be arguing from analogy in

the ancient sense of the term.

Instances of analogy the As health the body virtue As old age life evening day. :

:

:

:

As

the adjective

:

:

the substantive

:

soul.

:

:

:

:

the adverb

:

the verb.

Argument from analogy .

.

As As

II.

flame

fuel

:

:

:

light

:

flame.

the flame dies out with the fuel, so does the light with the flame.

In the loose modern sense Analogy means merely

a high degree of resemblance between two things.

We are said that A and B infer

from analogy when, having found resemble each other in several points, we

to argue

they will resemble each other in

that

point more.

in this sense is the

Analogy

some one

same thing

as

Example.

The

value of such an argument must depend

(1)

On

the importance of the ascertained points of

resemblance. (2)

On

(3)

On

the ratio which these bear to the ascertained

points of difference.

which the ascertained points of resemblance and difference bear to the whole the

ratio

number of difference.

possible

points of resemblance or

OF SOME OTHER POINTS

204

High degree of resemblance between

Instance.

the

Earth and Mars.

Mars

..

If

inhabited.

is

the points of difference

outweigh those of resem

blance, the force of the argument

The Moon

Instance.

differs

tant points, e. g. in not

The Moon

/.

In estimating the difference care

is

is

in impor an having atmosphere.

not inhabited.

points both

must be taken

turned the other way.

from the Earth

and

of resemblance

to see that they are inde

pendent of one another. If there were four points of resemblance, of which three were traceable as effects to the

we should

remaining one,

that

in

case really be

reduced to one point of resemblance.

Analogy

is

induction from a single instance, in which

the absence of

number

is

compensated

for

by the high

degree of resemblance.

200.

Nature

s

Tendency.

laws are never frustrated, but they are often

counteracted.

A

body

in the air has a

tendency to

fall to

the earth, but this effect does not take place so long as is

supported.

A

tendency

may

it

be defined as a potential

effect.

Explanation. 201.

To

explain a thing

not stand alone, but

We

is like

explain a fact

we show

it

to

is

simply to show that

it

does

other things.

when we

refer

it

be a case of some wider

to a law, fact.

i.

e.

when

CONNECTED WITH INDUCTION.

We than

explain a law by referring

to laws

it

205

more general

itself.

There are according

to

Mill (III. 12) three

modes of

explaining laws of causation

By

(1)

resolving the law of a

complex

effect into the

laws of the separate causes, together with the fact of their coexistence.

E. is

The

g.

shown

and a

law of planetary motion

to result

is

explained

when

it

from the combination of a centrifugal

centripetal force.

(2)

what was supposed to be the immediate cause of an effect was only a re

By showing

that

mote one. E.

The

g.

action of the nerves

is

shown

to intervene

between contact with an object and sensation.

By showing

(3)

a given law to be a case of

some

wider law.

The tendency

E. g.

shown

to

202.

is

of the

moon

towards the earth was

be a case of gravitation.

Different kinds of Laivs.

Sometimes any uniformity among physical phenomena But in a special sense The called a law of nature.

Laws

of Nature are the widest uniformities which can be

arrived

at, e. g.

the law of gravitation, the laws of motion.

Derivative Laws, or ties, e. g.

Laws

of Phenomena, are uniformi

which can be deduced from the laws of nature, the law of planetary motion.

206

OTHER POINTS CONNECTED WITH INDUCTION.

Empirical

Laws

are special uniformities which are not

deducible from any higher laws. e.

g.

A

drake has a curly feather in is a cure for ague.

Quinine

Scarlet flowers have

no

scent.

its tail.

CHAPTER Of 203.

A

XII.

Deductive Inferences.

DEDUCTIVE Inference

is

either

immediate or

mediate.

A is

Mediate Inference

is

so called because a middle term

employed. An Immediate Inference

term

so called because

is

no middle

is

employed. N. B. A Mediate Inference

is

the

same thing

as a

Syllogism.

An

immediate inference

is

the

comparison of two

propositions directly.

A tions

mediate inference

by means of a

the major premiss by It

may

is

the comparison of two proposi

third (namely, of the conclusion with

means of

also be said that

the minor).

a mediate inference

is

the

comparison of two terms by means of a third or middle term (namely, of the minor with the major by means of the middle).

In that sense of the term confined to the consequent

An

immediate inference

it

is

inference

may be

in

which

it

is

said that

one derived from a single

proposition.

A

mediate inference

tions conjointly.

is

one derived from two proposi

OF DEDUCTIVE INFERENCES.

208

Where

more than two propositions

there appear to be

antecedent of a mediate inference, the reasoning

in the

always be resolved into more than one syllogism.

may

Hence we may say

that

In an immediate inference the antecedent consists of

one proposition. In a mediate inference the antecedent consists of two propositions.

In an inductive inference the antecedent consists of one

or more propositions.

In the case of the syllogism the two propositions which

form the antecedent are called the Premisses

same term

;

and the

sometimes employed for the propositions which make up the antecedent in an inductive inference. In

all

is

cases the consequent

is

also

known

as the

Con

clusion.

Immediate Inference. 204.

An

immediate inference

is

either

Simple or

Compound.

A

compound immediate

inference

two or more simple immediate

is

a combination of

inferences.

Simple Immediate Inference. 205.

Of

simple immediate inferences there are three

kinds (1)

by Opposition,

(2)

by Conversion,

(3)

by Obversion.

OF DEDUCTIVE INFERENCES. As

it

is

209

impossible to get out of a proposition anything

contained in it, the consequent in an im mediate inference must always be the antecedent or part of the antecedent under a disguised form. but what

is

In immediate inference by opposition there of quantity

or

quality or

both

a change of material quality,

i.

e.

;

in

most

is

a change

cases

also

a transition from truth

to falsehood or the reverse.

In immediate inference by conversion there

is

a change

is

a change

in the position of the terms.

In immediate inference by obversion there of quality

both in

the

proposition

itself

and

in

its

predicate. If the proposition

is

changed

indicated by one of the three

immediate inference

is

to a further extent

than

is

ways above mentioned, the

compound.

CHAPTER Of

XIII.

Immediate Inference by Opposition.

206. BEFORE dealing

with

immediate inference by

opposition we must say something about itself,

which

is

opposition

a relation between propositions.

Opposition.

Two

propositions are said to be opposed

same

are the that they

in matter but differ in form.

must be the same

in matter.

when they It is plain

There can be

no opposition of any kind between two propositions which do not bear on the same point, e.g. Christmas is

coming, and

No

fishes talk.

one propositions then which are opposed another must always have the same terms. Now given any term S for a subject and any term

The

P

to

for a predicate,

A, E,

I,

O

we can make up

the four propositions

by taking account of quantity and qualityAll

S

is

P.

No

S

is

P.

Some S Some S

(A) (E)

is

P.

is

not P. (O)

(I)

OF IMMEDIATE INFERENCE BY OPPOSITION. The

may

2TI

between these four kinds of proposition

relations

be indicated thus

Contrary

Opposition

the

is

relation

between

two

universal propositions which differ in quality.

Sub-contrary Opposition particular propositions

Subaltern

Opposition

propositions which

Contradictory

differ

the relation between

is

which is

the

relation

between

two

only in quantity. is

Opposition

two propositions which

two

differ in quality.

differ

the

relation

between

both in quantity and in

quality.

Hence form.

contradictory opposition is logically the strongest In the other kind of opposition there is a difference

in quantity or quality, but

When

not in both.

the truth of one proposition

the truth of another, as in the sub-contraries,

there

is

no

is

compatible with

case of subalterns

opposition

in

meaning of the word between them, but

the the

and

ordinary

term

is

extended for convenience so as to cover any relation

OF IMMEDIATE INFERENCE BY OPPOSITION

212

between propositions based on a difference of quantity or quality or both.

Immediate Inference by 207.

of immediate inference

Opposition.

of opposition regarded as a form

The problem

is

this

Given the truth or falsehood of any one of the four be inferred with regard propositions, A, E, I, O, what can the truth

to

of the others

falsehood

or

the

in

same

matter? 208. In order to solve this problem,

we

lay

down

the

following

Laws of Contraries

Hence

true.

may if

both

one be

Opposition.

be

false,

cannot both be

but

true, the other

is

false,

but not

vice versa.

Sub-contraries

Hence

false.

if

may

both be true, but cannot both be

one be

false, the

other

is

true, but not

vice versa.

Subalterns

may

both be true and

But more particularly If the universal be not vice versa if

true, the

may

both be

particular

is

false.

true,

but

false,

but

;

the particular be false, the universal

is"

not vice versa. Contradictories cannot both be true and cannot both

be

false.

vice versa.

Hence

if

one be

true, the other is false,

and

OF IMMEDIATE INFERENCE BY OPPOSITION 213 Application of the Laws. 209. four

By applying

kinds

of

these

proposition

laws of opposition to the

we

obtain

the

following

results

If

If If

If

A A

be

true,

be

false,

E E

be true,

be

false,

If I be true, If I be false,

If If

O O

be

true,

be

false,

E E

A A A

is

false,

I

is

is

unknown,

I

is

is

O unknown, O unknown, O O false,

is

unknown,

is is is

A E E

false,

is false,

O unknown, O

is

false.

is

true.

true,

is

true,

I

is

false.

is

unknown,

I

is

true.

is

unknown,

is

false.

is

true.

is

false.

is

true.

is

true,

I

is

unknown,

I

is

true,

E E A A

Subalternation. 210. Immediate inference by subaltern opposition

known

also is

as Subalternation.

The

is

universal proposition

sometimes called the Subalternant and the particular

the Subalternate.

211. There

is

a peculiarity about immediate inference

by opposition which should not be left unnoticed. In other forms of inference we argue from the truth of the antecedent to the truth of the consequent

we may argue

also

;

in this

from the truth of the antecedent

to the falsity of the consequent or

from the

falsity of the

antecedent to the truth of the consequent or from the falsity

Now

of the antecedent to the it

is

falsity

only in Subalternation,

subalternant, that

we

of the consequent.

when we

start

from the

are arguing from the truth of the

OF IMMEDIATE INFERENCE BY OPPOSITION.

214

Nevertheless

antecedent to the truth of the consequent.

the various forms of immediate inference by opposition

all fall

under our

From

the

to the

judgement

A

more judgements

or

this proposition is

judgement

212.

the passage of

definition of inferring as

mind from one

the

that proposition

is

false

I

we pass

and so on.

plausible objection has been urged against

the doctrine that sub-contraries cannot both be is this.

another.

to

true

does not exclude

A

and

O

It

false.

does not exclude E.

This being so, it has been maintained that I and O may both be false, since they are possibly equivalent to A and

But those who reason thus

E.

1

are

get out

trying to

proposition something more than there and O make a statement about a part and are

of a

is

I

silent as

to the whole.

Though

We

it.

they do not exclude the universal

as a matter of fact, they exclude

ment.

in

it

as a matter of argu

if we assume beyond Moreover though it may as be true in one case, it cannot be true in

the evidence,

are going

the universal to be true.

a matter of fact both.

It is

a

good instance of

the fallacy of composition

423) to argue thus

(

A may

If I is true,

be .-.

A

If I

and

E

213. 1

As

I

be true

;

and

if

is

true,

E may

true.

and

O

are both true,

A

and

E

will

be both true.

being contraries can never be true together.

We

have seen already that contradictory oppo-

did myself in

my

Deductive Logic

;

but

my

error

was

pointed out to me first by Mr. W. E. Johnson in Mitid and afterwards by Mr. Keynes, to both of whom I am much obliged.

OF IMMEDIATE INFERENCE BY OPPOSITION. from one another

sites differ

in

more

215

respects than any

other kind.

We may

now add

that they are incompatible both as to

and falsehood, whereas the others are incompatible only as to one or the other. Lastly the contradictory is the proper refutation (clenchus) of an opponent s truth

liable to

we

If

position.

try

be refuted

to

establish

the

Let the opponent

in turn.

we

contrary, s

are

position

Red Indians are bad. If we can prove that Some Red Indians are not bad, we have refuted him

be

All

;

whereas

if

we

we may be opposed

to

refuted in turn.

one another

language from 214.

prove that

try to

its

The

use in

thing

No Red The

Indians are bad,

crept into

This

is

common

the square of opposition

that

is

essential

to

the double incompatibility as to truth

is

diametrically

phrase

may have

V

contradiction

and falsehood.

best seen from

The Opposition of Singulars*

A

singular proposition of which the subject

crete

is

a con

term, as dealing with a primary substance,

be regarded as the elementary type of proposition.

may It is

Consequently there can be between contrary and contradictory or between subalternant and subalternate. Hence opposi-

individual, but not particular.

no

distinction

1

Simplicius TOVTOJV

32

Comm.

and again 6 fvavnoi

TO.

in

Kara

Kara

Ench. cap. Sia/j.irpov

SidpfTpov.

xlviii

d\X^Acui/.

The

Cataplus 14, explains that the metaphor

is

has

\K

Eus. Pr. Ev. xv

Scholiast

on

derived from a

Lucian, circle.

2l6 OF IMMEDIATE INFERENCE tion

is

in this case

The

diction.

BY OPPOSITION.

reduced to one kind, namely, contra

contradictory of

of the Letters of Junius

Francis was the author

Francis was not the author

is

of the Letters of Junius.

A

kind of generality

proposition by

always P.

may be

expressing

We may

it

in

imparted to a singular This S is the form

then give

its

contrary as

This S

is

never

its

subaltern as

This S

is

sometimes P,

its

contradictory as

This S

is

sometimes not P.

P/

Immediate inference by opposition may be denned as an immediate inference based on the relation 215.

to

one another of two propositions which are the same

matter but different in form, both.

i.

e.

in

in quantity or quality or

CHAPTER

XIV.

Immediate Inference by Conversion.

Of 216.

A

is

proposition

said to be converted

when

its

When this is are transposed. subject and predicate done in such a way that the second proposition follows from the

first,

we have

the logical converse of the original

proposition.

Immediate Inference by Conversion. 217. In this form of immediate inference the antecedent

is

the consequent

Two

is

known

as the Convertend,

known

as the Converse.

Rides for Conversion.

(1)

No

(2)

There must be no change of

term must be

distributed in the

which was not distributed

The things

The

former of these rules :

we cannot argue latter

is

safely

conventional

inference in spite of

it,

but

it

in the converlend. quality.

founded

is

converse

in the nature of

from the part to the whole. we may draw a valid

:

will involve

something more

than conversion.

Two

kinds of Conversion.

218. (i) Simple,

(2)

By

In simple conversion there

limitation or per accidens. is

no change of

quantity.

2l8

OF IMMEDIATE INFERENCE BY CONVERSION.

In conversion by limitation the quantity of the original proposition

is

E

I

and

reduced.

can be converted simply,

A and E can be converted O cannot be converted. A

proposition,

converted

when

will

it

by

limitation,

be seen, admits of being simply

the quantity of the subject

that of the predicate

is

the

same

as

otherwise not.

:

E. .-.

No S No P

is

P.

is

S.

w I. .-.

A.

Some S

is

Some P

is S.

All S

P.

P.

is

v .

219.

.

^j

Some P

Reason why

A

is S.

must

be converted by

limitation.

A, being affirmative, does not distribute

Therefore when the predicate

is

made

its

predicate.

the subject,

the

proposition becomes particular. All butchers are /.

220.

Some men

Reason why

O, being particular,

But when the subject be distributed, either there

if

is

men.

are butchers.

O

does

made

cannot be converted. not

distribute

the predicate,

the proposition

is

it

negative.

its

subject.

will

have to

Therefore

must be a change of quality or there

will

be

OF IMMEDIATE INFERENCE BY CONVERSION. 219 a term distributed in the converse which was not distributed in the convertend.

/.

Some animals are not dogs. Some dogs are not animals.

The

221.

simple converse of an

often be true along with

it,

but

from that of the other and has separate evidence,

A

may

proposition

truth does not follow

its

to

be established

on

e. g.

All equilateral triangles are equiangular,

and All equiangular 222.

On

triangles are equilateral.

the theory of the quantified predicate every

proposition admits of simple conversion, being an equation

between

its

This

terms.

is

the case in

of expression, where the proposition

some

natural forms

singular, e. g.

(u) Virtue

is

the condition of happiness.

(A) Virtue

is

a condition of happiness,

(u)

223. to

is

The

When

square of three the

predicate

is

nine.

is

an

attributive,

be changed into a subject-term in conversion,

..

Some Some

No .

.

lie

has

it

e. g.

mistakes are criminal. crimes are mistakes. ever thrives in the long run.

Nothing which ever

224. Immediate

thrives in the long run

inference

by

conversion

is

a

may

lie.

be

defined as an immediate inference based on the trans position of the subject

and predicate

in a proposition.

CHAPTER Of Immediate 225.

To

XV.

Inference by Obversion.

obvert a proposition

is to change its quality In other words it is meaning. expressing negatively what was expressed affirmatively

without changing

its

or vice versa. If

we only changed

should get

its

the quality of a proposition,

contrary

or

sub-contrary,

might be, and should therefore seriously

But

ing.

this

change

set right

is

in the quality of the predicate, for

as

the

affect its

we

case

mean

by a further change

which we substitute the

contradictory term.

226.

Thus obversion

negatives

of the

make an

Law

rests

affirmative.

on the principle that two It is an exemplification

of Excluded Middle, namely, that

one or

other of a pair of contradictory terms must be applicable to a given subject, so that, when one may be predicated affirmatively, the other

may

be predicated negatively, and

vice versa.

227. Strictly speaking tradictory of the

original

obversion, but in practice for a negative term.

The

it

should always be the con

predicate that

we may

is

employed

substitute

inference will

still

in

a privative hold, since

OF IMMEDIATE INFERENCE BY OBVERSION. a proposition

is

always

made

with reference to

sphere of thought, within which positive are

221

some given

and

privative

positive and negative. remark will be evident from the

mutually incompatible as

as

The meaning

of this

examples. (A)

All S

is

P.

All just acts are expedient.

00

No

is

not-P.

No

S

just acts are inexpe

dient.

00

No

S

is

P.

No

(A)

All S

is

not-P.

Every display of passion

0)

Some S

display of passion

is

politic.

is

impolitic.

Some

P.

is

been (o)

Some S

(o)

Some S

not not-P.

is

Some

,

philosophers have slaves.

philosophers have

not been

(0

.

Some S

is

is

free.

not P.

Some

not-P.

been unprosperous. Some tyrants have been

.

tyrants

have

not

prosperous.

228. Obversion

is

also

known

as Permutation and as

Immediate Inference by Privative Conception. It may be defined as an immediate inference there

and

is

in

in

which

a change of quality both in the proposition

its

predicate, but no transposition of terms.

itself

CHAPTER Of Compound

XVI.

Immediate Inferences.

229. Compound forms^ of immediate inference are obtained by combining two or more simple forms. If we

both obvert and convert the same proposition we have

Conversion by Negation. 230. Conversion

mediate inference,

and there

and

itself It

is

in

in

by Negation is a compound im which the terms are transposed

a change of quality both one of the terms.

may assume two

in the proposition

forms.

In one the consequent has the contradictory of the original predicate for for

its

its

subject

and the

original subject

predicate.

In the other the consequent has the original predicate

and the contradictory of the

for

its

subject

for

its

predicate.

original subject

(i) All

S

is

P.

No not-P

is

S.

,

All lawyers are

honest.

No

dishonest

No S is P. Some not-P is No just man

o S.

i

.

is

not practical.

partial.

men

are lawyers.

.

Some

impartial

are just.

Some S is not P. Some not-P is S. Some statesmen are

men

.

Some unpractical men are statesmen.

OF COMPOUND IMMEDIATE INFERENCES. 223 When

the quality of the original

changed we must

E

In the case of

is

predicate

limitation has to be employed, so that

converse by negation coincides with that of O.

its

yield

no

result,

be

to

obvert and then convert.

first

when obverted

because

can

I

becomes 0, which

it

cannot be converted.

o.

S

All

A. .

.

is

Some P

P. is

not

A.

.-.

No S P

All

is

P.

is

not-S.

i.

o.

.-.

Some S Some P

not-S.

No selfish acts

certain. ..

Some

P.

is

not

not-S.

ways are

All safe

is

Some

are

certain

ways

.

.

are not unsafe.

critics

are kind.

praiseworthy. All praiseworthy acts are unselfish.

.-.

Some

kind

peoplearenot uncritical.

When

the

quality of the

original

is

subject

to

be

changed, we must first convert and then obvert. In the case of A limitation has to be employed, so that converse by negation coincides with that of

its

yield

no

because

result,

231. If

we

it

carry the

obverting the result,

I.

O

can

cannot be converted. first

form one step further by

we have

Conversion by Contraposition. Conversion by Contraposition is a compound immediate inference in which the terms are transposed and their quality changed. All

A. A.

.

.

All

S

is

P.

not-P

not-S.

E. is

o.

No S is P. Some not-P not-S.

o. is

not

o.

Some S is not P. Some not-P is not not-S. not-S.

OF COMPOUND IMMEDIATE INFERENCES.

224

All solid sub-

Nothing familiar

stances are

Some

is

material.

..All

dishonest.

immaterial

.Some

substances are

unstriking things are not

non-solid.

unfamiliar.

N.B.

If

negative,

prejudiced

persons are not

striking.

.

.-.

Some honest persons are not unprejudiced.

one of the terms be already

the change of quality will

as in the concrete

The above

make

or

privative it

positive,

example of O.

resolve themselves into three steps of simple

immediate inference in

this

order

(1) Obversion, (2) Conversion,

(3) Obversion.

E

In the case of

limitation has to

be employed, so that

contrapositive coincides with that of O.

its

232.

U

admits of an inference by contraposition

without conversion. All

S

is all

P.

All equilateral triangles are

equiangular. .-.

All not-S

not-P.

is

.-.

All non-equilateral triangles

are non-equiangular.

is

The

principle

that

when two terms

upon which

cluded from the one 233. If

we

is

this

kind of inference

are coextensive, whatever

is

rests

ex

excluded also from the other.

carry the second form one step further

by converting the

result

we have what Mr. Keynes

calls

Inversion.

Inversion

is

a

compound immediate

inference in which

OF COMPOUND IMMEDIATE INFERENCES. 225 there

and

a change of quality both in the proposition

is

in

subject, but

its

itself

no transposition of terms.

This form of inference applies to E and A. No Jews are Aryans. No S is P. E. i.

Some

.-.

not-S

P.

is

/.

Some

other than Jews are

Aryans.

The above

itself into three

resolves

immediate inference

of simple

steps

in this order

(1) Conversion.

(2) Obversion.

(3) Conversion. A. o.

.-.

All Jews are Semitic.

All S

is

Some

not-S

P. is

not P.

/.

Some other than Jews are not Semitic.

The above

involves

no

less

than

five steps

of obversion-

conversion.

We

234. that If

we

have seen that the inverse of

carry

on the same process one step

obvert the inverse,

O

is

no

further

obvert

it,

we

either

travel.

is

I,

and

:

This

still

will

further

and

not not-P.

have arrived at

we can

it,

by conversion-obversion or by for

we cannot

convert

are only retracing our steps.

however there are can

not-S

When we

a terminus.

obversion-conversion

we

is

O

we reach

Some go

E

reached by three steps of conversion-obversion.

is

it

O

and,

if

Even then

some side-branches on which we be seen,

if

we

take each of the

four propositions and try to draw therefrom

all

possible

inferences.

Q

OF COMPOUND IMMEDIATE INFERENCES.

226

A. All

S

is

P.

No No

S

is

not-P.

not-P

Original.

All not-P

Some

Obverse.

Converse by Negation

is S. is

not-S

not-S.

not-P.

is

(i).

Contrapositive.

Converse of the Contraposi tive

(= Obverse

of the In

verse).

(o)

(o)

Some

not-S

Some Some Some Some Some

P P

is S.

S S

not P.

is

Inverse.

Converse.

not not-S.

Converse by Negation

is

P.

Subaltern.

is

not not-P.

Subaltern of the Obverse.

is

(ii).

not-P

is

not-S.

Subaltern of the Contraposi

Some not-P

is

not

Subaltern of the Converse by

tive.

S.

Negation

(i).

E.

(o)

No

S

is

P.

All

S

is

not-P.

Some Some

not-P

No P

is S.

P Some Some

All

(o)

not-P

is

Original.

Obverse.

is S.

not-S

(i).

Converse.

Converse by Negation

not-S.

not-S

Converse by Negation

not not-S. Contrapositive.

is

is is

P.

Inverse,

not not-P. Obverse of the Inverse.

(ii).

OF COMPOUND IMMEDIATE INFERENCES. 227 Some Some Some Some

S

is

not P.

Subaltern.

S

is

not-P.

Subaltern of the Obverse.

is

not S.

Subaltern of the Converse.

is

not-S.

Subaltern of the Converse by

P P

Negation

(ii).

I.

Some S (o)

Some S

(o)

Some P Some P

is

P.

Original.

is

not not-P.

Obverse. Converse.

is S.

is

not not-S.

is

not P.

Obverse of the Converse. O.

Some S

Original.

Some S is not-P. Obverse. Some not-P is S. Converse by Negation Some not-P is not not-S. Contrapositive.

(o)

235.

The

foregoing

lists

show the wealth of implica

tion that

is

contained in a universal proposition.

we

A

or E,

assert

eleven be

We be

When

are committing ourselves to a dozen

statements in each case.

different

so that

we

(i).

If

any one of the

false, the original proposition cannot be true,

we have ample means

cannot however argue that

of putting if

it

to the test.

any one of the eleven This is the case

true, the original proposition is true.

only

when

there

is

no

loss of quantity.

There

are eleven

propositions which can be derived from A, but only from three of them can A be recovered. The same holds true

Q

2

OF COMPOUND IMMEDIATE INFERENCES.

228

On

of E.

the other

hand

I

O

and

can be recovered from

any of the three propositions which are

derived

from

them. 236. There

is

unfortunately

much

difference of

no

menclature with regard to compound immediate infer so that

ences,

is

it

impossible

to

be in

accord with

But before quitting the subject it may be well everyone. to explain the principle upon which we have gone. Negation properly means the substitution of a negative term but it may be taken to cover a change

for a positive

:

of quality in either direction.

may

affects both, it

and

the

This change of quality

affect either the subject or the predicate. is

it

to call

it

same thing

convenient to have another

Contraposition.

as

Thus

When name

it

for

Contraposition

is

Double Negation.

Hence Conversion by Negation is distinguished from Conversion by Contraposition by the fact that in the former process only one of the terms has its quality changed, whereas in the

latter

both have.

Moreover

in

Conversion by Negation the quality of the proposition itself is changed, whereas in Conversion by Contraposition it is

not.

In

Inversion

also

the

quality of

one of the terms

(namely, of the subject) is changed, but as there transposition of terms, it need not be confused with

is

no

Con

version by Negation.

Inversion version

is

is

to the subject of a proposition

what Ob-

to the predicate.

All the four

processes of Obversion, Conversion by

OF COMPOUND IMMEDIATE INFERENCES. 229 Negation, Conversion by Contraposition, and Inversion involve a change of quality in the terms. If the quality of the subject is changed,

are not transposed,

we have

If the quality of the predicate

are not transposed,

is

changed, and the terms

we have Obversion.

If the quality of the subject only is

terms are transposed, tion

and the terms

Inversion.

changed, and the

we have Conversion by Nega

(ii).

If the quality of the predicate only is changed,

terms tion

are

transposed,

we have Conversion

and

the

by Nega

(i).

If the quality of both subject

and predicate

is

changed,

and the terms are transposed, we have Conversion by Contraposition.

CHAPTER Of

XVII.

Other Forms of Immediate Inference.

237. HAVING treated of the main forms of immediate

whether simple or compound, we

inference,

close this subject with a brief allusion to

will

now

some other forms

which have been recognised by logicians. 238. Every statement of a relation

with an immediate inference in which the

presented from the opposite James we infer James was the grandson of

of Dick infer

Tom

from

;

Oxford

is

we

Bicester

is

fact is

(

by John

Tom

infer

same

Thus from John

side. hit

furnish us

may

is

Dick

from

;

;

is

the grandfather

north-east of Oxford

south-west of Bicester

hit

we

So and so

from

Academy the day after he arrived in London So and so arrived in London the day before he

visited the

we

infer

visited the infer

B

is

Academy less

than

from

;

A

;

A

is

greater than

and so on without

inferences as these are material, not formal.

be

laid

down

them except

for

limit.

No

the universal

B

we Such

law can

postulate,

that

Whatever

is

true in one

every other

form of words

is

true in

form of words which conveys the

same meaning.

OF O THER FORMS OF IMMEDIA TE INFERENCE. 239. There

23 1

a sort of inference which goes under

is

title of Immediate Inference by Added Determinants, which from some proposition already made another is inferred, in which the same attribute is attached both to

the in

the subject

.

and the predicate,

A A

.

horse

a quadruped.

is

white horse

is

a white quadruped.

The

attributes

definite qualities, like whiteness,

and must

Such inferences are very added must be

e. g.

deceptive.

no way involve a comparison. From A horse is a quadruped it may seem at first sight to follow that

in

A

swift horse is a swift

go

such

no means follows

But we need not

is

a quadruped which

A

from tall

bushman

bushman

man

swift

is

a

tall

man who

a

is

is

a

is

it

by

is

is

A

that

slow horse

slow for a horse.

man

Similarly,

does not follow that

it

man, but only tall

;

compared with most quad

All that really follows here

rupeds.

about

A slow horse is a slow quadruped

that

even a slow horse

for

is

quadruped.

how little formal validity there is an inference. From A horse is a quadruped

far to discover

for a

A

that

bushman

;

tall

A

bush

and so on

generally.

as

240. Very similar to the preceding is the process known Immediate Inference by Complex Conception, e. g.

A /.

horse

is

The head

This inference, which

it

differs in

a quadruped.

of a horse

is

the head of a quadruped.

by added determinants, from name rather than in nature, may be

like that

OF O THER FORMS OF IMMEDIA TE INFERENCE.

232

explained on the principle of Substitution.

The head

the identical proposition,

Starting from

of a quadruped

the head of a quadruped/ and being given that is

a quadruped, so that whatever

generally

we know

substitute the

manner we

to

is

true of

A

is

horse

quadruped

be true of horse, we are entitled to

narrower for the wider term, and

in

this

arrive at the proposition,

The head

of a horse

is

the head of a quadruped.

Such an inference is valid enough, if the same caution be observed as in the case of added determinants, that is,

if

no

difference be allowed to intervene in the rela

tion of the fresh conception to the generic

terms.

and the

specific

CHAPTER

XVIII.

Immediate Inference as applied

Of

to

Complex Propositions. 241. Before entering on this subject

show to

that the fourfold division

first

complex

242. Conjunctive Propositions

E. i.

o. 1

I,

A is B, If A is B, If A is B, If A is B, If

C C C C

(2) If

A A

52) applies as

much

may assume any

of the

(

is

always D.

is

never D.

is

sometimes D.

is

sometimes not

form of expression.

(1) If

be well to

O, as follows

The reader should be warned

this last

will

as to simple propositions.

four forms, A, E, A.

it

is

B,

it is

is

B,

it is

It

at

D

l .

once against the ambiguity of

may mean

sometimes not true that C is D. sometimes true that C is not D.

o. i.

That is to say, it fails to distinguish between the proposition itself and its obverse. Whenever this becomes of any importance the full forms just given ought to be employed. The same purpose however may be served by putting a hyphen between the some times and the not when the proposition is to be read as O, *

thus If

A

is

B,

C

is

sometimes-not D.

O.

AS APPLIED

234 OF IMMEDIATE INFERENCE These admit of being read

in the

form of simple pro

positions, thus

= All AB is CD. is B, C is always D = No AB is CD. A is B, C is never D = Some AB is CD. If A is B, C is sometimes D If A is B, C is sometimes not D=Some AB is not CD.

If

A

If

A. E. i.

o.

If kings are ambitious, their subjects always suffer.

=A11

cases of ambitious kings are cases of subjects suf

fering.

= No

A.

wind

If the

in the south, the river never freezes.

is

cases of wind in the south are cases of the river E.

freezing.

man

If a

plays recklessly, the luck sometimes

goes

against him.

= Some

cases of reckless playing are cases of luck going

against one. If a

book has

= Some

i.

merit, the public sometimes

public buying,

243.

do not buy

it.

cases of books having merit are not cases of the

The

o.

difference between the conjunctive

disjunctive proposition

lies,

as

we have

and the

seen, in this

that

in the conjunctive the truth, in the disjunctive the falsity,

of the antecedent implies the truth of the consequent.

The

disjunctive proposition therefore

conjunctive, consequently as a a negative term for

its

may be

simple proposition with

subject.

Either

A

is

B

or

C

is

= If A not B, CisD. = A11 not-AB CD. is

is

read as a

D.

TO COMPLEX PROPOSITIONS. Hence what has

been said of the conjunctive pro to the disjunctive, which may

just

becomes applicable

position

be constructed in as

235

all

four forms, but

is

commonly

treated

were always A.

if it

A is B or C is always D =A11 not-AB is CD. A is B or C is never D =No not-AB is CD. Either A is B or C is sometimes D =^Some not-AB is CD. Either A is B or C is sometimes not D = Some not-AB is not CD.

Either Either

men

Either

are immortal or their hopes

are

A. E. i.

o.

always

deceived.

i=All cases of

men being

being deceived. Either the sky

= No

is

mortal are cases of their hopes

A.

clear or there

is

never dew.

cases of the sky being cloudy are cases of dew.

Either children

tell

E.

the truth or else sometimes they are

frightened.

Some

cases of children not telling the truth are cases of

their

being frightened,

i.

Either he wins easily or else sometimes he does not attend to the game.

= Some

cases of his not winning easily are cases in which

he does not attend 244.

It

we

proposition of which

and consequent are treated

always,

as

to the

game.

must be understood

such. never,

are

indefinite

The &c.,

o.

that

in

the

complex

speaking both antecedent

and

either

affirmative or

signs of quantity and

though they

may appear

quality,

in

the

consequent, do not refer to that proposition itself, but to its connexion with the antecedent. We will not pursue

OF IMMEDIATE INFERENCE AS APPLIED

236

the complexities that

and

would

arise, if

we were

to quantify

and consequent themselves as which they are the terms.

qualify the antecedent

well as the whole proposition of

be

It will

sufficient to indicate these

A

some

If

some

If

is

it is

B,

by a single instance

some C

always true that

is

not D.

instances of an experiment are failures,

always true that some of

conditions are not

its

Here the whole proposition

A, the antecedent

is

it

is

fulfilled. I,

the

consequent O.

The

245.

ought

conveyed two statements

it

though

any more than

not,

is

disjunctive proposition

the

E

in

one breath.

