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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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