S

P

is

A

No P or C

meaning

directly

It asserts

A

B.

is

B

is

The

proposition

this

Mercier declares

If I

If

also, that

C

is

not D,

an immediate inference from the

is

proposition

Some one

is

itself.

guilty;

When

it is

General

either

Dreyfus

am

not guilty, Dreyfus must be guilty.

alternative rendering

If

Dreyfus

is

not guilty, I must be guilty/

inconvenient corollary. able

the form

way

he wishes us to read the proposition thus

I,

The

In the same

S.

D

ought to be interpreted as no more than this, If A is not B, C is D.

proposition, not the

or

is is

indeed by implication

But

it

be regarded

not considered to assert directly, but only

is

implicitly, that

Either

Yet

proposition, to

as conveying both with equal directness.

No

often treated as

that

proposition

it

:

seems

The

inference indeed

indistinguishable

but, since the

is

is

only an

so inevit

from the former

two members of a complex

proposition play the part of subject and predicate, to say

TO COMPLEX PROPOSITIONS. that the to

two statements are

would be tantamount

identical

same proposition can have two and two predicates. At the same time we may

asserting

subjects

grant that, form,

237

246.

when

a proposition

We

now

are

may be

is

expressed in disjunctive

which term we

indifferent

it is

inference

the

that

select as subject.

in a position to see

how immediate

applied to complex propositions.

Opposition. 247. to

The

relation of propositions in the

same matter

one another may be seen as clearly in the complex as Let us take as an instance a dis

in the simple form.

junctive

A

proposition.

A.

Either

E.

Either

i.

Either

A is B or C is always D. A is B or C is never D. A is B or C is sometimes

o.

Either

A is B or C

is

Contrary.

D.

Subaltern,

sometimes not D. Contradictory.

Conversion. 248. Conjunctive propositions

may be

converted as

easily as simple ones. A. /.

If

A

is

B,

C

is

always D.

If

C

is

D,

A

is

sometimes B.

If

A

is

B,

C

/.

If

C

is

D,

A

is

never B.

If

A

is

B,

C

is

sometimes D.

..

If

C

is

D,

A

is

sometimes B.

E.

i.

is

never D.

249. That the converse of

A

is

the proposition given

238 OF IMMEDIATE INFERENCE above may be seen by our

first

AS APPLIED the

reducing

proposition to simple form, then converting

it,

complex and finally

throwing back the result into complex form. If A is B, C is always D. A.

= A11 AB .

.

Some

= If C The

250. as though

it

last

is

CD.

CD

is

AB.

D,

A

is

is

sometimes B.

proposition must not be misunderstood

A

The meaning

contained an assertion of fact.

might be better conveyed by the form If C is D, it may be that A

is

B.

concrete instance will render this point clearer. If kings are ambitious, their subjects

may

always suffer

be converted into If

subjects suffer,

it

may be

that their

kings are

ambitious, i.e.

among

of subjects

even

if

the possible causes of suffering is

to

on the part

be found the ambition of their

rulers,

every actual case should be rightly referred to It is in this

other cause.

a necessary one.

some

sense only that the inference

But then

is

this is the only sense with

which we are concerned.

To judge

of conformity to fact

of deduction.

CD

is

AB

Some P

is

From

All

AB

is

is

CD

no part of the province it

follows that

Some

with the same necessity as that with which In the latter S follows from Some S is P.

may conform to fact. From All centaurs are animals it follows necessarily that Some animals are centaurs, but as a matter of fact

case also neither proposition

TO COMPLEX PROPOSITIONS. not the case. The consequent, always be as true as the antecedent.

this is will

All Centaurs /.

animals are Centaurs

251.

The

O

in

the

From

(if

there be such creatures).

proposition can of course

complex than

in

the

no more be form.

simple

the proposition If a

it

drawn,

rightly

there be such creatures) are animals.

(if

Some

converted

if

239

man

runs a race, he sometimes does not win

it/

certainly does not follow that If a

man

wins a race, he sometimes does not run

252. Disjunctive

propositions

cannot be

it.

converted

without losing their disjunctive form, the reason being that the consequent

when

affirmative, so that

is

it is

made

the antecedent, the proposition assumes the conjunctive

form. Either

A. /.

If

C

is

Either

E. .-.

If

C

is

Either

i.

/. If

C

is

A

is

D,

A

is

D,

A

or

it

C

or

B

is

always D.

be that

may

B

it is

is

D,

B

it

C

is

A

never true that

or

C

may

is

not B.

is

never D.

A

not B.

is

sometimes D.

be that

A

is

not B.

Obversion. 253.

A is B, If A is B, If

A. .*.

it is

it is

C

always true that

never true that

C

is

mother loves her children, she

If a

is

D.

not D. is

E.

always

kind to them. .

.

If a

mother loves her children, she unkind

to them.

is

never

240 OF IMMEDIATE INFERENCE AS APPLIED E. /.

If

A

is

If

A

is

B,

B,

man If a man

If a ..

i.

.

.

If

A

If

A is B,

is

C

it is

never true that

it is

always true that

D.

is

C

not D.

is

A.

tells lies, his

friends never trust him.

tells lies, his

friends always distrust him.

B,

it is

it is

sometimes true that

sometimes

not true that

If strangers are confident, savage

C is D. C is not D.

o.

dogs are some

times friendly. /. If

strangers are confident, savage dogs are

some

times not unfriendly.

A is B, If A is B, If

o. ..

sometimes not true that

it is it is

If a measure

sometimes true

that

C

is

C

is

D.

not D.

i.

is

good,

its

author

is

sometimes not

is

good,

its

author

is

sometimes un

popular. /. If

a measure popular.

254. it

The

disjunctive proposition

may

be ob verted as

stands without being reduced to the conjunctive form.

It will

be sufficient to indicate

A is B or C is D. Either A is B or C is not

this

by a

single example.

Either .-.

not-D.

Either a sinner must repent or he will be damned. ..

Either a sinner must repent or he will not be saved.

Conversion by Negation. 255.

It will

be expedient

now

to confine ourselves, at

examples, to a form of expression which leaves no chance of the quantity and quality of the

least in the abstract

TO COMPLEX PROPOSITIONS. whole proposition being confounded with

241 that of the

consequent.

The

student must bear in

negation

there

mind

that in conversion

always a change

is

of

quality

by the

in

always a transposition of terms, and that the quality of one of the terms is always changed. Further he must bear in mind that the process proposition, that there

is

admits of two forms that

the

in

the original

first

remains un

subject

changed, that

the second the

in

original

unchanged. 256. We have first to apply

this

remains

predicate

mode

of inference to

conjunctive propositions.

00 A. ..

If

A

is

B,

If

C

is

not D,

If a ..

E. .*.

If a If

A

If

C

man man is is

If the ..

..

A

If C

it is

D.

is

A

E.

is

a total abstainer, he never smokes.

it is

never true that

does not B,

it is

not D,

C

is

D.

fall,

the

wind

is

A

is

B.

i

.

sometimes high, that C is D.

sometimes not true

it is

ground been rain.

If there

B.

is

a smoker, he always drinks.

If the

..

C

never true that

not D, it is sometimes true that wind is high, rain never falls.

is is

always true that

is

is

B,

If rain If

o.

it

is

sometimes true

that

A

is

B.

i.

wet, there has sometimes not

has not been rain, the ground

is

times wet.

R

some

242

OF IMMEDIATE INFERENCE AS APPLIED (ii.)

A. .-.

If

A

If

C

is

B,

D,

is

not B. If .-.

E. .-.

always true that

it is

is

D.

A

is

o.

money

scarce, prices are always low.

is

If prices are low,

money is sometimes not abundant.

C

If

A

is

B,

it is

never true that

If

C

is

D,

it is

always true that

If a

C

sometimes not true that

is

it

is

A

D.

is

not B.

A.

merely does his duty, no one ever

man

thanks him. .-.

thank a man, he has always done more

If people

than his duty. i.

.-.

If

A

If

C

is

B,

it is

D,

is

not D.

it

sometimes true that

C

D.

is

sometimes not true that

is

C

is

o.

If a statesman

is patriotic,

he sometimes changes

his party. .-.

If a statesman

changes his party, he

is

sometimes

not unpatriotic. 257. Next

we have

apply the same

to

mode

of

inference to disjunctive propositions. (i-)

Either

A. .-.

Either

A C

not B.

is

B

is

or

D

it is

or

it

always true that is

never true

C

is

D.

that

A

is

E.

Either miracles are possible or ancient historians

.-.

are always untrustworthy. Either ancient historians are untrustworthy or

miracles are not impossible.

TO COMPLEX PROPOSITIONS. E. ..

Either

A

Either

C

B

is

not B.

or

D

is

never true that

it is

or

243

C

D.

is

A

is

done

to

sometimes true that

it is

i.

Either he loses his temper or nothing

is

displease him. If

/.

something is not done sometimes does not lose

Either

o.

A

B

is

or

it is

to displease

him, he

his temper,

sometimes not true that

C

A

is

isD. .*.

Either

C

D

is

not B.

or

is

it

sometimes true that

i.

Either there

a future

is

life

or

it is

sometimes not

true that justice prevails. /.

Either justice prevails or that there

sometimes true

is

it

not a future

is

life.

In the above examples the quality of the subject

is

retained, while the predicate

These

its

contradictory.

by

the negative force

facts are

is

original

changed

into

obscured to the eye

which the word

either

imparts to

the antecedent of a disjunctive proposition.

(ii.)

A. ..

Either

A

Either

C

that

A

is

B

not

is

is

B.

Either there or evil ..

is

or

is

it is

D

always true that

or

it

is

C

is

D.

sometimes not true

o.

more than one

principle at

work

merely apparent.

Either evil

is not merely apparent or there be no more than one principle at work.

R

2

may

OF IMMEDIATE INFERENCE AS APPLIED

244

Either

A

Either

C

A. .-.

B.

is

B

is

or

D

not

is

never true that

it is

or

it

C

is

D.

A

always true that

is

A.

Either the rivers will run back to their sources or the country will not be abandoned.

Either the country will not be abandoned or the

.-.

rivers will i.

Either

A

Either

C

that

A

.-.

is

or

D

B.

or

.-.

Either godliness

the

predicate its

C

is

D.

sometimes not true

is

much

amiss or godliness

sometimes gain. is

times not very

In

it

o.

Either things are very is

their sources.

sometimes true that

it is

not

is is

run back to

B

not gain or things are some

much

amiss.

above examples the quality of the original is

retained, while the subject

These

contradictory.

facts are

is

changed

into

obscured to the eye

by the same cause as before.

Whenever seems

the converse by negation of a proposition

difficult to

grasp,

let

the reader mentally reduce

it

to the equivalent conjunctive, e. g.

Either godliness

not very

=

much

is

not gain or things are sometimes

amiss.

If godliness is gain, things are

much

sometimes not very

amiss.

Conversion by Contraposition. 258. First as applied to conjunctive propositions. A. .-.

If

A

If

C

is is

B,

it is

not D,

always true that it is

C

is

always true that

D.

A

is

notJB.

A.

TO COMPLEX PROPOSITIONS. If a /.

If a

245

man is a smoker, he always drinks. man is a total abstainer, he is always

a non-

smoker. If

E. /.

A C

If

is

B.

never true that

it is

C

is

D.

A

sometimes not true that

it is

not

is

o.

wind

If the .-.

If rain

If

A

..

If

C

o.

B,

not D,

is

is

B,

fall,

the

wind

falls. is

sometimes not low.

C

sometimes not true that

it is

not D,

it is

ground

is

is

If the

high, rain never

is

does not

sometimes not true

is

D.

A is B.

that

o.

wet, there has sometimes not been

rain. /.

If there has not

been

rain, the

sometimes

is

ground

not unwet.

259. Next as applied to disjunctive propositions. A. .-.

Either

A

is

B

or

it

Either

C

is

D

or

it is

is

always true that

C

always true that

A

is is

D. B.

A.

Either miracles are possible or ancient historians are always untrustworthy. .

.

Either ancient historians are untrustworthy or mira cles are

E. .

.

Either

A

Either

C

B.

o.

always possible.

is is

B

or

D

or

never true that

it is it

is

C

is

D.

sometimes not true that

Either he loses his temper or nothing

is

A

done

is

to

displease him. .-.

Either something

is

done

sometimes does not lose

to displease his

temper.

him or he

OF IMMEDIATE INFERENCE AS APPLIED

246

A is B or Either C is D or Either

o. .

.

Either there

is

sometimes not true that

C

is

sometimes not true that A

is

B.

it is it is

a future

life

or

it

D. o.

sometimes not

is

true that justice prevails. /.

Either justice prevails or that there

260.

is

a future

it

is

sometimes not true

life.

On comparing the above results with the

by negation

(i.)

converse

of each of the same propositions, A, E, O,

was

the reader will see that they differ from the latter, as

The be expected, only in being obverted ( 23.1). and the here of inference be both tested, may validity to

in the case of conversion

by negation, by reducing the

disjunctive proposition to the conjunctive,

and so

to the

simple form, then performing the required process as in

simple propositions, and finally throwing the

result,

when

so obtained, back through the conjunctive into the dis

We

junctive form.

above

is

o.

Either

A is B

A

not B,

will

show

in

this

really the contrapositive of the

or

it is

manner

O

the

that

proposition.

sometimes not true that

C

is

D.

(Disjunctive.)

=

If

is

it is

sometimes not

true that

C

is

D.

(Conjunctive.)

= .-.

Some not-AB is not CD. Some not-CD is not AB.

=

If

=

Either

C

is

not

D

C

D

;

it is

(Simple.) (Contrapositive.)

sometimes not true that

A

is

B.

(Conjunctive.) is

or

it is

sometimes not true that

A is B.

(Disjunctive.)

TO COMPLEX PROPOSITIONS. Either there

is

a future

life

or

it is

247

sometimes not true

that justice prevails.

=

If there be not a future

sometimes not true

life, is is

that justice prevails.

=

Some

cases of there not being a future

life

are not

cases of justice prevailing. .

Some

.

cases of justice not prevailing are not cases of

there being a future

life.

=

If justice

=

Either justice prevails or

there

there

do not

a future

is

a future

is

it is

prevail,

sometimes not true that

life.

sometimes not true that

it is

life.

Inversion. 261. This form of inference

A

and

applicable only to

is

E

propositions.

262.

We

will take these

two propositions

first

in the

conjunctive form.

A If A

If

E. /.

it is

is

B,

is

not B,

never true that it is

C

is

D.

sometimes true that

C

is

D.

i.

man merely does his duty, no one ever thanks him. a man does more than his duty, people sometimes

If a .

If

.

thank him. If the reader

tion

(ii.)

compares

this

with the converse by nega

of E, he will find that

it

differs

from

it

only in

being converted. If

A. .-.

If

A is B, A is not

If a .

.

If a

it is

B,

always true that

it is

C

is

D.

sometimes not true that

C

man is a smoker, he always drinks. man is a non-smoker, he sometimes does

is

D.

o.

not drink.

OF IMMEDIATE INFERENCE AS APPLIED

248

would take

It

reach

five

conclusion

this

of obversion-conversion

steps

from

A.

Let

us

to this

verify

assertion.

E.

/.

If a

man man

E.

.

If a

man

If a

A.

.

is

a smoker, he always drinks.

is

a smoker, he

is

a total abstainer, he

is

never a total abstainer.

is

(Obversion.) never a smoker.

(Conversion.) A.

If a

/.

man

is

a total abstainer, he

is

a non-smoker, he

is

always a non-

smoker. i.

.

If a

.

man

(Obversion.) is

sometimes a

abstainer. o.

.

If a

.

man

is

(Conversion.) a non-smoker, he sometimes does not

drink.

203.

We

total

(Obversion.)

will

next take

E

and

A

in the disjunctive

form. Either

E.

Either

..

C

is

A is B or is never true that C is A is not B or is sometimes it

it

D.

D. true

that

i.

Either the rivers will run back to their sources or the

country will not be abandoned is

..

CD).

some

(= Some This conclusion (ii.)

not-AB

Either the rivers will not run back to their sources or in

of

(=No

E

cases the country will be abandoned

AB

is

differs

CD). from the converse by negation It is however so far

only in being converted.

from being self-evident that

it

may be

well to

work

it

out.

TO COMPLEX PROPOSITIONS.

The

inverse of E,

be remembered,

will

it

is

249

reached by the

following three steps (1) Conversion,

(2) Obversion, (3) Conversion.

Either

A

B

is

or

never true that

C

C

is

it is

D.

is

(Disjunctive)

=

If

A

is

not B,

never true that

it is

D.

(Conjunctive)

= No ..

.. .-.

=

CD. not AB.

not-AB

is

(Simple)

CD A B. All CD AB CD. Some No

is

(Converse)

is

(Obverse)

is

If

A

is

it is

B,

(Converse)

sometimes true that

C

is

D.

(Conjunctive)

=

Either is

.-.

B

not

is

or

it

is

sometimes true that

D.

A Either A Either

A.

A

C

(Disjunctive) is

B

is

not

or

it is

B

or

always true that it

is

C

is

D.

sometimes not true

that

CisD. Either miracles are possible or ancient historians are always untrustworthy. .-.

Either miracles are not possible or ancient historians are sometimes not untrustworthy.

This conclusion negation

(ii.),

i.e.

will

be found to be the converse by

the obverted converse, of the contra-

positive of the original.

CHAPTER Of 264. in

XIX.

Mediate Inferences or Syllogisms.

A syllogism is a combination of three propositions, The

which the third follows from the two conjointly.

two propositions are called the Premisses, the

third the

Conclusion. Middle Term.

Major Term. .

\ ,

Major Premiss. All mammals are warm-blooded. Minor Term. Middle Term.

Minor Premiss. All whales are mammals.

Minor Term. .

265.

As

.

Major Term. All whales are warm-blooded.

(

.

Antecedent Premisses.

;

(Consequent or I

v

_

.

Conclusion.

a syllogism consists of three propositions

and a proposition consists of two terms, there are sense six terms in a syllogism.

in

one

In another sense there

are only three, since each term occurs twice over.

The middle term

occurs twice in the premisses and

does not appear in the conclusion. Each of the other terms occurs once in a premiss and

once

in the conclusion.

The Major Term is the predicate of the conclusion. The Minor Term is the subject of the conclusion. The Middle Term is that by which the subject and into connexion predicate of the conclusion are brought

with one another.

OF MEDIATE INFERENCES OR SYLLOGISMS.

251

The major and minor term are called the Extremes as opposed to the Mean or middle term. 266. The Major Premiss is that which contains the major term.

The Minor Premiss is that which contains the minor term. The major premiss is generally put first, but this is not

necessary and

Whales

able.

of thought, which

doubtful whether

is

it

mammals is

warm-blooded

it

is

is

desir

the order

represented by writing the premisses

in the reverse order.

mammals.

All whales are

All .

.

mammals

are warm-blooded.

All whales are warm-blooded.

The reason why

the

names

major,

middle/ and

minor

terms were originally employed is that in a syllogism such as the above, which was regarded as the perfect

type

of

relative quantity

It

syllogism,

these

must be noticed however

term cannot be of

less

all

latter is the

three, of

that,

though the major

extent than the middle nor the

middle than the minor, there two, or

names represent the

in extension of the three terms.

is

nothing to prevent any

them from being coextensive.

case in Traduction.

The

252 OF If the

the

MEDIATE INFERENCES OR SYLLOGISMS. minor premiss were particular instead of universal, We should then have either apply.

names would not

a case of the intersection of two classes, from which

it

could not be told which of them was the larger, or the

minor term would actually be larger than the middle, standing to

in the relation of

it

genus

to species, as in

the following syllogism All Negroes have woolly hair.

..

When

Some Some

Africans are Negroes.

Africans have woolly hair.

a premiss

is

negative,

it

gives us

no

clue at

all

to

the relative extent of the terms employed.

267. Outside books on logic an argument

found stated in

full

generally stated

first

in as a

reason for

syllogistic form.

The

is

seldom

conclusion

is

and then one of the premisses thrown

it.

Problema or Quaestio. 268.

When

to discussion,

it

the conclusion is

solution or answer

called a is

is

put as a question open

Problema or

Quaestio.

The

supplied by the premisses, thus

Are the Chinese capable of progress or are they not ? They are for they are rational beings, and all rational :

beings are capable of progress.

OF MEDIATE INFERENCES OR SYLLOGISMS. 253 Enthymeme.

An Enthymeme is may or may not

269.

gism, which

name however ment

very commonly used

now

for

an argu

Enthymeme

of the First Order the major premiss

suppressed.

In

an Enthymeme of the Second Order the minor

premiss

is

In an is

The

be a valid argument.

defectively expressed.

In an is

is

properly a rhetorical syllo

suppressed. the Third Order the conclusion

Enthymeme of

suppressed.

The Problematic Enthymeme. 270.

be

An enthymeme

Does

A

distribute

because

it

its is

enthymeme of

second order.

or second order

Thus

subject or not

universal

universal propositions do.

giving an

first

expressed.

problematically

Yes,

of the

By the

we may

?

Yes,

is

by the

may

question reply

because

the former answer

first,

Either answer

or

the

to

latter

we

all

are

one of the

incomplete without the

other.

logical difference

the

The one we

are giving the major premiss, in the other

the

minor premiss of the syllogism;

between the two

principle, in the other its application.

in

the

is

that in

one the

CHAPTER Of Mood and 271. Syllogisms

may

differ

XX. Figure.

from one another

two

in

ways (1) in

Mood,

(2) in Figure.

272.

Mood

is

a difference

ing on the quantity and which they are made up.

273. Figure ing

is

among

syllogisms depend

quality of the

a difference

among

propositions of

syllogisms depend

upon

the position of the terms in the propositions.

274.

A

propositions, differently

:

syllogism

consisting

say EIO, so that the

may

of the

have

its

same kind of terms arranged

same mood may be

in different

figures.

There are 64 possible moods. There are 4 possible figures. .. There are 256 possible forms of syllogism. 275. That there are 64 possible moods may be seen as follows.

Suppose the premisses

to

be AA.

These may

four different conclusions, giving us the four

AAE, AAI, AAO.

yield

moods A A A,

But instead of having

A

for the

OF MOOD AND FIGURE. minor premiss, we might have the

number of moods

to 4

x

E

or

or O, bringing up

I

These

4.

255

all

have

A

for

major premiss. There will be the same number with E, I, and O. Altogether then the number of moods is the

4x4x4x4 = 256. 276.

That

there are four possible figures

may

be seen

as follows.

The

position of the terms in the conclusion

definition.

by

We

fixed

But as there are two terms

position in the premisses.

a premiss, of which the middle

in

is

have therefore only to consider their

always one, the

is

position of the middle term fixes that of the other two.

We

have therefore only to consider the position of the Now the middle term must either occupy the same position in both premisses or not. If it does middle term.

occupy the same position

in both,

in both or predicate in both

same

position

in both,

major and predicate the major and subject 277.

The

in

it

must

either be subject

does not occupy the must either be subject in the

it

;

minor or

the

in the

if it

else

predicate in

minor.

is that arrangement of terms which the middle term is subject in the

First Figure

in a syllogism in

major premiss and predicate in the minor. The Second Figure is that arrangement of terms a syllogism in which the middle term

is

predicate in

in

both

premisses.

The Third

arrangement of terms in a syllogism in which the middle term is subject in both premisses.

Figure

is

that

OF MOOD AND FIGURE.

256

The Fourth

is

Figure

arrangement of terms in

that

a syllogism in which the middle term

is

predicate in the

major premiss and subject in the minor. Let P major term (predicate of the conclusion). S minor term (subject of the conclusion).

= = M = middle term.

FIGURE

.-.

FIGURE

I.

II.

M

P.

P

M.

S

M.

S

M.

S

P.

S

P.

.-.

FIGURE

M M .-.

FIGURE

No

E. I.

0.

/.

0.

Some quadrupeds

No

E.

0.

.

.

M .-.

S

I.

II.

carnivorous animals have horns.

FIGURE

1.

P

S.

P.

Some quadrupeds have .*.

P.

Some quadrupeds have horns. Some quadrupeds are not carnivorous.

No

1.

FIGURE IV.

horned animals are carnivorous.

FIGURE E.

S

III.

horns.

are not carnivorous. III.

horned animals are carnivorous.

Some horned animals are quadrupeds. Some quadrupeds are not carnivorous. FIGURE IV.

No

E. 1.

O.

.*.

carnivorous animals have horns.

Some horned animals Some quadrupeds are

are quadrupeds.

not carnivorous.

M. S.

P.

CHAPTER Of 278. class

XXI.

Canon of Reasoning.

the

WHATEVER can be

affirmed or denied of a whole

can be affirmed or denied of everything contained

in that class.

The above axiom figure.

the

applies

directly

only to the

first

Hence first

figure

is

called the Perfect Figure,

the rest are called the Imperfect Figures.

The way as

it

the

makes

in

which the axiom

is

stated

is

convenient,

the principle intuitively manifest, but

drawback of regarding the predication

made

premiss as being

in extension,

i.e.

in the

as

it

has

minor

consisting

in inclusion in a class.

279. If

we may do

we wish

to express the principle intensively,

so as follows

Whatever has

certain attributes has also the attributes

which invariably accompany them. Thus, it

if

a whale has the attribute of suckling

its

young,

has also the attribute of warm-bloodedness, which

found invariably

to

accompany

the other. s

is

OF THE CANON OF REASONING.

258

Or, beginning from the

other end,

we may put

the

is

an

canon thus

An

an

of

attribute

Nota notae Either

est

mode

nota

rei

anything

itself.

ipsius.

statement

of

of

attribute

attribute of the thing

under

is

the

disad

vantage of taking the subject of the major premiss in intension.

280.

As a

subject

is

always used in extension and

a predicate generally in intension, the proper statement of the principle

is

unavoidably clumsy

and

If a thing has a certain attribute

which possess that

all

the things

have another

attribute

attri

bute also, then the thing in question possesses that other attribute.

All whales suckle their young. All

animals

that

suckle

their

young have warm

blood. /.

All whales have

281.

By

warm

blood.

Aristotle himself (Cat.

was expressed

in a neutral

Whatever

is

3,

1) the principle

form thus

stated of the predicate will be stated

also of the subject.

But there are two assumptions here, namely statement about the

predicate

that the original proposition

is

is

made

affirmative.

fore enlarge his statement as follows

that the

universally

and

Let us there

OF THE CANON OF REASONING. Whatever

is

259

affirmed or denied universally of the

predicate of an affirmative proposition

may be

affirmed or denied also of the subject.

The

student should bear in

is

usually stated, the

is

the second premiss.

mind

affirmative

In the above example

it is

the

that, as the

syllogism

proposition spoken

of

first.

The Three Axioms of Mediate Inference. 282. Instead of a single canon applying only to the

modern

perfect figure

logicians tend to substitute three

axioms which apply to all figures alike. (1) If two terms agree with the same

third term,

they agree with one another. (2) If

one term agrees and another disagrees with same third term, they disagree with one

the

another. (3) If

two terms disagree with the same third term, may or may not agree with one another.

they

283. all

The

first

of these axioms

affirmative conclusions

the second

is

is

the

principle of

;

the principle of

all

negative conclusions

the third points out the conditions under which

;

no con

clusion can be drawn.

284. Even more than the Dictum de

Omni

el

Nullo

axioms labour under the defect of representing For by predication as a mere matter of extension. these

agreement of terms

can only be meant coincidence

extension. S 2

in

OF THE CANON OF REASONING.

260

When

two terms agree with the same

it

is

said that

third term,

it

must be understood

the

same

Here same

part of

that they agree with

it.

are two terms which appear to agree with the

third

term All badgers are bald,

All babies are bald,

and yet no one would contend

that they agree with

one

another.

Here again are two terms of which one appears to agree and the other to disagree with the same third term All birds lay eggs,

No

lizards are birds,

and yet we cannot draw the conclusion, No Some lizards do not lay eggs.

lizards lay

eggs/ nor even

The

fact

is

that these

axioms do not of themselves

enable us to distinguish a good conclusion from a bad one.

They only do

so,

if

we assume along with them

the rules for the distribution of terms together with the rule of syllogism, that

no term must be

distributed in the

conclusion which was not distributed in the premisses.

Out of

the

conclusion, if

premisses

Some

last

given

we may

the

things which lay eggs are not lizards/

we duly keep before our minds

bution.

extract

the

laws of

distri

CHAPTER Of the

XXII.

General Rules of Syllogism. 285.

I.

PRIMARY.

(2)

A syllogism must consist of three propositions A syllogism must consist of three terms only.

(3)

The middle term must be

(1)

distributed in

only.

one or

both of the premisses. (4)

No

term must be distributed in the

which was not distributed (5) If both

must be

premisses

affirmative,

and II.

conclusion

in the premisses.

be affirmative, the conclusion vice versa.

DERIVATIVE.

one premiss be negative, the conclusion must

(6) If

be negative, and vice versa. (7) (8)

Two Two

(9) If

be

negative premisses prove nothing. particular premisses prove nothing.

one premiss be

particular, the conclusion

must

particular.

286.

The

first

two of the above rules deal with the

structure of the syllogism

and partake of the nature of

definition.

The second two

deal with the distribution of terms.

OF THE GENERAL RULES OF

262

The The The

SYLLOCIS.If.

next three relate to the quality of the propositions.

two

last

first five

relate to the quantity of the propositions.

rules are of the nature of definitions

and

axioms and do not admit of proof; the remaining four can be proved from them.

A

287. (i) parison of

may be

defined as the

two propositions by means

must

.-.It

syllogism

If there

com

of a third.

consist of three propositions only.

be more than two premisses, there

than one syllogism

if

;

there be

less,

there

is

no

is

more

syllogism,

but either an immediate inference or a mere assevera tion.

The

latter

case

comes under the

fallacy of

means giving a statement

the question, which

begging

as a reason

for itself.

Smoking

is

Why

unwholesome. ?

Because

A

(2)

may be

two terms by means of a

must

P.

S

is

P.

defined as the comparison of

third.

consist of three terms only.

/.

It

If

there be more than three terms, there

syllogism or

no

is

.. All

it is.

syllogism

All S

syllogism.

more than one

The

;

following

if is

..

are a fool.

S

are you.

S

S.

.. S

P.

are a fool.

either

there be less, there vituperation,

ment.

You You You

is

P.

no is

not argu

OF THE GENERAL RULES OF SYLLOGISM. 263 This also comes under the In conversation

question.

You

it

of

fallacy

begging the

might appear as follows

are a fool.

Why? Because you are yourself.

The

violation of this rule in the

the fallacy of Four Terms. fallacy of

many

This

way of

excess

is

called

be called the

to

ought

More than Three Terms,

since there

may be

as

as six

His views are

.

It

.

fallacy also arises

used in

All

true.

My views are like his. My views are true.

.

.

M

P.

is

All S

is

N.

S

is

P.

All

whenever an ambiguous word one of the three terms.

is

different senses for

its

The next two which are

fatal to

guard against the two fallacies most syllogisms whose constitution is

rules

unsound.

mean be

(3) If the

not compared in

with either of the extremes, part of

it

in

in the other,

its

we may be

whole extent

referring to

one

one premiss and to quite another part of so that there will be no real mean at all.

it

w

men are confident. brave men are confident. brave men are rash.

All rash All .-.

All

The

violation of this rule

is

.

.

known

All

P

is

All

S

is

M. M.

All

S

is

P.

as the fallacy of

Undistributed Middle. (4) If a

term be undistributed

distributed in the conclusion,

we

in

the

premiss and

are arguing from the

OF THE GENERAL RULES OF SYLLOGISM.

264

the

to

part

whole,

which

form

is

never

a

is

known

as the fallacy of

safe

of

reasoning.

The

violation of this rule

Process.

Illicit

ILLICIT PROCESS OF

.-.

All

Oxford men are educated.

No No

artisans are

artisans are educated.

No No

.

No

are entertaining.

liars

No No

P.

is

S

is

M.

S

is

P.

THE MINOR TERM.

M

P.

is

Some

M

No

is

is S.

entertaining person can be trusted.

The

.

can be trusted.

liar

Some

M

All

Oxford men.

ILLICIT PROCESS OF

/.

THE MAJOR TERM.

.-.

S

P.

next three rules are the three axioms of deductive

inference confined to the sphere within which they are really operative.

(5) for a

Two

judgements of agreement may give ground but not for one of

new judgement of agreement,

disagreement

;

and, conversely, a judgement of agreement

two judgements of agreement, but never out of a judgement of agreement combined with one of

may

arise out of

disagreement.

There

is

not

much semblance

of argument about the

following

/.

All prime ministers are proud.

All

All prime ministers are paid.

All

M M

No

S

No

paid persons are proud.

.-.

is

P.

is S. is

P.

OF THE GENERAL RULES OF SYLLOGISM. 265 Nor

will this

Some

stand examination

animals are snails

shell-less

shell-less

and no

No P

S.

is

Some S

Both of the above examples involves a double

for all slugs are

M.

is

M

All .-.

;

snails are slugs.

is

P.

violate

Rule 5

;

the former

process as well.

illicit

288. (6) A judgement of agreement combined with one of disagreement may give ground for a new judge ment of disagreement, but not for one of agreement;

and, conversely, a judgement of disagreement

may

arise

out of a judgement of agreement combined with one of

disagreement,

but

never

out

of

two

judgements

of

agreement.

This rule

in its

two parts

is

the contrapositive of 5,

the

second part of 6 being the contrapositive of the

first

part of 5,

and the

of the second part of

first

part of 6 the contrapositive

5.

If both premisses

be

affirmative, the conclusion

must

be affirmative. .-.If the conclusion be not affirmative, both premisses

are not affirmative. i.e.

If the conclusion

be negative, one premiss must

be negative. If the conclusion be affirmative, both premisses

be affirmative.

must

THE GENERAL RULES OF SYLLOGISM.

266 OF

..If both premisses be not

affirmative, the conclusion

is

not affirmative,

If

one premiss be negative, the conclusion must

i.e.

be negative.

Rule 5

may be

put in the form of a

U

proposition

All the cases of wholly affirmative premisses are

all

(he

cases of affirmative conclusion.

This admits of two inferences being drawn from

it.

(a) All cases of partly negative premisses are cases

of negative conclusion.

cases of negative conclusion are cases

All

()

of

partly negative premisses.

All S

.. All

is all

not-S

P.

not-P

is

(Contrapositive

without

conversion).

and All

not-P

is

not-S

(Converse

by Contra

position).

of Rule

Violations

6

are necessarily also violations

of Rule 5.

Here

is

an apparent instance. not twinkle

What does

No .

But

.

it

terms.

is

near.

planets twinkle.

All planets are near. is

It

not in syllogistic form, since there are four a really an instance of reasoning with

is

negative middle term.

Non-twinkling

stars are near.

All planets are non-twinkling stars. .-.

All planets are near.

OF THE GENERAL RULES OF SYLLOGISM. 267 289. (7)

ground

Two

judgements of disagreement give no

any new judgement

for

at

all.

If

all

that

we

know of Shadrach and Abednego is that they are not like Meshech, we cannot tell whether they are like each other or not.

.*.

No No No

fishes are

No P is M. No S is M. No S is P.

mammals.

newts are mammals.

newts are

Proof of

fishes.

the rule thai

.

.

two negative premisses prove

nothing. If both

premisses be negative, they are either both

universal or not.

Let them be both universal, namely EE. Then, in whatever figure they be put, they aid of obversion and,

may by the where necessary, of conversion be

brought into the form All

P

is

All

S

is

not-M, not-M

which involves undistributed middle.

Next

let

them not be both

universal.

Then, since two negative premisses even when both no conclusion, a fortiori they can give

universal can give

none when one or both are It 1

must be borne

This proof

Formal

Logic,

is

in

mind

taken from

117, rst edit.

particular

*.

that this like the rest

is

a rule

De Morgan and from Keynes,

OF THE GENERAL PULES OF SYLLOGISM.

268

It ought not to be taken to mean that we can never extract a conclusion from two propositions in

of syllogism.

This

negative form.

for instance, is very

may

easily

The

be done.

None who do not believe rightly can be No men at all believe rightly. No men at all can be saved.

.*.

No not-M is No S is M. No S is P.

.-.

Only

it is

we wish

make

it

saved.

P.

not in syllogistic form, as

to

following,

good reasoning.

it

has four terms.

we must read

a syllogism,

If

minor

the

as an affirmative All S

Again

this is

is

not-M.

good reasoning

No monkeys are men. No monkeys are without ..

Some

No No

hands.

M M

is

P.

is S.

creatures with hands are not

men. But, as before,

it

has four terms.

As

it

appears in

a syllogism

Some

.*.

All All ..

M M

Some

this

is

not-P.

form

is

not-P.

is

not-S.

not-S

is

not-P.

290. (8) This and the following rule

from those which

not-S

relate to the distribution

may

be proved

of terms.

OF THE GENERAL RULES OF SYLLOGISM. 269 Proof of

the rule that

two particular premisses prove nothing.

If both premisses

be particular, they must be either

both affirmative or both negative or one affirmative and

one negative. There are then three cases

But

II premisses distribute

no term

.*.

The middle term must be

..

There

OO IO

at

all.

undistributed.

OI

by Rule

distribute only

7.

one term, which must be the

middle term (Rule 3). The major term is undistributed .

or OI.

no conclusion.

is

are excluded

or

OO, and IO

II,

.

But one of

in the premisses.

the premisses being negative, the conclusion

must be negative.

.-. .

.

And every negative proposition distributes its predicate. The major term must be distributed in the conclusion. There would be an

/. There

illicit

process of the major.

no conclusion.

is

291. (9)

Proof of

the rule that,

if one premiss be

particular, the conclusion must be particular.

one premiss be particular, the other must be universal Rule (by 8). There are then four combinations possible If

A In

with

I,

A

with O,

E

with

I,

E

with O.

AI or IA premisses only one term

is

distributed.

This must be the middle term (Rule 3). .-. The minor term is undistributed in the premisses.

OF THE GENERAL RULES OF SYLLOGISM.

270

.-.It must be undistributed in the conclusion (Rule .

.

The

In the combination of

E

4).

conclusion must be particular.

A

O

with

and likewise

in that of

with I there are two terms distributed.

One

of these must be the middle term (Rule

.. There

3).

only one of the extremes distributed in the

is

premisses.

But one premiss .-.

.. .-.

is

negative.

The conclusion must be negative (Rule 6). The major term must be distributed in the conclusion. The one extreme that is distributed in the premisses must be the major term.

.-.

.

.

.-.

The minor term

is

undistributed in the premisses.

cannot be distributed in the conclusion (Rule The conclusion is particular. It

The combination

of

E

nitions

and the

O

with

292. Subtracting the

first

last four as

4).

is excluded by Rule 7. two rules as being defi

being derivative,

with an irreducible residuum in

3, 4,

and

5.

we

are

left

Rule 5 has

always hitherto been taken for granted instead of being expressed.

293.

except

i

The and

following

mnemonics contain

all

our rules

5.

Distribuas medium, nee quartus terminus adsit

;

Utraque nee praemissa negans, nee particulars

;

Sectetur partem conclusio deteriorem,

Et non

The part

distribuat, nisi

rule that

covers 6 and

cum

praemissa, negetve.

the conclusion 9.

must follow the weaker

OF THE GENERAL RULES OF SYLLOGISM.

271

294. All the rules of syllogism are implicitly at least

contained in the statement of the

Whatever

is

Canon of Reasoning

*

affirmed or denied universally of the

predicate of an affirmative proposition

may be

affirmed or denied also of the subject.

This statement implies (1) 3 propositions, namely, the affirmative proposition

(minor premiss), the universal predication (major premiss), the predication about the subject (conclusion)

terms,

(2) 3

namely,

the

(minor term), the (middle term), the term which of its subject (major term); proposition

(3) the distribution of the

cation

is

made

(4) the

of

it

were used

illicit

of

predicate is

the

same

predicated universally

middle term, since the predi

universally

absence of

;

subject of the affirmative

;

process;

if

for,

the

minor

would be a predication about illicitly, more than the something subject, and, if the major were there

it could only be by denying of the subject what had been affirmed of the predicate, which is against the

so used,

Canon ; (5) that

one premiss

is

affirmative, since

it is

so given

;

one premiss be negative, the conclusion must be negative, since what is denied of the predicate is to be denied also of the subject; (6) that,

1

Here

I

if

am under

126, ist edit.

obligations to Mr. Keynes,

Formal

Logic,

OF THE GENERAL RULES OF SYLLOGISM.

272

(7) that both premisses

given as affirmative

given as universal (9) that,

must be

if

minor, and

more than 295.

;

one premiss be that

universal, there will

(5, 6,

cannot be particular, since one

particular, the conclusion

must be

particular, since the one premiss if

is

;

(8) that both premisses is

cannot be negative, since one

particular while

is

the

conclusion

the

is

be a predication about something

the subject.

The

rules

7) should be

relating to the quality of the form

compared and contrasted with

the

following rules relating to the quality of the matter. (1) If both premisses be true, the conclusion

must be

true, but not vice versa.

(2) If the conclusion be false,

must be

false,

one or both premisses

but not vice versa.

Instances of true conclusion from false premisses. All

men

are bipeds.

All birds are

men.

.. All birds are bipeds.

.

Since truth can never give

hood may give

rise to truth,

of truth in the long run.

.

All

men

All

cows are men.

All

cows are quadrupeds.

rise to

are quadrupeds.

falsehood and false

we may hope

for a

triumph

CHAPTER Of the WE

296.

By

the

reduced

XXIII.

Determination of the Legitimate Moods. found that there were 64 possible moods.

application of the preceding rules these are

to the following

11

AAA. EAE.

LEGITIMATE MOODS.

AAI.

AEE.

EAO.

EIO.

AEO.

All.

AGO.

IAI.

OAO. The reader may satisfy himself down the 64 possible moods and

of this result by writing then striking out those

which violate any of the nine rules of syllogism.

This

is

a good exercise. 297. But a

end in

much

neater

way

of attaining the same

what pairs of premisses are legitimate accordance with Rules 7 and 8, and then to see what is first

to find

conclusions can be drawn from them. If the

major be A, there

choice of a minor.

is

nothing to

restrict us in

our

OF THE DETERMINATION OF THE

274 If the

If the If the

and

major be E, the minor must be affirmative (Rule major be I, the minor must be universal (Rule

7).

8).

major be O, the minor must be universal (Rule 8)

affirmative (Rule 7).

Hence

there result nine legitimate pairs of premisses.

AA.

AE.

EA.

EL

IA.

(IE).

AO.

AI.

OA. But though the union of an legitimate enough,

it is

I

major with an

nevertheless

doomed

E

minor

is

to sterility.

298. Proof that IE premisses can give no conclusion.

be a conclusion.

If possible let there

Then it must be negative (Rule 6). And every negative proposition distributes The major term must be distributed .

its

.

predicate.

in the

con

clusion.

But the major premiss I does not distribute either term. .-. There must be an illicit process of the major. 299. Disregarding

wherever we

draw a

IE

therefore

and remembering

that

we can

also

can draw a universal conclusion

particular,

we

arrive at the eleven

moods

already

given.

300.

A

Subaltern

Mood is one

which draws a particular

conclusion from premisses which warrant a universal. is

so called because

its

conclusion might

be inferred

It

by

LEGITIMATE MOODS.

275

subalternation from that of the syllogism with a universal

conclusion.

The moods AAI, AEO, EAO are AEE, EAE respectively. A subaltern mood is also called

subaltern to

AAA,

a syllogism with a

weakened conclusion.

T

2

CHAPTER Of the

Special Rules of the

OUR

301.

next task

eleven legitimate

With a view

moods

is

Rule

2.

how many

of the

are valid in the four figures.

doing so we lay down the following

to

FIGURE i.

Four Figures.

determine

to

Special Rules of the

Rule

XXIV.

The minor The major

Four

Figures.

I.

premiss must be affirmative. premiss must be universal.

FIGURE

II.

One premiss must be negative. The conclusion must be negative. The major premiss must be universal.

Rule

i.

Rule

2.

Rule

3.

Rule

i.

Rule

2.

The minor premiss must be affirmative. The conclusion must be particular.

Rule

i.

If the

Rule

2.

If the

FIGURE

III.

FIGURE IV. major premiss be must be universal.

minor premiss be

affirmative, the

minor

affirmative, the

con

clusion must be particular.

Rule

3.

If either premiss

be universal.

be negative, the major must

SPECIAL RULES OF THE FOUR FIGURES. 302. These

from the general

follow

rules

special

rules of syllogism taken in

277

connexion with the position of

the terms in the different figures.

The

special rules of the

Canon

of the

be proved

first

of Reasoning

like the rest

Proof of the

figure are really a repetition

itself;

Special Rules of the

FIGURE Proof of Rule

i.

If possible, let the

Then

nevertheless they can

from the general

rules.

Four Figures.

I.

The minor premiss must

be affirmative.

minor premiss be negative.

major must be affirmative (Rule 7) and the conclusion must be negative (Rule 6). the

But no

.

M

P

S

M

.S

P

affirmative proposition distributes its predicate

and

every negative proposition does.

And

the major term

premiss and

is

..

The major term

i.e.

there will be an

will

and undistributed

And premiss .

.

this follows is

illicit

.

It

in the conclusion,

process of the major term.

from the supposition that the minor

premiss must be affirmative. 2.

The major premiss must

Since the minor premiss not distributed there. .

be distributed in the premiss

negative.

The minor

Proof of Rule

is

predicate both in the major

in the conclusion.

must be

is

affirmative, the

distributed in the

be universal.

middle term

major premiss (Rule

3).

OF THE SPECIAL RULES

278 But

subject in the major premiss.

it is

The major premiss must be

..

FIGURE Proof of Rule If

the

not,

i

universal.

II.

One premiss must be

.

negative.

tributed.

One premiss must

..

Proof of Rule

One of .-. The

be negative.

is

P

negative.

The major premiss must

3.

S

be negative.

conclusion must be negative (Rule

Proof of Rule

M M

.*.

The conclusion must

2.

the premisses

S

P

term would be undis-

middle

The conclusion is negative. .-. The major term must be

6).

be universal.

the con

distributed in

clusion. .

.

It

But .-.

must be distributed

it is

in the

major premiss (Rule

4).

subject in the major premiss.

The major

premiss must be universal.

FIGURE Proof of Rule

i

The proof

the

is

depending on which is the same

.

III.

The minor premiss must

same

as in the

be affirmative.

first figure,

the position of the major term,

Proof of Rule

in both.

2.

The conclusion must

The minor premiss .-. The minor term

.

.

M M

P

S

P

be particular.

is

affirmative.

is

undistributed in the premiss.

.-.

It is

undistributed in the conclusion (Rule 4).

.-.

The

conclusion must be particular.

S

OF THE FOUR FIGURES.

279

FIGURE IV. Proof of Rule the

minor must

r

the

If

.

major premiss be affirmative,

be universal.

major premiss were affirmative and the particular, the middle term would be

If the

minor

undistributed in both.

.

..If the major premiss be

affirmative, the

.

P

M

M

S

S

P

minor must

be universal.

Proof of Rule the conclusion If the

2.

must

If

minor premiss

the

be affirmative,

be particular.

minor premiss be

affirmative, the

minor term

is

undistributed there. .-.It .

must be undistributed

in the conclusion.

.If the minor premiss be affirmative, the conclusion

must be Proof of Rule must

3.

If either premiss

be negative, the

major

be universal.

If either

premiss be negative, the conclusion

negative (Rule .-.

particular.

will

be

6).

The major term

will

be

distributed

in

the

con

clusion. .

.

It

..If

must be

distributed in the

major premiss (Rule 4). must

either premiss be negative, the conclusion

be universal.

CHAPTER XXV. Of the 303.

Determination of the Valid Moods

WE

in the

Four

found

that

Figures.

there

were

eight

pairs

of

premisses which could yield legitimate conclusions

AA. AE. AI. AO. EA.

EL

IA.

OA. which,

when

the conclusions were

appended

to

them,

gave us the following 1 1

LEGITIMATE MOODS.

AAA. AAI. AEE. AEO. AIL AGO. EAE. EAO. EIO. IAL

OAO. 304.

How many

different figures

?

of these

moods

are

valid

This question may be answered

in the in

two

ways (i)

by taking the eight

pairs

appending conclusions

to

of

premisses

them

in

and

accordance

with the special rules for the four figures;

DETERMINATION OF THE VALID MOODS. by applying the special rules for the four to the fully formed moods themselves.

(2)

We

adopt the

will

latter

281 figures

to

the

Figure I. minor premiss must

be

process,

leaving

it

student to verify the results by the former one.

Moods 305.

The

thai are valid in

rule

that

The

rule

OAO.

invalidates IAI,

Thus we first

figure,

are

left

with six

moods

that are valid in the

namely

AAA.

AIL

EAE.

Moods 306.

major premiss must be universal

the

that

the

AEE, AEO, AOO.

affirmative invalidates

The

AAI.

EIO.

that are valid in Figure II.

must be negative that one or other

rule that the conclusion

(which implies the

preceding rule

premiss must be negative) invalidates IAI.

The

Thus we second

are

left

with six

AEE.

Moods

The

EIO.

rule

that are valid in the

AOO.

EAO.

AEO.

that are valid in Figure III. that

rule

affirmative invalidates

The

moods

namely

figure,

invalidates

All,

OAO.

EAE.

307.

AAA, AAI,

major premiss must be universal

rule that the

invalidates

EAO.

that

the

minor premiss

AEE, AEO,

the

AAA, EAE.

AOO

conclusion

must

be

(as in Figure I).

must

be

universal

OF THE DETERMINATION OF THE VALID

282

Thus we

are

with six

left

moods

that are valid in the

third figure,

namely AAI. IAI.

Moods

AIL

EAO.

OAO.

thai are valid in Figure

EIO. IV.

308. The rule that, if the major premiss be affirmative, minor must be universal invalidates All, AGO. The rule that, if the minor premiss be affirmative, the

the

AAA, EAE.

conclusion must be particular invalidates

The

rule that,

must be universal

Thus we

are

fourth figure,

either premiss be negative, the

if

invalidates

left

with six

major

OAO. moods

that are valid in the

EAO.

EIO.

namely

AAI.

AEE.

IAI.

309. Putting the above results together

AEO. we

obtain the

following

Twenty-four Valid Combinations of Jllood and Figure.

FIGURE

I.

FIGURE

II.

FIGURE

III.

AAA. EAE. AIL EIO. [AAI. EAO.] EAE. AEE. EIO. AGO. [EAO. AEO.] AIL EAO. OAO. EIO. AAI. IAI. AAI. AEE. IAI. EAO. EIO. [AEO.]

FIGURE IV.

The

310.

are subaltern clusions it

is

(

five

of these that are inclosed in brackets

moods

300).

practically worthless.

Figure

I.

From All

Take

is

for

the premisses

men

are animals,

and All animals are mortal, we can draw the conclusion All

weakened con

or syllogisms with

Such a syllogism

men

are mortal.

valid

enough, but

instance

AAI

in

MOODS IN THE FOUR FIGURES. Who

then

would

himself with

content

283

the

lesser

inference

Some men which

is

are mortal,

already contained in the other

311. Subtracting then the are

left

and

moods

mood and

useful.

following

which are

)

These are indicated by

mnemonic

moods we

subaltern

with nineteen combinations of

loosely called

(often

five

?

figure

once valid

at

the vowels in the

lines

Barbara, Celarent, Darii, Ferioque

prioris;

Cesare, Camestres, Festino, Baroco secundae

;

Darapti, Disamis, Datisi, Felapton, Bocardo, Ferison habet ; quarta insuper addit tertia

Bramantip, Camenes, Dimaris, Fesapo, Fresison.

Quinque

subalterni, totidem generalibus orti,

nomen habent

nullum, nee,

The

lines

last

two

si

may be

bene

translated thus

subaltern moods, which are derived from the

moods

of

The

five

same number

name and, The student

with universal conclusions, have no

you draw the conclusion rightly, no use. however should never lose sight of the fact if

these subaltern moods, as

many

usum.

colligis,

questions.

it

He may the

affects the

that there are

answer to a good

supply names for himself by

last

vowel, merely changing Camenes may be called Camenos

e.g.

subaltern

to

figure, but will

not

the

l

1

Such a name

will indicate the

serve as a symbol for reduction.

.

mood and

CHAPTER Of the

Specialities

THE

312.

for

mnemonic

may

all

conclusion

is

down

figures,

can

satisfy

ourselves

way of arriving at the same result is to moods that are valid in each of the four

the six

major premisses, the read

in

together

be a special rule of the given

horizontal

lines.

Then,

FIGURE

there

is

if

will

figure.

I.

A

E

A

E

A

E

Universal.

A

A

I

I

A

A

Affirmative.

A

E

I

O

I

O

no

the

all

minor premisses, and the conclusions

anything can be predicated universally of these, that

There

the

that

arranging them in vertical columns, so that

may be

line

Camestres, Festino,

always negative.

313. Another write

by running through the

Cesare,

Baroco secundae/ we

which have

be educed from an inspection

lines, e.g.

second figure

the

of the Four Figures.

special rules of the four figures,

already been given,

of the

XXVI.

about the conclusion in Figure I since nothing which can be predicated of it universally. is

rule

SPECIALITIES OF THE FOUR FIGURES. FIGURE

E

A

E

A

TEX

I

E

E

O

A

O

E

A

A

TE

O

O

285

II.

Universal.

One

or other premiss negative.

Negative.

The to

rule that one or other premiss must be negative has be educed from a comparison of the two premisses.

FIGURE

There

A

I

A I is

since there

no is

III.

A

E

O

E

A

I

A

A

I

I

I

O

O

O

Affirmative.

Particular.

rule about the

major premiss in Figure III, which can be predicated of it uni nothing

versally.

FIGURE IV. the major be affirmative,

If *

*

T 1

J-

*~

"F

\

j

1

A

A *M

"F

\

^\

v

\ I

i

1

E

the minor must be universal.

\ I

If the

^e

minor be

affirmative,

conclusion must be par

ticular. I

4

I

A/

I

I

A/

I

Q

^ tne tive,

conclusion be negathe major must be uni

versal.

The

only universal statements that can be

made about

the fourth figure are that neither of the premisses can

be a particular negative, and that the conclusion cannot be a universal affirmative. These would serve to invalidate

OF THE SPECIALITIES

286

Hence

only three out of the eleven legitimate moods. recourse must be had in this figure

between the propositions. This form of statement is adopted.

The

to

why

a comparison

the hypothetical

reader will observe that the form of the third rule

of Figure 314.

The

is

IV has been altered for convenience. The following points should be specially

noted.

any kind of conclusion, and the only one which can prove A. first

figure proves

is

The second figure proves only negatives. The third figure proves only particulars. The fourth figure proves any conclusion except A. Reasons why the First

is

considered the Perfect

Figure. 315. (i)

It

Canon of

alone complies directly with the

Reasoning. (2) It suffices to prove every kind of conclusion,

and

is

the only figure in which a universal affirmative conclusion

can be established. (3)

It is

only in a mood of this figure that the major, middle,

and minor terms stand (4)

It is

only in

in their relative order of extension.

this figure that

cate in the conclusion are subject

both subject and predi

and predicate

also in the

premisses.

316. sufficient

truths

The of

fact that the first figure alone proves

itself to

assume

this

Scientific Figure.

assign

form, the

it

the primacy.

first

figure

is

As

A

is

scientific

also called the

OF THE FOUR FIGURES. Proof thai

A

287

can only be established in the first figure.

Let the conclusion be a universal affirmative All S

Then by Rule

5

is

P.

both premisses must be affirm

(285)

ative.

Now, must be

is

minor term

minor premiss. the minor premiss, since no

in the

.It must be subject in

affirmative distributes

..

universal, the

distributed there.

must be distributed

.-.It .

since the conclusion

its

The middle term must be

predicate.

predicate in the minor

premiss.

But the minor premiss ..

The

middle

term

is

is

affirmative.

undistributed

in

minor

the

premiss. ..

The

middle term must be distributed in the major premiss.

But the major premiss is affirmative. /. The middle term must be subject

in

the

major

premiss.

But when the middle term premiss and predicate as the

in the

is

subject in the

minor, we have what

is

major

known

first figure.

..A

can only be established

in the first figure.

Special Canons of the Imperfect Figures. 317.

The

intrinsic superiority of the

first

figure as

a mould in which to exhibit the cogency of reasoning

is

in

OF THE SPECIALITIES

283

no way more manifest than from the

difficulty of

providing

the imperfect figures with canons of their own.

The

fourth

figure

baffles

all

such attempts, but the

following have been suggested for the second and the third.

Canon of the Second Figiire or Dictum one term

If

is

contained

in,

de Diverso.

and another excluded from,

a third term, they are mutually excluded.

Canon of the Third Figure or Dictum el

Two or, if

de

Exemplo

de Excepto.

terms which contain a

common

part partly agree,

one contains a part which the other does

not, they

partly differ.

318.

Dictum

The

neat and compendious form, in which the

de Diverso has

deceptive.

For by

makes havoc of

a term/ and this fact

The If

been expressed, is unfortunately term or part of is meant

term

the whole statement.

canon, fully expressed, would be intolerably prolix one term is wholly or partly contained in, and

another wholly excluded from, the same third term, the one is wholly (Cesare) or partly (Festino) excluded

from the other

;

and

if

one term

is

wholly contained

in,

and another wholly or partly excluded from, the same third term, the one is wholly (Camestres) or partly (Baroco) excluded from the other.

The Dictum part

or

common some M,

to

de

Exemplo

is

P and S may be

as in

unexceptionable. all

M,

Disamis and Datisi.

The

as in Darapti,

OF THE FOUR FIGURES.

The

statement of the canon does not exclude the con

clusion in

do the

is

S

Excepto however

is

not so satisfactory.

de

to us to

open which would it

Some S

.-.

M M

Some

is

Some

P.

All

is S.

Sis not P.

The whole

an

illicit

not P, which

is

Bocardo.

Felapton.

All

draw the conclusion Some P

in all cases involve

well as the conclusion

No

but then neither

:

rules of syllogism.

It leaves

S,

Some P

three cases,

all

The Dictum not

289

M

is

is

S.

Some S

.-.

canon,

M

it

is

is

process, as is

sound.

Ferison.

No

not P.

not P.

.-.

M

is

P.

Some M is S. Some S is not P.

would seem, might be

satisfactorily

stated as follows

Dictum

Two

Exemplo

terms which contain a

or, if the

Bocardo, the

de

M

in

de Excepto,

common

second contains a part

some

et

(

all

M

part partly agree, in

Ferison) which the

Felapton and first

does not,

may be partly denied of the second. 319. The foregoing statement of the canons of the

first

second and third figures

is

made from

the point of view

of extension, like the usual one of the Dictum de et

Nulh, u

Omni

OF THE SPECIALITIES

290 If

we adopt

as used intension,

the point of view which regards the subject

and the predicate commonly

extension

in

we

shall gain in truth, and, so far as

in

concerns

the second figure, not lose in clearness.

Canon of

Second Figure or Dictum de Diverso.

the

If a subject has

an

attribute

which a

class has not, or

vice versa, the subject does not belong to the class.

Canon of

Third Figure or Dictum

the

et

If a certain attribute

whole or part of a of

some of

the

belonging to the

To

class,

de

Exemplo

de Excepto.

can be affirmed or denied of the it

may

also be affirmed or denied

things which exhibit another attribute

whole or part of that

class.

enable the reader the more easily to verify the

last

somewhat complicated statement, we here append concrete examples in the same matter of the six moods of the third figure.

It

a singular term in

its full

should be added that, here as elsewhere,

may

take the place of a class-name used

extent.

Darapti.

men are shortsighted. All selfish men are bad. Some bad men are shortsighted. All selfish

..

Disamis.

men are shortsighted. All selfish men are bad. Some bad men are shortsighted. Some

.

.

selfish

OF THE FOUR FIGURES.

29 1

Datisi.

men are shortsighted. Some selfish men are bad. Some bad men are shortsighted.

All selfish

.

.

Felapton.

No

men are longsighted. All selfish men are bad. Some bad men are not longsighted.

.-.

selfish

Bocardo.

men are not longsighted. men are bad. Some bad men are not longsighted.

Some

selfish

All selfish ..

Ferison.

No .

.

selfish men are longsighted. Some selfish men are bad. Some bad men are not longsighted.

SPECIAL USES OF THE 320. Lambert

s

Roughly

general acceptance.

The

first

figure

is

FOUR FIGURES.

statement on this subject has gained it is

as follows.

useful for proving the properties of

a thing.

The second

figure

is

useful for proving distinctions

between things.

The

third

figure

is

useful

for

proving instances

or

exceptions.

The

fourth figure

is

useful for proving the species of

a genus.

U

2

OF THE SPECIALITIES

292

FIGURE

M

is

or

I.

not P.

is

SisM. .

.

S

or

is

is

not P.

We

prove that S has or has not the property P by predicating of it M, which we know to possess or not to possess that property. All trees bear

.

.

The The

No

pine

is

fruit.

a tree.

pine bears

Aryans

fruit.

are black

men.

All Parsees are Aryans. .*.

No

Parsees are black men.

FIGURE

.-.

We is

P

is

M.

P

is

not

S

is

not M.

S

is

M.

S

is

not P.

S

is

not P.

that

.-.

the

establish

showing

II.

between S and P by

distinction

P has an

M.

attribute

which S

is

devoid

of,

or

devoid of an attribute which S has.

.-.

All fishes are coldblooded.

No

A

whale

is

not coldblooded.

A

A

whale

is

not a

fish.

FIGURE

M M .-.

is

.. III.

M M

P.

is S.

Some S

A

is

P.

fishes give milk.

whale gives milk. whale is not a fish.

.-.

is

not P.

is S.

Some S

is

not P.

OF

We

TtiE

FOUR FIGURES.

293

produce instances of S being P by showing that

P

S and

M.

events partially, in

at all

meet,

Thus,

if

we

wish to produce an instance of the compatibility of great

we might

learning with original powers of thought,

Hamilton was an

Sir William

William Hamilton was a

Sir .

Some men

.

say

original thinker.

man

of great learning.

of great learning are original thinkers.

Or we might urge an exception

the supposed rule

to

about Scotchmen being deficient in humour under the

same

..

figure, thus

Sir

Walter Scott was not deficient

Sir

Walter Scott was a Scotchman.

Some Scotchmen

in

are not deficient in

humour.

humour.

FIGURE IV. P

is

All .

.

M.

M

is

Some S

When

S. is

P.

.

.

the conclusion

All P is M. No M is S. No S is P. is

under

M .

affirmative,

a species of S by showing that itself falls

No P

P

.

is

is

Some S

we prove

falls

M.

S. is

not P.

that

P

is

under M, which

S.

Bramantip and Dimaris. Boers are white natives of Africa. All white natives of Africa are Africanders. .-.

Some

When that

P

is

Africanders are Boers.

the conclusion

is

a universal negative,

no species of S by showing

M, which we know

to

that all

be excluded from

S.

P

we prove

falls

under

OF THE SPECIALITIES

294

Camenes. All tomatos are fruits.

.

When that,

No No

.

fruits are roots.

the conclusion

whether

P be

fall,

P

that

is

is

a particular negative,

we prove

a species of S or not, there are at

events other species

showing

roots are tomatos.

This we do by

of S besides P.

excluded from

all

M, which we know

to

wholly or partially, under S.

Fesapo and Fresison.

No

fishes are snakes.

Snakes can swim. ..

Some swimming

No

things are not fishes.

Englishborn are white natives of Africa.

White natives of Africa are Africanders. ..

Some

321.

Africanders are not Englishborn.

The

multiplicity of

throws light upon the

canon

for

evidence of

it.

its

Not

method

difficulty

to

own, we

leave will lay

in the fourth figure

of formulating a single

it

however without some

down

the following

Three Axioms of the Fourth Figure. (1)

Whatever

is

affirmed of a whole term

partially affirmed of

that

(2)

it

whatever

is

may have

included in

term (Bramanttp, Dimaris).

Whatever

is

denied of a whole term

wholly denied of in that

it

whatever

term (Camenes).

is

may have

wholly included

OF THE FOUR FIGURES. Whatever

(3)

a term

affirmed of the whole or part of

is

may have

partially

wholly excluded from

is

295

denied of that

it

whatever

term (Fesapo,

IPresison). vS"

322.

more

A

trengthened Syllogis ins

Strengthened Syllogism

in the premisses than

is

-

one which assumes

necessary to prove the

is

conclusion.

The

observe

reader will

and Fesapo

Bramantip and Fresison

that

as

is

particular.

stronger premisses

is

in

is

compared

the

with

case with

Dimaris

In Bramantip and Fesapo

respectively.

In Dimaris and Fresison

both premisses are universal.

one premiss

this

Yet the conclusion of the

each case identical with that of

the weaker.

Among

the two dozen legitimate combinations of

mood

and

figure one third are strengthened syllogisms, there being two in each figure -

FIGURE

I.

FIGURE

II.

EAO,

FIGURE

III.

AAI,

FIGURE IV. It

is

only in

the

first

AAI,

AAI,

EAO. AEO. EAO. EAO.

and second

figures

that

the

syllogism with strengthened premiss coincides with the syllogism with weakened conclusion, which is otherwise

known are

as a subaltern

mood.

no subaltern moods,

ticulars.

In the third figure there

since

In the fourth figure

it

AEO

can prove only par is

a subaltern mood,

THE SPECIALITIES OF THE FOUR FIGURES.

296 but

is

it

not a strengthened syllogism

1

If the

.

major

premiss were particular, we should have an illicit process of the major term if the minor premiss were particular, ;

we should have is

The same

undistributed middle.

evidence

here requisite for the particular as for the universal.

Camenos. All tomatos are

No .

1

.

fruits

Some

On

fruits.

are roots.

roots are not tomatos.

.

.

All

P

No

M

ic,

147, ist edit.

is

Some S

the subject of Strengthened Syllogisms

Keynes Formal Lo

M.

is

I

am

S. is

not P.

indebted to

CHAPTER Of the 323.

XXVII.

Syllogism with Three Figures.

THE awkward

fourth figure

logical system of Aristotle, but

is

is

no part of the been added

said to have

by Galen. 324. In determining the

look only at the position premisses.

be

There,

subject in

it is

number of

figures

of the middle

clear, the

we may

term in the

middle term must either

one and predicate

the other or else

in

predicate in both or subject in both.

We

cannot

tell

the

major from the minor premiss, unless we take account of the conclusion, which fixes the major and the minor term. Looked at from this point of view then the first and the fourth figures run into

one, being that arrangement of terms in the premisses in which the middle term occupies a different position in one

325. Aristotle s rather to have been

from what

own way

it

does in the other.

of viewing the matter seems

Either the middle term

this.

intermediate between the two extremes

c _i\r

S

P

M

^ P

or else the two extremes are outside of c or, lastly,

p

S

T\T

they are inside of

P it

it

M M

is

really

298 OF

THE SYLLOGISM WITH THREE FIGURES.

The fourth figure

is

got by inverting the order of therirst

P

P-M-S The

-M

M

S.

clumsiness of the fourth figure

that a term

which

is

due just to this, used as predicate.

is is

naturally subject

Instead of reasoning thus All S All

.-.All

we reason

P

is

(Figure I)

SisP

thus All S All

..

326.

M

is

M

When

number of

M

is

M

P

is

Some P

(Figure IV)

is S.

the conclusion

possible

moods

is

is

set

same

the

out of sight, the as the

number

combinations that can be made of the four things, A, E,

I,

of

O,

taken two together, without restriction as to repetition.

These are the following sixteen

The fatal

AA AE

EA EE

AI

EI

AO

*e-

rules of

:

IA

OA

IE

OE-ef

le

-ee-.

syllogism relating to the

premisses are

to seven of these, which reduces the valid

moods

to nine

AA.

AE.

AI.

AO.

EA.

EL

But, as the order of the premisses four of these, namely,

EA, IA, IE,

OA

IA. is

IE.

now

OA.

indifferent,

are only repetitions

OF THE SYLLOGISM WITH THREE FIGURES. 299 of preceding ones.

Thus we

AA.

We

327.

will

AE.

now

AI.

left

with only

they admit.

Though

AO.

all

We

importance.

shall

first

the conclusions of which

them

of no

is

is

of

have therefore to recognise a

ence corresponding to that between the figures in the fourfold

the

into

the order of the premisses

the distribution of the terms in

moment,

Let

five really

El.

moods

put these

and draw from them

figure

are

moods

different

first

vital

differ

and fourth

scheme.

be premised that when the extreme in the premiss that stands it

predicate in the conclusion,

a Direct

when

Mood

we

first is

are said to have

;

the extreme in the premiss that stands second

is

predicate in the conclusion,

we

are said to

have an Indirect Mood.

FIGURE

I.

Mood A A. All

M

All

S

..All S or

or

is is is

P.

All

P

M.

All

M

P

..

(Barbara).

Some S is P (Barbari). Some Pis S (Bramantip).

or

is is

Some S Some P

M. S. is

P (Bramantip).

is

S (Barbari).

Mood AE. All

M

No S

is is

.-.

Illicit

or

Some P

P.

All

P

M.

No

M

Major.

is

not S (Fesapo).

is is

M. S.

No S is P ^Camenes). or Some S is not P (Camenos). or No P is S (Celarent). or Some P is not S (Celaront). .-.

OF THE SYLLOGISM WITH THREE FIGURES.

300

Mood A I. All

M

is

Some S

P is M. Some M is

All

P. is

M.

Some S is P (Darii). or Some P is S (Dimaris).

S.

Undistributed Middle,

.-.

.-.

Mood A 0. All

M

is

Some S

P is M. Some M is

All

P. is

not M.

.-.

Illicit

or

Illicit

.

No M is P. Some S is M. Some S is not P

Major. Minor.

not S.

Undistributed Middle,

.-.

Mood E I.

.

or

Illicit

Of

(^Ferio).

Minor.

moods

the above ten

No P

is

Some

M

..

Some S

or

Illicit

it

will

M. is is

S.

not

P

(Fresison).

Minor.

be seen that three are

altogether invalid.

Of

the remaining seven,

one yields no

than four

less

conclusions, one three, two yield two apiece, and the re

maining

one

three

each.

fourteen conclusions.

This gives

us

Barbari (subaltern to twice over. This reduces the whole number which half belong to the first and half under the fourfold division. 328.

The

application of the

imperfect figures

is

a

total

of

But two of our syllogisms, namely Barbara) and Bramantip occur to twelve, of

to the fourth figure

same method

a simpler matter, since

to the

we have now

only one position of the middle term, and consequently also of the major

and minor,

to deal with.

OF THE SYLLOGISM WITH THREE FIGURES. 301 FIGURE

II.

Mood A A. P

is

All S

is

All

.-.

M. M.

Undistributed Middle.

MoodAE.

.

.

or

All

P

is

M.

No

S

is

M.

No

S

is

P (Camestres).

Some S

No P

is

not

P

(Camestros).

S (Cesare). or Some P is not S (Cesaro). or

is

Mood A I. P is M. Some S is M.

All

.

.

Undistributed Middle.

Mood A 0. P is M. Some S is not M.

All

.

.

or

Some S

is

not

Illicit

Minor.

No P

is

Some S

M. is M.

..

Some S

is

or

Illicit

not

Minor.

P

(Baroco).

P

(Festino).

OF THE SYLLOGISM WITH THREE FIGURES.

302

Of owing

moods two

the above five to

remaining three

and El

are altogether invalid

the absence of a negative premiss.

yield

moods which

AE

yields four

Thus we

one apiece.

arrive at the

are valid in the second figure.

FIGURE

III.

Mood A A.

329.

M All M All

.-.

or

is

P.

is

S.

Some Sis P Some P is S

(Darapti). (Daraptis).

Mood A E. All

No

M M

.-. Illicit

or

is

P.

is S.

Major. w

Some P

not S (Felapton).

is

Mood A I. All

M

Some .-.

or

is

M

Some S Some P

P. is S. is

P

is

S (Disamis).

(Datisi).

Mood A 0. All

M

Some .-. Illicit

or

is

P.

M

is

not S.

Major,

Some P

is

Of

conclusions, while

not S (Bocardo).

the

AO six

OF THE SYLLOGISM WITH THREE FIGURES. 303

EL

Mood

M

No

Some .

M

Some S

.

or

Illicit

P. is S.

not

is

(Ferison).

are valid both directly and

remaining three either directly or indirectly. seven syllogisms, one of which is not

indirectly, the

in all

mnemonic

indicated by the

converted.

It

have called

Darapti with

stands

Darapti as Disamis does

We

lines.

passing Daraptis, as being

simply

P

Minor.

moods

In this figure two

This gives us

is

the

in

its

same

to Datisi, but has

in

it

conclusion relation

to

been over

looked owing to the accident of both premisses being the same kind of proposition. It spoils the symmetry of six valid syllogisms in each figure, which has perhaps been

Under

another reason for neglecting

it.

division of figure

its

indirect

mood

presents

itself as

be

called

a

syllogism. six

moods

it

falls

into

Darapti,

natural place as the

but under the

an uncomfortable

interloper.

fourfold It

it

cannot

mood from Darapti, since the which it is made up are the same in

different

of

propositions

kind with

to

the threefold

that,

and yet

Moreover

if

it

is

undoubtedly a different

we convert

the conclusion of the

that are valid in each of the four figures,

we

shall find that in every case except this the result, if

be legitimate, a

name

of

is

its

provided

own.

moods we may already employed.

avail

in the

mnemonic

lines

it

with

For the names of the subaltern ourselves

of

the

simple

device

OF THE SYLLOGISM WITH THREE FIGURES.

304

FIGURE

330.

FIGURE

I.

Barbari

= Bramantip. = Camenes. = Dimaris. = Minor. = Bramantip.

Celaront

Camenos.

Barbara Celarent

Darii Ferio

Camestres Festino

FIGURE

Disamis Datisi

Felapton Bocardo Ferison 331.

Camestros

FIGURE IV.

III.

it

Bramantip Camenes Dimaris

Illicit

Fesapo

Illicit

Fresison

Illicit

Camenos

Whenever

converting

Illicit

Cesaro

= Daraptis. = Datisi. = Disamis. = Minor. = Minor. = Minor.

Darapti

Illicit

Baroco

Illicit

is

an

conclusion

the

O

proposition

332. fold

is

Illicit

Illicit

is

division of figure

O, the

result

list

the

shows indirect

in

Camenos,

only a part of the

The preceding

= Barbari. = Celarent. = Darii. = Minor. = Minor. = Celaront. of

minor, except in the case of

illicit

the subaltern moods, Celaront and the

II.

= Camestres. = Cesare. = Minor. = Minor. = Camestros. = Cesaro.

Cesare

full

that

which

conclusion.

under the four

moods of

the

first

are to be found in the fourth and vice versa, whereas the indirect

found

moods of

the

second and

in those figures themselves.

third

are to be

CHAPTER Of 333. REDUCTION

XXVIII.

Reduction.

may

be taken as a general term

for

changing one form of reasoning into another. The syllogism required to be reduced may be called the

Reducend

may

which

The importance

334.

moods

bringing first

that to

;

it

conforms, when reduced,

be called the Reduct. of reduction

is

confined to

in the imperfect figures into those of the

or perfect figure.

335.

The

to extend the

object of reduction, as thus conceived,

sanction of the canon

is

of reasoning to

which do not obviously comply with it. Under the canon of reasoning, or dictum de omni et nullo,

syllogisms

the essence of mediate inference consists in showing that

a general principle applies to or a whole class of cases.

some

The

special case or cases

general principle

is

the

major premiss; the assertion that something falls under it is the minor premiss. Hence the major premiss in a perfect syllogism must be universal, but may be nega tive;

the

minor premiss must be

affirmative,

but

may

be particular.

Now

a good deal of our ordinary reasoning does not

OF REDUCTION.

306 conform

to

this

all

syllogistic

If

type.

canon of reasoning,

we adhere

reasoning

a

may by

to

the

show

that

therefore

becomes necessary

it

to

little

manipulation This process is reduc

be forced into compliance with

it.

tion in the

sense of the term.

commonly accepted

336. Reduction

is

of two kinds

(1) Direct or Ostensive. (2) Indirect or

337.

The problem

Per

Impossibile.

of direct or ostensive reduction

is this

Given any mood in one of the imperfect figures, how form of the premisses so as to arrive at the same conclusion in the perfect figure, or at one from

to alter the

which the old conclusion can be immediately

The

alteration of the premisses

is

inferred.

effected

by means

of immediate inference and, where necessary, of trans position.

338.

The problem

of indirect reduction or reductio

per (deductionem ad] impossilile

Given any

mood

in

one of the imperfect

show by means of a syllogism its

conclusion cannot be

is this

figures, to

in the perfect figure that

false.

Direct or Ostensive Reduction. 339. In the usual form of direct reduction the only

kind of immediate inference employed

is

conversion, either

simple or by limitation.

The mnemonic

lines,

Barbara, Celarent,

&c. pro

vide complete directions for the ostensive reduction of

all

OF REDUCTION. the

moods of

the

first

the second,

with

and fourth

third,

the exception

307 figures

to

Baroco and Bocardo.

of

For the present we may take c in the body of a word to which that word is the name

indicate that the syllogism of

cannot be reduced ostensively by the ordinary methods. Leaving these two forms of syllogism then for subsequent

we

treatment, It will

once with the remainder.

will deal at

be observed that the names of the moods which

are valid and useful in the first

initial

figure

consonant of any other figured

mood

that the reduct will be that

begins with the same

shows

that,

when

m

Where for

first

begin with the

The

four consonants in the alphabet, B, C, D, F.

appears

mulatto or

interpret

it

reduced,

to

it

in the

of the

Thus

letter.

will

the

mood first

B

figure

of

Make

which

Bramantip

become Barbara.

name of

a reducend,

it

stands

We may

metathesis of the premisses.

mean

indicates

and

the major the minor

the

minor the major.

When it

s

follows

one of the premisses of a reducend, which it is appended

indicates that the proposition to

must be simply converted as in Disamis, in the

first

conclusion,

it

figure

but

;

when

it

follows the conclusion,

indicates that the conclusion arrived at is

not identical in form with the original

capable of being

simple conversion.

Hence

s

in the

inferred

from

middle of a

it

by

name

done to the original premiss, while s at the end indicates something to be done to the

indicates something to be

new

conclusion.

p stands

for conversion

per accident.

What X

has just 2

OF REDUCTION.

3 o8

been said of the difference between at the

The

end of a word applies letters

1,

n,

r, t

s

also to p.

are meaningless.

FIGURE

II.

in the

middle and

OF REDUCTION.

39

OF REDUCTION.

310

Ferio.

Fesapo. E.

No P

A.

All

is

M

M.

\

is S.

I

= j

0.

.

Some S

.

is

not P.)

.-.

(

.

M.

\

Some M is S. Some S is not

1.

O.

is

.

E.

P.

is

Some S Some S

is

M.

is

not P.

I.

O.

Ferio.

Fresison.

No P

E.

M

No

(

I

P.

=

J

M

No

l

J

/.

(

P.

is

Some S Some S

is

M.

is

not P.

O.

Reduction of the Subaltern Moods.

The mnemonic

343.

lines

reduction of the three subaltern

do not provide

moods

for the

in the imperfect

The

figures Cesaro, Camestros, and Camenos.

first

of

these runs easily into Celarent.

Celaront.

Cesaro. E.

No P

is

M.

A.

All

S

is

M.

\

= [

O.

.

Some S

.

The name

here

may be

a symbol for reduction, reduct

But

Celaront.

is

Camenos

the reduct

have

to

it

first

if

is

draw the

(

nothing

in the

name

. .

P

E.

NoSisM.

is

full

/.

Some S

is

O.

be borne in mind that the

Camestros and

We

conclusion and then submit

by subalternation.

There

to indicate this last step.

Celarent. \

not P.

No

i

= [

O.

not P.

not Celaront but Celarent.

M.

All

E.

A.

Some Sis

in the case of

Camestros. A.

P.

M.

is is

considered also to serve as it

to simple conversion followed

is

M

All S |

not P. J

is

No

t

I

is

S.

E.

A.

. .

.-.

No

..

Some S

| I

M

AllPisM. No P is S. S

is

P. is

not P.

E.

OF REDUCTION.

311

As simple conversion followed by subalternation is the same thing as conversion per accidens, we may call these two moods for purposes of reduction Camestrop and Camenop.

Their names then

those in the

mnemonic

will

completely

tally

with

lines.

Reduction by Negation. 344.

we

We now

return to

Baroco and Bocardo, which

over for separate treatment.

left

The

reason

why

by

the

ostensively

position or both

In both

it is

these two

moods cannot be reduced

aid merely of conversion or trans

becomes

necessary,

if

plain

we

on an inspection of them.

are to obtain the

that the position of the middle term should

But the premisses of both consist of propositions, of which A admits only of con

in

one premiss.

A

and

O

version by limitation,

the

effect

of which would be to

produce two particular premisses, while of conversion at It

is

be

comes

first figure,

be changed

clear then that the

before

we can

to our aid

us to convert the

O

does not admit

all.

;

A

get

O any

proposition must cease to further.

Here obversion

while conversion by negation enables proposition without loss of quantity.

OF REDUCTION.

312

(Barooo) Fanobo.

Ferio.

\ P is M. Some S is not M. L Some S is not P. J

No

All

A.

O. O.

.

.

A.

men

All honest

=

Some S Some S No

are truth

Some

clever

men

are not

.

.

Some

men

are not

.

.Some

O.

Some

A.

All .

M

M

345. In the

n

signifies

I.

O.

men

clever

E.

men

clever

I.

men O.

is

not P.

Darii. All

\

not P.

M

is S.

Some not-P is M. Some not-P is S. Some S is not-P. Some S is not P.

is S.

Some Sis

employed

not P.

are not honest.

(Bocardo) Donamon.

.

is

are untruthful.

clever

honest.

O.

E.

P.

not-M.

untruthful

Some

truthful.

O.

is

is

are honest.

ful.

O.

not-M

)

new symbols Fanobo and Donamon b

is

as a sign of obversion (since o cannot be)

conversion by negation.

Donamon

In

;

the

n stands for a process which resolves itself obversion followed by simple conversion, the second for one which resolves itself into simple conversion followed into

first

by obversion, according

to the extended

meaning which

we have given to the term conversion by negation. The student who finds himself perplexed by this differ ence may have recourse to the cacophonous names

Dobsamosb and Fabsobo,

in

which the steps of simple

immediate inference replace the compound

result.

OF REDUCTION.

313

Extension of Reduction by Negation. 346.

The method

necessary

direct reduction of

be found on

will

Bocardo,

mood

of reduction by negation, though

the

only for

we

logical exercise,

a version of the

shall

mnemonic

They will furnish his own work.

be applicable to any

to

trial

in the imperfect figures.

Baroco and

As

this

process

a

is

good

here present the student with lines

him with

adapted for

this

purpose.

a test which he can apply to

Barbara, Celarent, Darii, Ferioque

prioris.

Benareb, Canebe, Dgnilob, FanobS secundae Cebamnes, Bamenenque modi duo prima reponunt ;

nomina, queis Benarob, Caneb5 sunt adjicienda, necnon Cebamnop, Bamenont, si plena requiris. Tertia

Fampabin, Denamon, nee

vice facta

Fabapib, Fmisabin, Fabisib itemque Debapob Donamon, Debisob habet. Dat quarta Caniabin ;

Cananbinp, Canene, Fimabin, quibus adde Denapob cum Denisob Bameben finem facient Canenoque, si modo jam cumulum Bamebont licet adjiciamus. ;

n here stands

for

conversion by negation, whether by

obversion-conversion or by conversion-obversion

obversion less

;

;

t

for

subalternation

;

1

the rest of the letters have the

and

same

r

are

;

b

for

meaning

signification as

in the original lines.

Which form

of conversion by negation n stands for

is

determined by the proposition which has to be arrived at.

Thus

in

Canebe

A

has to be converted by negation

OF REDUCTION.

314

E

and become the version-conversion

of Celarent. that

process would reduce

The above the subaltern

In

all

lines

A

is

therefore

is

other

the

since

required,

ob-

O.

to

make

moods

It

provision for the reduction of

as well as of their originals.

cases in which both premisses are universal, with

the exception of Fesapo, the mood admits of being reduced by negation in two ways, either as it stands or by In the case of Fesapo transposition of the premisses.

the

of

transposition

negative minor

in

the

the

leads either

premisses

first

figure or

to

to

a

the fallacy of

four terms.

Cebamnes and Bamenen with Cebamnop and Bamenont result from

In the second figure their

subalterns

transposing the premisses of Cesare and Camestres.

In the third figure

Fampabin and Denamon

are the

syllogisms which arise from transposing the premisses of Darapti and Felapton. The rest of the moods follow the old order of the lines.

In

the

fourth

Camabin, which

figure

transposing the premisses of Bramantip,

got like

Canene, being

The

subaltern

originals to

Bameben

Cananbinp.

for

to

by

moods

their

it

is

results

an

from

alternative

stands in the same relation

from Camenes.

display their relationship to their

names.

Thus Bamebont

is

subaltern

Bameben. It

should be mentioned that the reduct of Benarob

Barbari, but of Bamenont Barbara but of

Bamebont Barbara.

Even

;

of

this

is

Canebo Celaront, however

is

implied

OF REDUCTION. by the symbols, since neither p nor

t

315 could refer to any

thing but a universal proposition.

347.

employed Canebe.

To show how in

reduction by negation

argument we

Canebe (Camestres). we have a

things of which

All

may be

will take a concrete instance of

perfect

idea

we have

a perfect

are

perceptions.

..

A

substance

is

not a perception.

A

substance

is

not a thing of which

idea.

Celarent.

No

is

not-perception

a thing of which

we have

a

perfect idea.

.

.

A

substance

is

a not-perception.

A

substance

is

not a thing of which

we have a

perfect

idea.

We may

go on,

by obverting

if

the

we

please, to reduce this to

major

premiss, so

as

to

Barbara

obtain

the

contrapositive of the original.

Barbara. All not-perceptions are things of

which we have an

imperfect idea.

.-.

A A

substance

is

a not-perception.

substance

is

a thing of which

we have an

imperfect

idea. .*.

A

substance

is

perfect idea.

not a thing of which

we have

a

OF REDUCTION.

316

Indirect Reduction.

The

348.

Bocardo

impossibility

ostensively without the

was what led

terms

of

to

the

reducing

Baroco and

employment of negative

adoption

of the

indirect

method. Let us apply

it

to

Baroco.

Baroco.

P is M. Some S is not M.

All

All fishes are oviparous.

Some marine animals

are

not oviparous.

Some S

is

not P.

..

Some marine

animals are

not fishes. If possible, let this conclusion be false.

Then .-.

its

contradictory must be true.

It is true that

Combining

All S

this as

is

P. All

marine animals are

fishes.

minor with the original major, we

obtain premisses in the

first

figure

Barbara.

P

is

M.

All fishes are oviparous.

All S

is

P.

All marine animals are fishes

All

v/hich necessitate the conclusion,

All S

But being /.

its

One

M. All marine animals are oviparous. conclusion conflicts with the original minor,

is

this

contradictory,

of them must be

false.

OF REDUCTION. But the

original

minor

317

given as true.

is

The new conclusion is false. /.The syllogism in which it is drawn must be wrong

..

form or

either in

But

Reasoning /.

It is

.. It

is

which the Canon of

figure, to

applies.

in matter,

wrong

Now /.

first

not wrong in form.

be

same

the

in

is

it

in matter.

i.

e.

one of the premisses must

false.

the major premiss

given as true, being the

is

as in the original syllogism.

The minor I.e. It

All

But

S

is

this

premiss is

is

false.

false that

All marine animals are fishes.

P.

proposition has already been

shown

to

be

true. .-.

It

is

both true and I. e.

..

The

We

false.

are involved in a contradiction.

supposition which leads to

And

this

supposition

it

must be abandoned.

is

that the original conclusion

is

true.

is false. ..

to

The

original conclusion

The

essence of the reduction consists in the appeal

the

canon of reasoning.

showing

that

the

If

we stopped

new conclusion

contradicts

short

the

at

old

would be open to an objector to reply that the fault lay with our new syllogism. The premisses of Baroco are given as true, the premiss,

it

OF REDUCTION. question at

not being about their truth as pro

issue

drawn from

positions, but merely as to the conclusion

them

the

in

conform

canon It

second

which does not obviously

figure,

We

to the canon.

show

that the truth of the

indirectly implies the truth of this conclusion.

usual to place the two syllogisms side by side

is

thus

Baroco. All

P

is

Some S Some S

.-.

Barbara.

M.

P

is

M.

All S

is

P.

S

is

M.

All

M.

is

not

is

not P.

^^^""

.-.

But the student must not imagine

All

that this constitutes

reduction without his appending the reasoning in which the process really consists.

In Bocardo the two syllogisms

will

Bocardo.

Some All .-.

The

M

M

is

All S

\/

is S.

Some S

lines

Barbara.

not P.

is

stand thus

^

not P.

M All M All

.-.

is

P.

is

S.

is

P.

which we have drawn indicate the proposi one another.

tions which conflict with

The names Baroco and Bocardo were invented with The initial consonant tells that the indirect reduct is Barbara. The c is a direction to a view to this process.

substitute the contradictory of the old conclusion for the

proposition after which cases

is

o.

it

is

placed, which in both these

OF REDUCTION.

A

349. is

as

reason

a

proof gives

proof gives a reason be otherwise than as it is. indirect

Indirect proof then as

a thing value,

is,

is

it

not

why

it

why a

a

thing

thing cannot

inferior to direct proof,

is

negative, not positive;

is

it

why

is.

it

An

direct

319

inasmuch

only informs us that

But, like other things of less

is.

commoner.

it

Indirect reduction

is

a form of

indirect proof.

In indirect proof we

and combine is

it

may

take any true proposition,

with the contradictory of the one which

called in question, in such a

we

in indirect reduction

way

as to form a syllogism

are limited to

;

one of the pre

misses of an original syllogism.

On

350.

what principle does

on the

It rests

rules relating to

the propositions in a syllogism

The

first

If

indirect reduction rest

the material

?

quality of

295).

(

of these asserts that

both premisses be

true, the

conclusion must be

true.

The

second, which

is

the contrapositive of this, adds

that If the

conclusion be

must be

From

this last

If the

one or both premisses

it is

an easy deduction that false and one premiss be

conclusion be

the other premiss

In the

false,

false.

new

must be

syllogism which

true,

false.

we frame

the conclusion

OF REDUCTION.

320 because

one of the old premisses, which are not called in question but one of its premisses is true, being derived from the old syllogism therefore

is false,

it

conflicts with

;

;

the other premiss

is false.

Now

the other premiss

is

the

contradictory of the original conclusion and has already

been shown

to be

Therefore we are involved in

Therefore we must abandon the hypo

a contradiction. thesis

true.

which leads

to

it.

Extension of Indirect Reduction. 351.

so happens that

It

mood and

figure

for

which

two combinations of

the

process was originally

this

invented are just the two to which

it is

In Baroco the major premiss contradictory of the

is

least applicable.

combined with the

conclusion to prove the

falsity

of

the minor.

In Bocardo the minor premiss

is

combined with the

contradictory of the conclusion to prove the

falsity

of the

major.

Now

could we effect the indirect reduction of Baroeo by

retaining the minor premiss or that of

ing the the

major

same

?

first

figure at

in

all.

in the imperfect figures,

be indirectly reduced to the the major or

can

is

reason, namely, that

premiss in the

mood

The answer

Bocardo by

O

for

cannot be used as a

But,

we

retain

No/ and

both cases

if

we

take any other

shall find that

it

can

figure either

by retaining

by retaining the minor premiss.

The reader encum

first

verify this assertion for himself.

Instead of

bering our pages by exhibiting the process in each case

OF REDUCTION. we

will

321

follow the convenient example set

The

Spain and his predecessors. lines contain directions for

imperfect figures to the

reducing

first,

following all

the

by Peter of

mnemonic

moods

of the

whether by way of the major

or of the minor premiss.

Barbara, Celarent, Darii, Ferioque

prioris

;

Palace, Darece, Celic6, Baroco secundae,

sedem tertia

si

retinet

major

;

sed,

si

minor, inde

Cacanit, Cicari, Facini, Becanot,

Bocardo, Decllon habet quarta insuper addit Fampacsi, Dan&ces, necnon Fimsaci, Cenacop, ;

praeterea detur salva majore Cenicos.

Adde

subalternos CelacS, BalecS secundae

;

Bane cos

quartae tribuatur

Altera

praemissa manet, novus incipit ordo.

si

Namque

rite figurae.

secunda dabit Decsamg, minore retenta,

Facseme Decisosque modi reddantur eodem. Tertia praebebit salva majore Camacsit,

Fimacsi, pariterque Camicsi, deinde Cesacop, queis,

si

vis totum, licet

Quartaque Cacanip

annumerare Cesicos.

profert

Facsemse, Cicanis,

Becanop Decilos, retinet si sede minorem. Adde subalternos etiam Decpamo secundae

Facpemcque

The symbols

super

;

Facpems5

are constructed

and Bocardo, the

initial

quarta requirit.

on the model of Baroco

consonant indicating the

mood

of the indirect reduct and the c being put after the premiss

which

is

to

be replaced by the contradictory of the Y

OF REDUCTION.

322

m

conclusion, to shift

its

that the retained premiss will have

means

place in the reduct, if

it

As

was major becoming

in the

symbols

for direct

minor, and,

if

reduction, s

and p in the body of a word signify something

to

minor, major.

be done to the old premiss,

new

to the

now

signifies that the subaltern

in

The

Celaront.

contrary, not

1,

n, r are

contrary however

will

yield

the

minor.

original

do equally

into

falls

(Darapti)

contradictory of the

t

be employed

mood, Celarent, would

full

the

be

to

meaningless, but

mood may

Thus Camacsit

reduct.

the

The

conclusion.

end something

at the

done

being as

well,

incompatible with the truth of the original proposition as

The

the contradictory.

three

subaltern

moods of

the

imperfect figures should be reduced to the subalterns of the

first.

Converse Reduction. 352.

By Converse Reduction

is

meant

bringing

a syllogism in the perfect figure into one of the imperfect The process is only valuable as an exercise. ones.

353.

As

all

the

moods

reduced into those of the

assumed

that all the

first, it

figure

that,

It is

except

assumes more

might on

moods of

in

the

first

first

hearing be

figure can

But the relation

be

is

not

one of the perfections of the

first

reduced into those of the quite reciprocal.

of the imperfect figures can be

rest.

the

subaltern

in the premisses than

never

moods, what is necessary it

to

prove the conclusion, i. e. it never has a term superfluously This characteristic is shared with it by the distributed.

second

figure,

but not by the other two.

Thus Darapti

OF REDUCTION. takes

two

universal

to

propositions

conclusion which in Disamis with the aid of one;

323

and the same

established

is

the

is

same

the

prove

or Datisi

case with

as Now a compared weaker proposition in the same matter may always be

Bramantip substituted

a

Dimaris.

with

a

for

a

mood

if

the latter differs

it

never

but

stronger,

Hence

weaker.

follows

in the first figure to

one

a

stronger

for

we cannot reduce

that

in the third or fourth,

from the former by having one of

its

premisses strengthened.

The

354.

apart from the

reduction of

Barbara

conclusion of the reduct

When we

reducible to the fourth figure, stitute

A

another

mood

mood

for

it

which the

a different kind of proposition

is

from that of the reducend.

the

stands

Bramantip

to

rest, as being the only case in

say that Barbara

we mean

that

We

in that figure.

AAA itself and express

it

is

we can sub cannot take

in the fourth figure, the

conclusion being the exclusive prerogative of the

first.

Converse Use of Indirect Reduction. 355. It has reduction

proof of

is

we

much

noticed

Indirect Reduction

is

a reciprocal process.

take any syllogism and, while retaining one of

premisses, substitute the contradictory of

its

the other premiss, the conclusion of this will

indirect

that

Let us give a formal

this.

Proof (hat If

not been

a reciprocal process.

conclusion for

new syllogism

be the contradictory of that other premiss.

retaining the

same premiss

as before,

we

its

If then,

repeat the

v

2

same

OF REDUCTION.

3 24

we must

process on the

new

original one.

For one premiss

other

syllogism,

is,

it is

the original premiss

Felace (Cesare).

.

.

of the contradictory of the

the contradictory

is

original, that

No P

is

All S

is

No

is

S

No P

T^Some S

Here the major premiss it

Felace.

M

is

Some S

]Vh\^^

combining with

itself.

Ferio.

M P.

get back to the

unchanged, and the

is

in

the

of the original conclusion,

P.

is

the

we must

is

to

obtain as a

become

revert to the original

is

M.

No

S

is

same throughout.

the contradictory of the original minor. tradictory of this

M.

.^All S

P.

By

reduct the contradictory

first

we

is

not M.-^^-.

is

is

No P

new conclusion But the con

the next minor, that

minor

is,

itself.

356. We have an apparent exception to reciprocity whenever we are compelled to reduce the quantity of a proposition. to a lower level.

M

is

All S

is

All S

is

Some S

An

example

P:

-No S

M.,

Some

P.

Some

is

will

make

to sink

this clearer.

Festino.

Barbara. All

In such a case the next reduct has

Pi

is

M M

Darii. All

Pis is

not

M

is

P.

Some S isM. ome S is P.

CHAPTER XXIX. Of Complex 357.

A

Syllogisms.

Complex Syllogism

is

one which

is

com

posed, wholly or in part, of complex propositions.

358.

Though

there are only

two kinds of complex

proposition, there are three varieties of

complex syllogism.

For we may have (1) a syllogism in is

which the only complex premiss

conjunctive,

(2) a syllogism in which the only is

complex premiss

disjunctive.

(3) a syllogism in which one premiss

and the other

is

conjunctive

disjunctive.

Syllogism

Simple

Complex

(Categorical)

(Conditional)

Conjunctive (Hypothetical) 1

The Conjunctive Syllogism

simplex

Dilemma 1

.

is called by Cicero (De Inv. I, 45) the Disjunctive emtmeratio, and the dilemma For the last cp. Asconius on Verr. Div. 45.

coMclttsio,

complexio.

Disjunctive

OF COMPLEX SYLLOGISMS.

326

The Conjunctive Syllogism. 359.

A

only complex premiss

if

is

Conjunctive Syllogism is

one

in

which the

conjunctive.

The conclusion may be said to follow the weaker part, we consider a simple proposition as being weaker than Therefore

a conjunctive.

when both premisses will

are conjunctive, the conclusion

be conjunctive

when one premiss

is

;

simple, the conclusion will be

simple.

This gives us two kinds of conjunctive syllogism (1) (2)

The Wholly Conjunctive Syllogism. The Partly Conjunctive Syllogism.

The Wholly Conjunctive Syllogism. 360. Since

every

conjunctive

may be which is com

proposition

read as a simple one, every syllogism also

posed wholly of such propositions may be read as a simple Wholly conjunctive syllogisms therefore do syllogism. not differ essentially from simple ones. constructed

in

mood and

every

figure.

They may be

A

couple

of

instances will suffice.

Let

= P.

A

is

B

C

is

D=

E is F =

M. S.

Cesare.

A is

B, C is never D. E is F, C is always D. If E is F, A is never B.

If

/.

man is rash, he is never rational. man is brave, he is always rational. If a man is brave, he is never rash. If a

If a

If

.

.

OF COMPLEX SYLLOGISMS.

327

Disamis.

C If C If E If

.

.

is

D,

A

is

sometimes B.

If

is

D,

E

is

always F. sometimes B.

If

is

A

F,

is

The second

/. If

she goes, I sometimes go. she goes, he always goes. he goes, I sometimes go.

of these instances

may

be read as a simple

syllogism thus Disamis.

Some CD All /.

CD

is

Some EF

is

AB.

EF. is

AB.

The Partly Conjunctive Syllogism. It is this kind which is usually meant when

361.

conjunctive or hypothetical syllogism

Of

362.

other

and

the the

conjunctive

simple

conjunctive premiss lays true universally

theory, which

is

is

spoken

considered the

premiss

down a

the

of.

and the

the two premisses, one conjunctive

simple,

major,

is

be

the

For

the

to

minor.

certain relation to hold

between two propositions as a matter of applied in the minor to a matter of fact.

363. Taking a conjunctive proposition as a major a

premiss

may

,

there are four simple minors possible.

either assert or

For we

deny the antecedent or the consequent

of the conjunctive.

Constructive (i) If

.*.

A is A is

B.

C

D.

is

B,

Mood*.

C

is

The major premiss

Destructive

D.

(2) If

.-.

Mood.

A

is

B,

C

is

not D.

A

is

not B.

C

is

D.

form of argument was called by the Stoics the Xij^^a, the minor the Trp6ff\r]^/is, and the conclusion 1

the 2

/3

.

(Tn<j>opa.

in this

Diog. Laert. VII,

TpoTTos 5e tffTiv, olovtl a\rina.

A\\d

nfjv

TU -npSirov

76.

\6fov

olov 6 TOtovroy, Et TO a

TO dpa Scvrtpov.

Ibid.

,

ri

OF COMPLEX SYLLOGISMS.

328

Denial of the Antecedent. If A is B, C is D.

Assertion of the Consequent. (3) If

A

No The also

is

is

B,

C C

D.

is

D.

(4)

A is not B. No conclusion.

conclusion.

mood

constructive

known

The

is

as the

modus ponens.

mood

destructive

or assertion of the antecedent

or

denial

known as the modus tollens. 364. From a consideration of

of the consequent

also

is

we

Canon of

To and

the above four cases

the following

elicit

tlic

Conjunctive Syllogism.

assert the antecedent

to assert the

is

the consequent

consequent

to deny the antecedent deny but from asserting the consequent or denying the antece dent no conclusion follows.

to

When we

365.

is

take as a minor

get no universal conclusion.

C

declared to involve as a consequence is

it

possible for

C

to

or from other causes.

be

D A

(3),

we can

being

B

is

C

being D, yet under other circumstances

Granting the truth of the pro

If the sky falls,

position

D

is

For though

,

we

shall

catch larks,

it

does

not follow that there are no other conditions under which this result

can be attained.

366. Again, (4), 1

ita

it

is

Cic. Fin. IV,

perspicua, ut

oportere

:

when we take as a minor we get no conclusion

clear that

si illud

ita

55

fit

ilia

;

at

is

not

all.

B For

conclusio non solum vera, sed

ne rationem quidem reddi putent non autem hoc igitur ne illud quidem.

dialectic!

hoc

A

:

OF COMPLEX SYLLOGISMS. to say that to

deny

that

C C

What we have case

AB

I shall

D

:

A

whenever

D

in the

is

B

gives us

no

right

absence of that condition.

predicated has been merely inclusion of the

in the case

If I get

Granted

is

can be

329

CD.

run over by an omnibus

but, if I escape that danger,

not be killed in some other way

367. There

is

a

case

however

I

be

shall

does

it

killed.

follow that

?

in

obtain a conclusion both

which

we can

the

by asserting consequent and by denying the antecedent of a conjunctive proposi tion. It is when the relation predicated between the antecedent and the consequent

is

not that of inclusion,

but of coincidence, where in fact the conjunctive pro position conforms to the type U.

For example

Assertion of the Consequent. If

.

.

you

You You

repent, then always

repent.

Denial of the If

/.

and only are you forgiven.

are forgiven.

A ntecedent.

you repent, then always and only are you forgiven.

You do You are

net repent. not forgiven.

OF COMPLEX SYLLOGISMS.

33

The

antecedent

is

here given as the sole, and at the

same time

all-sufficing,

were not

all-sufficing,

it

from forgiveness,

who

for

repent are not

it

condition of the antecedent.

repentance could not be inferred

might

still

forgiven;

condition, the absence

If

if

be the case that some it

of forgiveness

were not the sole could not be in

from the absence of repentance, for it might still be the case that some who do not repent are forgiven. ferred

368.

The

partly conjunctive syllogism

may be

exactly

defined as follows

A complex syllogism which has for its major premiss a conjunctive proposition, of which in the minor premiss the antecedent

is

asserted or the consequent denied.

CHAPTER XXX. Of the Reduction of the Partly

Conjunctive

Syllogism. treated of have

SUCH syllogisms as those just a major and a middle term visible to the 369.

to is

A

B, we mean

is

A

matter of fact that

A

B.

is

expression as that

wanted

is

When

is

argument,

or

appear

to fact.

to

The

will

this

manner

to

first

figure,

simple type of

the

and the destructive

Barbara.

A

isB, CisD.-

A

is

B.

C

is

D.

All

.-.

j

Destructive Mood.

A

A

is

is

B,

not B.

all

be found that the constructive con

Constructive Mood.

If

such is

of the syllogism.

conjunctive to the second.

.-.

As a

actual state of the case

complete the form

junctive conforms to the

If

When

(rightly or wrongly)

The insertion therefore of some The case in hand or This case

reduced in it

B

eye, but

missing minor however

from hypothesis

latent in the transition

we say is

The

be destitute of a minor.

CisD. C is not

AB

is

CD.

This

is

AB.

This

is

CD

Camestres. ^

D.

i

= /.

AllABis

CD.

This

is

not

CD.

This

is

not AB.

OF THE REDUCTION OF THE

332

As

370.

the

conjunctive syllogism

partly

reducible to the simple form,

we may

is

thus

suspect a priori

that violations of its laws will correspond with violations of the laws of simple syllogism. On experiment we find this to

be the case.

Assertion of the Consequent. If

A

is

B,

C

is

D.

is

D.

i

C Denial of If

/

=

I

j

Undistributed Middle. All

AB

This

the Antecedent.

A

is

B,

A

is

not B.

C

is

is

CD.

is

CD.

Illicit

D.

All

,

AB

Major. is

CD.

j

\

\

C 371.

If

is

not D.

we judge

This

)

.-.

This

is is

not not

AB<

CD.

the foregoing arguments

by the which they belong, we see the assertion of the consequent involves two affirma

special rules of the figures to that

premisses in the second figure, and the denial of the antecedent a negative minor in the first.

tive

By making the consequent of we might avoid breaking the

tive

the major premiss nega rule of the

second

figure,

but this would only land us in the fallacy of two negative

premisses instead. If

A

is

B,

Similarly

C C

is

not D. j

is

not D.

by making

we might

)

_

i

1

No AB

is

CD.

This

not

CD.

is

the antecedent of the major premiss

avoid breaking the rule of the first but this would only land us in the fallacy of four figure, negative

terms instead.

PARTLY CONJUNCTIVE SYLLOGISM. If

A A

is

not B,

is

B.

gism

that

i

canon

its

first

To

gism

is

into the

harmony with

in

clause of the

first

We

this

is

and,

now

C

syllo

the con

A

For

affirmed in

is

being D)

see

character.

assert

to

syllo

figure

shall

mixed

conceivable cases of

all

included therein, namely,

or even

all

being B, the

this case

or

clause

deny the consequent is to corresponds with the Dictum de to

deny the antecedent Diverso ( 317). For whereas in the major

A

cases of

being

B

case

or

this

C

373.

being

The

D

We

are included in

some

lies

is

is

all

conceivable

being D, in the all

actual

from the same term. of the

in the transition

partly con

from hypothesis

might lay down as the appropriate axiom

of this form of argument, that abstract

C

or even

cases

are excluded

special characteristic

junctive syllogism to fact.

some cases

actual cases.

The second

theory

AB.

affirmed in the conclusion of something which

is

cases of

CD.

is

canon of the conjunctive

assert the antecedent

the major of

minor

is

corresponds with the Dictum de Omni.

sequent

is

not-AB

This

I

the second.

whereas something (namely

same

All i

constructive,

destructive, into

The

_

have seen that the partly conjunctive

when

falls,

when

D.

is

)

We

372.

C

333

true in the concrete

also true in fact,

What is true or What is

a proposition which

in

the

true in is

apt

But this does not vitally be neglected or denied. For though differentiate it from the ordinary syllogism.

to

in

the latter

we

think rather of the transition from a

PARTLY CONJUNCTIVE SYLLOGISM REDUCED.

334

truth

general

to

a

particular

bottom a general truth resting

upon a slender

that

men

all

die

;

but

few perhaps are the with the

we

men

that

is

which nature

at

We

believe

how few have we seen do so How men that have yet been compared !

are yet to be

is

yet

it,

nothing but an hypothesis

basis of observed fact.

assert that they are mortal.

thesis

application of

!

Yet of

This

always verifying.

is

all

of them

only an hypo

CHAPTER XXXI. Of A

374.

the Disjunctive Syllogism.

Disjunctive Syllogism

only complex premiss

The since

it

down an

lays

is

one

which the

in

disjunctive.

premiss

disjunctive

is

is

as

regarded

hypothesis which

is

the major,

applied to fact

in the minor.

375. Taking a disjunctive proposition with only two alternatives as the

minors possible.

major premiss, there are four simple For we may assert or deny either of

the alternatives.

Constructive Moods. (i) Either

A is B or C is D. A is not B. C

Either death tion or

is

is

(2) Either

D.

.-.

,\

We

is

not annihilation.

are immortal.

C

is

not D.

A

is

is

.

.

D.

B. is

shal-

low or the boys be drowned.

are im-

mortal.

Death

or

C

Either the water

annihila-

we

A is B

will

The boys are not drowned. The water is shallow.

OF THE DISJUNCTIVE SYLLOGISM.

336

Destructive Moods.

A

is

B

A

is

B.

(3) Either

No

A

or

C

is

D.

No

conclusion.

must be

successful student

is

No The

or your luck

No

conclusion.

moods

constructive

is

D.

is

D.

conclusion.

Your luck

clever.

C C

or

Either your play

either clever or industrious.

He

A is B

(4) Either

is

bad

is

is.

bad.

conclusion.

known

as

modi

known

as

modi ponendo

are also

tollendo

ponentes.

The

destructive

moods

are also

tollentes,

376.

It

is

formally valid. is

only the

The

constructive

moods

are

that

moods

validity of the two destructive

contingent upon the kind of alternatives selected. If these are

such as necessarily to exclude one another,

the conclusion will hold, but not otherwise. are of course mutually exclusive, whenever they

They embody

the result of a correct logical division, as

are either equilateral, isosceles, or scalene.

members, we are

affirm one of the

the rest.

When

members of

it

A

is

may more either

B

fitly

retain the wider expression

Either

the alternatives

patible

must come

selected

to us

in

But as

A

B

is

which includes

Any knowledge however which we that

if

we

denying

be symbolized

or C.

admits of being read in the shape

C/ we

in

justified

the major thus contains the dividing

a genus,

under the formula

is

Triangles

Here,

this

or

A

it.

have of the fact

the major are incom

from material sources

;

unless

OF THE DISJUNCTIVE SYLLOGISM.

337

indeed we have confined ourselves to a pair of contra

terms (A

dictory

B

either

is

or

There can

not-B).

be nothing in the form of the expression to imply the incompatibility of the alternatives, since the

employed when

is

When

a

man it

There

says

be rain either to-day or

will

we do not consider him confuted by

to-morrow, result, if

377. There

is

no

limit to the

But

number of members

there be

if

alternatives, the conclusion will itself

..

minor denies

A is A is A is

either

all

either is

C

B

or

B

or C.

or D.

.

.

A is either B or C or D. A is neither C nor D. A is B. either a state

is

or a capacity or an

an

affection of the soul.

affection of the soul.

not an affection

is

be disjunctive, unless

Virtue

either a state

or a capacity or

Virtue

in

more than two

but one.

not D.

Virtue

the

rains both days.

the disjunctive major.

the

same form

the alternatives are palpably compatible.

neither a capaan affection nor city

Virtue

of the soul.

is

of the soul. .-.

Virtue

is

either

a state

/.

Virtue

is

a

state.

or a capacity. 378. If to

two

we

take the disjunctive proposition as limited

alternatives,

we may

lay

down

the following

Canon of

To

the Disjunctive Syllogism. deny one alternative is to assert the other, but from

asserting either nothing follows.

z

OF THE DISJUNCTIVE SYLLOGISM.

338 If

we

take into account a plurality of alternatives,

we

must extend our canon thus

To

deny one member

is

to

affirm the

from affirming simply or disjunctively; but

rest,

either

any member

nothing follows. 379.

The

with disjunctive syllogism

two alternatives

may be exactly defined as follows for its major premiss complex syllogism which has con a disjunctive proposition, either the antecedent or is in the minor premiss simply denied. sequent of which

A

CHAPTER Of

XXXII.

Dilemma.

the

THE dilemma

belongs to the third kind of which one premiss is conjunctive complex and the other disjunctive. It would be possible however 380.

syllogism in

to

combine two such premisses

which should not be a dilemma, If

/.

We

C

is

E

D,

Either

A

is

Either

A

is

shall therefore

a valid syllogism

e.g.

F.

is

B B

into

or or

C E

is

D.

is

F.

have to define precisely the relation

which the two propositions which form the premisses This however will be done to stand to one another.

in

more advantage

at the

end of the discussion than

at the

beginning. 381.

dilemma,

The

It if

will

facilitate

the

comprehension of the

the following four points are borne in mind.

first relates

to the

major premiss

the second to the minor premiss the third to the conclusion

the

fourth to the

;

;

;

canon with which the dilemma

complies. z 2

OF THE DILEMMA.

340

The major premiss

(1)

is

a conjunctive

proposition

with more than one antecedent or more than one con

sequent or more than one of both. (2)

The minor

(3)

If

premiss must be disjunctive.

be

there

one antecedent or only one

only

consequent, the conclusion will be a simple proposition if

there be

itself

more than one of

;

both, the conclusion will

be disjunctive.

(4)

The dilemma

complies

with

The two

conjunctive syllogism.

the

canon of the

things therefore

which

are permissible in the minor are to affirm the antecedent

or deny the consequent.

382.

What

is

then that differentiates the dilemma

it

from any other conjunctive syllogism ? It is the presence of a disjunctive minor, which is rendered possible by the plurality of antecedents or consequents in the major. is

this

It

which constitutes the essence of the dilemma and

which determines

For

possible varieties.

its

if

only the

antecedent or only the consequent be more than one,

we

must, in order to obtain a disjunctive minor, affirm the

antecedent in the former case and deny the consequent in the latter; whereas, it is

open

if

there be

more than one of

to us to take either course.

types of dilemma. (i) Simple Constructive.

383.

If

A

is

Either .-.

E

is

F.

B

A

or is

C is D, E is B or C is D.

both,

This gives us four

F.

OF THE DILEMMA. If

.*,

or Friday, there

Wednesday

it is

It is either

There

341 is fish

for dinner.

or Friday.

Wednesday

for dinner.

is fish

(2) Simple Destructive. If

A

is

Either

A

.-.

If I

B,

C

D and E is F. not D or E is not

C

is

is

go with Miss Brown to the her ticket and for my own.

ball, I

Either I cannot pay for her ticket or

my I

is

Either .-.

B,

A

Either

I

;

Either

I shall

meet the

(4)

Complex

is

Either

is

H.

is

H.

meet the

bull; and, if

the lane, I shall meet the farmer.

B,

Either /.

shall

go up I must cross the

A

ball.

C is D and if E is F, G B or E is F. C is D or G

Either

If

cannot pay for

I

is

If I cross the field, I

.-.

for

Constructive.

Complex

(3)

A

must pay

own.

cannot go with Miss Brown to the

If

F.

not B.

is

A

is

D

is

not

not

B

C C is

;

and

field

or go

up the

lane.

bull or the farmer.

Destructive. if

E

is

D

F,

or or

E

is

G G

is

H.

is

not H.

not F.

OF THE DILEMMA.

342 were

If he

clever,

he would see his mistake

and

;

i

he were candid, he would acknowledge it. Either he does not see his mistake or he will not

acknowledge Either he

/.

A

384. clusion

A

is

it.

not clever or he

Simple Dilemma

is

not candid.

one of which the con

is

a simple proposition.

is

Complex Dilemma

one of which the conclusion

is

is

a disjunctive proposition.

There

a slight

is

inconvenience

this

attending

dilemma

minology, for even a simple

is

still

a

ter

complex

syllogism.

We

385.

now

will

give an exact definition of the

dilemma

A

dilemma

is

a complex syllogism having for

its

major

premiss a conjunctive proposition with more than one antecedent

which

more than one consequent or

or

in the jninor the antecedent

is

of

both,

disjunctively asserted

or the consequent disjunctively denied.

386.

must be noticed

It

that the simple destructive

dilemma would not admit of a If

we

If

A

is

Either

we should not

B,

C

C is

is

not

D or E is F, D or E is not

F,

not be denying the consequent.

F would make

would make

we

disjunctive consequent.

said

it

it

true that

C

E

F;

true that

is

is

D

and

E

For

C

is

not

is

D

so that in either case

should have one of the alternatives true, which

is

just

OF THE DILEMMA. what the disjunctive form

To

insists

Either

this to

343

C

is

D

or

E

is

F

the concrete instance, If

upon. apply have only to pay for Miss Brown s ticket or for l own, I can still go with her to the ball

my

I

.

387.

The

members

several

of a complex dilemma,

instead of being distributively assigned to one another,

may

be connected together as a whole, thus If either

.-.

In

A

is

B

E

or

is

F, either

Either

A

is

B

or

E

is

F.

Either

C

is

D

or

G

is

H.

this

is

is

D

G

or

is

H,

shape the likeness of the dilemma to the semi-

The major becomes apparent. now vaguer than before. For each antecedent

conjunctive

premiss

C

syllogism

has a disjunctive choice of consequents, instead of being limited to one.

This vagueness however does not

the conclusion.

For, so long as the conclusion

lished,

it

is

affect

estab

does not matter from which members of the

its own members flow. The complex destructive dilemma may be

major the

A

E

is

F, either

Either

C

is

not

D

or

G

is

Either

A

is

not

B

or

E

If either

/.

treated

in

same way is

B

or

is

C

is

D

or

G

is

H.

not H. not F.

The authors of the Palaestra Logica challenge the right of the simple destructive dilemma to be called a dilemma at all, on the ground that the minor premiss would be better expressed thus It cannot be both that C is D and that E is F. But, to be con 1

they should expunge also the complex destructive dilemma, which the same remark applies.

sistent,

to

OF THE DILEMMA.

344

The Polylemma.

we have

388. For the sake of simplicity

limited the

examples to the case of two antecedents or consequents. But we may have as many of either as we please, so as to have a Trilemma, a Tetralemma, and so on. Trilemma,

A

If

is

Either .-.

C

B,

A

Either

is

is

B

C

is

D

and

;

E E

if

or

is

F,

is

F

D

or

G

H

is

and

;

or

G

is

H

if

K K

is

L,

is

L.

or

M

is

N.

M

is

N.

Refutation of the Dilemma. 389. So complex a piece of reasoning as the dilemma naturally affords

the

between

conjunction

assumed

in

the

We may

points of attack.

many

major,

consequent or the exhaustiveness of the

we may we may find a

alternatives implied in the minor, or

the terms, or

ambiguity in reasoning

itself.

Take

deny

and

antecedent

detect

some

flaw in the

dilemma by which

for instance the

the Stoics sought to fortify themselves against the idea of

pain Levis est,

si

ferre

possum

;

brevis est,

si

ferre

non possum.

(Seneca, Epist. xxiv,

which

may be

If I

14)

,

formulated thus

can bear pain,

it is

slight

;

if I

cannot bear

it,

it is

V,

88.

brief.

Either I can bear .-.

1

Pain

is

it

or not.

either slight or brief.

Cp. Cic. Fin.

I,

40

;

II,

22, 94,

95

:

7.

D.

Ill,

38

;

OF THE DILEMMA. Here the major denies what

is,

fortunately or

human body

fortunately, a fact, that the

345 un

capable of

is

and prolonged pain. The weak point in a dilemma is usually the minor premiss, where there is a tacit assumption that the alter enduring intense

natives offered are exclusive

Thus

and exhaustive.

the

dilemma against examinations If students are idle, examinations are unavailing; if

they are industrious, examinations are

and

super

fluous.

Students are either idle or industrious. .

.

Examinations are either unavailing or superfluous

leaves out of sight the

commonest case of

who will be

all,

that of

industrious, they have an immediate if but motive for exertion, idle, they have not.

students

if

The Rebutting of a Dilemma. 390.

A

dilemma

is

when another dilemma

said to be rebutted or retorted,

made

is

out which apparently

proves an opposite conclusion. This is a dialectical fallacy based on the fact, which is generally overlooked, that a disjunctive denial

not really opposed to a disjunctive

is

assertion.

The most is

mode

of rebutting a complex dilemma and by transposing denying the consequents in the

usual

major. If

A

is

Either .-.

Either

B,

A

C is D and if E is F, G B or E is F. C is D or G ;

is

H.

is

H.

is

OF THE DILEMMA.

346

The same If

A

is

rebutted

B,

Either

A G

= Either

C

Either .-.

Under

this

G

is

not

E

is

B

is

not

H

is

not

D

or

H

;

is

F.

C

or or

and

G

is

is

if

to enter

A

will love

you say what is is what say unjust, the for, if

you

made

to

it,

upon public life me and if

will love just, the gods

men

not D.

is

son

to her

together with the retort

ought

C

H.

not

:

I

F,

not D.

Do not enter upon public life hate you; and if you just, men will will hate

is

form comes the dilemma addressed by the

Athenian mother

gods

E

;

:

I

for, if I

say what

say what

is

is

unjust,

me.

But the two conclusions here are quite compatible. man must, on the given premisses, be both hated and he

loved, whatever course

takes.

So

far

indeed are two

propositions of the form

Either

and Either

C is D or G is H, C is not D or G is

not H,

from being incompatible, that they express precisely the same thing when contradictory alternatives have been selected, e. g.

Either a triangle

is

equilateral or non-equilateral.

Either a triangle

is

non-equilateral or equilateral.

Equally illusory

is

the famous instance of rebutting

OF THE DILEMMA.

347

of Protagoras

and

Euathlus (Aul. Cell. Nod. Aft. v. 10). Euathlus was a pupil of Protagoras in rhetoric.

He

dilemma contained

a

paid

half

the

the

in

story

demanded by

fee

preceptor before

his

when

receiving lessons, and agreed to pay the remainder

won

he

his

first

case.

practise at the bar, his

became evident

it

that

he meant to bilk

Accordingly Protagoras himself instituted a

tutor.

and

lawsuit against him,

before

But as he never proceeded to

the

jurors

in the preliminary proceedings

propounded

him

to

the

following

dilemma

Most

foolish young man, whatever be the issue of this must you pay me what I claim for, if the verdict be in given your favour, you are bound by our bargain and suit,

:

;

be given against you, you are bound by the decision

if it

of the jurors.

But Protagoras had not taught his pupil he rebutted the dilemma as follows

no purpose

to

;

for

Most sapient master, whatever be suit,

I

the

not pay you what you claim

shall

verdict be given

in

decision of the jurors

my ;

favour,

and

if it

I

am

issue :

of this

for,

if

the

absolved by the

be given against me,

I

am

absolved by our bargain.

The

jurors are said to have been so puzzled by the

conflicting plausibility of the

the case

the

till

that a grave injustice

dilemma was of Euathlus

arguments

Greek Kalends.

was thus done

really invincible.

we

It

that they is

adjourned

evident however

to Protagoras.

His

In the counter-dilemma

are meant to infer that Protagoras would

OF THE DILEMMA.

34 8

actually lose his fee, instead of merely getting

way get

rather than another.

and

he actually lose

it

it.

in

one

it on one plea but in neither case would

lose his fee, in the sense of getting

and not getting

it

In either case he would both

on another

:

CHAPTER Of 391.

THE

XXXIII.

Trains of Reasoning.

formal logician

is

only concerned to examine

whether the conclusion duly follows from the premisses he need not concern himself with the truth or falsity of :

his

But the

data.

premisses

of one

syllogism

may

themselves be conclusions deduced from other syllogisms, the

of which

premisses

established

may

are thus linked together

turn have been

in their

yet earlier syllogisms.

by

When

we have what

is

syllogisms

called a Train

of Reasoning. 392.

It is

plain that

all

truths cannot be established

by reasoning. For the attempt to do so would involve us in an infinite regress, wherein the number of syllogisms required would increase at each step ratio.

we

To

in

a geometrical

establish the premisses of a given syllogism

should require two preceding syllogisms

their premisses, four at the next, sixteen

;

;

at the next step

and so on ad

;

to establish

backwards, eight

infinitum.

Thus

very possibility of reasoning implies truths that are to us prior to

of reasoning

all

may

;

the

known

reasoning and, however long a train be, we must ultimately come to truths ;

which are either self-evident or are taken

for granted.

OF TRAINS OF REASONING.

35 393.

Any

which establishes

syllogism

premisses of another

one

of

the

called in reference to that other

is

a Pro-syllogism, while a syllogism which has for one of its

premisses the conclusion of another syllogism

in reference to that other

is

called

an Epi-syllogism.

The Epicheirema. 394.

The name Epicheirema

with one or both of

Thus

the following

is

All All .-.

All virtue

its

All

a double epicheirema

B C C

is

A, for

it is

E.

is

B, for

it is

F.

is

A.

praiseworthy, for

is

given to a syllogism

is

premisses supported by a reason.

it

promotes the general

welfare.

Generosity

pone /.

Generosity 395.

An

is

a virtue, for

it

prompts men

to post

self to others. is

praiseworthy. said to

is

epicheirema

be of the

first

or

second order according as the major or minor premiss is thus supported. The double epicheirema is a com bination of the two orders

396.

An

epicheirema,

1

it

.

will

be seen, consists of one

syllogism fully expressed together with one, or,

it

may

be

two enthymemes ( 269). In the above instance, if the reasoning which supports the premisses were set forth at 1

De

This, Cicero tells us,

Inv.

I,

67-

is

the

full

type of rhetorical reasoning,

OF TRAINS OF REASONING full

length,

we should

351

have, in place of the enthymemes,

the two following pro-syllogisms

A11E

(1)

B B

All All

/.

is

A.

is

E.

is

A.

Whatever promotes the general welfare

is

praise

worthy.

Every

virtue

..Every

virtue

promotes the general welfare. is

praiseworthy.

(2) All

All .

All

.

F C C

Whatever prompts men

is

B.

is

F.

is

B.

to

postpone

self to others is

a virtue.

Generosity prompts .

.

Generosity 397.

is

men

The enthymemes

are both of the

first

postpone

self to others.

in

the

instance above given

having the major premiss nothing to prevent one or both

order,

But there

suppressed.

to

a virtue.

is

of them from being of the second order All

All .-.

All

All

B C C

is

A, because

all

D

is.

is

B, because

all

E

is.

is

A.

Mahometans

are fanatics, because

all

Monotheists

are.

These men are Mahometans, because are. /.

These men

are fanatics.

all

Persians

OF TRAINS OF REASONING.

352

Here

is

it

the minor premiss in each syllogism that

is

suppressed, namely,

Mahometans

(1) All

These men

(2)

are Monotheists.

are Persians.

The 398.

The

Sorites

is

Sorties.

and most compen

the neatest

dious form that can be assumed by a train of reasoning.

sometimes more appropriately called the chain1 argument and may be defined as It

is

,

A

train of reasoning, in

syllogism

is

which one premiss of each

epi-

supported by a pro-syllogism, the other being

taken for granted.

This

inner essence.

is its

399. In series

its

outward form

common

it

may

be described as

with that which preceded

it,

while in the con

clusion one of the terms in the last proposition either subject or predicate to

400.

A

sorites

may

A

of which has one term in

of propositions, each

one of the terms

becomes

in the

first.

be either

(i) Progressive,

or (2) Regressive.

Progressive Sorites.

1

is

The

Regressive Sorites.

All

A

is

B.

All

D

is

E.

All

B

is

C.

All

C

is

D.

transference of the

name

perhaps due to Cic. Fin. IV,

Sorites to the chain-argument

50.

OF TRAINS OF REASONING.

.-.

All

C

D.

All

B

All

D is E. A is E.

All

A A

All

is

The usual form

.-.

the progressive;

is

as a

commonly described

is

series

All

353

is

C.

is

B.

is

E.

so that the sorites

of propositions

in

which the predicate of each becomes the subject of the next, while in the conclusion the last predicate

denied

or

of the

however exactly

first

The

subject.

these

reverses

is

affirmed

regressive

attributes

;

form

and would

be described as a series of propositions, in which the subject of each becomes the predicate of the to

require

next, while in the conclusion the

first

predicate

is

affirmed

or denied of the last subject.

The the

regressive sorites,

same propositions

in reverse order.

a special different,

major?

name if

to

as the progressive one, only written

Why it,

be observed, consists of

will

it

then,

it

may

though we do

be asked, do we give

not consider a syllogism

the minor premiss happens to precede the

It is

because the

sorites is not a

mere

series of

propositions, but a compressed train of reasoning; the two trains of reasoning

may

component syllogisms in such a manner real difference between them.

The

Progressive Sorites

is

a pro-syllogism, while the major

Regressive Sorites

is

as to exhibit a

a train of reasoning in which

the minor premiss of each epi-syllogism

The

and

be resolved into their

is

is

supported by

taken for granted.

a train of reasoning in which

the major premiss of each epi-syllogism

a pro-syllogism, while the minor

is

is

supported by

taken for granted.

A a

OF TRAINS OF REASONING.

354

Progressive Sorites.

Regressive Sorites.

(1) All

B

is

C.

(i) All

All

A

is

B.

All

All

A

is

C.

(2) All

C

is

D.

.

.

.-.

(

A is C. All A is D. (3) All D is E. All A is D. .All A is E.

2

)

All

.-.

.-.

(3)

C C

is

E.

is

D.

is

E.

All

C is E. B is C.

All

B

All

is

E.

All

B

is

E.

All

A

is

B.

.-.AllAisE.

.

Here

All

D

a concrete example of the two kinds of resolved each into its component syllogisms

401. sorites,

is

Progressive Sorites. All Bideford

men are Devonshire men. men are Englishmen.

All Devonshire All

All .\

Englishmen are Teutons. Teutons are Aryans.

All Bideford

men

are Aryans.

men are Englishmen. Bideford men are Devonshire men. Bideford men are Englishmen.

(1) All Devonshire

All ..

All

(2) All

Englishmen are Teutons.

All Bidtford .

.

All Bideford

(3) All

.

Englishmen. Teutons.

Teutons are Aryans.

All Bideford .

men are men are

All Bideford

men men

are Teutons. are Aryans.

OF TRAINS OF REASONING.

355

Regressive Sorites. All

Teutons are Aryans.

All Englishmen are Teutons. All All .-.

All Bideford

(1) All

All .-.

All

men

are Aryans.

Teutons are Aryans. Englishmen are Teutons. Englishmen are Aryans.

All

Englishmen are Aryans. Devonshiremen are Englishmen.

All

Devonshiremen are Aryans.

(2) All

/.

Devonshiremen are Englishmen. Bideford men are Devonshiremen,

(3) All

Devonshiremen are Aryans. men are Devonshiremen.

All Bideford .-.

402. as

many

All Bideford

When

men

are Aryans.

expanded, the

sorites

between the

first

and the

inspection by counting the

last.

This

number

found

to contain

mence with

;

evident also on

\ve

have to

com

the second proposition of the sorites as the

major premiss of the first syllogism. form the subject of the conclusion syllogisms

is

of middle terms.

In expanding the progressive form

same.

is

syllogisms as there are propositions intermediate

in the regressive

In the progressive is

the

same

in all the

form the predicate

is

the

In both the same series of means, or middle terms, A a 2

OF TRAINS OF REASONING.

356

employed, the difference lying in the extremes that are compared with one another through them.

is

It is apparent from the figure that form we work from within outwards,

form from without

employ the term Bideford

Bideford lastly,

with

as a

Englishmen

mean

the

as a ;

in

the regressive

former

we

mean

connect

next

to

first

we employ

connect the same subject with the wider term Teutons and,

men

to

;

we employ

original subject

In

Devonshiremen

men

Englishmen

inwards.

in the progressive

Teutons

Bideford

men

as a

mean

to

connect the

with the ultimate predicate

Aryans.

we first use Teutons mean whereby to bring Englishmen under Aryans next we use Englishmen as a mean whereby to bring Reversely, in the regressive form

as a

;

Devonshiremen and,

lastly,

we use

under the same predicate Aryans; Devonshiremen as a mean whereby

OF TRAINS OF REASONING. Bideford

to bring the ultimate subject

A

In

the

men

under the

Aryans.

original predicate

403.

357

be either Regular or Irregular. form the terms which connect each regular sorites

may

proposition in the series with

predecessor, that

its

is

to

say, the middle terms, maintain a fixed relative position

so

that,

if

the

middle term be

subject

in

one,

always be predicate in the other, and vice versa. irregular form

The

this

symmetrical arrangement

syllogisms

which

is

will

;

will

In the

violated.

compose a regular

whether progressive or regressive,

it

sorites,

always be in the

first figure.

In the irregular

the

fall

into

404. For the regular sorites the following rules

may

sorites

syllogisms

may

different figures.

be

laid

down.

(1)

Only one premiss can be first, if

particular,

namely, the

the sorites be progressive, the

last, if it

be regressive. (2)

Only cne premiss can be negative, namely, the last, if

the sorites be progressive, the

first, if it

be regressive. 405.

Proof of the Rules for

ihe

Regular

Sorites.

(i) In the progressive sorites the proposition which stands first is the only one which appears as a

minor premiss of the others If

in the is

expanded form.

used in

any proposition,

its

Each

turn as a major.

therefore, but the

first

were

OF TRAINS OF REASONING. would be a

particular, there

which involves undistributed

minor be

affirmative, as

particular major, if

middle,

must be

it

the

in the first

figure.

In the regressive except the a

sorites, if any proposition were particular, we should have

last

conclusion in the syllogism in occurred as a premiss, and so a par ticular major in the next syllogism, which particular

which

again

it

is

inadmissible, as involving undistributed

middle. (2)

In the progressive the

last

were

sorites, if

negative,

any premiss before

we

should

have a

negative conclusion in the syllogism in it

occurs.

minor

in

which

This Avould necessitate a negative the next syllogism, which is inad

missible in the

first

process of the major. In the regressive

which stands

first

is

figure, as involving

sorites

the

illicit

proposition

the only one which ap

pears as a major premiss in the expanded form.

Each of

the

others

is

used in

its

turn as a

minor.

If any premiss, therefore, but the first were negative, we should have a negative minor in the first figure,

which involves

illicit

process

of the major. 40G.

The

above given do not apply to the except so far as that only one premiss

rules

irregular sorites,

can be particular and only one negative, which follows

OF TRAINS OF REASONING.

359

from the general rules of syllogism. But there is nothing to prevent any one premiss from being particular or any

one premiss from being negative, as the subjoined ex amples will show. Both the instances chosen belong to the progressive order of sorites.

Barbara. All All

B C

is

A.

All

is

B.

All

Some C All

D

is

Some A

D.

is

/.

All

B C C

is

A.

is

B.

is

A.

E. is

E.

Disamis.

Some C All

C

Some

is

A

is

is

All

D

Some Some

is

E.

A is D. A is E.

All

A

is

B.

All

B

is

C.

All

B

is

C.

All

A

is

B.

All

A

is

C.

is

E is D. No A is E.

All

D.

Darii.

(3)

No D

D.

A.

Barbara.

/.

C.

OF TRAINS OF REASONING.

360

Cesare.

(2)

No D

A No A All

.-.

All

/.

A

chain-argument

E

No A No A

may be composed

it is

same laws

is

D.

is

D.

is

E.

This

Progressive.

A

is

If

C

is

E If A If

B,

C

is

F,

E G

is

B,

G

D,

is

as the simple sorites, to which

immediately reducible.

If

D.

is

consisting

of conjunctive instead of simple propositions. subject to the

C.

C.

Camestres.

(3)

407.

is

is

Regressive.

is

D.

If

E C

is

F.

If

is

H.

is

H.

A If A If

.-.

is

F,

is

D,

G

is

H.

is

F.

is

B,

E C

is

B,

Gis H.

isD.

CHAPTER XXXIV. Of 408.

AFTER examining

thoughts depend,

most

Fallacies.

familiar

it

is

the conditions

on which correct

expedient to classify

forms of

error.

It is

some of

the

by the treatment of its claim to be

the Fallacies that logic chiefly vindicates

considered a practical rather than a speculative science.

To

explain and give a

name

to fallacies

is

like

setting

up so many sign-posts on the various turns which

it

is

possible to take off the road of truth.

409.

By

a fallacy

is

meant a piece of reasoning which

appears to establish a conclusion without really doing so.

The term

applies both to the legitimate deduction of a

conclusion from false premisses and to the illegitimate

deduction of a conclusion from any premisses. are errors incidental to conception

There

and judgement, which

might well be brought under the name but the fallacies with which we shall concern ourselves are confined to ;

errors connected with inference.

OF FALLACIES.

3 62 410.

When any

inference leads to a false conclusion,

the error

may have arisen either in the thought the signs by which the thought is conveyed.

itself

or in

The main

sources of fallacy then are confined to two (1)

thought,

(2) language.

411. This cies,

which

the basis of Aristotle s division of falla

is

has

not

yet

been superseded.

according to him, are either in the of

Outside of language there

it.

but thought.

Fallacies,

language or outside

no source of error

is

For things themselves do not deceive

us,

but error arises owing to a misinterpretation of things the mind. err either in its by Thought however

form or there

in

some

is

matter.

its

may The former is

whenever thought disagrees with

its

arrive at the important distinction

Material

the case

violation of the laws of thought

fallacies,

object.

;

Hence we

between Formal and

both of which, however,

same negative head of

where

the latter

fall

under the

fallacies other than those

of lan

guage. In the language

the signs of thought).

(in

Fallacy

/

In the Form.

Outside the language (in

the thought

itself)

In the Matter.

412.

may

There are then three heads

be referred

namely, Formal

to

which

fallacies

Fallacies, Fallacies of

OF FALLACIES.

363

Language, which are commonly known as Fallacies of Ambiguity, and,

Material Fallacies.

lastly,

413. Aristotle himself only goes so far as the the

in

step

division

them according as they are of

first

of fallacies, being content to class

language or outside

in the

After that he proceeds at once to enumerate the

it.

We

infimae species under each of the two

main heads.

shall presently imitate this

for reasons of ex

procedure

For the whole phraseology of the subject is derived from Aristotle s treatise on Sophistical Refuta pediency.

and we must either keep to his method or break Sufficient confusion has from tradition altogether. away s language while Aristotle arisen from retaining already tions,

neglecting his meaning.

do not approach Their fallacies from the same point of view as Aristotle. is to discover the most fertile sources of error in object

Modern

414.

solitary

reasoning;

writers

his

on

was

logic

to

enumerate the various

tricks of refutation which could be employed by a sophist in controversy. Aristotle s classification is an appendix

to the Art of Dialectic.

Another cause of confusion

415. logic

of

is

the identification of Aristotle

commonly known under and Extra dictionem, with

fallacies,

dictione

Logical and Material, which

is

s

in

this

of

part

twofold division the

the

titles

of In

division

into

based on quite a different

principle.

Aristotle s division perhaps allows to

language,

in

making

that

the

an undue importance

principle

of division,

OF FALLACIES.

36 4

and so throwing formal and material

common

head.

fallacies

under a

Accordingly another classification

has

been adopted, which concentrates attention from the

first

upon the process of thought, which ought

certainly to

be of primary importance in the eyes of the logician. This classification is as follows.

Whenever in the course of our reasoning we are in volved in error, either the conclusion follows from the premisses or

is

does not.

it

If

does not, the

it

called a Logical Fallacy.

must

fault

and we have then what

in the process of reasoning,

lie

on the other hand, the fault must

If,

conclusion does follow from the premisses, the in the premisses themselves,

lie is

called

a Material Fallacy.

conclusion the

will

meaning

appear to follow from the premisses

of the terms

found that the appearance ambiguity in the language. strictly is

and we then have what Sometimes, however, the

examined, when

is

is

it

deceptive owing to

Such

until

will

be

some

fallacies as these are,

speaking, non-logical, since the

meaning of words

extraneous to the science which deals with thought.

But they are called Semi-logical. Thus we arrive by a different road at the same three heads as before, namely, (i)

Formal

or

Purely

Logical

logical Fallacies or Fallacies of

Fallacies,

(2)

Semi-

Ambiguity, (3) Material

Fallacies.

416. For the sake of distinctness

two

divisions side

the infimae species.

by

side, before

we

will

we proceed

to

place the

enumerate

OF FALLACIES.

365

In the language ^Fallacy of Ambiguity).

Fallacy

the Form.

{In In the Matter.

Formal or purely logical.

Logical Fallacy

J

-

Semi-logical (Fallacy of Ambiguity).

^Material.

417. fallacies,

Of one it

is

of these three heads, namely, formal

not necessary to say much, as they have

been amply treated of in the preceding pages. A formal fallacy arises from the breach of any of the general rules of syllogism.

Consequently

it

would be a formal

to present as a syllogism anything less

than two premisses. a woman is called

what

own

Under s

fallacy

which had more or

the latter variety

comes

reason/ which asserts upon

its

evidence something which requires to be proved.

When

the

conclusion thus merely reasserts one of the

premisses, the other

must be

either absent or irrelevant.

on the other hand, there are more than two premisses, is more than one syllogism or the superfluous no at is but a all, premiss premiss proposition irrelevant

If,

either there

to the conclusion.

418. liable to

The remaining

rules of the syllogism are

be broken than the

first;

more

so that the following

OF FALLACIES.

366

scheme presents the varieties of formal commonly enumerated

which are

fallacy

/Four Terms. Undistributed Middle.

Formal Fallacy

-{

T1

Illicit

Process.

\Negative Premisses and Conclusion. 419.

The

Fallacy of Four

Terms

a violation of the

is

second of the general rules of syllogism is

a palpable instance of All

men who

All educated .-.

Here

All educated

the middle term

write

men men is

is

285).

Here

books are authors.

could write books. are authors.

altered in the

the destruction of the argument. the actual writing of

(

it

The

minor premiss

to

difference between

books and the power to write them one who is an author

precisely the difference between

and one who

The cess

is

not.

Fallacies of Undistributed Middle

have been treated of under

287.

Negative Premisses and Conclusion

and

Illicit

Pro

The heading

covers violations

of the general rules of syllogism relating to negative pre

misses

(

285).

Here

is

an instance of the particular form

cf the fallacy which consists in the attempt to extract an affirmative conclusion out of

All

salmon are

fish, for

to the class

The

two negative premisses

neither salmon nor fish belong

mammalia.

accident of a conclusion being true often helps to

conceal the fact that

it

is

illegitimately arrived at.

OF FALLACIES. The find

36 7

formal fallacies \vhich have just been enumerated

no place

The

in Aristotle s division.

reason

is

plain.

His object was to enumerate the various modes in which a sophist might snatch an apparent victory, whereas by openly violating any of the laws of syllogism a disputant

would be simply courting

We

420. fallacies,

now

revert

or rather of

defeat.

Aristotle

to

Modes

the species he enumerates in their order,

modern usage has departed from Let

of the terms.

deception

was not

in

the

We

take

will

and notice how

the original

be borne in mind

it

that,

meaning

when

the

not

language, Aristotle did

trouble himself to determine whether

of

classification

s

of Refutation.

lay in the matter

it

or in the form of thought.

The

following scheme presents the Aristotelian classi

fication to the eye at a glance

:

Equivocation.

Amphiboly. Composition. 1

In the language

Division. |

Accent.

\Figure of Speech.

Modes

of

Refutation

/

Accident. \

A

dido secundunt quid.

Ignoratio Elenclii.

Outside the language j Consequent.

Petitio Principii.

Non causa pro causa. Many Questions. 1

The Greek

due

is

irapa TTJV \tiv, the exact

to the statement.

The

Koi ra Trpay/j.a.Ta aoiftta^dTtuf.

meaning of which

Stoics spoke of ruv napd TTJP

D. L, VII,

43.

is

<poiv^v

OF FALLACIES.

368 421.

The

Fallacy of Equivocation (6/xww/xia) consists

an ambiguous use of any of the three terms of a If, for instance, anyone were to argue thus syllogism.

in

No human No

/.

is made of human beings, made of paper

being

All pages are

pages are

paper,

the conclusion would appear paradoxical,

term were there taken

in a different sense

if

the

minor

from that which

it bore in its This therefore would be proper premiss. an instance of the fallacy of Equivocal Minor.

For a glaring instance of the Major, we may

No .

courageous creature

of Equivocal

flies,

The eagle is a courageous The eagle does not fly

.

fallacy

take the following

the conclusion here

creature,

becomes unsound only by

the major

being taken ambiguously. It is

however

to

the middle term

that

an ambiguity

most frequently attaches. In this case the fallacy of equivocation assumes the special name of the Fallacy of Ambiguous Middle. Take as an instance the following Faith

..

To To

is

a moral virtue.

believe in the

believe in

Book

the

of

Book

Mormon is faith. Mormon is a

of

moral

virtue.

Here

the premisses

singly might be granted

conclusion would probably be

Nor

is

the reason far to seek.

felt

It is

to

;

but the

be unsatisfactory.

evident that belief in

OF FALLACIES.

369

a book cannot be faith in any sense in which that quality

can rightly be pronounced to be a moral virtue. 422. The Fallacy of Amphiboly (dpi/3oA.t a)

an

is

ambiguity attaching to the construction of a proposition rather than to the terms of which

of Aristotle

s

examples

may

composed

One

J .

this

is

TO PovKtaQai Aa/Sefc

which

is

it

rois iroXepiovSj

fit

mean

be interpreted to

wishing to take the

enemy, or

wishing to take me.

The

the fact of

either

my

enemies

the fact of the

languages are espe

classical

tion in

owing to the oblique construc which the accusative becomes subject to the verb.

Thus

in

cially liable to this fallacy

Latin

we have

(though of course,

if

oracle

the

delivered at

it

all,

to

given

Pyrrhus

must have been

in

Greek) Aio

te,

Aeacida,

Romanes

Pyrrhus the Romans

shall,

vincere posse I

say,

2 .

subdue (IVhately),

which Pyrrhus, as the story runs, interpreted to mean he could conquer the Romans, whereas the oracle

that

subsequently explained to him that the real meaning was that the

Romans

could conquer him.

Shakspeare makes witch

1

s

the

Duke

of

York

Similar to

point

prophecy in Henry VI (Second Part, Act The duke yet lives that Henry shall depose.

A Stoic example of

d^
this,

as

out, is the

is auAiy rpls ne-nrajKf (

i,

sc. 4),

= The house

has fallen three times, or, The flute-girl has had a fall), which would rather come under the head of Aristotle s division, 423.

See D. 2

L. VII,

Cicero,

DC

62.

Div.

\\,

116

;

Quintilian, lust. Oraf.

vii. 9,

Bb

6.

OF FALLACIES.

37

An

instance of amphiboly

Windsor

Hoc

Castle

may be

read on the walls of

The

Wykeham.

fecit

king was

incensed with the bishop for daring to record that he

made he

the tower, but the latter adroitly replied that

really

meant

to indicate

To

making of him. famous sentence

me

from 423.

the

I will

was

that the tower

same head may be referred the wear no clothes to distinguish

Christian brethren.

my

The

Fallacy of Composition (o-wtfeo-ts)

wise a case of ambiguous construction.

expounded by ought Is

Of

to

be taken separately,

course

like

e. g.

man who is not Then it is possible

it is.

is

consists, as

It

words together which

Aristotle, in taking

possible for a

it

what

was the

writing to write for a

man

?

to write

without writing.

And

again

Can you carry Then you can

this, that,

carry

and the other ?

this, that,

and the

a fallacy against which horses would protest,

Yes.

other, if

they could.

It is doubtless example which has led to a convenient misuse of the term fallacy of composition

this

among modern

writers,

arguing from the

The

by

whom

it

is

defined to consist in

distributive to the collective use of a term.

Fallacy of Division

consists in

(Stcu peo-ts),

on

the other hand,

taking words separately which ought to be

taken together, 70; 1

last

e. g.

a

tOrjica.

Sov\ov OVT

f\(vdtpov

,

Evidently the original of the line in Terence s Andria, 37 feci ex servo ut esses libertus mihi.

OF FALLACIES.

371

where the separation of SoGAov from OVTO. would lead interpretation exactly contrary to what is intended.

And

an

to

again TTfVTrjKOVT

(tcaTov \tire 5fos

a.vfip jjv

A^iA-Asus,

where the separation of dvSpwv from

l/cai-ov

leads to a

ludicrous error.

Any reader whose youth may have been nourished on The Fairchild Family may possibly recollect a sentence this wise Henry/ said Mr. Are you a thief and a liar too ? miss the keen delight which can

which ran somewhat on is

Fairchild,

But

I

am

this true

afraid he will

be extracted

?

The

by modern

Henry

said,

a thief and a

Are_j>0#

424.

age from turning the tables upon

at a certain

Mr. Fairchild thus true

?

liar

is

now meant

the middle term

this

been accommodated

meaning which they have assigned

So

that

by the

fallacy of

arguing from the collective to the

of a term.

distributive use

when

is

?

fallacy of division has

writers to the

to the fallacy of composition. division

Mr. Fairchild,

too

Further,

it

is

laid

down

that

used distributively in the major and in the minor, we have the fallacy premiss collectively of composition whereas, when the middle term is used is

;

collectively in the

minor,

we have

major premiss and

the fallacy of division.

the two examples

distribulively in the

Thus

the

the second division. (i)

.-.

first

of

appended would be composition and

Two

and three are odd and even.

Five

is

two and

Five

is

odd and even.

three.

B b 2

OF FALLACIES.

372

The Germans are an intellectual Hans and Fritz are Germans.

(2)

.

As

are intellectual people.

They

.

the

possibility

of this

confined to the middle term,

when

people.

and

is

not

add

that

of ambiguity

sort

seems desirable to

major or minor term

either the

in the premiss

it

is

used distributively

we have

collectively in the conclusion,

the fallacy of composition, and in the converse case the

Here

fallacy of division.

which the minor term

in

is is

an instance of the at fault

Anything over a hundredweight

These

sacks

kind

latter

is

are

(collectively)

too heavy to

over

a

lift.

hundred

weight. ..

These sacks

(distributively) are too

The ambiguity of the

in

spoken nor

English

the

word

language

to

all

the

is

pair

heavy to

lift.

a great assistance of fallacies just

of.

425.

The

less

than a mistake in Greek accentuation.

Fallacy of Accent

(TrpocrooSta) is

more As an

neither

instance Aristotle gives Iliad xxiii. 328, where the ancient

copies of

Homer made

KaraTTvOeTai

place of ov

o//,/3/3o>

with

that the fallacy

is

nonsense of the words TO fuv ov

by writing ov with the acute accent

one which cannot

1

the circumflex in Aristotle

remarks

easily occur

in verbal

.

argument, but rather in writing and poetry. This goes to show that the ancient Greeks did not distinguish pronunciation between the rough and smooth breathing any more than their modern representatives. 1

in

OF FALLACIES. Modern

373

writers explain the fallacy of accent to be the

mistake of laying the stress upon the wrong part of a Thus when the country parson reads out, sentence.

Thou

shalt not bear false witness against thy neighbour,

emphasis upon the word against, his audience ignorant leap to the conclusion that it is not amiss to tell lies, provided they be in favour of one s with

a

strong

neighbour.

The

426.

Fallacy of Figure of Speech (TO cr^^a. T^?

results

Aeews) between the

from any confusion of grammatical forms, as genders of nouns or the different

different

voices of verbs, or their use as transitive or intransitive, e.

g.

vyiawtiv has the same grammatical form as re//eiv or

otKoSo/teiV,

but the former

A

transitive.

Socrates

of

The

intransitive, while the latter are

this

by Aristophanes

philosopher

KapSoTros

is

sophism of

is

kind in

is

put into the

there represented

(670-80). arguing that

as

must be masculine because KAewviyxos

surface this

is

mouth

Clouds

the

connected with language, but

it

is

is.

On the

essentially

a fallacy of false analogy.

To

this

head

may

be referred what

is

known

as the

Fallacy Paronymous Terms. This is a species of equivocation which consists in slipping from the use of of

one part of speech to that of another, which

is

derived

from the same source, but has a different meaning. Thus this fallacy would be committed if, starting from the fact that there is a certain probability that a

consist of thirteen trumps, that

it

was probable, or

one were

that

to

hand

at whist will

proceed to argue

he had proved

it.

OF FALLACIES.

374 427. lie

We

turn

now

to the tricks of refutation

which

outside the language, whether the deception be due to

the assumption of a false premiss or to

some unsoundness

in the reasoning.

428.

The

first

(TO o-iyx/Je/ifyKos).

list

is

the Fallacy of Accident

fallacy consists in confounding

an accidental difference, which

essential with able, since

on the This

many

same

things are the

they differ in accidents.

Here

an

not allow

in essence,

the sort of

is

is

while

example

that

Aristotle gives Is Plato different

a

man ?

To

from Socrates

Then Plato is we answer No: the Yes/

this

?

Yes.

different

Is Socrates

from man.

difference of accidents

between Plato and Socrates does not go so deep as the underlying essence.

affect

To

put the thing

to

more

assuming that whatever is dif ferent from a given subject must be different from it in all respects, so that it is impossible for them to have a

plainly, the fallacy lies in

common

Here Socrates and Plato, though predicate. from one another, are not so different but that The attempt to they have the common predicate man. prove that they have not involves an illicit process of the different

major. 429.

The

next fallacy suffers from the want of a con

venient name. Aeyeo-$cu Kal

by Aristotle TO a-7rA.ws roSe y -n-rj more briefly, TO cm-Aws 17 /U.T/, or TO

It is called

[j.r)

Kvpt ws or,

and by the Latin writers secundum quid ad dictum simpliciter.

71-77

K0

"

aTrXw?,

taking what

is

Fallacia a dicto

said in a particular respect as

It

consists

though

it

in

held

OF FALLACIES. true without

any

restriction, e. g. that

existent (TO fly oV)

non-existent

375 because the non

a matter of opinion, that therefore the

is

or again that because the existent (TO oV)

is,

is

not a man, that therefore the existent

if

an Indian, who as a whole

is

Or

not.

again,

black, has white teeth,

is

we

should be committing this species of fallacy in declaring

him in

to

More

For he

be both white and not-white.

a certain

respect

difficulty,

for instance, a thing it is

opposite

about an equal degree.

When,

arise

may

and half black, are we to This question the philoso

half white

pher propounds, but does not answer.

would seem

in

and not-white

it

Is

seems,

force of

it

lies It

such a case that a thing

may

be both white

The

fact

is

at the

same

time.

not really a

fair

so subtle

that even such a question

a thing white or not-white is

The

on the Law of Contradiction.

are the ambiguities of language as

only white (dTrAws).

white or black?

in the implied attack

is

when

(n-fj),

is

not

absolutely

says Aristotle,

qualities exist in a thing in

say that

but

straightforward as

?

We

one.

are entitled

some

times to take the bull by the horns, and answer with the

adventurous interlocutor in one of Plato

Both and

neither.

It

may be

s

dialogues

both in a certain respect,

and yet neither absolutely. The same sort of difficulties

attach

Excluded Middle, and may be met might, for instance, be urged that

to the

Law

of

same way. It could not be said

in the it

with truth of the statue seen by Nebuchadnezzar in his

dream

either that

it

made of gold: but

was made of gold or

that

it

was not

the apparent plausibility of the objec-

OF FALLACIES.

376 tion

would be due merely

It is

not true, on the one hand, that

(in the sense of being

and

it

is

to the

composed

ambiguity of language.

entirely of that metal)

not true, on the other, that

gold (in the sense of no gold

But

position).

the

let

was made of gold

it

at all

it

;

was not made of

entering inlo

its

ambiguous proposition be

com up

split

two meanings, and the stringency of the Law of Excluded Middle will at once appear

into

its

(1) It

must

either

have been composed entirely of

gold or not. (2) Either gold

must have entered

into

its

composi

tion or not.

By some of the it

writers this fallacy

is

treated as the converse

the fallacy of accident being assimilated to

last,

under the

title

Fallacia a dicto simpliciter ad

of the

dictum secundum quid. may be defined thus.

In

this

sense the two fallacies

The Fallacy of Accident consists in assuming that what holds true as a general rule will hold true under some special circumstances which may entirely alter the case.

The Converse that

Fallacy of Accident consists in assuming

what holds true under some special circumstances

must hold

true as a general rule.

The man who,

acting on the assumption that alcohol

a poison, refuses to take the doctor,

is

it

when he

is

guilty of the fallacy of accident

who, having had

it

is

ordered to do so by

prescribed for him

;

the

man

when he was

ill,

OF FALLACIES. continues to take

377

morning, noon, and night, commits

it

the converse fallacy.

There ought

be added a third head to cover the

to

fallacy of arguing from one special case to another.

430.

This

ayi ota). itself

The next

Elenchi (eAe y^ov

fallacy is Ignoratio

when by reasoning

fallacy arises

one establishes a conclusion other than what

required to upset the adversary

assertion.

s

It

an inadequate conception of the true nature of Aristotle therefore full

valid in

at the pains

is

is

is

due to

refutation.

to define refutation at

length, thus

A

refutation (eXeyxos)

same

is

the

term, but of the

synonymous

consequence from the

same term,

same

relation,

and

the

in

same

not

of a

as a necessary

assumption of the

data, without

point originally at issue, in the

and the

denial of one

not name, but thing, and by means,

respect,

same way, and

and

at

the

in the

same

time.

The

elenchus then

is

the exact

contradictory of the

assertion under the terms of the law of contra

opponent

s

diction.

To

syllogisms,

establish by a syllogism, or series any other proposition, however slightly

ferent, is to

commit

this fallacy.

the contradiction be established, the identical

Even it

if

the substance of

not enough unless

is

words of the opponent are employed

contradictory.

Thus,

thing about AWTTIOV,

if his

it is

thesis asserts or denies

in the

some

not enough for you to prove the

contradictory with regard to ipdriov.

of a further question

of dif

and answer

There to

will

identify

be need the two,

OF FALLACIES.

378

though they are admittedly synonymous. Such was the rigour with which the rules of the game of dialectic were enforced

among

Under

the Greeks

the head of

!

Ignoratio Elenchi

has become

it

usual to speak of various forms of argument which have

been labelled by the Latin writers under such names as argumentum ad hominem/ ad populum, ad verecunad ad baculum all of them diam/ ignorantiam,

By

argumentum ad reni or ad judicium. argumentum ad hominem was perhaps meant

to the

opposed

the

a piece of reasoning which availed to silence a particular

Thus

person, without touching the truth of the question. a quotation from Scripture

is

sufficient to stop the moutli

Hume

of a believer in the inspiration of the Bible.

s

Essay on Miracles is a noteworthy instance of the argu mentum ad hominem in this sense of the term. He insists strongly

he

knew

on the evidence

for certain miracles

that the prejudices of his hearers

their ever accepting,

miracles,

would prevent

and then asks triumphantly

if

which are declared to have taken place

enlightened age

which

these in

an

in the full glare of publicity, are palpably

imposture, what credence can be attached to accounts of

extraordinary occurrences of remote antiquity, and con

nected with

an obscure corner

of the

globe

?

The

argumentum ad judicium would take miracles as a whole, and endeavour to sift the amount of truth which may lie in the accounts 1

On

this

we have of them

subject

see

the

in every

author

(B. H. Blackwell, Oxford), pp. 46-59.

s

J

age

.

Attempts

at

Truth

OF FALLACIES. In

ordinary discourse

at

argumentum ad hominem

379

the

present

is

used for

day the term the form of

irrelevancy which consists in attacking the character of the

opponent instead of combating his arguments, as well-known instructions to a barrister

in the

abuse the

The

No

case

:

plaintiff s attorney.

argumentum ad populum

to the passions of one

or to give is

illustrated

it

s

consists in an appeal

An

audience.

appeal to passion,

a less question-begging name, to feeling,

not necessarily amiss.

The

heart of

man

is

the in

strument upon which the rhetorician plays, and he has to

answer

the

for

harmony or

discord that

the

comes

of his performance.

The

argumentum ad verecundiam

the feeling of reverence

much used by

or shame.

the old to the

is

It

is

an appeal to an argument

young and by Conservatives

to Radicals.

The

argumentum ad ignorantiam consists simply in on the ignorance of the person addressed, so that trading it

covers any kind of fallacy that

is

likely to

prove effective

with the hearer.

The

argumentum ad baculum

is

unquestionably a

form of irrelevancy. To knock a man down when he differs from you in opinion may prove your strength, but hardly your

A

logic.

sub-variety of this form of irrelevancy

lately at a socialist lecture in

Oxford,

at

was exhibited

which an under

graduate, unable or unwilling to meet the arguments of the speaker, uncorked a bottle, which had the effect of instan-

OF FALLACIES.

380

This might be

taneously dispersing the audience.

down a

set

argumentum ad nasum. 431. We now come to the Fallacy of the Consequent, term which has been more hopelessly abused than any. as the

What the

meant by

Aristotle

consequent

in

same thing

and

is

was simply the assertion of the

it

a conjunctive proposition, which amounts to as the simple conversion of

a fallacy of distribution.

Aristotle

s

A

(

219),

example

is

this

If

has rained, the ground

If the

/.

This

it

fallacy,

ground

he

in dealing with

tells

is

wet,

is

us,

it

is

wet.

has rained.

often

employed

in rhetoric

Thus

a speaker,

presumptive evidence.

wanting to prove that a man is an adulterer, will argue that he is a showy dresser, and has been seen about at

Both these things however may be the

nights.

case,

and

yet the charge not be true.

The

432.

Fallacy of Petitio

or

(TO Iv apxfj aiTeia-OaL or A.a u/3ai/etv) to (

consists in

The word

an unfair assumption of the point aireto-$cu in Aristotle s

Greek method of This

answer.

Assumptio Principii which we now come,

dialectic

name

for

it

at

issue.

points to the

by means of question and

fact is rather disguised

by the mysterious The fallacy would be begging the question. committed when you asked your opponent to grant,

phrase

overtly

or covertly, the very proposition originally pro

pounded

As

for discussion.

the

question of the precise nature of this fallacy

OF FALLACIES. of

is

some importance we

himself (Top. question in

one takes

viii.

13,

five

but in the case of

and most

First

glaringly,

itself

when to

be

does not readily escape detection,

"

that

synonyms,"

is,

where the name

definition

! .

which has taking to

were

People seem to beg the

3):

have the same meaning, it does so more Secondly, when one assumes universally that

and the easily

words of Aristotle

granted the very thing that has

for

This by

proved.

will take the

2,

ways.

381

to

be proved in particular,

to

prove that

assume

that

as, if

a

man under

there

is

one science of

there

is

one science of opposites

For he seems to be taking with several other things what he ought

contraries,

for granted

along have proved by itself. Thirdly, when one assumes the particulars where the universal has to be proved for in so doing a man is generally.

to

;

taking for granted separately what he was

the question at issue by splitting

when

the point to be proved

deals with health

by

itself

for

and

granted.

bound

to prove

Again, when one assumes

along with several other things.

up, for instance,

if,

one were to take each

disease,

Lastly,

it

that the art of medicine

is

if

one were

to

take for

granted one of a pair of necessary consequences, as that 1

Some

light is

obscure passage by a com synonym is defined. To take modern sense affords an easy countenanced by Alexander Aphrodisien-

thrown upon

this

parison with Cat. I, 3, where the word here in its later and interpretation, sis,

but

it

which

is flat

is

against the usage of Aristotle,

who elsewhere

gives the name synonym, not to two names for the same thing, but to two things going under the same name. See Trendelenburg

on the passage.

OF FALLACIES.

382 the side

is

incommensurable with

when

the diagonal,

required to prove that the diagonal

is

it is

incommensurable

with the side.

To sum up

we may beg

briefly,

the question in five

ways (1)

By

simply asking the opponent to grant the point

which requires (2)

to be

proved

;

by asking him to grant some more general which involves it

truth

;

(3)

by asking him it

(4)

involves

to grant the particular truths

by asking him in detail

(5)

to grant the

The

component

parts of

it

;

by asking him of

which

;

grant a necessary consequence

to

it.

of these

five

ways, namely, that of begging

the question straight

off,

lands us in the formal fallacy

first

already spoken of

417), which violates the

(

general rules of syllogism,

derived from a single premiss, to wit,

The in

first

of the

inasmuch as a conclusion itself.

second, strange to say, gives us a sound syllogism

Barbara, a

fact

which countenances the blasphemers

of the syllogism in the charge they bring against

containing in itself a petitio principii. expression might have been clear that his quarrel in

is

is

such an argument.

it

of

Certainly Aristotle s

more guarded.

But

it

is

with the matter, not with the form

The

fallacy consists in

assuming

a proposition which the opponent would be entitled to

OF FALLACIES. Elsewhere Aristotle

deny.

when a

us that the fallacy arises

tells

not evident by

truth

383

own

its

is

light

taken to

be so \

The

third

an

us

gives

mode

simplicem, a

per enumerationem

inductio

of argument which would of course

be unfair as against an opponent

who was denying

the

universal.

The The (

fourth

more

a

is

prolix form of the

first.

on Immediate Inference by Relation

rests

fifth

238).

Under

the head of petitio principii

of Arguing in a Circle, which

In

reasoning.

its

comes

the fallacy

incidental to a train of

is

most compressed form

it

may be

repre

sented thus

B C C

(i)

.-.

433.

The

ws alnov)

is

is

A.

is

B.

is

A.

(2)

.-.

A.

is

C.

is

A.

Non

another,

complete misinterpretation.

consists in

It

contradiction into the discussion, controverted.

Aristotle, often impose

The

is

causa pro causa (TO /AT) amov the name of which has led to a

Fallacy of

on the position

C B B

instance he gives

upon is

importing a

and then fathering it Such arguments, says

the users of

them themselves.

too recondite to be of general

interest.

434. Lastly, the Fallacy of 1 "OTO.V

TO

TO t

/XT)

5i

avTOv

apxfjs.

-yvu0Toi>

Anal. Pr.

Si

Many

avrov

II. 16,

TIS I

Questions (TO

emxtipy ad fin.

TO.

Sewifvvai, TOT

OF FALLACIES.

384

form of interrogation, demanded to what is not really

St o lpwT^fj,ara ev Troteu/) is a deceptive

when a

single

answer

a single question.

is

In dialectical discussions the respon

dent was limited to a simple fallacy the question

is

yes

no

or

so framed as

;

and

that either

in this

answer

would seem to imply the acceptance of a proposition which would be repudiated. The old stock instance will Come now, sir, answer do as well as another "yes"

or

"no."

Have you

left

off beating

your father yet

1

?

Either answer leads to an apparent admission of impiety.

A

late Senior

Proctor once enraged a

with this form of fallacy.

horse

;

The man was

at

and the distinguished stranger asked him

what did you paint your horse 1

man

D. L.

II,

135.

a fair

exhibiting a blue

With

?

Another form

desierisne facere adulterium an non.

is

Postulo uti respondeas, Aul. Cell. XVI. 2, 5.

EXERCISES.

c c

EXERCISES. (Key sent by the author on receipt of Address

16

Museum Road,

PART

3^. 6d.

Oxford.)

I.

CHAPTER

I.

Classify the following words according as they are categorematic, syncategorematic, or acategorematic :

come

peradventure

why

through

inordinately

pshaw

therefore

circumspect inasmuch

puss

sameness

back

disconsolate

candle.

grand touch cage

CHAPTER

stop

II.

Classify the following things according

stances, qualities, or relations

as

they are sub

:

God

likeness

weight

blueness

grass

ocean

introduction

imposition thinness

man

air

spirit

Socrates

raillery

heat

mortality

plum

fire.

c c 2

EXERCISES.

388

CHAPTER 1.

Give

privative, 2.

and

each of

six instances

and

Select from the following list of words such as are terms, whether they are (i) abstract or concrete, (2) sin

common,

(3)

univocal or equivocal: table

however

very

decidedly butt

tiresome

infection

bluff

Czar

short

although

Caesarism

elderly

Nihilist.

van enter

distance

4.

Which

Solomon

of the following words are abstract terms

?

quadruped

event

through

hate

desirability

thorough

fact

thoroughness

faction

expressly wish

inconvenient

will

garden

inconvenience

volition

grind.

light

Refer the following terms to their proper place under

each of the divisions

5.

attributive, abstract, singular,

relative terms.

state

gular or

3.

III.

in

the scheme

:

horse

husband

London

free

lump

empty

liberty

rational

capital

impotent

reason

Capitol

impetuosity

irrationality

grave

impulsive

double

platinum.

Give

six

instances

each of proper names and desig

nations. 6.

Give

six instances

tative terms.

each of connotative and non-conno-

EXERCISES. 7.

389

Give the extension and intension of

sermon

animal

sky

clock

square

gold

sport bird

fish

element

student

fluid

art

river

line

gas

servant

language.

CHAPTER Arrange the following terms nivorous, thing, matter, substance, animal.

IV.

order of extension

in

mammal, organism,

PART

II.

CHAPTER

I.

Give a name to each of the following sentences (1) Oh, that

I

had wings

like a

(3)

(4)

Is

(5)

Hearts

there balm in Gilead

may be

:

dove!

The more, the merrier. Come rest in this bosom, my own

(2)

car

vertebrate, cat,

stricken deer.

?

trumps.

CHAPTER

II.

Analyse the following propositions into subject, copula, and predicate

:

(1)

He

(2)

There are

being dead yet speaketh.

(3) Little (4)

There

foolish politicians.

does he care. is

a land of pure delight.

EXERCISES.

39 (5) All s well that (6)

Sweet

(7)

Now

(8)

Who

(9)

Great

came

it

ends well.

the breath of morn,

is

runs

to pass that the beggar died.

read.

may

Diana of the Ephesians.

is

Such things are. (n) Not more than others I deserve. (12) The day will come when Ilium s towers (10)

CHAPTER ..

Express (1)

in logical

Some swans

shall perish.

III.

form, affixing the proper symbol

:

are not white.

(2) All things are possible to

them

that believe.

No

(3) politicians are unprincipled. (4) Some stones float on water. (5)

The snow

(6)

Eggs are

(7) All

(8)

has melted.

edible.

kings are not wise.

Moths are not

butterflies.

(i i)

Some men are born great. Not all who are called are chosen, It is not good for man to be alone.

(12)

Men

(9)

(10)

(13)

of talents have been

Tis none but a

known

bullet does not

Every

(15)

Amongst Unionists are Whigs. Not all truths are to be told. Not all your efforts can save him. The whale is a mammal.

(17) (

r

8)

(19)

Cotton

(20)

An

(21)

No news is good news No friends are like old

(22)

is

honest

grown

man

fail in life.

s

about

kill.

(14)

(16)

to

madman would throw

in

Cyprus. the noblest work of God.

friends.

fire.

EXERCISES.

391

(23) Only the ignorant affect to despise knowledge. (24) All that trust in Him shall not be ashamed. (25) All is not gold that glitters. (26)

The

(27)

Not

to

(28)

The

king, minister,

(29)

Amongst dogs

(30)

A

sun shines upon the evil and upon the good. go on is to go back.

fool

is

and general are a pretty trio. are hounds.

not always wrong.

(31) Alexander

was magnanimous.

(33)

Food is necessary to life. There are three things to be

(34)

By penitence

(35)

Money is Few men

(32)

(36)

(37) All

the Eternal

the miser

succeed

is lost,

s

s

considered.

wrath

s

appeased.

end.

in life.

save honour.

is mean to hit a man when he is down. Nothing but coolness could have saved him. (40) Books are generally useful. (41) He envies others virtue who has none himself. (42) Thankless are all such offices.

(38) It (39)

(43)

Only doctors understand this subject. two were correct.

(44) All her guesses but

were twelve. seldom charitable.

(45) All the Apostles

(46) Gossip

is

(47) Better to play for nothing than (48) All

(49)

We have

Give

2.

quantify

men have

six

work

examples of indefinite propositions, and then

them according

to their matter.

propositions

of each of the following

:

(1)

(2) (3)

with

for nothing.

faith.

no king but Caesar.

Compose three

3.

kinds

not

common

terms for subjects

;

with abstract terms for subjects with singular terms for predicates ;

;

EXERCISES.

392

(5)

with collective terms for predicates with attributives in their subjects

(6)

with abstract terms for predicates.

(4)

CHAPTER 1.

IV.

Point out what terms are distributed or undistributed

in the following propositions

:

(2)

The Chinese The angle in

(3)

Not one of the crew

(4)

The weather

(1)

The same

are industrious. a semi-circle

is

a right angle.

may be performed upon any

exercise

Prove that

is

survived.

sometimes not propitious.

positions in the preceding 2.

;

;

of the pro

list.

in a negative proposition the predicate

must

be distributed.

CHAPTER Affix its proper

V.

symbol to each of the following proposi

tions: (1)

No

(2)

There are Irishmen and Irishmen.

lover he

who

Of

Some

(5)

No

(8)

only disagree,

creatures rational.

(4)

(7)

not always fond.

Men

(3)

(6)

is

wise

men

Popes are

are poor.

some

fallible beings.

Some step-mothers are not unjust. The most original of the Roman poets was Some of the immediate inferences are all

Lucretius. the forms

of conversion. (9)

(10)

quidquid honestum

est,

idem

utile videtur,

nee

utile

quidquam,quodnon honestum. Cic.de Ojf. Ill, 20. Dead languages are not the only ones worth studying.

EXERCISES.

CHAPTER 1.

Give

six

393

VI.

examples of terms standing one to another as

genus to species. 2.

To

which of the heads of predicables,

refer the following statements (1)

A

circle

is

by one (3)

And why

if

would you

any,

?

the largest space that can be contained

line.

(2) All the angles of a

Man

?

alone

among

square are right angles. animals possesses the faculty of

laughter. (4)

Some

(5)

Most

(6) All

3.

fungi are poisonous.

natives of Africa are negroes.

democracies are governments.

(7)

Queen Anne

(8)

A

(9)

An

dead.

is

the animal you saw yesterday. honest man s the noblest work of God.

horse

is

In what relation do these attributes stand to an isosceles

triangle

?

(1) that the angles at the

base are equal;

(2) that the three angles are equal to

CHAPTER

two

right angles.

VIII.

Examine the following attempts at definition both by the If you are dissatisfied with material and by the formal rules. where of them, substitute, you can, a better definition. any Point out any that seem to you to coincide in meaning. (1)

An

acute-angled triangle

is

one which has an acute

angle. (2)

An archdeacon

is

one who exercises archidiaconal

functions. (5)

Architecture

is

frozen music.

EXERCISES.

394 (4)

An

attributive

a

is

term which cannot stand

as a

subject. a.

(5)

b.

(6)

Bread Bread

is

the staff of

is

food

in

life.

the form of loaves.

A candle is a kind of light used before gas was invented. it

The

cause of anything is the antecedent which Mill (III. 5, invariably follows. 5).

a.

(7)

b. The cause of a phenomenon is the antecedent, or the concurrence of antecedents, on which it is

Ibid. invariably and unconditionally consequent. c. cause is the assemblage of phenomena, which

A

some other phenomenon

occurring,

mences, or has d.

A

cause

invariably

Mill (III.

its origin.

5,

com

6.)

that without which something would

is

not be. (8)

Caviare

is

(9)

A

is

circle a.

(10)

a kind of food. a plane figure contained by one line.

A citizen

is

a person both of

whose parents were

citizens.

A

b. citizen is one who is qualified to exercise Arist. Pol. III. deliberative and judicial functions.

12.

i, c.

A

citizen

is

a

man who

pays taxes,

(n) Credit is the bond of society. a. Death is the separation of the (12) body.

soul

from the

Plato, Phaedo.

b.

Death

c.

Mors

is

the extinction of the

vital forces.

naturae animantium dissolutio.

est

Lac-

tantius. d.

Mors

e.

Death

est aeterni doloris perpessio. is

(13) Deliberation is

the end of is

Ibid.

life.

that species of investigation

concerned with matters of action.

which

EXERCISES.

A A A

a.

(14)

b, c.

(15) (16)

An

an animal of the canine species.

dog

is

dog

is

a domestic animal that barks.

dog

is

a wild animal that howls.

eccentricity

by speech or

Fame

(18)

A

is

fault

is

the

is

Eloquence

(17)

395

power of influencing the life in

others breath.

quality productive of evil

a

feelings

writing.

a fancied is

a peculiar idiosyncrasy.

or incon

venience. a.

(19)

A

gentleman

a

is

person

who moves

in

good

society. b.

A

gentleman

is

a

man who

respects himself and

others. c.

A

is a person who has no visible means The Tichborne Claimant. A gentleman is a person who has nothing to do

gentleman

of subsistence. d.

and does e.

it.

A gentleman

is

a

man

of gentle birth and gentle

manners. f. a.

(20)

b. c.

a

(21)

A gentleman is a man of independent means. Grammar is the science of language. Grammar is a branch of philology. Grammar is the art of speaking and writing

language with propriety. a. b.

Humour is thinking in jest while feeling in earnest. Humour is the perception of unexpected incon

gruities.

(22)

a.

Induction

is

the operation

of discovering and

proving general propositions. Mill (III. i, 2). is b. Induction experience or observation con Whewell. sciously looked at in a general form. c.

that

is the process by which we conclude true of certain individuals of a class is

Induction

what

is

EXERCISES.

396

of the \vhole class, or that what is true at be true in similar circumstances

true

certain times will at

all

Mill (III.

times.

2,

i).

the colligation of facts by means of 4. appropriate conceptions. See Mill III. 2, d.

Induction

e.

Induction

Mill (III. (23)

3,

is

is

from Experience.

Generalisation

i).

Horace.

a.

Ira furor brevis est.

b.

Ira cupiditas est poenae exigendae.

c.

Ira est cupiditas puniendi eius, a

Seneca.

quo

Posidonius (apud Lact.). Ira est incitatio animi ad nocendum

te inique

putes laesum. d.

ei,

qui aut

nocuit, aut nocere voluit.

(24)

motus animi ad coercenda peccata

Ira est

e.

gentis.

a. Justice is

minding one

being meddlesome. b.

is

Justice

man

insur-

Lactantius. s

own

business and not

Plato.

an inner state of the soul that sets a

peace with himself and the world. Justice is that sort of state in consequence of at

c.

which men are able to do what is just, and in con sequence of which they deal justly, and wish for

what d.

you e.

is

Arist. E.

just.

Justice

is

f. Justice to one s foes. g. Justice

(25)

(26)

N.

v. i,

3.

Justice is telling the truth and restoring have taken.

s

friends

is

doing good

is

the interest of the stronger.

and harm

that dimension of a solid which would be

Length measured by the longest is

Simonides.

rendering to each his due. to one

what

line.

Win wood

a.

Life

is

bottled sunshine.

h.

Life

is

the opposite of death.

Reade.

EXERCISES. c.

Life

397

the definite combination of heterogeneous

is

changes, both simultaneous and successive, in corre spondence with external coexistences and sequences.

Herbert Spencer. (27)

a.

Logic

is

the science of the formal laws of thought.

Sir William Hamilton. b.

Logic

may be

considered as the science and also

as the art of reasoning.

Whately.

the science which treats of the operations of the human understanding in the pursuit of truth. c.

Logic

is

d. Logic is the science of the operations of the understanding which are subservient to the estimation of evidence : both the process itself of advancing from known truths to unknown, and all other in

tellectual

operations Mill (Introd. 7). e.

Logic

is

in

so far as auxiliary to this.

the science of proof or evidence.

the entire theory of the ascertainment of reasoned or inferred truth. f. Logic

g. Logic

is

is

the

science

Truth by means of Evidence. h.

Logic

is

of the

Investigation Mill (III. 5, 2).

the Art of Thinking, which

of

means of

correct thinking, and the Science of the Conditions of correct thinking. Mill (Exam, of Sir Wm. H.,

3rd ed. p. 448). /.

dans

La la

logique est 1 art de bien conduire sa raison connaissance des choses, tant pour s instruire

soi-meme, que pour en instruire

les autres.

Logique

de Port Royal. j.

Logic

is

the science of the conditions on which

correct thoughts depend, and the art of attaining to correct and avoiding incorrect thoughts. Fowler. k. Logic is the science of argument, and proof. Palaestra Logica.

i.e.

of inference

39 8

EXERCISES. Love is the opposite of hatred. Love is the fulfilling of the law. Love is the union of hearts.

a.

(28)

b. c.

Man is an animal that makes exchanges. Man is a rational biped. Man is a religious animal. Man is a self-conscious rational mind-entity,

a.

(29)

b. c.

d.

volved in body.

Man Man

e.

f.

means of

in

Laurie.

born of human parents.

is

any being that

is

an animal that expresses general ideas by

is

signs. is

(30) Necessity

the mother of invention.

(31) Nec-manifestum furtum quid sit, ex iis quae diximus nam quod manifestum non est, id sci intellegitur licet nec-manifestum est. Justinian (Inst. IV. i, 3). ;

(32)

A

net

is

(33)

Noon

is

a collection of holes strung together.

the time

when

the shadows of bodies are

shortest.

(34)

North

is

the direction in which

we

look towards the

position of the sun at midnight. (35)

An

oligarchy

is

the supremacy of the rich in a state.

Arist. Pol.

(36)

A

parable

is

a

heavenly

story

no

with

earthly

meaning. (37)

A

(38)

Peace

(39)

parallelogram is a four-sided figure, opposite sides parallel and equal.

a.

is

having

its

the absence of war.

Philosophy

is

the rule of

life.

the attempt of man to ascertain his relations to God, to the universe, and to his fellowb.

Philosophy

is

creatures. c.

ratio.

Philosophia nihil aliud est Seneca.

quam

recta vivendi

EXERCISES. (40)

A

plant

399

an organised being possessing vegetable

is

life.

(41) Politeness

the

is

that lubricates

oil

the wheels of

society.

(42)

Prudence a.

(43)

the ballast of the moral vessel.

is

The ridiculous

is

some

fault or ugliness,

unaccom

panied with pain, and not tending to destruction. Arist. Poet. b.

The

ridiculous

is

that

which gives you a sense

of superiority. (44) Rust is the red desquamation of old iron. (45) The sun is the centre of the solar system. (46)

is the recognition, adjustment and mainten ance of the proper and fitting relations of the

Sense

of ordinary life. (47) Superstition is a tendency to look for constancy where constancy is not to be expected. affairs

(48)

(49)

A

tip is an extra gratuity paid out of good-will, over and above what can be demanded by contract. a.

Virtue

the capacity of ruling over men.

is

Plato,

Meno. b.

Virtue

attain

to desire noble things and

is

them.

be able to

Ibid.

c.

Virtue

d.

Virtue

is

the procuring good things justly.

e.

Virtue

is

is

Ibid.

acting virtuously. that line of conduct which tends to

produce happiness. f. Virtue

is

the preference for the desire which

is

be higher over that which is felt to be lower. Virtus est vitium fugere. Horace. g.

felt to

h.

Virtus est

malis

ac

vitiis

fortiter

repugnare.

Lactantius. /. Virtus est iram cohibere, cupiditatem compescere, libidinem refraenare. Lactantius.

j.

Virtue

is

the will to do right.

EXERCISES.

400 k.

Virtue

the control of the feelings and actions

is

by reason. (50)

a.

Wealth

veniences of b.

Wealth

is

sum of the

the

is

all

useful or agreeable things

possess exchangeable value. c.

Wealth

d.

is

which

Mill.

the possession of the valuable by the

Ruskin.

valiant.

e.

necessaries and con

life.

Wealth Wealth

contribute to

is is

the material means to happiness. is held to

any material product which

human

happiness.

CHAPTER

IX.

Criticise the following as divisions (1)

Books

(2)

Chair into

into octavo, quarto, green,

and

blue.

back, legs, arms. arm-chair, rocking-chair, cane-bottomed chair,

a. seat, b.

(3) (4)

(5)

(6)

wooden chair. Church into Gothic, episcopal, high, and low. Ends into those which are ends only, means and ends, and means only. Figure into curvilinear and rectilinear. Great Britain into England, Scotland, Wales, and Ireland.

(7)

(8) (9)

Horses into race-horses, hunters, hacks, thorough breds, ponies, and mules. Library into public and private. Pictures into sacred, historical, landscape, and mytho logical.

(10) Plant into stem, root, and branches, (n) Science into physical, moral, metaphysical,

medical.

and

EXERCISES.

401

(12) Ship into frigate, brig, schooner, and merchant-man. (13) Thing into good, bad, and indifferent. (14) Triangle into a.

acute-angled, right-angled, and obtuse-angled.

b.

equilateral, isosceles,

(15) Vertebrate

and (16)

and scalene.

animals into quadrupeds, birds,

fishes,

reptiles.

Warship

into battle-ship, cruiser, coast defence vessel,

torpedo-boat, and destroyer.

PART

III.

CHAPTER What (1)

principles are referred to here

Nee eventus modo hoc docuit (stultorum iste magister est), sed eadem ratio, quae fuit futuraque, donee res eaedem manebunt, immutabilis est. Liv. XXII. 39,

(2)

10.

Agitur de parricidio, quod sine multis causis suscipi

non potest agitur,

;

qui

apud homines autem prudentissimos intellegunt

quidem maleficium Rose.

Am.

What (i)

I

Pro

Cic.

de nilo posse fatendumst. Lucr.

CHAPTER inductive methods,

following examples

neminem ne minimum

sine causa admittere.

73.

(3) Nil igitur fieri

1.

V.

if

I.

205.

IX. any, are employed in the

?

own myself

entirely satisfied

.

.

.

that there

such thing as colour really inhering bodies, but that it is altogether in the

what confirms me

in this opinion

is

is

no

external

in

light.

And

that in propor-

Dd

EXERCISES.

402

tion to the light colours are

still

more or

less vivid

;

there be no light, then are there no colours perceived. Berkeley (Eraser s edit. Vol. I, p. 277).

and

(2)

if

Wealth causes

Christianity, for the wealthiest nations

are Christian. (3)

He

said he had always throughout Kerry found that wherever there was a local branch of the National League actively working there were also Moon lighters

;

and he believed they were connected.

Standard, Nov. 30, 1888. (4)

Professor Zdekauer, the first authority in Russia, said he had witnessed five epidemics of cholera, each of

which was preceded by an epidemic of influenza,

now raging. He considered it highly pro bable that the present disease would be succeeded by cholera next spring. Standard, Dec. 2, 1889. such as that

(5)

The

increase of agrarian crime, say the Judges, was coincident with the activity of the Land League, and

the decrease of agrarian crime with the inactivity of the Land League. Standard, Feb. 14, 1890. (6)

In reply to my question about the porpoise-grease with which his body was anointed, Captain Webb

informed

me

him

of course this point could settled by the direct experience of a performing a feat under exactly similar

at

all

only be

swimmer

know

that he did not

...

that

conditions both with and without the

News, Sept. 2.

What

principle

A

is

it

helped

However

oil.

Daily

17, 1875.

appealed to here

?

different cause,

says

Doctor

The same

may

give

effect

Sly,

:

Poor Lubin weeps lest he should His wife, lest he should live.

die,

PRIOR.

EXERCISES.

CHAPTER 1.

Found arguments upon the (1)

(2) (3) (4)

As health

the body

:

:

403

XI.

following analogies virtue

:

:

the soul.

a law statesmanship. As a picture painting As the eye the body Athens Greece. its As the size of the universe that of Socrates power, wisdom, and thought that of Socrates. As fallacies the doctrine of false notions logic :

:

:

:

:

:

:

:

:

:

:

:

(5)

:

:

:

the interpretation of nature. Christ wives their husbands. (6) As the Church As reason the sensible world the intellec speech (7) :

:

:

:

:

:

:

:

:

tual world. (8)

As assertion and denial avoidance

2.

Show how (1) (2)

3.

:

:

the intellect

:

pursuit and

the following lend themselves to metaphor

As the bowl As old age :

:

Bacchus

life

:

:

:

:

the shield

evening

:

Ares.

:

day.

Criticise the following

tempore

(ut fluvio) leviora et

magis

inflata

devehente, graviora et solida mergente. 4.

:

the emotions.

ad nos

Bacon.

Exhibit the analogy that underlies these metaphors

The great question which is now before the United Kingdom might be called Local Option in Government, just as the Bill Sir William

Harcourt

to-day might be described as Daily Chronicle, Feb. 27, 1893. 5.

Home

is

to introduce

Rule

in

Drink.

Examine the following argument is to building what literature is to language. No nation is without some kind of literature. .*. No nation is without some kind of architecture.

Architecture

D d

2

EXERCISES.

404

CHAPTER 1.

XIII.

Give the logical opposites of the following propositions

Knowledge

(1)

(2) All

is

never useless.

Europeans are

civilised.

(4)

Some monks are not illiterate. Happy is the man that findeth wisdom.

(5)

No

(6)

Every mistake

(7)

Some

(3)

material substances are devoid of weight. is not culpable.

Irishmen are phlegmatic.

2. Granting the truth of the following propositions, what other propositions can be inferred by opposition to be true or

false?

Men of science are often mistaken. He can t be wrong, whose life is in

(1) (2)

(3) Sir

The soul that sinneth it women are not vain.

(4)

the right.

Walter Scott was the author of Waverley. shall die.

(5) All 3.

Granting the

falsity

of the following propositions, what

other propositions can be inferred by opposition to be true or false?

Some men

(1)

are not mortal.

Air has no weight. (3) All actors are improper characters. (4) None but dead languages are worth studying. (5) Some elements are compound.

(2)

4.

Examine

Now

if

this

Christ

argument is

preached that he hath been raised from

the dead, how say some resurrection of the dead

is no no resur rection of the dead, neither hath Christ been raised. i

Cor. xv.

12, 13.

among you ?

But

if

that there

there

is

EXERCISES. 5.

405

Explain and illustrate these statements

To

establish the universal

is

more constructive

of your

own

position than to establish the particular. To refute the particular is more destructive of your opponent s position than to refute the universal. All statesmen are dishonest.

6.

This statesman

is

not dishonest.

Can the above propositions (1)

be both true,

(2)

be both false?

What name would you

give to

them

in relation to

one

another? 7.

Why

do we derive more information from refuting from refuting a universal ?

a particular than 8.

Why

the opposition between sub-contraries apparent,

is

not real

?

CHAPTER

XIV.

1. Give, as far as possible, the logical converse of each of the following propositions

(1) (2)

(3)

Energy commands

success.

Mortals cannot be happy. There are mistakes which are criminal.

ends well.

(4)

All s well that

(5)

Envious

(6)

A

(7)

Some Frenchmen

term

men is

are disliked.

a kind of

(8) All things in

word or

collection of words.

are not vivacious.

heaven and earth were hateful to him.

The

square of three is nine. (9) (10) All cannot receive this saying. (11)

The magic

of property turns sand into gold.

EXERCISES.

406

He who

(12)

Will

fights

and runs away

live to fight

another day.

am what I am. Some dogs are larger I

(13) (14)

than some ponies.

(16)

Someone has blundered. P struck Q^

(17)

Amas.

(15)

2.

In the following passages

correct

is

the use of logical language

?

(r)

More

(2)

heaven or earth: but the converse pro position is by no means true. If Mr. Chamberlain had learned logic, he would be

things

may be contained

in

my

philosophy than

exist in

aware that a proposition does not imply its converse. Being a practical man, he must know that he is

From the perfectly gratuitous talking nonsense. assumption that the Liberals will not be able to Church in Wales he draws the wholly erroneous inference that the Tories are both able disestablish the

and willing to do (3)

so.

That great wits are

to

Daily News, Jan. i, 1892. madness near allied has become

Unluckily the world forgets that the proposition, even if true, is not convertible, as logicians say. Genius may be akin to

a proverb consolatory to the world.

madness, but its

shape?,

is

it

does not follow that madness,

akin to genius.

Daily News,

in all

May

23,

1891. (4)

The Democrats

themselves admitted that, if they could not carry the Empire State, there would be a Republican President. They have carried it, and, though a proposition does not necessarily imply its converse, their hopes will of course be immensely raised. Daily News, Nov. 5, 1891.

EXERCISES.

CHAPTER

407

XV.

Obvert the following propositions (1) All just acts are expedient. (2) (3) (4)

No display of passion is politic. Some clever people are not prudent. Some philosophers have been slaves.

The same

exercise

may

be performed upon any of the

propositions in the preceding

lists.

CHAPTER 1.

XVI.

Give the converse by negation of

women are lovely. Some statesmen are not

(1) All

(2)

practical.

lawyers are honest. All doctors are skilful. (4) (5) Some men are not rational. (3) All

(6) 2.

Some

tyrants have not been unprosperous.

Give the converse by contraposition of (1) All solid

(2) All (3) (4)

the

substances are material.

men who do

not row play cricket.

impeccable beings are other than human. Some prejudiced persons are not dishonest.

All

(5) All

the pieces that are not white are red. white are not red.

(6) All the pieces that are (7)

No A

(8)

Some wholesome

(9) All

(10)

is

not-A.

No good men

(n) Some sandy 3.

things are not pleasant.

metals are elements. are insincere.

soils

are not unfertile.

Prove indirectly the truth of the contrapositive of All

A

is

B.

EXERCISES.

408

Criticise the following as

4.

All wise

(1)

men

immediate inferences

are modest.

/.

No immodest men

.

.

Some German students are not industrious. Some industrious students are not Germans.

.

.

.

.

(2)

are wise.

Absolute difference excludes

(3)

(4)

(5) .

.

all

likeness.

Any likeness is a proof of sameness. None but the brave deserve the fair. All brave

men

deserve the

fair.

All discontented men are unhappy. No contented men are unhappy.

Books being a source of instruction, our knowledge must come from our libraries.

(6)

All

(7) .

Some non-Semitic

.

Wherever the Wherever the

(8) .

(9) .

Jews are Semitic.

.

.

people are not Jews.

kitten

is,

the cat

is.

cat

the kitten

is.

is,

None but metaphysicians understand Hegel. Some metaphysicians understand Hegel. All the equilateral triangles are all the equiangular.

(10) /.

Any

triangle

which

is

not equilateral

is

not equi

angular, All wise

(i i) .

(12)

5.

.

No

men are cautious. men are incautious.

unwise

Anima, inquit, quae peccaverit, ipsa morietur. Ergo quae non peccaverit, ipsa vivet. 8. Hurter.) (St. Jerome Ep ut. IX.

Show by what kind

of inference each of the subjoined

propositions follows from All discontented (1) All (2)

men

are unhappy.

happy men are contented.

Some

discontented

men

are unhappy.

EXERCISES.

409

Some contented men are happy. (4) Some unhappy men are not contented. (5) No discontented men are happy. (6) Some happy men are contented. (7) Some contented men are not unhappy. (8) Some unhappy men are discontented. (9) No happy men are discontented. (10) Some discontented men are not happy, (u) Some happy men are not discontented. (12) None but unhappy men are discontented. From how many of these propositions can the original one And why not from all be derived (3)

?

?

6.

Why

does conversion by contraposition only apply by

limitation to

Why

does

E? not apply at

it

of the proposition 7.

From

Some

All not-x

is

y does

(1) (2)

Show

all

to

I ?

Illustrate this

by means

things are substances. it

Some x Some x

follow that is

y,

is

not y

?

the relation of these two propositions to the original.

8. Show that the contradictory of E is the same as the converse of the contradictory of its converse by limitation.

CHAPTER 1.

What

None

(1) .*.

No

.

A B

(2)

2.

kind of inference have

.

Draw

but the ignorant despise knowledge.

wise

is is

XVII.

we here?

man

despises knowledge.

superior to B. inferior to A.

inferences

from the following propositions

Philip was the father of Alexander.

The Roman

as,

in

the later ages of the Republic, was

reduced to the twenty-fourth part of

its

original value.

EXERCISES,

410

CHAPTER 1.

Convert the following propositions

(2)

If a man is wise, he is humble. Where there is sincerity, there

(3)

When

(4)

The

(1)

2.

XVIII.

(5)

If there

(6)

Not

Express

is

no

were no void, all would be solid. is sometimes to go back.

to go on

in a single proposition

he was divine, he was not covetous covetous, he was not divine. If

3.

affectation.

night-dogs run, all sorts of deer are chased. nearer the Church, the further from God.

;

and

if

he was

Exhibit the exact logical relation to one another of the

following pairs of propositions (1)

be false, the premisses are false. conclusion be true, the premisses are not

If the conclusion If the

necessarily true. (2)

If

one premiss be negative, the conclusion must be negative.

conclusion be negative, one of the premisses must be negative.

If the

(3)

The

truth of the universal involves the truth of the

particular.

The

falsity

of the particular involves the falsity of

the universal. (4)

From

the truth of the particular no conclusion follows

as to the universal.

From the falsity of

the universal no conclusion follows

as to the particular. (5)

If the conclusion in the fourth figure

be negative, the

major premiss must be universal. If the major premiss in the fourth figure be the conclusion must be affirmative.

particular,

EXERCISES. (6)

If

411

both premisses be affirmative, the conclusion must

be affirmative. be negative, one of the premisses

If the conclusion

must be negative. (7)

Who once Who once

has doubted never quite believes. believed will never wholly doubt.

The Method

4.

of Agreement stands on the ground that is not connected

whatever circumstance can be eliminated with the

phenomenon by any law

;

Method of Difference

the

stands on the ground that whatever circumstance cannot be Do eliminated is connected with the phenomenon by a law.

these

two

principles imply

one another

CHAPTER

?

XIX.

Fill up the following enthymemes, mentioning to which order they belong, and state which of them are expressed in

problematic form (1)

I

am fond of music for I always like a comic song. men are born to suffering, and therefore you ;

(2)

All

(3)

must expect your share. Job must have committed some secret he

fell

sins:

for

into dreadful misfortunes.

(4)

Latin was the language of the Vestals, and therefore

(5)

None but

(6)

The human

no lady need be ashamed of speaking

it.

physicians came to the meeting. were therefore no nurses there.

There

soul extends through the whole body,

in every member. be trusted, and you are a traitor. Whatever has no parts does not perish by the

for

No

it is

found

traitor can

dissolution of

man

is

its

parts.

imperishable.

Therefore the soul of

EXERCISES.

412

The

(9)

Christ had to suffer and to rise from the dead.

This

Jestis,

Acts

Christ. (10) .

.

Is

whom

I

preach unto you,

is

the

xvii. 3.

Both health and wealth may be used well or is a good in itself.

ill.

Neither health nor wealth

the suppressed premiss in any case disputable on material

grounds

?

CHAPTERS XX

XXVIII.

I.

Refer the following arguments to their proper

show what

figure, or

No

(1)

miser

a true friend, for he does not assist

is

with

his friend

his purse.

Governments are good which promote prosperity. The government of Burmah does not promote

(2)

.*.

prosperity. not a good government.

It is

Men

(3)

are sinners.

Saints are .

.

.

.

men.

Saints are sinners.

Nothing

(4)

(5)

mood and

rules of syllogism they violate

is

property but that which hand.

of

man s

The The

horse

is

horse

is

not the product of not property.

Some Europeans

man

is

s

the product hand.

at least are not Aryans, because

the Finns are not. (6)

Saturn

visible (7)

visible from the earth, and the moon from the earth. Therefore the moon from Saturn.

is

visible

Some men fore

is

is

of self-command are poor, and there

some noble characters are poor.

EXERCISES.

413

Sparing the rod spoils the child so John will turn out very good, for his mother beats him every day. :

(8)

Some

(9)

effects of labour are not painful, since

virtue

is

The courageous

(10)

every

an effect of labour.

are confident.

are confident and the experienced Therefore the experienced are

courageous. tale-bearer

No

is to be trusted, and therefore no is talker to be trusted, for all tale-bearers great are great talkers.

(11)

Socrates was wise, and wise men alone are happy therefore Socrates was happy.

(12)

Malum

:

est avaritia multos enim magnis incommodis adfecit pecuniae cupiditas. Cic. De Inv.

(13)

I,

(14)

.

.

;

95-

Half a loaf is better than no bread. No bread is better than no friends. Half a loaf is better than no friends.

Whatever

(15)

is

used as the

medium

of exchange

is

money. /.

(16)

.

.

Cattle are money. Cattle are used as the

medium of exchange.

No joke is always in season. An examination is no joke. An examination is always in

season.

II.

the major No matter thinks the minor, the following conclusions 1.

From

(1) (2) (3)

(4)

Name

draw, by supplying

Some part of man does not think. The soul of man is not matter. Some part of man is not matter. Some substance does not think. the figured

mood

into

which each syllogism

falls.

EXERCISES.

414

Construct syllogisms

2.

whether they are

stating

in

the following moods and figures,

valid or invalid,

and giving your

reasons in each case

AEE

in the first figure;

third 3.

Prove that

term 4.

;

All

in

Brass

EAO

in the

second

;

IAI

in

the

the fourth.

is

not a metal, using as your middle

compound body. Construct syllogisms to prove or disprove (1)

Some

(2)

No men

(3)

Laws

taxes are necessary. are free.

are salutary.

Prove by a syllogism in Bocardo that Some Socialists are not unselfish, and reduce your syllogism directly and in 5.

directly. 6. Prove the following propositions in the second and reduce the syllogisms you use to the first

7.

(1)

All negroes are not averse to education.

(2)

Only murderers should be hanged.

Prove

in

Baroco and

Some

also in Ferio that

figure,

Irishmen

are not Celts. 8.

Construct

words the same syllogism

in

in all the four

figures. 9.

Invent instances to show that false premisses

may

give

true conclusions. III. 1.

What moods

are peculiar to the

figures respectively 2.

What moods

3.

Why

figure

?

first,

second, and third

?

are

common

to

all

the figures

can there be no subaltern moods

?

in

the third

EXERCISES. What

4.

the only kind of conclusion that can be drawn

is

in all the figures

Show

5.

415

that

?

IEO

the special

violates

rules

of

the

all

figures. 6.

In what figures

7.

Show

that

AEO

is

AEE

is

valid

?

superfluous

in

any

figure.

Prove that O cannot be a premiss in the a minor premiss anywhere but in the second. 8.

Show

9.

that in the

first

first figure,

figure the conclusion

nor

must have

the quality of the major premiss and the quantity of the minor.

do the premisses EA yield a universal conclusion two figures and only a particular one in the last

Why

10.

in the first

two

?

Show

11.

that,

the major term be distributed in the

if

premiss and undistributed in the conclusion, the

mood must

be AAI.

IV.

in

1.

Why

2.

What

is it is

enough

the least

to distribute the middle

number of terms

the premisses of a syllogism 3.

What

is

distributed in 4.

Why

in the

term once

?

that can be distributed

?

the greatest number of terms that can be the premisses of a syllogism ?

must there be

at least

one more term distributed

premisses than in the conclusion

?

Prove that the number of distributed terms in the premisses cannot exceed those in the conclusion by more 5.

than two. 6.

Prove that the number of undistributed terms

premisses cannot exceed those in the conclusion by than one.

in the

more

EXERCISES.

416

7. Prove that wherever the minor premiss major must be universal.

is

8. Prove that wherever the minor term major premiss must be universal.

distributed the

If the

9.

middle term be twice distributed, what

figure are possible

When

10.

is

negative the

mood and

?

the middle term

is

distributed in both premisses,

what must be the quantity of the conclusion ? 11. If the major term of a syllogism be the predicate of the major premiss, what do we know about the minor premiss

?

Prove

12.

that, if the conclusion

term can only be distributed once

be universal, the middle

in the premisses.

V. 1.

Examine the following arguments

the special rules of the four figures.

in

accordance with

If necessary, restate

them.

Some one like me has come. None but Orestes is like me.

(1)

.

.

Orestes has come.

Their syllogism runs somewhat like this. France and the United States are Republics they have both shown strong tendencies to corrup

(2)

;

tion

;

therefore Republics are liable to be corrupt. It would be interesting to lay such a syllogism before a professor of logic, and ask him what he thinks of it, and how many marks it would be likely to score in an examina

tion.

The Daily Chronicle, Dec. 23, 1892.

No

(3)

.

.

one who allows

God God

allows is

evil.

not good.

evil

is

good.

EXERCISES. 2.

Why

is it

417

that in the second figure there

two terms distributed

must always be

?

3. In what figures can a conclusion be drawn when only one term is distributed in the premisses ?

4.

In what

moods of the

terms distributed 5.

Prove that (1)

(2)

(3)

in

(5) (6)

the minor premiss is particular, the major must be negative. When the minor premiss is negative, both premisses must be universal.

When

the conclusion

The

Show what

7.

If All

Is

negative, the major premiss

conclusion cannot be a universal affirmative.

is

affirmative.

relation (i) bears to the

and what relation

Some P

is

universal.

Neither of the premisses can be a particular negative. When the major premiss is particular, the conclusion

must be

6.

?

the fourth figure

When

must be (4)

different figures are there three

in the premisses

(3)

and

P and no S

is

(6)

first

rule of Figure IV,

bear to one another.

M, show

that

Some S

is

not

P and

not S.

the conclusion here wider than the premisses

?

Job was patient. Job was a man. /.

Some men

are patient.

VI. 1. To what moods only of the first figure are those of the second directly reducible by the ordinary method ? And why ?

2.

To what moods

only of the

third directly reducible

?

first

figure are those of the

And why ? E e

EXERCISES.

4l8

m

0.

name

in the In the ordinary mnemonic lines when there is of a figured mood, there is always a consonant at the

Why is this Why are the

end.

?

4.

premisses of Fesapo and Fresison not reduction like those of the other moods of the

in

transposed fourth figure

?

In what sense

5.

to a universal

is it

possible to reduce a particular

mood

?

Prove that

first

to the

second figure the minor premiss cannot be retained negative moods.

in the

6.

Why

7.

reduction of the

in the indirect

cannot Ferio be reduced indirectly to the third

by retaining the major premiss ? Prove that Baroco cannot be reduced

figure 8.

indirectly to the

fourth figure.

Prove that no other mood

9.

indirectly reduced to 10.

Why

in the

second figure can be

Camestros.

cannot Ferio be indirectly reduced to Barbari

?

CHAPTER XXIX. 1.

Show by

reduction that this If

A If A If

.

2.

.

C

is is

is

is

valid reasoning

not D, not B,

E

is

not F.

G

is

not D.

not B,

E

is

not F.

Examine the following arguments (1) If Dion is a horse, Dion is an animal. But Dion is not a horse. ..

(2)

(3)

Dion

is

not an animal.

you have faith you can remove mountains. But the mountains are not removed. If

If a thing

not be.

must be,

it

can be. But,

Therefore,

if

a thing

if it

must

can,

be,

it

it

also

can

cannot be.

EXERCISES. 3.

With

419

the following major construct as

many

conjunctive

syllogisms as you can

Homer

If

wrote the

Iliad,

he was the greatest poet of

antiquity. 4.

Reduce

to logical form and supply a concrete instance of

the following reasoning

.

5.

If

C

If

A E

If

.

is

not D,

is

not B,

is

F,

Invent a concrete

C

is

A is E is

B. F.

sometimes D. following kind of

instance of the

reasoning If

If

.-.

A A

is

is

C C

B, either

is

D

is

not D.

or

B,

E

is

F.

Eis

F.

CHAPTER XXXI. 1.

two arguments and

Assign their proper place to these

invent concrete instances (i)

.

2.

.

A is A is A is

either

B

or C.

(2)

B

..

A A

not B. C.

Granted that everything some x to be y ?

is

C

or D.

either

G

or D.

x or

y,

is

either

is

B.

is

either

is

it

still

possible for 3.

Fill

(1) .

.

up these enthymemes

Zeno

is

Some

cobbler

not mistaken. is

a king,

(2) Either Jesus was him. 4.

mad

or bad or else

we must

believe

Examine the following (i)

Unum quidem

certe,

nemo

qui mihi non concedat,

erit tarn iniquus Cluentio,

si

constet .corruptum illud

E e 2

EXERCISES.

420

esse indicium, aut ab Avito aut ab Oppianico esse

corruptum. Si doceo non ab Avito, vinco ab Oppi anico si ostendo ab Oppianico, purgo Avitum. Cic. ;

Pro

Clu.

64.

Quoniam habes istum equum, aut emeris oportet aut hereditate possideas aut munere acceperis aut domi tibi natus sit aut, si horum nihil est, surripueris

(2)

necesse est

:

sed neque emisti neque hereditate venit necesse

neque donatus est neque domi natus est est

Cic.

ergo surripueris.

De

Inv.

I,

;

84.

CHAPTERS XXIX XXXII. 1. Fill up the following enthymemes, and state the exact nature of the resulting syllogism

If

(1)

Livy

is

a faultless historian, we must believe all but that it is impossible to do.

that he tells us If

(2)

;

climate.

must

He

(3)

is

.

.

is

to be feared therefore that one

a victim.

either very good, very bad, or is

commonplace.

not very good.

Either a slave is capable of virtue or he is not. Either he ought not to be a slave or he is not a

man.

Does not

(5)

It

fall

But he (4)

:

they stay abroad, the wife will die while the husband s lungs will not stand the English

his feebleness of character indicate either

a bad training or a natural imbecility

Those who ask shan don t want.

(6)

If a

(7)

man

t

have

;

those

be mad, he deviates from the

standard of intellect. .

.

If all

men

?

who don

be alike mad, no one

is

mad.

t

ask

common

EXERCISES. cannot dig

I

(8)

If

(9)

I I

If

(10)

to beg

;

go on swimming, stop swimming,

we

I

I I

am

421 ashamed.

shall cut

shall

my

throat

and

;

if

be drowned.

are to be friends with the king, we shall be useful to him, if we keep our arms, and, if

more

we are to fight with if we keep our arms. (u)

I

we

him,

shall fight better,

Xen. Anab.

20.

II. i,

cannot go on this tour: for, if I do, a bicycle and wear a great-coat.

I

must ride

Either John does not respect his father, or he does not love him.

(12)

.

.

Either John If

(13)

not wise or he

is

is

not amiable.

God were

and,

if

good, he would will to destroy he were almighty, he would be able.

you give to a beggar, you feel a fool ; and, refuse to give to him, you feel a beast.

If

(14)

A

(15) /.

newspaper

is

if

evil,

you

either truthful or untruthful.

Either believe your daily paper or give up taking it

in.

The infinite divisibility of space implies that of time. the latter therefore be impossible, the former must be

2.

If

Formulate

equally so. ference. 3.

this

argument

as an

Examine the following arguments and

immediate

refer

them

in

to their

proper head (1)

we have

a dusty spring, there

is always a good therefore have a poor harvest this year, for the spring has not been

If

wheat harvest.

We shall

dusty. (2)

Virtues are either feelings, capacities, or states; and as they are neither feelings nor capacities,

they must be

states.

EXERCISES.

422

Everything must be either just or unjust. Justice is a thing, and is not unjust.

(3)

/.

Justice

is

just.

Similarly holiness

But the

is

holy.

tem

virtues of knowledge, justice, courage,

perance, and holiness, were declared to be dif ferent from one another. .

.

Justice

(4)

unholy and holiness unjust.

is

he observes the sabbath or

If

pork, he

is

if

he refuses to eat

a Jew.

But he both observes the sabbath and refuses to eat /.

pork. is a Jew.

He

If this triangle

(5)

But neither ..

It is

and

its

angles

its

nor

sides

its

angles are equal.

not equilateral.

If the

(6)

equilateral, its sides

is

be equal.

will

barometer

falls,

there will be either wind

or rain.

There /.

4.

neither wind nor rain.

is

The barometer

has not fallen.

Rebut the following dilemmas If

(1)

/.

the truth,

I tell

a

lie, I

Either

I

must

Either

I shall

I

tell

shall offend

I

my

shall offend tell

the people

;

and

if

conscience.

the truth or

tell

a

lie.

offend the people or offend

my

con

science.

he

(2)

If

(3)

If

is

sensible to shame, he ought not to be

scolded, and

if

he

is

don t wear

my

Proctors and, the men.

if I

I

he won

not,

gown, do,

I

I

shall

t

mind

it.

be fined by the be laughed at by

shall

EXERCISES.

CHAPTER 1.

Formulate

into their

XXXIII.

the following trains of reasoning, resolve

component

parts,

No Church

may

contain

Institutions are useful; for they teach

matters,

religious

them

and point out any violations of

the rules of syllogism which they (1)

423

latter are useful,

not business matters, which being profitable.

Mr. Darwin long ago taught us that the clover crop is dependent on the number of maiden ladies in For the ladies keep cats, and the the district. cats destroy the field-mice, which prey on the

(2)

bees, which, in their turn, are all-important agents in the fertilisation of the clover flowers.

games are duties; for whatever is neces sary to health is a duty, and exercise is necessary to health, and these games are exercise.

(3)

Athletic

(4)

The

iron-trade leads to the improvement of a new for furnaces require to be fed with fuel, which causes land to be cleared.

country

a stone a

Is

(5)

;

a

body ? seems so.

body ? Yes.

Then

Yes.

Well,

is

not an animal

And

It are you an animal ? you are a stone, being an

animal. If

(6)

A

E But if A If

/.

is is is

B,

C

F,

G

B,

E

is

is is

D.

H. F.

is D, G is sometimes H. good things are fair. Eros is without the fair, else he would not desire Eros is without the good.

If

C

All

(7)

.

.

Plat. Symp. 201 (8)

c.

men

are fallible, for they are finite. All Popes are men, for they are born of

All

women.

it.

EXERCISES.

424 (9)

autem perabsurdum, bonum esse aliquid, quod non expetendum sit, aut expetendum quod non ergo placens, aut, si id, non etiam diligendum etiam probandum ita etiam laudabile id autem

Illud

;

:

honestum.

honestum (10)

Ita

fit

:

ut,

quod bonum

Cic. Fin. Ill,

sit.

sit,

id

etiam

27.

si pecuniam non habetis non estis indigetis pecuniam habetis, pauperes autem pecuniae mercaturae enim, ni ita esset, operam non daretis pauperes igitur estis. Cic.

Si

indigetis pecuniae,

;

:

;

;

De (i i)

Inv.

I,

88.

The

principles which all mankind allow for true are innate those that men of right reason admit are ;

by all mankind mind are men of reason

principles allowed

of our

;

;

we and

therefore,

agreeing, our principles are innate.

Why,

we

Locke, Essay

20.

I. 3,

(12)

those

if

thou never wast at court, thou never sawest

good manners if thou never sawest good manners, then thy manners must be wicked and wicked ness is sin, and sin is damnation. Thou art in ;

;

a parlous state, shepherd. Like It, Act III, sc. 2.

2. is

In

Adam

Shakespeare, As Ton

Smith, Wealth of Nations, Bk. IV, ch. stated thus

2,

there

some reasoning which may be

Nothing but augmentation of capital increases industry. Nothing but saving out of revenue augments capital. /.

Nothing but saving out of revenue increases industry.

/.

Restrictions on importation are adverse to the increase of

Restrictions on importation diminish revenue.

industry. Is this valid

?

If so, formulate

it

syllogistically.

EXERCISES. 3.

425

Resolve the following into their component syllogisms (1)

All

A

is

B.

All

C

is

A.

All

D

is

E E

All All

.-.

If

A

is

If

C

is

If

E

is

If

G

is

If

A

is

(2)

.

.

is is

C.

D. B.

not B, not D,

C E

not F, not H,

G is not H. K is not L. K is not L.

not B,

is

not D.

is

not F.

(See Lectures in the Lyceum,

p. 339.)

CHAPTER XXXIV. 1.

Point out any ambiguities which underlie the following

propositions (1)

Every one who has read the book

recommend

those

who have

in

French

not to read

will it

in

English. (2)

I

will

not do this because he did

(3)

These are

(4)

By an

all

my

old statute of the date of

accorded

it.

books.

that

Edward

every year once or more often (5)

III

it

was

Parliament should be holden if

need

be.

They found Mary and Joseph and the babe lying in a manger.

(6)

The

(7)

Heres meus uxori meae

king and his minister are feeble and un

scrupulous.

argenteorum dato, quae

triginta volet.

pondo vasorum

EXERCISES.

426 2.

when

Examine the following arguments, formulating them sound, and referring them, when unsound, to the proper

head of

fallacy

(1)

We

know that thou art a teacher come from God no man can do these signs that thou doest, except God be with him. S. John iii. 2.

;

for

Walter Scott

Sir

(2)

popular. reads them.

novels have

s

Well, that

s

ceased

to be

only because nobody

What we produce is property. The sheriff produces a prisoner.

(3)

A

/.

is

prisoner

property.

metals are not necessarily expect some metals to be liquid.

As

(4)

all

solid,

we may

Moses was the son of Pharaoh s daughter. Moses was the daughter of Pharaoh s son.

(5) /.

If

(6)

Aeschines took part

the success of

condemning

it

my

in

the public rejoicings over he is inconsistent in

policy,

now

;

if

he did not, he was a

traitor then. It

(7)

wrong

is

to stick knives into people.

Surgeons ought to be punished.

.

.

If a thing admits of being taught, there

(8)

.

.

It is

(9)

must be

both teachers and learners of it. If there are neither teachers nor learners of a thing, that thing does not admit of being taught. unnecessary to lend books,

mon, and wrong to lend them,

if

if

they are

com

they are rare.

Therefore books should not be lent from public libraries.

Seeing

(10) .

(n)

.

What St.

is

is

believing.

not seen cannot be believed.

Paul was not of Jewish blood, for he was a

Roman

citizen.

EXERCISES.

To call To call To call

you an animal is to speak the truth. you an ass is to call you an animal. you an ass is to speak the truth. Pain chastens folly. A life of ease must therefore be one of folly incurable.

(12)

.

.

427

(13)

We

(14)

cannot be happy in

this

world; for

we must

either indulge our passions or combat them. It must be clear to the most unlettered mind that, as all things were originally created by the Deity,

(15)

including the hair on our heads and the beards on our faces, there can be no such thing as property. The crime was committed by the criminal.

(16)

.

.

The criminal was committed by the magistrate. The crime was committed by the magistrate. General councils are as

(17)

men

of

likely to err as the fallible

whom

they consist. dogs are heavier than living ones, because

(18)

Dead

(19)

vitality is buoyant. Deliberation is concerned with actions.

Actions are means. /.

Deliberation

is

concerned with means.

No

beast so fierce but has a touch of pity But I have none therefore I am no beast.

(20)

;

:

(21) .

.

Practical pursuits are better than theoretical. Mathematics are better than logic.

Death must be a good.

For either the soul, ceasing to be, ceases to suffer, or, continuing to be, lives in a better state.

(22)

What

(23) .

.

.

.

(24)

No

/.

right should

be enforced by law.

animals perished in the Flood.

If

he robs, he is not honourable. he pays all his dues, he does not rob.

If

he pays

If

(25)

is

Charity should be so enforced. All animals were in the Ark.

all

his dues,

he

is

honourable.

EXERCISES.

428 (26)

.

.

A dove can fly a mile in a minute. A swallow can fly faster than a dove. A swallow can fly more than a mile in

a minute.

must soap myself, because it s Sunday. Then do you only soap yourself, on Sunday I

(27)

If the

(28)

charge

is

false,

ignorant or malicious.

Therefore he

is

the author of

it

But the charge

is

either

true.

neither.

All the angles of a triangle are equal to

(29)

?

is

two

right

angles.

The

.

.

(30)

angle at the vertex is an angle of a triangle. equal to two right angles. Si gravis est dolor, brevis est si longus, levis. It is

;

Ergo (31)

.

.

fortiter ferendus.

You are not what I am. I am a man. You are not a man. The extension of the franchise

is necessary, for it imperative that the right of voting should be granted to classes who have hitherto not pos

(32)

is

sessed this privilege. If

(33)

Hannibal

is

really victorious,

he does not need

while, if he is deluding us, we ought certainly not to encourage him by sending them.

supplies

Livy,

;

xxiii. 13,

5.

Laws must

punish, and punishment hurts. All laws therefore are hurtful.

(34)

(35)

.

.

(36)

The sun is an insensible thing. The Persians worship the sun. The Persians worship an insensible thing. Some ores are not metals for they are not ;

and some metals are not

.

(38)

Grecian soldiers put the Persians to flight. Grecian soldier could rout the Persians. Every The resurrection of Jesus Christ is either an isolated

All the

(37) .

fluids,

fluids.

EXERCISES.

429 But

fact or else admits of parallel.

isolated fact,

it

if it

be an

cannot be rendered probable to

one who denies the authority of Christianity and, if it admit of parallel, it no longer proves ;

what

is required. Therefore it is either incapable of being substantiated or else makes nothing for the truth of Christianity.

The

(39)

resurrection

of Christ in the flesh and His

ascension into heaven were events either intrin sically incredible in their

nature or not.

If the

former, the prevalent belief in them can only be accounted for by miracles if the latter, they ought to be believed even without miracles. ;

St. Aug.,

De

Civ. Dei, xxii.

8.

(40)

Only contented people are wise. Therefore the tramp contented in his rags is necessarily a wise man.

(41)

Four-legged things are brutes. Tables are four-legged things. Tables are brutes.

..

The

apparent volcanoes in the moon are not vol canoes for eruptions are produced by gases only,

(42)

;

and there are no gases

To

(43)

read the Scriptures

in the

is

moon.

our duty.

Therefore the

Captain was wrong in punishing the helmsman for reading the Bible at the time when the ship struck.

The

(44)

divine

law

orders

that

kings

should

be

honoured.

.

.

Louis Quatorze is a king. The divine law orders that Louis Quatorze should be honoured.

Those who desire the same object are unanimous. Caesar and Pompey both desire the same object, namely, supreme power.

(45)

.

.

They

are unanimous.

EXERCISES.

430

Either the ministers

(46)

left at

home

not be ciphers.

will

they

If

cabinet government, which

is

will

be ciphers or

they are ciphers, equivalent to con

government, will receive a rude blow. If they are not ciphers, the cabinet will be con sidering matters of the utmost importance in the absence, and the gratuitous absence, of two of its

stitutional

most important members. June 5, 1878.

patent stove saves half the ordinary amount Therefore two would save it all.

One

(47)

of

fuel.

One number must win

(48)

My .

.

It

ticket

is

in the lottery.

one number.

must win.

All

(49)

The Standard, Wed.,

good shepherds are prepared to

lay

down

their

the sheep. in this age are so prepared. in this age are good shepherds.

lives for

(50)

Few Few You

(51)

To

.

.

cannot define the sun for a definition must be clearer than the thing defined, and nothing :

can be clearer than the source of

all light.

give the monopoly of the home market to the produce of domestic industry . . must in almost all cases be either a useless or a hurtful regula .

tion.

produce of domestic can be brought

If the

there as cheap as that of foreign industry, the regulation is

is

generally

Nations, Bk.

evidently useless hurtful.

iv,

(52)

Verberare est

Ergo

et vapulare.

(53)

The

ages of

Adam

if it cannot, it Smith, Wealth of ;

ch. 2.

actio.

all

the

members of

this

over 150.

The baby /.

Its

age

is

is

a

member

over 150.

of this family.

family are

EXERCISES. Romulus must be an

(54)

it

not at

is

all

431

historical person

likely that the

;

because

Romans, whose

memory was only burdened with seven kings, should have forgotten the most famous of them, namely, the first. Deus aut

(55)

non

et

vult tollere vult, aut

mala et non potest, aut potest vult neque potest, aut et

neque

Si vult et non potest, imbecillis quod in Deum non cadit si potest et non vult, si neque vult invidus, quod aeque alienum a Deo neque potest, et invidus et imbecillis est, ideoque neque Deus si et vult et potest, quod solum Deo convenit, unde ergo sunt mala? aut cur ilia non

vult et potest. est,

;

;

;

tollit?

Gold

(56)

is

/.

(57)

is

Epicurus apud Lact. De Ira Dei, 13. But gold is also heavy and heavy

yellow.

;

not-yellow.

Gold is yellow and not-yellow. Professor Joseph Jastrow, of the University of Wisconsin, proposes the following little problem

means of testing diversity of opinion Granted that A is B, to prove that B is A.

in logic as a

B If

everything else) is either A or not A. not A, then by our first premiss we have the syllogism (like

B

is

.

.

A

is

B,

B

is

A

is

not A, not A, which

Therefore Is this

(58)

:

B

is

is

absurd.

A.

reasoning correct, he asks, or is it not? The Academy, Jan. 16, 1897.

Perhaps

I

may be

allowed in return to propound

a sophism for the consideration of the Professor. In the unlikely event of his failing to solve it, he

must be held responsible for the consequences to public morality.

EXERCISES.

43 2

An An .

.

.

.

indifferent act

is

not-right.

indifferent act

is

not-wrong.

Not-wrong

is

not-right.

(By contraposition) Right is wrong. The Academy, Jan.

Quando nos sumus, mors non est quando mors est, nos non sumus. Mors ergo nihil ad nos.

(59)

Epicurus apud Lact.

Nam

(60)

homicida nefarius

si

stinctor est,

eidem

necat, quia

hominem

23, 1897.

;

Di-v. lust. III. 17.

quia hominis ex-

est,

sceleri obstrictus est, qui se

Lact. Div. Inst.

necat.

III. 18.

Consulat unusquisque affectus suos: jam intelleget,

(61)

neminem posse

sine ira et castigatione imperio

ira non fuerit, imperium non Deus autem habet imperium. erit. quoque Ergo et iram, qua constat imperium, habeat

subjugari.

necesse

est.

Doctors say

(62)

this

How

(63)

is

Ubi ergo

Lactantius, it

is

De

healthy to

impossible, for gravel

Ira Dei, 23. live is

on gravel; but

very indigestible.

do you know when a verb ought to be put

into the subjunctive in the oblique oration it is in a dependent clause.

?

When

How

do you know that a clause

When

the verb

Whoever

(64)

is

in

is

dependent

?

the subjunctive.

divulges the mysteries to the uninitiated

commits impiety.

The

hierophant

divulges the

mysteries

to

the

uninitiated. .

.

The

hierophant commits impiety.

D

L. VII,

186.

INDEX. The

references are to the pages.

Abstraction, 31, 35, 51.

Acategorematic words,

Art, 4,

Accent, fallacy of, 372, 373. Accident, 87, 99.

Attributive, 18, 24-6, 33.

Accident, fallacy of, 374, 376. dicto secundum quid, fallacy

A

of,

5.

Attribute, 21-3, 30-3. essential and non-essential, 89.

17.

374-7-

Amphiboly, fallacy of, 369, 370. Analogous words, 19. Analogy, 19, 20.

Bacon, 144, 162. Bain, Prof., 48 n, 181 n. Basis of division, 128, 129.

Berkeley,

Bishop,

162,

149,

183.

Aristotelian, 202, 203.

Cannan, C., 182

modern, 203, 204. Antecedent, various meanings of, 171 n. of a complex proposition, 61. of an inference,

1

n.

of reasoning, 257-60.

the conjunctive syllogism, 328. the disjunctive syllogism, 337, 338.

38.

Canons of the inductive methods,

Antecedents, 170.

A A A

Canon

posteriori truth, 67.

177-

priori truth, 67.

Categorematic words, 16,

propositions, 71, 72. conversion of, 218.

Categories, the, 106-13.

Arguing

Cause, conception

in a circle, 383.

Argumentum ad hominem,

169-75.

definition of, 174.

&c.,

378-80. Aristotle, 15, 490, 93, 297. Aristotle s categories, 106-13.

Causes, combination

composition

of,

of,

174.

174.

Circulus in definiendo, 116. Clarke, Father, 70, 94, 100.

division of fallacies, 362-84.

Class, 34.

heads of predicables, 101-5.

Coexistence,

Arithmetic, 150.

of,

19.

uniformities

165-8.

F f

of,

INDEX.

434

Consequent, of a complex pro

Colligation of facts, 150-2.

position, 61.

Combination of causes, 174.

Common

terms, 33.

arrived at

nature

by abstraction,

32.

Consequent, fallacy

of, 13.

Complex

61-5,

proposition,

233-7conversion

of an inference, 138. various meanings of, 171 n. 380.

Contingent truth, 4. Contradiction, law of, 6-8, 375.

237-9.

of,

of,

Consequents, 170.

conversion by contraposition

Contradictory opposition, 211. propositions, 212, 215.

244-7. conversion by of,

negation

of,

terms, 28.

division of, 62.

Converse, 217Converse fallacy of accident, 376.

inversion of,

Conversion, 217.

240-4.

obversion

of,

3479.

by contraposition, 223,

239, 240.

opposition applied to, 237.

Complex

syllogism, 325-48.

Composition, fallacy

of,

214.

Composition of causes, 174.

Compound Concept,

by limitation, 217, 218. by negation, 222, 223, 240-4, immediate inference by, 2 1 7-9. of complex propositions, 237-9.

sentence, 64, 65.

per accidens, 217.

9.

Conception,

224,

244-7.

rules of, 217.

8.

Conception of cause, 169-75.

simple, 217.

Convertend, 217.

Conceptualism, 14, 94. Conceptualists, 13-5. Conclusion, 250, 252.

Copula, 16, 18, 55-9. modality of the, 57~9-

predicate of, 250.

Correlatives, 40.

subject of, 250.

Crucial instance, 202.

Concomitants, 170.

Deduction and Induction,

Condition, 172.

Conjunctive proposition, 62, 233, 234,

237, 245, 2 47.

239-42,

244,

Conjunctive syllogism, 326-34.

canon of

the, 328.

partly, 327-30.

137,

138.

Deductive inference, 137. Definition, 114-126.

Definition

Definition

and Description, 126. and Division, 112,

"3-

reduction of the partly, 331-4Connotation of terms, 42, 43, 45.

nominal, 123, 124.

Consequent, defined, 171.

rules for,

real, 123, 124. 1 1

5-9.

INDEX.

435

Denotation of terms, 42. Derivative laws, 205. rules of syllogism, 206.

Elimination, 197. Empirical laws, 206.

Description, 126.

Epicheirema, 350-2.

Designations, 36-8, 46.

Epi-syllogism, 350.

Enthymeme,

E

Determination, 51. Dialectic,

108,

215,

377,

363,

253.

propositions, 71, 72. of, 218.

conversion

Equivocation, fallacy

378-

Dictum de omni et nullo, 257,259. de diverse, 288. de exemplo et excepto, 288. Difference, 87, 88, 119, 120.

Excluded middle, law

Experiment, 160-4.

generic, 134.

Experimental

methods

specific, 133, 144.

Dilemma, 339-48. proposition,

39

four

inquiry,

i76n.

of,

Explanation, 204, 205. Extension of terms, 41-7.

rebutted, 345-8. 2

2 4>

62,

242-9-

Fallacy, 361-84.

Disjunctive syllogism, 335-8. canon of the, 337.

definition of, 361.

Distinction, 135. Distribution of terms, 77-81. four rules for the, 80, 81.

logical, 363-5-

formal, 262-8, 364-7.

Distributive use of terms, 38.

material, 363-5. of ambiguity, 263. Figure of speech, fallacy

Divided whole, 127. Dividing members, 127.

Figure, definition of, 254. Figures, the four, 255, 256.

by dichotomy, 132.

Form and

matter,

Four terms,

3.

fallacy of, 263.

terms, 24.

Fowler, Dr., 181 n.

things, 21.

Fundamentum

Effect, definition of, 174.

causes, 175.

373.

special uses of, 291-4.

rules for, 129-131.

Division, fallacy of, 370-2. Divisions of propositions, 60.

proportional

of,

special canons of, 287-90. special rules of, 276-9.

Division, 127-136.

Effects

6-8,

external and internal, 153.

essential, 96-8.

234-7>

of,

220, 375, 376.

Experience, 153-5.

accidental, 96.

Disjunctive

368.

of,

Euclid, 149.

to

Divisionis, 128.

Generalisation, 51. their

Genus, 87. as used by Aristotle, 101, ica.

INDEX.

436

Immediate

Genus, cognate, 133.

forms

proximate, 120.

Grammar,

compound

of,

176, 181-4, 197.

subaltern, 133.

summum,

inference,

222-9. Indirect method of difference,

generalissimum, 94.

Induction, 141-206.

51, 120, 133.

apparent, 148-152.

5, 17-

Greek, 167.

axioms

Latin, 59, 152.

by simple enumeration, 144,145. denned, 141, 153.

of,

153-9.

Hamilton, Sir William, 82, 139.

imperfect, 144-206.

Heads

perfect, 141, 142, 149.

of Predicables, 87-105.

as given

of

scientific, 145-206. Induction and Deduction, 137,

names

138, 146, 157Inductive inference, 141-99, 157.

Aristotle, 101-5.

by

intermixture

Homogeneous

effects, 175.

Homogeneous of,

substances,

syllogism, 142, 143.

47.

and gravity, 167. n. Inference, ambiguity of, inductive and deductive, 138. Inertia

168 n, 178 n. Hypothesis, 200-2.

Hume,

n

a working, 164.

meaning

Identity,

law

of,

5-7.

Elenchi,

of,

Ignotum per aeque ignotum,

117.

n,

Illicit

process, fallacy of, 264. Imagination, 8, 126.

Immediate

inference, 207-9. as applied to complex proposi

233-49.

by added determinants, 231. by complex conception, 231, 232.

by conversion, 2 1 7-9. by ob version, 220, 221. by opposition, 210-6.

classification of, 136.

inductive, 141-99. traductive, 146, 147. Inferring, 8, 137.

Infimae species, 95, 133-5. Intension of terms, 41-7. acquired and original, 44, 45. Intermixture of effects, chemical, 174. 175-

heterogeneous or heteropathic, i?5-

homogeneous or mechanical, 175-

by privative conception, 221.

Intuition, 67.

by

Inversion, 224, 225.

relation, 230.

137, 139.

deductive, 207-9.

377-80.

tions,

139, 140.

parts of, 138. Inferences in general, 137-40.

fallacy

Ignoratio

of,

Inference, the, 9,

Idealism, 14, 19. Ideas, doctrine of, 14.

INDEX. Inverse variation, law I

of,

50-2.

Metaphysics, 23.

Method,

propositions, fi, 72. conversion of, 218.

15, 199.

the deductive, 200.

W. S., 48 n, 51 Johnson, W. E., 2i^n. Jevons,

Methods, inductive, 176-99. of agreement, 167, 176-

n, 188.

Method

9, 188, 189, 191, 196,

method of agreement and

Joint

437

concomitant variations,

difference, 181 n.

176, 177, 184-6, 197.

the, 9, 54.

difference, 168, 176, 177,

Judgement,

the unit of thought, 16.

Judging,

81,

8.

186,

187,

189,

double agreement, 181 residues,

Keyne?, J. N., 48, 85

n,

21411,

224, 267, 296 n.

Language, 10, n, 18. Law, ambiguity of, i,

Laws

different

kinds

Logic, definition

n.

190, 197, 199.

158,

of,

107,

174,

139, 148-52,

176,

198,

199,

205.

Minor premiss,

205, 6.

251.

Minto, Prof., 48

Mnemonic

n.

lines, 283,

313, 321.

Modality of the copula, 57-9.

thought, 3, 5-8.

parts

190,

168, 176, 177, 187,

Mill, J. S., 2.

of nature, 2, 205.

derivation

179-

Middle term, 250, 255, 256.

of causation, 156, 159. of uniformity, 156, 158.

Laws,

168,

93, 197-9-

Kepler, 150-2.

Law Law

198.

Mode,

of, i.

the, 57.

Moods

of a syllogism, 254, 255. determination of the legiti

of, 10.

of, 15.

mate, 273-5.

Logical whole, 136.

subaltern, 274, 275.

Major premiss, 251.

Name,

term, 350.

Many questions, fallacy of, 383,4. Many- worded names, Mechanical

1

combination

premisses

of

Noun,

axioms of, 259. Mediate inferences, 250-3.

Observation, 160-4.

Membra

Obversion,

Metaphysical whole, 136.

con

Nominalists, 13-5. Non causa pro causa, fallacy

intermixture of effects, 174. Mediate inference, 207, 208.

dividentia, 127.

and

clusion, fallacy of, 366.

7.

causes, 174.

definition of, 18.

Negative

of,

383. 1 8.

223-9.

208, 209, 220, 221,

INDEX.

433 Occam,

Problema, ^52. Problematic enthymeme, 253.

191.

Occasion, 173, 175. Opposition, 210, 211.

Processes of thought, 8-10. Products of thought, 9-15.

contradictory, 211. contrary, 211.

Proper names,

immediate inference by, 21216.

laws

of, 212.

45. Property, 88.

four kinds of, 99.

of singulars, 215, 216.

O

36.

Roman,

Proposition,

n,

15,

16,53-136.

accidental, 68.

subaltern, all, 213. sub-contrary, 211.

affirmative, 71.

propositions, 71, 72.

complex or conditional, 61-4.

not convertible, 218, 219.

conjunctive

or

hypothetical,

62-4.

Paronymous

terms,

fallacy

of,

373-

definition of, 54. disjunctive, 62, 63. divisions of, 60-76. essential, 68.

Partition, 135. Permutation, 221. Petitio principii, fallacy of, 380-3.

exceptive, 74-6.

Phenomenon, 169,

exclusive, 74~6.

170.

Philosophy, 154. Plato, 14, Plurality

extensive, 73, 74.

1 80.

of

causes,

178,

179,

192, 193. Porphyry, the five words of, 93100. tree of, 94.

Predicable, 87.

Predicaments, the ten, 106. Predicate, 16, 54, 87, 219. quantification of the, 82-6,

219. quantity of the, 77, 78. used in intension, 73, 86. Predication, 57.

Premisses, 250, 251.

Primary existences,

15. rules of syllogism, 261. substances, 22.

general, 70, 71. indefinite, 68. intensive, 73, 74.

modal,

58.

negative, 71. particular, 68, 69.

parts of the, 54. quality of, 71.

Proposition, quantity of, 68. real or synthetical, 65-8. simple or categorical, 61. singular, 70.

tautologous or identical, 76. universal, 68-70. verbal or analytical, 65-8.

Proprium, 99, 101, 102, 104, 105. Pro-syllogism, 350. Protasis, a, 108.

INDEX. Quaestio, 252. Quality, a, 22. Quality of propositions, 71. of the form, 61, 71.

439

Secondary substances, 22, Shute, R., i26n.

and

Sign

cause distinguished,

168.

of the matter, 61, 272. Quality of terms, 30. Quantification of the predicate,

Simple apprehension, Sorites, 352-60.

82-6, 219. Quantity of propositions,

Species, 87.

7-

of terms, 41-7-

8.

Specialisation, 51.

cognate, 133. infimae, 95, 133-6praedicabilis, 92.

Realism, 14, 94.

subaltern, 133.

Realists, 13-5.

subjicibilis, 92.

Real kinds, 95, 125.

Stoics,

Reason and cause distinguished,

Subalternant, 213.

166.

64 n, 367

n,

369

n.

Subalternate, 213.

Reasoning, canon

of,

257.

trains of, 349-60.

Subalternation, 213. Subaltern mood, 274.

Reduct, 305.

Subaltern opposition, 211. Subaltern species and genera, 95.

Reduction, 305-24.

Subalterns, 212.

Reducend, 305.

by negation, 311-5.

Sub-contraries, 212.

converse, 322, 323. converse use of indirect, 323. direct or ostensive, 306-11.

Sub-contrary opposition, 211.

indirect or perimpossibile, 306,

316-22. of the partly conjunctive syl logism, 331-4. of the subaltern moods, 310,

1

6, 54.

quantity of, 77, So. used in extension, 73, 86. Subject- term, 24-6, 219.

Substance, 21-3.

primary and secondary, and imaginary, 33.

Summum

Reid, I78n.

immediate

genus,

51,

94,

120, 133.

Relation, a, 22, 40. inference

by, 230.

Suppositio materialis, 19.

Syllogism, 250-348.

complex, 325-48.

Schoolmen, 92, 100, 106. Science, 4,

15, 22.

real

311-

Relation,

Sub-division, 133.

Subject,

5.

Secondary existences, 15.

conjunctive, 326-34. definition of, 250.

disjunctive, 335 -8.

in,

INDEX.

440

Syllogism, inductive, 142, 143. with three figures, 297-304.

Syncategorematic words, 17.

Synonym,

91, 104, 105.

Term,

singular, 12, 13, 33-8.

Testimony, 153.

Thing, confused Son-

with

name,

division of, 21-3. 21.

Tendency, 204.

meaning

Term, 16-20, 24-52.

name for the absolute summum genus, in.

absolute, 40. abstract, 30-3.

Thought,

i, 10, 11.

three acts or processes of, 8, 9. three fundamental laws of, 5-8. three products of, 9-15.

attributive, 18, 24-6, 33.

collective, 38-40.

common,

of,

33-6.

concrete, 30-3.

connotative, 41. contradictory, 28.

Undistributed middle, fallacy

of,

definition of, 17.

263, 366. Universals, nature of, 13-5. Uni vocal and equivocal words,

derivation of, 16. distribution of a, 77-81.

U

contrary, 28.

distributive

and

19.

propositions, 82, 84-6.

collective use

of a, 38.

n.

divisions of, 24-49.

Venn, Dr., 48 Verb, 1 8.

general, 33.

Verification, 200.

incompatible, 30. individual, 39.

major, middle, and minor, 250. negative, 27-30.

non-connotative, 41. positive, 27-30.

Welton, J., 27 n, 450, 48 n. Whately, Archbishop, 157. Whewell, Dr., 150, 151, 198, 199.

Words, acategorematic,

17.

privative, 27-30.

categorematic, 16, 19.

quantity of a, 41-7relative, 40, 41.

Syncategorematic, 17. their relation to terms, 16, 17.

repugnant, 30.

univocal and equivocal, 19.

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